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2009 ASHRAE® HANDBOOK

FUNDAMENTALS

Inch-Pound Edition

American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. 1791 Tullie Circle, N.E., Atlanta, GA 30329 (404) 636-8400

http://www.ashrae.org

©2009 by the American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. All rights reserved. DEDICATED TO THE ADVANCEMENT OF THE PROFESSION AND ITS ALLIED INDUSTRIES

No part of this publication may be reproduced without permission in writing from ASHRAE, except by a reviewer who may quote brief passages or reproduce illustrations in a review with appropriate credit; nor may any part of this book be reproduced, stored in a retrieval system, or transmitted in any way or by any means—electronic, photocopying, recording, or other—without permission in writing from ASHRAE. Requests for permission should be submitted at www.ashrae.org/permissions. Volunteer members of ASHRAE Technical Committees and others compiled the information in this handbook, and it is generally reviewed and updated every four years. Comments, criticisms, and suggestions regarding the subject matter are invited. Any errors or omissions in the data should be brought to the attention of the Editor. Additions and corrections to Handbook volumes in print will be published in the Handbook published the year following their verification and, as soon as verified, on the ASHRAE Internet Web site. DISCLAIMER ASHRAE has compiled this publication with care, but ASHRAE has not investigated, and ASHRAE expressly disclaims any duty to investigate, any product, service, process, procedure, design, or the like that may be described herein. The appearance of any technical data or editorial material in this publication does not constitute endorsement, warranty, or guaranty by ASHRAE of any product, service, process, procedure, design, or the like. ASHRAE does not warrant that the information in this publication is free of errors. The entire risk of the use of any information in this publication is assumed by the user. ISBN 978-1-933742-54-0 ISSN 1523-7222

The paper for this book is both acid- and elemental-chlorine-free and was manufactured with pulp obtained from sources using sustainable forestry practices. The printing used soy-based inks.

ASHRAE Research: Improving the Quality of Life The American Society of Heating, Refrigerating and AirConditioning Engineers is the world’s foremost technical society in the fields of heating, ventilation, air conditioning, and refrigeration. Its members worldwide are individuals who share ideas, identify needs, support research, and write the industry’s standards for testing and practice. The result is that engineers are better able to keep indoor environments safe and productive while protecting and preserving the outdoors for generations to come. One of the ways that ASHRAE supports its members’ and industry’s need for information is through ASHRAE Research. Thousands of individuals and companies support ASHRAE Research

annually, enabling ASHRAE to report new data about material properties and building physics and to promote the application of innovative technologies. Chapters in the ASHRAE Handbook are updated through the experience of members of ASHRAE Technical Committees and through results of ASHRAE Research reported at ASHRAE meetings and published in ASHRAE special publications and in ASHRAE Transactions. For information about ASHRAE Research or to become a member, contact ASHRAE, 1791 Tullie Circle, Atlanta, GA 30329; telephone: 404-636-8400; www.ashrae.org.

Preface The 2009 ASHRAE Handbook—Fundamentals covers basic principles and data used in the HVAC&R industry. The ASHRAE Technical Committees that prepare these chapters strive not only to provide new information, but also to clarify existing information, delete obsolete materials, and reorganize chapters to make the Handbook more understandable and easier to use. An accompanying CDROM contains all the volume’s chapters in both I-P and SI units. This edition includes a new chapter (35), Sustainability, which defines this concept for HVAC&R and describes the principles, design considerations, and detailed evaluations needed in designing sustainable HVAC&R systems. Also new for this volume, chapter order and groupings have been revised for more logical flow and use. Some of the other revisions and additions to the volume are as follows: • Chapter 1, Psychrometrics, has new information on the composition of dry air, and revised table data for thermodynamic properties of water and moist air. • Chapter 6, Mass Transfer, has added examples on evaluating diffusion coefficients, and on heat transfer and moisture removal rates. • Chapter 7, Fundamentals of Control, includes new content on dampers, adaptive control, direct digital control (DDC) system architecture and specifications, and wireless control. • Chapter 9, Thermal Comfort, has a new section on thermal comfort and task performance, based on multiple new studies done in laboratory and office environments. • Chapter 10, Indoor Environmental Health, was reorganized to describe hazard sources, health effects, exposure standards, and exposure controls. New and updated topics include mold, Legionella, indoor air chemistry, thermal impacts, and water quality standards. • Chapter 14, Climatic Design Information, has new climate data for 5564 stations (an increase of 1142 new stations compared to 2005 Fundamentals) on the CD-ROM accompanying this book. A subset of data for selected stations is also included in the printed chapter for convenient access. • Chapter 15, Fenestration, has been revised to include new examples of solar heat gain coefficient (SHGC) calculations, and new research results on shading calculations and U-factors for various specialized door types. • Chapter 16, Ventilation and Infiltration, has new, detailed examples, updates from ASHRAE Standards 62.1 and 62.2, discussion of relevant LEED® aspects, and new information on airtightness and ventilation rates for commercial buildings. • Chapter 18, Nonresidential Cooling and Heating Load Calculations, has been updated to reflect new ASHRAE research results on climate data and on heat gains from office equipment, lighting, and commercial cooking appliances.

• Chapter 20, Space Air Diffusion, has been completely rewritten to harmonize with related chapters in other volumes, with major sections on fully mixed, partially mixed, stratified, and task/ambient systems and the principles behind their design and operation. • Chapter 21, Duct Design, has new data for round and rectangular fittings in agreement with the ASHRAE Duct Fitting Database, as well as new content on duct leakage requirements, spiral duct roughness, and flexible duct pressure loss correction. • Chapter 23, Insulation for Mechanical Systems, has added tables from ASHRAE Standard 90.1-2007, and a new section on writing specifications. • Chapter 24, Airflow Around Buildings, has added a detailed discussion on computational evaluation of airflow, plus new references including updated versions of design standards and manuals of practice. • Chapters 25, 26, and 27 carry new titles, reorganized as chapters on Heat, Air, and Moisture Control Fundamentals, Material Properties, and Examples, respectively, with updated content throughout. • Chapter 29, Refrigerants, has new content on stratospheric ozone depletion, global climate change, and global environmental characteristics of refrigerants. • Chapter 30, Thermophysical Properties of Refrigerants, has updated data for R-125, R-245fa, R-170, R-290, R-600, and R-600a. • Chapter 36, Measurement and Instruments, has revised content on measurement of air velocity, infiltration, airtightness, and outdoor air ventilation, plus new information on particle image velocimetry (PIV) and data acquisition and recording. This volume is published, both as a bound print volume and in electronic format on a CD-ROM, in two editions: one using inchpound (I-P) units of measurement, the other using the International System of Units (SI). Corrections to the 2006, 2007, and 2008 Handbook volumes can be found on the ASHRAE Web site at http://www.ashrae.org and in the Additions and Corrections section of this volume. Corrections for this volume will be listed in subsequent volumes and on the ASHRAE Web site. Reader comments are enthusiastically invited. To suggest improvements for a chapter, please comment using the form on the ASHRAE Web site or, using the cutout page(s) at the end of this volume’s index, write to Handbook Editor, ASHRAE, 1791 Tullie Circle, Atlanta, GA 30329, or fax 678-539-2187, or e-mail [emailprotected] ashrae.org. Mark S. Owen Editor

The four-volume ASHRAE Handbook is a reference for engineers working in HVAC&R and for professionals in allied fields. The print edition is revised on a four-year cycle, with one volume published each year. Tables of contents for the four most recent volumes appear on these pages, and a composite index is at the end of this volume. In addition to the CD-ROM accompanying this book, ASHRAE publishes a HandbookCD+ containing all four volumes plus supplemental material and features. The Society also produces educational materials, standards, design guides, databases, and many other useful publications. See the online bookstore of the ASHRAE Web site (www.ashrae.org) for information on these publications.

2009 FUNDAMENTALS PRINCIPLES Chapter

1. 2. 3. 4. 5. 6. 7. 8.

Psychrometrics Thermodynamics and Refrigeration Cycles Fluid Flow Heat Transfer Two-Phase Flow Mass Transfer Fundamentals of Control Sound and Vibration

INDOOR ENVIRONMENTAL QUALITY Chapter

9. 10. 11. 12. 13.

Thermal Comfort Indoor Environmental Health Air Contaminants Odors Indoor Environmental Modeling

LOAD AND ENERGY CALCULATIONS Chapter 14. 15. 16. 17. 18. 19.

Climatic Design Information Fenestration Ventilation and Infiltration Residential Cooling and Heating Load Calculations Nonresidential Cooling and Heating Load Calculations Energy Estimating and Modeling Methods

HVAC DESIGN Chapter 20.

Space Air Diffusion

21. 22. 23. 24.

Duct Design Pipe Sizing Insulation for Mechanical Systems Airflow Around Buildings

BUILDING ENVELOPE Chapter 25. 26. 27.

Heat, Air, and Moisture Control in Building Assemblies—Fundamentals Heat, Air, and Moisture Control in Building Assemblies—Material Properties Heat, Air, and Moisture Control in Building Assemblies—Examples

MATERIALS Chapter 28. 29. 30. 31. 32. 33.

Combustion and Fuels Refrigerants Thermophysical Properties of Refrigerants Physical Properties of Secondary Coolants (Brines) Sorbents and Desiccants Physical Properties of Materials

GENERAL Chapter 34. 35. 36. 37. 38. 39.

Energy Resources Sustainability Measurement and Instruments Abbreviations and Symbols Units and Conversions Codes and Standards

2008 HVAC SYSTEMS AND EQUIPMENT AIR-CONDITIONING AND HEATING SYSTEMS

HEATING EQUIPMENT AND COMPONENTS

Chapter

Chapter 30. 31. 32. 33. 34. 35. 36.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

HVAC System Analysis and Selection Decentralized Cooling and Heating Central Heating and Cooling Air Handling and Distribution In-Room Terminal Systems Panel Heating and Cooling Combined Heat and Power Systems Applied Heat Pump and Heat Recovery Systems Small Forced-Air Heating and Cooling Systems Steam Systems District Heating and Cooling Hydronic Heating and Cooling Condenser Water Systems Medium- and High-Temperature Water Heating Infrared Radiant Heating Ultraviolet Lamp Systems Combustion Turbine Inlet Cooling

AIR-HANDLING EQUIPMENT AND COMPONENTS Chapter 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

Duct Construction Room Air Distribution Equipment Fans Humidifiers Air-Cooling and Dehumidifying Coils Desiccant Dehumidification and Pressure-Drying Equipment Mechanical Dehumidifiers and Related Components Air-to-Air Energy Recovery Equipment Air-Heating Coils Unit Ventilators, Unit Heaters, and Makeup Air Units Air Cleaners for Particulate Contaminants Industrial Gas Cleaning and Air Pollution Control Equipment

Automatic Fuel-Burning Systems Boilers Furnaces Residential In-Space Heating Equipment Chimney, Vent, and Fireplace Systems Hydronic Heat-Distributing Units and Radiators Solar Energy Equipment

COOLING EQUIPMENT AND COMPONENTS Chapter 37. 38. 39. 40. 41. 42.

Compressors Condensers Cooling Towers Evaporative Air-Cooling Equipment Liquid Coolers Liquid-Chilling Systems

GENERAL COMPONENTS Chapter 43. 44. 45. 46. 47.

Centrifugal Pumps Motors, Motor Controls, and Variable-Speed Drives Pipes, Tubes, and Fittings Valves Heat Exchangers

PACKAGED, UNITARY, AND SPLIT-SYSTEM EQUIPMENT Chapter 48. 49.

Unitary Air Conditioners and Heat Pumps Room Air Conditioners and Packaged Terminal Air Conditioners

GENERAL Chapter 50. 51.

Thermal Storage Codes and Standards

CD-ROM with all content from 2009 Fundamentals inside back cover

2007 HVAC APPLICATIONS COMFORT APPLICATIONS

ENERGY-RELATED APPLICATIONS

Chapter

Chapter 32. 33. 34.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Residences Retail Facilities Commercial and Public Buildings Places of Assembly Hotels, Motels, and Dormitories Educational Facilities Health Care Facilities Justice Facilities Automobiles and Mass Transit Aircraft Ships

INDUSTRIAL APPLICATIONS Chapter 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

Industrial Air Conditioning Enclosed Vehicular Facilities Laboratories Engine Test Facilities Clean Spaces Data Processing and Electronic Office Areas Printing Plants Textile Processing Plants Photographic Material Facilities Museums, Galleries, Archives, and Libraries Environmental Control for Animals and Plants Drying and Storing Selected Farm Crops Air Conditioning of Wood and Paper Product Facilities Power Plants Nuclear Facilities Mine Air Conditioning and Ventilation Industrial Drying Systems Ventilation of the Industrial Environment Industrial Local Exhaust Systems Kitchen Ventilation

Geothermal Energy Solar Energy Use Thermal Storage

BUILDING OPERATIONS AND MANAGEMENT Chapter 35. 36. 37. 38. 39. 40. 41. 42.

Energy Use and Management Owning and Operating Costs Testing, Adjusting, and Balancing Operation and Maintenance Management Computer Applications Building Energy Monitoring Supervisory Control Strategies and Optimization HVAC Commissioning

GENERAL APPLICATIONS Chapter 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59.

Building Envelopes Building Air Intake and Exhaust Design Control of Gaseous Indoor Air Contaminants Design and Application of Controls Sound and Vibration Control Water Treatment Service Water Heating Snow Melting and Freeze Protection Evaporative Cooling Fire and Smoke Management Radiant Heating and Cooling Seismic and Wind Restraint Design Electrical Considerations Room Air Distribution Integrated Building Design Chemical, Biological, Radiological, and Explosive Incidents Codes and Standards

2006 REFRIGERATION REFRIGERATION SYSTEM PRACTICES Chapter

1. 2 3. 4. 5. 6. 7. 8.

Liquid Overfeed Systems System Practices for Halocarbon Refrigerants System Practices for Ammonia and Carbon Dioxide Refrigerants Secondary Coolants in Refrigeration Systems Refrigerant System Chemistry Control of Moisture and Other Contaminants in Refrigerant Systems Lubricants in Refrigerant Systems Refrigerant Containment, Recovery, Recycling, and Reclamation

FOOD STORAGE AND EQUIPMENT Chapter

9. 10. 11. 12. 13. 14. 15.

Thermal Properties of Foods Cooling and Freezing Times of Foods Commodity Storage Requirements Food Microbiology and Refrigeration Refrigeration Load Refrigerated-Facility Design Methods of Precooling Fruits, Vegetables, and Cut Flowers

FOOD REFRIGERATION Chapter 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

Industrial Food-Freezing Systems Meat Products Poultry Products Fishery Products Dairy Products Eggs and Egg Products Deciduous Tree and Vine Fruit Citrus Fruit, Bananas, and Subtropical Fruit Vegetables Fruit Juice Concentrates and Chilled-Juice Products Beverages Processed, Precooked, and Prepared Foods Bakery Products

29.

Chocolates, Candies, Nuts, Dried Fruits, and Dried Vegetables

DISTRIBUTION OF CHILLED AND FROZEN FOOD Chapter 30. 31. 32.

Cargo Containers, Rail Cars, Trailers, and Trucks Marine Refrigeration Air Transport

INDUSTRIAL APPLICATIONS Chapter 33. 34. 35. 36. 37.

Insulation Systems for Refrigerant Piping Ice Manufacture Ice Rinks Concrete Dams and Subsurface Soils Refrigeration in the Chemical Industry

LOW-TEMPERATURE APPLICATIONS Chapter 38. 39. 40.

Cryogenics Ultralow-Temperature Refrigeration Biomedical Applications of Cryogenic Refrigeration

REFRIGERATION EQUIPMENT Chapter 41. 42. 43. 44. 45.

Absorption Cooling, Heating, and Refrigeration Equipment Forced-Circulation Air Coolers Component Balancing in Refrigeration Systems Refrigerant-Control Devices Factory Dehydrating, Charging, and Testing

UNITARY REFRIGERATION EQUIPMENT Chapter 46. 47. 48.

Retail Food Store Refrigeration and Equipment Food Service and General Commercial Refrigeration Equipment Household Refrigerators and Freezers

GENERAL 49.

Codes and Standards

LICENSE AGREEMENT 2009 ASHRAE Handbook—Fundamentals CD-ROM The 2009 ASHRAE Handbook—Fundamentals is distributed with an accompanying CDROM, which provides electronic access to the volume’s content. The License for this CD-ROM is for personal use only; this CD-ROM may not be used on a LAN or WAN. Using the CD-ROM indicates your acceptance of the terms and conditions of this agreement. If you do not agree with them, you should not use this CD-ROM. The title and all copyrights and ownership rights in the program and data are retained by ASHRAE. You assume responsibility for the selection of the program and data to achieve your intended results and for the installation, use, and results obtained from the program and data. You may use the program and data on a single machine. You may copy the program and data into any machine-readable form for back-up purposes in support of your use of the program or data on a single machine. You may not copy or transfer the program or data except as expressly provided for in this license. To do so will result in the automatic termination of your license, and ASHRAE will consider options available to it to recover damages from unauthorized use of its intellectual property. Specifically, you may not copy nor transfer the program or data onto a machine other than your own unless the person to whom you are copying or transferring the program or data also has a license to use them. Distribution to third parties of ASHRAE intellectual property in print or electronic form from this CD-ROM is also prohibited except when authorized by ASHRAE. If you wish to reprint data from this CD-ROM in print or electronic form (such as posting content on a Web site), visit www.ashrae.org/permissions and go to Handbook Reprint Permissions.

CONTENTS Contributors

vii

ASHRAE Technical Committees, Task Groups, and Technical Resource Groups

ix

ASHRAE Research: Improving the Quality of Life

x

Preface

x

PRINCIPLES Chapter

1. Psychrometrics (TC 1.1, Thermodynamics and Psychrometrics, TC 8.3, Absorption and HeatOperated Machines) 2. Thermodynamics and Refrigeration Cycles (TC 1.1) 3. Fluid Flow (TC 1.3, Heat Transfer and Fluid Flow) 4. Heat Transfer (TC 1.3) 5. Two-Phase Flow (TC 1.3) 6. Mass Transfer (TC 1.3) 7. Fundamentals of Control (TC 1.4, Control Theory and Application) 8. Sound and Vibration (TC 2.6, Sound and Vibration Control)

1.1 2.1 3.1 4.1 5.1 6.1 7.1 8.1

INDOOR ENVIRONMENTAL QUALITY Chapter

9. Thermal Comfort (TC 2.1, Physiology and Human Environment) 10. Indoor Environmental Health (Environmental Health Committee) 11. Air Contaminants (TC 2.3, Gaseous Air Contaminants and Gas Contaminant Removal Equipment) 12. Odors (TC 2 .3) 13. Indoor Environmental Modeling (TC 4.10, Indoor Environmental Modeling)

9.1 10.1 11.1 12.1 13.1

LOAD AND ENERGY CALCULATIONS Chapter

Climatic Design Information (TC 4.2, Climatic Information) Fenestration (TC 4.5, Fenestration) Ventilation and Infiltration (TC 4.3, Ventilation Requirements and Infiltration ) Residential Cooling and Heating Load Calculations (TC 4.1, Load Calculation Data and Procedures) 18. Nonresidential Cooling and Heating Load Calculations (TC 4.1) 19. Energy Estimating and Modeling Methods (TC 4.7, Energy Calculations) 14. 15. 16. 17.

14.1 15.1 16.1 17.1 18.1 19.1

HVAC DESIGN Chapter

20. Space Air Diffusion (TC 5.3, Room Air Distribution) 21. Duct Design (TC 5.2, Duct Design)

20.1 21.1

22. Pipe Sizing (TC 6.1, Hydronic and Steam Equipment and Systems) 23. Insulation for Mechanical Systems (TC 1.8, Mechanical Systems Insulation) 24. Airflow Around Buildings (TC 4.3)

22.1 23.1 24.1

BUILDING ENVELOPE Chapter

25. Heat, Air, and Moisture Control in Building Assemblies—Fundamentals (TC 4.4, Building Materials and Building Envelope Performance) 26. Heat, Air, and Moisture Control in Building Assemblies—Material Properties (TC 4.4) 27. Heat, Air, and Moisture Control in Insulated Assemblies—Examples (TC 4.4)

25.1 26.1 27.1

MATERIALS Chapter

28. 29. 30. 31. 32. 33.

Combustion and Fuels (TC 6.10, Fuels and Combustion) Refrigerants (TC 3.1, Refrigerants and Secondary Coolants) Thermophysical Properties of Refrigerants (TC 3.1) Physical Properties of Secondary Coolants (Brines) (TC 3.1) Sorbents and Desiccants (TC 8.12, Dessicant Dehumidification Equipment and Components) Physical Properties of Materials (TC 1.3)

28.1 29.1 30.1 31.1 32.1 33.1

Energy Resources (TC 2.8, Building Environmental Impacts and Sustainability) Sustainability (TC 2.8) Measurement and Instruments (TC 1.2, Instruments and Measurements) Abbreviations and Symbols (TC 1.6, Terminology) Units and Conversions (TC 1.6) Codes and Standards

34.1 35.1 36.1 37.1 38.1 39.1

GENERAL Chapter

34. 35. 36. 37. 38. 39.

INDEX

I.1 Composite index to the 2006 Refrigeration, 2007 HVAC Applications, 2008 HVAC Systems and Equipment, and 2009 Fundamentals volumes

CHAPTER 1

PSYCHROMETRICS Composition of Dry and Moist Air ............................................ 1.1 U.S. Standard Atmosphere ......................................................... 1.1 Thermodynamic Properties of Moist Air ................................... 1.2 Thermodynamic Properties of Water at Saturation ................... 1.2 Humidity Parameters ................................................................. 1.2 Perfect Gas Relationships for Dry and Moist Air............................................................................... 1.12

Thermodynamic Wet-Bulb and Dew-Point Temperature.......... Numerical Calculation of Moist Air Properties....................... Psychrometric Charts............................................................... Typical Air-Conditioning Processes......................................... Transport Properties of Moist Air............................................ Symbols ....................................................................................

P

flat interface surface between moist air and the condensed phase. Saturation conditions change when the interface radius is very small (e.g., with ultrafine water droplets). The relative molecular mass of water is 18.015268 on the carbon-12 scale. The gas constant for water vapor is

SYCHROMETRICS uses thermodynamic properties to analyze conditions and processes involving moist air. This chapter discusses perfect gas relations and their use in common heating, cooling, and humidity control problems. Formulas developed by Herrmann et al. (2009) may be used where greater precision is required. Hyland and Wexler (1983a, 1983b), Nelson and Sauer (2002), and Herrmann et al. (2009) developed formulas for thermodynamic properties of moist air and water modeled as real gases. However, perfect gas relations can be substituted in most air-conditioning problems. Kuehn et al. (1998) showed that errors are less than 0.7% in calculating humidity ratio, enthalpy, and specific volume of saturated air at standard atmospheric pressure for a temperature range of 60 to 120°F. Furthermore, these errors decrease with decreasing pressure.

Rw = 1545.349/18.015268 = 85.780 ft·lbf /lbw ·°R

(2)

U.S. STANDARD ATMOSPHERE The temperature and barometric pressure of atmospheric air vary considerably with altitude as well as with local geographic and weather conditions. The standard atmosphere gives a standard of reference for estimating properties at various altitudes. At sea level, standard temperature is 59°F; standard barometric pressure is 14.696 psia or 29.921 in. Hg. Temperature is assumed to decrease linearly with increasing altitude throughout the troposphere (lower atmosphere), and to be constant in the lower reaches of the stratosphere. The lower atmosphere is assumed to consist of dry air that behaves as a perfect gas. Gravity is also assumed constant at the standard value, 32.1740 ft/s2. Table 1 summarizes property data for altitudes to 30,000 ft. Pressure values in Table 1 may be calculated from

COMPOSITION OF DRY AND MOIST AIR Atmospheric air contains many gaseous components as well as water vapor and miscellaneous contaminants (e.g., smoke, pollen, and gaseous pollutants not normally present in free air far from pollution sources). Dry air is atmospheric air with all water vapor and contaminants removed. Its composition is relatively constant, but small variations in the amounts of individual components occur with time, geographic location, and altitude. Harrison (1965) lists the approximate percentage composition of dry air by volume as: nitrogen, 78.084; oxygen, 20.9476; argon, 0.934; neon, 0.001818; helium, 0.000524; methane, 0.00015; sulfur dioxide, 0 to 0.0001; hydrogen, 0.00005; and minor components such as krypton, xenon, and ozone, 0.0002. Harrison (1965) and Hyland and Wexler (1983a) used a value 0.0314 (circa 1955) for carbon dioxide. Carbon dioxide reached 0.0379 in 2005, is currently increasing by 0.00019 percent per year and is projected to reach 0.0438 in 2036 (Gatley et al. 2008; Keeling and Whorf 2005a, 2005b). Increases in carbon dioxide are offset by decreases in oxygen; consequently, the oxygen percentage in 2036 is projected to be 20.9352. Using the projected changes, the relative molecular mass for dry air for at least the first half of the 21st century is 28.966, based on the carbon-12 scale. The gas constant for dry air using the current Mohr and Taylor (2005) value for the universal gas constant is Rda = 1545.349/28.966 = 53.350 ft·lbf /lbda ·°R

1.13 1.13 1.14 1.15 1.19 1.19

p = 14.696(1 – 6.8754 u 10 –6Z) 5.2559

(3)

The equation for temperature as a function of altitude is Table 1 Standard Atmospheric Data for Altitudes to 30,000 ft Altitude, ft –1000 –500 0 500 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 15,000 20,000 30,000

(1)

Moist air is a binary (two-component) mixture of dry air and water vapor. The amount of water vapor varies from zero (dry air) to a maximum that depends on temperature and pressure. Saturation is a state of neutral equilibrium between moist air and the condensed water phase (liquid or solid); unless otherwise stated, it assumes a The preparation of this chapter is assigned to TC 1.1, Thermodynamics and Psychrometrics.

Temperature, °F 62.6 60.8 59.0 57.2 55.4 51.9 48.3 44.7 41.2 37.6 34.0 30.5 26.9 23.4 5.5 –12.3 –47.8

Source: Adapted from NASA (1976).

1.1

Pressure, psia 15.236 14.966 14.696 14.430 14.175 13.664 13.173 12.682 12.230 11.778 11.341 10.914 10.506 10.108 8.296 6.758 4.371

1.2

2009 ASHRAE Handbook—Fundamentals t = 59 – 0.00356620Z

(4)

where Z = altitude, ft p = barometric pressure, psia t = temperature, °F

Equations (3) and (4) are accurate from 16,500 ft to 36,000 ft. For higher altitudes, comprehensive tables of barometric pressure and other physical properties of the standard atmosphere, in both SI and I-P units, can be found in NASA (1976).

THERMODYNAMIC PROPERTIES OF MOIST AIR Table 2, developed from formulas by Herrmann et al. (2009), shows values of thermodynamic properties of moist air based on the International Temperature Scale of 1990 (ITS-90). This ideal scale differs slightly from practical temperature scales used for physical measurements. For example, the standard boiling point for water (at 14.696 psia) occurs at 211.95°F on this scale rather than at the traditional 212°F. Most measurements are currently based on the International Temperature Scale of 1990 (ITS-90) (Preston-Thomas 1990). The following properties are shown in Table 2: t = Fahrenheit temperature, based on the International Temperature Scale of 1990 (ITS-90) and expressed relative to absolute temperature T in degrees Rankine (°R) by the following relation: T = t + 459.67 Ws = humidity ratio at saturation; gaseous phase (moist air) exists in equilibrium with condensed phase (liquid or solid) at given temperature and pressure (standard atmospheric pressure). At given values of temperature and pressure, humidity ratio W can have any value from zero to Ws. vda = specific volume of dry air, ft3/lbda. vas = vs vda, difference between specific volume of moist air at saturation and that of dry air, ft3/lbda, at same pressure and temperature. vs = specific volume of moist air at saturation, ft3/lbda. hda = specific enthalpy of dry air, Btu/lbda. In Table 2, hda has been assigned a value of 0 at 0°F and standard atmospheric pressure. has = hs hda, difference between specific enthalpy of moist air at saturation and that of dry air, Btu/lbda, at same pressure and temperature. hs = specific enthalpy of moist air at saturation, Btu/lbda. sda = specific entropy of dry air, Btu/lbda · °R. In Table 2, sda is assigned a value of 0 at °F and standard atmospheric pressure. ss = specific entropy of moist air at saturation Btu/lbda · °R.

THERMODYNAMIC PROPERTIES OF WATER AT SATURATION Table 3 shows thermodynamic properties of water at saturation for temperatures from 80 to 300°F, calculated by the formulations described by IAPWS (2007). Symbols in the table follow standard steam table nomenclature. These properties are based on the International Temperature Scale of 1990 (ITS-90). The internal energy and entropy of saturated liquid water are both assigned the value zero at the triple point, 32.018°F. Between the triple-point and critical-point temperatures of water, two states (saturated liquid and saturated vapor) may coexist in equilibrium. The water vapor saturation pressure is required to determine a number of moist air properties, principally the saturation humidity ratio. Values may be obtained from Table 3 or calculated from the following formulas (Hyland and Wexler 1983b). The 1983 formulas are within 300 ppm of the latest IAPWS formulations. For higher accuracy, developers of software and others are referred to IAPWS (2007) and (2008). The saturation pressure over ice for the temperature range of 148 to 32°F is given by

ln pws = C1/T + C2 + C3T + C4T 2 + C5T 3 + C6T 4 + C7 ln T

(5)

where C1 C2 C3 C4 C5 C6 C7

= 1.021 416 5 E+04 = 4.893 242 8 E+00 = 5.376 579 4 E03 = 1.920 237 7 E07 = 3.557 583 2 E10 = 9.034 468 8 E14 = 4.163 501 9 E00

The saturation pressure over liquid water for the temperature range of 32 to 392°F is given by lnpws = C8/T + C9 + C10T + C11T 2 + C12T 3 + C13 ln T

(6)

where C8 C9 C10 C11 C12 C13

= 1.044 039 7 E+04 = 1.129 465 0 E+01 = 2.702 235 5 E02 = 1.289 036 0 E05 = 2.478 068 1 E09 = 6.545 967 3 E+00

In both Equations (5) and (6), pws = saturation pressure, psia T = absolute temperature, °R = °F + 459.67

The coefficients of Equations (5) and (6) were derived from the Hyland-Wexler equations, which are given in SI units. Because of rounding errors in the derivations and in some computers’ calculating precision, results from Equations (5) and (6) may not agree precisely with Table 3 values. The vapor pressure ps of water in saturated moist air differs negligibly from the saturation vapor pressure pws of pure water at the same temperature. Consequently, ps can be used in equations in place of pws with very little error: ps = xws p where xws is the mole fraction of water vapor in saturated moist air at temperature t and pressure p, and p is the total barometric pressure of moist air.

HUMIDITY PARAMETERS Basic Parameters Humidity ratio W (alternatively, the moisture content or mixing ratio) of a given moist air sample is defined as the ratio of the mass of water vapor to the mass of dry air in the sample: W = Mw /Mda

(7)

W equals the mole fraction ratio xw /xda multiplied by the ratio of molecular masses (18.015268/28.966 = 0.621945): W = 0.621945xw /xda

(8)

Specific humidity J is the ratio of the mass of water vapor to total mass of the moist air sample: J = Mw /(Mw + Mda)

(9a)

In terms of the humidity ratio, J = W/(1 + W)

(9b)

Absolute humidity (alternatively, water vapor density) dv is the ratio of the mass of water vapor to total volume of the sample: dv = Mw /V

(10)

Psychrometrics Table 2

1.3 Thermodynamic Properties of Moist Air at Standard Atmospheric Pressure, 14.696 psia Specific Volume, ft3/lbda

Specific Enthalpy, Btu/lbda

Specific Entropy, Btu/lbda ·°F Temp., °F t sda ss

Temp., °F t

Humidity Ratio Ws , lbw /lbda

vda

vas

vs

–80 –79 –78 –77 –76 –75 –74 –73 –72 –71

0.0000049 0.0000053 0.0000057 0.0000062 0.0000067 0.0000072 0.0000078 0.0000084 0.0000090 0.0000097

9.553 9.578 9.603 9.629 9.654 9.680 9.705 9.730 9.756 9.781

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

9.553 9.578 9.604 9.629 9.654 9.680 9.705 9.730 9.756 9.781

–19.218 –18.977 –18.737 –18.497 –18.256 –18.016 –17.776 –17.535 –17.295 –17.055

0.005 0.005 0.006 0.006 0.007 0.007 0.008 0.009 0.009 0.010

–19.213 –18.972 –18.731 –18.490 –18.250 –18.009 –17.768 –17.527 –17.286 –17.045

–0.04593 –0.04530 –0.04467 –0.04404 –0.04341 –0.04279 –0.04216 –0.04154 –0.04092 –0.04030

–0.04592 –0.04528 –0.04465 –0.04402 –0.04339 –0.04277 –0.04214 –0.04152 –0.04090 –0.04027

–80 –79 –78 –77 –76 –75 –74 –73 –72 –71

–70 –69 –68 –67 –66 –65 –64 –63 –62 –61

0.0000104 0.0000112 0.0000120 0.0000129 0.0000139 0.0000149 0.0000160 0.0000172 0.0000184 0.0000198

9.806 9.832 9.857 9.882 9.908 9.933 9.958 9.984 10.009 10.034

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

9.806 9.832 9.857 9.882 9.908 9.933 9.959 9.984 10.009 10.035

–16.815 –16.574 –16.334 –16.094 –15.853 –15.613 –15.373 –15.132 –14.892 –14.652

0.011 0.012 0.012 0.013 0.014 0.015 0.017 0.018 0.019 0.020

–16.804 –16.563 –16.321 –16.080 –15.839 –15.598 –15.356 –15.115 –14.873 –14.632

–0.03968 –0.03907 –0.03845 –0.03784 –0.03723 –0.03662 –0.03601 –0.03541 –0.03480 –0.03420

–0.03966 –0.03904 –0.03842 –0.03781 –0.03719 –0.03658 –0.03597 –0.03536 –0.03475 –0.03414

–70 –69 –68 –67 –66 –65 –64 –63 –62 –61

–60 –59 –58 –57 –56 –55 –54 –53 –52 –51

0.0000212 0.0000227 0.0000243 0.0000260 0.0000279 0.0000298 0.0000319 0.0000341 0.0000365 0.0000390

10.060 10.085 10.110 10.136 10.161 10.186 10.212 10.237 10.262 10.288

0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.001 0.001

10.060 10.085 10.111 10.136 10.161 10.187 10.212 10.237 10.263 10.288

–14.412 –14.171 –13.931 –13.691 –13.451 –13.210 –12.970 –12.730 –12.490 –12.249

0.022 0.023 0.025 0.027 0.029 0.031 0.033 0.035 0.038 0.040

–14.390 –14.148 –13.906 –13.664 –13.422 –13.180 –12.937 –12.695 –12.452 –12.209

–0.03360 –0.03300 –0.03240 –0.03180 –0.03120 –0.03061 –0.03002 –0.02942 –0.02883 –0.02825

–0.03354 –0.03293 –0.03233 –0.03173 –0.03113 –0.03053 –0.02993 –0.02933 –0.02874 –0.02814

–60 –59 –58 –57 –56 –55 –54 –53 –52 –51

–50 –49 –48 –47 –46 –45 –44 –43 –42 –41

0.0000416 0.0000445 0.0000475 0.0000507 0.0000541 0.0000577 0.0000615 0.0000656 0.0000699 0.0000744

10.313 10.338 10.364 10.389 10.414 10.439 10.465 10.490 10.515 10.541

0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001

10.314 10.339 10.364 10.390 10.415 10.440 10.466 10.491 10.517 10.542

–12.009 –11.769 –11.529 –11.289 –11.048 –10.808 –10.568 –10.328 –10.087 –9.847

0.043 0.046 0.049 0.053 0.056 0.060 0.064 0.068 0.073 0.078

–11.966 –11.723 –11.479 –11.236 –10.992 –10.748 –10.504 –10.259 –10.015 –9.770

–0.02766 –0.02707 –0.02649 –0.02591 –0.02532 –0.02474 –0.02417 –0.02359 –0.02301 –0.02244

–0.02755 –0.02695 –0.02636 –0.02577 –0.02518 –0.02459 –0.02400 –0.02341 –0.02283 –0.02224

–50 –49 –48 –47 –46 –45 –44 –43 –42 –41

–40 –39 –38 –37 –36 –35 –34 –33 –32 –31

0.0000793 0.0000844 0.0000898 0.0000956 0.0001017 0.0001081 0.0001150 0.0001222 0.0001298 0.0001379

10.566 10.591 10.617 10.642 10.667 10.693 10.718 10.743 10.769 10.794

0.001 0.001 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002

10.567 10.593 10.618 10.644 10.669 10.695 10.720 10.745 10.771 10.796

–9.607 –9.367 –9.127 –8.886 –8.646 –8.406 –8.166 –7.926 –7.685 –7.445

0.083 0.088 0.094 0.100 0.106 0.113 0.120 0.128 0.136 0.144

–9.524 –9.279 –9.033 –8.787 –8.540 –8.293 –8.046 –7.798 –7.550 –7.301

–0.02187 –0.02129 –0.02072 –0.02015 –0.01959 –0.01902 –0.01846 –0.01789 –0.01733 –0.01677

–0.02166 –0.02107 –0.02049 –0.01990 –0.01932 –0.01874 –0.01816 –0.01757 –0.01699 –0.01641

–40 –39 –38 –37 –36 –35 –34 –33 –32 –31

–30 –29 –28 –27 –26 –25 –24 –23 –22 –21

0.0001465 0.0001555 0.0001650 0.0001751 0.0001857 0.0001970 0.0002088 0.0002213 0.0002345 0.0002485

10.819 10.845 10.870 10.895 10.920 10.946 10.971 10.996 11.022 11.047

0.003 0.003 0.003 0.003 0.003 0.003 0.004 0.004 0.004 0.004

10.822 10.847 10.873 10.898 10.924 10.949 10.975 11.000 11.026 11.051

–7.205 –6.965 –6.725 –6.485 –6.244 –6.004 –5.764 –5.524 –5.284 –5.044

0.153 0.163 0.173 0.184 0.195 0.207 0.219 0.233 0.246 0.261

–7.052 –6.802 –6.552 –6.301 –6.050 –5.797 –5.545 –5.291 –5.037 –4.782

–0.01621 –0.01565 –0.01509 –0.01454 –0.01398 –0.01343 –0.01288 –0.01233 –0.01178 –0.01123

–0.01583 –0.01525 –0.01467 –0.01409 –0.01351 –0.01293 –0.01234 –0.01176 –0.01118 –0.01060

–30 –29 –28 –27 –26 –25 –24 –23 –22 –21

–20 –19 –18 –17 –16 –15 –14 –13 –12 –11

0.0002632 0.0002786 0.0002949 0.0003121 0.0003302 0.0003493 0.0003694 0.0003905 0.0004127 0.0004361

11.072 11.098 11.123 11.148 11.174 11.199 11.224 11.249 11.275 11.300

0.005 0.005 0.005 0.006 0.006 0.006 0.007 0.007 0.007 0.008

11.077 11.103 11.128 11.154 11.179 11.205 11.231 11.257 11.282 11.308

–4.803 –4.563 –4.323 –4.083 –3.843 –3.602 –3.362 –3.122 –2.882 –2.642

0.277 0.293 0.310 0.329 0.348 0.368 0.389 0.412 0.436 0.460

–4.527 –4.270 –4.013 –3.754 –3.495 –3.234 –2.973 –2.710 –2.446 –2.181

–0.01068 –0.01014 –0.00959 –0.00905 –0.00851 –0.00797 –0.00743 –0.00689 –0.00635 –0.00582

–0.01002 –0.00943 –0.00885 –0.00826 –0.00768 –0.00709 –0.00650 –0.00591 –0.00532 –0.00473

–20 –19 –18 –17 –16 –15 –14 –13 –12 –11

hda

has

hs

1.4

2009 ASHRAE Handbook—Fundamentals Table 2

Thermodynamic Properties of Moist Air at Standard Atmospheric Pressure, 14.696 psia (Continued ) Specific Volume, ft3/lbda

Specific Enthalpy, Btu/lbda

Specific Entropy, Btu/lbda ·°F Temp., °F t sda ss

Temp., °F t

Humidity Ratio Ws , lbw /lbda

vda

vas

vs

hda

has

hs

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1

0.0004607 0.0004866 0.0005138 0.0005425 0.0005725 0.0006041 0.0006373 0.0006721 0.0007087 0.0007471

11.325 11.351 11.376 11.401 11.427 11.452 11.477 11.502 11.528 11.553

0.008 0.009 0.009 0.010 0.010 0.011 0.012 0.012 0.013 0.014

11.334 11.360 11.385 11.411 11.437 11.463 11.489 11.515 11.541 11.567

–2.402 –2.161 –1.921 –1.681 –1.441 –1.201 –0.961 –0.720 –0.480 –0.240

0.487 0.514 0.543 0.574 0.606 0.639 0.675 0.712 0.751 0.792

–1.915 –1.647 –1.378 –1.107 –0.835 –0.561 –0.286 –0.009 0.271 0.552

–0.00528 –0.00475 –0.00422 –0.00369 –0.00316 –0.00263 –0.00210 –0.00157 –0.00105 –0.00052

–0.00414 –0.00354 –0.00294 –0.00234 –0.00174 –0.00114 –0.00053 0.00008 0.00069 0.00130

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1

0 1 2 3 4 5 6 7 8 9

0.0007875 0.0008298 0.0008741 0.0009207 0.0009695 0.0010207 0.0010743 0.0011306 0.0011895 0.0012512

11.578 11.604 11.629 11.654 11.680 11.705 11.730 11.755 11.781 11.806

0.015 0.015 0.016 0.017 0.018 0.019 0.020 0.021 0.022 0.024

11.593 11.619 11.645 11.671 11.698 11.724 11.750 11.777 11.803 11.830

0.000 0.240 0.480 0.720 0.961 1.201 1.441 1.681 1.921 2.161

0.835 0.880 0.928 0.978 1.030 1.085 1.142 1.203 1.266 1.332

0.835 1.121 1.408 1.698 1.991 2.286 2.583 2.884 3.187 3.494

0.00000 0.00052 0.00104 0.00156 0.00208 0.00260 0.00311 0.00363 0.00414 0.00466

0.00192 0.00254 0.00317 0.00379 0.00443 0.00506 0.00570 0.00635 0.00700 0.00766

0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

0.0013158 0.0013835 0.0014544 0.0015286 0.0016062 0.0016874 0.0017724 0.0018613 0.0019543 0.0020515

11.831 11.857 11.882 11.907 11.933 11.958 11.983 12.008 12.034 12.059

0.025 0.026 0.028 0.029 0.031 0.032 0.034 0.036 0.038 0.040

11.856 11.883 11.910 11.936 11.963 11.990 12.017 12.044 12.071 12.099

2.402 2.642 2.882 3.122 3.362 3.603 3.843 4.083 4.323 4.563

1.401 1.474 1.550 1.630 1.714 1.801 1.892 1.988 2.088 2.193

3.803 4.116 4.432 4.752 5.076 5.403 5.735 6.071 6.411 6.756

0.00517 0.00568 0.00619 0.00670 0.00721 0.00771 0.00822 0.00872 0.00923 0.00973

0.00832 0.00898 0.00965 0.01033 0.01102 0.01171 0.01241 0.01312 0.01383 0.01455

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

0.0021531 0.0022593 0.0023703 0.0024863 0.0026075 0.0027340 0.0028662 0.0030042 0.0031482 0.0032986

12.084 12.110 12.135 12.160 12.185 12.211 12.236 12.261 12.287 12.312

0.042 0.044 0.046 0.048 0.051 0.054 0.056 0.059 0.062 0.065

12.126 12.153 12.181 12.209 12.236 12.264 12.292 12.320 12.349 12.377

4.803 5.044 5.284 5.524 5.764 6.004 6.244 6.485 6.725 6.965

2.303 2.417 2.537 2.662 2.793 2.930 3.073 3.222 3.378 3.541

7.106 7.461 7.821 8.186 8.557 8.934 9.317 9.707 10.103 10.506

0.01023 0.01073 0.01123 0.01173 0.01222 0.01272 0.01321 0.01371 0.01420 0.01469

0.01528 0.01602 0.01677 0.01753 0.01830 0.01908 0.01987 0.02067 0.02148 0.02231

20 21 22 23 24 25 26 27 28 29

30 31 32 32 33 34 35 36 37 38 39

0.0034555 0.0036192 0.0037900 0.003790 0.003947 0.004109 0.004278 0.004452 0.004633 0.004821 0.005015

12.337 12.362 12.388 12.3877 12.4130 12.4382 12.4635 12.4888 12.5141 12.5394 12.5647

0.068 0.072 0.075 0.0753 0.0786 0.0820 0.0855 0.0892 0.0930 0.0969 0.1010

12.405 12.434 12.463 12.4630 12.4915 12.5202 12.5490 12.5780 12.6071 12.6363 12.6657

7.205 7.445 7.686 7.686 7.926 8.166 8.406 8.646 8.887 9.127 9.367

3.711 3.888 4.073 4.073 4.244 4.420 4.603 4.793 4.990 5.194 5.405

10.916 11.334 11.759 11.759 12.169 12.586 13.009 13.439 13.877 14.321 14.772

0.01518 0.01567 0.01616 0.01616 0.01665 0.01714 0.01762 0.01811 0.01859 0.01908 0.01956

0.02315 0.02400 0.02486 0.02486 0.02570 0.02654 0.02740 0.02827 0.02915 0.03004 0.03095

30 31 32 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

0.005216 0.005425 0.005640 0.005864 0.006095 0.006335 0.006582 0.006839 0.007104 0.007379

12.5899 12.6152 12.6405 12.6658 12.6911 12.7163 12.7416 12.7669 12.7922 12.8175

0.1053 0.1097 0.1143 0.1191 0.1240 0.1292 0.1345 0.1400 0.1457 0.1516

12.6952 12.7249 12.7548 12.7849 12.8151 12.8455 12.8761 12.9069 12.9379 12.9691

9.607 9.848 10.088 10.328 10.568 10.808 11.049 11.289 11.529 11.769

5.625 5.852 6.087 6.331 6.583 6.844 7.115 7.395 7.685 7.985

15.232 15.699 16.175 16.659 17.151 17.653 18.164 18.684 19.214 19.755

0.02004 0.02052 0.02100 0.02148 0.02196 0.02243 0.02291 0.02338 0.02386 0.02433

0.03187 0.03280 0.03375 0.03472 0.03570 0.03669 0.03770 0.03873 0.03978 0.04084

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

0.007663 0.007956 0.008260 0.008574 0.008899 0.009235 0.009582 0.009940 0.010311 0.010694

12.8427 12.8680 12.8933 12.9186 12.9439 12.9691 12.9944 13.0197 13.0450 13.0702

0.1578 0.1641 0.1707 0.1776 0.1847 0.1920 0.1996 0.2075 0.2156 0.2241

13.0005 13.0322 13.0640 13.0962 13.1285 13.1611 13.1940 13.2272 13.2606 13.2943

12.010 12.250 12.490 12.730 12.971 13.211 13.451 13.691 13.932 14.172

8.296 8.617 8.950 9.294 9.650 10.018 10.399 10.792 11.199 11.620

20.306 20.867 21.440 22.024 22.621 23.229 23.850 24.484 25.131 25.792

0.02480 0.02527 0.02574 0.02621 0.02668 0.02715 0.02761 0.02808 0.02854 0.02901

0.04192 0.04302 0.04414 0.04528 0.04645 0.04763 0.04884 0.05006 0.05132 0.05259

50 51 52 53 54 55 56 57 58 59

Psychrometrics Table 2 Temp., °F t

1.5 Thermodynamic Properties of Moist Air at Standard Atmospheric Pressure, 14.696 psia (Continued ) Specific Volume, ft3/lbda

Humidity Ratio Ws , lbw /lbda

vda

60 61 62 63 64 65 66 67 68 69

0.011089 0.011498 0.011921 0.012357 0.012807 0.013272 0.013753 0.014249 0.014761 0.015289

13.0955 13.1208 13.1461 13.1713 13.1966 13.2219 13.2472 13.2724 13.2977 13.3230

70 71 72 73 74 75 76 77 78 79

0.015835 0.016398 0.016979 0.017578 0.018197 0.018835 0.019494 0.020173 0.020874 0.021597

80 81 82 83 84 85 86 87 88 89

vas

Specific Enthalpy, Btu/lbda

Specific Entropy, Btu/lbda ·°F Temp., °F t sda ss

vs

hda

has

hs

0.2328 0.2418 0.2512 0.2609 0.2709 0.2813 0.2920 0.3031 0.3146 0.3265

13.3283 13.3626 13.3973 13.4322 13.4675 13.5032 13.5392 13.5755 13.6123 13.6494

14.412 14.653 14.893 15.133 15.373 15.614 15.854 16.094 16.335 16.575

12.055 12.504 12.968 13.448 13.944 14.456 14.986 15.532 16.097 16.680

26.467 27.157 27.861 28.581 29.318 30.070 30.840 31.626 32.431 33.255

0.02947 0.02993 0.03039 0.03085 0.03131 0.03177 0.03223 0.03268 0.03314 0.03360

0.05389 0.05522 0.05657 0.05795 0.05936 0.06080 0.06226 0.06376 0.06529 0.06685

60 61 62 63 64 65 66 67 68 69

13.3482 13.3735 13.3988 13.4241 13.4493 13.4746 13.4999 13.5251 13.5504 13.5757

0.3388 0.3515 0.3646 0.3782 0.3922 0.4067 0.4217 0.4372 0.4533 0.4698

13.6870 13.7250 13.7634 13.8022 13.8415 13.8813 13.9216 13.9624 14.0037 14.0455

16.815 17.056 17.296 17.536 17.776 18.017 18.257 18.498 18.738 18.978

17.282 17.903 18.545 19.208 19.892 20.598 21.327 22.079 22.855 23.656

34.097 34.959 35.841 36.744 37.668 38.615 39.584 40.576 41.593 42.634

0.03405 0.03450 0.03496 0.03541 0.03586 0.03631 0.03676 0.03720 0.03765 0.03810

0.06844 0.07007 0.07173 0.07343 0.07516 0.07694 0.07875 0.08060 0.08250 0.08444

70 71 72 73 74 75 76 77 78 79

0.022343 0.023112 0.023905 0.024723 0.025566 0.026436 0.027333 0.028257 0.029211 0.030193

13.6010 13.6262 13.6515 13.6768 13.7020 13.7273 13.7526 13.7778 13.8031 13.8284

0.4869 0.5046 0.5229 0.5418 0.5613 0.5814 0.6022 0.6237 0.6459 0.6688

14.0879 14.1308 14.1744 14.2185 14.2633 14.3087 14.3548 14.4015 14.4490 14.4972

19.219 19.459 19.699 19.940 20.180 20.420 20.661 20.901 21.142 21.382

24.482 25.335 26.215 27.122 28.059 29.025 30.021 31.049 32.109 33.202

43.701 44.794 45.914 47.062 48.239 49.445 50.682 51.950 53.250 54.584

0.03854 0.03899 0.03943 0.03988 0.04032 0.04076 0.04120 0.04164 0.04208 0.04252

0.08642 0.08845 0.09052 0.09264 0.09481 0.09703 0.09930 0.10163 0.10401 0.10645

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99

0.031206 0.032251 0.033327 0.034437 0.035581 0.036760 0.037976 0.039228 0.040520 0.041851

13.8536 13.8789 13.9042 13.9294 13.9547 13.9800 14.0052 14.0305 14.0558 14.0810

0.6925 0.7170 0.7422 0.7683 0.7952 0.8230 0.8518 0.8814 0.9120 0.9436

14.5462 14.5959 14.6464 14.6977 14.7499 14.8030 14.8570 14.9119 14.9678 15.0247

21.622 21.863 22.103 22.344 22.584 22.825 23.065 23.305 23.546 23.786

34.329 35.492 36.691 37.928 39.203 40.518 41.874 43.272 44.714 46.201

55.952 57.355 58.795 60.272 61.787 63.343 64.939 66.578 68.260 69.987

0.04296 0.04340 0.04383 0.04427 0.04470 0.04514 0.04557 0.04600 0.04643 0.04686

0.10895 0.11150 0.11412 0.11681 0.11955 0.12237 0.12525 0.12821 0.13124 0.13434

90 91 92 93 94 95 96 97 98 99

100 101 102 103 104 105 106 107 108 109

0.043222 0.044636 0.046094 0.047596 0.049145 0.050741 0.052386 0.054082 0.055830 0.057632

14.1063 14.1316 14.1568 14.1821 14.2074 14.2326 14.2579 14.2831 14.3084 14.3337

0.9763 1.0100 1.0448 1.0807 1.1178 1.1561 1.1957 1.2365 1.2787 1.3222

15.0826 15.1416 15.2016 15.2628 15.3252 15.3887 15.4535 15.5196 15.5871 15.6559

24.027 24.267 24.508 24.748 24.989 25.229 25.470 25.710 25.951 26.191

47.734 49.315 50.945 52.626 54.359 56.146 57.989 59.889 61.849 63.870

71.761 73.582 75.453 77.374 79.348 81.375 83.459 85.600 87.800 90.061

0.04729 0.04772 0.04815 0.04858 0.04901 0.04943 0.04986 0.05028 0.05071 0.05113

0.13752 0.14079 0.14413 0.14756 0.15108 0.15469 0.15839 0.16219 0.16608 0.17008

100 101 102 103 104 105 106 107 108 109

110 111 112 113 114 115 116 117 118 119

0.059490 0.061405 0.063380 0.065416 0.067516 0.069680 0.071913 0.074215 0.076590 0.079040

14.3589 14.3842 14.4095 14.4347 14.4600 14.4852 14.5105 14.5358 14.5610 14.5863

1.3672 1.4136 1.4615 1.5111 1.5622 1.6150 1.6696 1.7259 1.7842 1.8443

15.7261 15.7978 15.8710 15.9458 16.0222 16.1003 16.1801 16.2617 16.3452 16.4306

26.432 26.672 26.913 27.154 27.394 27.635 27.875 28.116 28.356 28.597

65.954 68.104 70.321 72.608 74.967 77.401 79.911 82.502 85.174 87.932

92.386 94.777 97.234 99.762 102.362 105.036 107.787 110.617 113.530 116.529

0.05155 0.05197 0.05240 0.05282 0.05324 0.05365 0.05407 0.05449 0.05491 0.05532

0.17419 0.17840 0.18272 0.18716 0.19172 0.19640 0.20121 0.20615 0.21123 0.21644

110 111 112 113 114 115 116 117 118 119

120 121 122 123 124 125 126 127 128 129

0.081566 0.084173 0.086863 0.089638 0.092503 0.095459 0.098510 0.101661 0.104914 0.108273

14.6116 14.6368 14.6621 14.6873 14.7126 14.7379 14.7631 14.7884 14.8136 14.8389

1.9065 1.9707 2.0370 2.1056 2.1765 2.2498 2.3255 2.4038 2.4848 2.5686

16.5180 16.6075 16.6991 16.7929 16.8891 16.9876 17.0886 17.1922 17.2985 17.4075

28.838 29.078 29.319 29.559 29.800 30.041 30.281 30.522 30.763 31.003

90.777 93.714 96.746 99.875 103.105 106.441 109.885 113.442 117.116 120.912

119.615 122.792 126.064 129.434 132.905 136.481 140.166 143.964 147.879 151.915

0.05574 0.05615 0.05657 0.05698 0.05739 0.05781 0.05822 0.05863 0.05904 0.05945

0.22180 0.22731 0.23298 0.23881 0.24480 0.25096 0.25730 0.26382 0.27054 0.27745

120 121 122 123 124 125 126 127 128 129

1.6

2009 ASHRAE Handbook—Fundamentals Table 2 Thermodynamic Properties of Moist Air at Standard Atmospheric Pressure, 14.696 psia (Concluded ) Specific Volume, ft3/lbda

Temp., °F t

Humidity Ratio Ws , lbw /lbda

vda

130 131 132 133 134 135 136 137 138 139

0.111742 0.115326 0.119029 0.122856 0.126811 0.130899 0.135127 0.139499 0.144022 0.148702

14.8641 14.8894 14.9147 14.9399 14.9652 14.9904 15.0157 15.0410 15.0662 15.0915

140 141 142 143 144 145 146 147 148 149

0.153545 0.158558 0.163750 0.169127 0.174699 0.180473 0.186460 0.192668 0.199109 0.205794

150 151 152 153 154 155 156 157 158 159

vas

Specific Enthalpy, Btu/lbda has

hs

Specific Entropy, Btu/lbda ·°F Temp., °F t sda ss

vs

hda

2.6552 2.7449 2.8376 2.9336 3.0329 3.1357 3.2422 3.3525 3.4668 3.5851

17.5194 17.6343 17.7523 17.8735 17.9981 18.1262 18.2579 18.3935 18.5330 18.6766

31.244 31.485 31.725 31.966 32.207 32.447 32.688 32.929 33.170 33.410

124.833 128.886 133.074 137.404 141.880 146.510 151.298 156.252 161.378 166.684

156.077 160.370 164.799 169.370 174.087 178.957 183.986 189.181 194.548 200.095

0.05985 0.06026 0.06067 0.06108 0.06148 0.06189 0.06229 0.06270 0.06310 0.06350

0.28457 0.29190 0.29945 0.30723 0.31525 0.32352 0.33204 0.34083 0.34989 0.35925

130 131 132 133 134 135 136 137 138 139

15.1167 15.1420 15.1672 15.1925 15.2177 15.2430 15.2683 15.2935 15.3188 15.3440

3.7078 3.8350 3.9668 4.1036 4.2454 4.3927 4.5455 4.7042 4.8691 5.0404

18.8245 18.9769 19.1340 19.2960 19.4632 19.6357 19.8138 19.9977 20.1878 20.3844

33.651 33.892 34.133 34.373 34.614 34.855 35.096 35.337 35.577 35.818

172.177 177.866 183.758 189.863 196.190 202.750 209.553 216.610 223.934 231.538

205.828 211.757 217.890 224.236 230.804 237.605 244.649 251.947 259.512 267.356

0.06390 0.06430 0.06470 0.06510 0.06550 0.06590 0.06630 0.06670 0.06709 0.06749

0.36891 0.37888 0.38918 0.39982 0.41082 0.42219 0.43395 0.44612 0.45871 0.47175

140 141 142 143 144 145 146 147 148 149

0.212734 0.219942 0.227432 0.235218 0.243316 0.251741 0.260512 0.269647 0.279167 0.289093

15.3693 15.3945 15.4198 15.4450 15.4703 15.4956 15.5208 15.5461 15.5713 15.5966

5.2185 5.4037 5.5963 5.7969 6.0057 6.2232 6.4498 6.6862 6.9328 7.1902

20.5878 20.7982 21.0161 21.2419 21.4759 21.7187 21.9706 22.2323 22.5041 22.7868

36.059 36.300 36.541 36.782 37.023 37.263 37.504 37.745 37.986 38.227

239.434 247.638 256.166 265.032 274.257 283.857 293.854 304.270 315.127 326.451

275.493 283.938 292.706 301.814 311.279 321.121 331.359 342.015 353.113 364.678

0.06789 0.06828 0.06867 0.06907 0.06946 0.06985 0.07024 0.07063 0.07103 0.07142

0.48525 0.49925 0.51376 0.52881 0.54443 0.56065 0.57750 0.59501 0.61322 0.63217

150 151 152 153 154 155 156 157 158 159

160 161 162 163 164 165 166 167 168 169

0.299450 0.310262 0.321556 0.333363 0.345715 0.358645 0.372193 0.386399 0.401307 0.416968

15.6218 15.6471 15.6723 15.6976 15.7228 15.7481 15.7733 15.7986 15.8238 15.8491

7.4591 7.7401 8.0340 8.3415 8.6636 9.0010 9.3550 9.7265 10.1168 10.5272

23.0809 23.3872 23.7063 24.0391 24.3864 24.7491 25.1283 25.5251 25.9406 26.3763

38.468 38.709 38.950 39.191 39.432 39.673 39.914 40.155 40.396 40.637

338.268 350.609 363.504 376.988 391.097 405.871 421.354 437.594 454.641 472.553

376.736 389.318 402.454 416.179 430.529 445.544 461.268 477.749 495.037 513.190

0.07180 0.07219 0.07258 0.07297 0.07335 0.07374 0.07413 0.07451 0.07490 0.07528

0.65190 0.67245 0.69389 0.71625 0.73959 0.76399 0.78950 0.81621 0.84418 0.87351

160 161 162 163 164 165 166 167 168 169

170 171 172 173 174 175 176 177 178 179

0.433435 0.450767 0.469029 0.488293 0.508636 0.530148 0.552926 0.577078 0.602726 0.630005

15.8743 15.8996 15.9248 15.9501 15.9753 16.0006 16.0258 16.0511 16.0763 16.1016

10.9591 11.4141 11.8939 12.4006 12.9361 13.5029 14.1035 14.7408 15.4182 16.1393

26.8334 27.3137 27.8188 28.3507 28.9114 29.5035 30.1293 30.7919 31.4946 32.2409

40.878 41.119 41.360 41.601 41.842 42.083 42.324 42.565 42.807 43.048

491.391 511.224 532.125 554.177 577.471 602.109 628.201 655.873 685.265 716.533

532.269 552.343 573.485 595.778 619.313 644.192 670.525 698.439 728.072 759.581

0.07566 0.07604 0.07643 0.07681 0.07719 0.07757 0.07795 0.07833 0.07871 0.07908

0.90430 0.93664 0.97066 1.00649 1.04425 1.08412 1.12627 1.17088 1.21818 1.26840

170 171 172 173 174 175 176 177 178 179

180 181 182 183 184 185 186 187 188 189

0.659068 0.690090 0.723265 0.758816 0.796999 0.838106 0.882474 0.930497 0.982632 1.039415

16.1268 16.1521 16.1773 16.2026 16.2278 16.2531 16.2783 16.3036 16.3288 16.3541

16.9081 17.7293 18.6082 19.5506 20.5636 21.6549 22.8335 24.1100 25.4966 27.0078

33.0349 33.8814 34.7855 35.7532 36.7915 37.9080 39.1118 40.4136 41.8255 43.3619

43.289 43.530 43.771 44.012 44.253 44.495 44.736 44.977 45.218 45.460

749.853 785.424 823.471 864.252 908.058 955.227 1006.148 1061.271 1121.123 1186.321

793.142 828.954 867.242 908.264 952.311 999.722 1050.884 1106.248 1166.341 1231.780

0.07946 0.07984 0.08021 0.08059 0.08096 0.08134 0.08171 0.08209 0.08246 0.08283

1.32183 1.37876 1.43955 1.50459 1.57433 1.64930 1.73010 1.81742 1.91207 2.01501

180 181 182 183 184 185 186 187 188 189

190 191 192 193 194 195 196 197 198 199 200

1.101481 1.169588 1.244642 1.327743 1.420236 1.523781 1.640457 1.772899 1.924494 2.099679 2.304372

16.3793 16.4046 16.4298 16.4551 16.4803 16.5056 16.5308 16.5561 16.5813 16.6066 16.6318

28.6605 30.4750 32.4757 34.6920 37.1600 39.9242 43.0402 46.5787 50.6306 55.3146 60.7896

45.0398 46.8796 48.9056 51.1471 53.6403 56.4297 59.5710 63.1348 67.2119 71.9212 77.4214

45.701 45.942 46.183 46.425 46.666 46.907 47.149 47.390 47.631 47.873 48.114

1257.596 1335.818 1422.030 1517.499 1623.770 1742.754 1876.841 2029.062 2203.315 2404.702 2640.031

1303.297 1381.760 1468.214 1563.924 1670.436 1789.661 1923.990 2076.452 2250.946 2452.574 2688.145

0.08320 0.08357 0.08394 0.08431 0.08468 0.08505 0.08542 0.08579 0.08616 0.08652 0.08689

2.12736 2.25046 2.38593 2.53570 2.70217 2.88826 3.09767 3.33503 3.60635 3.91946 4.28482

190 191 192 193 194 195 196 197 198 199 200

Psychrometrics

1.7 Table 3 Thermodynamic Properties of Water at Saturation Specific Volume, ft3/lbw

Specific Enthalpy, Btu/lbw

Specific Entropy, Btu/lbw ·°F

Sat. Solid hi /hf

Evap. hig /hfg

Sat. Vapor hg

Sat. Solid si /sf

Evap. sig /sfg

Sat. Vapor sg

Temp., °F t

1953807 1814635 1686036 1567159 1457224 1355519 1261390 1174239 1093518 1018724

–193.38 –192.98 –192.59 –192.19 –191.80 –191.40 –191.00 –190.60 –190.20 –189.80

1219.19 1219.23 1219.28 1219.33 1219.38 1219.42 1219.46 1219.51 1219.55 1219.59

1025.81 1026.25 1026.69 1027.13 1027.58 1028.02 1028.46 1028.90 1029.35 1029.79

–0.4064 –0.4054 –0.4043 –0.4033 –0.4023 –0.4012 –0.4002 –0.3992 –0.3981 –0.3971

3.2112 3.2029 3.1946 3.1864 3.1782 3.1700 3.1619 3.1539 3.1458 3.1379

2.8048 2.7975 2.7903 2.7831 2.7759 2.7688 2.7617 2.7547 2.7477 2.7408

–80 –79 –78 –77 –76 –75 –74 –73 –72 –71

949394 885105 825469 770128 718753 671043 626720 585529 547234 511620

949394 885105 825469 770128 718753 671043 626720 585529 547234 511620

–189.40 –189.00 –188.59 –188.19 –187.78 –187.38 –186.97 –186.56 –186.15 –185.74

1219.63 1219.67 1219.71 1219.75 1219.78 1219.82 1219.85 1219.89 1219.92 1219.95

1030.23 1030.67 1031.11 1031.56 1032.00 1032.44 1032.88 1033.33 1033.77 1034.21

–0.3961 –0.3950 –0.3940 –0.3930 –0.3919 –0.3909 –0.3899 –0.3888 –0.3878 –0.3868

3.1299 3.1220 3.1141 3.1063 3.0985 3.0907 3.0830 3.0753 3.0677 3.0601

2.7338 2.7270 2.7201 2.7133 2.7065 2.6998 2.6931 2.6865 2.6799 2.6733

–70 –69 –68 –67 –66 –65 –64 –63 –62 –61

0.01734 0.01734 0.01735 0.01735 0.01735 0.01735 0.01735 0.01735 0.01735 0.01736

478487 447651 418943 392207 367299 344086 322445 302263 283436 265866

478487 447651 418943 392207 367299 344086 322445 302263 283436 265866

–185.33 –184.92 –184.50 –184.09 –183.67 –183.26 –182.84 –182.42 –182.00 –181.58

1219.98 1220.01 1220.04 1220.07 1220.09 1220.12 1220.15 1220.17 1220.19 1220.21

1034.65 1035.09 1035.54 1035.98 1036.42 1036.86 1037.30 1037.75 1038.19 1038.63

–0.3858 –0.3847 –0.3837 –0.3827 –0.3816 –0.3806 –0.3796 –0.3785 –0.3775 –0.3765

3.0525 3.0449 3.0374 3.0299 3.0225 3.0151 3.0077 3.0004 2.9931 2.9858

2.6667 2.6602 2.6537 2.6473 2.6409 2.6345 2.6282 2.6219 2.6156 2.6093

–60 –59 –58 –57 –56 –55 –54 –53 –52 –51

0.000978 0.001045 0.001115 0.001191 0.001270 0.001355 0.001445 0.001540 0.001641 0.001749

0.01736 0.01736 0.01736 0.01736 0.01736 0.01736 0.01736 0.01737 0.01737 0.01737

249464 234148 219841 206472 193976 182292 171363 161139 151570 142611

249464 234148 219841 206472 193976 182292 171363 161139 151570 142611

–181.16 –180.74 –180.32 –179.89 –179.47 –179.04 –178.62 –178.19 –177.76 –177.33

1220.24 1220.26 1220.28 1220.29 1220.31 1220.33 1220.34 1220.36 1220.37 1220.38

1039.07 1039.52 1039.96 1040.40 1040.84 1041.28 1041.73 1042.17 1042.61 1043.05

–0.3755 –0.3744 –0.3734 –0.3724 –0.3713 –0.3703 –0.3693 –0.3683 –0.3672 –0.3662

2.9786 2.9714 2.9642 2.9571 2.9500 2.9429 2.9359 2.9288 2.9219 2.9149

2.6031 2.5970 2.5908 2.5847 2.5786 2.5726 2.5666 2.5606 2.5546 2.5487

–50 –49 –48 –47 –46 –45 –44 –43 –42 –41

–40 –39 –38 –37 –36 –35 –34 –33 –32 –31

0.001862 0.001983 0.002111 0.002246 0.002389 0.002541 0.002701 0.002871 0.003051 0.003241

0.01737 0.01737 0.01737 0.01737 0.01738 0.01738 0.01738 0.01738 0.01738 0.01738

134222 126363 118999 112096 105624 99555 93860 88516 83500 78790

134222 126363 118999 112096 105625 99555 93860 88516 83500 78790

–176.90 –176.47 –176.04 –175.60 –175.17 –174.73 –174.30 –173.86 –173.42 –172.98

1220.39 1220.41 1220.41 1220.42 1220.43 1220.44 1220.44 1220.45 1220.45 1220.45

1043.49 1043.94 1044.38 1044.82 1045.26 1045.70 1046.15 1046.59 1047.03 1047.47

–0.3652 –0.3642 –0.3631 –0.3621 –0.3611 –0.3600 –0.3590 –0.3580 –0.3570 –0.3559

2.9080 2.9011 2.8942 2.8874 2.8806 2.8739 2.8671 2.8604 2.8537 2.8471

2.5428 2.5370 2.5311 2.5253 2.5196 2.5138 2.5081 2.5024 2.4968 2.4911

–40 –39 –38 –37 –36 –35 –34 –33 –32 –31

–30 –29 –28 –27 –26 –25 –24 –23 –22 –21

0.003442 0.003654 0.003878 0.004115 0.004365 0.004629 0.004908 0.005202 0.005512 0.005839

0.01738 0.01738 0.01739 0.01739 0.01739 0.01739 0.01739 0.01739 0.01739 0.01740

74366 70209 66303 62631 59179 55931 52876 50000 47294 44745

74366 70209 66303 62631 59179 55931 52876 50001 47294 44745

–172.54 –172.10 –171.66 –171.22 –170.77 –170.33 –169.88 –169.43 –168.99 –168.54

1220.46 1220.46 1220.46 1220.46 1220.45 1220.45 1220.45 1220.44 1220.43 1220.43

1047.91 1048.36 1048.80 1049.24 1049.68 1050.12 1050.56 1051.01 1051.45 1051.89

–0.3549 –0.3539 –0.3529 –0.3518 –0.3508 –0.3498 –0.3488 –0.3477 –0.3467 –0.3457

2.8405 2.8339 2.8273 2.8208 2.8143 2.8078 2.8013 2.7949 2.7885 2.7821

2.4855 2.4800 2.4744 2.4689 2.4634 2.4580 2.4525 2.4471 2.4418 2.4364

–30 –29 –28 –27 –26 –25 –24 –23 –22 –21

–20 –19 –18 –17 –16 –15 –14

0.006184 0.006548 0.006932 0.007335 0.007761 0.008209 0.008681

0.01740 0.01740 0.01740 0.01740 0.01740 0.01740 0.01741

42345 40084 37953 35944 34050 32264 30580

42345 40084 37953 35944 34050 32264 30580

–168.09 –167.64 –167.19 –166.73 –166.28 –165.82 –165.37

1220.42 1220.41 1220.40 1220.39 1220.38 1220.36 1220.35

1052.33 1052.77 1053.21 1053.65 1054.10 1054.54 1054.98

–0.3447 –0.3436 –0.3426 –0.3416 –0.3406 –0.3396 –0.3385

2.7758 2.7694 2.7632 2.7569 2.7506 2.7444 2.7382

2.4311 2.4258 2.4205 2.4153 2.4101 2.4049 2.3997

–20 –19 –18 –17 –16 –15 –14

Temp., °F t

Absolute Pressure pws , psia

Sat. Solid vi /vf

–80 –79 –78 –77 –76 –75 –74 –73 –72 –71

0.000116 0.000125 0.000135 0.000145 0.000157 0.000169 0.000182 0.000196 0.000211 0.000227

0.01732 0.01732 0.01732 0.01732 0.01732 0.01733 0.01733 0.01733 0.01733 0.01733

1953807 1814635 1686036 1567159 1457224 1355519 1261390 1174239 1093518 1018724

–70 –69 –68 –67 –66 –65 –64 –63 –62 –61

0.000244 0.000263 0.000283 0.000304 0.000326 0.000350 0.000376 0.000404 0.000433 0.000464

0.01733 0.01733 0.01733 0.01733 0.01734 0.01734 0.01734 0.01734 0.01734 0.01734

–60 –59 –58 –57 –56 –55 –54 –53 –52 –51

0.000498 0.000533 0.000571 0.000612 0.000655 0.000701 0.000749 0.000801 0.000857 0.000916

–50 –49 –48 –47 –46 –45 –44 –43 –42 –41

Evap. vig /vfg

Sat. Vapor vg

Note: Subscript i denotes values for t d 32°F and subscript f denotes values for t t 32°F.

1.8

2009 ASHRAE Handbook—Fundamentals Table 3 Thermodynamic Properties of Water at Saturation (Continued ) Specific Volume, ft3/lbw

Specific Enthalpy, Btu/lbw

Specific Entropy, Btu/lbw ·°F

Sat. Solid hi /hf

Evap. hig /hfg

Sat. Vapor hg

Sat. Solid si /sf

Evap. sig /sfg

Sat. Vapor sg

Temp., °F t

28990 27490 26073 24736 23473 22279 21152 20086 19078 18125 17223 16370 15563

–164.91 –164.46 –164.00 –163.54 –163.08 –162.62 –162.15 –161.69 –161.23 –160.76 –160.29 –159.83 –159.36

1220.33 1220.32 1220.30 1220.28 1220.26 1220.24 1220.22 1220.20 1220.17 1220.15 1220.12 1220.10 1220.07

1055.42 1055.86 1056.30 1056.74 1057.18 1057.63 1058.07 1058.51 1058.95 1059.39 1059.83 1060.27 1060.71

–0.3375 –0.3365 –0.3355 –0.3344 –0.3334 –0.3324 –0.3314 –0.3303 –0.3293 –0.3283 –0.3273 –0.3263 –0.3252

2.7321 2.7259 2.7198 2.7137 2.7077 2.7016 2.6956 2.6896 2.6837 2.6777 2.6718 2.6659 2.6600

2.3946 2.3895 2.3844 2.3793 2.3743 2.3692 2.3642 2.3593 2.3543 2.3494 2.3445 2.3396 2.3348

–13 –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1

14799 14076 13391 12742 12127 11545 10992 10469 9972 9501

14799 14076 13391 12742 12127 11545 10992 10469 9972 9501

–158.89 –158.42 –157.95 –157.48 –157.00 –156.53 –156.05 –155.58 –155.10 –154.62

1220.04 1220.01 1219.98 1219.95 1219.92 1219.88 1219.85 1219.81 1219.77 1219.74

1061.15 1061.59 1062.03 1062.47 1062.91 1063.35 1063.79 1064.23 1064.67 1065.11

–0.3242 –0.3232 –0.3222 –0.3212 –0.3201 –0.3191 –0.3181 –0.3171 –0.3160 –0.3150

2.6542 2.6483 2.6425 2.6368 2.6310 2.6253 2.6196 2.6139 2.6082 2.6025

2.3300 2.3251 2.3204 2.3156 2.3109 2.3062 2.3015 2.2968 2.2921 2.2875

0 1 2 3 4 5 6 7 8 9

0.01744 0.01744 0.01744 0.01744 0.01745 0.01745 0.01745 0.01745 0.01745 0.01745

9055 8631 8228 7846 7484 7139 6812 6501 6205 5925

9055 8631 8228 7846 7484 7139 6812 6501 6205 5925

–154.15 –153.67 –153.18 –152.70 –152.22 –151.74 –151.25 –150.77 –150.28 –149.79

1219.70 1219.66 1219.61 1219.57 1219.53 1219.48 1219.44 1219.39 1219.34 1219.29

1065.55 1065.99 1066.43 1066.87 1067.31 1067.75 1068.19 1068.63 1069.06 1069.50

–0.3140 –0.3130 –0.3120 –0.3109 –0.3099 –0.3089 –0.3079 –0.3069 –0.3058 –0.3048

2.5969 2.5913 2.5857 2.5802 2.5746 2.5691 2.5636 2.5581 2.5527 2.5473

2.2829 2.2783 2.2738 2.2692 2.2647 2.2602 2.2557 2.2513 2.2468 2.2424

10 11 12 13 14 15 16 17 18 19

0.050485 0.052967 0.055560 0.058268 0.061096 0.064048 0.067130 0.070347 0.073704 0.077206 0.080858 0.084668 0.088640

0.01746 0.01746 0.01746 0.01746 0.01746 0.01746 0.01746 0.01747 0.01747 0.01747 0.01747 0.01747 0.01747

5658 5404 5162 4932 4714 4506 4308 4119 3939 3768 3605 3450 3302

5658 5404 5162 4932 4714 4506 4308 4119 3939 3768 3605 3450 3302

–149.30 –148.81 –148.32 –147.83 –147.34 –146.85 –146.35 –145.86 –145.36 –144.86 –144.36 –143.86 –143.36

1219.24 1219.19 1219.14 1219.09 1219.03 1218.98 1218.92 1218.86 1218.80 1218.74 1218.68 1218.62 1218.56

1069.94 1070.38 1070.82 1071.26 1071.69 1072.13 1072.57 1073.01 1073.44 1073.88 1074.32 1074.76 1075.19

–0.3038 –0.3028 –0.3018 –0.3007 –0.2997 –0.2987 –0.2977 –0.2967 –0.2957 –0.2946 –0.2936 –0.2926 –0.2916

2.5418 2.5364 2.5311 2.5257 2.5204 2.5151 2.5098 2.5045 2.4992 2.4940 2.4888 2.4836 2.4784

2.2380 2.2337 2.2293 2.2250 2.2207 2.2164 2.2121 2.2078 2.2036 2.1994 2.1952 2.1910 2.1868

20 21 22 23 24 25 26 27 28 29 30 31 32

32 33 34 35 36 37 38 39

0.08865 0.09229 0.09607 0.09998 0.10403 0.10823 0.11258 0.11708

0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602

3302.02 3178.06 3059.30 2945.51 2836.45 2731.91 2631.68 2535.57

3302.04 3178.08 3059.32 2945.52 2836.46 2731.92 2631.70 2535.59

–0.02 0.99 2.00 3.00 4.01 5.02 6.02 7.03

1075.21 1074.64 1074.07 1073.50 1072.93 1072.37 1071.80 1071.23

1075.19 1075.63 1076.07 1076.51 1076.95 1077.38 1077.82 1078.26

0.0000 0.0020 0.0041 0.0061 0.0081 0.0102 0.0122 0.0142

2.1869 2.1813 2.1757 2.1701 2.1646 2.1591 2.1536 2.1482

2.1868 2.1833 2.1797 2.1762 2.1727 2.1693 2.1658 2.1624

32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49 50 51 52

0.12173 0.12656 0.13155 0.13671 0.14205 0.14757 0.15328 0.15919 0.16530 0.17161 0.17813 0.18487 0.19184

0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01603

2443.39 2354.97 2270.13 2188.72 2110.58 2035.58 1963.56 1894.41 1827.99 1764.19 1702.88 1643.98 1587.36

2443.41 2354.98 2270.15 2188.74 2110.60 2035.59 1963.58 1894.42 1828.00 1764.20 1702.90 1643.99 1587.38

8.03 9.04 10.04 11.05 12.05 13.05 14.06 15.06 16.06 17.06 18.07 19.07 20.07

1070.67 1070.10 1069.53 1068.97 1068.40 1067.84 1067.27 1066.70 1066.14 1065.57 1065.01 1064.44 1063.88

1078.70 1079.14 1079.57 1080.01 1080.45 1080.89 1081.33 1081.76 1082.20 1082.64 1083.07 1083.51 1083.95

0.0162 0.0182 0.0202 0.0222 0.0242 0.0262 0.0282 0.0302 0.0321 0.0341 0.0361 0.0381 0.0400

2.1427 2.1373 2.1319 2.1266 2.1212 2.1159 2.1106 2.1053 2.1001 2.0948 2.0896 2.0844 2.0792

2.1590 2.1556 2.1522 2.1488 2.1454 2.1421 2.1388 2.1355 2.1322 2.1289 2.1257 2.1225 2.1192

40 41 42 43 44 45 46 47 48 49 50 51 52

Temp., °F t

Absolute Pressure pws , psia

Sat. Solid vi /vf

–13 –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1

0.009177 0.009700 0.010249 0.010827 0.011435 0.012075 0.012747 0.013453 0.014194 0.014974 0.015792 0.016651 0.017553

0.01741 0.01741 0.01741 0.01741 0.01741 0.01741 0.01742 0.01742 0.01742 0.01742 0.01742 0.01742 0.01742

28990 27490 26073 24736 23473 22279 21151 20086 19078 18125 17223 16370 15563

0 1 2 3 4 5 6 7 8 9

0.018499 0.019492 0.020533 0.021625 0.022770 0.023971 0.025229 0.026547 0.027929 0.029375

0.01743 0.01743 0.01743 0.01743 0.01743 0.01743 0.01743 0.01744 0.01744 0.01744

10 11 12 13 14 15 16 17 18 19

0.030890 0.032476 0.034136 0.035874 0.037692 0.039593 0.041582 0.043662 0.045837 0.048109

20 21 22 23 24 25 26 27 28 29 30 31 32

Evap. vig /vfg

Sat. Vapor vg

*Extrapolated to represent metastable equilibrium with undercooled liquid.

Psychrometrics

1.9 Table 3 Thermodynamic Properties of Water at Saturation (Continued ) Specific Volume, ft3/lbw

Specific Enthalpy, Btu/lbw

Specific Entropy, Btu/lbw ·°F

Evap. hig /hfg

Sat. Vapor hg

Sat. Solid si /sf

Evap. sig /sfg

Sat. Vapor sg

Temp., °F t

21.07 22.07 23.07 24.08 25.08 26.08 27.08

1063.31 1062.75 1062.18 1061.62 1061.05 1060.49 1059.92

1084.38 1084.82 1085.26 1085.69 1086.13 1086.56 1087.00

0.0420 0.0439 0.0459 0.0478 0.0497 0.0517 0.0536

2.0741 2.0689 2.0638 2.0587 2.0536 2.0486 2.0435

2.1160 2.1129 2.1097 2.1065 2.1034 2.1003 2.0972

53 54 55 56 57 58 59

1206.07 1166.16 1127.74 1090.74 1055.12 1020.82 987.77 955.93 925.25 895.68

28.08 29.08 30.08 31.08 32.08 33.08 34.08 35.08 36.08 37.08

1059.36 1058.79 1058.23 1057.66 1057.10 1056.53 1055.97 1055.40 1054.84 1054.27

1087.44 1087.87 1088.31 1088.74 1089.18 1089.61 1090.05 1090.48 1090.92 1091.35

0.0555 0.0575 0.0594 0.0613 0.0632 0.0651 0.0670 0.0689 0.0708 0.0727

2.0385 2.0335 2.0285 2.0236 2.0186 2.0137 2.0088 2.0039 1.9990 1.9942

2.0941 2.0910 2.0879 2.0849 2.0818 2.0788 2.0758 2.0728 2.0699 2.0669

60 61 62 63 64 65 66 67 68 69

867.17 839.70 813.21 787.67 763.04 739.28 716.36 694.25 672.90 652.31

867.19 839.72 813.23 787.69 763.06 739.30 716.38 694.26 672.92 652.32

38.08 39.08 40.08 41.08 42.08 43.07 44.07 45.07 46.07 47.07

1053.71 1053.14 1052.57 1052.01 1051.44 1050.88 1050.31 1049.74 1049.18 1048.61

1091.78 1092.22 1092.65 1093.08 1093.52 1093.95 1094.38 1094.82 1095.25 1095.68

0.0746 0.0765 0.0784 0.0802 0.0821 0.0840 0.0859 0.0877 0.0896 0.0914

1.9894 1.9846 1.9798 1.9750 1.9702 1.9655 1.9607 1.9560 1.9513 1.9467

2.0640 2.0610 2.0581 2.0552 2.0523 2.0495 2.0466 2.0438 2.0409 2.0381

70 71 72 73 74 75 76 77 78 79

0.01607 0.01608 0.01608 0.01608 0.01608 0.01609 0.01609 0.01609 0.01609 0.01610

632.43 613.23 594.70 576.80 559.52 542.83 526.70 511.11 496.05 481.50

632.44 613.25 594.72 576.82 559.54 542.84 526.71 511.13 496.07 481.51

48.07 49.07 50.07 51.07 52.06 53.06 54.06 55.06 56.06 57.06

1048.05 1047.48 1046.91 1046.34 1045.78 1045.21 1044.64 1044.07 1043.51 1042.94

1096.11 1096.55 1096.98 1097.41 1097.84 1098.27 1098.70 1099.13 1099.56 1100.00

0.0933 0.0951 0.0970 0.0988 0.1007 0.1025 0.1043 0.1062 0.1080 0.1098

1.9420 1.9374 1.9328 1.9281 1.9236 1.9190 1.9144 1.9099 1.9054 1.9009

2.0353 2.0325 2.0297 2.0270 2.0242 2.0215 2.0188 2.0160 2.0133 2.0107

80 81 82 83 84 85 86 87 88 89

0.69899 0.72122 0.74405 0.76751 0.79161 0.81636 0.84178 0.86788 0.89468 0.92220

0.01610 0.01610 0.01611 0.01611 0.01611 0.01612 0.01612 0.01612 0.01612 0.01613

467.43 453.83 440.68 427.97 415.67 403.77 392.27 381.14 370.37 359.94

467.45 453.85 440.70 427.98 415.68 403.79 392.28 381.15 370.38 359.96

58.05 59.05 60.05 61.05 62.05 63.05 64.04 65.04 66.04 67.04

1042.37 1041.80 1041.23 1040.67 1040.10 1039.53 1038.96 1038.39 1037.82 1037.25

1100.43 1100.86 1101.28 1101.71 1102.14 1102.57 1103.00 1103.43 1103.86 1104.29

0.1116 0.1134 0.1152 0.1171 0.1189 0.1207 0.1225 0.1242 0.1260 0.1278

1.8964 1.8919 1.8874 1.8830 1.8786 1.8741 1.8697 1.8654 1.8610 1.8566

2.0080 2.0053 2.0027 2.0000 1.9974 1.9948 1.9922 1.9896 1.9870 1.9845

90 91 92 93 94 95 96 97 98 99

100 101 102 103 104 105 106 107 108 109

0.95044 0.97943 1.00917 1.03970 1.07102 1.10315 1.13611 1.16992 1.20459 1.24014

0.01613 0.01613 0.01614 0.01614 0.01614 0.01615 0.01615 0.01616 0.01616 0.01616

349.85 340.09 330.63 321.48 312.62 304.03 295.72 287.66 279.86 272.30

349.87 340.10 330.65 321.50 312.63 304.05 295.73 287.68 279.88 272.32

68.04 69.04 70.03 71.03 72.03 73.03 74.03 75.02 76.02 77.02

1036.68 1036.11 1035.54 1034.97 1034.39 1033.82 1033.25 1032.68 1032.11 1031.53

1104.71 1105.14 1105.57 1106.00 1106.42 1106.85 1107.28 1107.70 1108.13 1108.55

0.1296 0.1314 0.1332 0.1350 0.1367 0.1385 0.1403 0.1420 0.1438 0.1455

1.8523 1.8480 1.8437 1.8394 1.8351 1.8308 1.8266 1.8224 1.8181 1.8139

1.9819 1.9794 1.9769 1.9743 1.9718 1.9693 1.9669 1.9644 1.9619 1.9595

100 101 102 103 104 105 106 107 108 109

110 111 112 113 114 115 116 117 118 119 120

1.27660 1.31397 1.35228 1.39155 1.43179 1.47304 1.51530 1.55860 1.60296 1.64839 1.69493

0.01617 0.01617 0.01617 0.01618 0.01618 0.01618 0.01619 0.01619 0.01620 0.01620 0.01620

264.97 257.87 250.99 244.32 237.85 231.58 225.50 219.60 213.88 208.33 202.95

264.99 257.89 251.01 244.34 237.87 231.60 225.51 219.62 213.90 208.35 202.96

78.02 79.02 80.02 81.01 82.01 83.01 84.01 85.01 86.00 87.00 88.00

1030.96 1030.39 1029.82 1029.24 1028.67 1028.09 1027.52 1026.94 1026.37 1025.79 1025.22

1108.98 1109.41 1109.83 1110.25 1110.68 1111.10 1111.53 1111.95 1112.37 1112.80 1113.22

0.1473 0.1490 0.1508 0.1525 0.1543 0.1560 0.1577 0.1595 0.1612 0.1629 0.1647

1.8098 1.8056 1.8014 1.7973 1.7931 1.7890 1.7849 1.7808 1.7767 1.7727 1.7686

1.9570 1.9546 1.9522 1.9498 1.9474 1.9450 1.9427 1.9403 1.9380 1.9356 1.9333

110 111 112 113 114 115 116 117 118 119 120

Temp., °F t

Absolute Pressure pws , psia

Sat. Solid vi /vf

53 54 55 56 57 58 59

0.19903 0.20646 0.21414 0.22206 0.23024 0.23868 0.24740

0.01603 0.01603 0.01603 0.01603 0.01603 0.01603 0.01603

1532.94 1480.62 1430.31 1381.92 1335.38 1290.60 1247.51

1532.96 1480.64 1430.32 1381.94 1335.39 1290.61 1247.53

60 61 62 63 64 65 66 67 68 69

0.25639 0.26567 0.27524 0.28511 0.29529 0.30579 0.31662 0.32777 0.33927 0.35113

0.01603 0.01604 0.01604 0.01604 0.01604 0.01604 0.01604 0.01605 0.01605 0.01605

1206.05 1166.14 1127.72 1090.73 1055.11 1020.80 987.75 955.91 925.23 895.67

70 71 72 73 74 75 76 77 78 79

0.36334 0.37592 0.38889 0.40224 0.41599 0.43015 0.44473 0.45973 0.47518 0.49108

0.01605 0.01605 0.01606 0.01606 0.01606 0.01606 0.01606 0.01607 0.01607 0.01607

80 81 82 83 84 85 86 87 88 89

0.50744 0.52427 0.54159 0.55940 0.57772 0.59656 0.61593 0.63585 0.65632 0.67736

90 91 92 93 94 95 96 97 98 99

Evap. vig /vfg

Sat. Vapor vg

Sat. Solid hi /hf

1.10

2009 ASHRAE Handbook—Fundamentals Table 3 Thermodynamic Properties of Water at Saturation (Continued ) Specific Volume, ft3/lbw

Specific Enthalpy, Btu/lbw

Specific Entropy, Btu/lbw ·°F

Evap. hig /hfg

Sat. Vapor hg

Sat. Solid si /sf

Evap. sig /sfg

Sat. Vapor sg

Temp., °F t

89.00 90.00 91.00 92.00 92.99 93.99 94.99 95.99 96.99

1024.64 1024.06 1023.49 1022.91 1022.33 1021.76 1021.18 1020.60 1020.02

1113.64 1114.06 1114.48 1114.91 1115.33 1115.75 1116.17 1116.59 1117.01

0.1664 0.1681 0.1698 0.1715 0.1732 0.1749 0.1766 0.1783 0.1800

1.7646 1.7606 1.7565 1.7526 1.7486 1.7446 1.7406 1.7367 1.7328

1.9310 1.9287 1.9264 1.9241 1.9218 1.9195 1.9173 1.9150 1.9128

121 122 123 124 125 126 127 128 129

157.10 153.22 149.44 145.77 142.21 138.74 135.38 132.10 128.92 125.83

97.99 98.99 99.98 100.98 101.98 102.98 103.98 104.98 105.98 106.98

1019.44 1018.86 1018.28 1017.70 1017.12 1016.54 1015.96 1015.37 1014.79 1014.21

1117.43 1117.85 1118.26 1118.68 1119.10 1119.52 1119.94 1120.35 1120.77 1121.19

0.1817 0.1834 0.1851 0.1868 0.1885 0.1902 0.1918 0.1935 0.1952 0.1969

1.7288 1.7249 1.7210 1.7171 1.7133 1.7094 1.7056 1.7017 1.6979 1.6941

1.9106 1.9084 1.9061 1.9039 1.9018 1.8996 1.8974 1.8953 1.8931 1.8910

130 131 132 133 134 135 136 137 138 139

122.81 119.88 117.04 114.28 111.59 108.97 106.43 103.95 101.54 99.20

122.82 119.90 117.06 114.29 111.60 108.99 106.44 103.97 101.56 99.22

107.98 108.98 109.98 110.98 111.97 112.97 113.97 114.97 115.97 116.97

1013.62 1013.04 1012.46 1011.87 1011.29 1010.70 1010.12 1009.53 1008.94 1008.35

1121.60 1122.02 1122.43 1122.85 1123.26 1123.68 1124.09 1124.50 1124.91 1125.33

0.1985 0.2002 0.2019 0.2035 0.2052 0.2068 0.2085 0.2101 0.2118 0.2134

1.6903 1.6865 1.6827 1.6790 1.6752 1.6715 1.6678 1.6640 1.6603 1.6566

1.8888 1.8867 1.8846 1.8825 1.8804 1.8783 1.8762 1.8742 1.8721 1.8701

140 141 142 143 144 145 146 147 148 149

0.01634 0.01635 0.01635 0.01636 0.01636 0.01637 0.01637 0.01638 0.01638 0.01639

96.92 94.70 92.54 90.43 88.38 86.39 84.45 82.55 80.71 78.92

96.93 94.71 92.55 90.45 88.40 86.40 84.46 82.57 80.73 78.93

117.97 118.97 119.97 120.97 121.97 122.97 123.97 124.97 125.98 126.98

1007.77 1007.18 1006.59 1006.00 1005.41 1004.82 1004.23 1003.64 1003.04 1002.45

1125.74 1126.15 1126.56 1126.97 1127.38 1127.79 1128.20 1128.61 1129.02 1129.43

0.2151 0.2167 0.2183 0.2200 0.2216 0.2232 0.2249 0.2265 0.2281 0.2297

1.6530 1.6493 1.6456 1.6420 1.6384 1.6347 1.6311 1.6275 1.6239 1.6203

1.8680 1.8660 1.8640 1.8620 1.8599 1.8580 1.8560 1.8540 1.8520 1.8500

150 151 152 153 154 155 156 157 158 159

4.7472 4.8616 4.9783 5.0973 5.2187 5.3426 5.4689 5.5978 5.7292 5.8632

0.01639 0.01640 0.01640 0.01641 0.01642 0.01642 0.01643 0.01643 0.01644 0.01644

77.170 75.467 73.808 72.191 70.616 69.080 67.584 66.125 64.703 63.317

77.186 75.483 73.824 72.207 70.632 69.097 67.600 66.141 64.720 63.333

127.98 128.98 129.98 130.98 131.98 132.98 133.98 134.98 135.99 136.99

1001.86 1001.26 1000.67 1000.08 999.48 998.88 998.29 997.69 997.09 996.49

1129.83 1130.24 1130.65 1131.06 1131.46 1131.87 1132.27 1132.68 1133.08 1133.48

0.2313 0.2329 0.2346 0.2362 0.2378 0.2394 0.2410 0.2426 0.2442 0.2458

1.6168 1.6132 1.6096 1.6061 1.6026 1.5991 1.5955 1.5920 1.5886 1.5851

1.8481 1.8461 1.8442 1.8423 1.8403 1.8384 1.8365 1.8346 1.8327 1.8308

160 161 162 163 164 165 166 167 168 169

170 171 172 173 174 175 176 177 178 179

5.9998 6.1390 6.2810 6.4258 6.5733 6.7237 6.8769 7.0331 7.1922 7.3544

0.01645 0.01645 0.01646 0.01647 0.01647 0.01648 0.01648 0.01649 0.01650 0.01650

61.965 60.647 59.362 58.109 56.886 55.694 54.531 53.396 52.289 51.208

61.982 60.664 59.379 58.125 56.903 55.710 54.547 53.412 52.305 51.225

137.99 138.99 139.99 141.00 142.00 143.00 144.00 145.00 146.01 147.01

995.90 995.30 994.70 994.10 993.49 992.89 992.29 991.69 991.08 990.48

1133.89 1134.29 1134.69 1135.09 1135.49 1135.89 1136.29 1136.69 1137.09 1137.49

0.2474 0.2489 0.2505 0.2521 0.2537 0.2553 0.2569 0.2584 0.2600 0.2616

1.5816 1.5782 1.5747 1.5713 1.5678 1.5644 1.5610 1.5576 1.5542 1.5508

1.8290 1.8271 1.8252 1.8234 1.8215 1.8197 1.8179 1.8160 1.8142 1.8124

170 171 172 173 174 175 176 177 178 179

180 181 182 183 184 185 186 187 188 189

7.5196 7.6879 7.8593 8.0339 8.2118 8.3930 8.5775 8.7653 8.9566 9.1514

0.01651 0.01651 0.01652 0.01653 0.01653 0.01654 0.01654 0.01655 0.01656 0.01656

50.154 49.125 48.121 47.141 46.184 45.251 44.339 43.448 42.579 41.730

50.171 49.142 48.138 47.158 46.201 45.267 44.355 43.465 42.596 41.747

148.01 149.02 150.02 151.02 152.03 153.03 154.03 155.04 156.04 157.04

989.87 989.27 988.66 988.05 987.44 986.84 986.23 985.62 985.01 984.39

1137.89 1138.28 1138.68 1139.07 1139.47 1139.86 1140.26 1140.65 1141.05 1141.44

0.2631 0.2647 0.2663 0.2678 0.2694 0.2709 0.2725 0.2741 0.2756 0.2772

1.5475 1.5441 1.5408 1.5374 1.5341 1.5308 1.5274 1.5241 1.5208 1.5175

1.8106 1.8088 1.8070 1.8052 1.8035 1.8017 1.7999 1.7982 1.7964 1.7947

180 181 182 183 184 185 186 187 188 189

Temp., °F t

Absolute Pressure pws , psia

Sat. Solid vi /vf

121 122 123 124 125 126 127 128 129

1.74259 1.79140 1.84137 1.89254 1.94492 1.99853 2.05341 2.10957 2.16704

0.01621 0.01621 0.01622 0.01622 0.01623 0.01623 0.01623 0.01624 0.01624

197.72 192.65 187.73 182.96 178.32 173.82 169.45 165.21 161.09

197.74 192.67 187.75 182.97 178.34 173.84 169.47 165.22 161.10

130 131 132 133 134 135 136 137 138 139

2.22584 2.28600 2.34754 2.41050 2.47489 2.54074 2.60809 2.67694 2.74735 2.81932

0.01625 0.01625 0.01626 0.01626 0.01626 0.01627 0.01627 0.01628 0.01628 0.01629

157.09 153.20 149.42 145.75 142.19 138.73 135.36 132.09 128.91 125.81

140 141 142 143 144 145 146 147 148 149

2.89289 2.96810 3.04496 3.12350 3.20377 3.28578 3.36957 3.45516 3.54260 3.63190

0.01629 0.01630 0.01630 0.01631 0.01631 0.01632 0.01632 0.01633 0.01633 0.01634

150 151 152 153 154 155 156 157 158 159

3.72311 3.81626 3.91137 4.00849 4.10764 4.20885 4.31218 4.41764 4.52527 4.63511

160 161 162 163 164 165 166 167 168 169

Evap. vig /vfg

Sat. Vapor vg

Sat. Solid hi /hf

Psychrometrics

1.11 Table 3 Thermodynamic Properties of Water at Saturation (Continued )

Temp., °F t

Absolute Pressure pws , psia

Specific Volume, ft3/lbw Sat. Solid vi /vf

Evap. vig /vfg

Specific Enthalpy, Btu/lbw

Sat. Vapor vg

Specific Entropy, Btu/lbw ·°F

Sat. Solid hi /hf

Evap. hig /hfg

Sat. Vapor hg

Sat. Solid si /sf

Evap. sig /sfg

Sat. Vapor sg

Temp., °F t

190 191 192 193 194 195 196 197 198 199

9.3497 9.5515 9.7570 9.9662 10.1791 10.3958 10.6163 10.8407 11.0690 11.3013

0.01657 0.01658 0.01658 0.01659 0.01659 0.01660 0.01661 0.01661 0.01662 0.01663

40.901 40.092 39.301 38.528 37.773 37.036 36.315 35.611 34.924 34.251

40.918 40.108 39.317 38.545 37.790 37.053 36.332 35.628 34.940 34.268

158.05 159.05 160.06 161.06 162.07 163.07 164.08 165.08 166.09 167.09

983.78 983.17 982.55 981.94 981.32 980.71 980.09 979.47 978.86 978.24

1141.83 1142.22 1142.61 1143.00 1143.39 1143.78 1144.17 1144.56 1144.94 1145.33

0.2787 0.2802 0.2818 0.2833 0.2849 0.2864 0.2879 0.2895 0.2910 0.2925

1.5143 1.5110 1.5077 1.5045 1.5012 1.4980 1.4948 1.4916 1.4884 1.4852

1.7930 1.7912 1.7895 1.7878 1.7861 1.7844 1.7827 1.7810 1.7793 1.7777

190 191 192 193 194 195 196 197 198 199

200 201 202 203 204 205 206 207 208 209

11.5376 11.7781 12.0227 12.2715 12.5246 12.7819 13.0437 13.3099 13.5806 13.8558

0.01663 0.01664 0.01665 0.01665 0.01666 0.01667 0.01667 0.01668 0.01669 0.01669

33.594 32.952 32.324 31.710 31.110 30.524 29.950 29.389 28.840 28.304

33.611 32.968 32.341 31.727 31.127 30.540 29.967 29.406 28.857 28.321

168.10 169.10 170.11 171.12 172.12 173.13 174.14 175.14 176.15 177.16

977.62 976.99 976.37 975.75 975.13 974.50 973.88 973.25 972.62 972.00

1145.71 1146.10 1146.48 1146.87 1147.25 1147.63 1148.01 1148.40 1148.78 1149.15

0.2940 0.2956 0.2971 0.2986 0.3001 0.3016 0.3031 0.3047 0.3062 0.3077

1.4820 1.4788 1.4756 1.4724 1.4693 1.4661 1.4630 1.4599 1.4567 1.4536

1.7760 1.7743 1.7727 1.7710 1.7694 1.7678 1.7661 1.7645 1.7629 1.7613

200 201 202 203 204 205 206 207 208 209

210 212 214 216 218 220 222 224 226 228

14.1357 14.7094 15.3023 15.9149 16.5475 17.2008 17.8753 18.5714 19.2896 20.0307

0.01670 0.01671 0.01673 0.01674 0.01676 0.01677 0.01679 0.01680 0.01681 0.01683

27.779 26.764 25.792 24.862 23.971 23.118 22.301 21.517 20.766 20.046

27.796 26.781 25.809 24.879 23.988 23.135 22.317 21.534 20.783 20.063

178.17 180.18 182.20 184.21 186.23 188.25 190.27 192.29 194.31 196.33

971.37 970.11 968.85 967.58 966.31 965.03 963.75 962.47 961.19 959.89

1149.53 1150.29 1151.04 1151.79 1152.54 1153.28 1154.02 1154.76 1155.49 1156.22

0.3092 0.3122 0.3152 0.3182 0.3211 0.3241 0.3271 0.3300 0.3330 0.3359

1.4505 1.4443 1.4382 1.4320 1.4259 1.4198 1.4138 1.4078 1.4018 1.3959

1.7597 1.7565 1.7533 1.7502 1.7471 1.7440 1.7409 1.7378 1.7348 1.7318

210 212 214 216 218 220 222 224 226 228

230 232 234 236 238 240 242 244 246 248

20.7949 21.5830 22.3955 23.2329 24.0958 24.9849 25.9006 26.8436 27.8145 28.8140

0.01684 0.01686 0.01687 0.01689 0.01691 0.01692 0.01694 0.01695 0.01697 0.01698

19.356 18.693 18.057 17.447 16.861 16.299 15.758 15.239 14.740 14.260

19.373 18.710 18.074 17.464 16.878 16.316 15.775 15.256 14.757 14.277

198.35 200.37 202.40 204.42 206.45 208.47 210.50 212.53 214.56 216.59

958.60 957.30 956.00 954.69 953.38 952.06 950.74 949.42 948.09 946.75

1156.95 1157.68 1158.40 1159.11 1159.83 1160.54 1161.24 1161.95 1162.65 1163.34

0.3388 0.3418 0.3447 0.3476 0.3505 0.3534 0.3563 0.3592 0.3620 0.3649

1.3899 1.3840 1.3782 1.3723 1.3665 1.3607 1.3550 1.3492 1.3435 1.3378

1.7288 1.7258 1.7229 1.7199 1.7170 1.7141 1.7113 1.7084 1.7056 1.7028

230 232 234 236 238 240 242 244 246 248

250 252 254 256 258 260 262 264 266 268

29.8426 30.9009 31.9897 33.1095 34.2611 35.4450 36.6620 37.9127 39.1978 40.5181

0.01700 0.01702 0.01703 0.01705 0.01707 0.01708 0.01710 0.01712 0.01714 0.01715

13.799 13.356 12.929 12.518 12.123 11.743 11.377 11.024 10.685 10.357

13.816 13.373 12.946 12.535 12.140 11.760 11.394 11.041 10.702 10.374

218.62 220.65 222.68 224.72 226.75 228.79 230.83 232.87 234.90 236.94

945.41 944.07 942.72 941.37 940.01 938.65 937.28 935.90 934.52 933.14

1164.03 1164.72 1165.41 1166.09 1166.76 1167.44 1168.10 1168.77 1169.43 1170.08

0.3678 0.3706 0.3735 0.3763 0.3792 0.3820 0.3848 0.3876 0.3904 0.3932

1.3322 1.3266 1.3209 1.3154 1.3098 1.3043 1.2988 1.2933 1.2878 1.2824

1.7000 1.6972 1.6944 1.6917 1.6890 1.6862 1.6836 1.6809 1.6782 1.6756

250 252 254 256 258 260 262 264 266 268

270 272 274 276 278 280 282 284 286 288

41.8742 43.2669 44.6968 46.1647 47.6714 49.2175 50.8039 52.4313 54.1004 55.8121

0.01717 0.01719 0.01721 0.01722 0.01724 0.01726 0.01728 0.01730 0.01731 0.01733

10.042 9.738 9.445 9.162 8.890 8.627 8.373 8.128 7.892 7.664

10.059 9.755 9.462 9.180 8.907 8.644 8.390 8.146 7.909 7.681

238.99 241.03 243.07 245.12 247.16 249.21 251.26 253.31 255.36 257.41

931.75 930.35 928.95 927.54 926.13 924.71 923.29 921.86 920.42 918.98

1170.73 1171.38 1172.02 1172.66 1173.30 1173.92 1174.55 1175.17 1175.78 1176.40

0.3960 0.3988 0.4016 0.4044 0.4071 0.4099 0.4127 0.4154 0.4182 0.4209

1.2769 1.2715 1.2662 1.2608 1.2555 1.2502 1.2449 1.2396 1.2344 1.2291

1.6730 1.6704 1.6678 1.6652 1.6626 1.6601 1.6575 1.6550 1.6525 1.6500

270 272 274 276 278 280 282 284 286 288

290 292 294 296 298 300

57.5672 59.3664 61.2105 63.1003 65.0368 67.0206

0.01735 0.01737 0.01739 0.01741 0.01743 0.01745

7.444 7.231 7.025 6.827 6.635 6.449

7.461 7.248 7.043 6.844 6.652 6.467

259.47 261.52 263.58 265.64 267.70 269.76

917.53 916.08 914.62 913.15 911.68 910.20

1177.00 1177.60 1178.20 1178.79 1179.38 1179.96

0.4236 0.4264 0.4291 0.4318 0.4345 0.4372

1.2239 1.2187 1.2136 1.2084 1.2033 1.1982

1.6476 1.6451 1.6427 1.6402 1.6378 1.6354

290 292 294 296 298 300

1.12

2009 ASHRAE Handbook—Fundamentals

Density U of a moist air mixture is the ratio of total mass to total volume: U = (Mda + Mw)/V = (1/v)(1 + W)

(11)

where v is the moist air specific volume, ft3/lbda, as defined by Equation (26).

Humidity Parameters Involving Saturation

WP = -----Ws

(12) t, p

(13) t, p

Combining Equations (8), (12), and (13) I P = -----------------------------------------------------------1 + 1 – I W s e 0.621945

pwV = nw RT

where pda pw V nda nw R T

= = = = = = =

partial pressure of dry air partial pressure of water vapor total mixture volume number of moles of dry air number of moles of water vapor universal gas constant, 1545.349 ft·lbf /lb mol· °R absolute temperature, °R

The mixture also obeys the perfect gas equation:

xw = pw /(pda + pw) = pw /p

(21)

pw W = 0.621945 --------------p – pw

(22)

The degree of saturation P is defined in Equation (12), where p ws Ws = 0.621945 ----------------p – p ws

(23)

The term pws represents the saturation pressure of water vapor in the absence of air at the given temperature t. This pressure pws is a function only of temperature and differs slightly from the vapor pressure of water in saturated moist air. The relative humidity I is defined in Equation (13). Substituting Equation (21) for xw and xws, pw I = ------p ws

(24) t, p

Substituting Equation (23) for Ws into Equation (14), P I = --------------------------------------------1 – 1 – P pw e p

(25)

Both I and P are zero for dry air and unity for saturated moist air. At intermediate states, their values differ, substantially so at higher temperatures. The specific volume v of a moist air mixture is expressed in terms of a unit mass of dry air: v = V/Mda = V/(28.966nda)

When moist air is considered a mixture of independent perfect gases (i.e., dry air and water vapor), each is assumed to obey the perfect gas equation of state as follows:

Water vapor:

(20)

(26)

where V is the total volume of the mixture, Mda is the total mass of dry air, and nda is the number of moles of dry air. By Equations (16) and (26), with the relation p = pda + pw,

PERFECT GAS RELATIONSHIPS FOR DRY AND MOIST AIR

pdaV = nda RT

xda = pda /( pda + pw) = pda /p

From Equations (8), (20), and (21), the humidity ratio W is

(15)

Thermodynamic wet-bulb temperature t* is the temperature at which water (liquid or solid), by evaporating into moist air at drybulb temperature t and humidity ratio W, can bring air to saturation adiabatically at the same temperature t* while total pressure p is constant. This parameter is considered separately in the section on Thermodynamic Wet-Bulb and Dew-Point Temperature.

Dry air:

(19)

(14)

Dew-point temperature td is the temperature of moist air saturated at pressure p, with the same humidity ratio W as that of the given sample of moist air. It is defined as the solution td ( p, W) of the following equation: Ws( p, td) = W

( pda + pw)V = (nda + nw)RT

and

Relative humidity I is the ratio of the mole fraction of water vapor xw in a given moist air sample to the mole fraction xws in an air sample saturated at the same temperature and pressure: xw I = -------x ws

(18)

where p = pda + pw is the total mixture pressure and n = nda + nw is the total number of moles in the mixture. From Equations (16) to (19), the mole fractions of dry air and water vapor are, respectively,

The following definitions of humidity parameters involve the concept of moist air saturation: Saturation humidity ratio Ws(t, p) is the humidity ratio of moist air saturated with respect to water (or ice) at the same temperature t and pressure p. Degree of saturation P is the ratio of air humidity ratio W to humidity ratio Ws of saturated moist air at the same temperature and pressure:

pV = nRT or

(16) (17)

R da T RT v = ------------------------------------= -------------p – pw 28.966 p – p w

(27)

Using Equation (22), R da T 1 + 1.607858W RT 1 + 1.607858W v = ------------------------------------------------- = ------------------------------------------------------28.966p p

(28)

In Equations (27) and (28), v is specific volume, T is absolute temperature, p is total pressure, pw is partial pressure of water vapor, and W is humidity ratio. In specific units, Equation (28) may be expressed as v = 0.370486(t + 459.67)(1 + 1.607858W )/p where v = specific volume, ft3/lbda

Psychrometrics

1.13

t = dry-bulb temperature, °F W = humidity ratio, lbw /lbda p = total pressure, in. Hg

1093 – 0.556t* W s* – 0.240 t – t* W = -------------------------------------------------------------------------------------1093 + 0.444t – t*

The enthalpy of a mixture of perfect gases equals the sum of the individual partial enthalpies of the components. Therefore, the specific enthalpy of moist air can be written as follows: h = hda + Whg

hda | 0.240t

(30)

hg | 1061 + 0.444t

(31)

where t is the dry-bulb temperature in °F. The moist air specific enthalpy in Btu/lb da then becomes h = 0.240t + W(1061 + 0.444t)

For any state of moist air, a temperature t* exists at which liquid (or solid) water evaporates into the air to bring it to saturation at exactly this same temperature and total pressure (Harrison 1965). During adiabatic saturation, saturated air is expelled at a temperature equal to that of the injected water. In this constant-pressure process, • Humidity ratio increases from initial value W to Ws*, corresponding to saturation at temperature t* • Enthalpy increases from initial value h to hs*, corresponding to saturation at temperature t* • Mass of water added per unit mass of dry air is (Ws* W), which adds energy to the moist air of amount (Ws* W)hw*, where hw* denotes specific enthalpy in Btu/lbw of water added at temperature t* Therefore, if the process is strictly adiabatic, conservation of enthalpy at constant total pressure requires that (33)

Ws*, hw*, and hs* are functions only of temperature t* for a fixed value of pressure. The value of t* that satisfies Equation (33) for given values of h, W, and p is the thermodynamic wet-bulb temperature. A psychrometer consists of two thermometers; one thermometer’s bulb is covered by a wick that has been thoroughly wetted with water. When the wet bulb is placed in an airstream, water evaporates from the wick, eventually reaching an equilibrium temperature called the wet-bulb temperature. This process is not one of adiabatic saturation, which defines the thermodynamic wet-bulb temperature, but one of simultaneous heat and mass transfer from the wet bulb. The fundamental mechanism of this process is described by the Lewis relation [Equation (38) in Chapter 5]. Fortunately, only small corrections must be applied to wet-bulb thermometer readings to obtain the thermodynamic wet-bulb temperature. As defined, thermodynamic wet-bulb temperature is a unique property of a given moist air sample independent of measurement techniques. Equation (33) is exact because it defines the thermodynamic wetbulb temperature t*. Substituting the approximate perfect gas relation [Equation (32)] for h, the corresponding expression for hs*, and the approximate relation for saturated liquid water h*w | t* – 32 into Equation (33), and solving for the humidity ratio,

h*w | – 143.35 – 0.48(32 – t*)

(36)

1220 – 0.04t* W s* – 0.240 t – t* W = ----------------------------------------------------------------------------------1220 + 0.444t – 0.48t*

(37)

A wet/ice-bulb thermometer is imprecise when determining moisture content at 32°F. The dew-point temperature td of moist air with humidity ratio W and pressure p was defined as the solution td (p, w) of Ws ( p, td). For perfect gases, this reduces to pws(td) = pw = ( pW )/(0.621945 + W)

(32)

THERMODYNAMIC WET-BULB AND DEW-POINT TEMPERATURE

h + (Ws* W)hw* = hs*

where t and t* are in °F. Below freezing, the corresponding equations are

(29)

where hda is the specific enthalpy for dry air in Btu/lbda and hg is the specific enthalpy for saturated water vapor in Btu/lbw at the temperature of the mixture. As an approximation,

(34)

(35)

(38)

where pw is the water vapor partial pressure for the moist air sample and pws(td) is the saturation vapor pressure at temperature td . The saturation vapor pressure is obtained from Table 3 or by using Equation (5) or (6). Alternatively, the dew-point temperature can be calculated directly by one of the following equations (Peppers 1988): Between dew points of 32 to 200°F, td = C14 + C15 D + C16D2 + C17D3 + C18 ( pw )0.1984

(39)

Below 32°F, td = 90.12 + 26.142D+ 0.8927D2

(40)

where td D pw C14 C15 C16 C17 C18

= = = = = = = =

dew-point temperature, °F ln pw water vapor partial pressure, psia 100.45 33.193 2.319 0.17074 1.2063

NUMERICAL CALCULATION OF MOIST AIR PROPERTIES The following are outlines, citing equations and tables already presented, for calculating moist air properties using perfect gas relations. These relations are accurate enough for most engineering calculations in air-conditioning practice, and are readily adapted to either hand or computer calculating methods. For more details, refer to Tables 15 through 18 in Chapter 1 of Olivieri (1996). Graphical procedures are discussed in the section on Psychrometric Charts. SITUATION 1. Given: Dry-bulb temperature t, Wet-bulb temperature t*, Pressure p To Obtain

Use

pws (t*) W s* W pws (t) Ws P I v h pw td

Table 3 or Equation (5) or (6) Sat. press. for temp. t* Equation (23) Using pws (t*) Equation (35) or (37) Table 3 or Equation (5) or (6) Sat. press. for temp. t Equation (23) Using pws (t) Equation (12) Using Ws Equation (25) Using pws (t) Equation (28) Equation (32) Equation (38) Table 3 with Equation (38), (39), or (40)

Comments

1.14

2009 ASHRAE Handbook—Fundamentals

SITUATION 2. Given: Dry-bulb temperature t, Dew-point temperature td , Pressure p To Obtain

Use

Comments

pw = pws (td) W pws (t) Ws P I v h t*

Table 3 or Equation (5) or (6) Equation (22) Table 3 or Equation (5) or (6) Equation (23) Equation (12) Equation (25) Equation (28) Equation (32) Equation (23) and (35) or (37) with Table 3 or with Equation (5) or (6)

Sat. press. for temp. td Sat. press. for temp. td Using pws (t) Using Ws Using pws (t)

Requires trial-and-error or numerical solution method

SITUATION 3. Given: Dry-bulb temperature t, Relative humidity IPressure p To Obtain pws(t) pw W Ws P v h td t*

Use

Comments

Table 3 or Equation (5) or (6) Equation (24) Equation (22) Equation (23) Equation (12) Equation (28) Equation (32) Table 3 with Equation (38), (39), or (40) Equation (23) and (35) or (37) with Table 3 or with Equation (5) or (6)

Sat. press. for temp. t

Using pws (t) Using Ws

The dry-bulb temperature ranges covered by the charts are Charts 1, 4, 5 Chart 2 Chart 3

Normal temperature Low temperature High temperature

32 to 120°F 40 to 50°F 60 to 250°F

Charts 6 to 8 are for 400 to 600°F and cover the same pressures as charts 1, 4, 5, and 6. They were produced by Nelson (2002) and are available on the CD-ROM included with Gatley (2005). Psychrometric properties or charts for other barometric pressures can be derived by interpolation. Sufficiently exact values for most purposes can be derived by methods described in the section on Perfect Gas Relationships for Dry and Moist Air. Constructing charts for altitude conditions has been discussed by Haines (1961), Karig (1946), and Rohsenow (1946). Comparison of Charts 1 and 4 by overlay reveals the following: • The dry-bulb lines coincide. • Wet-bulb lines for a given temperature originate at the intersections of the corresponding dry-bulb line and the two saturation curves, and they have the same slope. • Humidity ratio and enthalpy for a given dry- and wet-bulb temperature increase with altitude, but there is little change in relative humidity. • Volume changes rapidly; for a given dry-bulb and humidity ratio, it is practically inversely proportional to barometric pressure. The following table compares properties at sea level (Chart 1) and 5000 ft (Chart 4):

Requires trial-and-error or numerical solution method

Moist Air Property Tables for Standard Pressure Table 2 shows thermodynamic properties for standard atmospheric pressure at temperatures from 80 to 200°F. Properties of intermediate moist air states can be calculated using the degree of saturation P: Volume

v = vda + Pvas

(41)

Enthalpy

h = hda + Phas

(42)

These equations are accurate to about 160°F. At higher temperatures, errors can be significant. Hyland and Wexler (1983a) include charts that can be used to estimate errors for v and h for standard barometric pressure. Nelson and Sauer (2002) provide psychrometric tables and charts up to 600°F and 1.0 lbw/lbda.

PSYCHROMETRIC CHARTS A psychrometric chart graphically represents the thermodynamic properties of moist air. The choice of coordinates for a psychrometric chart is arbitrary. A chart with coordinates of enthalpy and humidity ratio provides convenient graphical solutions of many moist air problems with a minimum of thermodynamic approximations. ASHRAE developed five such psychrometric charts. Chart No. 1 is shown as Figure 1; the others may be obtained through ASHRAE. Charts 1, 2, and 3 are for sea-level pressure, Chart 4 is for 5000 ft altitude (24.89 in. Hg), and Chart 5 is for 7500 ft altitude (22.65 in. Hg). All charts use oblique-angle coordinates of enthalpy and humidity ratio, and are consistent with the data of Table 2 and the properties computation methods of Goff (1949) and Goff and Gratch (1945), as well as Hyland and Wexler (1983a). Palmatier (1963) describes the geometry of chart construction applying specifically to Charts 1 and 4.

Chart No.

db

wb

h

W

rh

v

1 4

100 100

81 81

44.6 49.8

0.0186 0.0234

45 46

14.5 17.6

Figure 1 shows humidity ratio lines (horizontal) for the range from 0 (dry air) to 0.03 lbw/lbda. Enthalpy lines are oblique lines across the chart precisely parallel to each other. Dry-bulb temperature lines are straight, not precisely parallel to each other, and inclined slightly from the vertical position. Thermodynamic wet-bulb temperature lines are oblique and in a slightly different direction from enthalpy lines. They are straight but are not precisely parallel to each other. Relative humidity lines are shown in intervals of 10%. The saturation curve is the line of 100% rh, whereas the horizontal line for W = 0 (dry air) is the line for 0% rh. Specific volume lines are straight but are not precisely parallel to each other. A narrow region above the saturation curve has been developed for fog conditions of moist air. This two-phase region represents a mechanical mixture of saturated moist air and liquid water, with the two components in thermal equilibrium. Isothermal lines in the fog region coincide with extensions of thermodynamic wet-bulb temperature lines. If required, the fog region can be further expanded by extending humidity ratio, enthalpy, and thermodynamic wet-bulb temperature lines. The protractor to the left of the chart shows two scales: one for sensible/total heat ratio, and one for the ratio of enthalpy difference to humidity ratio difference. The protractor is used to establish the direction of a condition line on the psychrometric chart. Example 1 illustrates use of the ASHRAE Psychrometric Chart to determine moist air properties. Example 1. Moist air exists at 100°Fdry-bulb temperature, 65°F thermodynamic wet-bulb temperature, and 14.696 psia (29.921 in. Hg) pressure. Determine the humidity ratio, enthalpy, dew-point temperature, relative humidity, and specific volume. Solution: Locate state point on Chart 1 (Figure 1) at the intersection of 100°F dry-bulb temperature and 65°F thermodynamic wet-bulb temperature lines. Read humidity ratio W = 0.00523 lbw /lbda.

Psychrometrics Fig. 1

1.15

ASHRAE Psychrometric Chart No. 1

Fig. 1

ASHRAE Psychrometric Chart No. 1

1.16

2009 ASHRAE Handbook—Fundamentals

The enthalpy can be found by using two triangles to draw a line parallel to the nearest enthalpy line (30 Btu/lbda) through the state point to the nearest edge scale. Read h = 29.80 Btu/lbda. Dew-point temperature can be read at the intersection of W = 0.00523 lbw/lbda with the saturation curve. Thus, td = 40°F. Relative humidity I can be estimated directly. Thus, I = 13%. Specific volume can be found by linear interpolation between the volume lines for 14.0 and 14.5 ft3/lbda. Thus, v = 14.22 ft3/lbda.

TYPICAL AIR-CONDITIONING PROCESSES The ASHRAE psychrometric chart can be used to solve numerous process problems with moist air. Its use is best explained through illustrative examples. In each of the following examples, the process takes place at a constant total pressure of 14.696 psia.

Moist Air Sensible Heating or Cooling Adding heat alone to or removing heat alone from moist air is represented by a horizontal line on the ASHRAE chart, because the humidity ratio remains unchanged. Figure 2 shows a device that adds heat to a stream of moist air. For steady-flow conditions, the required rate of heat addition is 1q2

= m· da h 2 – h 1

Solution: Figure 3 schematically shows the solution. State 1 is located on the saturation curve at 35°F. Thus, h1 = 13.01 Btu/lbda, W1 = 0.00428 lbw /lbda, and v1 = 12.55 ft3/lbda. State 2 is located at the intersection of t = 100°F and W2 = W1 = 0.00428 lbw /lbda. Thus, h2 = 28.77 Btu/lbda. The mass flow of dry air is

Schematic of Device for Heating Moist Air

From Equation (43), 1q2

= 95,620 28.77 – 13.01 = 1,507,000 Btu/h

Moist Air Cooling and Dehumidification Moisture condensation occurs when moist air is cooled to a temperature below its initial dew point. Figure 4 shows a schematic cooling coil where moist air is assumed to be uniformly processed. Although water can be removed at various temperatures ranging from the initial dew point to the final saturation temperature, it is assumed that condensed water is cooled to the final air temperature t2 before it drains from the system. For the system in Figure 4, the steady-flow energy and material balance equations are m· da h 1 = m· da h 2 + 1q2 + m· w h w2 m· da W 1 = m· da W 2 + m· w Thus, m· w = m· da W 1 – W 2

(43)

Example 2. Moist air, saturated at 35°F, enters a heating coil at a rate of 20,000 cfm. Air leaves the coil at 100°F. Find the required rate of heat addition.

Fig. 2

m· da = 20,000 u 60 e 12.55 = 95,620 lb da e h

1q 2

= m· da > h 1 – h 2 – W 1 – W 2 h w2 @

(44) (45)

Example 3. Moist air at 85°F dry-bulb temperature and 50% rh enters a cooling coil at 10,000 cfm and is processed to a final saturation condition at 50°F. Find the tons of refrigeration required. Solution: Figure 5 shows the schematic solution. State 1 is located at the intersection of t = 85°F and I = 50%. Thus, h1 = 34.62 Btu/lbda, W1 = 0.01292 lbw /lbda, and v1 = 14.01 ft3/lbda. State 2 is located on the saturation curve at 50°F. Thus, h2 = 20.30 Btu/lbda and W2 = 0.00766 lbw /lbda. From Table 2, hw2 = 18.11 Btu/lbw. The mass flow of dry air is m· da = 10,000 e 14.01 = 713.8 lb da /min From Equation (45), 1q 2

= 713.8 > 34.62 – 20.30 – 0.01292 – 0.00766 18.11 @ = 10,150 Btu/min, or 50.75 tons of refrigeration

Adiabatic Mixing of Two Moist Airstreams A common process in air-conditioning systems is the adiabatic mixing of two moist airstreams. Figure 6 schematically shows the problem. Adiabatic mixing is governed by three equations: Fig. 2

Schematic of Device for Heating Moist Air

Fig. 4 Schematic of Device for Cooling Moist Air

Fig. 3 Schematic Solution for Example 2

Fig. 3 Schematic Solution for Example 2

Fig. 4 Schematic of Device for Cooling Moist Air

Psychrometrics

1.17

Fig. 5 Schematic Solution for Example 3

Fig. 5

Fig. 7 Schematic Solution for Example 4

Schematic Solution for Example 3 Fig. 7

Fig. 6 Adiabatic Mixing of Two Moist Airstreams

Schematic Solution for Example 4

Fig. 8 Schematic Showing Injection of Water into Moist Air

Fig. 6

Fig. 8 Schematic Showing Injection of Water into Moist Air

Adiabatic Mixing of Two Moist Airstreams

According to Equation (46),

m· da1 h 1 + m· da2 h 2 = m· da3 h 3 m· da1 + m· da2 = m· da3 W + m· W = m· W m· da1

1

da2

2

da3

m· da1 m· da2 Line 3–2- = ----------1–3- = ----------- or Line - = 1096 -------------------------------------------------- = 0.735 · Line 1–3 Line 1–2 1491 m da2 m· da3 Consequently, the length of line segment 1–3 is 0.735 times the length of entire line 1–2. Using a ruler, State 3 is located, and the values t3 = 65.9°F and t3* = 56.6°F found.

3

Eliminating m· da3 gives W2 – W3 m· da1 h2 – h3 ---------------- = -------------------- = ----------m· da2 h3 – h1 W3 – W1

Adiabatic Mixing of Water Injected into Moist Air (46)

according to which, on the ASHRAE chart, the state point of the resulting mixture lies on the straight line connecting the state points of the two streams being mixed, and divides the line into two segments, in the same ratio as the masses of dry air in the two streams. Example 4. A stream of 5000 cfm of outdoor air at 40°F dry-bulb temperature and 35°F thermodynamic wet-bulb temperature is adiabatically mixed with 15,000 cfm of recirculated air at 75°F dry-bulb temperature and 50% rh. Find the dry-bulb temperature and thermodynamic wetbulb temperature of the resulting mixture. Solution: Figure 7 shows the schematic solution. States 1 and 2 are located on the ASHRAE chart: v1 = 12.65 ft3/lbda, and v2 = 13.68 ft3/lbda. Therefore, m· da1 = 5000 e 12.65 = 395 lb da e min m· da2 = 15,000 e 13.68 = 1096 lb da e min

Steam or liquid water can be injected into a moist airstream to raise its humidity, as shown in Figure 8. If mixing is adiabatic, the following equations apply: m· da h 1 + m· w h w = m· da h 2 m· da W 1 + m· w = m· da W 2 Therefore, h2 – h1 'h--------------------- = ------= hw 'W W2 – W1

(47)

according to which, on the ASHRAE chart, the final state point of the moist air lies on a straight line in the direction fixed by the specific enthalpy of the injected water, drawn through the initial state point of the moist air. Example 5. Moist air at 70°F dry-bulb and 45°F thermodynamic wet-bulb temperature is to be processed to a final dew-point temperature of 55°F

1.18 Fig. 9

2009 ASHRAE Handbook—Fundamentals Schematic Solution for Example 5

Fig. 10 Schematic of Air Conditioned Space

Fig. 10

Schematic of Air Conditioned Space

Fig. 11 Schematic Solution for Example 6

Fig. 9 Schematic Solution for Example 5 by adiabatic injection of saturated steam at 230°F. The rate of dry airflow m· da is 200 lbda/min. Find the final dry-bulb temperature of the moist air and the rate of steam flow required. Solution: Figure 9 shows the schematic solution. By Table 3, the enthalpy of the steam hg = 1157 Btu/lbw. Therefore, according to Equation (47), the condition line on the ASHRAE chart connecting States 1 and 2 must have a direction: 'h/'W = 1157 Btu/lbw The condition line can be drawn with the 'h/'W protractor. First, establish the reference line on the protractor by connecting the origin with the value 'h/'W = 1157 Btu/lbw. Draw a second line parallel to the reference line and through the initial state point of the moist air. This second line is the condition line. State 2 is established at the intersection of the condition line with the horizontal line extended from the saturation curve at 55°F (td2 = 55°F). Thus, t2 = 72.2°F. Values of W2 and W1 can be read from the chart. The required steam flow is m· w = m· da W 2 – W 1 = 200 60 0.00920 – 0.00070 = 102 lb steam e h

Air conditioning required for a space is usually determined by (1) the quantity of moist air to be supplied, and (2) the supply air condition necessary to remove given amounts of energy and water from the space at the exhaust condition specified. Figure 10 shows a space with incident rates of energy and moisture gains. The quantity qs denotes the net sum of all rates of heat gain in the space, arising from transfers through boundaries and from sources within the space. This heat gain involves energy addition alone and does not include energy contributions from water (or water vapor) addition. It is usually called the sensible heat gain. The quantity 6 m· w denotes the net sum of all rates of moisture gain on the space arising from transfers through boundaries and from sources within the space. Each pound of water vapor added to the space adds an amount of energy equal to its specific enthalpy. Assuming steady-state conditions, governing equations are m· h + q + m· h = m· h s

Schematic Solution for Example 6

or q s + ¦ m· w h w = m· da h 2 – h 1 ·

Space Heat Absorption and Moist Air Moisture Gains

da 1

Fig. 11

¦

w w

da 2

m· da W 1 + ¦ m· w = m· da W 2

¦ mw

= m· da W 2 – W 1

(48) (49)

The left side of Equation (48) represents the total rate of energy addition to the space from all sources. By Equations (48) and (49), q s + ¦ m· w h w h2 – h1 'h--------------------- = ------= ------------------------------------'W W2 – W1 m·

¦

(50)

w

according to which, on the ASHRAE chart and for a given state of withdrawn air, all possible states (conditions) for supply air must lie on a straight line drawn through the state point of withdrawn air, with its direction specified by the numerical value of > q s + 6 m· w h w @ e 6m· w . This line is the condition line for the given problem. Example 6. Moist air is withdrawn from a room at 80°F dry-bulb temperature and 66°F thermodynamic wet-bulb temperature. The sensible rate of heat gain for the space is 30,000 Btu/h. A rate of moisture gain of 10 lbw /h occurs from the space occupants. This moisture is assumed as saturated water vapor at 90°F. Moist air is introduced into the room at a dry-bulb temperature of 60°F. Find the required thermodynamic wetbulb temperature and volume flow rate of the supply air.

Psychrometrics

1.19

Table 4 Calculated Diffusion Coefficients for WaterAir at 14.696 psia Barometric Pressure Temp., °F

ft2/h

Temp., °F

ft2/h

Temp., °F

ft2/h

100 50 40 30 20 10

0.504 0.600 0.655 0.682 0.709 0.736 0.767 0.794 0.825 0.853

40 50 60 70 80 90 100 110 120 130

0.884 0.915 0.942 0.973 1.008 1.042 1.073 1.104 1.139 1.170

140 150 200 250 300 350 400 450 500

1.205 1.240 1.414 1.600 1.794 1.996 2.205 2.422 2.647

0 10 20 30

Fig. 12 Viscosity of Moist Air

Solution: Figure 11 shows the schematic solution. State 2 is located on the ASHRAE chart. From Table 3, the specific enthalpy of the added water vapor is hg = 1100.43 Btu/lbw. From Equation (50), 'h 30,000 + 10 1100.43 -------- = ---------------------------------------------------------- = 4100 Btu/lb w 'W 10 With the 'h/'W protractor, establish a reference line of direction 'h/'W = 4100 Btu/lbw . Parallel to this reference line, draw a straight line on the chart through State 2. The intersection of this line with the 60°F dry-bulb temperature line is State 1. Thus, t1* = 56.4°F. An alternative (and approximately correct) procedure in establishing the condition line is to use the protractor’s sensible/total heat ratio scale instead of the 'h/'W scale. The quantity 'Hs /'Ht is the ratio of rate of sensible heat gain for the space to rate of total energy gain for the space. Therefore,

Fig. 12 Viscosity of Moist Air Fig. 13 Thermal Conductivity of Moist Air

'H s qs 30,000 --------- = --------------------------------- = ----------------------------------------------------------- = 0.732 'H t q s + 6 m· w h w 30,000 + 10 u 1100.43 Note that 'Hs /'Ht = 0.732 on the protractor coincides closely with 'h/'W = 4100 Btu/lbw. The flow of dry air can be calculated from either Equation (48) or (49). From Equation (48), q s + 6 m· w h w 30,000 + 10 u 1100.43 m· da = --------------------------------- = ----------------------------------------------------------h2 – h1 60 30.73 – 24.00 = 101.5 lb da /min 3

At State 1, v 1 = 13.29 ft /lb da . Therefore, supply volume = m· da v 1 = 101.5 u 13.29 = 1349 cfm

TRANSPORT PROPERTIES OF MOIST AIR For certain scientific and experimental work, particularly in the heat transfer field, many other moist air properties are important. Generally classified as transport properties, these include diffusion coefficient, viscosity, thermal conductivity, and thermal diffusion factor. Mason and Monchick (1965) derive these properties by calculation. Table 4 and Figures 12 and 13 summarize the authors’ results on the first three properties listed. Note that, within the boundaries of ASHRAE Psychrometric Charts 1, 2, and 3, viscosity varies little from that of dry air at normal atmospheric pressure, and thermal conductivity is essentially independent of moisture content.

SYMBOLS C1 to C18 = constants in Equations (5), (6), and (39) dv = absolute humidity of moist air, mass of water per unit volume of mixture, lbw/ft3 h = specific enthalpy of moist air, Btu/lbda Hs = rate of sensible heat gain for space, Btu/h hs* = specific enthalpy of saturated moist air at thermodynamic wetbulb temperature, Btu/lbda Ht = rate of total energy gain for space, Btu/h

Fig. 13 Thermal Conductivity of Moist Air hw* = specific enthalpy of condensed water (liquid or solid) at thermodynamic wet-bulb temperature and a pressure of 14.696 psia, Btu/lbw Mda = mass of dry air in moist air sample, lbda m· da = mass flow of dry air, per unit time, lbda/min Mw = mass of water vapor in moist air sample, lbw m· w = mass flow of water (any phase), per unit time, lbw/min n = nda + nw, total number of moles in moist air sample nda = moles of dry air nw = moles of water vapor p = total pressure of moist air, psia pda = partial pressure of dry air, psia ps = vapor pressure of water in moist air at saturation, psia. Differs slightly from saturation pressure of pure water because of presence of air. pw = partial pressure of water vapor in moist air, psia pws = pressure of saturated pure water, psia qs = rate of addition (or withdrawal) of sensible heat, Btu/h R = universal gas constant, 1545.329 ft·lbf /lb mole·°R Rda = gas constant for dry air, ft·lbf /lbda ·°R Rw = gas constant for water vapor, ft·lbf /lbw ·°R s = specific entropy, Btu/lbda ·°R or Btu /lbw ·°R T = absolute temperature, °R t = dry-bulb temperature of moist air, °F td = dew-point temperature of moist air, °F

1.20

2009 ASHRAE Handbook—Fundamentals

t* V v vT W W s*

= = = = = =

xda = xw = xws = Z =

thermodynamic wet-bulb temperature of moist air, °F total volume of moist air sample, ft3 specific volume, ft3/lbda or ft3/lbw total gas volume, ft3 humidity ratio of moist air, lbw/lbda humidity ratio of moist air at saturation at thermodynamic wet-bulb temperature, lbw/lbda mole fraction of dry air, moles of dry air per mole of mixture mole fraction of water, moles of water per mole of mixture mole fraction of water vapor under saturated conditions, moles of vapor per mole of saturated mixture altitude, ft

Greek D = ln( pw), parameter used in Equations (39) and (40) J = specific humidity of moist air, mass of water per unit mass of mixture P = degree of saturation W/Ws , dimensionless U = moist air density I = relative humidity

Subscripts as da f fg

= = = =

g i ig s t w

= = = = = =

difference between saturated moist air and dry air dry air saturated liquid water difference between saturated liquid water and saturated water vapor saturated water vapor saturated ice difference between saturated ice and saturated water vapor saturated moist air total water in any phase

REFERENCES Gatley, D.P. 2005. Understanding psychrometrics, 2nd ed. ASHRAE. Gatley, D.P. S. Herrmann, and H.J. Kretzschmar. 2008. A twenty-first century molar mass for dry air. HVAC&R Research 14:655-662. Goff, J.A. 1949. Standardization of thermodynamic properties of moist air. Heating, Piping, and Air Conditioning 21(11):118-128. Goff, J.A. and S. Gratch. 1945. Thermodynamic properties of moist air. ASHVE Transactions 51:125. Haines, R.W. 1961. How to construct high altitude psychrometric charts. Heating, Piping, and Air Conditioning 33(10):144. Harrison, L.P. 1965. Fundamental concepts and definitions relating to humidity. In Humidity and moisture measurement and control in science and industry, vol. 3. A. Wexler and W.A. Wildhack, eds. Reinhold, New York. Herrmann, S., H.J. Kretzschmar, and D.P. Gatley. 2009. Thermodynamic properties of real moist air, dry air, steam, water, and ice. HVAC&R Research (forthcoming). Hyland, R.W. and A. Wexler. 1983a. Formulations for the thermodynamic properties of dry air from 173.15 K to 473.15 K, and of saturated moist air from 173.15 K to 372.15 K, at pressures to 5 MPa. ASHRAE Transactions 89(2A):520-535. Hyland, R.W. and A. Wexler. 1983b. Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K. ASHRAE Transactions 89(2A):500-519.

IAPWS. 1992. Revised supplementary release on saturation properties of ordinary water system. International Association for the Properties of Water and Steam, Oakville, ON, Canada. IAPWS. 2006. Release on an equation of state for H2O ice Ih. International Association for the Properties of Water and Steam, Oakville, ON, Canada. IAPWS. 2007. Revised release on the IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam. International Association for the Properties of Water and Steam, Oakville, ON, Canada. IAPWS. 2008. Revised release on the pressure along the melting and sublimation curves of ordinary water substance. International Association for the Properties of Water and Steam, Oakville, ON, Canada. Karig, H.E. 1946. Psychrometric charts for high altitude calculations. Refrigerating Engineering 52(11):433. Keeling, C.D. and T.P. Whorf. 2005a. Atmospheric carbon dioxide record from Mauna Loa. Scripps Institution of Oceanography—CO2 Research Group. (Available at http://cdiac.ornl.gov/trends/co2/sio-mlo.html) Keeling, C.D. and T.P. Whorf. 2005b. Atmospheric CO2 records from sites in the SIO air sampling network. Trends: A compendium of data on global change. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory. Kuehn, T.H., J.W. Ramsey, and J.L. Threlkeld. 1998. Thermal environmental engineering, 3rd ed. Prentice-Hall, Upper Saddle River, NJ. Lemmon, E.W., R.T. Jacobsen, S.G. Penoncello, and D.G. Friend. 2000. Thermodynamic properties of air and mixture of nitrogen, argon, and oxygen from 60 to 2000 K at pressures to 2000 MPa. Journal of Physical and Chemical Reference Data 29:331-385. Mason, E.A. and L. Monchick. 1965. Survey of the equation of state and transport properties of moist gases. In Humidity and moisture measurement and control in science and industry, vol. 3. A. Wexler and W.A. Wildhack, eds. Reinhold, New York. Mohr, P.J. and P.N. Taylor. 2005. CODATA recommended values of the fundamental physical constants: 2002. Reviews of Modern Physics 77:1-107. NASA. 1976. U.S. Standard atmosphere, 1976. National Oceanic and Atmospheric Administration, National Aeronautics and Space Administration, and the United States Air Force. Available from National Geophysical Data Center, Boulder, CO. Nelson, H.F. and H.J. Sauer, Jr. 2002. Formulation of high-temperature properties for moist air. International Journal of HVAC&R Research 8(3):311-334. NIST. 1990. Guidelines for realizing the international temperature scale of 1990 (ITS-90). NIST Technical Note 1265. National Institute of Technology and Standards, Gaithersburg, MD. Olivieri, J. 1996. Psychrometrics—Theory and practice. ASHRAE. Palmatier, E.P. 1963. Construction of the normal temperature. ASHRAE psychrometric chart. ASHRAE Journal 5:55. Peppers, V.W. 1988. A new psychrometric relation for the dewpoint temperature. Unpublished. Available from ASHRAE. Preston-Thomas, H. 1990. The international temperature scale of 1990 (ITS90). Metrologia 27(1):3-10. Rohsenow, W.M. 1946. Psychrometric determination of absolute humidity at elevated pressures. Refrigerating Engineering 51(5):423.

BIBLIOGRAPHY Kusuda, T. 1970. Algorithms for psychrometric calculations. NBS Publication BSS21 (January) for sale by Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

CHAPTER 2

THERMODYNAMICS AND REFRIGERATION CYCLES THERMODYNAMICS ................................................................ 2.1 Stored Energy.............................................................................. 2.1 Energy in Transition.................................................................... 2.1 First Law of Thermodynamics ................................................... 2.2 Second Law of Thermodynamics ............................................... 2.2 Thermodynamic Analysis of Refrigeration Cycles..................... 2.3 Equations of State ...................................................................... 2.3 Calculating Thermodynamic Properties .................................... 2.4 COMPRESSION REFRIGERATION CYCLES.......................... 2.6 Carnot Cycle .............................................................................. 2.6 Theoretical Single-Stage Cycle Using a Pure Refrigerant or Azeotropic Mixture............................................................. 2.7 Lorenz Refrigeration Cycle ........................................................ 2.8

Theoretical Single-Stage Cycle Using Zeotropic Refrigerant Mixture ................................................................ 2.9 Multistage Vapor Compression Refrigeration Cycles .............. 2.10 Actual Refrigeration Systems ................................................... 2.11 ABSORPTION REFRIGERATION CYCLES ........................... 2.13 Ideal Thermal Cycle................................................................. 2.13 Working Fluid Phase Change Constraints............................... 2.13 Working Fluids ......................................................................... 2.14 Absorption Cycle Representations ........................................... 2.15 Conceptualizing the Cycle ....................................................... 2.15 Absorption Cycle Modeling ..................................................... 2.16 Ammonia/Water Absorption Cycles ......................................... 2.18 Symbols .................................................................................... 2.19

T

Nuclear (atomic) energy derives from the cohesive forces holding protons and neutrons together as the atom’s nucleus.

HERMODYNAMICS is the study of energy, its transformations, and its relation to states of matter. This chapter covers the application of thermodynamics to refrigeration cycles. The first part reviews the first and second laws of thermodynamics and presents methods for calculating thermodynamic properties. The second and third parts address compression and absorption refrigeration cycles, two common methods of thermal energy transfer.

ENERGY IN TRANSITION Heat Q is the mechanism that transfers energy across the boundaries of systems with differing temperatures, always toward the lower temperature. Heat is positive when energy is added to the system (see Figure 1). Work is the mechanism that transfers energy across the boundaries of systems with differing pressures (or force of any kind), always toward the lower pressure. If the total effect produced in the system can be reduced to the raising of a weight, then nothing but work has crossed the boundary. Work is positive when energy is removed from the system (see Figure 1). Mechanical or shaft work W is the energy delivered or absorbed by a mechanism, such as a turbine, air compressor, or internal combustion engine. Flow work is energy carried into or transmitted across the system boundary because a pumping process occurs somewhere outside the system, causing fluid to enter the system. It can be more easily understood as the work done by the fluid just outside the system on the adjacent fluid entering the system to force or push it into the system. Flow work also occurs as fluid leaves the system.

THERMODYNAMICS A thermodynamic system is a region in space or a quantity of matter bounded by a closed surface. The surroundings include everything external to the system, and the system is separated from the surroundings by the system boundaries. These boundaries can be movable or fixed, real or imaginary. Entropy and energy are important in any thermodynamic system. Entropy measures the molecular disorder of a system. The more mixed a system, the greater its entropy; an orderly or unmixed configuration is one of low entropy. Energy has the capacity for producing an effect and can be categorized into either stored or transient forms.

STORED ENERGY Thermal (internal) energy is caused by the motion of molecules and/or intermolecular forces. Potential energy (PE) is caused by attractive forces existing between molecules, or the elevation of the system. PE = mgz

Flow work (per unit mass) = pv

(3)

where p is the pressure and v is the specific volume, or the volume displaced per unit mass evaluated at the inlet or exit. A property of a system is any observable characteristic of the system. The state of a system is defined by specifying the minimum

(1)

where m = mass g = local acceleration of gravity z = elevation above horizontal reference plane

Fig. 1 Energy Flows in General Thermodynamic System

Kinetic energy (KE) is the energy caused by the velocity of molecules and is expressed as KE = mV 2/2

(2)

where V is the velocity of a fluid stream crossing the system boundary. Chemical energy is caused by the arrangement of atoms composing the molecules. The preparation of the first and second parts of this chapter is assigned to TC 1.1, Thermodynamics and Psychrometrics. The third part is assigned to TC 8.3, Absorption and Heat-Operated Machines.

Fig. 1 Energy Flows in General Thermodynamic System

2.1

2.2

2009 ASHRAE Handbook—Fundamentals

set of independent properties. The most common thermodynamic properties are temperature T, pressure p, and specific volume v or density U. Additional thermodynamic properties include entropy, stored forms of energy, and enthalpy. Frequently, thermodynamic properties combine to form other properties. Enthalpy h is an important property that includes internal energy and flow work and is defined as h { u + pv

V -2 + gz· § u + pv + ----m in ¦ © ¹ in 2 2

V - + gz· + Q – W – ¦ m out § u + pv + ----© ¹ out 2 V2 V2 = mf § u + ------ + gz· – m i § u + ------ + gz· © ¹f © ¹i 2 2

(4)

where u is the internal energy per unit mass. Each property in a given state has only one definite value, and any property always has the same value for a given state, regardless of how the substance arrived at that state. A process is a change in state that can be defined as any change in the properties of a system. A process is described by specifying the initial and final equilibrium states, the path (if identifiable), and the interactions that take place across system boundaries during the process. A cycle is a process or a series of processes wherein the initial and final states of the system are identical. Therefore, at the conclusion of a cycle, all the properties have the same value they had at the beginning. Refrigerant circulating in a closed system undergoes a cycle. A pure substance has a homogeneous and invariable chemical composition. It can exist in more than one phase, but the chemical composition is the same in all phases. If a substance is liquid at the saturation temperature and pressure, it is called a saturated liquid. If the temperature of the liquid is lower than the saturation temperature for the existing pressure, it is called either a subcooled liquid (the temperature is lower than the saturation temperature for the given pressure) or a compressed liquid (the pressure is greater than the saturation pressure for the given temperature). When a substance exists as part liquid and part vapor at the saturation temperature, its quality is defined as the ratio of the mass of vapor to the total mass. Quality has meaning only when the substance is saturated (i.e., at saturation pressure and temperature). Pressure and temperature of saturated substances are not independent properties. If a substance exists as a vapor at saturation temperature and pressure, it is called a saturated vapor. (Sometimes the term dry saturated vapor is used to emphasize that the quality is 100%.) When the vapor is at a temperature greater than the saturation temperature, it is a superheated vapor. Pressure and temperature of a superheated vapor are independent properties, because the temperature can increase while pressure remains constant. Gases such as air at room temperature and pressure are highly superheated vapors.

Net amount of energy = Net increase of stored added to system energy in system or [Energy in] – [Energy out] = [Increase of stored energy in system] Figure 1 illustrates energy flows into and out of a thermodynamic system. For the general case of multiple mass flows with uniform properties in and out of the system, the energy balance can be written

system

where subscripts i and f refer to the initial and final states, respectively. Nearly all important engineering processes are commonly modeled as steady-flow processes. Steady flow signifies that all quantities associated with the system do not vary with time. Consequently, V2 m· §© h + ------ + gz·¹ 2 all streams

¦

entering

V -2 + gz· + · – · = 0 m· §© h + ----¹ Q W 2 all streams

¦

(6)

leaving

where h = u + pv as described in Equation (4). A second common application is the closed stationary system for which the first law equation reduces to Q – W = [m(uf – ui)]system

(7)

SECOND LAW OF THERMODYNAMICS The second law of thermodynamics differentiates and quantifies processes that only proceed in a certain direction (irreversible) from those that are reversible. The second law may be described in several ways. One method uses the concept of entropy flow in an open system and the irreversibility associated with the process. The concept of irreversibility provides added insight into the operation of cycles. For example, the larger the irreversibility in a refrigeration cycle operating with a given refrigeration load between two fixed temperature levels, the larger the amount of work required to operate the cycle. Irreversibilities include pressure drops in lines and heat exchangers, heat transfer between fluids of different temperature, and mechanical friction. Reducing total irreversibility in a cycle improves cycle performance. In the limit of no irreversibilities, a cycle attains its maximum ideal efficiency. In an open system, the second law of thermodynamics can be described in terms of entropy as GQ dS system = ------- + Gm i s i – Gm e s e + dI T

FIRST LAW OF THERMODYNAMICS The first law of thermodynamics is often called the law of conservation of energy. The following form of the first-law equation is valid only in the absence of a nuclear or chemical reaction. Based on the first law or the law of conservation of energy, for any system, open or closed, there is an energy balance as

(5)

(8)

where dSsystem Gmi si Gme se GQ/T

total change within system in time dt during process entropy increase caused by mass entering (incoming) entropy decrease caused by mass leaving (exiting) entropy change caused by reversible heat transfer between system and surroundings at temperature T dI = entropy caused by irreversibilities (always positive) = = = =

Equation (8) accounts for all entropy changes in the system. Rearranged, this equation becomes GQ = T [(Gme se – Gmi si) + dSsys – dI ]

(9)

In integrated form, if inlet and outlet properties, mass flow, and interactions with the surroundings do not vary with time, the general equation for the second law is S f – S i system =

GQ

³rev ------T- + ¦ ms in – ¦ ms out + I

(10)

Thermodynamics and Refrigeration Cycles

2.3

In many applications, the process can be considered to operate steadily with no change in time. The change in entropy of the system is therefore zero. The irreversibility rate, which is the rate of entropy production caused by irreversibilities in the process, can be determined by rearranging Equation (10): · I =

· Q

¦ m· s out – ¦ m· s in – ¦ ----------T

(11)

surr

Equation (6) can be used to replace the heat transfer quantity. Note that the absolute temperature of the surroundings with which the system is exchanging heat is used in the last term. If the temperature of the surroundings is equal to the system temperature, heat is transferred reversibly and the last term in Equation (11) equals zero. Equation (11) is commonly applied to a system with one mass flow in, the same mass flow out, no work, and negligible kinetic or potential energy flows. Combining Equations (6) and (11) yields h out – h in · I = m· s out – s in – ---------------------T surr

(13)

THERMODYNAMIC ANALYSIS OF REFRIGERATION CYCLES Refrigeration cycles transfer thermal energy from a region of low temperature TR to one of higher temperature. Usually the highertemperature heat sink is the ambient air or cooling water, at temperature T0 , the temperature of the surroundings. The first and second laws of thermodynamics can be applied to individual components to determine mass and energy balances and the irreversibility of the components. This procedure is illustrated in later sections in this chapter. Performance of a refrigeration cycle is usually described by a coefficient of performance (COP), defined as the benefit of the cycle (amount of heat removed) divided by the required energy input to operate the cycle: Useful refrigerating effect COP { ----------------------------------------------------------------------------------------------------Net energy supplied from external sources

(14)

For a mechanical vapor compression system, the net energy supplied is usually in the form of work, mechanical or electrical, and may include work to the compressor and fans or pumps. Thus, Q evap COP = -------------W net

(15)

In an absorption refrigeration cycle, the net energy supplied is usually in the form of heat into the generator and work into the pumps and fans, or Q evap COP = -----------------------------Q gen + W net

COP K R = ---------------------- COP rev

(16)

In many cases, work supplied to an absorption system is very small compared to the amount of heat supplied to the generator, so the work term is often neglected.

(17)

The Carnot cycle usually serves as the ideal reversible refrigeration cycle. For multistage cycles, each stage is described by a reversible cycle.

EQUATIONS OF STATE The equation of state of a pure substance is a mathematical relation between pressure, specific volume, and temperature. When the system is in thermodynamic equilibrium, f ( p,v,T ) = 0

(12)

In a cycle, the reduction of work produced by a power cycle (or the increase in work required by a refrigeration cycle) equals the absolute ambient temperature multiplied by the sum of irreversibilities in all processes in the cycle. Thus, the difference in reversible and actual work for any refrigeration cycle, theoretical or real, operating under the same conditions, becomes · · · Wactual = Wreversible + T 0 ¦ I

Applying the second law to an entire refrigeration cycle shows that a completely reversible cycle operating under the same conditions has the maximum possible COP. Departure of the actual cycle from an ideal reversible cycle is given by the refrigerating efficiency:

(18)

The principles of statistical mechanics are used to (1) explore the fundamental properties of matter, (2) predict an equation of state based on the statistical nature of a particular system, or (3) propose a functional form for an equation of state with unknown parameters that are determined by measuring thermodynamic properties of a substance. A fundamental equation with this basis is the virial equation, which is expressed as an expansion in pressure p or in reciprocal values of volume per unit mass v as pv 2 3 ------- = 1 + Bcp + Ccp + Dcp + } RT

(19)

pv 2 3 ------- = 1 + B e v + C e v + D e v + } RT

(20)

where coefficients B', C', D', etc., and B, C, D, etc., are the virial coefficients. B' and B are the second virial coefficients; C' and C are the third virial coefficients, etc. The virial coefficients are functions of temperature only, and values of the respective coefficients in Equations (19) and (20) are related. For example, B' = B/RT and C' = (C – B2)/(RT) 2. The universal gas constant R is defined as pv T R = lim ------------po 0 T

(21)

where pv T is the product of the pressure and the molar specific volume along an isotherm with absolute temperature T. The current best value of R is 1545.32 ft·lbf /(lb mol·°R). The gas constant R is equal to the universal gas constant R divided by the molecular weight M of the gas or gas mixture. The quantity pv/RT is also called the compressibility factor Z, or Z = 1 + (B/v) + (C/v2) + (D/v3) + …

(22)

An advantage of the virial form is that statistical mechanics can be used to predict the lower-order coefficients and provide physical significance to the virial coefficients. For example, in Equation (22), the term B/v is a function of interactions between two molecules, C/v 2 between three molecules, etc. Because lower-order interactions are common, contributions of the higher-order terms are successively less. Thermodynamicists use the partition or distribution function to determine virial coefficients; however, experimental values of the second and third coefficients are preferred. For dense fluids, many higher-order terms are necessary that can neither be satisfactorily predicted from theory nor determined from experimental measurements. In general, a truncated virial expansion of four terms is valid for densities of less than one-half the value at the critical

2.4

2009 ASHRAE Handbook—Fundamentals

point. For higher densities, additional terms can be used and determined empirically. Computers allow the use of very complex equations of state in calculating p-v-T values, even to high densities. The BenedictWebb-Rubin (B-W-R) equation of state (Benedict et al. 1940) and Martin-Hou equation (1955) have had considerable use, but should generally be limited to densities less than the critical value. Strobridge (1962) suggested a modified Benedict-Webb-Rubin relation that gives excellent results at higher densities and can be used for a p-v-T surface that extends into the liquid phase. The B-W-R equation has been used extensively for hydrocarbons (Cooper and Goldfrank 1967): 2

2

P = RT e v + B o RT – A o – C o e T e v + bRT – a e v 6

2

2

+ aD e v + > c 1 + J e v e

–J e v

3

@ev T

2

3

(23)

where the constant coefficients are Ao, Bo, Co, a, b, c, D, and J. The Martin-Hou equation, developed for fluorinated hydrocarbon properties, has been used to calculate the thermodynamic property tables in Chapter 30 and in ASHRAE Thermodynamic Properties of Refrigerants (Stewart et al. 1986). The Martin-Hou equation is – kT e T c

– kT e T c

A3 + B3 T + C3 e A2 + B2 T + C2 e RT- + -------------------------------------------------------- + -------------------------------------------------------p = ---------2 3 v–b v – b v – b – kT e T c

A4 + B4 T A5 + B5 T + C5 e av + --------------------- + --------------------------------------------------------- + A 6 + B 6 T e (24) 4 5 v – b v – b where the constant coefficients are Ai , Bi , Ci , k, b, and a. Strobridge (1962) suggested an equation of state that was developed for nitrogen properties and used for most cryogenic fluids. This equation combines the B-W-R equation of state with an equation for high-density nitrogen suggested by Benedict (1937). These equations have been used successfully for liquid and vapor phases, extending in the liquid phase to the triple-point temperature and the freezing line, and in the vapor phase from 18 to 1800°R, with pressures to 150,000 psi. The Strobridge equation is accurate within the uncertainty of the measured p-v-T data: n n n 2 p = RTU + Rn 1 T + n 2 + ----3- + -----4 + -----5 U T T2 T4 3

+ Rn 6 T + n 7 U + n 8 TU

CALCULATING THERMODYNAMIC PROPERTIES Although equations of state provide p-v-T relations, thermodynamic analysis usually requires values for internal energy, enthalpy, and entropy. These properties have been tabulated for many substances, including refrigerants (see Chapters 1, 30, and 33), and can be extracted from such tables by interpolating manually or with a suitable computer program. This approach is appropriate for hand calculations and for relatively simple computer models; however, for many computer simulations, the overhead in memory or input and output required to use tabulated data can make this approach unacceptable. For large thermal system simulations or complex analyses, it may be more efficient to determine internal energy, enthalpy, and entropy using fundamental thermodynamic relations or curves fit to experimental data. Some of these relations are discussed in the following sections. Also, the thermodynamic relations discussed in those sections are the basis for constructing tables of thermodynamic property data. Further information on the topic may be found in references covering system modeling and thermodynamics (Howell and Buckius 1992; Stoecker 1989). At least two intensive properties (properties independent of the quantity of substance, such as temperature, pressure, specific volume, and specific enthalpy) must be known to determine the remaining properties. If two known properties are either p, v, or T (these are relatively easy to measure and are commonly used in simulations), the third can be determined throughout the range of interest using an equation of state. Furthermore, if the specific heats at zero pressure are known, specific heat can be accurately determined from spectroscopic measurements using statistical mechanics (NASA 1971). Entropy may be considered a function of T and p, and from calculus an infinitesimal change in entropy can be written as § ws · § ws · ds = ¨ ------¸ dT + ¨ ------¸ dp wT © ¹p © wp¹T

4

(26)

Likewise, a change in enthalpy can be written as

n 10 n 11 3 n 2 + U -----9 + ------+ ------- exp – n 16 U 2 3 4 T T T 5 n 12 n 13 n 14 2 6 + U ------+ ------- + ------- exp – n 16 U + n 15 U T2 T3 T4

corresponding states provides useful approximations, and numerous modifications have been reported. More complex treatments for predicting properties, which recognize similarity of fluid properties, are by generalized equations of state. These equations ordinarily allow adjustment of the p-v-T surface by introducing parameters. One example (Hirschfelder et al. 1958) allows for departures from the principle of corresponding states by adding two correlating parameters.

§ wh· § wh· dh = ¨ ------¸ dT + ¨ ------¸ dp © wT¹p © wp¹T (25)

The 15 coefficients of this equation’s linear terms are determined by a least-square fit to experimental data. Hust and McCarty (1967) and Hust and Stewart (1966) give further information on methods and techniques for determining equations of state. In the absence of experimental data, Van der Waals’ principle of corresponding states can predict fluid properties. This principle relates properties of similar substances by suitable reducing factors (i.e., the p-v-T surfaces of similar fluids in a given region are assumed to be of similar shape). The critical point can be used to define reducing parameters to scale the surface of one fluid to the dimensions of another. Modifications of this principle, as suggested by Kamerlingh Onnes, a Dutch cryogenic researcher, have been used to improve correspondence at low pressures. The principle of

(27)

Using the Gibbs relation Tds dh – vdp and the definition of specific heat at constant pressure, cp { (wh/wT )p , Equation (27) can be rearranged to yield cp § wh · dp ds = ----- dT + ¨ ¸ – v -----w p T T © ¹T

(28)

Equations (26) and (28) combine to yield (ws/wT)p = cp /T. Then, using the Maxwell relation (ws/wp)T = –(wv/wT)p , Equation (26) may be rewritten as cp § wv · ds = ----- dT – ¨ ------¸ dp T © wT¹p This is an expression for an exact derivative, so it follows that

(29)

Thermodynamics and Refrigeration Cycles § 2 · § wc p· wv ¨ ¸ = – T ¨¨ 2¸¸ © w p ¹T © w T ¹p

2.5

(30)

Phase Equilibria for Multicomponent Systems

Integrating this expression at a fixed temperature yields p

§ 2 · wv c p = c p0 – T ¨ 2¸ dp T ¨ ¸ 0 ©wT ¹

³

(31)

where cp0 is the known zero-pressure specific heat, and dpT is used to indicate that integration is performed at a fixed temperature. The second partial derivative of specific volume with respect to temperature can be determined from the equation of state. Thus, Equation (31) can be used to determine the specific heat at any pressure. Using Tds dh – vdp, Equation (29) can be written as § wv · dh = c p dT + v – T ¨ ¸ dp © w T ¹p

(32)

Equations (28) and (32) may be integrated at constant pressure to obtain T1

cp

³ ----T- dTp

s T1 , p0 = s T0 , p0 +

If vapor pressure and liquid and vapor density data (all relatively easy measurements to obtain) are known at saturation, then changes in enthalpy and entropy can be calculated using Equation (37).

To understand phase equilibria, consider a container full of a liquid made of two components; the more volatile component is designated i and the less volatile component j (Figure 2A). This mixture is all liquid because the temperature is low (but not so low that a solid appears). Heat added at a constant pressure raises the mixture’s temperature, and a sufficient increase causes vapor to form, as shown in Figure 2B. If heat at constant pressure continues to be added, eventually the temperature becomes so high that only vapor remains in the container (Figure 2C). A temperature-concentration (T- x) diagram is useful for exploring details of this situation. Figure 3 is a typical T- x diagram valid at a fixed pressure. The case shown in Figure 2A, a container full of liquid mixture with mole fraction xi,0 at temperature T0 , is point 0 on the T- x diagram. When heat is added, the temperature of the mixture increases. The point at which vapor begins to form is the bubble point. Starting at point 0, the first bubble forms at temperature T1 (point 1 on the diagram). The locus of bubble points is the bubble-point curve, which provides bubble points for various liquid mole fractions xi.

(33) Fig. 2 Mixture of i and j Components in Constant Pressure Container

T0 T1

h T1 , p0 = h T0 , p0 +

and

³ cp dT

(34)

T0

Integrating the Maxwell relation (ws/wp)T = –(wv/wT)p gives an equation for entropy changes at a constant temperature as p1

s T0 , p 1 = s T0 , p 0 –

§wv ·

³ ¨©w T¸¹p dpT p

(35)

Likewise, integrating Equation (32) along an isotherm yields the following equation for enthalpy changes at a constant temperature: p1

h T0 , p1 = h T0 , p 0 +

³ p

§ wv · v – T ¨ ¸ dp © w T¹p

Fig. 2 Mixture of i and j Components in Constant-Pressure Container

(36) Fig. 3 Temperature-Concentration (T-x) Diagram for Zeotropic Mixture

Internal energy can be calculated from u = h – pv. When entropy or enthalpy are known at a reference temperature T0 and pressure p0, values at any temperature and pressure may be obtained by combining Equations (33) and (35) or Equations (34) and (36). Combinations (or variations) of Equations (33) through (36) can be incorporated directly into computer subroutines to calculate properties with improved accuracy and efficiency. However, these equations are restricted to situations where the equation of state is valid and the properties vary continuously. These restrictions are violated by a change of phase such as evaporation and condensation, which are essential processes in air-conditioning and refrigerating devices. Therefore, the Clapeyron equation is of particular value; for evaporation or condensation, it gives h fg s fg §dp · = ------ = ---------¨------ ¸ dT v Tv © ¹sat fg fg

(37)

where sfg = entropy of vaporization hfg = enthalpy of vaporization vfg = specific volume difference between vapor and liquid phases

Fig. 3

Temperature-Concentration (T-x) Diagram for Zeotropic Mixture

2.6

2009 ASHRAE Handbook—Fundamentals

When the first bubble begins to form, the vapor in the bubble may not have the same mole fraction as the liquid mixture. Rather, the mole fraction of the more volatile species is higher in the vapor than in the liquid. Boiling prefers the more volatile species, and the T- x diagram shows this behavior. At Tl, the vapor-forming bubbles have an i mole fraction of yi,l. If heat continues to be added, this preferential boiling depletes the liquid of species i and the temperature required to continue the process increases. Again, the T- x diagram reflects this fact; at point 2 the i mole fraction in the liquid is reduced to xi,2 and the vapor has a mole fraction of yi,2. The temperature required to boil the mixture is increased to T2. Position 2 on the T-x diagram could correspond to the physical situation shown in Figure 2B. If constant-pressure heating continues, all the liquid eventually becomes vapor at temperature T3. The vapor at this point is shown as position 3c in Figure 3. At this point the i mole fraction in the vapor yi,3 equals the starting mole fraction in the all-liquid mixture xi,1. This equality is required for mass and species conservation. Further addition of heat simply raises the vapor temperature. The final position 4 corresponds to the physical situation shown in Figure 2C. Starting at position 4 in Figure 3, heat removal leads to initial liquid formation when position 3c (the dew point) is reached.The locus of dew points is called the dew-point curve. Heat removal causes the liquid phase of the mixture to reverse through points 3, 2, 1, and to starting point 0. Because the composition shifts, the temperature required to boil (or condense) this mixture changes as the process proceeds. This is known as temperature glide. This mixture is therefore called zeotropic. Most mixtures have T- x diagrams that behave in this fashion, but some have a markedly different feature. If the dew-point and bubble-point curves intersect at any point other than at their ends, the mixture exhibits azeotropic behavior at that composition. This case is shown as position a in the T- x diagram of Figure 4. If a container of liquid with a mole fraction xa were boiled, vapor would be formed with an identical mole fraction ya . The addition of heat at constant pressure would continue with no shift in composition and no temperature glide. Perfect azeotropic behavior is uncommon, although nearazeotropic behavior is fairly common. The azeotropic composition is pressure-dependent, so operating pressures should be considered for their effect on mixture behavior. Azeotropic and near-azeotropic refrigerant mixtures are widely used. The properties of an azeotropic mixture are such that they may be conveniently treated as pure substance properties. Phase equilibria for zeotropic mixtures, however, require special treatment, using an equation-of-state approach Fig. 4

Azeotropic Behavior Shown on T-x Diagram

with appropriate mixing rules or using the fugacities with the standard state method (Tassios 1993). Refrigerant and lubricant blends are a zeotropic mixture and can be treated by these methods (Martz et al. 1996a, 1996b; Thome 1995).

COMPRESSION REFRIGERATION CYCLES CARNOT CYCLE The Carnot cycle, which is completely reversible, is a perfect model for a refrigeration cycle operating between two fixed temperatures, or between two fluids at different temperatures and each with infinite heat capacity. Reversible cycles have two important properties: (1) no refrigerating cycle may have a coefficient of performance higher than that for a reversible cycle operated between the same temperature limits, and (2) all reversible cycles, when operated between the same temperature limits, have the same coefficient of performance. Proof of both statements may be found in almost any textbook on elementary engineering thermodynamics. Figure 5 shows the Carnot cycle on temperature-entropy coordinates. Heat is withdrawn at constant temperature TR from the region to be refrigerated. Heat is rejected at constant ambient temperature T0. The cycle is completed by an isentropic expansion and an isentropic compression. The energy transfers are given by Q0 = T0(S2 – S3) Qi = TR (S1 – S4) = TR (S2 – S3) Wnet = Qo – Qi Thus, by Equation (15), TR COP = -----------------T0 – TR

(38)

Example 1. Determine entropy change, work, and COP for the cycle shown in Figure 6. Temperature of the refrigerated space TR is 400°R, and that of the atmosphere T0 is 500°R. Refrigeration load is 200 Btu. Solution: 'S = S1 – S4 = Qi/TR = 200/400 = 0.500 Btu/°R W = 'S(T0 – TR) = 0.5(500 – 400) = 50 Btu COP = Qi /(Qo – Qi) = Qi /W = 200/50 = 4 Flow of energy and its area representation in Figure 6 are Energy

Btu

Area

Qi Qo W

200 250 50

b a+b a

Fig. 5 Carnot Refrigeration Cycle

Fig. 4 Azeotropic Behavior Shown on T-x Diagram

Fig. 5 Carnot Refrigeration Cycle

Thermodynamics and Refrigeration Cycles The net change of entropy of any refrigerant in any cycle is always zero. In Example 1, the change in entropy of the refrigerated space is 'SR = –200/400 = –0.5 Btu/°R and that of the atmosphere is 'So = 250/ 500 = 0.5 Btu/°R. The net change in entropy of the isolated system is ' Stotal = ' SR + ' So = 0.

The Carnot cycle in Figure 7 shows a process in which heat is added and rejected at constant pressure in the two-phase region of a refrigerant. Saturated liquid at state 3 expands isentropically to the low temperature and pressure of the cycle at state d. Heat is added isothermally and isobarically by evaporating the liquid-phase refrigerant from state d to state 1. The cold saturated vapor at state 1 is compressed isentropically to the high temperature in the cycle at state b. However, the pressure at state b is below the saturation pressure corresponding to the high temperature in the cycle. The compression process is completed by an isothermal compression process from state b to state c. The cycle is completed by an isothermal and isobaric heat rejection or condensing process from state c to state 3. Applying the energy equation for a mass of refrigerant m yields (all work and heat transfer are positive)

bWc d Q1

3Wd

= m(h3 – hd)

1Wb

2.7 The net work for the cycle is Wnet = 1Wb + bWc – 3Wd = Area d1bc3d and

TR d Q1 COP = ----------- = -----------------W net T0 – TR

THEORETICAL SINGLE-STAGE CYCLE USING A PURE REFRIGERANT OR AZEOTROPIC MIXTURE A system designed to approach the ideal model shown in Figure 7 is desirable. A pure refrigerant or azeotropic mixture can be used to maintain constant temperature during phase changes by maintaining constant pressure. Because of concerns such as high initial cost and increased maintenance requirements, a practical machine has one compressor instead of two and the expander (engine or turbine) is replaced by a simple expansion valve, which throttles refrigerant from high to low pressure. Figure 8 shows the theoretical single-stage cycle used as a model for actual systems. Applying the energy equation for a mass m of refrigerant yields 4Q1

= m(h1 – h4)

(39a)

= m(hb – h1)

1W2

= m(h2 – h1)

(39b)

= T0(Sb – Sc) – m(hb – hc)

2Q3

= m(h2 – h3)

(39c)

h3 = h4

(39d)

= m(h1 – hd) = Area defld

Fig. 6 Temperature-Entropy Diagram for Carnot Refrigeration Cycle of Example 1

Constant-enthalpy throttling assumes no heat transfer or change in potential or kinetic energy through the expansion valve. The coefficient of performance is h1 – h4 4Q 1 COP = --------- = ----------------W h 2 – h1 1 2

(40)

The theoretical compressor displacement CD (at 100% volumetric efficiency) is CD = m· v 1

(41)

Fig. 8 Theoretical Single-Stage Vapor Compression Refrigeration Cycle

Fig. 6 Temperature-Entropy Diagram for Carnot Refrigeration Cycle of Example 1 Fig. 7 Carnot Vapor Compression Cycle

Fig. 7

Carnot Vapor Compression Cycle

Fig. 8 Theoretical Single-Stage Vapor Compression Refrigeration Cycle

2.8

2009 ASHRAE Handbook—Fundamentals

which is a measure of the physical size or speed of the compressor required to handle the prescribed refrigeration load. Example 2. A theoretical single-stage cycle using R-134a as the refrigerant operates with a condensing temperature of 90°F and an evaporating temperature of 0°F. The system produces 15 tons of refrigeration. Determine the (a) thermodynamic property values at the four main state points of the cycle, (b) COP, (c) cycle refrigerating efficiency, and (d) rate of refrigerant flow. Solution: (a) Figure 9 shows a schematic p-h diagram for the problem with numerical property data. Saturated vapor and saturated liquid properties for states 1 and 3 are obtained from the saturation table for R-134a in Chapter 30. Properties for superheated vapor at state 2 are obtained by linear interpolation of the superheat tables for R-134a in Chapter 30. Specific volume and specific entropy values for state 4 are obtained by determining the quality of the liquid-vapor mixture from the enthalpy. h4 – hf 41.645 – 12.207 x 4 = --------------- = ------------------------------------------ = 0.3237 hg – hf 103.156 – 12.207 v4 = vf + x4(vg – vf ) = 0.01185 + 0.3237(2.1579 – 0.01185) = 0.7065 ft3/lb s4 = sf + x4(sg – sf ) = 0.02771 + 0.3237(0.22557 – 0.02771) = 0.09176 Btu/lb·°R The property data are tabulated in Table 1. (b) By Equation (40),

(c) By Equations (17) and (38), COP T 3 – T 1 3.98 90 - = -------------------------- = 0.78 or 78% K R = --------------------------------459.6 T1 (d) The mass flow of refrigerant is obtained from an energy balance on the evaporator. Thus, · m· h 1 – h 4 = Q i = 15 tons

Table 1 Thermodynamic Property Data for Example 2 1 2 3 4

15 tons 200Btu e min ton m· = -------------------------------------------------------------------- = 48.8 lb/min 103.156 – 41.645 Btu/lb

The saturation temperatures of the single-stage cycle strongly influence the magnitude of the coefficient of performance. This influence may be readily appreciated by an area analysis on a temperature-entropy (T- s) diagram. The area under a reversible process line on a T- s diagram is directly proportional to the thermal energy added or removed from the working fluid. This observation follows directly from the definition of entropy [see Equation (8)]. In Figure 10, the area representing Qo is the total area under the constant-pressure curve between states 2 and 3. The area representing the refrigerating capacity Qi is the area under the constant pressure line connecting states 4 and 1. The net work required Wnet equals the difference (Qo – Qi), which is represented by the shaded area shown on Figure 10. Because COP = Qi /Wnet , the effect on the COP of changes in evaporating temperature and condensing temperature may be observed. For example, a decrease in evaporating temperature TE significantly increases Wnet and slightly decreases Qi. An increase in condensing temperature TC produces the same results but with less effect on Wnet . Therefore, for maximum coefficient of performance, the cycle should operate at the lowest possible condensing temperature and maximum possible evaporating temperature.

LORENZ REFRIGERATION CYCLE

– 41.645- = 3.98 COP = 103.156 ----------------------------------------118.61 – 103.156

State

and

t, °F

p, psia

v, ft3/lb

h, Btu/lb

s, Btu/lb °R

0 104.3 90.0 0

21.171 119.01 119.01 21.171

2.1579 0.4189 0.0136 0.7065

103.156 118.61 41.645 41.645

0.22557 0.22557 0.08565 0.09176

The Carnot refrigeration cycle includes two assumptions that make it impractical. The heat transfer capacities of the two external fluids are assumed to be infinitely large so the external fluid temperatures remain fixed at T0 and TR (they become infinitely large thermal reservoirs). The Carnot cycle also has no thermal resistance between the working refrigerant and external fluids in the two heat exchange processes. As a result, the refrigerant must remain fixed at T0 in the condenser and at TR in the evaporator. The Lorenz cycle eliminates the first restriction in the Carnot cycle by allowing the temperature of the two external fluids to vary during heat exchange. The second assumption of negligible thermal resistance between the working refrigerant and two external fluids remains. Therefore, the refrigerant temperature must change during the two heat exchange processes to equal the changing temperature of the external fluids. This cycle is completely reversible when operating between two fluids that each have a finite but constant heat capacity.

Fig. 10 Areas on T-s Diagram Representing Refrigerating Effect and Work Supplied for Theoretical Single-Stage Cycle

Fig. 9 Schematic p-h Diagram for Example 2

Fig. 9 Schematic p-h Diagram for Example 2

Fig. 10 Areas on T- s Diagram Representing Refrigerating Effect and Work Supplied for Theoretical Single-Stage Cycle

Thermodynamics and Refrigeration Cycles

2.9

Figure 11 is a schematic of a Lorenz cycle. Note that this cycle does not operate between two fixed temperature limits. Heat is added to the refrigerant from state 4 to state 1. This process is assumed to be linear on T-s coordinates, which represents a fluid with constant heat capacity. The refrigerant temperature is increased in isentropic compression from state 1 to state 2. Process 2-3 is a heat rejection process in which the refrigerant temperature decreases linearly with heat transfer. The cycle ends with isentropic expansion between states 3 and 4. The heat addition and heat rejection processes are parallel so the entire cycle is drawn as a parallelogram on T- s coordinates. A Carnot refrigeration cycle operating between T0 and TR would lie between states 1, a, 3, and b; the Lorenz cycle has a smaller refrigerating effect and requires more work, but this cycle is a more practical reference when a refrigeration system operates between two single-phase fluids such as air or water. The energy transfers in a Lorenz refrigeration cycle are as follows, where 'T is the temperature change of the refrigerant during each of the two heat exchange processes. Qo = (T0 + 'T/2)(S2 – S3) Qi = (TR – 'T/2)(S1 – S4) = (TR – 'T/2)(S2 – S3) Wnet = Qo – QR Thus by Equation (15), T R – 'T e 2 COP = ------------------------------T 0 – T R + 'T

(42)

Example 3. Determine the entropy change, work required, and COP for the Lorenz cycle shown in Figure 11 when the temperature of the refrigerated space is TR = 400°R, ambient temperature is T0 = 500°R, 'T of the refrigerant is 10°R, and refrigeration load is 200 Btu. Solution: 1

'S =

GQ i

- = ³4 -------T

Qi 200 ------------------------------ = --------- = 0.5063 Btu e qR T R – 'T e 2 395

Q o = > T 0 + 'T e 2 @ ' S = 500 + 5 0.5063 = 255.68 Btu W net = Q o – Q R = 255.68 – 200 = 55.68 Btu T R – 'T e 2 400 – 10 e 2 395 COP = ------------------------------ = ------------------------------------ = --------- = 3.591 T 0 – T R + 'T 500 – 400 + 10 110

Note that the entropy change for the Lorenz cycle is larger than for the Carnot cycle when both operate between the same two temperature reservoirs and have the same capacity (see Example 1). That is, both the heat rejection and work requirement are larger for the

Lorenz cycle. This difference is caused by the finite temperature difference between the working fluid in the cycle compared to the bounding temperature reservoirs. However, as discussed previously, the assumption of constant-temperature heat reservoirs is not necessarily a good representation of an actual refrigeration system because of the temperature changes that occur in the heat exchangers.

THEORETICAL SINGLE-STAGE CYCLE USING ZEOTROPIC REFRIGERANT MIXTURE A practical method to approximate the Lorenz refrigeration cycle is to use a fluid mixture as the refrigerant and the four system components shown in Figure 8. When the mixture is not azeotropic and the phase change occurs at constant pressure, the temperatures change during evaporation and condensation and the theoretical single-stage cycle can be shown on T-s coordinates as in Figure 12. In comparison, Figure 10 shows the system operating with a pure simple substance or an azeotropic mixture as the refrigerant. Equations (14), (15), (39), (40), and (41) apply to this cycle and to conventional cycles with constant phase change temperatures. Equation (42) should be used as the reversible cycle COP in Equation (17). For zeotropic mixtures, the concept of constant saturation temperatures does not exist. For example, in the evaporator, the refrigerant enters at T4 and exits at a higher temperature T1. The temperature of saturated liquid at a given pressure is the bubble point and the temperature of saturated vapor at a given pressure is called the dew point. The temperature T3 in Figure 12 is at the bubble point at the condensing pressure and T1 is at the dew point at the evaporating pressure. Areas on a T-s diagram representing additional work and reduced refrigerating effect from a Lorenz cycle operating between the same two temperatures T1 and T3 with the same value for 'T can be analyzed. The cycle matches the Lorenz cycle most closely when counterflow heat exchangers are used for both the condenser and evaporator. In a cycle that has heat exchangers with finite thermal resistances and finite external fluid capacity rates, Kuehn and Gronseth (1986) showed that a cycle using a refrigerant mixture has a higher coefficient of performance than one using a simple pure substance as a refrigerant. However, the improvement in COP is usually small. Performance of a mixture can be improved further by reducing the heat exchangers’ thermal resistance and passing fluids through them in a counterflow arrangement. Fig. 12 Areas on T-s Diagram Representing Refrigerating Effect and Work Supplied for Theoretical Single-Stage Cycle Using Zeotropic Mixture as Refrigerant

Fig. 11 Processes of Lorenz Refrigeration Cycle

Fig. 11 Processes of Lorenz Refrigeration Cycle

Fig. 12 Areas on T-s Diagram Representing Refrigerating Effect and Work Supplied for Theoretical Single-Stage Cycle Using Zeotropic Mixture as Refrigerant

2.10

2009 ASHRAE Handbook—Fundamentals MULTISTAGE VAPOR COMPRESSION REFRIGERATION CYCLES

Multistage or multipressure vapor compression refrigeration is used when several evaporators are needed at various temperatures, such as in a supermarket, or when evaporator temperature becomes very low. Low evaporator temperature indicates low evaporator pressure and low refrigerant density into the compressor. Two small compressors in series have a smaller displacement and usually operate more efficiently than one large compressor that covers the entire pressure range from the evaporator to the condenser. This is especially true in ammonia refrigeration systems because of the large amount of superheating that occurs during the compression process. Thermodynamic analysis of multistage cycles is similar to analysis of single-stage cycles, except that mass flow differs through various components of the system. A careful mass balance and energy balance on individual components or groups of components ensures correct application of the first law of thermodynamics. Care must also be used when performing second-law calculations. Often, the refrigerating load is comprised of more than one evaporator, so the total system capacity is the sum of the loads from all evaporators. Likewise, the total energy input is the sum of the work into all compressors. For multistage cycles, the expression for the coefficient of performance given in Equation (15) should be written as COP =

¦ Qi /Wnet

(43)

When compressors are connected in series, the vapor between stages should be cooled to bring the vapor to saturated conditions before proceeding to the next stage of compression. Intercooling usually minimizes the displacement of the compressors, reduces the work requirement, and increases the COP of the cycle. If the refrigerant temperature between stages is above ambient, a simple intercooler that removes heat from the refrigerant can be used. If the temperature is below ambient, which is the usual case, the refrigerant itself must be used to cool the vapor. This is accomplished with a flash intercooler. Figure 13 shows a cycle with a flash intercooler installed. The superheated vapor from compressor I is bubbled through saturated liquid refrigerant at the intermediate pressure of the cycle. Some of this liquid is evaporated when heat is added from the superheated refrigerant. The result is that only saturated vapor at the intermediate pressure is fed to compressor II. A common assumption is to operate the intercooler at about the geometric mean of the evaporating and condensing pressures. This operating point provides the same pressure ratio and nearly equal volumetric efficiencies for the two compressors. Example 4 illustrates the thermodynamic analysis of this cycle. Example 4. Determine the thermodynamic properties of the eight state points shown in Figure 13, the mass flows, and the COP of this theoretical multistage refrigeration cycle using R-134a. The saturated evaporator temperature is 0°F, the saturated condensing temperature is 90°F, and the refrigeration load is 15 tons. The saturation temperature of the refrigerant in the intercooler is 40°F, which is nearly at the geometric mean pressure of the cycle. Solution: Thermodynamic property data are obtained from the saturation and superheat tables for R-134a in Chapter 30. States 1, 3, 5, and 7 are obtained directly from the saturation table. State 6 is a mixture of liquid and vapor. The quality is calculated by h6 – h7 41.645 – 24.890 x 6 = ---------------= ------------------------------------------ = 0.19955 h3 – h7 108.856 – 24.890

Fig. 13 Schematic and Pressure-Enthalpy Diagram for Dual-Compression, Dual-Expansion Cycle of Example 4

Fig. 13 Schematic and Pressure-Enthalpy Diagram for Dual-Compression, Dual-Expansion Cycle of Example 4 Table 2 Thermodynamic Property Values for Example 4

State

Temperature, Pressure, °F psia

1 2 3 4 5 6 7 8

0.00 49.03 40.00 96.39 90.00 40.00 40.00 0.00

Specific Enthalpy, Btu/lb

Specific Entropy, Btu/lb·°R

2.1579 0.9766 0.9528 0.4082 0.01359 0.2002 0.01252 0.3112

103.156 110.65 108.856 116.64 41.645 41.645 24.890 24.890

0.22557 0.22557 0.22207 0.22207 0.08565 0.08755 0.05403 0.05531

s6 = s7 + x6 (s3 – s7) = 0.05402 + 0.19955(0.22207 – 0.05402) = 0.08755 Btu/lb·°R Similarly for state 8, x8 = 0.13951, v8 = 0.3112 ft3/lb, s8 = 0.05531 Btu/lb·°R States 2 and 4 are obtained from the superheat tables by linear interpolation. The thermodynamic property data are summarized in Table 2. Mass flow through the lower circuit of the cycle is determined from an energy balance on the evaporator. · Qi m· 1 = ---------------= h1 – h8 m· = m· = m· 1

Then,

21.171 49.741 49.741 119.01 119.01 49.741 49.741 21.171

Specific Volume, ft3/lb

2

7

15 tons 200 Btu e min ton ------------------------------------------------------------------ = 38.33 lb/min 103.156 – 24.890 Btu/lb = m· 8

For the upper circuit of the cycle,

v6 = v7 + x6 (v3 – v7) = 0.01252 + 0.19955(0.9528 – 0.01252) = 0.2002 ft3/lb

m· 3 = m· 4 = m· 5 = m· 6

Thermodynamics and Refrigeration Cycles Assuming the intercooler has perfect external insulation, an energy balance on it is used to compute m· 3 . m· 6 h 6 + m· 2 h 2 = m· 7 h 7 + m· 3 h 3 Rearranging and solving for m· 3 ,

2.11 Solution: The mass flow of refrigerant is the same through all components, so it is only computed once through the evaporator. Each component in the system is analyzed sequentially, beginning with the evaporator. Equation (6) is used to perform a first-law energy balance on each component, and Equations (11) and (13) are used for the second-law analysis. Note that the temperature used in the second-law analysis is the absolute temperature.

h7 – h2 24.890 – 110.65 m· 3 = m· 2 ---------------= 38.33 lb e min ------------------------------------------ = 48.91 lb/min h6 – h3 41.645 – 108.856 · W I = m· 1 h 2 – h 1 = 38.33 lb/min 110.65 – 103.156 Btu e lb · W II

Table 3

Measured

= 287.2 Btu/min = m· 3 h 4 – h 3 = 48.91 lb/min 116.64 – 108.856 Btu e lb

= 380.7 Btu/min · Qi 15 tons 200 Btu e min ton COP = -------------------- = 4.49 · · - = --------------------------------------------------------------- 287.2 + 380.7 Btu/min W I + W II

Examples 2 and 4 have the same refrigeration load and operate with the same evaporating and condensing temperatures. The twostage cycle in Example 4 has a higher COP and less work input than the single-stage cycle. Also, the highest refrigerant temperature leaving the compressor is about 96°F for the two-stage cycle versus about 104°F for the single-stage cycle. These differences are more pronounced for cycles operating at larger pressure ratios.

Measured and Computed Thermodynamic Properties of R-22 for Example 5

State 1 2 3 4 5 6 7

Pressure, Temperature, psia °F 45.0 44.0 210.0 208.0 205.0 204.0 46.5

15.0 25.0 180.0 160.0 94.0 92.0 9.0

Computed Specific Enthalpy, Btu/lb

Specific Entropy, Btu/lb·°R

Specific Volume, ft3/lb

106.4 108.1 128.8 124.8 37.4 36.8 36.8

0.2291 0.2330 0.2374 0.2314 0.0761 0.0750 0.0800

1.213 1.276 0.331 0.318 0.014 0.014 0.308

Fig. 14 Schematic of Real, Direct-Expansion, Single-Stage Mechanical Vapor-Compression Refrigeration System

ACTUAL REFRIGERATION SYSTEMS Actual systems operating steadily differ from the ideal cycles considered in the previous sections in many respects. Pressure drops occur everywhere in the system except in the compression process. Heat transfers between the refrigerant and its environment in all components. The actual compression process differs substantially from isentropic compression. The working fluid is not a pure substance but a mixture of refrigerant and oil. All of these deviations from a theoretical cycle cause irreversibilities within the system. Each irreversibility requires additional power into the compressor. It is useful to understand how these irreversibilities are distributed throughout a real system; this insight can be useful when design changes are contemplated or operating conditions are modified. Example 5 illustrates how the irreversibilities can be computed in a real system and how they require additional compressor power to overcome. Input data have been rounded off for ease of computation. Example 5. An air-cooled, direct-expansion, single-stage mechanical vaporcompression refrigerator uses R-22 and operates under steady conditions. A schematic of this system is shown in Figure 14. Pressure drops occur in all piping, and heat gains or losses occur as indicated. Power input includes compressor power and the power required to operate both fans. The following performance data are obtained: Ambient air temperature t0 Refrigerated space temperature tR · Q evap Refrigeration load · W comp Compressor power input · Condenser fan input W CF · Evaporator fan input W EF

= = = = = =

Fig. 14 Schematic of Real, Direct-Expansion, Single-Stage Mechanical Vapor-Compression Refrigeration System Fig. 15 Pressure-Enthalpy Diagram of Actual System and Theoretical Single-Stage System Operating Between Same Inlet Air Temperatures TR and TO

90°F 20°F 2 tons 3.0 hp 0.2 hp 0.15 hp

Refrigerant pressures and temperatures are measured at the seven locations shown in Figure 14. Table 3 lists the measured and computed thermodynamic properties of the refrigerant, neglecting the dissolved oil. A pressure-enthalpy diagram of this cycle is shown in Figure 15 and is compared with a theoretical single-stage cycle operating between the air temperatures tR and t0. Compute the energy transfers to the refrigerant in each component of the system and determine the second-law irreversibility rate in each component. Show that the total irreversibility rate multiplied by the absolute ambient temperature is equal to the difference between the actual power input and the power required by a Carnot cycle operating between tR and t0 with the same refrigerating load.

Fig. 15 Pressure-Enthalpy Diagram of Actual System and Theoretical Single-Stage System Operating Between Same Inlet Air Temperatures tR and t0

2.12

2009 ASHRAE Handbook—Fundamentals Table 4 Energy Transfers and Irreversibility Rates for Refrigeration System in Example 5

Evaporator: Energy balance ·

7Q1

= m· h 1 – h 7 = 24,000 Btu/h

24,000 m· = ---------------------------------= 345 lb/h 106.4 – 36.8 Second law ·

7I1

· Q = m· s 1 – s 7 – 7--------1 TR 24,000 = 345 0.2291 – 0.0800 – ---------------- = 1.405 Btu/h ˜ qR 479.67

Suction Line: Energy balance · · Q 1 2 = m h 2 – h 1 = 345 108.1 – 106.4 = 586 Btu/h

Component

· Q , Btu/h

· W , Btu/h

Evaporator Suction line Compressor Discharge line Condenser Liquid line Expansion device

24,000 586 –494 –1380 –30,153 –207 0

0 0 7635 0 0 0 0

1.405 0.279 2.417 0.441 1.278 |0 1.725

–7648

7635

7.545

Totals

·

5I 6

Compressor: Energy balance · · · 2Q3 = m h 3 – h 2 + 2W3 = 345 128.8 – 108.1 – 3.0 2545 = – 494 Btu/h Second law · · 2Q3 · 2I 3 = m s 3 – s 2 – -------T0 = 345 0.2374 – 0.2330 – – 494 e 549.67 = 2.417 Btu/h ˜ qR Discharge Line: Energy balance = m· h 4 – h 3 = 345 124.8 – 128.8 = – 1380 Btu/h

·

· 3Q 4 = m· s 4 – s 3 – -------T0 = 345 0.2314 – 0.2374 – – 1380 e 549.67 = 0.441 Btu/h ˜ qR

Condenser: Energy balance ·

4Q5

= m· h 5 – h 4 = 345 37.4 – 124.8 = – 30,153 Btu/h

Second law ·

4I 5

= 0 Btu/h ˜ qR Expansion Device: Energy balance · Q = m· h 7 – h 6 = 0

6 7

Second law ·

6I 7

= m· s 7 – s 6 = 345 0.0800 – 0.0750 = 1.725 Btu/h ˜ qR

These results are summarized in Table 4. For the Carnot cycle, TR 479.67 COP Carnot = ----------------- = ---------------- = 6.852 T0 – TR 70 The Carnot power requirement for the 2 ton load is · Q evap 24 ,000 · = ------------------------- = ---------------- = 3502 Btu/h W Carnot 6.852 COP Carnot The actual power requirement for the compressor is · · · W comp = W Carnot + I total T 0 = 3502 + 7.545 u 549.67 = 7649 Btu/h This result is within computational error of the measured power input to the compressor of 7635 Btu/h.

Second law 3I 4

· Q 5 6 = m· s 6 – s 5 – -------T0 = 345 0.0750 – 0.0761 – – 207 e 549.67

· · 1Q 2 · 1I 2 = m s 2 – s 1 – -------- = 345 0.2330 – 0.2291 – 586 e 549.67 T0 = 0.279 Btu/h ˜ qR

·

19 4 32 6 17 |0 23

Second law

Second law

3Q 4

· · · I , Btu/h·°R I e I total , %

Q· = m· s 5 – s 4 – 4--------5 T0 = 345 0.0761 – 0.2314 – – 30,153 e 549.67 = 1.278 Btu/h ˜ qR

Liquid Line: Energy balance · Q = m· h 6 – h 5

5 6

= 345 36.8 – 37.4 = – 207 Btu/h

The analysis demonstrated in Example 5 can be applied to any actual vapor compression refrigeration system. The only required information for second-law analysis is the refrigerant thermodynamic state points and mass flow rates and the temperatures in which the system is exchanging heat. In this example, the extra compressor power required to overcome the irreversibility in each component is determined. The component with the largest loss is the compressor. This loss is due to motor inefficiency, friction losses, and irreversibilities caused by pressure drops, mixing, and heat transfer between the compressor and the surroundings. The unrestrained expansion in the expansion device is the next largest, but could be reduced by using an expander rather than a throttling process. An expander may be economical on large machines. All heat transfer irreversibilities on both the refrigerant side and the air side of the condenser and evaporator are included in the analysis. Refrigerant pressure drop is also included. Air-side pressure drop irreversibilities of the two heat exchangers are not included, but these are equal to the fan power requirements because all the fan power is dissipated as heat. An overall second-law analysis, such as in Example 5, shows the designer components with the most losses, and helps determine which components should be replaced or redesigned to improve performance. However, it does not identify the nature of the losses;

Thermodynamics and Refrigeration Cycles

2.13 Qhot + Qcold = –Qmid (positive heat quantities are into the cycle)

Fig. 16 Thermal Cycles

(44)

The second law requires that Q hot Q cold Q mid ----------- + ------------- + ------------ t 0 T hot T cold T mid

(45)

with equality holding in the ideal case. From these two laws alone (i.e., without invoking any further assumptions) it follows that, for the ideal forward cycle, T cold T hot – T mid Q cold COP ideal = ------------- = --------------------------- u ----------------------------T mid – T cold Q hot T hot

Fig. 16 Thermal Cycles this requires a more detailed second-law analysis of the actual processes in terms of fluid flow and heat transfer (Liang and Kuehn 1991). A detailed analysis shows that most irreversibilities associated with heat exchangers are due to heat transfer, whereas air-side pressure drop causes a very small loss and refrigerant pressure drop causes a negligible loss. This finding indicates that promoting refrigerant heat transfer at the expense of increasing the pressure drop often improves performance. Using a thermoeconomic technique is required to determine the cost/benefits associated with reducing component irreversibilities.

ABSORPTION REFRIGERATION CYCLES An absorption cycle is a heat-activated thermal cycle. It exchanges only thermal energy with its surroundings; no appreciable mechanical energy is exchanged. Furthermore, no appreciable conversion of heat to work or work to heat occurs in the cycle. Absorption cycles are used in applications where one or more of the exchanges of heat with the surroundings is the useful product (e.g., refrigeration, air conditioning, and heat pumping). The two great advantages of this type of cycle in comparison to other cycles with similar product are • No large, rotating mechanical equipment is required • Any source of heat can be used, including low-temperature sources (e.g., waste heat)

IDEAL THERMAL CYCLE All absorption cycles include at least three thermal energy exchanges with their surroundings (i.e., energy exchange at three different temperatures). The highest- and lowest-temperature heat flows are in one direction, and the mid-temperature one (or two) is in the opposite direction. In the forward cycle, the extreme (hottest and coldest) heat flows are into the cycle. This cycle is also called the heat amplifier, heat pump, conventional cycle, or Type I cycle. When the extreme-temperature heat flows are out of the cycle, it is called a reverse cycle, heat transformer, temperature amplifier, temperature booster, or Type II cycle. Figure 16 illustrates both types of thermal cycles. This fundamental constraint of heat flow into or out of the cycle at three or more different temperatures establishes the first limitation on cycle performance. By the first law of thermodynamics (at steady state),

(46)

The heat ratio Qcold /Qhot is commonly called the coefficient of performance (COP), which is the cooling realized divided by the driving heat supplied. Heat rejected to ambient may be at two different temperatures, creating a four-temperature cycle. The ideal COP of the fourtemperature cycle is also expressed by Equation (46), with Tmid signifying the entropic mean heat rejection temperature. In that case, Tmid is calculated as follows: Q mid hot + Q mid cold T mid = --------------------------------------------------Q mid hot Q mid cold -------------------- + ----------------------T mid hot T mid cold

(47)

This expression results from assigning all the entropy flow to the single temperature Tmid. The ideal COP for the four-temperature cycle requires additional assumptions, such as the relationship between the various heat quantities. Under the assumptions that Qcold = Qmid cold and Qhot = Qmid hot , the following expression results: T cold T cold T hot – T mid hot COP ideal = ------------------------------------ u ---------------------- u ------------------T mid cold T mid hot T hot

(48)

WORKING FLUID PHASE CHANGE CONSTRAINTS Absorption cycles require at least two working substances: a sorbent and a fluid refrigerant; these substances undergo phase changes. Given this constraint, many combinations are not achievable. The first result of invoking the phase change constraints is that the various heat flows assume known identities. As illustrated in Figure 17, the refrigerant phase changes occur in an evaporator and a condenser, and the sorbent phase changes in an absorber and a desorber (generator). For the forward absorption cycle, the highest-temperature heat is always supplied to the generator, Qhot { Qgen

(49)

and the coldest heat is supplied to the evaporator: Qcold { Qevap

(50)

For the reverse absorption cycle, the highest-temperature heat is rejected from the absorber, and the lowest-temperature heat is rejected from the condenser. The second result of the phase change constraint is that, for all known refrigerants and sorbents over pressure ranges of interest,

and

Qevap | Qcond

(51)

Qgen | Qabs

(52)

These two relations are true because the latent heat of phase change (vapor l condensed phase) is relatively constant when far removed from the critical point. Thus, each heat input cannot be independently adjusted.

2.14

2009 ASHRAE Handbook—Fundamentals Temperature Glide

The ideal single-effect forward-cycle COP expression is T evap T cond T gen – T abs COP ideal d --------------------------- u --------------------------------- u ------------T cond – T evap T abs T gen

(53)

Equality holds only if the heat quantities at each temperature may be adjusted to specific values, which is not possible, as shown the following discussion. The third result of invoking the phase change constraint is that only three of the four temperatures Tevap, Tcond , Tgen, and Tabs may be independently selected. Practical liquid absorbents for absorption cycles have a significant negative deviation from behavior predicted by Raoult’s law. This has the beneficial effect of reducing the required amount of absorbent recirculation, at the expense of reduced lift (Tcond – Tevap) and increased sorption duty. In practical terms, for most absorbents, Qabs /Qcond | 1.2 to 1.3

(54)

Tgen – Tabs | 1.2(Tcond – Tevap)

(55)

and

The net result of applying these approximations and constraints to the ideal-cycle COP for the single-effect forward cycle is T evap T cond Q cond COP ideal | 1.2 --------------------------- | -------------- | 0.8 Q abs T gen T abs

(56)

In practical terms, the temperature constraint reduces the ideal COP to about 0.9, and the heat quantity constraint further reduces it to about 0.8. Another useful result is Tgen min = Tcond + Tabs – Tevap

(57)

where Tgen min is the minimum generator temperature necessary to achieve a given evaporator temperature. Alternative approaches are available that lead to nearly the same upper limit on ideal-cycle COP. For example, one approach equates the exergy production from a “driving” portion of the cycle to the exergy consumption in a “cooling” portion of the cycle (Tozer and James 1997). This leads to the expression T evap T cond COP ideal d ------------- = ------------T abs T gen

(58)

Another approach derives the idealized relationship between the two temperature differences that define the cycle: the cycle lift, defined previously, and drop (Tgen – Tabs).

Fig. 17

Single-Effect Absorption Cycle

Fig. 17

Single-Effect Absorption Cycle

One important limitation of simplified analysis of absorption cycle performance is that the heat quantities are assumed to be at fixed temperatures. In most actual applications, there is some temperature change (temperature glide) in the various fluids supplying or acquiring heat. It is most easily described by first considering situations wherein temperature glide is not present (i.e., truly isothermal heat exchanges). Examples are condensation or boiling of pure components (e.g., supplying heat by condensing steam). Any sensible heat exchange relies on temperature glide: for example, a circulating high-temperature liquid as a heat source; cooling water or air as a heat rejection medium; or circulating chilled glycol. Even latent heat exchanges can have temperature glide, as when a multicomponent mixture undergoes phase change. When the temperature glide of one fluid stream is small compared to the cycle lift or drop, that stream can be represented by an average temperature, and the preceding analysis remains representative. However, one advantage of absorption cycles is they can maximize benefit from low-temperature, high-glide heat sources. That ability derives from the fact that the desorption process inherently embodies temperature glide, and hence can be tailored to match the heat source glide. Similarly, absorption also embodies glide, which can be made to match the glide of the heat rejection medium. Implications of temperature glide have been analyzed for power cycles (Ibrahim and Klein 1998), but not yet for absorption cycles.

WORKING FLUIDS Working fluids for absorption cycles fall into four categories, each requiring a different approach to cycle modeling and thermodynamic analysis. Liquid absorbents can be nonvolatile (i.e., vapor phase is always pure refrigerant, neglecting condensables) or volatile (i.e., vapor concentration varies, so cycle and component modeling must track both vapor and liquid concentration). Solid sorbents can be grouped by whether they are physisorbents (also known as adsorbents), for which, as for liquid absorbents, sorbent temperature depends on both pressure and refrigerant loading (bivariance); or chemisorbents, for which sorbent temperature does not vary with loading, at least over small ranges. Beyond these distinctions, various other characteristics are either necessary or desirable for suitable liquid absorbent/refrigerant pairs, as follows: Absence of Solid Phase (Solubility Field). The refrigerant/ absorbent pair should not solidify over the expected range of composition and temperature. If a solid forms, it will stop flow and shut down equipment. Controls must prevent operation beyond the acceptable solubility range. Relative Volatility. The refrigerant should be much more volatile than the absorbent so the two can be separated easily. Otherwise, cost and heat requirements may be excessive. Many absorbents are effectively nonvolatile. Affinity. The absorbent should have a strong affinity for the refrigerant under conditions in which absorption takes place. Affinity means a negative deviation from Raoult’s law and results in an activity coefficient of less than unity for the refrigerant. Strong affinity allows less absorbent to be circulated for the same refrigeration effect, reducing sensible heat losses, and allows a smaller liquid heat exchanger to transfer heat from the absorbent to the pressurized refrigerant/absorption solution. On the other hand, as affinity increases, extra heat is required in the generators to separate refrigerant from the absorbent, and the COP suffers. Pressure. Operating pressures, established by the refrigerant’s thermodynamic properties, should be moderate. High pressure requires heavy-walled equipment, and significant electrical power may be needed to pump fluids from the low-pressure side to the highpressure side. Vacuum requires large-volume equipment and special means of reducing pressure drop in the refrigerant vapor paths.

Thermodynamics and Refrigeration Cycles Stability. High chemical stability is required because fluids are subjected to severe conditions over many years of service. Instability can cause undesirable formation of gases, solids, or corrosive substances. Purity of all components charged into the system is critical for high performance and corrosion prevention. Corrosion. Most absorption fluids corrode materials used in construction. Therefore, corrosion inhibitors are used. Safety. Precautions as dictated by code are followed when fluids are toxic, inflammable, or at high pressure. Codes vary according to country and region. Transport Properties. Viscosity, surface tension, thermal diffusivity, and mass diffusivity are important characteristics of the refrigerant/absorbent pair. For example, low viscosity promotes heat and mass transfer and reduces pumping power. Latent Heat. The refrigerant latent heat should be high, so the circulation rate of the refrigerant and absorbent can be minimized. Environmental Soundness. The two parameters of greatest concern are the global warming potential (GWP) and the ozone depletion potential (ODP). For more information on GWP and ODP, see Chapter 5 of the 2006 ASHRAE Handbook—Refrigeration. No refrigerant/absorbent pair meets all requirements, and many requirements work at cross-purposes. For example, a greater solubility field goes hand in hand with reduced relative volatility. Thus, selecting a working pair is inherently a compromise. Water/lithium bromide and ammonia/water offer the best compromises of thermodynamic performance and have no known detrimental environmental effect (zero ODP and zero GWP). Ammonia/water meets most requirements, but its volatility ratio is low and it requires high operating pressures. Ammonia is also a Safety Code Group B2 fluid (ASHRAE Standard 34), which restricts its use indoors. Advantages of water/lithium bromide include high (1) safety, (2) volatility ratio, (3) affinity, (4) stability, and (5) latent heat. However, this pair tends to form solids and operates at deep vacuum. Because the refrigerant turns to ice at 32°F, it cannot be used for low-temperature refrigeration. Lithium bromide (LiBr) crystallizes at moderate concentrations, as would be encountered in air-cooled chillers, which ordinarily limits the pair to applications where the absorber is water-cooled and the concentrations are lower. However, using a combination of salts as the absorbent can reduce this crystallization tendency enough to allow air cooling (Macriss 1968). Other disadvantages include low operating pressures and high viscosity. This is particularly detrimental to the absorption step; however, alcohols with a high relative molecular mass enhance LiBr absorption. Proper equipment design and additives can overcome these disadvantages. Other refrigerant/absorbent pairs are listed in Table 5 (Macriss and Zawacki 1989). Several appear suitable for certain cycles and may solve some problems associated with traditional pairs. However, information on properties, stability, and corrosion is limited. Also, some of the fluids are somewhat hazardous.

ABSORPTION CYCLE REPRESENTATIONS The quantities of interest to absorption cycle designers are temperature, concentration, pressure, and enthalpy. The most useful plots use linear scales and plot the key properties as straight lines. Some of the following plots are used: • Absorption plots embody the vapor-liquid equilibrium of both the refrigerant and the sorbent. Plots on linear pressure-temperature coordinates have a logarithmic shape and hence are little used. • In the van’t Hoff plot (ln P versus –1/T ), the constant concentration contours plot as nearly straight lines. Thus, it is more readily constructed (e.g., from sparse data) in spite of the awkward coordinates.

2.15 Table 5

Refrigerant/Absorbent Pairs

Refrigerant

Absorbents

H2O

Salts Alkali halides LiBr LiClO3 CaCl2 ZnCl2 ZnBr Alkali nitrates Alkali thiocyanates Bases Alkali hydroxides Acids H2SO4 H3PO4

NH3

H2O Alkali thiocyanates

TFE (Organic)

NMP E181 DMF Pyrrolidone

SO2

Organic solvents

• The Dühring diagram (solution temperature versus reference temperature) retains the linearity of the van’t Hoff plot but eliminates the complexity of nonlinear coordinates. Thus, it is used extensively (see Figure 20). The primary drawback is the need for a reference substance. • The Gibbs plot (solution temperature versus T ln P) retains most of the advantages of the Dühring plot (linear temperature coordinates, concentration contours are straight lines) but eliminates the need for a reference substance. • The Merkel plot (enthalpy versus concentration) is used to assist thermodynamic calculations and to solve the distillation problems that arise with volatile absorbents. It has also been used for basic cycle analysis. • Temperature-entropy coordinates are occasionally used to relate absorption cycles to their mechanical vapor compression counterparts.

CONCEPTUALIZING THE CYCLE The basic absorption cycle shown in Figure 17 must be altered in many cases to take advantage of the available energy. Examples include the following: (1) the driving heat is much hotter than the minimum required Tgen min: a multistage cycle boosts the COP; and (2) the driving heat temperature is below Tgen min: a different multistage cycle (half-effect cycle) can reduce the Tgen min. Multistage cycles have one or more of the four basic exchangers (generator, absorber, condenser, evaporator) present at two or more places in the cycle at different pressures or concentrations. A multieffect cycle is a special case of multistaging, signifying the number of times the driving heat is used in the cycle. Thus, there are several types of two-stage cycles: double-effect, half-effect, and two-stage, triple-effect. Two or more single-effect absorption cycles, such as shown in Figure 17, can be combined to form a multistage cycle by coupling any of the components. Coupling implies either (1) sharing component(s) between the cycles to form an integrated single hermetic cycle or (2) exchanging heat between components belonging to two hermetically separate cycles that operate at (nearly) the same temperature level. Figure 18 shows a double-effect absorption cycle formed by coupling the absorbers and evaporators of two single-effect cycles

2.16 Fig. 18

2009 ASHRAE Handbook—Fundamentals Double-Effect Absorption Cycle

Fig. 18

Fig. 19

Generic Triple-Effect Cycles

Double-Effect Absorption Cycle

into an integrated, single hermetic cycle. Heat is transferred between the high-pressure condenser and intermediate-pressure generator. The heat of condensation of the refrigerant (generated in the high-temperature generator) generates additional refrigerant in the lower-temperature generator. Thus, the prime energy provided to the high-temperature generator is cascaded (used) twice in the cycle, making it a double-effect cycle. With the generation of additional refrigerant from a given heat input, the cycle COP increases. Commercial water/lithium bromide chillers normally use this cycle. The cycle COP can be further increased by coupling additional components and by increasing the number of cycles that are combined. This way, several different multieffect cycles can be combined by pressure-staging and/or concentration-staging. The double-effect cycle, for example, is formed by pressure-staging two single-effect cycles. Figure 19 shows twelve generic triple-effect cycles identified by Alefeld and Radermacher (1994). Cycle 5 is a pressure-staged cycle, and Cycle 10 is a concentration-staged cycle. All other cycles are pressure- and concentration-staged. Cycle 1, which is called a dual-loop cycle, is the only cycle consisting of two loops that does not circulate absorbent in the low-temperature portion of the cycle. Each of the cycles shown in Figure 19 can be made with one, two, or sometimes three separate hermetic loops. Dividing a cycle into separate hermetic loops allows the use of a different working fluid in each loop. Thus, a corrosive and/or high-lift absorbent can be restricted to the loop where it is required, and a conventional additive-enhanced absorbent can be used in other loops to reduce system cost significantly. As many as 78 hermetic loop configurations can be synthesized from the twelve triple-effect cycles shown in Figure 19. For each hermetic loop configuration, further variations are possible according to the absorbent flow pattern (e.g., series or parallel), the absorption working pairs selected, and various other hardware details. Thus, literally thousands of distinct variations of the triple-effect cycle are possible. The ideal analysis can be extended to these multistage cycles (Alefeld and Radermacher 1994). A similar range of cycle variants is possible for situations calling for the half-effect cycle, in which the available heat source temperature is below tgen min.

ABSORPTION CYCLE MODELING Analysis and Performance Simulation A physical-mathematical model of an absorption cycle consists of four types of thermodynamic equations: mass balances, energy balances, relations describing heat and mass transfer, and equations for thermophysical properties of the working fluids.

Fig. 19 Generic Triple-Effect Cycles Fig. 20 Single-Effect Water-Lithium Bromide Absorption Cycle Dühring Plot

Fig. 20 Single-Effect Water/Lithium Bromide Absorption Cycle Dühring Plot As an example of simulation, Figure 20 shows a Dühring plot of a single-effect water/lithium bromide absorption chiller. The chiller is hot-water-driven, rejects waste heat from the absorber and the condenser to a stream of cooling water, and produces chilled water. A simulation of this chiller starts by specifying the assumptions (Table 6) and the design parameters and operating conditions at the design point (Table 7). Design parameters are the specified UA values and the flow regime (co/counter/crosscurrent, pool, or film) of all heat exchangers (evaporator, condenser, generator, absorber, solution heat exchanger) and the flow rate of weak solution through the solution pump. One complete set of input operating parameters could be the design point values of the chilled-water and cooling water temperatures tchill in, tchill out , tcool in, tcool out , hot-water flow rate m· hot , and total cooling capacity Qe. With this information, a cycle simulation calculates the required hot-water temperatures; cooling-water flow rate; and temperatures, pressures, and concentrations at all internal state points. Some additional assumptions are made that reduce the number of unknown parameters. With these assumptions and the design parameters and operating conditions as specified in Table 7, the cycle simulation can be conducted by solving the following set of equations:

Thermodynamics and Refrigeration Cycles

2.17

Table 6 Assumptions for Single-Effect Water/Lithium Bromide Model (Figure 20)

Table 7 Design Parameters and Operating Conditions for Single-Effect Water/Lithium Bromide Absorption Chiller Operating Conditions

Assumptions • Generator and condenser as well as evaporator and absorber are under same pressure • Refrigerant vapor leaving the evaporator is saturated pure water • Liquid refrigerant leaving the condenser is saturated • Strong solution leaving the generator is boiling • Refrigerant vapor leaving the generator has the equilibrium temperature of the weak solution at generator pressure • Weak solution leaving the absorber is saturated • No liquid carryover from evaporator • Flow restrictors are adiabatic • Pump is isentropic • No jacket heat losses • The LMTD (log mean temperature difference) expression adequately estimates the latent changes

Design Parameters

Condenser

UAcond = 342,300 Btu/h·°F, countercurrent film

tcool out = 95°F

Absorber

UAabs = 354,300 Btu/h·°F, countercurrent film-absorber

tcool in = 80.6°F

Generator

UAgen = 271,800 Btu/h·°F, pool-generator

Solution

UAsol = 64,100 Btu/h·°F, countercurrent · = 95,200 lb/h m· Q

General

Mass Balances m· refr + m· strong = m· weak

(59)

m· strong [ strong = m· weak [ weak

(60)

chill in

chill

chill out

· Q cond = m· h – h liq, cond refr vapor, gen = m· h –h cool out

cool

cool mean

· Q abs = m· refr h vapor, evap + m· strong h strong, gen · – m· weak h weak, abs – Q sol = m· h –h cool

cool mean

cool in

Evaporator

tvapor,evap = 35.2°F psat,evap = 0.1 psia

Condenser

Tliq,cond = 115.2°F psat,cond = 1.48 psia

Absorber

[weak = 59.6% tweak = 105.3°F tstrong,abs = 121.8°F

Generator

[strong = 64.6% tstrong,gen = 218.3°F tweak,gen = 198.3°F tweak,sol = 169°F

Solution

tstrong,sol = 144.3°F tweak,sol = 169°F m· vapor = 7380 lb/h m· = 87,800 lb/h

(62)

(63)

weak, abs in

– h hot

out

· Q sol = m· strong h strong, gen – h strong, sol = m· h –h weak

weak, sol

weak, abs

(64)

(65)

Heat Transfer Equations t chill in – t chill out · Q evap = UA evap -------------------------------------------------------------§ t chill in – t vapor, evap · ln ¨ ----------------------------------------------------¸ © t chill out – t vapor, evap¹ t cool out – t cool mean · Q cond = UA cond -----------------------------------------------------------§ t liq, cond – t cool mean· ln ¨ --------------------------------------------------¸ © t liq, cond – t cool out ¹

= 7.33 u106 Btu/h

General

Performance Parameters · Q evap = 7.33 u106 Btu/h · m chill = 677,000 lb/h · Q cond = 7.92 u106 Btu/h · m cool = 1.260 u 106 lb/h · Q abs = 10.18 u 106 Btu/h tcool,mean = 88.7°F · Q gen = 10.78 u 106 Btu/h thot in = 257°F thot out = 239°F · Q sol = 2.815 u 106 Btu/h H = 65.4% COP = 0.68

strong

· Q gen = m· refr h vapor, gen + m· strong h strong, gen · – m· weak h – Q sol = m· hot h hot

evap

Table 8 Simulation Results for Single-Effect Water/Lithium Bromide Absorption Chiller Internal Parameters

(61)

m· hot = 590,000 lb/h

weak

Energy Balances · Q evap = m· h – h liq, cond refr vapor, evap · = m h –h

tchill in = 53.6°F tchill out = 42.8°F

Evaporator UAevap = 605,000 Btu/h·°F, countercurrent film

(66)

t hot in – t strong, gen – t hot out – t weak, gen · Q gen = UA gen ---------------------------------------------------------------------------------------------------------- (69) § t hot in – t strong, gen· ln ¨ ---------------------------------------------¸ © t hot out – t weak, gen¹ t strong, gen – t weak, sol – t strong, sol – t weak, abs · Q sol = UA sol ----------------------------------------------------------------------------------------------------------------------§ t strong, gen – t weak, sol· ln ¨ ----------------------------------------------------¸ (70) © t strong, sol – t weak, abs¹ Fluid Property Equations at each state point Thermal Equations of State: Two-Phase Equilibrium:

(67)

t strong, abs – t cool mean – t weak, abs – t cool in · Q abs = UA abs ------------------------------------------------------------------------------------------------------------------§ t strong, abs – t cool mean· ln ¨ -------------------------------------------------------¸ (68) © t weak, abs – t cool in ¹

hwater (t,p), hsol (t, p,[) twater,sat ( p), tsol,sat ( p,[)

The results are listed in Table 8. A baseline correlation for the thermodynamic data of the H2O/ LiBr absorption working pair is presented in Hellman and Grossman (1996). Thermophysical property measurements at higher temperatures are reported by Feuerecker et al. (1993). Additional hightemperature measurements of vapor pressure and specific heat appear in Langeliers et al. (2003), including correlations of the data.

Double-Effect Cycle Double-effect cycle calculations can be performed in a manner similar to that for the single-effect cycle. Mass and energy balances

2.18

2009 ASHRAE Handbook—Fundamentals Table 9 Inputs and Assumptions for Double-Effect Water-Lithium Bromide Model (Figure 21)

Fig. 21 Double-Effect Water-Lithium Bromide Absorption Cycle with State Points

Inputs Capacity

· Q evap

500 tons (refrig.)

Evaporator temperature

t10

41.1°F

Desorber solution exit temperature

t14

339.3°F

Condenser/absorber low temperature

t1, t8

108.3°F

Solution heat exchanger effectiveness

H

0.6

Assumptions • • • • • •

Fig. 21 Double-Effect Water/Lithium Bromide Absorption Cycle with State Points of the model shown in Figure 21 were calculated using the inputs and assumptions listed in Table 9. The results are shown in Table 10. The COP is quite sensitive to several inputs and assumptions. In particular, the effectiveness of the solution heat exchangers and the driving temperature difference between the high-temperature condenser and the low-temperature generator influence the COP strongly.

• • • • • • • •

Steady state Refrigerant is pure water No pressure changes except through flow restrictors and pump State points at 1, 4, 8, 11, 14, and 18 are saturated liquid State point 10 is saturated vapor Temperature difference between high-temperature condenser and lowtemperature generator is 9°F Parallel flow Both solution heat exchangers have same effectiveness Upper loop solution flow rate is selected such that upper condenser heat exactly matches lower generator heat requirement Flow restrictors are adiabatic Pumps are isentropic No jacket heat losses No liquid carryover from evaporator to absorber Vapor leaving both generators is at equilibrium temperature of entering solution stream

Table 10 State Point Data for Double-Effect Water/Lithium Bromide Cycle (Figure 21)

AMMONIA/WATER ABSORPTION CYCLES Ammonia/water absorption cycles are similar to water/lithium bromide cycles, but with some important differences because of ammonia’s lower latent heat compared to water, the volatility of the absorbent, and the different pressure and solubility ranges. The latent heat of ammonia is only about half that of water, so, for the same duty, the refrigerant and absorbent mass circulation rates are roughly double that of water/lithium bromide. As a result, the sensible heat loss associated with heat exchanger approaches is greater. Accordingly, ammonia/water cycles incorporate more techniques to reclaim sensible heat, described in Hanna et al. (1995). The refrigerant heat exchanger (RHX), also known as refrigerant subcooler, which improves COP by about 8%, is the most important (Holldorff 1979). Next is the absorber heat exchanger (AHX), accompanied by a generator heat exchanger (GHX) (Phillips 1976). These either replace or supplement the traditional solution heat exchanger (SHX). These components would also benefit the water/lithium bromide cycle, except that the deep vacuum in that cycle makes them impractical there. The volatility of the water absorbent is also key. It makes the distinction between crosscurrent, cocurrent, and countercurrent mass exchange more important in all of the latent heat exchangers (Briggs 1971). It also requires a distillation column on the high-pressure side. When improperly implemented, this column can impose both cost and COP penalties. Those penalties are avoided by refluxing the column from an internal diabatic section (e.g., solution-cooled rectifier [SCR]) rather than with an external reflux pump. The high-pressure operating regime makes it impractical to achieve multieffect performance via pressure-staging. On the other hand, the exceptionally wide solubility field facilitates concentration staging. The generator-absorber heat exchange (GAX) cycle is an especially advantageous embodiment of concentration staging (Modahl and Hayes 1988). Ammonia/water cycles can equal the performance of water/ lithium bromide cycles. The single-effect or basic GAX cycle yields the same performance as a single-effect water/lithium bromide

Point

h, Btu/lb

m· , lb/min

p, psia

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

50.6 50.6 78.3 106.2 76.1 76.1 1143.2 76.2 76.2 1078.6 86.7 86.7 129.4 162.7 116.4 116.4 1197.4 185.0 185.0

1263.4 1263.4 1263.4 1163.7 1163.7 1163.7 42.3 99.8 99.8 99.8 727.3 727.3 727.3 669.9 669.9 669.9 57.4 57.4 57.4

0.13 1.21 1.21 1.21 1.21 0.13 1.21 1.21 0.13 0.13 1.21 16.21 16.21 16.21 16.21 1.21 16.21 16.21 1.21

COP = 1.195 't = 9.0°F H · Q abs · Q gen · Q cond

= 0.600 106

Btu/h = 7.936 u = 3.488 u 106 Btu/h = 3.085 u 106 Btu/h

Q, Fraction 0.0

0.0 0.004 0.0 0.063 1.0 0.0

0.0 0.008 0.0 0.105 · Q evap · Q gen · Q shx1 · Q shx2 · W p1 · W p2

t, °F

x, % LiBr

108.3 108.3 168.1 208.0 137.9 127.8 186.2 108.3 41.1 41.1 186.2 186.2 278.0 339.3 231.6 210.3 312.2 217.0 108.3

59.5 59.5 64.6 64.6 64.6 0.0 0.0 0.0 0.0 59.5 59.5 59.5 64.6 64.6 64.6 0.0 0.0 0.0

= 6.000 u 106 Btu/h = 5.019 u 106 Btu/h = 2.103 u 106 Btu/h = 1.862 u 106 Btu/h = 0.032 hp = 0.258 hp

cycle; the branched GAX cycle (Herold et al. 1991) yields the same performance as a water/lithium bromide double-effect cycle; and the VX GAX cycle (Erickson and Rane 1994) yields the same performance as a water/lithium bromide triple-effect cycle. Additional

Thermodynamics and Refrigeration Cycles

2.19

Table 11 Inputs and Assumptions for Single-Effect Ammonia/Water Cycle (Figure 22)

Table 12 State Point Data for Single-Effect Ammonia/Water Cycle (Figure 22)

Inputs Capacity High-side pressure Low-side pressure Absorber exit temperature Generator exit temperature Rectifier vapor exit temperature Solution heat exchanger effectiveness Refrigerant heat exchanger effectiveness

· Q evap phigh plow t1 t4 t7 Hshx Hrhx

500 tons (refrig.) 211.8 psia 74.7 psia 105°F 203°F 131°F 0.692 0.629

Assumptions • • • • • • • • •

Steady state No pressure changes except through flow restrictors and pump States at points 1, 4, 8, 11, and 14 are saturated liquid States at point 12 and 13 are saturated vapor Flow restrictors are adiabatic Pump is isentropic No jacket heat losses No liquid carryover from evaporator to absorber Vapor leaving generator is at equilibrium temperature of entering solution stream

Point

h, Btu/lb

m· , lb/min

p, psia

1 2 3 4 5 6 7 8 9 10 11 12 13 14

–24.55 –24.05 38.47 83.81 10.61 10.61 579.51 76.61 35.28 35.28 522.55 563.88 613.91 51.72

1408.2 1408.2 1408.2 1203.0 1203.0 1203.0 205.2 205.2 205.2 205.2 205.2 205.2 209.9 4.6

74.7 211.8 211.8 211.8 211.8 74.7 211.8 211.8 211.8 74.7 74.7 74.7 211.8 211.8

COP = 0.571 'trhx = 36.00°F

Fig. 22 Single-Effect Ammonia-Water Absorption Cycle

'tshx = 30.1°F Hrhx = 0.629 Hshx = 0.692 · Q abs = 9.784 u 106 Btu/h · Q cond = 6.192 u 106 Btu/h

Fig. 22

Single-Effect Ammonia/Water Absorption Cycle

advantages of the ammonia/water cycle include refrigeration capability, air-cooling capability, all mild steel construction, extreme compactness, and capability of direct integration into industrial processes. Between heat-activated refrigerators, gas-fired residential air conditioners, and large industrial refrigeration plants, this technology has accounted for the vast majority of absorption activity over the past century. Figure 22 shows the diagram of a typical single-effect ammoniawater absorption cycle. The inputs and assumptions in Table 11 are used to calculate a single-cycle solution, which is summarized in Table 12. Comprehensive correlations of the thermodynamic properties of the ammonia/water absorption working pair are found in Ibrahim and Klein (1993) and Tillner-Roth and Friend (1998a, 1998b), both of which are available as commercial software. Figure 29 in Chapter 30 of this volume was prepared using the Ibrahim and Klein correlation, which is also incorporated in REFPROP7 (National Institute of Standards and Technology). Transport properties for ammonia/water mixtures are available in IIR (1994) and in Melinder (1998).

SYMBOLS cp COP g h I

= = = = =

specific heat at constant pressure, Btu/lb·°F coefficient of performance local acceleration of gravity, ft/s2 enthalpy, Btu/lb irreversibility, Btu/°R

Q, Fraction 0.0

0.0 0.006 1.0 0.0 0.049 0.953 1.0 1.0 0.0 · Q evap · Q gen · Q rhx · Qr · Q shx · W

t, °F

x, Fraction NH3

105.0 105.5 163.0 203.0 135.6 132.0 131.0 100.1 64.1 41.1 42.8 87.0 174.5 174.5

0.50094 0.50094 0.50094 0.41612 0.41612 0.41612 0.99809 0.99809 0.99809 0.99809 0.99809 0.99809 0.98708 0.50094

= 6.00 u 106 Btu/h = 1.051 u 107 Btu/h = 5.089 u 105 Btu/h = 5.805 u 105 Btu/h = 5.283 u 106 Btu/h = 9.22 hp

· I = irreversibility rate, Btu/h·°R m = mass, lb m· = mass flow, lb/min p = pressure, psia Q = heat energy, Btu · Q = rate of heat flow, Btu/h R = ideal gas constant, ft·lb/lb·°R s = specific entropy, Btu/lb·°R S = total entropy, Btu/°R t = temperature, °F T = absolute temperature, °R u = internal energy, Btu/lb v = specific volume, ft3/lb V = velocity of fluid, ft/s W = mechanical or shaft work, Btu · W = rate of work, power, Btu/h x = mass fraction (of either lithium bromide or ammonia) x = vapor quality (fraction) z = elevation above horizontal reference plane, ft Z = compressibility factor H = heat exchanger effectiveness K = efficiency U = density, lb/ft3 Subscripts abs = absorber cg = condenser to generator cond = condenser or cooling mode evap = evaporator fg = fluid to vapor gen = generator gh = high-temperature generator o, 0 = reference conditions, usually ambient p = pump R = refrigerating or evaporator conditions rhx = refrigerant heat exchanger shx = solution heat exchanger sol = solution

2.20

2009 ASHRAE Handbook—Fundamentals REFERENCES

Alefeld, G. and R. Radermacher. 1994. Heat conversion systems. CRC Press, Boca Raton. Benedict, M. 1937. Pressure, volume, temperature properties of nitrogen at high density, I and II. Journal of American Chemists Society 59(11): 2224-2233 and 2233-2242. Benedict, M., G.B. Webb, and L.C. Rubin. 1940. An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures. Journal of Chemistry and Physics 4:334. Briggs, S.W. 1971. Concurrent, crosscurrent, and countercurrent absorption in ammonia-water absorption refrigeration. ASHRAE Transactions 77(1):171. Cooper, H.W. and J.C. Goldfrank. 1967. B-W-R constants and new correlations. Hydrocarbon Processing 46(12):141. Erickson, D.C. and M. Rane. 1994. Advanced absorption cycle: Vapor exchange GAX. Proceedings of the International Absorption Heat Pump Conference, Chicago. Feuerecker, G., J. Scharfe, I. Greiter, C. Frank, and G. Alefeld. 1993. Measurement of thermophysical properties of aqueous LiBr solutions at high temperatures and concentrations. Proceedings of the International Absorption Heat Pump Conference, New Orleans, AES-30, pp. 493-499. American Society of Mechanical Engineers, New York. Hanna, W.T., et al. 1995. Pinch-point analysis: An aid to understanding the GAX absorption cycle. ASHRAE Technical Data Bulletin 11(2). Hellman, H.-M. and G. Grossman. 1996. Improved property data correlations of absorption fluids for computer simulation of heat pump cycles. ASHRAE Transactions 102(1):980-997. Herold, K.E., et al. 1991. The branched GAX absorption heat pump cycle. Proceedings of Absorption Heat Pump Conference, Tokyo. Hirschfelder, J.O., et al. 1958. Generalized equation of state for gases and liquids. Industrial and Engineering Chemistry 50:375. Holldorff, G. 1979. Revisions up absorption refrigeration efficiency. Hydrocarbon Processing 58(7):149. Howell, J.R. and R.O. Buckius. 1992. Fundamentals of engineering thermodynamics, 2nd ed. McGraw-Hill, New York. Hust, J.G. and R.D. McCarty. 1967. Curve-fitting techniques and applications to thermodynamics. Cryogenics 8:200. Hust, J.G. and R.B. Stewart. 1966. Thermodynamic property computations for system analysis. ASHRAE Journal 2:64. Ibrahim, O.M. and S.A. Klein. 1993. Thermodynamic properties of ammonia-water mixtures. ASHRAE Transactions 99(1):1495-1502. Ibrahim, O.M. and S.A. Klein. 1998. The maximum power cycle: A model for new cycles and new working fluids. Proceedings of the ASME Advanced Energy Systems Division, AES vol. 117. American Society of Mechanical Engineers. New York. IIR. 1994. R123—Thermodynamic and physical properties. NH3–H2O. International Institute of Refrigeration, Paris. Kuehn, T.H. and R.E. Gronseth. 1986. The effect of a nonazeotropic binary refrigerant mixture on the performance of a single stage refrigeration cycle. Proceedings of the International Institute of Refrigeration Conference, Purdue University, p. 119. Langeliers, J., P. Sarkisian, and U. Rockenfeller. 2003. Vapor pressure and specific heat of Li-Br H2O at high temperature. ASHRAE Transactions 109(1):423-427. Liang, H. and T.H. Kuehn. 1991. Irreversibility analysis of a water to water mechanical compression heat pump. Energy 16(6):883. Macriss, R.A. 1968. Physical properties of modified LiBr solutions. AGA Symposium on Absorption Air-Conditioning Systems, February. Macriss, R.A. and T.S. Zawacki. 1989. Absorption fluid data survey: 1989 update. Oak Ridge National Laboratories Report ORNL/Sub84-47989/4. Martin, J.J. and Y. Hou. 1955. Development of an equation of state for gases. AIChE Journal 1:142.

Martz, W.L., C.M. Burton, and A.M. Jacobi. 1996a. Liquid-vapor equilibria for R-22, R-134a, R-125, and R-32/125 with a polyol ester lubricant: Measurements and departure from ideality. ASHRAE Transactions 102(1):367-374. Martz, W.L., C.M. Burton, and A.M. Jacobi. 1996b. Local composition modeling of the thermodynamic properties of refrigerant and oil mixtures. International Journal of Refrigeration 19(1):25-33. Melinder, A. 1998. Thermophysical properties of liquid secondary refrigerants. Engineering Licentiate Thesis, Department of Energy Technology, The Royal Institute of Technology, Stockholm. Modahl, R.J. and F.C. Hayes. 1988. Evaluation of commercial advanced absorption heat pump. Proceedings of the 2nd DOE/ORNL Heat Pump Conference, Washington, D.C. NASA. 1971. Computer program for calculation of complex chemical equilibrium composition, rocket performance, incident and reflected shocks and Chapman-Jouguet detonations. SP-273. U.S. Government Printing Office, Washington, D.C. Phillips, B. 1976. Absorption cycles for air-cooled solar air conditioning. ASHRAE Transactions 82(1):966. Dallas. Stewart, R.B., R.T. Jacobsen, and S.G. Penoncello. 1986. ASHRAE thermodynamic properties of refrigerants. Strobridge, T.R. 1962. The thermodynamic properties of nitrogen from 64 to 300 K, between 0.1 and 200 atmospheres. National Bureau of Standards Technical Note 129. Stoecker, W.F. and J.W. Jones. 1982. Refrigeration and air conditioning, 2nd ed. McGraw-Hill, New York. Tassios, D.P. 1993. Applied chemical engineering thermodynamics. Springer-Verlag, New York. Thome, J.R. 1995. Comprehensive thermodynamic approach to modeling refrigerant-lubricant oil mixtures. International Journal of Heating, Ventilating, Air Conditioning and Refrigeration Research 1(2): 110. Tillner-Roth, R. and D.G. Friend. 1998a. Survey and assessment of available measurements on thermodynamic properties of the mixture {water + ammonia}. Journal of Physical and Chemical Reference Data 27(1)S: 45-61. Tillner-Roth, R. and D.G. Friend. 1998b. A Helmholtz free energy formulation of the thermodynamic properties of the mixture {water + ammonia}. Journal of Physical and Chemical Reference Data 27(1)S:63-96. Tozer, R.M. and R.W. James. 1997. Fundamental thermodynamics of ideal absorption cycles. International Journal of Refrigeration 20 (2):123-135.

BIBLIOGRAPHY Bogart, M. 1981. Ammonia absorption refrigeration in industrial processes. Gulf Publishing Co., Houston. Herold, K.E., R. Radermacher, and S.A. Klein. 1996. Absorption chillers and heat pumps. CRC Press, Boca Raton. Jain, P.C. and G.K. Gable. 1971. Equilibrium property data for aquaammonia mixture. ASHRAE Transactions 77(1):149. Moran, M.J. and H. Shapiro. 1995. Fundamentals of engineering thermodynamics, 3rd ed. John Wiley & Sons, New York. Pátek, J. and J. Klomfar. 1995. Simple functions for fast calculations of selected thermodynamic properties of the ammonia-water system. International Journal of Refrigeration 18(4):228-234. Stoecker, W.F. 1989. Design of thermal systems, 3rd ed. McGraw-Hill, New York. Van Wylen, C.J. and R.E. Sonntag. 1985. Fundamentals of classical thermodynamics, 3rd ed. John Wiley & Sons, New York. Zawacki, T.S. 1999. Effect of ammonia-water mixture database on cycle calculations. Proceedings of the International Sorption Heat Pump Conference, Munich.

CHAPTER 3

FLUID FLOW Fluid Properties .............................................................................................................................. 3.1 Basic Relations of Fluid Dynamics ................................................................................................. 3.2 Basic Flow Processes...................................................................................................................... 3.3 Flow Analysis .................................................................................................................................. 3.5 Noise in Fluid Flow....................................................................................................................... 3.13 Symbols ......................................................................................................................................... 3.14

F

LOWING fluids in HVAC&R systems can transfer heat, mass, and momentum. This chapter introduces the basics of fluid mechanics related to HVAC processes, reviews pertinent flow processes, and presents a general discussion of single-phase fluid flow analysis.

Fig. 1 Velocity Profiles and Gradients in Shear Flows

FLUID PROPERTIES Solids and fluids react differently to shear stress: solids deform only a finite amount, whereas fluids deform continuously until the stress is removed. Both liquids and gases are fluids, although the natures of their molecular interactions differ strongly in both degree of compressibility and formation of a free surface (interface) in liquid. In general, liquids are considered incompressible fluids; gases may range from compressible to nearly incompressible. Liquids have unbalanced molecular cohesive forces at or near the surface (interface), so the liquid surface tends to contract and has properties similar to a stretched elastic membrane. A liquid surface, therefore, is under tension (surface tension). Fluid motion can be described by several simplified models. The simplest is the ideal-fluid model, which assumes that the fluid has no resistance to shearing. Ideal fluid flow analysis is well developed (e.g., Schlichting 1979), and may be valid for a wide range of applications. Viscosity is a measure of a fluid’s resistance to shear. Viscous effects are taken into account by categorizing a fluid as either Newtonian or non-Newtonian. In Newtonian fluids, the rate of deformation is directly proportional to the shearing stress; most fluids in the HVAC industry (e.g., water, air, most refrigerants) can be treated as Newtonian. In non-Newtonian fluids, the relationship between the rate of deformation and shear stress is more complicated.

Fig. 1 Velocity Profiles and Gradients in Shear Flows where the proportionality factor P is the absolute or dynamic viscosity of the fluid. The ratio of F to A is the shearing stress W, and V/Y is the lateral velocity gradient (Figure 1A). In complex flows, velocity and shear stress may vary across the flow field; this is expressed by W = P dv -----dy

The velocity gradient associated with viscous shear for a simple case involving flow velocity in the x direction but of varying magnitude in the y direction is illustrated in Figure 1B. Absolute viscosity P depends primarily on temperature. For gases (except near the critical point), viscosity increases with the square root of the absolute temperature, as predicted by the kinetic theory of gases. In contrast, a liquid’s viscosity decreases as temperature increases. Absolute viscosities of various fluids are given in Chapter 33. Absolute viscosity has dimensions of force u time/length2. At standard indoor conditions, the absolute viscosities of water and dry air (Fox et al. 2004) are

Density The density U of a fluid is its mass per unit volume. The densities of air and water (Fox et al. 2004) at standard indoor conditions of 68°F and 14.696 psi (sea-level atmospheric pressure) are Uwater = 62.4 lbm

P water = 6.76 u 10–4 lbm/ft·s = 2.10 u 10–5 lbf ·s/ft2

/ft3

P air = 1.22 u 10–5 lbm /ft·s = 3.79 u 10–7 lbf ·s/ft2

Uair = 0.0753 lbm /ft3

Another common unit of viscosity is the centipoise (1 centipoise = 1 g/(s˜m) = 1 mPa˜s). At standard conditions, water has a viscosity close to 1.0 centipoise. In fluid dynamics, kinematic viscosity Q is sometimes used in lieu of absolute or dynamic viscosity. Kinematic viscosity is the ratio of absolute viscosity to density:

Viscosity Viscosity is the resistance of adjacent fluid layers to shear. A classic example of shear is shown in Figure 1, where a fluid is between two parallel plates, each of area A separated by distance Y. The bottom plate is fixed and the top plate is moving, which induces a shearing force in the fluid. For a Newtonian fluid, the tangential force F per unit area required to slide one plate with velocity V parallel to the other is proportional to V/Y: F/A = P (V/Y )

(2)

Q = P /U At standard indoor conditions, the kinematic viscosities of water and dry air (Fox et al. 2004) are

(1)

Q water = 1.08 u 10–5 ft2/s The preparation of this chapter is assigned to TC 1.3, Heat Transfer and Fluid Flow.

Q air = 1.62 u 10–4 ft2/s

3.1

3.2

2009 ASHRAE Handbook—Fundamentals

The stoke (1 cm2/s) and centistoke (1 mm2/s) are common units for kinematic viscosity. Note that the inch-pound system of units often requires the conversion factor gc = 32.1740 lbm ·ft/s2 ·lbf to make some equations containing lbf and lbm dimensionally consistent. The conversion factor gc is not shown in the equations, but is included as needed.

BASIC RELATIONS OF FLUID DYNAMICS This section discusses fundamental principles of fluid flow for constant-property, homogeneous, incompressible fluids and introduces fluid dynamic considerations used in most analyses.

Continuity in a Pipe or Duct Conservation of mass applied to fluid flow in a conduit requires that mass not be created or destroyed. Specifically, the mass flow rate into a section of pipe must equal the mass flow rate out of that section of pipe if no mass is accumulated or lost (e.g., from leakage). This requires that m· =

³ Uv dA = constant

(3)

where m· is mass flow rate across the area normal to flow, v is fluid velocity normal to differential area dA, and U is fluid density. Both U and v may vary over the cross section A of the conduit. When flow is effectively incompressible (U = constant) in a pipe or duct flow analysis, the average velocity is then V = (1/A)³ v dA, and the mass flow rate can be written as m· = UVA

(4)

Q = m· e U = AV

(5)

or

where Q is volumetric flow rate.

Bernoulli Equation and Pressure Variation in Flow Direction The Bernoulli equation is a fundamental principle of fluid flow analysis. It involves the conservation of momentum and energy along a streamline; it is not generally applicable across streamlines. Development is fairly straightforward. The first law of thermodynamics can apply to both mechanical flow energies (kinetic and potential energy) and thermal energies. The change in energy content 'E per unit mass of flowing fluid is a result of the work per unit mass w done on the system plus the heat per unit mass q absorbed or rejected: 'E = w + q

(6)

Fluid energy is composed of kinetic, potential (because of elevation z), and internal (u) energies. Per unit mass of fluid, the energy change relation between two sections of the system is §v 2 · § p· ' ¨----- + gz + u¸ = E M – ' ¨ ---¸ + q 2 © ¹ © U¹

(7)

where the work terms are (1) external work EM from a fluid machine (EM is positive for a pump or blower) and (2) flow work p/U (where p = pressure), and g is the gravitational constant. Rearranging, the energy equation can be written as the generalized Bernoulli equation: § 2 p· '¨ v----- + gz + u + --- ¸ = E M + q 2 U © ¹

(8)

The expression in parentheses in Equation (8) is the sum of the kinetic energy, potential energy, internal energy, and flow work per unit mass flow rate. In cases with no work interaction, no heat transfer, and no viscous frictional forces that convert mechanical energy into internal energy, this expression is constant and is known as the Bernoulli constant B: 2 v - gz § --p- · ---+ + ¨ U¸ = B 2 © ¹

(9)

Alternative forms of this relation are obtained through multiplication by U or division by g: 2

Uv p + -------- + Ugz = UB 2

(10)

2 p v B--- + U ----- + z = --J 2g g

(11)

where J = Ug is the specific weight or weight density. Note that Equations (9) to (11) assume no frictional losses. The units in the first form of the Bernoulli equation [Equation (9)] are energy per unit mass; in Equation (10), energy per unit volume; in Equation (11), energy per unit weight, usually called head. Note that the units for head reduce to just length (i.e., ft·lbf/lbf to ft). In gas flow analysis, Equation (10) is often used, and Ugz is negligible. Equation (10) should be used when density variations occur. For liquid flows, Equation (11) is commonly used. Identical results are obtained with the three forms if the units are consistent and fluids are homogeneous. Many systems of pipes, ducts, pumps, and blowers can be considered as one-dimensional flow along a streamline (i.e., variation in velocity across the pipe or duct is ignored, and local velocity v = average velocity V ). When v varies significantly across the cross section, the kinetic energy term in the Bernoulli constant B is expressed as DV 2/2, where the kinetic energy factor (D > 1) expresses the ratio of the true kinetic energy of the velocity profile to that of the average velocity. For laminar flow in a wide rectangular channel, D = 1.54, and in a pipe, D = 2.0. For turbulent flow in a duct, D | 1. Heat transfer q may often be ignored. Conversion of mechanical energy to internal energy 'u may be expressed as a loss EL. The change in the Bernoulli constant ('B = B2 – B1) between stations 1 and 2 along the conduit can be expressed as 2 2 §p · §p · V V ¨ ---- + D ------ + gz¸ + E M – E L = ¨ ---- + D ------ + gz¸ U 2 2 U © ¹2 © ¹1

(12)

or, by dividing by g, in the form 2 2 §p · §p · V V ¨ ---- + D ------ + z¸ + H M – H L = ¨ ---- + D ------ + z¸ J J 2g 2g © ¹1 © ¹2

(13)

Note that Equation (12) has units of energy per mass, whereas each term in Equation (13) has units of energy per weight, or head. The terms EM and EL are defined as positive, where gHM = EM represents energy added to the conduit flow by pumps or blowers. A turbine or fluid motor thus has a negative HM or EM. The terms EM and HM (= EM /g) are defined as positive, and represent energy added to the fluid by pumps or blowers. The simplicity of Equation (13) should be noted; the total head at station 1 (pressure head plus velocity head plus elevation head) plus the head added by a pump (HM) minus the head lost through friction (HL) is the total head at station 2.

Fluid Flow

3.3

Laminar Flow

Turbulence

When real-fluid effects of viscosity or turbulence are included, the continuity relation in Equation (5) is not changed, but V must be evaluated from the integral of the velocity profile, using local velocities. In fluid flow past fixed boundaries, velocity at the boundary is zero, velocity gradients exist, and shear stresses are produced. The equations of motion then become complex, and exact solutions are difficult to find except in simple cases for laminar flow between flat plates, between rotating cylinders, or within a pipe or tube. For steady, fully developed laminar flow between two parallel plates (Figure 2), shear stress Wvaries linearly with distance y from the centerline (transverse to the flow; y = 0 in the center of the channel). For a wide rectangular channel 2b tall, W can be written as

Fluid flows are generally turbulent, involving random perturbations or fluctuations of the flow (velocity and pressure), characterized by an extensive hierarchy of scales or frequencies (Robertson 1963). Flow disturbances that are not chaotic but have some degree of periodicity (e.g., the oscillating vortex trail behind bodies) have been erroneously identified as turbulence. Only flows involving random perturbations without any order or periodicity are turbulent; velocity in such a flow varies with time or locale of measurement (Figure 3). Turbulence can be quantified statistically. The velocity most often used is the time-averaged velocity. The strength of turbulence is characterized by the root mean square (RMS) of the instantaneous variation in velocity about this mean. Turbulence causes the fluid to transfer momentum, heat, and mass very rapidly across the flow. Laminar and turbulent flows can be differentiated using the Reynolds number Re, which is a dimensionless relative ratio of inertial forces to viscous forces:

§y· W = ¨--- ¸ W w = P dv -----dy ©b¹

(14)

where Ww is wall shear stress [b(dp/ds)], and s is flow direction. Because velocity is zero at the wall ( y = b), Equation (14) can be integrated to yield 2

2

§ b – y · dp v = ¨ ---------------- ¸ -----© 2P ¹ ds

(19)

where A is the cross-sectional area of the pipe, duct, or tube, and Pw is the wetted perimeter. For a round pipe, Dh equals the pipe diameter. In general, laminar flow in pipes or ducts exists when the Reynolds number (based on Dh) is less than 2300. Fully turbulent flow exists when ReDh > 10,000. For 2300 < ReDh < 10,000, transitional flow exists, and predictions are unreliable.

BASIC FLOW PROCESSES Wall Friction

(17)

Fig. 2 Dimension for Steady, Fully Developed Laminar Flow Equations

Fig. 2 Dimensions for Steady, Fully Developed Laminar Flow Equations Fig. 3

Dh = 4A/Pw

(16)

A parabolic velocity profile can also be derived for a pipe of radius R. V is 1/2 of the maximum velocity, and the pressure drop can be written as § 8PV · dp -¸ ------ = – ¨ ----------ds © R2 ¹

(18)

where L is the characteristic length scale and Q is the kinematic viscosity of the fluid. In flow through pipes, tubes, and ducts, the characteristic length scale is the hydraulic diameter Dh, given by

(15)

The resulting parabolic velocity profile in a wide rectangular channel is commonly called Poiseuille flow. Maximum velocity occurs at the centerline (y = 0), and the average velocity V is 2/3 of the maximum velocity. From this, the longitudinal pressure drop in terms of V can be written as § 3PV · dp ------ = – ¨ ---------¸ ds © b2 ¹

ReL = VL/Q

Velocity Fluctuation at Point in Turbulent Flow

Fig. 3 Velocity Fluctuation at Point in Turbulent Flow

At the boundary of real-fluid flow, the relative tangential velocity at the fluid surface is zero. Sometimes in turbulent flow studies, velocity at the wall may appear finite and nonzero, implying a fluid slip at the wall. However, this is not the case; the conflict results from difficulty in velocity measurements near the wall (Goldstein 1938). Zero wall velocity leads to high shear stress near the wall boundary, which slows adjacent fluid layers. Thus, a velocity profile develops near a wall, with velocity increasing from zero at the wall to an exterior value within a finite lateral distance. Laminar and turbulent flow differ significantly in their velocity profiles. Turbulent flow profiles are flat and laminar profiles are more pointed (Figure 4). As discussed, fluid velocities of the turbulent profile near the wall must drop to zero more rapidly than those of the laminar profile, so shear stress and friction are much greater in turbulent flow. Fully developed conduit flow may be characterized by the pipe factor, which is the ratio of average to maximum (centerline) velocity. Viscous velocity profiles result in pipe factors Fig. 4 Velocity Profiles of Flow in Pipes

Fig. 4 Velocity Profiles of Flow in Pipes

3.4

2009 ASHRAE Handbook—Fundamentals Fig. 7

Fig. 5

Boundary Layer Flow to Separation

Pipe Factor for Flow in Conduits

Fig. 7 Boundary Layer Flow to Separation Fig. 5 Pipe Factor for Flow in Conduits Fig. 6

Fig. 8 Geometric Separation, Flow Development, and Loss in Flow Through Orifice

Flow in Conduit Entrance Region

Fig. 6 Flow in Conduit Entrance Region of 0.667 and 0.50 for wide rectangular and axisymmetric conduits. Figure 5 indicates much higher values for rectangular and circular conduits for turbulent flow. Because of the flat velocity profiles, the kinetic energy factor D in Equations (12) and (13) ranges from 1.01 to 1.10 for fully developed turbulent pipe flow.

Boundary Layer The boundary layer is the region close to the wall where wall friction affects flow. Boundary layer thickness (usually denoted by G is thin compared to downstream flow distance. For external flow over a body, fluid velocity varies from zero at the wall to a maximum at distance G from the wall. Boundary layers are generally laminar near the start of their formation but may become turbulent downstream. A significant boundary-layer occurrence exists in a pipeline or conduit following a well-rounded entrance (Figure 6). Layers grow from the walls until they meet at the center of the pipe. Near the start of the straight conduit, the layer is very thin and most likely laminar, so the uniform velocity core outside has a velocity only slightly greater than the average velocity. As the layer grows in thickness, the slower velocity near the wall requires a velocity increase in the uniform core to satisfy continuity. As flow proceeds, the wall layers grow (and centerline velocity increases) until they join, after an entrance length Le. Applying the Bernoulli relation of Equation (10) to core flow indicates a decrease in pressure along the layer. Ross (1956) shows that, although the entrance length Le is many diameters, the length in which pressure drop significantly exceeds that for fully developed flow is on the order of 10 hydraulic diameters for turbulent flow in smooth pipes. In more general boundary-layer flows, as with wall layer development in a diffuser or for the layer developing along the surface of a strut or turning vane, pressure gradient effects can be severe and may even lead to boundary layer separation. When the outer flow velocity (v1 in Figure 7) decreases in the flow direction, an adverse pressure gradient can cause separation, as shown in the figure. Downstream from the separation point, fluid backflows near the

Fig. 8

Geometric Separation, Flow Development, and Loss in Flow Through Orifice

wall. Separation is caused by frictional velocity (thus local kinetic energy) reduction near the wall. Flow near the wall no longer has energy to move into the higher pressure imposed by the decrease in v1 at the edge of the layer. The locale of this separation is difficult to predict, especially for the turbulent boundary layer. Analyses verify the experimental observation that a turbulent boundary layer is less subject to separation than a laminar one because of its greater kinetic energy.

Flow Patterns with Separation In technical applications, flow with separation is common and often accepted if it is too expensive to avoid. Flow separation may be geometric or dynamic. Dynamic separation is shown in Figure 7. Geometric separation (Figures 8 and 9) results when a fluid stream passes over a very sharp corner, as with an orifice; the fluid generally leaves the corner irrespective of how much its velocity has been reduced by friction. For geometric separation in orifice flow (Figure 8), the outer streamlines separate from the sharp corners and, because of fluid inertia, contract to a section smaller than the orifice opening. The smallest section is known as the vena contracta and generally has a limiting area of about six-tenths of the orifice opening. After the vena contracta, the fluid stream expands rather slowly through turbulent or laminar interaction with the fluid along its sides. Outside the jet, fluid velocity is comparatively small. Turbulence helps spread out the jet, increases losses, and brings the velocity distribution back to a more uniform profile. Finally, downstream, the velocity profile returns to the fully developed flow of Figure 4. The entrance and exit profiles can profoundly affect the vena contracta and pressure drop (Coleman 2004). Other geometric separations (Figure 9) occur in conduits at sharp entrances, inclined plates or dampers, or sudden expansions. For these geometries, a vena contracta can be identified; for sudden

Fluid Flow

3.5

Fig. 9 Examples of Geometric Separation Encountered in Flows in Conduits

Table 1 Body Shape

Drag Coefficients 103 < Re < 2 u 105

Re > 3 u 105

0.36 to 0.47 1.12 0.1 to 0.3 1.0 to 1.1 1.0 to 1.2 ~2.0

~0.1 1.12 < 0.1 0.35 1.0 to 1.2 ~2.0

Sphere Disk Streamlined strut Circular cylinder Elongated rectangular strut Square strut

Fig. 9

Fig. 10

Examples of Geometric Separation Encountered in Flows in Conduits

Fig. 11 Effect of Viscosity Variation on Velocity Profile of Laminar Flow in Pipe

Separation in Flow in Diffuser

Fig. 10

Separation in Flow in Diffuser

expansion, its area is that of the upstream contraction. Ideal-fluid theory, using free streamlines, provides insight and predicts contraction coefficients for valves, orifices, and vanes (Robertson 1965). These geometric flow separations produce large losses. To expand a flow efficiently or to have an entrance with minimum losses, design the device with gradual contours, a diffuser, or a rounded entrance. Flow devices with gradual contours are subject to separation that is more difficult to predict, because it involves the dynamics of boundary-layer growth under an adverse pressure gradient rather than flow over a sharp corner. A diffuser is used to reduce the loss in expansion; it is possible to expand the fluid some distance at a gentle angle without difficulty, particularly if the boundary layer is turbulent. Eventually, separation may occur (Figure 10), which is frequently asymmetrical because of irregularities. Downstream flow involves flow reversal (backflow) and excess losses. Such separation is commonly called stall (Kline 1959). Larger expansions may use splitters that divide the diffuser into smaller sections that are less likely to have separations (Moore and Kline 1958). Another technique for controlling separation is to bleed some low-velocity fluid near the wall (Furuya et al. 1976). Alternatively, Heskested (1970) shows that suction at the corner of a sudden expansion has a strong positive effect on geometric separation.

Drag Forces on Bodies or Struts Bodies in moving fluid streams are subjected to appreciable fluid forces or drag. Conventionally, the drag force FD on a body can be expressed in terms of a drag coefficient CD: § V 2· F D = C D UA ¨ ------ ¸ ©2 ¹

(20)

where A is the projected (normal to flow) area of the body. The drag coefficient CD is a strong function of the body’s shape and angularity, and the Reynolds number of the relative flow in terms of the body’s characteristic dimension. For Reynolds numbers of 103 to 105, the CD of most bodies is constant because of flow separation, but above 105, the CD of rounded bodies drops suddenly as the surface boundary layer undergoes transition to turbulence. Typical CD values are given in Table 1; Hoerner (1965) gives expanded values.

Fig. 11 Effect of Viscosity Variation on Velocity Profile of Laminar Flow in Pipe

Nonisothermal Effects When appreciable temperature variations exist, the primary fluid properties (density and viscosity) may no longer assumed to be constant, but vary across or along the flow. The Bernoulli equation [Equations (9) to (11)] must be used, because volumetric flow is not constant. With gas flows, the thermodynamic process involved must be considered. In general, this is assessed using Equation (9), written as dp

V

2

³ -----U- + -----2- + gz = B

(21)

Effects of viscosity variations also appear. In nonisothermal laminar flow, the parabolic velocity profile (see Figure 4) is no longer valid. In general, for gases, viscosity increases with the square root of absolute temperature; for liquids, viscosity decreases with increasing temperature. This results in opposite effects. For fully developed pipe flow, the linear variation in shear stress from the wall value Ww to zero at the centerline is independent of the temperature gradient. In the section on Laminar Flow, W is defined as W = ( y/b) Ww , where y is the distance from the centerline and 2b is the wall spacing. For pipe radius R = D/2 and distance from the wall y = R – r (see Figure 11), then W = Ww (R – y)/R. Then, solving Equation (2) for the change in velocity yields Ww · W w R – y dy = – § -----dv = ---------------------¨ -¸ r dr RP © ¹ RP

(22)

When fluid viscosity is lower near the wall than at the center (because of external heating of liquid or cooling of gas by heat transfer through the pipe wall), the velocity gradient is steeper near the wall and flatter near the center, so the profile is generally flattened. When

3.6

2009 ASHRAE Handbook—Fundamentals

liquid is cooled or gas is heated, the velocity profile is more pointed for laminar flow (Figure 11). Calculations for such flows of gases and liquid metals in pipes are in Deissler (1951). Occurrences in turbulent flow are less apparent than in laminar flow. If enough heating is applied to gaseous flows, the viscosity increase can cause reversion to laminar flow. Buoyancy effects and the gradual approach of the fluid temperature to equilibrium with that outside the pipe can cause considerable variation in the velocity profile along the conduit. Colborne and Drobitch (1966) found the pipe factor for upward vertical flow of hot air at a Re < 2000 reduced to about 0.6 at 40 diameters from the entrance, then increased to about 0.8 at 210 diameters, and finally decreased to the isothermal value of 0.5 at the end of 320 diameters.

FLOW ANALYSIS Fluid flow analysis is used to correlate pressure changes with flow rates and the nature of the conduit. For a given pipeline, either the pressure drop for a certain flow rate, or the flow rate for a certain pressure difference between the ends of the conduit, is needed. Flow analysis ultimately involves comparing a pump or blower to a conduit piping system for evaluating the expected flow rate.

Generalized Bernoulli Equation Internal energy differences are generally small, and usually the only significant effect of heat transfer is to change the density U. For gas or vapor flows, use the generalized Bernoulli equation in the pressure-over-density form of Equation (12), allowing for the thermodynamic process in the pressure-density relation: 2

2

³

2

V V dp ------ + D 1 -----1- + E M = D 2 -----2- + E L U 2 2 1

Solution: The following form of the generalized Bernoulli relation is used in place of Equation (12), which also could be used: ( p1/U1 g) + D1(V12/2g) + z1 + HM The term

(24)

can be calculated as follows: 2

2

§ D· § 9 e 12· 2 A 1 = S ¨ ----¸ = S ¨ -------------¸ = 0.44 ft 2 © ¹ © 2 ¹ §400 ft 3 · § 1 min· 2 V 1 = Q e A 1 = ¨----------------- ¸ ¨ --------------¸ e 0.44 ft = 15.1 ft e s © min ¹ © 60s ¹ 2 V1 e

subscripts on the right side of Equation (24) are changed to 4. Note that p1 = p4 = p, U1 = U4 = U, and V1 = V4 = 0. Thus, ( p/Ug) + 0 + 2 + HM = ( p/Ug) + 0 + 10 + (24.5 + 237)

(25)

2

2g = 15.1 e 2 32 = 3.56 ft

The term V22/2g can be calculated in a similar manner. In Equation (24), HM is evaluated by applying the relation between any two points on opposite sides of the blower. Because conditions at stations 1 and 4 are known, they are used, and the location-specifying

(26)

so HM = 269.5 ft of air. For standard air, this corresponds to 3.89 in. of water. The head difference measured across the blower (between stations 2 and 3) is often taken as HM. It can be obtained by calculating the static pressure at stations 2 and 3. Applying Equation (24) successively between stations 1 and 2 and between 3 and 4 gives ( p1/Ug) + 0 + 2 + 0 = ( p2 /Ug) + (1.06 u 3.56) + 0 + 24.5 ( p3 /Ug) + (1.03 u 9.70) + 0 + 0 = ( p4 /Ug) + 0 + 10 + 237

(27)

where D just ahead of the blower is taken as 1.06, and just after the blower as 1.03; the latter value is uncertain because of possible uneven discharge from the blower. Static pressures p1 and p4 may be taken as zero gage. Thus, p2 /Ug = –26.2 ft of air p3 /Ug = 237 ft of air

Example 1. Specify a blower to produce isothermal airflow of 400 cfm through a ducting system (Figure 12). Accounting for intake and fitting losses, equivalent conduit lengths are 60 and 165 ft, and flow is isothermal. Head at the inlet (station 1) and following the discharge (station 4), where velocity is zero, is the same. Frictional losses HL are evaluated as 24.5 ft of air between stations 1 and 2, and 237 ft between stations 3 and 4.

V12/2g

Fig. 12 Blower and Duct System for Example 1

(23)

Elevation changes involving z are often negligible and are dropped. The pressure form of Equation (10) is generally unacceptable when appreciable density variations occur, because the volumetric flow rate differs at the two stations. This is particularly serious in frictionloss evaluations where the density usually varies over considerable lengths of conduit (Benedict and Carlucci 1966). When the flow is essentially incompressible, Equation (20) is satisfactory.

= ( p2 /U2 g) + D2(V22/2g) + z2 + HL

Fig. 12 Blower and Duct System for Example 1

(28)

The difference between these two numbers is 263.2 ft, which is not the HM calculated after Equation (24) as 269.5 ft. The apparent discrepancy results from ignoring the velocity at stations 2 and 3. Actually, HM is HM = ( p3 /Ug) + D3(V32 /2g) – [( p2/Ug) + D2( V22 /2g)] = 237 + (1.03 u 9.70) – [–26.2 + (1.06 u 3.54)] = 247 – (–22.5) = 269.5 ft of air

(29)

The required blower head is the same, no matter how it is evaluated. It is the specific energy added to the system by the machine. Only when the conduit size and velocity profiles on both sides of the machine are the same is EM or HM simply found from 'p = p3 – p2.

Conduit Friction The loss term EL or HL of Equation (12) or (13) accounts for friction caused by conduit-wall shearing stresses and losses from conduit-section changes. HL is the head loss (i.e., loss of energy per unit weight). In real-fluid flow, a frictional shear occurs at bounding walls, gradually influencing flow further away from the boundary. A lateral velocity profile is produced and flow energy is converted into heat (fluid internal energy), which is generally unrecoverable (a loss). This loss in fully developed conduit flow is evaluated using the Darcy-Weisbach equation: § L· § V 2· H L f = f ¨ ----¸ ¨ ------ ¸ © D¹ © 2g ¹

(30)

where L is the length of conduit of diameter D and f is the DarcyWeisbach friction factor. Sometimes a numerically different relation is used with the Fanning friction factor (1/4 of the Darcy friction factor f ). The value of f is nearly constant for turbulent flow, varying only from about 0.01 to 0.05.

Fluid Flow

3.7

For fully developed laminar-viscous flow in a pipe, loss is evaluated from Equation (17) as follows: 2 · L· § V · 64 - § --L- § 8PV 32LQV- = -------------H L f = ----¨ ---------¸ = ---------------¨ -¸ ¨ ------ ¸ 2 2 VD e Q © D¹ © 2g ¹ Ug © R ¹ D g

(31)

where Re = VD/v and f = 64/Re. Thus, for laminar flow, the friction factor varies inversely with the Reynolds number. The value of 64/Re varies with channel shape. A good summary of shape factors is provided by Incropera and DeWitt (2002). With turbulent flow, friction loss depends not only on flow conditions, as characterized by the Reynolds number, but also on the roughness height H of the conduit wall surface. The variation is complex and is expressed in diagram form (Moody 1944), as shown in Figure 13. Historically, the Moody diagram has been used to determine friction factors, but empirical relations suitable for use in modeling programs have been developed. Most are applicable to limited ranges of Reynolds number and relative roughness. Churchill (1977) developed a relationship that is valid for all ranges of Reynolds numbers, and is more accurate than reading the Moody diagram: § 8 · f = 8 ¨ -----------¸ © Re Dh ¹

12

1 + ----------------------1.5 A + B

§ · 1 ¨ -¸ A = 2.457 ln ¨ -----------------------------------------------------------------¸ 0.9 ¨ §7 e Re · + § 0.27H e D · ¸ Dh ¹ h¹ ¹ © ©©

1 e 12

(32a)

16

(32b)

§37,530 ·16 B = ¨---------------- ¸ © Re D h ¹

(32c)

Inspection of the Moody diagram indicates that, for high Reynolds numbers and relative roughness, the friction factor becomes independent of the Reynolds number in a fully rough flow or fully turbulent regime. A transition region from laminar to turbulent flow occurs when 2000 < Re < 10,000. Roughness height H, which may increase with conduit use, fouling, or aging, is usually tabulated for different types of pipes as shown in Table 2. Table 2

Effective Roughness of Conduit Surfaces

Material Commercially smooth brass, lead, copper, or plastic pipe Steel and wrought iron Galvanized iron or steel Cast iron

Fig. 13 Relation Between Friction Factor and Reynolds Number

Fig. 13 Relation Between Friction Factor and Reynolds Number (Moody 1944)

H, jin 60 1800 6000 10,200

3.8

2009 ASHRAE Handbook—Fundamentals

Noncircular Conduits. Air ducts are often rectangular in cross section. The equivalent circular conduit corresponding to the noncircular conduit must be found before the friction factor can be determined. For turbulent flow, hydraulic diameter Dh is substituted for D in Equation (30) and in the Reynolds number. Noncircular duct friction can be evaluated to within 5% for all except very extreme cross sections (e.g., tubes with deep grooves or ridges). A more refined method for finding the equivalent circular duct diameter is given in Chapter 13. With laminar flow, the loss predictions may be off by a factor as large as two.

Valve, Fitting, and Transition Losses Valve and section changes (contractions, expansions and diffusers, elbows, bends, or tees), as well as entrances and exits, distort the fully developed velocity profiles (see Figure 4) and introduce extra flow losses that may dissipate as heat into pipelines or duct systems. Valves, for example, produce such extra losses to control the fluid flow rate. In contractions and expansions, flow separation as shown in Figures 9 and 10 causes the extra loss. The loss at rounded entrances develops as flow accelerates to higher velocities; this higher velocity near the wall leads to wall shear stresses greater than those of fully developed flow (see Figure 6). In flow around bends, the velocity increases along the inner wall near the start of the bend. This increased velocity creates a secondary fluid motion in a double helical vortex pattern downstream from the bend. In all these devices, the disturbance produced locally is converted into turbulence and appears as a loss in the downstream region. The return of a disturbed flow pattern into a fully developed velocity profile may be quite slow. Ito (1962) showed that the secondary motion following a bend takes up to 100 diameters of conduit to die out but the pressure gradient settles out after 50 diameters. In a laminar fluid flow following a rounded entrance, the entrance length depends on the Reynolds number: Le /D = 0.06 Re

(33)

At Re = 2000, Equation (33) shows that a length of 120 diameters is needed to establish the parabolic velocity profile. The pressure gradient reaches the developed value of Equation (30) in fewer flow diameters. The additional loss is 1.2V 2/2g; the change in profile from uniform to parabolic results in a loss of 1.0V 2/2g (because D = 2.0), and the remaining loss is caused by the excess friction. In turbulent fluid flow, only 80 to 100 diameters following the rounded entrance are needed for the velocity profile to become fully developed, but the friction loss per unit length reaches a value close to that of the fully developed flow value more quickly. After six diameters, the loss rate at a Reynolds number of 105 is only 14% above that of fully developed flow in the same length, whereas at 107, it is only 10% higher (Robertson 1963). For a sharp entrance, flow separation (see Figure 9) causes a greater disturbance, but fully developed flow is achieved in about half the length required for a rounded entrance. In a sudden expansion, the pressure change settles out in about eight times the diameter change (D2 – D1), whereas the velocity profile may take at least a 50% greater distance to return to fully developed pipe flow (Lipstein 1962). Instead of viewing these losses as occurring over tens or hundreds of pipe diameters, it is possible to treat the entire effect of a disturbance as if it occurs at a single point in the flow direction. By treating these losses as a local phenomenon, they can be related to the velocity by the loss coefficient K: Loss of section = K(V 2/2g)

(34)

Chapter 22 and the Pipe Friction Manual (Hydraulic Institute 1961) have information for pipe applications. Chapter 21 gives information for airflow. The same type of fitting in pipes and ducts

Table 3 Fitting Loss Coefficients of Turbulent Flow 'P e Ug K = -----------------2 V e 2g 0.5 0.05

Fitting

Geometry

Entrance

Sharp Well-rounded

Contraction

Sharp (D2/D1 = 0.5)

0.38

90° Elbow

Miter Short radius Long radius Miter with turning vanes

1.3 0.90 0.60 0.2

Globe valve Angle valve Gate valve

Open Open Open 75% open 50% open 25% open Closed

Any valve Tee

10 5 0.19 to 0.22 1.10 3.6 28.8 f

Straight-through flow Flow through branch

0.5 1.8

may yield a different loss, because flow disturbances are controlled by the detailed geometry of the fitting. The elbow of a small threaded pipe fitting differs from a bend in a circular duct. For 90° screw-fitting elbows, K is about 0.8 (Ito 1962), whereas smooth flanged elbows have a K as low as 0.2 at the optimum curvature. Table 3 lists fitting loss coefficients.These values indicate losses, but there is considerable variance. Note that a well-rounded entrance yields a rather small K of 0.05, whereas a gate valve that is only 25% open yields a K of 28.8. Expansion flows, such as from one conduit size to another or at the exit into a room or reservoir, are not included. For such occurrences, the Borda loss prediction (from impulse-momentum considerations) is appropriate: 2

2

V 1 § A ·2 V1 – V2 Loss at expansion = ------------------------- = ------ ¨1 – -----1- ¸ 2g 2g © A 2 ¹

(35)

Expansion losses may be significantly reduced by avoiding or delaying separation using a gradual diffuser (see Figure 10). For a diffuser of about 7° total angle, the loss is only about one-sixth of the loss predicted by Equation (35). The diffuser loss for total angles above 45 to 60° exceeds that of the sudden expansion, but is moderately influenced by the diameter ratio of the expansion. Optimum diffuser design involves numerous factors; excellent performance can be achieved in short diffusers with splitter vanes or suction. Turning vanes in miter bends produce the least disturbance and loss for elbows; with careful design, the loss coefficient can be reduced to as low as 0.1. For losses in smooth elbows, Ito (1962) found a Reynolds number effect (K slowly decreasing with increasing Re) and a minimum loss at a bend curvature (bend radius to diameter ratio) of 2.5. At this optimum curvature, a 45° turn had 63%, and a 180° turn approximately 120%, of the loss of a 90° bend. The loss does not vary linearly with the turning angle because secondary motion occurs. Note that using K presumes its independence of the Reynolds number. Some investigators have documented a variation in the loss coefficient with the Reynolds number. Assuming that K varies with Re similarly to f, it is convenient to represent fitting losses as adding to the effective length of uniform conduit. The effective length of a fitting is then Leff /D = K/fref

(36)

where fref is an appropriate reference value of the friction factor. Deissler (1951) uses 0.028, and the air duct values in Chapter 21 are based on an fref of about 0.02. For rough conduits, appreciable

Fluid Flow

3.9

Fig. 14 Diagram for Example 2

§ fL z1 – z2 = 32 ft = ¨ 1 + ----- + D ©

2

·

8Q 6 K¸¹ --------------S gD 2

4

Because f depends on Q (unless flow is fully turbulent), iteration is required. The usual procedure is as follows:

Fig. 14 Diagram for Example 2 errors can occur if the relative roughness does not correspond to that used when fref was fixed. It is unlikely that fitting losses involving separation are affected by pipe roughness. The effective length method for fitting loss evaluation is still useful. When a conduit contains a number of section changes or fittings, the values of K are added to the f L /D friction loss, or the Leff /D of the fittings are added to the conduit length L /D for evaluating the total loss HL. This assumes that each fitting loss is fully developed and its disturbance fully smoothed out before the next section change. Such an assumption is frequently wrong, and the total loss can be overestimated. For elbow flows, the total loss of adjacent bends may be over- or underestimated. The secondary flow pattern after an elbow is such that when one follows another, perhaps in a different plane, the secondary flow of the second elbow may reinforce or partially cancel that of the first. Moving the second elbow a few diameters can reduce the total loss (from more than twice the amount) to less than the loss from one elbow. Screens or perforated plates can be used for smoothing velocity profiles (Wile 1947) and flow spreading. Their effectiveness and loss coefficients depend on their amount of open area (Baines and Peterson 1951). Example 2. Water at 68°F flows through the piping system shown in Figure 14. Each ell has a very long radius and a loss coefficient of K = 0.31; the entrance at the tank is square-edged with K = 0.5, and the valve is a fully open globe valve with K = 10. The pipe roughness is 0.01 in. The density U = 62.4 lbm/ft3 and kinematic viscosity Q = 1.08 u 10–5 ft2/s. a. If pipe diameter D = 6 in., what is the elevation H in the tank required to produce a flow of Q = 2.1 ft3/s? Solution: Apply Equation (13) between stations 1 and 2 in the figure. Note that p1 = p2, V1 | 0. Assume D | 1. The result is z1 – z2 = H – 40 ft = HL + V22 /2g

2

8Q 6 K·¸¹ --------------S gD 2

4

where L = 340 ft, 6K = 0.5 + (2 u 0.31) + 10 = 11.1, and V 2/2g = V 22/2g = 8Q2/S2gD4. Then, substituting into Equation (13), H = 40 ft + § 1 + fL ----- + © D

6

2

Q =

4

S gD z 1 – z 2 ---------------------------------------§ fL · 8 ¨ ----- + ¦ K + 1¸ ©D ¹

3. Use this value of Q to recalculate Re and get a new value of f. 4. Repeat until the new and old values of f agree to two significant figures. Iteration

f

Q, cfs

Re

f

0 1

0.0223 0.0231

1.706 1.690

4.02 E + 05 3.98 E + 05

0.0231 0.0231

As shown in the table, the result after two iterations is Q | 1.69 ft3/s. If the resulting flow is in the fully rough zone and the fully rough value of f is used as first guess, only one iteration is required. c. For H = 72 ft, what diameter pipe is needed to allow Q = 1.9 cfs? Solution: The energy equation in part (b) must now be solved for D with Q known. This is difficult because the energy equation cannot be solved for D, even with an assumed value of f. If Churchill’s expression for f is stored as a function in a calculator, program, or spreadsheet with an iterative equation solver, a solution can be generated. In this case, D | 0.526 ft = 6.31 in. Use the smallest available pipe size greater than 6.31 in. and adjust the valve as required to achieve the desired flow. Alternatively, (1) guess an available pipe size, and (2) calculate Re, f, and H for Q = 1.9 ft3/s. If the resulting value of H is greater than the given value of H = 72 ft, a larger pipe is required. If the calculated H is less than 72 ft, repeat using a smaller available pipe size.

Control Valve Characterization for Liquids Control valves are characterized by a discharge coefficient Cd . As long as the Reynolds number is greater than 250, the orifice equation holds for liquids: Q = Cd Ao 2 ' p e U

(37)

where Ao is the area of the orifice opening and 'p is the pressure drop across the valve. The discharge coefficient is about 0.63 for sharp-edged configurations and 0.8 to 0.9 for chamfered or rounded configurations.

From Equations (30) and (34), total head loss is § fL H L = ¨ ----- + ©D

1. Assume a value of f, usually the fully rough value for the given values of H and D. 2. Use this value of f in the energy calculation and solve for Q.

2

· 8Q K¹ --------------2 4 S gD

To calculate the friction factor, first calculate Reynolds number and relative roughness: Re = VD/v = 4Q/(SDv) = 495,150 H/D = 0.0017 From the Moody diagram or Equation (32), f = 0.023. Then HL = 47.5 ft and H = 87.5 ft. b. For H = 72 ft and D = 6 in., what is the flow? Solution: Applying Equation (13) again and inserting the expression for head loss gives

Incompressible Flow in Systems Flow devices must be evaluated in terms of their interaction with other elements of the system [e.g., the action of valves in modifying flow rate and in matching the flow-producing device (pump or blower) with the system loss]. Analysis is by the general Bernoulli equation and the loss evaluations noted previously. A valve regulates or stops the flow of fluid by throttling. The change in flow is not proportional to the change in area of the valve opening. Figures 15 and 16 indicate the nonlinear action of valves in controlling flow. Figure 15 shows flow in a pipe discharging water from a tank that is controlled by a gate valve. The fitting loss coefficient K values are from Table 3; the friction factor f is 0.027. The degree of control also depends on the conduit L/D ratio. For a relatively long conduit, the valve must be nearly closed before its high K value becomes a significant portion of the loss. Figure 16 shows a control damper (essentially a butterfly valve) in a duct discharging air from a plenum held at constant pressure. With a long duct, the

3.10

2009 ASHRAE Handbook—Fundamentals

Fig. 15 Valve Action in Pipeline

Fig. 17 Matching of Pump or Blower to System Characteristics

Fig. 17 Matching of Pump or Blower to System Characteristics Fig. 18 Differential Pressure Flowmeters Fig. 15 Valve Action in Pipeline Fig. 16 Effect of Duct Length on Damper Action Fig. 18 Differential Pressure Flowmeters

Fig. 16

Effect of Duct Length on Damper Action

damper does not affect the flow rate until it is about one-quarter closed. Duct length has little effect when the damper is more than half closed. The damper closes the duct totally at the 90° position (K = f). Flow in a system (pump or blower and conduit with fittings) involves interaction between the characteristics of the flow-producing device (pump or blower) and the loss characteristics of the pipeline or duct system. Often the devices are centrifugal, in which case the head produced decreases as flow increases, except for the lowest flow rates. System head required to overcome losses increases roughly as the square of the flow rate. The flow rate of a given system is that where the two curves of head versus flow rate intersect (point 1 in Figure 17). When a control valve (or damper) is partially closed, it increases losses and reduces flow (point 2 in Figure 17). For cases of constant head, the flow decrease caused by valving is not as great as that indicated in Figures 15 and 16.

Flow Measurement The general principles noted (the continuity and Bernoulli equations) are basic to most fluid-metering devices. Chapter 36 has further details. The pressure difference between the stagnation point (total pressure) and the ambient fluid stream (static pressure) is used to give a point velocity measurement. Flow rate in a conduit is measured by placing a pitot device at various locations in the cross section and

spatially integrating over the velocity found. A single-point measurement may be used for approximate flow rate evaluation. When flow is fully developed, the pipe-factor information of Figure 5 can be used to estimate the flow rate from a centerline measurement. Measurements can be made in one of two modes. With the pitotstatic tube, the ambient (static) pressure is found from pressure taps along the side of the forward-facing portion of the tube. When this portion is not long and slender, static pressure indication will be low and velocity indication high; as a result, a tube coefficient less than unity must be used. For parallel conduit flow, wall piezometers (taps) may take the ambient pressure, and the pitot tube indicates the impact (total pressure). The venturi meter, flow nozzle, and orifice meter are flow-ratemetering devices based on the pressure change associated with relatively sudden changes in conduit section area (Figure 18). The elbow meter (also shown in Figure 18) is another differential pressure flowmeter. The flow nozzle is similar to the venturi in action, but does not have the downstream diffuser. For all these, the flow rate is proportional to the square root of the pressure difference resulting from fluid flow. With area-change devices (venturi, flow nozzle, and orifice meter), a theoretical flow rate relation is found by applying the Bernoulli and continuity equations in Equations (12) and (3) between stations 1 and 2: Q = Cd Ao

2g'h

(38)

where 'h = h1 – h2 = (p1 – p2)/Ug (h = static head). The actual flow rate through the device can differ because the approach flow kinetic energy factor D deviates from unity and because of small losses. More significantly, jet contraction of orifice flow is neglected in deriving Equation (38), to the extent that it can reduce the effective flow area by a factor of 0.6. The effect of all these factors can be combined into the discharge coefficient Cd: 2

Sd 2g'h Qtheoretical = --------- -------------4 1 – E4

(39)

where E = d/D = ratio of throat (or orifice) diameter to conduit diameter. Sometimes the following alternative coefficient is used:

Fluid Flow

3.11

Fig. 19 Flowmeter Coefficients

'p 32PV dV ------- = ------ – ------------- = A – BV dT UL UD 2

(44)

Equation (44) can be rearranged and integrated to yield the time to reach a certain velocity: dV

1

- = – --- ln A – BV ³ dT = ³ ---------------A – BV B

T =

(45)

and § – 32QT· ' p § D2 · UL -¸ V = ------- ¨ --------- ¸ 1 – ------ exp ¨ --------------L © 32P ¹ 'p © D2 ¹

(46)

For long times (Tof), the steady velocity is ' p § R2 · ' p § D2 · V f = ------- ¨ --------- ¸ = ------- ¨ ------ ¸ L © 8P ¹ L © 32P ¹ Fig. 19

Flowmeter Coefficients Cd -------------------4 1–E

as given by Equation (17). Then, Equation (47) becomes (40)

The general mode of variation in Cd for orifices and venturis is indicated in Figure 19 as a function of Reynolds number and, to a lesser extent, diameter ratio E. For Reynolds numbers less than 10, the coefficient varies as Re . The elbow meter uses the pressure difference inside and outside the bend as the metering signal (Murdock et al. 1964). Momentum analysis gives the flow rate as 2

R- 2g'h Qtheoretical = Sd --------- -----4 2D

(41)

where R is the radius of curvature of the bend. Again, a discharge coefficient Cd is needed; as in Figure 19, this drops off for lower Reynolds numbers (below 105). These devices are calibrated in pipes with fully developed velocity profiles, so they must be located far enough downstream of sections that modify the approach velocity.

§ – ff Vf T · UL V = V f 1 – ------ exp ¨ -------------------¸ 'p © 2D ¹

(48)

64Q f f = ----------Vf D

(49)

where

The general nature of velocity development for start-up flow is derived by more complex techniques; however, the temporal variation is as given here. For shutdown flow (steady flow with 'p = 0 at T > 0), flow decays exponentially as e–T. Turbulent flow analysis of Equation (42) also must be based on the quasi-steady approximation, with less justification. Daily et al. (1956) indicate that frictional resistance is slightly greater than the steady-state result for accelerating flows, but appreciably less for decelerating flows. If the friction factor is approximated as constant, 'p fV 2 dV ------- = ------ – ---------- = A – BV 2 dT UL 2D

Unsteady Flow Conduit flows are not always steady. In a compressible fluid, acoustic velocity is usually high and conduit length is rather short, so the time of signal travel is negligibly small. Even in the incompressible approximation, system response is not instantaneous. If a pressure difference 'p is applied between the conduit ends, the fluid mass must be accelerated and wall friction overcome, so a finite time passes before the steady flow rate corresponding to the pressure drop is achieved. The time it takes for an incompressible fluid in a horizontal, constant-area conduit of length L to achieve steady flow may be estimated by using the unsteady flow equation of motion with wall friction effects included. On the quasi-steady assumption, friction loss is given by Equation (30); also by continuity, V is constant along the conduit. The occurrences are characterized by the relation § 1· dp f V 2 dV ------- + ¨ ---¸ ------- + ---------- = 0 dT © U¹ ds 2D

(42)

where Tis the time and s is the distance in flow direction. Because a certain 'p is applied over conduit length L, ' p fV 2 dV ------- = ------- – ---------dT UL 2D For laminar flow, f is given by Equation (31):

(47)

(43)

(50)

and for the accelerating flow, 1 - tanh – 1 § B · T = -----------¨V ----- ¸ A ¹ © AB

(51)

A e B tanh T AB

(52)

or V =

Because the hyperbolic tangent is zero when the independent variable is zero and unity when the variable is infinity, the initial (V = 0 at T = 0) and final conditions are verified. Thus, for long times (Tof),

Vf =

AeB =

'p e UL ----------------- = f f e 2D

'p § 2D· ------ ¨ -------¸ UL © f f ¹

(53)

which is in accord with Equation (30) when f is constant (the flow regime is the fully rough one of Figure 13). The temporal velocity variation is then V = Vf tanh ( f fVf T/2D)

(54)

In Figure 20, the turbulent velocity start-up result is compared with the laminar one, where initially the turbulent is steeper but of the

3.12

2009 ASHRAE Handbook—Fundamentals ahead of the influence of the body as station 1, V2 = 0. Solving Equation (57) for p2 gives

Fig. 20 Temporal Increase in Velocity Following Sudden Application of Pressure

2 k e k – 1

§ – 1· U 1 V1 p s = p 2 = p 1 1 + ¨ k----------¸ -----------© 2 ¹ kp 1

(58)

where ps is the stagnation pressure. Because kp/U is the square of acoustic velocity a and Mach number M = V/a, the stagnation pressure relation becomes k e k – 1

§ – 1· 2 p s = p 1 1 + ¨ k----------¸ M 1 © 2 ¹

Fig. 20 Temporal Increase in Velocity Following Sudden Application of Pressure same general form, increasing rapidly at the start but reaching Vf asymptotically.

Compressibility All fluids are compressible to some degree; their density depends somewhat on the pressure. Steady liquid flow may ordinarily be treated as incompressible, and incompressible flow analysis is satisfactory for gases and vapors at velocities below about 4000 to 8000 fpm, except in long conduits. For liquids in pipelines, a severe pressure surge or water hammer may be produced if flow is suddenly stopped. This pressure surge travels along the pipe at the speed of sound in the liquid, alternately compressing and decompressing the liquid. For steady gas flows in long conduits, pressure decrease along the conduit can reduce gas density significantly enough to increase velocity. If the conduit is long enough, velocities approaching the speed of sound are possible at the discharge end, and the Mach number (ratio of flow velocity to speed of sound) must be considered. Some compressible flows occur without heat gain or loss (adiabatically). If there is no friction (conversion of flow mechanical energy into internal energy), the process is reversible (isentropic), as well, and follows the relationship

where k, the ratio of specific heats at constant pressure and volume, has a value of 1.4 for air and diatomic gases. The Bernoulli equation of steady flow, Equation (21), as an integral of the ideal-fluid equation of motion along a streamline, then becomes dp V 2 ------ + ------ = constant U 2

(55)

where, as in most compressible flow analyses, the elevation terms involving z are insignificant and are dropped. For a frictionless adiabatic process, the pressure term has the form 2

³

For Mach numbers less than one, 2

U1 V1 M1 § 2 – k · 4 p s = p 1 + -----------2 1 + ------- + ¨ ----------- ¸ M 1 + } 4 © 24 ¹

(60)

When M = 0, Equation (60) reduces to the incompressible flow result obtained from Equation (9). Appreciable differences appear when the Mach number of approaching flow exceeds 0.2. Thus, a pitot tube in air is influenced by compressibility at velocities over about 13,000 fpm. Flows through a converging conduit, as in a flow nozzle, venturi, or orifice meter, also may be considered isentropic. Velocity at the upstream station 1 is negligible. From Equation (57), velocity at the downstream station is

V2 =

p1 · § p2 · k – 1 e k 2k - § -------------¨ ¸ 1 – ¨ ----- ¸ k – 1 © U1 ¹ © p1 ¹

(61)

The mass flow rate is m· = V2 A 2 U 2

p/Uk = constant k = cp /cv

³

(59)

dp k p2 p1 ------ = ----------- § ----- – ----- · k – 1 © U2 U1 ¹ U 1

(56)

Then, between stations 1 and 2 for the isentropic process, 2

2

V2 – V1 p § k · p k – 1 e k + ------------------ = 0 -----1 ¨ -----------¸ §¨ ----2- ·¸ – 1 U 1 © k – 1¹ p 2 © 1¹

(57)

Equation (57) replaces the Bernoulli equation for compressible flows and may be applied to the stagnation point at the front of a body. With this point as station 2 and the upstream reference flow

2ek k + 1 e k § p2 · 2k - p U § p----2- · ---------– ¨ ----- ¸ 1 1 ¨p ¸ k–1 © 1¹ © p1 ¹

= A2

(62)

The corresponding incompressible flow relation is m· in = A 2 U 2 ' p e U = A 2 2U p 1 – p 2

(63)

The compressibility effect is often accounted for in the expansion factor Y: m· = Y m· in = A 2 Y 2U p 1 – p 2

(64)

Y is 1.00 for the incompressible case. For air (k = 1.4), a Y value of 0.95 is reached with orifices at p2 /p1 = 0.83 and with venturis at about 0.90, when these devices are of relatively small diameter (D2 /D1 > 0.5). As p2 /p1 decreases, flow rate increases, but more slowly than for the incompressible case because of the nearly linear decrease in Y. However, downstream velocity reaches the local acoustic value and discharge levels off at a value fixed by upstream pressure and density at the critical ratio: p2 ----p1

c

§ 2 ·k e k – 1 = ¨ ------------¸ = 0.53 for air © k + 1¹

(65)

Fluid Flow

3.13

At higher pressure ratios than critical, choking (no increase in flow with decrease in downstream pressure) occurs and is used in some flow control devices to avoid flow dependence on downstream conditions. For compressible fluid metering, the expansion factor Y must be included, and the mass flow rate is 2 2U'p m· = C d Y Sd --------- -------------4 1 – E4

Fig. 21 Cavitation in Flows in Orifice or Valve

(66)

Compressible Conduit Flow When friction loss is included, as it must be except for a very short conduit, incompressible flow analysis applies until pressure drop exceeds about 10% of the initial pressure. The possibility of sonic velocities at the end of relatively long conduits limits the amount of pressure reduction achieved. For an inlet Mach number of 0.2, discharge pressure can be reduced to about 0.2 of the initial pressure; for inflow at M = 0.5, discharge pressure cannot be less than about 0.45p1 (adiabatic) or about 0.6p1 (isothermal). Analysis must treat density change, as evaluated from the continuity relation in Equation (3), with frictional occurrences evaluated from wall roughness and Reynolds number correlations of incompressible flow (Binder 1944). In evaluating valve and fitting losses, consider the reduction in K caused by compressibility (Benedict and Carlucci 1966). Although the analysis differs significantly, isothermal and adiabatic flows involve essentially the same pressure variation along the conduit, up to the limiting conditions.

Cavitation Liquid flow with gas- or vapor-filled pockets can occur if the absolute pressure is reduced to vapor pressure or less. In this case, one or more cavities form, because liquids are rarely pure enough to withstand any tensile stressing or pressures less than vapor pressure for any length of time (John and Haberman 1980; Knapp et al. 1970; Robertson and Wislicenus 1969). Robertson and Wislicenus (1969) indicate significant occurrences in various technical fields, chiefly in hydraulic equipment and turbomachines. Initial evidence of cavitation is the collapse noise of many small bubbles that appear initially as they are carried by the flow into higher-pressure regions. The noise is not deleterious and serves as a warning of the occurrence. As flow velocity further increases or pressure decreases, the severity of cavitation increases. More bubbles appear and may join to form large fixed cavities. The space they occupy becomes large enough to modify the flow pattern and alter performance of the flow device. Collapse of cavities on or near solid boundaries becomes so frequent that, in time, the cumulative impact causes cavitational erosion of the surface or excessive vibration. As a result, pumps can lose efficiency or their parts may erode locally. Control valves may be noisy or seriously damaged by cavitation. Cavitation in orifice and valve flow is illustrated in Figure 21. With high upstream pressure and a low flow rate, no cavitation occurs. As pressure is reduced or flow rate increased, the minimum pressure in the flow (in the shear layer leaving the edge of the orifice) eventually approaches vapor pressure. Turbulence in this layer causes fluctuating pressures below the mean (as in vortex cores) and small bubble-like cavities. These are carried downstream into the region of pressure regain where they collapse, either in the fluid or on the wall (Figure 21A). As pressure reduces, more vapor- or gasfilled bubbles result and coalesce into larger ones. Eventually, a single large cavity results that collapses further downstream (Figure 21B). The region of wall damage is then as many as 20 diameters downstream from the valve or orifice plate. Sensitivity of a device to cavitation is measured by the cavitation index or cavitation number, which is the ratio of the available pressure above vapor pressure to the dynamic pressure of the reference flow:

Fig. 21 Cavitation in Flows in Orifice or Valve 2 po – pv V = ------------------------2 UV o

(67)

where pv is vapor pressure, and the subscript o refers to appropriate reference conditions. Valve analyses use such an index to determine when cavitation will affect the discharge coefficient (Ball 1957). With flow-metering devices such as orifices, venturis, and flow nozzles, there is little cavitation, because it occurs mostly downstream of the flow regions involved in establishing the metering action. The detrimental effects of cavitation can be avoided by operating the liquid-flow device at high enough pressures. When this is not possible, the flow must be changed or the device must be built to withstand cavitation effects. Some materials or surface coatings are more resistant to cavitation erosion than others, but none is immune. Surface contours can be designed to delay the onset of cavitation.

NOISE IN FLUID FLOW Noise in flowing fluids results from unsteady flow fields and can be at discrete frequencies or broadly distributed over the audible range. With liquid flow, cavitation results in noise through the collapse of vapor bubbles. Noise in pumps or fittings (e.g., valves) can be a rattling or sharp hissing sound, which is easily eliminated by raising the system pressure. With severe cavitation, the resulting unsteady flow can produce indirect noise from induced vibration of adjacent parts. See Chapter 47 of the 2007 ASHRAE Handbook— HVAC Applications for more information on sound control. The disturbed laminar flow behind cylinders can be an oscillating motion. The shedding frequency f of these vortexes is characterized by a Strouhal number St = fd/V of about 0.21 for a circular cylinder of diameter d, over a considerable range of Reynolds numbers. This oscillating flow can be a powerful noise source, particularly when f is close to the natural frequency of the cylinder or some nearby structural member so that resonance occurs. With cylinders of another shape, such as impeller blades of a pump or blower, the characterizing Strouhal number involves the trailing-edge thickness of the member. The strength of the vortex wake, with its resulting vibrations and noise potential, can be reduced by breaking up flow with downstream splitter plates or boundary-layer trip devices (wires) on the cylinder surface. Noises produced in pipes and ducts, especially from valves and fittings, are associated with the loss through such elements. The sound pressure of noise in water pipe flow increases linearly with head loss; broadband noise increases, but only in the lowerfrequency range. Fitting-produced noise levels also increase with fitting loss (even without cavitation) and significantly exceed noise levels of the pipe flow. The relation between noise and loss is not surprising because both involve excessive flow perturbations. A valve’s pressure-flow characteristics and structural elasticity may be such that for some operating point it oscillates, perhaps in resonance with part of the piping system, to produce excessive noise. A change in the operating point conditions or details of the valve geometry can result in significant noise reduction. Pumps and blowers are strong potential noise sources. Turbomachinery noise is associated with blade-flow occurrences. Broad-

3.14

2009 ASHRAE Handbook—Fundamentals

band noise appears from vortex and turbulence interaction with walls and is primarily a function of the operating point of the machine. For blowers, it has a minimum at the peak efficiency point (Groff et al. 1967). Narrow-band noise also appears at the bladecrossing frequency and its harmonics. Such noise can be very annoying because it stands out from the background. To reduce this noise, increase clearances between impeller and housing, and space impeller blades unevenly around the circumference.

SYMBOLS A Ao B CD Cd Dh EL EM F

= = = = = = = = =

f FD fref g gc HL HM K k L Le Leff m· p Pw Q q R Re s St u V v w y Y z

= = = = = = = = = = = = = = = = = = = = = = = = = = = =

area, ft2 area of orifice opening Bernoulli constant drag coefficient discharge coefficient hydraulic diameter loss during conversion of energy from mechanical to internal external work from fluid machine tangential force per unit area required to slide one of two parallel plates Darcy-Weisbach friction factor, or shedding frequency drag force reference value of friction factor gravitational acceleration, ft/s2 gravitational constant = 32.17 lbm ·ft/s 2 ·lbf head lost through friction head added by pump loss coefficient ratio of specific heats at constant pressure and volume length entrance length effective length mass flow rate pressure wetted perimeter volumetric flow rate heat per unit mass absorbed or rejected pipe radius Reynolds number flow direction Strouhal number internal energy velocity fluid velocity normal to differential area dA work per unit mass distance from centerline distance between two parallel plates, ft, or expansion factor elevation

Greek D E J G 'E 'p 'u H T P

= = = = = = = = = =

Q U V W Ww

= = = = =

kinetic energy factor d/D = ratio of throat (or orifice) diameter to conduit diameter specific weight or weight density boundary layer thickness change in energy content per unit mass of flowing fluid pressure drop across valve conversion of energy from mechanical to internal roughness height time proportionality factor for absolute or dynamic viscosity of fluid, lbf ·s/ft2 kinematic viscosity, ft2/s density, lbm/ft3 cavitation index or number shear stress, lbf /ft2 wall shear stress

Ball, J.W. 1957. Cavitation characteristics of gate valves and globe values used as flow regulators under heads up to about 125 ft. ASME Transactions 79:1275. Benedict, R.P. and N.A. Carlucci. 1966. Handbook of specific losses in flow systems. Plenum Press Data Division, New York. Binder, R.C. 1944. Limiting isothermal flow in pipes. ASME Transactions 66:221. Churchill, S.W. 1977. Friction-factor equation spans all fluid flow regimes. Chemical Engineering 84(24):91-92. Colborne, W.G. and A.J. Drobitch. 1966. An experimental study of nonisothermal flow in a vertical circular tube. ASHRAE Transactions 72(4):5. Coleman, J.W. 2004. An experimentally validated model for two-phase sudden contraction pressure drop in microchannel tube header. Heat Transfer Engineering 25(3):69-77. Daily, J.W., W.L. Hankey, R.W. Olive, and J.M. Jordan. 1956. Resistance coefficients for accelerated and decelerated flows through smooth tubes and orifices. ASME Transactions 78:1071-1077. Deissler, R.G. 1951. Laminar flow in tubes with heat transfer. National Advisory Technical Note 2410, Committee for Aeronautics. Fox, R.W., A.T. McDonald, and P.J. Pritchard. 2004. Introduction to fluid mechanics. Wiley, New York. Furuya, Y., T. Sate, and T. Kushida. 1976. The loss of flow in the conical with suction at the entrance. Bulletin of the Japan Society of Mechanical Engineers 19:131. Goldstein, S., ed. 1938. Modern developments in fluid mechanics. Oxford University Press, London. Reprinted by Dover Publications, New York. Groff, G.C., J.R. Schreiner, and C.E. Bullock. 1967. Centrifugal fan sound power level prediction. ASHRAE Transactions 73(II):V.4.1. Heskested, G. 1970. Further experiments with suction at a sudden enlargement. Journal of Basic Engineering, ASME Transactions 92D:437. Hoerner, S.F. 1965. Fluid dynamic drag, 3rd ed. Hoerner Fluid Dynamics, Vancouver, WA. Hydraulic Institute. 1990. Engineering data book, 2nd ed. Parsippany, NJ. Incropera, F.P. and D.P. DeWitt. 2002. Fundamentals of heat and mass transfer, 5th ed. Wiley, New York. Ito, H. 1962. Pressure losses in smooth pipe bends. Journal of Basic Engineering, ASME Transactions 4(7):43. John, J.E.A. and W.L. Haberman. 1980. Introduction to fluid mechanics, 2nd ed. Prentice Hall, Englewood Cliffs, NJ. Kline, S.J. 1959. On the nature of stall. Journal of Basic Engineering, ASME Transactions 81D:305. Knapp, R.T., J.W. Daily, and F.G. Hammitt. 1970. Cavitation. McGraw-Hill, New York. Lipstein, N.J. 1962. Low velocity sudden expansion pipe flow. ASHRAE Journal 4(7):43. Moody, L.F. 1944. Friction factors for pipe flow. ASME Transactions 66:672. Moore, C.A. and S.J. Kline. 1958. Some effects of vanes and turbulence in two-dimensional wide-angle subsonic diffusers. National Advisory Committee for Aeronautics, Technical Memo 4080. Murdock, J.W., C.J. Foltz, and C. Gregory. 1964. Performance characteristics of elbow flow meters. Journal of Basic Engineering, ASME Transactions 86D:498. Robertson, J.M. 1963. A turbulence primer. University of Illinois–Urbana, Engineering Experiment Station Circular 79. Robertson, J.M. 1965. Hydrodynamics in theory and application. PrenticeHall, Englewood Cliffs, NJ. Robertson, J.M. and G.F. Wislicenus, eds. 1969 (discussion 1970). Cavitation state of knowledge. American Society of Mechanical Engineers, New York. Ross, D. 1956. Turbulent flow in the entrance region of a pipe. ASME Transactions 78:915. Schlichting, H. 1979. Boundary layer theory, 7th ed. McGraw-Hill, New York. Wile, D.D. 1947. Air flow measurement in the laboratory. Refrigerating Engineering: 515.

REFERENCES

BIBLIOGRAPHY

Baines, W.D. and E.G. Peterson. 1951. An investigation of flow through screens. ASME Transactions 73:467.

Olson, R.M. 1980. Essentials of engineering fluid mechanics, 4th ed. Harper and Row, New York.

CHAPTER 4

HEAT TRANSFER Heat Transfer Processes ................................................................................................................. 4.1 Thermal Conduction........................................................................................................................ 4.3 Thermal Radiation ........................................................................................................................ 4.11 Thermal Convection ...................................................................................................................... 4.16 Heat Exchangers ........................................................................................................................... 4.21 Heat Transfer Augmentation......................................................................................................... 4.23 Symbols ......................................................................................................................................... 4.30

H

where v means “proportional to” and L = wall thickness. However, this relation does not take wall material into account: if the wall is foam instead of concrete, q would clearly be less. The constant of proportionality is a material property, thermal conductivity k. Thus,

EAT transfer is energy transferred because of a temperature difference. Energy moves from a higher-temperature region to a lower-temperature region by one or more of three modes: conduction, radiation, and convection. This chapter presents elementary principles of single-phase heat transfer, with emphasis on HVAC applications. Boiling and condensation are discussed in Chapter 5. More specific information on heat transfer to or from buildings or refrigerated spaces can be found in Chapters 14 to 19, 23, and 27 of this volume and in Chapter 13 of the 2006 ASHRAE Handbook—Refrigeration. Physical properties of substances can be found in Chapters 26, 28, 32, and 33 of this volume and in Chapter 9 of the 2006 ASHRAE Handbook—Refrigeration. Heat transfer equipment, including evaporators, condensers, heating and cooling coils, furnaces, and radiators, is covered in the 2008 ASHRAE Handbook—HVAC Systems and Equipment. For further information on heat transfer, see the Bibliography.

t s1 – t s2 A c t s1 – t s2 q = k ------------------------------ = ----------------------L L e kA c

(1)

where k has units of Btu/h·ft·°F. The denominator L/(kAc) can be considered the conduction resistance associated with the driving potential (ts1 – ts2). This is analogous to current flow through an electrical resistance, I = (V1 – V2)/R, where (V1 – V2) is driving potential, R is electrical resistance, and current I is rate of flow of charge instead of rate of heat transfer q. Thermal resistance has units h·°F/Btu. A wall with a resistance of 3 h·°F/Btu requires (ts1 – ts2) = 3°F for heat transfer q of 1 Btu/h. The thermal/electrical resistance analogy allows tools used to solve electrical circuits to be used for heat transfer problems.

HEAT TRANSFER PROCESSES Conduction Consider a wall that is 33 ft long, 10 ft tall, and 0.3 ft thick (Figure 1A). One side of the wall is maintained at ts1 = 77°F, and the other is kept at ts2 = 68°F. Heat transfer occurs at rate q through the wall from the warmer side to the cooler. The heat transfer mode is conduction (the only way energy can be transferred through a solid).

Convection Consider a surface at temperature ts in contact with a fluid at tf (Figure 1B). Newton’s law of cooling expresses the rate of heat transfer from the surface of area As as

• If ts1 is raised from 77 to 86°F while everything else remains the same, q doubles because ts1 – ts2 doubles. • If the wall is twice as tall, thus doubling the area Ac of the wall, q doubles. • If the wall is twice as thick, q is halved.

ts – tf q = h c A s t s – t f = ---------------------1 e hc As

(2)

where hc is the heat transfer coefficient (Table 1) and has units of Btu/h·ft2 ·°F. The convection resistance 1/(hc As) has units of h·°F/Btu. If tf > ts, heat transfers from the fluid to the surface, and q is written as just q = hc As(tf – ts). Resistance is the same, but the sign of the temperature difference is reversed. For heat transfer to be considered convection, fluid in contact with the surface must be in motion; if not, the mode of heat transfer is conduction. If fluid motion is caused by an external force (e.g., fan, pump, wind), it is forced convection. If fluid motion results from buoyant forces caused by the surface being warmer or cooler than the fluid, it is free (or natural) convection.

From these relationships, t s1 – t s2 A c q v -----------------------------L Fig. 1 (A) Conduction and (B) Convection

Table 1

Heat Transfer Coefficients by Convection Type

Convection Type Free, gases Free, liquids Forced, gases Forced, liquids Boiling, condensation

Fig. 1 (A) Conduction and (B) Convection The preparation of this chapter is assigned to TC 1.3, Heat Transfer and Fluid Flow.

4.1

hc , Btu/h·ft2 ·°F 0.35 to 4.5 1.8 to 180 4.5 to 45 9 to 3500 450 to 18,000

4.2

2009 ASHRAE Handbook—Fundamentals Fig. 1

Radiation

Interface Resistance Across Two Layers

Matter emits thermal radiation at its surface when its temperature is above absolute zero. This radiation is in the form of photons of varying frequency. These photons leaving the surface need no medium to transport them, unlike conduction and convection (in which heat transfer occurs through matter). The rate of thermal radiant energy emitted by a surface depends on its absolute temperature and its surface characteristics. A surface that absorbs all radiation incident upon it is called a black surface, and emits energy at the maximum possible rate at a given temperature. The heat emission from a black surface is given by the Stefan-Boltzmann law: qemitted, black = AsVTs4

Fig. 2

where Eb = VTs4 is the blackbody emissive power in Btu/h·ft2; Ts is absolute surface temperature, °R; and V = 0.1712 u 10–8 Btu/h·ft2 ·°R4 is the Stefan-Boltzmann constant. If a surface is not black, the emission per unit time per unit area is E = HVTs4

2 )(t + t where hr = VH( ts2 + t surr s surr) is often called a radiation heat transfer coefficient. The disadvantage of this form is that hr depends on ts, which is often the desired result of the calculation.

Combined Radiation and Convection

where E is emissive power, and H is emissivity, where 0 d H d 1. For a black surface, H = 1. Nonblack surfaces do not absorb all incident radiation. The absorbed radiation is qabsorbed = DAsG where absorptivity D is the fraction of incident radiation absorbed, and irradiation G is the rate of radiant energy incident on a surface per unit area of the receiving surface due to emission and reflection from surrounding surfaces. For a black surface, D = 1. A surface’s emissivity and absorptivity are often both functions of the wavelength distribution of photons emitted and absorbed, respectively, by the surface. However, in many cases, it is reasonable to assume that both D and H are independent of wavelength. If so, D = H (a gray surface). Two surfaces at different temperatures that can “see” each other can exchange energy through radiation. The net exchange rate depends on the surfaces’ (1) relative size, (2) relative orientation and shape, (3) temperatures, and (4) emissivity and absorptivity. However, for a small area As in a large enclosure at constant temperature tsurr, the irradiation on As from the surroundings is the blackbody emissive power of the surroundings Eb,surr. So, if ts > tsurr, net heat loss from gray surface As in the radiation exchange with the surroundings at Tsurr is qnet = qemitted – qabsorbed = HAs Ebs – DAs Eb,surr 4 ) = HAsV(ts4 – t sum

Interface Resistance Across Two Layers

(3)

where D = H for the gray surface. If ts < tsurr , the expression for qnet is the same with the sign reversed, and qnet is the net gain by As. Note that qnet can be written as

When tsurr = tf in Equation (4), the total heat transfer from a surface by convection and radiation combined is then q = qrad + qconv = (ts – tf)As (hr + hc) The temperature difference ts – tf is in either °R or °F; the difference is the same. Either can be used; however, absolute temperatures must be used to calculate hr . (Absolute temperatures are °R = °F + 459.67.) Note that hc and hr are always positive, and that the direction of q is determined by the sign of (ts – tf).

Contact or Interface Resistance Heat flow through two layers encounters two conduction resistances L1/k1A and L 2/k 2 A (Figure 2). At the interface between two layers are gaps across which heat is transferred by a combination of conduction at contact points and convection and radiation across gaps. This multimode heat transfer process is usually characterized using a contact resistance coefficient R cont s or contact conductance hcont. 'T - = h q = --------------------cont A 't Rscont eA where 't is the temperature drop across the interface. R cont s is in ft2 ·h·°F/Btu, and hcont is in Btu/h·ft2 ·°F. The contact or interface resistance is Rcont = R cont s /A = 1/hcont A, and the resistance of the two layers combined is the sum of the resistances of the two layers and the contact resistance. Contact resistance can be reduced by lowering surface roughnesses, increasing contact pressure, or using a conductive grease or paste to fill the gaps.

Heat Flux The conduction heat transfer can be written as

E bs – E b, surr q net = ------------------------------1 e HA s

k t s1 – t s2 q qs = ----- = -------------------------Ac L

In this form, Ebs – Eb,surr is analogous to the driving potential in an electric circuit, and 1/(HAs) is analogous to electrical resistance. This is a convenient analogy when only radiation is being considered, but if convection and radiation both occur at a surface, convection is described by a driving potential based on the difference in the first power of the temperatures, whereas radiation is described by the difference in the fourth power of the temperatures. In cases like this, it is often useful to express net radiation as

where qs is heat flux in Btu/h·ft2. Similarly, for convection the heat flux is

qnet = hr As(ts – tsurr) = (ts – tsurr)/(1/hr As)

(4)

q qs = ----- = h c t s – t f As and net heat flux from radiation at the surface is q net 4 4 qsnet = --------- = HV t s – t surr As

Heat Transfer

4.3 Table 2

Fig. 2 Thermal Circuit

One-Dimensional Conduction Shape Factors Heat Transfer Rate

Thermal Resistance

t1 – t2 q x = kA x ------------L

L --------kA x

Hollow cylinder of length L with negligible heat transfer from end surfaces

2SkL t i – t o q r = ------------------------------ro ln § ---- · © ri ¹

ln r o e r i R = --------------------2SkL

Hollow sphere

4Sk ti – t o q r = --------------------------1 1 --- + ---ri ro

1 e ri – 1 e ro R = --------------------------4Sk

Configuration Constant crosssectional area slab

Fig. 3 Thermal Circuit

Overall Resistance and Heat Transfer Coefficient In Equation (1) for conduction in a slab, Equation (4) for radiative heat transfer rate between two surfaces, and Equation (2) for convective heat transfer rate from a surface, the heat transfer rate is expressed as a temperature difference divided by a thermal resistance. Using the electrical resistance analogy, with temperature difference and heat transfer rate instead of potential difference and current, respectively, tools for solving series electrical resistance circuits can also be applied to heat transfer circuits. For example, consider the heat transfer rate from a liquid to the surrounding gas separated by a constant cross-sectional area solid, as shown in Figure 3. The heat transfer rate from the fluid to the adjacent surface is by convection, then across the solid body by conduction, and finally from the solid surface to the surroundings by both convection and radiation. A circuit using the equations for resistances in each mode is also shown. From the circuit, the heat transfer rate is tf 1 – tf 2 q = ------------------------------R1 + R2 + R3 where R1 = 1/hA

R2 = L/kA

1 e hc A 1 e hr A R 3 = ------------------------------------------------ 1 e hc A + 1 e hr A

Fig. 3

Thermal Circuit Diagram for an Insulated Water Pipe

Resistance R3 is the parallel combination of the convection and radiation resistances on the right-hand surface, 1/hc A and 1/hr A. Equivalently, R3 = 1/hrc A, where hrc on the air side is the sum of the convection and radiation heat transfer coefficients (i.e., hrc = hc + hr). The heat transfer rate can also be written as q = UA(tf 1 – tf 2) where U is the overall heat transfer coefficient that accounts for all the resistances involved. Note that tf 1 – tf 2 1------------------- = ------= R1 + R2 + R3 q UA The product UA is overall conductance, the reciprocal of overall resistance. The surface area A on which U is based is not always constant as in this example, and should always be specified when referring to U. Heat transfer rates are equal from the warm liquid to the solid surface, through the solid, and then to the cool gas. Temperature drops across each part of the heat flow path are related to the resistances (as voltage drops are in an electric circuit), so that tf1 – t1 = qR1

t1 – t2 = qR2

t2 – tf2 = qR3

THERMAL CONDUCTION One-Dimensional Steady-State Conduction Steady-state heat transfer rates and resistances for (1) a slab of constant cross-sectional area, (2) a hollow cylinder with radial heat transfer, and (3) a hollow sphere are given in Table 2.

Fig. 4 Thermal Circuit Diagram for Insulated Water Pipe (Example 1) Example 1. Chilled water at 41°F flows in a copper pipe with a thermal conductivity kp of 2772 Btu·in/h·ft2 ·°F, with internal and external diameters of ID = 4 in. and OD = 4.7 in. The tube is covered with insulation 2 in. thick, with ki = 1.4 Btu·in/h·ft2 ·°F. The surrounding air is at ta = 77°F, and the heat transfer coefficient at the outer surface ho = 1.76 Btu/h·ft2 ·°F). Emissivity of the outer surface is H = 0.85. The heat transfer coefficient inside the tube is hi = 176 Btu/h·ft2 ·°F. Contact resistance between the insulation and the pipe is assumed to be negligible. Find the rate of heat gain per unit length of pipe and the temperature at the pipe-insulation interface. Solution: The outer diameter of the insulation is Dins = 4.7 + 2(2) = 8.7 in. For L = 1 ft,

4.4

2009 ASHRAE Handbook—Fundamentals S corners+edges = 4 u S corner + 4 u S edge

–3 1 R 1 = -----------------= 1.65 u 10 h · qF/Btu h i SIDL

= 4 u 0.15 8 e 12 ft + 4 u 0.54 33 – 2 u 8 e 12 ft = 68.8 ft

ln OD e ID –5 R 2 = ----------------------------- = 3.37 u 10 h · qF/Btu 2Sk p L

and the heat transfer rate is q corners+edges = S corners+edges k 'T

ln D ins e OD R 3 = -------------------------------- = 0.254 h · qF/Btu 2Sk i L

= 68.8 ft > 5.2 e 12 Btu/ft·h·°F @ 68 – 46 °F = 656 Btu/h

1 R c = ------------------------ = 0.0756 h · qF/Btu h o SD ins L

which leads to

Assuming insulation surface temperature ts = 70°F (i.e., 530°R) and 2 )(t + t 2 tsurr = ta = 537°R, hr = HV(ts2 + t surr s surr) = 0.88 Btu/h·ft ·°F.

q total = 42114 + 656 Btu/h = 42,770 Btu/h Note that the edges and corners are 1.3% of the total.

Extended Surfaces

1 R r = ----------------------- = 0.151 h · qF/Btu h r SD ins L

Heat transfer from a surface can be increased by attaching fins or extended surfaces to increase the area available for heat transfer. A few common fin geometries are shown in Figures 5 to 8. Fins provide a large surface area in a low volume, thus lowering material costs for a given performance. To achieve optimum design, fins are generally located on the side of the heat exchanger with lower heat transfer coefficients (e.g., the air side of an air-to-water coil). Equipment with extended surfaces includes natural- and forced-convection coils and shell-and-tube evaporators and condensers. Fins are also used inside tubes in condensers and dry expansion evaporators. Fin Efficiency. As heat flows from the root of a fin to its tip, temperature drops because of the fin material’s thermal resistance. The temperature difference between the fin and surrounding fluid is therefore greater at the root than at the tip, causing a corresponding variation in heat flux. Therefore, increases in fin length result in proportionately less additional heat transfer. To account for this effect, fin efficiency I is defined as the ratio of the actual heat transferred from the fin to the heat that would be transferred if the entire fin were at its root or base temperature:

Rr Rc = 0.050 h · qF/Btu R 4 = ----------------Rr + Rc Rtot = R1 + R2 + R3 + R4 = 0.306 h·°F/Btu Finally, the rate of heat gain by the cold water is ta – t = 118 Btu/h q rc = ----------R tot Temperature at the pipe/insulation interface is ts2 = t + qrc (R1 + R2) = 41.2°F Temperature at the insulation’s surface is ts3 = ta – qrc R4 = 71.1°F which is very close to the assumed value of 70°F.

Two- and Three-Dimensional Steady-State Conduction: Shape Factors Mathematical solutions to a number of two and three-dimensional conduction problems are available in Carslaw and Jaeger (1959). Complex problems can also often be solved by graphical or numerical methods, as described by Adams and Rogers (1973), Croft and Lilley (1977), and Patankar (1980). There are many two- and threedimensional steady-state cases that can be solved using conduction shape factors. Using the conduction shape factor S, the heat transfer rate is expressed as q = Sk(t1 – t2) = (t1 – t2)/(1/Sk)

(5)

where k is the material’s thermal conductivity, t1 and t2 are temperatures of two surfaces, and 1/(Sk) is thermal resistance. Conduction shape factors for some common configurations are given in Table 3. Example 2. The walls and roof of a house are made of 8 in. thick concrete with k = 5.2 Btu·in/h·ft2 ·°F. The inner surface is at 68°F, and the outer surface is at 46°F. The roof is 33 × 33 ft, and the walls are 16 ft high. Find the rate of heat loss from the house through its walls and roof, including edge and corner effects.

q I = --------------------------hA s t r – t e

where q is heat transfer rate into/out of the fin’s root, te is temperature of the surrounding environment, tr is temperature at fin root, and As is surface area of the fin. Fin efficiency is low for long or thin fins, or fins made of low-thermal-conductivity material. Fin efficiency decreases as the heat transfer coefficient increases because of increased heat flow. For natural convection in air-cooled condensers and evaporators, where the air-side h is low, fins can be fairly large and fabricated from low-conductivity materials such as steel instead of from copper or aluminum. For condensing and boiling, where large heat transfer coefficients are involved, fins must be very short for optimum use of material. Fin efficiencies for a few geometries are shown in Figures 5 to 8. Temperature distribution and fin efficiencies for various fin shapes are derived in most heat transfer texts. Constant-Area Fins and Spines. Fins or spines with constant cross-sectional area [e.g., straight fins (option A in Figure 7), cylindrical spines (option D in Figure 8)], the efficiency can be calculated as tanh mWc I = --------------------------mWc

Solution: The rate of heat transfer excluding the edges and corners is first determined: Atotal = (33 – 2 × 8/12)(33 – 2 × 8/12) + 4(33 – 2 × 8/12)(16 – 8/12) = 2945 ft2 2

2

kA total 5.2 Btu·in/h·ft ·°F 2945 ft q walls+ceiling = ---------------- 'T = ----------------------------------------------------------------------------- 68 – 46 °F L 8 in. = 42,114 Btu/h The shape factors for the corners and edges are in Table 2:

(6)

where m P Ac Wc Ac /P

= = = = =

hP e kA c fin perimeter fin cross-sectional area corrected fin/spine length = W + Ac /P d/4 for a cylindrical spine with diameter d = a/4 for an a × a square spine = yb = G/2 for a straight fin with thickness G

(7)

Heat Transfer

4.5 Table 3

Configuration Edge of two adjoining walls

Corner of three adjoining walls (inner surface at T1 and outer surface at T2 )

Isothermal rectangular block embedded in semiinfinite body with one face of block parallel to surface of body

Thin isothermal rectangular plate buried in semiinfinite medium

Multidimensional Conduction Shape Factors Shape Factor S, ft 0.54W

Restriction W > L/5

0.15L

L W 2.756L --------------------------------------- § ---- · 0.59 © d ¹ L >> d, W, H d ln § 1 + ----- · © W¹

SW ------------------------ln 4W e L 2SW ------------------------ln 4W e L

d = 0, W > L d >> W W>L

2SW -------------------------ln 2Sd e L

d > 2W W >> L

Cylinder centered inside square of length L

2SL --------------------------------ln 0.54W e R

L >> W W > 2R

Isothermal cylinder buried in semi-infinite medium

2SL ------------------------------–1 cosh d e R

L >> R

2SL -----------------------ln 2d e R

L >> R d > 3R

2SL ----------------------------------------------ln L e 2d L ln --- 1 – ----------------------R ln L e R

d >> R L >> d

Horizontal cylinder of length L midway between two infinite, parallel, isothermal surfaces

Isothermal sphere in semi-infinite medium

Isothermal sphere in infinite medium

2SL -----------------4d ln § ------ · ©R¹

4SR --------------------------1 – R e 2d

4SR

L >> d

4.6 Fig. 4

2009 ASHRAE Handbook—Fundamentals Efficiency of Annular Fins of Constant Thickness

Fig. 5

Efficiency of Annular Fins of Constant Thickness

Fig. 5 Efficiency of Annular Fins of Constant Thickness Efficiency of Annular Fins with Constant Metal Area for Heat Flow

Fig. 6 Efficiency of Annular Fins with Constant Metal Area for Heat Flow g

y

yp

p

Fig. 6 Efficiency of Several Types of Straight Fins

Fig. 7 Efficiency of Several Types of Straight Fins

Fig. 8 Efficiency of Four Types of Spines

Heat Transfer

4.7

Empirical Expressions for Fins on Tubes. Schmidt (1949) presents approximate, but reasonably accurate, analytical expressions (for computer use) for the fin efficiency of circular, rectangular, and hexagonal arrays of fins on round tubes, as shown in Figures 5, 9, and 10, respectively. Rectangular fin arrays are used for an in-line tube arrangement in finned-tube heat exchangers, and hexagonal arrays are used for staggered tubes. Schmidt’s empirical solution is given by tanh mr b Z I = ----------------------------mr b Z where rb is tube radius, m = given by

(8)

2h e kG , G = fin thickness, and Z is

Z = [(re/rb) – 1][1 + 0.35 ln(re/rb)]

where < and E are defined as previously, and M and L are defined by Figure 10 as a/2 or b (whichever is less) and 0.5 a e 2 2 + b 2 , respectively. For constant-thickness square fins on a round tube (L = M in Figure 9), the efficiency of a constant-thickness annular fin of the same area can be used. For more accuracy, particularly with rectangular fins of large aspect ratio, divide the fin into circular sectors as described by Rich (1966). Other sources of information on finned surfaces are listed in the References and Bibliography. Surface Efficiency. Heat transfer from a finned surface (e.g., a tube) that includes both fin area As and unfinned or prime area Ap is given by q = (hp Ap + Ihs As)(tr – te)

Assuming the heat transfer coefficients for the fin and prime surfaces are equal, a surface efficiency Is can be derived as

where re is the actual or equivalent fin tip radius. For circular fins, re/rb is the actual ratio of fin tip radius to tube radius. For rectangular fins (Figure 9), r e e r b = 1.28< E – 0.2

< = M e rb

E = LeMt1

where M and L are defined by Figure 9 as a/2 or b/2, depending on which is greater. For hexagonal fins (Figure 10), r e e r b = 1.27< E – 0.3

Fig. 8 Rectangular Tube Array

(9)

A p + IA s I s = --------------------A

(10)

where A = As + Ap is the total surface area, the sum of the fin and prime areas. The heat transfer in Equation (8) can then be written as tr – te q = I s hA t r – t e = ----------------------1 e I s hA

(11)

where 1/(IshA) is the finned surface resistance. Example 3. An aluminum tube with k = 1290 Btu·in/h·ft2 ·°F, ID = 1.8 in., and OD = 2 in. has circular aluminum fins G = 0.04 in. thick with an outer diameter of Dfin = 3.9 in. There are N ' = 76 fins per foot of tube length. Steam condenses inside the tube at ti = 392°F with a large heat transfer coefficient on the inner tube surface. Air at tf = 77°F is heated by the steam. The heat transfer coefficient outside the tube is 7 Btu/h·ft2 ·°F. Find the rate of heat transfer per foot of tube length. Solution: From Figure 5’s efficiency curve, the efficiency of these circular fins is W = D fin – OD e 2 = 3.9 – 2 e 2 = 0.95 in.

½ ° ° ° ¾I = 0.89 ° 2 h 7 Btu/h·ft · qF W ----------------- = 0.95 in. ----------------------------------------------------------------------------- = 0.49 °° 2 kG e 2 1290 Btu·in/h·ft ·qF 0.02 in. ¿

3.9 e 2 X e e X b = -------------- = 1.95 in. 2e2

Fig. 9 Rectangular Tube Array

The fin area for L = 1 ft is 2

Fig. 9 Hexagonal Tube Array

As = NcL × 2S(Dfin – OD 2)/4 = 1338 in2 = 9.29 ft2 The unfinned area for L = 1 ft is Ap = S × OD × L(1 – NcG) = S(2/12) ft × 1 ft(1 – 76 × 0.04/12) = 0.39 ft2 and the total area A = As + Ap = 9.68 ft2. Surface efficiency is IA f + A s I s = -------------------- = 0.894 A and resistance of the finned surface is 1 R s = ------------ = 0.0165 h·°F/Btu I s hA Tube wall resistance is ln OD e ID ln 2 e 1.8 R wall = ----------------------------- = ------------------------------------------------------------------------------------2SLk tube 2S 1 ft 1290 e 12 Btu·in/h·ft ·°F

Fig. 10 Hexagonal Tube Array

= 1.56 u 10

–4

h·°F/Btu

4.8

2009 ASHRAE Handbook—Fundamentals

The rate of heat transfer is then ti – tf q = ----------------------- = 18 ,912 Btu/h R s + R wall

V = material’s volume As = surface area exposed to convective and/or radiative heat transfer k = material’s thermal conductivity

The temperature is given by

Had Schmidt’s approach been used for fin efficiency, m =

2h e kG = 6.25 ft

–1

dt Mcp ----- = q net + q gen dW

rb = OD/2 = 1 in. = 0.0833 ft

Z = [(Dfin/OD) – 1] [1 + 0.35 ln(Dfin /OD)] = 1.172 tanh mr b Z I = ---------------------------- = 0.89 mr b Z the same I as given by Figure 5.

Contact Resistance. Fins can be extruded from the prime surface (e.g., short fins on tubes in flooded evaporators or water-cooled condensers) or can be fabricated separately, sometimes of a different material, and bonded to the prime surface. Metallurgical bonds are achieved by furnace-brazing, dip-brazing, or soldering; nonmetallic bonding materials, such as epoxy resin, are also used. Mechanical bonds are obtained by tension-winding fins around tubes (spiral fins) or expanding the tubes into the fins (plate fins). Metallurgical bonding, properly done, leaves negligible thermal resistance at the joint but is not always economical. Contact resistance of a mechanical bond may or may not be negligible, depending on the application, quality of manufacture, materials, and temperatures involved. Tests of plate-fin coils with expanded tubes indicate that substantial losses in performance can occur with fins that have cracked collars, but negligible contact resistance was found in coils with continuous collars and properly expanded tubes (Dart 1959). Contact resistance at an interface between two solids is largely a function of the surface properties and characteristics of the solids, contact pressure, and fluid in the interface, if any. Eckels (1977) modeled the influence of fin density, fin thickness, and tube diameter on contact pressure and compared it to data for wet and dry coils. Shlykov (1964) showed that the range of attainable contact resistances is large. Sonokama (1964) presented data on the effects of contact pressure, surface roughness, hardness, void material, and the pressure of the gas in the voids. Lewis and Sauer (1965) showed the resistance of adhesive bonds, and Clausing (1964) and Kaspareck (1964) gave data on the contact resistance in a vacuum environment.

Transient Conduction Often, heat transfer and temperature distribution under transient (i.e., varying with time) conditions must be known. Examples are (1) cold-storage temperature variations on starting or stopping a refrigeration unit, (2) variation of external air temperature and solar irradiation affecting the heat load of a cold-storage room or wall temperatures, (3) the time required to freeze a given material under certain conditions in a storage room, (4) quick-freezing objects by direct immersion in brines, and (5) sudden heating or cooling of fluids and solids from one temperature to another. Lumped Mass Analysis. Often, the temperature within a mass of material can be assumed to vary with time but be uniform within the mass. Examples include a well-stirred fluid in a thin-walled container, or a thin metal plate with high thermal conductivity. In both cases, if the mass is heated or cooled at its surface, the temperature can be assumed to be a function of time only and not location within the body. Such an approximation is valid if h V e As Bi = --------------------- d 0.1 k where Bi = Biot number h = surface heat transfer coefficient

(12)

where M = body mass cp = specific heat qgen = internal heat generation qnet = net heat transfer rate to substance (into substance is positive, and out of substance is negative)

Equation (12) applies to liquids and solids. If the material is a gas being heated or cooled at constant volume, replace cp with the constant-volume specific heat cv. The term qnet may include heat transfer by conduction, convection, or radiation and is the difference between the heat transfer rates into and out of the body. The term qgen may include a chemical reaction (e.g., curing concrete) or heat generation from a current passing through a metal. For a lumped mass M initially at a uniform temperature t0 that is suddenly exposed to an environment at a different temperature tf, the time taken for the temperature of the mass to change to tf is given by the solution of Equation (12) as tf – tf hA s W ln --------------- = – ----------t0 – tf Mc p

(13)

where M cp As h W tf t0 tf

= = = = = = = =

mass of solid specific heat of solid surface area of solid surface heat transfer coefficient time required for temperature change final solid temperature initial uniform solid temperature surrounding fluid temperature

Example 4. A copper sphere with diameter d = 0.0394 in. is to be used as a sensing element for a thermostat. It is initially at a uniform temperature of t0 = 69.8°F. It is then exposed to the surrounding air at tf = 68ºF. The combined heat transfer coefficient is h = 10.63 Btu/h·ft2 ·°F. Determine the time taken for the temperature of the sensing element to reach tf = 69.6°F. The properties of copper are U = 557.7 lbm/ft3

cp = 0.0920 Btu/lbm ·°F

k = 232 Btu/h·ft·°F

Solution: Bi = h(d/2)/k = 10.63(0.0394/12/2)/232 = 1 × 10–5, which is much less than 1. Therefore, lumped analysis is valid. M = U(4SR3/3) = 10.31 × 10–6 lbm As = Sd 2 = 0.00487 in2 Using Equation (13), W = 6.6 s.

Nonlumped Analysis. When the Biot number is greater than 0.1, variation of temperature with location within the mass is significant. One example is the cooling time of meats in a refrigerated space: the meat’s size and conductivity do not allow it to be treated as a lumped mass that cools uniformly. Nonlumped problems require solving multidimensional partial differential equations. Many common cases have been solved and presented in graphical forms (Jakob 1949, 1957; Myers 1971; Schneider 1964). In other cases, numerical methods (Croft and Lilley 1977; Patankar 1980) must be used. Estimating Cooling Times for One-Dimensional Geometries. When a slab of thickness 2L or a solid cylinder or solid sphere with outer radius rm is initially at a uniform temperature t1, and its surface is suddenly heated or cooled by convection with a fluid at tf, a mathematical solution is available for the temperature t as a function of

Heat Transfer

4.9

Table 4 Values of c1 and P1 in Equations (14) to (17) Slab

Solid Cylinder

Solid Sphere

Bi

c1

P1

c1

P1

c1

P1

0.5 1.0 2.0 4.0 6.0 8.0 10.0 30.0 50.0

1.0701 1.1191 1.1785 1.2287 1.2479 1.2570 1.2620 1.2717 1.2727

0.6533 0.8603 1.0769 1.2646 1.3496 1.3978 1.4289 1.5202 1.5400

1.1143 1.2071 1.3384 1.4698 1.5253 1.5526 1.5677 1.5973 1.6002

0.9408 1.2558 1.5995 1.9081 2.0490 2.1286 2.1795 2.3261 2.3572

1.1441 1.2732 1.4793 1.7202 1.8338 1.8920 1.9249 1.9898 1.9962

1.1656 1.5708 2.0288 2.4556 2.6537 2.7654 2.8363 3.0372 3.0788

location and time W. The solution is an infinite series. However, after a short time, the temperature is very well approximated by the first term of the series. The single-term approximations for the three cases are of the form Y = Y0 f (P 1n)

(14)

These solutions are presented graphically (McAdams 1954) by Gurnie-Lurie charts (Figures 11 to 13). The charts are also valid for Fo < 0.2. Example 5. Apples, approximated as 2.36 in. diameter solid spheres and initially at 86°F, are loaded into a chamber maintained at 32°F. If the surface heat transfer coefficient h = 2.47 Btu/h·ft2 ·°F, estimate the time required for the center temperature to reach t = 33.8°F. Properties of apples are U = 51.8 lbm/ft3 cp = 0.860 Btu/lbm ·°F

tc – t 32 – 33.8 Y = ------------- = ---------------------- = 0.0333 tc – t1 32 – 86 0 r n = ----- = ---------------- = 0 0.1967 rm

From Equations (14) and (17) with lim(sin 0/0) = 1, Y = Y0 = c1 exp(–P21Fo). For Bi = 1, from Table 4, c1= 1.2732 and P1 = 1.5708. Thus,

t0 – tf 2 Y 0 = -------------- = c 1 exp – P 1 Fo t1 – tf t0 = temperature at center of slab, cylinder, or sphere 2

= DW/L c = Fourier number = thermal diffusivity of solid = k/Ucp = L for slab, ro for cylinder, sphere = x/L for slab, r/rm for cylinder = coefficients that are functions of Bi = Biot number = hLc /k = function of P1n, different for each geometry = distance from midplane of slab of thickness 2L cooled on both sides U = density of solid cp = constant pressure specific heat of solid k = thermal conductivity of solid

The single term solution is valid for Fo > 0.2. Values of c1 and P1 are given in Table 4 for a few values of Bi, and Couvillion (2004) provides a procedure for calculating them. Expressions for c1 for each case, along with the function f (P1n), are as follows: Slab 4 sin P 1 c 1 = ------------------------------------2P 1 + sin 2P 1

(15)

Long solid cylinder f P1 n = J0 P1 n

J1 P1 2 c 1 = ------ u ------------------------------------------2 P1 J P + J 2 P 0

1

1

(16)

1

where J0 is the Bessel function of the first kind, order zero. It is available in math tables, spreadsheets, and software packages. J0(0) = 1. Solid sphere sin P 1 n f P 1 n = ---------------------P1 n

hr m 2.47 u 0.1967 e 2 - = --------------------------------------------- = 1 Bi = -------k 0.243

2 k 0.243 D = -------- = ------------------------------ = 0.00545 ft e h Uc p 51.8 u 0.860

t – tf Y = --------------t1 – tf

f P 1 n = cos P 1 n

rm= d/2 = 1.18 in. = 0.098 ft

Solution: Assuming that it will take a long time for the center temperature to reach 33.8°F, use the one-term approximation Equation (14). From the values given,

where

Fo D Lc n c1, P1 Bi f (P1n) x

k = 0.243 Btu/h·ft·°F

4 > sin P 1 – P 1 cos P 1 @ c 1 = ---------------------------------------------------------2P 1 – sin 2P 1

1 0.00545W 1 Y DW Fo = – ----- ln ----- = – ------------------2 ln 0.0333 = 1.476 = ------ = -----------------------------2 2 2 1.5708 0.1967 e 2 rm P1 c1 W = 2.62 h Note that Fo = 0.2 corresponds to an actual time of 1280 s.

Multidimensional Cooling Times. One-dimensional transient temperature solutions can be used to find the temperatures with twoand three-dimensional temperatures of solids. For example, consider a solid cylinder of length 2L and radius rm exposed to a fluid at tc on all sides with constant surface heat transfer coefficients h1 on the end surfaces and h2 on the cylindrical surface, as shown in Figure 14. The two-dimensional, dimensionless temperature Y(x1,r1,W) can be expressed as the product of two one-dimensional temperatures Y1(x1,W) u Y2(r1,W), where Y1 = dimensionless temperature of constant cross-sectional area slab at (x1,W), with surface heat transfer coefficient h1 associated with two parallel surfaces Y2 = dimensionless temperature of solid cylinder at (r1,W) with surface heat transfer coefficient h2 associated with cylindrical surface

From Figures 11 and 12 or Equations (14) to (16), determine Y1 at (x1/L, DW/L2, h1L/k) and Y2 at (r1/rm, DW/r2m, h2rm /k). Example 6. A 2.76 in. diameter by 4.92 in. high soda can, initially at t1 = 86°F, is cooled in a chamber where the air is at tf = 32°F. The heat transfer coefficient on all surfaces is h = 3.52 Btu/h·ft2 ·°F. Determine the maximum temperature in the can W = 1 h after starting the cooling. Assume the properties of the soda are those of water, and that the soda inside the can behaves as a solid body. Solution: Because the cylinder is short, the temperature of the soda is affected by the heat transfer rate from the cylindrical surface and end surfaces. The slowest change in temperature, and therefore the maximum temperature, is at the center of the cylinder. Denoting the dimensionless temperature by Y, Y = Ycyl u Ypl

(17)

where Ycyl is the dimensionless temperature of an infinitely long 2.76 in. diameter cylinder, and Ypl is the dimensionless temperature of a

4.10

2009 ASHRAE Handbook—Fundamentals

Fig. 10 Transient Temperatures for Infinite Slab

Fig. 11

Transient Temperatures for Infinite Slab, m = 1/Bi

Fig. 11 Transient Temperatures for Infinite Cylinder

Fig. 12 Transient Temperatures for Infinite Cylinder, m = 1/Bi

Heat Transfer

4.11

Fig. 12 Transient Temperatures for Spheres

Fig. 13

Transient Temperatures for Sphere, m = 1/Bi Bipl = hL/k = 3.52 × (4.92/12/2)/0.3406 = 2.119

Fig. 13 A Solid Cylinder Exposed to Fluid

Fopl = (5.46 × 10–3) × 1/(4.92/12/2)2 = 0.1299 Fopl < 0.2, so the one-term approximation is not valid. Using Figure 11, Ypl = 0.9705. Thus, Y = 0.572 u 0.9705 = 0.5551 = (t – tf)/(t1 – tf) Ÿ 62.0°F

Fig. 14 Solid Cylinder Exposed to Fluid 4.92 in. thick slab. Each of them is found from the appropriate Biot and Fourier number. For evaluating the properties of water, choose a temperature of 59°F and a pressure of 1 atm. The properties of water are U = 62.37 lbm /ft3

k = 0.3406 Btu/h·ft·°F

D = k/U = 5.46 × 10–3 ft2/h

cp = 1.0 Btu/lbm ·°F W=1h

1. Determine Ycyl at n = 0. Bicyl = hrm /k = 3.52 u (2.76/12/2) = 1.188 Focyl = DW/rm2 = (5.46 u 10–3 ) u 1/(2.76/12/2)2 = 0.4129 Focyl > 0.2, so use the one-term approximation with Equations (14) and (16). Ycyl = c1 exp(–P21Focyl )J0(0) Interpolating in Table 4 for Bicyl = 1.188, Pcyl = 1.3042, J0(0) = 1, ccyl = 1.237, Ycyl = 0.572. 2. Determine Ypl at n = 0.

Note: The solution may not be exact because convective motion of the soda during heat transfer has been neglected. The example illustrates the use of the technique. For well-stirred soda, with uniform temperature within the can, the lumped mass solution should be used.

THERMAL RADIATION Radiation, unlike conduction and convection, does not need a solid or fluid to transport energy from a high-temperature surface to a lower-temperature one. (Radiation is in fact impeded by such a material.) The rate of radiant energy emission and its characteristics from a surface depend on the underlying material’s nature, microscopic arrangement, and absolute temperature. The rate of emission from a surface is independent of the surfaces surrounding it, but the rate and characteristics of radiation incident on a surface do depend on the temperatures and spatial relationships of the surrounding surfaces.

Blackbody Radiation The total energy emitted per unit time per unit area of a black surface is called the blackbody emissive power Wb and is given by the Stefan-Boltzmann law: Wb = VT 4

(18)

4.12

2009 ASHRAE Handbook—Fundamentals

where V = 0.1712 × 10–8 Btu/h·ft2 ·°R4 is the Stefan-Boltzmann constant. Energy is emitted in the form of photons or electromagnetic waves of many different frequencies or wavelengths. Planck showed that the spectral distribution of the energy radiated by a blackbody is C1 W bO = ----------------------------------5 C 2 e OT O e – 1

(19)

where WbO = blackbody spectral (monochromatic) emissive power, Btu/h·ft3 O = wavelength, ft T = temperature, °R C1 = first Planck’s law constant = 1.1870 u 108 Btu·Pm4/h·ft2 C2 = second Planck’s law constant = 2.5896 u 104 Pm·°R

The blackbody spectral emissive power WbO is the energy emitted per unit time per unit surface area at wavelength O per unit wavelength band around O; that is, the energy emitted per unit time per unit surface area in the wavelength band dO is equal to WbOdO. The Stefan-Boltzmann law can be obtained by integrating Equation (19) over all wavelengths: f

³ WbO d O = VT

4

= Wb

Wien showed that the wavelength O max , at which the monochromatic emissive power is a maximum (not the maximum wavelength), is given by OmaxT = 5216 Pm·°R

(20)

Equation (20) is Wien’s displacement law; the maximum spectral emissive power shifts to shorter wavelengths as temperature increases, such that, at very high temperatures, significant emission eventually occurs over the entire visible spectrum as shorter wavelengths become more prominent. For additional details, see Incropera et al. (2007).

Actual Radiation The blackbody emissive power Wb and blackbody spectral emissive power WbO are the maxima at a given surface temperature. Actual surfaces emit less and are called nonblack. The emissive power W of a nonblack surface at temperature T radiating to the hemispherical region above it is given by W = HVT 4

(21)

where H is the total emissivity. The spectral emissive power WO of a nonblack surface is given by WO = HOWbO

(22)

where HO is the spectral emissivity, and WbO is given by Equation (19). The relationship between H and HO is given by f

W = HVT 4 =

or 1 H = --------VT 4

where D = absorptivity (fraction of incident radiant energy absorbed) U = reflectivity (fraction of incident radiant energy reflected) W = transmissivity (fraction of incident radiant energy transmitted)

This is also true for spectral values. For an opaque surface, W = 0 and U + D = 1. For a black surface, D = 1, U = 0, and W = 0. Kirchhoff’s law relates emissivity and absorptivity of any opaque surface from thermodynamic considerations; it states that, for any surface where incident radiation is independent of angle or where the surface emits diffusely, HO = DO. If the surface is gray, or the incident radiation is from a black surface at the same temperature, then H = D as well, but many surfaces are not gray. For most surfaces listed in Table 5, the total absorptivity for solar radiation is different from the total emissivity for low-temperature radiation, because HO and DO vary with wavelength. Much solar radiation is at short wavelengths. Most emissions from surfaces at moderate temperatures are at longer wavelengths. Platinum black and gold black are almost perfectly black and have absorptivities of about 98% in the infrared region. A small opening in a large cavity approaches blackbody behavior because most of the incident energy entering the cavity is absorbed by repeated reflection within it, and very little escapes the cavity. Thus, the absorptivity and therefore the emissivity of the opening are close to unity. Some flat black paints also exhibit emissivities of 98% over a wide range of conditions. They provide a much more durable surface than gold or platinum black, and are frequently used on radiation instruments and as standard reference in emissivity or reflectance measurements. Example 7. In outer space, the solar energy flux on a surface is 365 Btu/h·ft2. Two surfaces are being considered for an absorber plate to be used on the surface of a spacecraft: one is black, and the other is specially coated for a solar absorptivity of 0.94 and infrared emissivity of 0.1. Coolant flowing through the tubes attached to the plate maintains the plate at 612°R. The plate surface is normal to the solar beam. For each surface, determine the (1) heat transfer rate to the coolant per unit area of the plate, and (2) temperature of the surface when there is no coolant flow. Solution: For the black surface, H = D = 1, U = 0

Heat flux to coolant = Absorbed energy flux – Emitted energy flux = 365 – 240.2 = 124.8 Btu/h·ft2

f

³ HO WbO dO

D+U+W=1

Absorbed energy flux = 365 Btu/h·ft2 At Ts = 612°R, emitted energy flux = Wb = 0.1712 × 10–8 × 6124 = 240.2 Btu/h·ft2. In space, there is no convection, so an energy balance on the surface gives

f

³ WO d O = ³ HO WbO dO 0

this condition in some regions of the spectrum. The simplicity is desirable, but use care, especially if temperatures are high. Grayness is sometimes assumed because of the absence of information relating HO as a function of O. Emissivity is a function of the material, its surface condition, and its surface temperature. Table 5 lists selected values; Modest (2003) and Siegel and Howell (2002) have more extensive lists. When radiant energy reaches a surface, it is absorbed, reflected, or transmitted through the material. Therefore, from the first law of thermodynamics,

(23)

If HO does not depend on O, then, from Equation (23), H = HO, and the surface is called gray. Gray surface characteristics are often assumed in calculations. Several classes of surfaces approximate

For the special surface, use solar absorptivity to determine the absorbed energy flux, and infrared emissivity to calculate the emitted energy flux. Absorbed energy flux = 0.94 × 365 = 343.1 Btu/h·ft2 Emitted energy flux = 0.1 × 240.2 = 24.02 Btu/h·ft2 Heat flux to coolant = 343.1 – 24.02= 319.08 Btu/h·ft2

Heat Transfer

4.13

Table 5 Emissivities and Absorptivities of Some Surfaces Surface

Total Hemispherical Solar Emissivity Absorptivity*

Aluminum Foil, bright dipped Alloy: 6061 Roofing Asphalt

0.03 0.04 0.24 0.88

Brass Oxidized Polished Brick Concrete, rough

0.60 0.04 0.90 0.91

Copper Electroplated Black oxidized in Ebanol C Plate, oxidized

0.03 0.16 0.76

Glass Polished Pyrex Smooth Granite Gravel Ice Limestone

0.10 0.37

0.60 0.47 0.91

0.87 to 0.92 0.80 0.91 0.44 0.30 0.96 to 0.97 0.92

Marble Polished or white Smooth Mortar, lime Nickel Electroplated Solar absorber, electro-oxidized on copper Paints Black Parsons optical, silicone high heat, epoxy Gloss Enamel, heated 1000 h at 710°F Silver chromatone White Acrylic resin Gloss Epoxy Paper, roofing or white Plaster, rough Refractory Sand Sandstone, red Silver, polished Snow, fresh Soil Water White potassium zirconium silicate

• All surfaces are gray or black • Emission and reflection are diffuse (i.e., not a function of direction) • Properties are uniform over the surfaces • Absorptivity equals emissivity and is independent of temperature of source of incident radiation • Material located between radiating surfaces neither emits nor absorbs radiation

Fik Ai = Fki Ak

(24a)

Decomposition relation. For three surfaces i, j, and k, with Aij indicating one surface with two parts denoted by Ai and Aj,

0.03 0.05 to 0.11

0.22 0.85

0.87 to 0.92

0.94 to 0.97

0.90 0.85 0.85 0.88 to 0.86 0.89 0.90 to 0.94 0.75 0.59 0.02 0.82 0.94 0.90 0.87

The foregoing discussion addressed emission from a surface and absorption of radiation leaving surrounding surfaces. Before radiation exchange among a number of surfaces can be addressed, the amount of radiation leaving one surface that is incident on another must be determined. The fraction of all radiant energy leaving a surface i that is directly incident on surface k is the angle factor Fik (also known as view factor, shape factor, and configuration factor). The angle factor from area Ak to area Aj, Fki, is similarly defined, merely by interchanging the roles of i and k. The following relations assume

These assumptions greatly simplify problems, and give good approximate results in many cases. Some of the relations for the angle factor are given below. Reciprocity relation.

0.89 to 0.92 0.56 0.90

0.90 0.80 0.24

Angle Factor

Ak Fk-ij = Ak Fk-i + Ak Fk-j

(24b)

Aij Fij-k = Ai Fi-k + Aj Fj-k

(24c)

Law of corresponding corners. This law is discussed by Love (1968) and Suryanarayana (1995). Its use is shown in Example 8. Summation rule. For an enclosure with n surfaces, some of which may be inside the enclosure, n

¦ Fik

(24d)

= 1

k=1

0.20 0.26 0.25

Note that a concave surface may “see itself,” and Fii z 0 for such a surface. Numerical values of the angle factor for common geometries are given in Figure 15. For equations to compute angle factors for many configurations, refer to Siegel and Howell (2002). Example 8. A picture window, 10 ft long and 6 ft high, is installed in a wall as shown in Figure 16. The bottom edge of the window is on the floor, which is 20 by 33.3 ft. Denoting the window by 1 and the floor by 234, find F234-1. Solution: From decomposition rule,

0.13 0.98 0.13

A234 F234-1 = A2 F2-1 + A3 F3-1 + A4 F4-1 By symmetry, A2 F2-1 = A4 F4-1 and A234-1 = A3 F3-1 + 2A2 F2-1. A23 F23-15 = A2 F2-1+ A2F2-5

Source: Mills (1999) *Values are for extraterrestrial conditions, except for concrete, snow, and water.

+ A3F3-1 + A3F3-5 From the law of corresponding corners, A2 F2-1 = A3 F3-5, so therefore A23 F23-5 = A2 F2-5 + A3 F3-1 + 2A2 F2-1. Thus,

Without coolant flow, heat flux to the coolant is zero. Therefore, absorbed energy flux = emitted energy flux. For the black surface, 365 = 0.1714 u 10–8u Ts4 Ÿ Ts = 679.3°R For the special surface, 0.94 u 365 = 0.1 u 0.1714 u 10–8u Ts4 Ÿ Ts = 1189°R

A234 F234-1 = A3 F3-1 + A23 F23-15 – A2 F2-5 – A3 F3-1 = A23 F23-15 – A2 F2-5 A234 = 666 ft2

A23 = 499.5 ft2

A2 = 166.5 ft2

From Figure 15A with Y/X = 33.3/20 = 1.67 and Z/X = 6/15 = 0.4, F2315 = 0.061. With Y/X = 33.3/5 = 6.66 and Z/X = 6/5 = 1.2, F25 = 0.041. Substituting the values, F234-1 = 1/666(499.5 × 0.061 – 166.5 × 0.041) = 0.036.

4.14 Fig. 14

2009 ASHRAE Handbook—Fundamentals Radiation Angle Factors for Various Geometries

Fig. 15 Radiation Angle Factors for Various Geometries

Fig. 15 Diagram for Example 5

Fig. 16 Diagram for Example 8

Radiant Exchange Between Opaque Surfaces A surface Ai radiates energy at a rate independent of its surroundings. It absorbs and reflects incident radiation from surrounding surfaces at a rate dependent on its absorptivity. The net heat transfer rate qi is the difference between the rate radiant energy leaves the surface and the rate of incident radiant energy; it is the rate at which energy must be supplied from an external source to maintain the surface at a constant temperature. The net radiant heat flux from a surface Ai is denoted by qsi . Several methods have been developed to solve specific radiant exchange problems. The radiosity method and thermal circuit method are presented here. Consider the heat transfer rate from a surface of an n-surface enclosure with an intervening medium that does not participate in radiation. All surfaces are assumed gray and opaque. The radiosity Ji is the total rate of radiant energy leaving surface i per unit area (i.e., the sum of energy flux emitted and energy flux reflected): Ji = HiWb + UiGi

(25)

Heat Transfer

4.15

where Gi is the total rate of radiant energy incident on surface i per unit area. For opaque gray surfaces, the reflectivity is

The temperature of the surface is then § W bi·1 e 4 T i = ¨ ---------¸ © V ¹

Ui = 1 – Di = 1 – Hi Thus, Ji = HiWb + (1– Hi)Gi

(26)

Note that for a black surface, H = 1, U = 0, and J = Wb . The net radiant energy transfer qi is the difference between the total energy leaving the surface and the total incident energy: qi = Ai(Ji – Gi)

(27)

Eliminating Gi between Equations (26) and (27), W bi – J i q i = ------------------------------ 1 – Hi e Hi Ai

(28)

Radiosity Method. Consider an enclosure of n isothermal surfaces with areas of A1, A2, …, An, and emissivities of H1, H2, …, Hn, respectively. Some may be at uniform but different known temperatures, and the remaining surfaces have uniform but different and known heat fluxes. The radiant energy flux incident on a surface Gi is the sum of the radiant energy reaching it from each of the n surfaces: n

Gi Ai =

n

n

¦ Fki Jk Ak = ¦ Fik Jk Ai

k=1

or G i =

k=1

¦ Fik Jk

(29)

k=1

Substituting Equation (29) into Equation (26), n

J i = H i W bi + 1 – H i ¦ F ik J k

(30)

k=1

(34)

A surface in radiant balance is one for which radiant emission is balanced by radiant absorption (i.e., heat is neither removed from nor supplied to the surface). These are called reradiating, insulated, or refractory surfaces. For these surfaces, qi = 0 in Equation (31). After solving for the radiosities, Wbi can be found by noting that qi = 0 in Equation (33) gives Wbi = Ji. Thermal Circuit Method. Another method to determine the heat transfer rate is using thermal circuits for radiative heat transfer rates. Heat transfer rates from surface i to surface k and surface k to surface i, respectively, are given by qi-k = Ai Fi-k(Ji – Jk )

and

qk-i = Ak Fik-i (Jk – Ji )

Using the reciprocity relation Ai Fi-k = Ak Fk-i, the net heat transfer rate from surface i to surface k is Ji – Jk q ik = q i-k – q k-i = A i F i-k J i – J k = --------------------1 e A i F i-k

(35)

Equations (28) and (35) are analogous to the current in a resistance, with the numerators representing a potential difference and the denominator representing a thermal resistance. This analogy can be used to solve radiative heat transfer rates among surfaces, as illustrated in Example 9. Using angle factors and radiation properties as defined assumes that the surfaces are diffuse radiators, which is a good assumption for most nonmetals in the infrared region, but poor for highly polished metals. Subdividing the surfaces and considering the variation of radiation properties with angle of incidence improves the approximation but increases the work required for a solution. Also note that radiation properties, such as absorptivity, have significant uncertainties, for which the final solutions should account.

Combining Equations (30) and (28), q J i = -----i + Ai

n

¦ Fik Jk

(31)

k=1

Note that in Equations (30) and (31), the summation includes surface i. Equation (30) is for surfaces with known temperatures, and Equation (31) for those with known heat fluxes. An opening in the enclosure is treated as a black surface at the temperature of the surroundings. The resulting set of simultaneous, linear equations can be solved for the unknown Ji s. Once the radiosities (Ji s) are known, the net radiant energy transfer to or from each surface or the emissive power, whichever is unknown is determined. For surfaces where Ebi is known and qi is to be determined, use Equation (28) for a nonblack surface. For a black surface, Ji = Wbi and Equation (31) can be rearranged to give q -----i = W bi – Ai

Example 9. Consider a 13.1 ft wide, 16.4 ft long, 8.2 ft high room as shown in Figure 17. Heating pipes, embedded in the ceiling (1), keep its temperature at 104°F. The floor (2) is at 86°F, and the side walls (3) are at 64°F. The emissivity of each surface is 0.8. Determine the net radiative heat transfer rate to/from each surface. Solution: Consider the room as a three-surface enclosure. The corresponding thermal circuit is also shown. The heat transfer rates are found after finding the radiosity of each surface by solving the thermal circuit. From Figure 15A, F1-2 = F2-1 = 0.376

Fig. 16 Diagrams for Example 9

n

¦ Fik Jk

(32)

k=1

At surfaces where qi is known and Ebi is to be determined, rearrange Equation (28): § 1 – H i· E bi = J i + q i ¨ -------------¸ © Ai Hi ¹

(33) Fig. 17

Diagrams for Example 9

4.16

2009 ASHRAE Handbook—Fundamentals Table 6

From the summation rule, F1-1 + F1-2 + F1-3 = 1. With F1-1 = 0,

Path Length, CO2, % by Volume 0.1 0.3 ft

F1-3 = 1 – F1-2 = 0.624 = F2-3 1–H 1 – 0.8 - = 0.00116 ft–2 = R R1 = -------------1- = -------------------------2 A1 H1 215.3 u 0.8

10 100 1000

1–H 1 – 0.8 - = 5.16 × 10–4 ft–2 R3 = -------------3- = -------------------------A3 H3 484.4 u 0.8

1 1 R13 = ---------------- = --------------------------------- = 7.44 × 10–3 ft–2 = R23 A 1 F 1-3 215.3 u 0.624

Surface 2:

W b2 – J 2 J 1 – J 2 J 3 – J 2 --------------------- + ---------------- + ---------------- = 0 R2 R 12 R 23

Surface 3:

W b3 – J 3 J 1 – J 3 J 2 – J 3 --------------------- + ---------------- + ---------------- = 0 R3 R 13 R 23

W b1 = 0.1712 u 10

–8

W b2 = 152.2 Btu/h·ft

4

u 564 = 173.2 Btu/h·ft 2

2

W b3 = 129.1 Btu/h·ft

2

Substituting the values and solving for J1, J2, and J3, J1 = 166.3 Btu/h·ft2

J2 = 150.7 Btu/h·ft2

J3 = 132.8 Btu/h·ft2

W b1 – J 1 173.2 – 166.3 q 1 = -------------------- = --------------------------------- = 5948 Btu/h 0.00116 R1 q 2 = 1293 Btu/h

q 3 = – 7241 Btu/h

Radiation in Gases Monatomic and diatomic gases such as oxygen, nitrogen, hydrogen, and helium are essentially transparent to thermal radiation. Their absorption and emission bands are confined mainly to the ultraviolet region of the spectrum. The gaseous vapors of most compounds, however, have absorption bands in the infrared region. Carbon monoxide, carbon dioxide, water vapor, sulfur dioxide, ammonia, acid vapors, and organic vapors absorb and emit significant amounts of energy. Radiation exchange by opaque solids may be considered a surface phenomenon unless the material is transparent or translucent, though radiant energy does penetrate into the material. However, the penetration depths are small. Penetration into gases is very significant. Beer’s law states that the attenuation of radiant energy in a gas is a function of the product pg L of the partial pressure of the gas and the path length. The monochromatic absorptivity of a body of gas of thickness L is then D OL = 1 – e –D O L

0.06 0.12 0.19

10

50

100

0.09 0.16 0.23

0.06 0.22 0.47

0.17 0.39 0.64

0.22 0.47 0.70

Relative Humidity, %

Hg

10 50 75

0.10 0.19 0.22

Estimated emissivity for carbon dioxide and water vapor in air at 75°F is a function of concentration and path length (Table 6). Values are for an isothermal hemispherically shaped body of gas radiating at its surface. Among others, Hottel and Sarofim (1967), Modest (2003), and Siegel and Howell (2002) describe geometrical calculations in their texts on radiation heat transfer. Generally, at low values of pg L, the mean path length L (or equivalent hemispherical radius for a gas body radiating to its surrounding surfaces) is four times the mean hydraulic radius of the enclosure. A room with a dimensional ratio of 1:1:4 has a mean path length of 0.89 times the shortest dimension when considering radiation to all walls. For a room with a dimensional ratio of 1:2:6, the mean path length for the gas radiating to all surfaces is 1.2 times the shortest dimension. The mean path length for radiation to the 2 by 6 face is 1.18 times the shortest dimension. These values are for cases where the partial pressure of the gas times the mean path length approaches zero ( pg L | 0). The factor decreases with increasing values of pg L. For average rooms with approximately 8 ft ceilings and relative humidity ranging from 10 to 75% at 75°F, the effective path length for carbon dioxide radiation is about 85% of the ceiling height, or 6.8 ft. The effective path length for water vapor is about 93% of the ceiling height, or 7.4 ft. The effective emissivity of the water vapor and carbon dioxide radiating to the walls, ceiling, and floor of a room 16 by 48 ft with 8 ft ceilings is in Table 7. Radiation heat transfer from the gas to the walls is then

Performing a balance on each of the three Ji nodes gives W b1 – J 1 J 2 – J 1 J 3 – J 1 -------------------- + ---------------- + ---------------- = 0 R1 R 12 R 13

0.03 0.09 0.16

Relative Humidity, % 1.0

Table 7 Emissivity of Moist Air and CO2 in Typical Room

1 1 R12 = ---------------- = --------------------------------- = 0.01235 ft–2 A 1 F 1-2 215.3 u 0.376

Surface 1:

Emissivity of CO2 and Water Vapor in Air at 75°F

(36)

Because absorption occurs in discrete wavelength bands, the absorptivities of all the absorption bands must be summed over the spectral region corresponding to the temperature of the blackbody radiation passing through the gas. The monochromatic absorption coefficient DO is also a function of temperature and pressure of the gas; therefore, detailed treatment of gas radiation is quite complex.

q = VA w H g T g4 – T w4

(37)

The preceding discussion indicates the importance of gas radiation in environmental heat transfer problems. In large furnaces, gas radiation is the dominant mode of heat transfer, and many additional factors must be considered. Increased pressure broadens the spectral bands, and interaction of different radiating species prohibits simple summation of emissivity factors for the individual species. Nonblackbody conditions require separate calculations of emissivity and absorptivity. Hottel and Sarofim (1967) and McAdams (1954) discuss gas radiation more fully.

THERMAL CONVECTION Convective heat transfer coefficients introduced previously can be estimated using correlations presented in this section.

Forced Convection Forced-air coolers and heaters, forced-air- or water-cooled condensers and evaporators, and liquid suction heat exchangers are examples of equipment that transfer heat primarily by forced convection. Although some generalized heat transfer coefficient correlations have been mathematically derived from fundamentals, they are usually obtained from correlations of experimental data. Most correlations for forced convection are of the form

Heat Transfer

4.17 hL c Nu = -------- = f Re Lc Pr k

where Nu h Lc ReLc V Pr cp P U Q k

= = = = = = = = = = =

Nusselt number convection heat transfer coefficient characteristic length UVLc /P=VLc /Q fluid velocity Prandtl number = cp P/k fluid specific heat fluid dynamic viscosity fluid density kinematic viscosity = P/U fluid conductivity

Fluid velocity and characteristic length depend on the geometry. External Flow. When fluid flows over a flat plate, a boundary layer forms adjacent to the plate. The velocity of fluid at the plate surface is zero and increases to its maximum free-stream value at the edge of the boundary layer (Figure 18). Boundary layer formation is important because the temperature change from plate to fluid occurs across this layer. Where the boundary layer is thick, thermal resistance is great and the heat transfer coefficient is small. Flow within the boundary layer immediately downstream from the leading edge is laminar. As flow proceeds along the plate, the laminar boundary layer increases in thickness to a critical value. Then, turbulent eddies develop in the boundary layer, except in a thin laminar sublayer adjacent to the plate. The boundary layer beyond this point is turbulent. The region between the breakdown of the laminar boundary layer and establishment of the turbulent boundary layer is the transition region. Because turbulent eddies greatly enhance heat transport into the main stream, the heat transfer coefficient begins to increase rapidly through the transition region. For a flat plate with a smooth leading edge, the turbulent boundary layer starts at distance xc from the leading edge where the Reynolds number Re = Vxc /Q is in the range 300,000 to 500,000 (in some cases, higher). In a plate with a blunt front edge or other irregularities, it can start at much smaller Reynolds numbers. Internal Flow. For tubes, channels, or ducts of small diameter at sufficiently low velocity, the laminar boundary layers on each wall grow until they meet. This happens when the Reynolds number based on tube diameter, Re = Vavg D/Q, is less than 2000 to 2300. Beyond this point, the velocity distribution does not change, and no transition to turbulent flow takes place. This is called fully developed laminar flow. When the Reynolds number is greater than 10,000, the boundary layers become turbulent before they meet, and fully developed turbulent flow is established (Figure 19). If flow is turbulent, three different flow regions exist. Immediately next to the wall is a laminar sublayer, where heat transfer occurs by thermal conduction; next is a transition region called the buffer layer, where

both eddy mixing and conduction effects are significant; the final layer, extending to the pipe’s axis, is the turbulent region, where the dominant mechanism of transfer is eddy mixing. In most equipment, flow is turbulent. For low-velocity flow in small tubes, or highly viscous liquids such as glycol, the flow may be laminar. The characteristic length for internal flow in pipes and tubes is the inside diameter. For noncircular tubes or ducts, the hydraulic diameter Dh is used to compute the Reynolds and Nusselt numbers. It is defined as Cross-sectional area for flow D h = 4 u --------------------------------------------------------------------Total wetted perimeter

(38)

Inserting expressions for cross-sectional area and wetted perimeter of common cross sections shows that the hydraulic diameter is equal to • • • •

The diameter of a round pipe Twice the gap between two parallel plates The difference in diameters for an annulus The length of the side for square tubes or ducts

Table 8 lists various forced-convection correlations. In general, the Nusselt number is determined by the flow geometry, Reynolds number, and Prandtl number. One often useful form for internal flow is known as Colburn’s analogy: fF Nu j = -------------------- = ---1e3 2 RePr where fF is the Fanning friction factor and j is the Colburn j-factor. It is related to the friction factor by the interrelationship of the transport of momentum and energy in turbulent flow. These factors are plotted in Figure 20. Fig. 18 Boundary Layer Buildup in Entrance Region of Tube or Channel

Fig. 19

Boundary Layer Build-up in Entrance Region of Tube or Channel

Fig. 19 Typical Dimensionless Representation of Forced-Convection Heat Transfer

Fig. 17 External Flow Boundary Layer Build-up (Vertical Scale Magnified)

Fig. 18

External Flow Boundary Layer Build-up (Vertical Scale Magnified)

Fig. 20

Typical Dimensionless Representation of ForcedConvection Heat Transfer

4.18

2009 ASHRAE Handbook—Fundamentals

Fig. 20 Heat Transfer Coefficient for Turbulent Flow of Water Inside Tubes

Fig. 21 Regimes of Free, Forced, and Mixed Convection— Flow in Horizontal Tubes

Fig. 22 Regimes of Free, Forced, and Mixed Convection— Flow in Horizontal Tubes Fig. 21 Heat Transfer Coefficient for Turbulent Flow of Water Inside Tubes Simplified correlations for atmospheric air are also given in Table 8. Figure 21 gives graphical solutions for water. With a uniform tube surface temperature and heat transfer coefficient, the exit temperature can be calculated using ts – te hA - = – --------ln -----------ts – ti m· c p

(39)

where ti and te are the inlet and exit bulk temperatures of the fluid, ts is the pipe/duct surface temperature, and A is the surface area inside the pipe/duct. The convective heat transfer coefficient varies in the direction of flow because of the temperature dependence of the fluid properties. In such cases, it is common to use an average value of h in Equation (39) computed either as the average of h evaluated at the inlet and exit fluid temperatures or evaluated at the average of the inlet and exit temperatures. With uniform surface heat flux qs, the temperature of fluid at any section can be found by applying the first law of thermodynamics: m· cp(t – ti) = qsA

(40)

The surface temperature can be found using qs = h(ts – t)

(41)

With uniform surface heat flux, surface temperature increases in the direction of flow along with the fluid. Natural Convection. Heat transfer with fluid motion resulting solely from temperature differences (i.e., from temperaturedependent density and gravity) is natural (free) convection. Naturalconvection heat transfer coefficients for gases are generally much lower than those for forced convection, and it is therefore important not to ignore radiation in calculating the total heat loss or gain. Radiant transfer may be of the same order of magnitude as natural convection, even at room temperatures; therefore, both modes must be considered when computing heat transfer rates from people, furniture, and so on in buildings (see Chapter 9). Natural convection is important in a variety of heating and refrigeration equipment, such as (1) gravity coils used in high-humidity cold-storage rooms and in roof-mounted refrigerant condensers, (2) the evaporator and condenser of household refrigerators, (3) baseboard radiators and convectors for space heating, and (4) cooling panels for air conditioning. Natural convection is also involved in heat loss or gain to equipment casings and interconnecting ducts and pipes.

Consider heat transfer by natural convection between a cold fluid and a hot vertical surface. Fluid in immediate contact with the surface is heated by conduction, becomes lighter, and rises because of the difference in density of the adjacent fluid. The fluid’s viscosity resists this motion. The heat transfer rate is influenced by fluid properties, temperature difference between the surface at ts and environment at tf , and characteristic dimension Lc . Some generalized heat transfer coefficient correlations have been mathematically derived from fundamentals, but they are usually obtained from correlations of experimental data. Most correlations for natural convection are of the form hL c Nu = -------- = f Ra Lc Pr k where Nu H Lc K RaLc 't g E Q D Pr

= = = = = = = = = = =

Nusselt number convection heat transfer coefficient characteristic length fluid thermal conductivity Rayleigh number = gE 'tL3c /QD _ts – tf | gravitational acceleration coefficient of thermal expansion fluid kinematic viscosity = P/U fluid thermal diffusivity = k/Ucp Prandtl number = Q/D

Correlations for a number of geometries are given in Table 9. Other information on natural convection is available in the Bibliography under Heat Transfer, General. Comparison of experimental and numerical results with existing correlations for natural convective heat transfer coefficients indicates that caution should be used when applying coefficients for (isolated) vertical plates to vertical surfaces in enclosed spaces (buildings). Altmayer et al. (1983) and Bauman et al. (1983) developed improved correlations for calculating natural convective heat transfer from vertical surfaces in rooms under certain temperature boundary conditions. Natural convection can affect the heat transfer coefficient in the presence of weak forced convection. As the forced-convection effect (i.e., the Reynolds number) increases, “mixed convection” (superimposed forced-on-free convection) gives way to pure forced convection. In these cases, consult other sources [e.g., Grigull et al. (1982); Metais and Eckert (1964)] describing combined free and forced convection, because the heat transfer coefficient in the mixed-convection region is often larger than that calculated based on the natural- or forced-convection calculation alone. Metais and Eckert (1964) summarize natural-, mixed-, and forced-convection regimes for vertical

Heat Transfer

4.19 Table 8 Forced-Convection Correlations

I. General Correlation

Nu = f (Re, Pr)

II. Internal Flows for Pipes and Ducts: Characteristic length = D, pipe diameter, or Dh, hydraulic diameter. UV avg D h m· D h QD h 4Q 4m· Re = --------------------where m· = mass flow rate, Q = volume flow rate, Pwet = wetted perimeter, - = ----------- = ----------- = -------------- = -------------QP wet A = cross-sectional area, and Q = kinematic viscosity P Ac P Ac Q PP wet (P/U). c f Nu Colburn’s analogy ------------------- = --1/3 2 Re Pr 1/3 0.14 P Re Pr L Re Pr P 0.42 -· ---- ---------------- § ----- · Nu = 1.86 § ----------------· § ---Laminar : Re < 2300 © L e D ¹ © Ps ¹ D 8 © Ps ¹

(T8.1) a

(T8.2)

Developing

0.065 D e L Re Pr Nu = 3.66 + -------------------------------------------------------------2/3 1 + 0.04 > D e L Re Pr @

Fully developed, round

Nu = 3.66

Uniform surface temperature

(T8.4a)

Nu = 4.36

Uniform heat flux

(T8.4b)

Nu = 0.023 Re4/5Pr 0.4

Heating fluid Re t 10,000

(T8.5a)b

Fully developed

Nu = 0.023 Re4/5Pr 0.3

(T8.5b)b

Evaluate properties at bulk temperature tb except Ps and ts at surface temperature

Cooling fluid Re t 10,000

f s e 2 Re – 1000 Pr D 2/3 - 1 + § ---- · Nu = --------------------------------------------------------------------1/2 2/3 ©L¹ 1 + 12.7 f s e 2 Pr – 1

1 f s = -----------------------------------------------2 1.58 ln Re – 3.28

For fully developed flows, set D/L = 0.

Multiply Nu by (T/Ts)0.45 for gases and by (Pr/Prs)0.11 for liquids

Turbulent:

Nu = 0.027 Re

4/5

Pr

(T8.3)

P 0.14 ----- · © Ps ¹

1/3 §

c

(T8.6)

a

For viscous fluids

(T8.7)

For noncircular tubes, use hydraulic mean diameter Dh in the equations for Nu for an approximate value of h. III. External Flows for Flat Plate: Characteristic length = L = length of plate. Re = VL/Q. All properties at arithmetic mean of surface and fluid temperatures. Nu = 0.332 Re1/2Pr 1/3

Laminar boundary layer: Re < 5 × 105

Nu = 0.664

Re1/2Pr 1/3 Re4/5Pr 1/3

Local value of h

(T8.8)

Average value of h

(T8.9)

Local value of h

(T8.10)

Nu = 0.037 Re4/5Pr 1/3

Average value of h

(T8.11)

Nu = (0.37 Re4/5 – 871)Pr 1/3

Average value Rec = 5 × 105

(T8.12)

Turbulent boundary layer: Re > 5 × 105

Nu = 0.0296

Turbulent boundary layer beginning at leading edge: All Re Laminar-turbulent boundary layer: Re > 5 × 105

IV. External Flows for Cross Flow over Cylinder: Characteristic length = D = diameter. Re = VD/Q. All properties at arithmetic mean of surface and fluid temperatures. 1/2

1/3

5/8 0.62 Re Pr Re Nu = 0.3 + ------------------------------------------------ 1 + § ------------------- · © 282 ,000 ¹ 2/3 1/4 > 1 + 0.4 e Pr @

Average value of h

4/5

(T8.14)

d

V. Simplified Approximate Equations: h is in Btu/h·ft2 ·°F, V is in ft/s, D is in ft, and t is in °F. Flows in pipes Re > 10,000

Atmospheric air (32 to 400°F): h = (0.3323 – 2.384 × 10–4t)V 0.8/D 0.2 Water (5 to 400°F): h = (67.25 + 1.146t)V 0.8/D 0.2 Water (40 to 220°F: h = (91.25 + 1.004t)V 0.8/D 0.2 (McAdams 1954)

Flow over cylinders

Atmospheric air: 32°F < t < 400°F, where t = arithmetic mean of air and surface temperature. h = 0.5198V 0.471/D 0.529

(T8.15a)e (T8.15b)e (T8.15c)g

35 < Re < 5000

(T8.16a)

5000 < Re < 50,000

(T8.16b)

h = (80.36 + 0.2107t)V 0.471/D 0.529

35 < Re < 5000

(T8.17a)

h = (108.9 + 0.6555t)V 0.633/D 0.367

5000 < Re < 50,000

(T8.17b)f

h = (0.5477 – 1.832 ×

10–4t)V 0.633/D 0.367

Water: 40°F < t < 195°F, where t = arithmetic mean of water and surface temperature.

Sources: aSieder gMcAdams

and Tate (1936), (1954).

bDittus

and Boelter (1930),

cGnielinski

(1990),

dChurchill

and Bernstein (1977),

eBased

on Nu = 0.023

Re 4/5Pr 1/3, fBased

on Morgan (1975).

4.20

2009 ASHRAE Handbook—Fundamentals Table 9 Natural Convection Correlations

I. General relationships

Nu = f (Ra, Pr) or f (Ra)

Characteristic length depends on geometry

(T9.1) 2

Ra = Gr Pr

3

cp P Pr = --------- ' t = t s – t f k

gEU 'T L Gr = -------------------------------2 P

II. Vertical plate 1/4

0.67Ra Nu = 0.68 + -------------------------------------------------------9/16 4/9 > 1 + 0.492 e Pr @

ts = constant

Characteristic dimension: L = height Properties at (ts + tf)/2 except E at tf

1/6 ­ ½2 0.387Ra Nu = ® 0.825 + ----------------------------------------------------------¾ 9/16 8/27 ¿ ¯ > 1 + 0.492 e Pr @

qss = constant 1/6 ­ ½2 0.387Ra Characteristic dimension: L = height Nu = ® 0.825 + ----------------------------------------------------------- ¾ 8/27 9/16 Properties at ts, L/2 – tf except E at tf ¯ ¿ > 1 + 0.437 e Pr @ Equations (T9.2) and (T9.3) can be used for vertical cylinders if D/L > 35/Gr1/4 where D is diameter and L is axial length of cylinder III. Horizontal plate Characteristic dimension = L = A/P, where A is plate area and P is perimeter Properties of fluid at (ts + tf)/2 Downward-facing cooled plate and upward-facing heated plate Nu = 0.96 Ra1/6 Nu = 0.59 Ra1/4 Nu = 0.54 Ra1/4 Nu = 0.15 Ra1/3 Downward-facing heated plate and upward-facing cooled plate Nu = 0.27 Ra1/4 IV. Horizontal cylinder Characteristic length = d = diameter Properties of fluid at (ts + tf)/2 except E at tf V. Sphere

1/6 ­ ½2 0.387 Ra Nu = ® 0.6 + ----------------------------------------------------------¾ 8/27 9/16 ¯ ¿ > 1 + 0.559 e Pr @

10–1 < Ra < 109

(T9.2)a

109 < Ra < 1012

(T9.3)a

10–1 < Ra < 1012

(T9.4)a

1 < Ra < 200 200 < Ra < 104 2.2 × 104 < Ra < 8 × 106 8 × 106 < Ra < 1.5 × 109 105 < Ra < 1010

(T9.5) b (T9.6) b (T9.7) b (T9.8) b (T9.9)

b

109 < Ra < 1013

(T9.10)c

0.589 Ra Nu = 2 + -------------------------------------------------------9/16 4/9 > 1 + 0.469 e Pr @

Ra < 1011

(T9.11)d

§ 3.3 · 2 ------- = ln ¨ 1 + -----------n-¸ Nu © cRa ¹

10–8 < Ra < 106

(T9.12)e

1/4

Characteristic length = D = diameter Properties at (ts + tf)/2 except E at tf VI. Horizontal wire Characteristic dimension = D = diameter Properties at (ts + tf)/2 VII. Vertical wire

c (Ra D/L)0.25 > 2 × 10–3

Characteristic dimension = D = diameter; L = length of wire

Nu = c (Ra D/L)0.25 + 0.763 c (1/6)(Ra D/L)(1/24)

Properties at (ts + tf)/2

0.671 In both Equations (T9.12) and (T9.13), c = --------------------------------------------------------------- and 9/16 4/9 1 0.492 e Pr > + @ 1 n = 0.25 + ------------------------------------0.175 10 + 5 Ra

(T9.13)e

VIII. Simplified equations with air at mean temperature of 70°F: h is in Btu/h·ft2 ·°F, L and D are in ft, and 't is in °F. -----t · h = 0.272 §' ©L ¹

Vertical surface

h = 0.182 ' t

h = 0.178 ' t Sources:

and Chu (1975a),

bLloyd

and Moran (1974), Goldstein et al. (1973),

and horizontal tubes. Figure 22 shows the approximate limits for horizontal tubes. Other studies are described by Grigull et al. (1982). Example 10. Chilled water at 41°F flows inside a freely suspended 0.7874 in. OD pipe at a velocity of 8.2 fps. Surrounding air is at 86°F, 70% rh. The pipe is to be insulated with cellular glass having a thermal conductivity of 0.026 Btu/h·ft·°F. Determine the radial thickness of the insulation to prevent condensation of water on the outer surface. Solution: In Figure 23,

1/3

'T h = 0.213 § ------- · ©D ¹

Horizontal cylinder

a Churchill

1/4

1/4

1/3

cChurchill

and Chu (1975b),

tfi = 41°F

dChurchill

105 < Ra < 109

(T9.14)

Ra > 109

(T9.15)

105 < Ra < 109

(T9.16)

Ra > 109

(T9.17)

(1990),

tfo = 86°F

eFujii

et al. (1986).

di = OD of tube = 0.7874 in.

ki = thermal conductivity of insulation material = 0.026 Btu/h·ft·°F From the problem statement, the outer surface temperature to of the insulation should not be less than the dew-point temperature of air. The dew-point temperature of air at 86°F, 70% rh = 75.07°F. To determine the outer diameter of the insulation, equate the heat transfer rate per unit length of pipe (from the outer surface of the pipe to the water) to the heat transfer rate per unit length from the air to the outer surface:

Heat Transfer

4.21 For a parallel or counterflow heat exchanger, the mean temperature difference is given by

Fig. 22 Diagram for Example 10

'tm = 't1 – 't2/ln('t1/'t2)

Fig. 23 Diagram for Example 10 t fo – t o t o – t fi --------------------------------------- = --------------1 d 1 1 ---------------------- + ------- ln ----oh ot d o di h i d i 2k i

(42)

where 't1 and 't2 are temperature differences between the fluids at each end of the heat exchanger; 'tm is the logarithmic mean temperature difference (LMTD). For the special case of 't1 = 't2 (possible only with a counterflow heat exchanger with equal capacities), which leads to an indeterminate form of Equation (44), 'tm = t1 = 't2. Equation (44) for 'tm is true only if the overall coefficient and the specific heat of the fluids are constant through the heat exchanger, and no heat losses occur (often well-approximated in practice). Parker et al. (1969) give a procedure for cases with variable overall coefficient U. For heat exchangers other than parallel and counterflow, a correction factor [see Incropera et al. (2007)] is needed for Equation (44) to obtain the correct mean temperature difference.

NTU-Effectiveness (H) Analysis

Heat transfer from the outer surface is by natural convection to air, so the surface heat transfer coefficient hot is the sum of the convective heat transfer coefficient ho and the radiative heat transfer coefficient hr. With an assumed emissivity of 0.7 and using Equation (4), hr = 0.757 Btu/h·ft·°F. To determine the value of do, the values of the heat transfer coefficients associated with the inner and outer surfaces (hi and ho, respectively) are needed. Compute the value of hi using Equation (T8.6). Properties of water at an assumed temperature of 41°F are Uw = 62.43 lbm/ft3 Pw = 1.02 × 10–3 lbm/ft·s cpw = 1.003 Btu/lbm·°F Uvd kw = 0.3298 Btu/lbm ·ft·°F Prw = 11.16 Red = --------- = 32,944f s = P 2 ·°F hi = 1033 Btu/h·ft 0.02311 Nud = 205.6 To compute ho using Equation (T9.10), the outer diameter of the insulation material must be found. Determine it by iteration by assuming a value of do, computing the value of ho, and determining the value of do from Equation (42). If the assumed and computed values of do are close to each other, the correct solution has been obtained. Otherwise, recompute ho using the newly computed value of do and repeat the process. Assume do = 2 in. Properties of air at tf= 81°F and 1 atm are

Calculations using Equations (43) and (44) for 'tm are convenient when inlet and outlet temperatures are known for both fluids. Often, however, the temperatures of fluids leaving the exchanger are unknown. To avoid trial-and-error calculations, the NTU-H method uses three dimensionless parameters: effectiveness H, number of transfer units (NTU), and capacity rate ratio cr; the mean temperature difference in Equation (44) is not needed. Heat exchanger effectiveness His the ratio of actual heat transfer rate to maximum possible heat transfer rate in a counterflow heat exchanger of infinite surface area with the same mass flow rates and inlet temperatures. The maximum possible heat transfer rate for hot fluid entering at thi and cold fluid entering at tci is qmax = Cmin(thi – tci )

Pr = 0.729 E = 0.00183 (at 460 + 86 = 546°R) Ra = 71,745 Nu = 7.157 ho = 0.646 Btu/h·ft2 ·°F hot = 0.646 + 0.757 = 1.403 Btu/h·ft2·°F From Equation (42), do = 1.743 in. Now, using the new value of 1.743 in. for the outer diameter, the new values of ho and hot are 0.666 Btu/h · ft2 · °F and 1.421 Btu/h · ft2·°F, respectively. The updated value of do is 1.733 in. Repeating the process, the final value of do = 1.733 in. Thus, an outer diameter of 1.7874 in. (corresponding to an insulation radial thickness of 0.5 in.) keeps the outer surface temperature at 75.4°F, higher than the dew point. (Another method to find the outer diameter is to iterate on the outer surface temperature for different values of do.)

HEAT EXCHANGERS Mean Temperature Difference Analysis With heat transfer from one fluid to another (separated by a solid surface) flowing through a heat exchanger, the local temperature difference 't varies along the flow path. Heat transfer rate may be calculated using (43)

where U is the overall uniform heat transfer coefficient, A is the area associated with the coefficient U, and 'tm is the appropriate mean temperature difference.

(45)

where Cmin is the smaller of the hot [Ch = ( m· cp)h] and cold [Cc = ( m· cp)h] fluid capacity rates, W/°F; Cmax is the larger. The actual heat transfer rate is

U = 0.0732 lbm/ft3 k = 0.01483 Btu/h·ft·°F P = 1.249 × 10–5 lbm/ft·s

q = UA 'tm

(44)

q = Hqmax

(46)

or a given exchanger type, heat transfer effectiveness can generally be expressed as a function of the number of transfer units (NTU) and the capacity rate ratio cr : H = f(NTU, cr , Flow arrangement)

(47)

where NTU = UA/Cmin cr = Cmin /Cmax

Effectiveness is independent of exchanger inlet temperatures. For any exchanger in which cr is zero (where one fluid undergoing a phase change, as in a condenser or evaporator, has an effective cp = f), the effectiveness is H = 1 – exp(–NTU)

(48)

The mean temperature difference in Equation (44) is then given by t hi – t ci H 't m = ------------------------NTU

(49)

After finding the heat transfer rate q, exit temperatures for constant-density fluids are found from

4.22

2009 ASHRAE Handbook—Fundamentals Table 10

Equations for Computing Heat Exchanger Effectiveness, N = NTU

Flow Configuration

Effectiveness H

Parallel flow

1 – exp > – N 1 – c r @ ------------------------------------------------1 + cr

Counterflow

1 – exp > – N 1 – c r @ -------------------------------------------------------1 – c r exp > – N 1 – c r @

cr z 1

(T10.2)

N ------------1+N

cr = 1

(T10.3)

2 ----------------------------------------------------------------------------– aN – aN 1 + cr + a 1 + e e 1 – e

a =

Shell-and-tube (one-shell pass, 2, 4, etc. tube passes) Shell-and-tube (n-shell pass, 2n, 4n, etc. tube passes)

Comments (T10.1)

1 – H 1 c r· n 1 – H 1 c r· n § ------------------ – 1 § ------------------ – cr © 1 – H1 ¹ © 1 – H1 ¹

–1

2

1 + cr

(T10.4)

H1 = effectiveness of one-shell pass shell-and-tube heat exchanger

(T10.5)

J = exp(–cr N 0.78) – 1

(T10.6)

J = 1 – exp(–N)

(T10.7)

J = 1 – exp(–N cr)

(T10.8)

Cross-flow (single phase) Both fluids unmixed Cmax (mixed), Cmin (unmixed)

§ JN 0.22· 1 – exp ¨ ---------------¸ © cr ¹ 1 – exp c r J -----------------------------cr

Cmax (unmixed), Cmin (mixed)

1 – exp(– J/cr)

Both fluids mixed

N -----------------------------------------------------------------------------------–Nc –N N e 1 – e + cr N e 1 – e r – 1

All exchangers with cr = 0

1 – exp(–N)

Fig. 23 Cross Section of Double-Pipe Heat Exchanger in Example 11

(T10.9) (T10.10)

inner, thin-walled 1.5 in. diameter pipe at 104°F with a velocity of 1.6 fps. Flue gases enter the annular space with a mass flow rate of 0.265 lbm/s at 392°F. To increase the heat transfer rate to the gases, 16 rectangular axial copper fins are attached to the outer surface of the inner pipe. Each fin is 2.4 in. high (radial height) and 0.04 in. thick, as shown in Figure 24. The gas-side surface heat transfer coefficient is 20 Btu/h·ft2 ·°F. Find the heat transfer rate and the exit temperatures of the gases and water. The heat exchanger has the following properties: Water in the pipe

tci = 104°F

Gases

thi = 392°F

vc = 1.6 ft/s m· h = 0.265 lbm/s

Length of heat exchanger Ltube = 16.4 ft

d = 1.5 in. L = 2.4 in.

t = 0.04 in.

N = number of fins = 16

Solution: The heat transfer rate is computed using Equations (45) and (46), and exit temperatures from Equation (50). To find the heat transfer rates, UA and Hare needed. 1 1 1 -------- = -------------------- + ------------ I s hA o hA i UA

Fig. 24 Cross Section of Double-Pipe Heat Exchanger in Example 11 q t e – t i = --------· m cp

(50)

Effectiveness for selected flow arrangements are given in Table 10. Afgan and Schlunder (1974), Incropera, et al. (2007), and Kays and London (1984) present graphical representations for convenience. NTUs as a function of H expressions are available in Incropera et al. (2007). Example 11. Flue gases from a gas-fired furnace are used to heat water in a 16.4 ft long counterflow, double-pipe heat exchanger. Water enters the

where hi = convective heat transfer coefficient on water side ho = gas-side heat transfer coefficient Is = surface effectiveness = (Auf + Af I)/Ao I = fin efficiency Auf = surface area of unfinned surface = L tube (Sd – Nt ) = 5.56 ft2 Af = fin surface area = 2LNL tube = 105.0 ft2 Ao = Auf + Af = 110.6 ft2 Ai = SdL tube = 6.44 ft2 Step 1. Find hi using Equation (T8.6). Properties of water at an assumed mean temperature of 113°F are U = 61.8 lbm /ft3

cpc = 0.999 Btu/lbm·°F k = 0.368 Btu/h·ft·°F

P = 4.008 × 10–4 lbm /ft·s Pr = 3.91

Uv c d 61.8 u 1.6 u 1.5 e 12 Re = ----------- = ---------------------------------------------------- = 30,838 –4 P 4.008 u 10

Heat Transfer

4.23

fs/2 = [1.58 ln(Re) – 3.28]–2/2 = (1.58 ln 30,838 – 3.28)–2/2 = 0.00294

Fig. 24 Plate Parameters

–3

2.94 u 10 u 30,838 – 1000 u 3.91 Nu d = ------------------------------------------------------------------------------------------------------------- = 169.6 – 3 1/2 2/3 1 + 12.7 u 5.87 e 2 u 10 u 3.91 – 1 u 0.368- = 499 Btu/h·ft 2 · °F h i = 169.6 -------------------------------1.5 e 2 Step 2. Compute fin efficiency I and surface effectiveness Is . For a rectangular fin with the end of the fin not exposed, tanh mL I = ----------------------mL For copper, k = 232 Btu/h·ft·°F. mL = (2ho/kt)1/2L = [(2×20)/(232 × 0.04/12)]1/2 × 2.4/12 = 1.44 tanh1.44 I = --------------------- = 0.62 1.44 Is = (Auf + IAf )/A0 = (5.56 + 0.62 × 105.0)/110.6 = 0.64 Step 3. Find heat exchanger effectiveness. For air at an assumed mean temperature of 347°F, cph = 0.243 Btu/lbm ·°F. Ch = m· h cph = 0.265 × 3600 × 0.243 = 231.8 Btu/h·°F m· c = Uvc Sd 2/4 = [61.8 × 1.6 × S × (1.5/12)2] = 1.21 lbm /s Cc = m· c cpc = 1.21 × 3600 × 0.999 = 4373 Btu/h·°F cr = Cmin /Cmax = 231.8/4373 = 0.0530 UA = [1/(0.64 × 20 × 110.5) + 1/(499 × 6.44)]–1 = 982.1 Btu/h·°F NTU = UA/Cmin = 982.1/231.8 = 4.24 From Equation (T10.2), 1 – exp > – N 1 – c r @ H = -----------------------------------------------------1 – c r exp > – N 1 – c r @ 1 – exp > – 4.26 u 1 – 0.0530 @ = ------------------------------------------------------------------------------------------------- = 0.983 1 – 0.0530 u exp > – 4.26 u 1 – 0.0530 @ Step 4. Find heat transfer rate: qmax = Cmin u (thi – tci ) = 231.8 u (392 – 104) = 66,758 Btu/h q = Hqmax = 0.983 u 66,758 = 65,634 Btu/h Step 5. Find exit temperatures: q t he = t hi – ------ = 392 – 65,634 ---------------- = 108.9°F Ch 231.8 q t ce = t ci – ------ = 104 + 65,634 ---------------- = 119°F Cc 4373

The mean temperature of water now is 111.5°F. The properties of water at this temperature are not very different from those at the assumed value of 113°F. The only property of air that needs to be updated is the specific heat, which at the updated mean temperature of 250°F is 0.242 Btu/lbm ·°F, which is not very different from the assumed value of 0.243 Btu/lbm ·°F. Therefore, no further iteration is necessary.

Plate Heat Exchangers Plate heat exchangers (PHEs) are used regularly in HVAC&R. The three main types of plate exchangers are plate-and-frame (gasket or semi-welded), compact brazed (CBE), and shell-andplate. The basic plate geometry is shown in Figure 25. Plate Geometry. Different geometric parameters of a plate are defined as follows (Figure 25):

Fig. 25 Plate Parameters • Chevron angle E varies between 22 and 65°. This angle also defines the thermal hydraulic softness (low thermal efficiency and pressure drop) and hardness (high thermal efficiency and pressure drop). • Enlargement factor I is the ratio of developed length to protracted length. • Mean flow channel gap b is the actual gap available for the flow: b = p – t. • Channel flow area Ax is the actual flow area: Ax = bw. • Channel equivalent diameter de is defined as de = 4Axಚ/P, where P = 2(b + Iw) = 2Iw, because b Recr , 10 < Recr < 400, water.

Muley and Manglik (1999)

Nu = [0.2668 – 0.006967(90 – E) + 7.244 u 10–5 (90 – E)2] u (20.78 – 50.94I + 41.16I2 – 10.51I3) u Re {0.728 + 0.0543 sin[S(90 – E)/45] + 3.7} Pr 1/3 (P/P w )0.14 f = [2.917 – 0.1277(90 – E) + 2.016 u 10–3 (90 – E)2] u (5.474 – 19.02I + 18.93I2 – 5.341I3) u Re –{0.2+ 0.0577 sin[S(90 – E)/45] + 2.1}

Re t 103, 30 d E d 60, 1 d I d 1.5.

Kumar (1984)

f = C2 /(Re) p Nu = C1 Re m Pr 0.33 (P/P w )0.17 C1, C2, m, and p are constants and given as

Water, herringbone plates, I = 1.17.

E

Re

C1

m

d30

d10 >10

0.718 0.348

0.349 0.663

45

100 300 400 500

0.718 0.400 0.300 0.630 0.291 0.130 0.562 0.306 0.108 0.562 0.331 0.087

0.349 0.598 0.663 0.333 0.591 0.732 0.326 0.529 0.703 0.326 0.503 0.718

50

60

t65

Heavner et al. (1993)

Wanniarachchi et al. (1995)

Nu = C1(I)1–m Re m Pr 0.5(P/P w)0.17 f = C2(I) p +1 Re –p C1, C2, m, and p are constants and given as

Re 100 300 300 400 500

C2

p

50.0 19.40 2.990 47.0 18.29 1.441 34.0 11.25 0.772 24.0 3.24 0.760 24.0 2.80 0.639

1.0 0.589 0.183 1.0 0.652 0.206 1.0 0.631 0.161 1.0 0.457 0.215 1.0 0.451 0.213

400 < Re < 10 000, 3.3 < Pr < 5.9, water chevron plate (0° d E d 67°).

E

Eavg

C1

m

C2

p

67/67 67/45 67/0 45/45 45/0

67 56 33.5 45 22.5

0.089 0.118 0.308 0.195 0.278

0.718 0.720 0.667 0.692 0.683

0.490 0.545 1.441 0.687 1.458

0.1814 0.1555 0.1353 0.1405 0.0838

Nu = (Nu13+ Nut 3)1/3 Pr1/3 (P/P w )0.17 Nu1 = 3.65(E)–0.455 (I)0.661 Re 0.339 Nut = 12.6(E)–1.142 (I)1–m Re m m = 0.646 + 0.0011(E) f = ( f13 + ft3)1/3 f1 = 1774(E)–1.026 (I)2 Re –1 ft = 46.6(E)–1.08 (I)1+p Re –p p = 0.00423(E) + 0.0000223(E)2

1 d Re d 104, herringbone plates (20° d E d 62, E ! 62° = 62°).

Source: Ayub (2003).

Passive Techniques Finned-Tube Coils. Heat transfer coefficients for finned coils follow the basic equations of convection, condensation, and evaporation. The fin arrangement affects the values of constants and exponential powers in the equations. It is generally necessary to refer to test data for the exact coefficients. For natural-convection finned coils (gravity coils), approximate coefficients can be obtained by considering the coil to be made of tubular and vertical fin surfaces at different temperatures and then applying the natural-convection equations to each. This is difficult because the natural-convection coefficient depends on the temperature difference, which varies at different points on the fin. Fin efficiency should be high (80 to 90%) for optimum naturalconvection heat transfer. A low fin efficiency reduces temperatures near the tip. This reduces 't near the tip and also the coefficient h,

which in natural convection depends on 't. The coefficient of heat transfer also decreases as fin spacing decreases because of interfering convection currents from adjacent fins and reduced free-flow passage; 2 to 4 in. spacing is common. Generally, high coefficients result from large temperature differences and small flow restriction. Edwards and Chaddock (1963) give coefficients for several circular fin-on-tube arrangements, using fin spacing G as the characteristic length and in the form Nu = f (RaG, G/Do), where Do is the fin diameter. Forced-convection finned coils are used extensively in a wide variety of equipment. Fin efficiency for optimum performance is smaller than that for gravity coils because the forced-convection coefficient is almost independent of the temperature difference between surface and fluid. Very low fin efficiencies should be

Heat Transfer

4.25

avoided because an inefficient surface gives a high (uneconomical) pressure drop. An efficiency of 70 to 90% is often used. As fin spacing is decreased to obtain a large surface area for heat transfer, the coefficient generally increases because of higher air velocity between fins at the same face velocity and reduced equivalent diameter. The limit is reached when the boundary layer formed on one fin surface (see Figure 19) begins to interfere with the boundary layer formed on the adjacent fin surface, resulting in a decrease of the heat transfer coefficient, which may offset the advantage of larger surface area. Selection of fin spacing for forced-convection finned coils usually depends on economic and practical considerations, such as fouling, frost formation, condensate drainage, cost, weight, and volume. Fins for conventional coils generally are spaced 6 to 14 per inch apart, except where factors such as frost formation necessitate wider spacing. There are several ways to obtain higher coefficients with a given air velocity and surface, usually by creating air turbulence, generally with a higher pressure drop: (1) staggered tubes instead of inline tubes for multiple-row coils; (2) artificial additional tubes, or collars or fingers made by forming the fin materials; (3) corrugated fins instead of plane fins; and (4) louvered or interrupted fins. Figure 26 shows data for one-row coils. Thermal resistances plotted include the temperature drop through the fins, based on one square foot of total external surface area. Internal Enhancement. Several examples of tubes with internal roughness or fins are shown in Figure 27. Rough surfaces of the spiral repeated rib variety are widely used to improve in-tube heat transfer with water, as in flooded chillers. Roughness may be produced by spirally indenting the outer wall, forming the inner wall, or inserting coils. Longitudinal or spiral internal fins in tubes can be produced by extrusion or forming and substantially increase surface area. Efficiency of extruded fins can usually be taken as unity (see the section on Fin Efficiency). Twisted strips (vortex flow devices) can be inserted as original equipment or as a retrofit (Manglik and Bergles 2002). From a practical point of view, the twisted tape width should be such that the tape can be easily inserted or removed. Ayub

and Al-Fahed (1993) discuss clearance between the twisted tape and tube inside dimension. Microfin tubes (internally finned tubes with about 60 short fins around the circumference) are widely used in refrigerant evaporation and condensers. Because gas entering the condenser in vaporcompression refrigeration is superheated, a portion of the condenser that desuperheats the flow is single phase. Some data on singlephase performance of microfin tubes, showing considerably higher heat transfer coefficients than for plain tubes, are available [e.g., Al-Fahed et al. (1993); Khanpara et al. (1986)], but the upper Reynolds numbers of about 10,000 are lower than those found in practice. ASHRAE research [e.g., Eckels (2003)] is addressing this deficiency. The increased friction factor in microfin tubes may not require increased pumping power if the flow rate can be adjusted or the length of the heat exchanger reduced. Nelson and Bergles (1986) discuss performance evaluation criteria, especially for HVAC applications. In chilled-water systems, fouling may, in some cases, seriously reduce the overall heat transfer coefficient U. In general, fouled enhanced tubes perform better than fouled plain tubes, as shown in studies of scaling caused by cooling tower water (Knudsen and Roy 1983) and particulate fouling (Somerscales et al. 1991). A comprehensive review of fouling with enhanced surfaces is presented by Somerscales and Bergles (1997). Fire-tube boilers are frequently fitted with turbulators to improve the turbulent convective heat transfer coefficient (addressing the dominant thermal resistance). Also, because of high gas temperatures, radiation from the convectively heated insert to the tube wall can represent as much as 50% of the total heat transfer. (Note, however, that the magnitude of convective contribution decreases as the radiative contribution increases because of the reduced temperature difference.) Two commercial bent-strip inserts, a twisted-strip insert, and a simple bent-tab insert are depicted in Figure 28. Design equations for convection only are included in Table 12. Beckermann and Goldschmidt (1986) present procedures to include radiation,

Fig. 25 Overall Air-Side Thermal Resistance and Pressure Drop for One-Row Coils

Fig. 26 Typical Tube-Side Enhancements

Fig. 26 Overall Air-Side Thermal Resistance and Pressure Drop for One-Row Coils (Shepherd 1946)

Fig. 27

Typical Tube-Side Enhancements

4.26

2009 ASHRAE Handbook—Fundamentals

and Junkhan et al. (1985, 1988) give friction factor data and performance evaluations. Enhanced Surfaces for Gases. Several such surfaces are depicted in Figure 29. The offset strip fin is an example of an interrupted fin that is often found in compact plate fin heat exchangers used for heat recovery from exhaust air. Design equations in Table 12 apply to laminar and transitional flow as well as to turbulent flow, which is a necessary feature because the small hydraulic diameter of these surfaces drives the Reynolds number down. Data for other surfaces (wavy, spine, louvered, etc.) are available in the References. Microchannel Heat Exchangers. Microchannels for heat transfer enhancement are widely used, particularly for compact heat exchangers in automotive, aerospace, fuel cell, and high-flux electronic cooling applications. Bergles (1964) demonstrated the potential of narrow passages for heat transfer enhancement; more recent experimental and numerical work includes Adams et al. (1998), Costa et al. (1985), Kandlikar (2002), Ohadi et al. (2008), Pei et al. (2001), and Rin et al. (2006). Compared with channels of normal size, microchannels have many advantages. Because microchannels have an increased heat transfer surface area per unit volume and a large surface-to-volume ratio, they provide much higher heat transfer rates. This feature allows heat exchangers to be compact and lightweight. Despite their thin walls, microchannels can withstand high operating pressures: for example, a microchannel with a hydraulic diameter of 0.03 in. and a wall thickness of 0.012 in. can easily withstand operating pressures of up to 2030 psi. This feature makes microchannels particularly suitable for use with high-pressure refrigerants such as carbon dioxide (CO2). For high-flux electronics (with heat flux at 1 kW/cm2 or higher), microchannels can provide cooling with small temperature gradients (Ohadi et al. 2008). Microchannels have been used for both single-phase and phase-change heat transfer applications. Drawbacks of microchannels include large pressure drop, high cost of manufacture, dirt clogging, and flow maldistribution, especially for two-phase flows. Most of these weaknesses, however, may be solved by optimizing design of the surface and the heat exchanger manifold and feed system. Microchannels are fabricated by a variety of processes, depending on the dimensions and plate material (e.g., metals, plastics, silicon). Conventional machining and electrical discharge machining are two typical options; semiconductor fabrication processes are appropriate for microchannel fabrication in chip-cooling applications. Using microfabrication techniques developed by the electronics industry, three-dimensional structures as small as 0.1 Pm long can be manufactured.

Fluid flow and heat transfer in microchannels may be substantially different from those encountered in the conventional tubes. Early research indicates that deviations might be particularly important for microchannels with hydraulic diameters less than 100 Pm. Recent Progress. The automotive, aerospace, and cryogenic industries have made major progress in compact evaporator development. Thermal duty and energy efficiency have substantially increased, and space constraints have become more important, encouraging greater heat transfer rates per unit volume. The hot side of the evaporators in these applications is generally air, gas, or a condensing vapor. Air-side fin geometry improvements derive from increased heat transfer coefficients and greater surface area densities. To decrease the air-side heat transfer resistance, more aggressive fin designs have been used on the evaporating side, resulting in narrower flow passages. The narrow refrigerant channels with large aspect ratios are brazed in small cross-ribbed sections to improve Fig. 27 Turbulators for Fire-Tube Boilers

Fig. 28

Fig. 28 Enhanced Surfaces For Gases

Fig. 29

Enhanced Surfaces for Gases

Turbulators for Fire-Tube Boilers

Heat Transfer

4.27

flow distribution along the width of the channels. Major recent changes in designs involve individual, small-hydraulic-diameter flow passages, arranged in multichannel configuration for the evaporating fluid. Figure 30 shows a plate-fin evaporator geometry widely used in compact refrigerant evaporators. The refrigerant-side passages are made from two plates brazed together, and air-side fins are placed between two refrigerant microchannel flow passages. Figure 31 depicts two representative microchannel geometries widely used in the compact heat exchanger industry, with corresponding approximate nominal dimensions provided in Table 13 (Zhao 1997). Plastic heat exchangers have been suggested for HVAC applications (Pescod 1980) and are being manufactured for refrigerated sea water (RSW) applications. They can be made of materials impervious to corrosion [e.g., by acidic condensate when cooling a gaseous stream (flue gas heat recovery)], and are easily manufactured with enhanced surfaces. Several companies now offer heat exchangers in plastic, including various enhancements.

Active Techniques Unlike passive techniques, active techniques require external power to sustain the enhancement mechanism. Table 14 lists the more common active heat transfer augmentation techniques and the corresponding heat transfer mode believed most applicable to the particular technique. Various active techniques and their world-wide status are listed in Table 15. Except for mechanical aids, which are universally used for selected applications, most other active techniques have found limited commercial applications and are still in development. However, with increasing demand for smart and miniaturized thermal management systems, actively controlled

Fig. 29 Typical Refrigerant and Air-Side Flow Passages in Compact Automotive Microchannel Heat Exchanger

Fig. 30 Typical Refrigerant and Air-Side Flow Passages in Compact Automotive Microchannel Heat Exchanger

heat transfer augmentation techniques will soon become necessary for some advanced thermal management systems. All-electric ships, airplanes, and cars use electronics for propulsion, auxiliary systems, sensors, countermeasures, and other system needs. Advances in power electronics and control systems will allow optimized and tactical allocation of total installed power among system components. This in turn will require smart (online/ on-demand), compact heat exchangers and thermal management systems that can communicate and respond to transient system needs. This section briefly overviews active techniques and recent progress; for additional details, see Ohadi et al (1996). Mechanical Aids. Augmentation by mechanical aids involves stirring the fluid mechanically. Heat exchangers that use mechanical enhancements are often called mechanically assisted heat exchangers. Stirrers and mixers that scrape the surface are extensively used in chemical processing of highly viscous fluids, such as blending a flow of highly viscous plastic with air. Surface scraping can also be applied to duct flow of gases. Hagge and Junkhan (1974) reported tenfold improvement in the heat transfer coefficient for laminar airflow over a flat plate. Table 16 lists selected works on mechanical aids, suction, and injection. Injection. This method involves supplying a gas to a flowing liquid through a porous heat transfer surface or injecting a fluid of a similar type upstream of the heat transfer test section. Injected bubbles produce an agitation similar to that of nucleate boiling. Gose et al. (1957) bubbled gas through sintered or drilled heated surfaces and found that the heat transfer coefficient increased 500% in laminar flow and about 50% in turbulent flow. Tauscher et al. (1970) demonstrated up to a fivefold increase in local heat transfer coefficients by injecting a similar fluid into a turbulent tube flow, but the effect dies out at a length-to-diameter ratio of 10. Practical application of injection appears to be rather limited because of difficulty in cost-effectively supplying and removing the injection fluid. Suction. The suction method involves removing fluid through a porous heated surface, thus reducing heat/mass transfer resistance at the surface. Kinney (1968) and Kinney and Sparrow (1970) reported that applying suction at the surface increased heat transfer coefficients for laminar film and turbulent flows, respectively. Jeng et al. (1995) conducted experiments on a vertical parallel channel with asymmetric, isothermal walls. A porous wall segment was embedded in a segment of the test section wall, and enhancement occurred as hot air was sucked from the channel. The local heat transfer coefficient increased with increasing porosity. The maximum heat transfer enhancement obtained was 140%. Fluid or Surface Vibration. Fluid or surface vibrations occur naturally in most heat exchangers; however, naturally occurring vibration is rarely factored into thermal design. Vibration equipment is expensive, and power consumption is high. Depending on frequency

Fig. 30 Microchannel Dimensions

Fig. 31 Microchannel Dimensions

4.28

2009 ASHRAE Handbook—Fundamentals Table 12 Equations for Augmented Forced Convection (Single Phase)

Description

Equation

Comments

I. Turbulent in-tube flow of liquids 1/7

Spiral repeated riba

ha ­ 0.036 § e · 0.212 § p · – 0.21 § D · 0.29 – 0.024 7 ½ ---------------- = ® 1 + 2.64 Re Pr ¾ © d¹ © 90 ¹ © d¹ hs ¯ ¿ fa ­ w e x p y D z 2.94 ---- = ® 1 + 29.1 Re § ----· § ---- · § ------ · § 1 + ---------- · sin E © d ¹ © d ¹ © 90 ¹ © fs n ¹ ¯ w = 0.67 – 0.06( p/d) – 0.49(D/90)

Re = GD/P

15/16 ½16/15

¾ ¿

x = 1.37 – 0.157( p/d) y = –1.66 × 10–6 Re – 0.33D/90 z = 4.59 + 4.11 × 10–6 Re – 0.15( p/d) k e D f s e 2 Re Pr h s = --------------------------------------------------------------------1/2 2/3 1 + 12.7 f s e 2 Pr – 1 fs = (1.58 ln Re – 3.28)–2 hD h 0.4 § GD h · ---------- = 0.023 Pr ¨ ----------- ¸ k © P ¹

Finsb

0.8

§ AF · ¨ --------- ¸ © AF i ¹

0.1

§ A i· ¨ -----¸ © A¹

0.5

sec D

3

Note that in computing Re for fins and twistedstrip inserts there is allowance for reduced cross-sectional area.

GDh –0.2 § A F · 0.5 0.75 --------f h = 0.046 § ----------- · sec D © P ¹ © AF i ¹ hd e k ------------------------------ = 1 + 0.769 e y hd e k y o f

Twisted-strip insertsc

GD § hd ------ · = 0.023 § --------- · © k ¹ yof © P ¹

0.8

Pr

S ---------------------- · © S – 4G e d ¹

0.4 §

0.8

S + 2 – 2G e d · § ------------------------------© S – 4G e d ¹

0.2

I

I = (Pb /P w )n n = 0.18 for liquid heating, 0.30 for liquid cooling 0.0791 - § --------------------+ 2 – 2G e d- · 1.25 § S - · 1.75 § S 2.752 ------------------------------f = ---------------------------1 + ------------- · 0.25 © S – 4G e d ¹ © © S – 4G e d ¹ 1.29 ¹ GD e P y II. Turbulent in-tube flow of gases Bent-strip insertsd

hD § T w· ------- ¨ ------¸ k © Tb ¹

Twisted-strip insertsd

hD § T w· ------- ¨ ------¸ k © Tb ¹

Bent-tab insertsd

hD § T w· ------- ¨ ------¸ k © Tb ¹

0.45

0.45

0.45

GD 0.6 = 0.258 § --------- · © P ¹

or

hD § T w· ------- ¨ ------¸ k © Tb¹

0.45

GD 0.63 = 0.208 § --------- · © P ¹

Respectively, for configurations shown in Figure 28.

GD 0.65 = 0.122 § --------- · © P ¹ GD 0.54 = 0.406 § --------- · © P ¹

Note that in computing Re there is no allowance for flow blockage of the insert.

III. Offset strip fins for plate-fin heat exchangerse GD h --------- = 0.6522 §© ----------h-·¹ P cp G

– 0.5403

D

– 0.1541 0.1499 – 0.0678

G

J

1.340 – 5 GD 0.504 0.456 – 1.055 1 + 5.269 u 10 § ----------h-· D G J © P ¹

4.429 GD – 0.7422 – 0.1856 – 0.3053 –0.2659 – 8 GD 0.920 3.767 0.236 f h = 9.6243 § ----------h-· D G J 1 + 7.669 u 10 § ----------h-· D G J © P ¹ © P ¹

0.1

0.1

h/cpG, fh, and GDh /P are based on the hydraulic mean diameter given by Dh = 4shl/[2(sl + hl + th) + ts] Sources: aRavigururajan and Bergles (1985), bCarnavos (1979), cManglik and Bergles (1993), dJunkhan et al. (1985), eManglik and Bergles (1990).

Table 13 Microchannel Dimensions Channel geometry Hydraulic diameter Dh, in. Number of channels Length L, in. Height H, in. Width W, in. Wall thickness, in.

Microchannel I

Microchannel II

Rectangular 0.028 28 11.8 0.059 1.1 0.016

Triangular 0.034 25 11.8 0.075 1.07 0.012

and amplitude of vibration, forced convection from a wire to air is enhanced by up to 300% (Nesis et al. 1994). Using standing waves in a fluid reduced input power by 75% compared with a fan that provided the same heat transfer rate (Woods 1992). Lower frequencies are preferable because they consume less power and are less harmful to users’ hearing. Vibration has not found industrial applications at this stage of development. Rotation. Rotation heat transfer enhancement occurs naturally in rotating electrical machinery, gas turbine blades, and some other equipment. The rotating evaporator, rotating heat pipe,

Heat Transfer

4.29

Table 14 Active Heat Transfer Augmentation Techniques and Most Relevant Heat Transfer Modes Heat Transfer Mode Forced Convection Boil- Evapo- Conden- Mass (Gases) (Liquids) ing ration sation Transfer

Technique Mechanical aids Surface vibration Fluid vibration Electrostatic/electrohydrodynamic Suction/injection Jet impingement Rotation Induced flow *** = Highly significant — = Not significant

NA ** ** **

** ** ** **

* ** ** ***

* ** ** ***

NA ** — ***

** *** ** ***

* ** * **

** ** * **

NA NA *** NA

NA ** *** NA

** NA *** NA

** * *** *

** = Significant * = Somewhat significant NA = Not believed to be applicable

Table 15 Worldwide Status of Active Techniques Technique

Country or Countries

Mechanical aids

Universally used in selected applications (e.g., fluid mixers, liquid injection jets) Surface vibration Most recent work in United States; not significant Fluid vibration Sweden; mostly used for sonic cleaning Electrostatic/electroJapan, United States, United Kingdom; hydrodynamic successful prototypes demonstrated Other electrical methods United Kingdom, France, United States Suction/injection No recent significant developments Jet impingement France, United States; high-temperature units and aerospace applications Rotation United States (industry), United Kingdom (R&D) Induced flow United States; particularly combustion

Table 16 Selected Studies on Mechanical Aids, Suction, and Injection Source

Process

Heat Transfer Surface

Valencia et al. (1996)

Natural convection

Finned tube

Air

0.5

Jeng et al. (1995) Natural convection/ suction

Asymmetric isothermal wall

Air

1.4

Inagaki and Turbulent natural Komori (1993) convection/suction

Vertical plate

Air

1.8

Dhir et al. (1992) Forced convection/ injection

Tube

Air

1.45

Duignan et al. (1993)

Forced convection/ film boiling

Horizontal plate

Air

2.0

Son and Dhir (1993)

Forced convection/ injection

Annuli

Air

1.85

Malhotra and Majumdar (1991)

Water to bed/ stirring

Granular bed

Air

3.0

Fluid Dmax

Aksan and Borak Pool of water/ (1987) stirring

Tube coils

Hagge and Forced convection/ Junkhan (1974) scraping

Cylindrical wall

Air

11.0

Hu and Shen (1996)

Converging ribbed tube

Air

1.0

Turbulent natural convection

Water 1.7

D = Enhancement factor (ratio of enhanced to unenhanced heat transfer coefficient)

high-performance distillation column, and Rotex absorption cycle heat pump are typical examples of previous work in this area. In rotating evaporators, the rotation effectively distributes liquid on the outer part of the rotating surface. Rotating the heat transfer surface also seems promising for effectively removing condensate and decreasing liquid film thickness. Heat transfer coefficients have been substantially increased by using centrifugal force, which may be several times greater than the gravity force. As shown in Table 17, heat transfer enhancement varies from slight improvement up to 450%, depending on the system and rotation speed. The rotation technique is of particular interest for use in two-phase flows, particularly in boiling and condensation. This technique is not effective in the gas-to-gas heat recovery mode in laminar flow, but its application is more likely in turbulent flow. High power consumption, sealing and vibration problems, moving parts, and the expensive equipment required for rotation are some of this technique’s drawbacks. Electrohydrodynamics. Electrohydrodynamic (EHD) enhancement of single-phase heat transfer refers to coupling an electric field with the fluid field in a dielectric fluid medium. The net effect is production of secondary motions that destabilize the thermal boundary layer near the heat transfer surface, leading to heat transfer coefficients that are often an order of magnitude higher than those achievable by most conventional enhancement techniques. EHD heat transfer enhancement has applicability to both single-phase and phase-change heat transfer processes, although only enhancement of single-phase flows is discussed here. Selected work in EHD enhancement of single-phase flow is shown in Table 18. High enhancement magnitudes have been found for single-phase air and liquid flows. However, high enhancement magnitude is not enough to warrant practical implementation. EHD electrodes must be compatible with cost-effective, mass-production technologies, and power consumption must be kept low, to minimize the required power supply cost and complexity. The following brief overview discusses recent work on EHD enhancement of air-side heat transfer; additional details are in Ohadi et al. (2001). EHD Air-Side Heat Transfer Augmentation. In a typical liquid-toair heat exchanger, air-side thermal resistance is often the limiting factor to improving the overall heat transfer coefficient. Electrohydrodynamic enhancement of air-side heat transfer involves ionizing air molecules under a high-voltage, low-current electric field, leading to generation of secondary motions that are known as corona or ionic wind, generated between the charged electrode and receiving (ground) electrode. Typical wind velocities of 200 to 600 fpm have been verified experimentally. Studies of this enhancement method include Ohadi et al. (1991), who studied laminar and turbulent forced-convection heat transfer of air in tube flow, and Owsenek and Seyed-Yagoobi (1995), who investigated heat transfer augmentation of natural convection with the corona wind effect. Other studies are documented in Ohadi et al. (2001). The general finding has been that corona wind is effective for Reynolds numbers up to transitional values, 2300 or less, and becomes less effective as Re increases. At high Reynolds numbers, turbulence-induced effects overwhelm the corona wind effect. Most studies addressed EHD air-side enhancement in classical geometries, but recent work has focused on issues of practical significance. These include (1) EHD applicability in highly compact heat exchangers, (2) electrode designs to minimize power consumptions to avoid joule heating and costly power supply requirements, and (3) cost-effective mass production of EHD-enhanced surfaces. Lawler et al. (2002) examined air-side enhancement of an air-toair heat exchanger with 4 to 6 fins per inch (fpi) spacing. Unlike previous studies, this study investigated placing electrodes on the heat transfer surface itself, integrated into the surface as an embedded wire, thus avoiding suspended wires in the flow field. This arrangement could greatly simplify manufacturing/fabrication for

4.30

2009 ASHRAE Handbook—Fundamentals Table 17 Selected Studies on Rotation

Source

Process

Heat Transfer Surface

Fluid

Rotational Speed, rpm

Dmax

Prakash and Zerle (1995) Mochizuki et al. (1994) Lan (1991) McElhiney and Preckshot (1977) Nichol and Gacesa (1970) Astaf’ev and Baklastov (1970) Tang and McDonald (1971) Marto and Gray (1971)

Natural convection Natural convection Solidification External condensation External condensation External condensation Nucleate boiling In-tube boiling

Ribbed duct Serpentine duct Vertical tube Horizontal tube Vertical cylinder Circular disk Horizontal heated circular cylinder Vertical heated circular cylinder

Air Air Water Steam Steam Steam R-113 Water

Given as a function Given as a function 400 40 2700 2500 1400 2660

1.3 3.0 NA 1.7 4.5 3.4 1 + 0.12 1 H v = --- Uv 

 x 1 x x @  ---- + ----------- Ul   Uv

1.18 1 x > gV U l U v @ 0.25  -  + -------------------------------------------------------------------2 0.5  G Ul

(8)

where h is from the appropriate equation in Table 3. The value of the heat transfer coefficient for stagnant gas depends on the geometry and flow conditions. For flow parallel to a condenser tube, for example, hg j = ---------------- cp g G

2 2 dp  3 1 x x - = G  ------------------------ + -------------dz   mom  Ul 1 Hv Uv Hv

(11c)

1

A generalized expression for Hv was suggested by Butterworth (1975): ql

r

 1 x- U v  l  P l  -   -----  H v = 1 + Al  ---------x  ---   Ul   Pv 

1

Sl

(11d)

This generalized form represents the models of several researchers; constants and exponents needed for each model are given in Table 4. The homogeneous model provides a simple method for computing the acceleration and gravitational components of pressure drop. It assumes that flow can be characterized by average fluid properties and that the velocities of liquid and vapor phases are equal (Collier and Thome 1996; Wallis 1969). The following discussion of several empirical correlations for computing frictional pressure drop in two-phase internal flow is based on Ould Didi et al. (2002).

Friedel Correlation A common strategy in both two-phase heat transfer and pressure drop modeling is to begin with a single-phase model and determine an appropriate two-phase multiplier to correct for the enhanced energy and momentum transfer in two-phase flow. The Friedel (1979) correlation follows this strategy: dp  2 dp - ) ------ = ----lo dz  dz l

(12a)

In this case,

Other Impurities

2

Vapor entering the condenser often contains a small percentage of impurities such as oil. Oil forms a film on the condensing surfaces, creating additional resistance to heat transfer. Some allowance should be made for this, especially in the absence of an oil separator or when the discharge line from the compressor to the condenser is short.

dp  dp   dp dp  - = ------  + ------  + ---- ------ dz dz dz   total   static   mom  dz  fric

(11a)

The momentum pressure gradient accounts for the acceleration of the flow, usually caused by evaporation of liquid or condensation of vapor. In this case,

(12b)

0.079 f = --------------0.25 Re

(12c)

with

PRESSURE DROP Total pressure drop for two-phase flow in tubes consists of friction, change in momentum, and gravitational components:

dp  > G tot 1 x @ -  = 4f ------------------------------------l dz 2U l D  l

Table 4 Constants in Equation (11d) for Different Void Fraction Correlations Model Homogeneous (Collier 1972) Lockhart and Martinelli (1949) Baroczy (1963) Thom (1964) Zivi (1964) Turner and Wallis (1965)

Al

ql

rl

Sl

1.0 0.28 1.0 1.0 1.0 1.0

1.0 0.64 0.74 1.0 1.0 0.72

1.0 0.36 0.65 0.89 0.67 0.40

0 0.07 0.13 0.18 0 0.08

5.12

2009 ASHRAE Handbook—Fundamentals and C = 20 for most cases of interest in internal flow in HVAC&R systems.

and G tot D Re = --------------P

(12d)

with P = Pl used to calculate fl for use in Equation (12b). The twophase multiplier )lo2 is determined by 2 3.24FH ) lo = E + ----------------------------------0.045 0.035 Fr h We l

(12e)

Grönnerud Correlation Much of the two-phase pressure drop modeling has been based on adiabatic air/water data. To address this, Grönnerud (1979) developed a correlation based on refrigerant flow data, also using a two-phase multiplier:  dp- dp ------ = ) gd  ----dz  dz  l

where 2

G tot Fr h = ------------2 gDU h 2  Ul   fv 

2

x + x  -----  ---   U v  f l 

E = 1 F

(12f)

0.91

 Ul  H =  -----   Uv 

0.19

P v  -----   Pl 

Ul e Uv  dp ) gd = 1 +  ------ ---------------------------dz  Fr P l e P v 0.25

(12h)

 1 

Pv  -----  Pl 

 dp 1.8 10 0.5 x f Fr   ------ = f Fr x + 4  x    dz Fr

(12i)

2

(12j)

(14c)

2

G tot Fr l = ------------2 gDU l

(14d)

If Frl is greater than or equal to 1, fFr = 1.0. If Frl < 1,

1

(12k)

0.3

f Fr = Fr l

This method is generally recommended when the viscosity ratio P l /P v is less than 1000.

Lockhart and Martinelli Correlation One of the earliest two-phase pressure drop correlations was proposed by Martinelli and Nelson (1948) and rendered more useful by Lockhart and Martinelli (1949). A relatively straightforward implementation of this model requires that Rel be calculated first, based on Equation (12d) and liquid properties. If Rel > 4000, dp 2  dp ------ = ) ltt  ------ dz  dz l

(13b)

2

(14e)

A simple, purely empirical correlation was proposed by MüllerSteinhagen and Heck (1986): dp ------ = / 1 dz

x

1/3

 dp 3 +  ------ x  dz vo

(15a)

where  dp - + 2 / =  ---- dz lo

(13a)

2 C 1 ) ltt = 1 + ------ + -----X tt X 2 tt

1 + 0.0055 ln  ------   Frl 

Müller-Steinhagen and Heck Correlation

where

 dp -  ---- dz vo

 dp - x  ---- dz lo

(15b)

and 2

 dp 2G tot -  ----dz  = f l -----------DU l  lo

and (dp/dz)l is calculated using Equation (12b). If Rel < 4000, 2  dp ) Vtt  ------  dz v

dp -----dz

(14b)

The friction factor fFr in this method depends on the liquid Froude number, defined by

Note that friction factors in Equation (12g) are calculated from Equations (12c) and (12d) using the vapor and liquid fluid properties, respectively. The homogeneous density Uh is given by  x 1 x U h =  ----- + ----------- Ul   Uv

1

The liquid-only pressure gradient in Equation (14a) is calculated as before, using Equation (12b) with x = 0 and

0.7

G tot D --------------Vt Uh

We l

with

(12g)

= x 0.78(1 – x) 0.224

(14a)

(15c)

2

(13c)

 dp tot - = f 2G  ----v ------------dz DU  vo v

(15d)

where 2

2

) Vtt = 1 + CX tt + X tt

(13d)

In both cases, 0.9

1 x  X tt = -----------   x 

 U v 0.5  Pl  0.1  -----  ------   Ul   P v 

(13e)

where friction factors in Equations (15c) and (15d) are again calculated from Equations (12c) and (12d) using the liquid and vapor properties, respectively. The general nature of annular vapor/liquid flow in vertical pipes is indicated in Figure 8 (Wallis 1970), which plots the effective vapor friction factor versus the liquid fraction (1 – Hv), where Hv is the vapor void fraction as defined by Equations (11c) or (11d).

Two-Phase Flow

5.13

The effective vapor friction factor in Figure 8 is defined as 2.5

f eff =

 dp Hv D --------------------------- ------ 2  dz   4Q v  2U v  ---------2-  SD 

(16a)

where D is the pipe diameter, Uv is gas density, and Qv is volumetric flow rate. The friction factor of vapor flowing by itself in the pipe (presumed smooth) is denoted by fv . Wallis’ analysis of the flow occurrences is based on interfacial friction between the gas and liquid. The wavy film corresponds to a conduit with roughness height of about four times the liquid film thickness. Thus, the pressure drop relation for vertical flow is  U v   4Q v  2  1 + 75 1 H v  dp - ------ = 0.01  -------5-  -----------  --------------------------------2.5 dz  D  S    Hv

Pressure Drop in Plate Heat Exchangers (16b)

This corresponds to the Martinelli-type analysis with 2

Heck (1986) correlation worked quite well for a database of horizontal flows that included air/water, air/oil, steam, and several refrigerants. Ould Didi et al. (2002) also found that this method offered accuracies nearly as good or better than several other models; the Friedel (1979) and Grönnerud (1979) correlations also performed favorably. Note, however, that mean deviations of as much as 30% are common using these correlations; calculations for individual flow conditions can easily deviate 50% or more from measured pressure drops, so use these models as approximations only. Evaporators and condensers often have valves, tees, bends, and other fittings that contribute to the overall pressure drop of the heat exchanger. Collier and Thome (1996) summarize methods predicting the two-phase pressure drop in these fittings.

f two-phase = ) v f v

(16c)

1 + 75 1 H v 2 ) v = --------------------------------Hv

(16d)

when

The friction factor fv (of the vapor alone) is taken as 0.02, an appropriate turbulent flow value. This calculation can be modified for more detailed consideration of factors such as Reynolds number variation in friction, gas compressibility, and entrainment (Wallis 1970).

For a description of plate heat exchanger geometry, see the Plate Heat Exchangers section of Chapter 4. Ayub (2003) presented simple correlations for Fanning friction factor based on design and field data collected over a decade on ammonia and R-22 direct-expansion and flooded evaporators in North America. The goal was to formulate equations that could be readily used by a design and field engineer without reference to complicated two-phase models. Correlations within the plates are formulated as if the entire flow were saturated vapor. The correlation is accordingly adjusted for the chevron angle, and thus generalized for application to any type of commercially available plate, with a statistical error of r10%: f = (n/Re m)(–1.89 + 6.56R – 3.69R 2)

for 30 d E d 65 where R = (30/E), and E is the chevron angle in degrees. The values of m and n depend on Re.

Recommendations Although many references recommend the Lockhart and Martinelli (1949) correlation, recent reviews of pressure drop correlations found other methods to be more accurate. Tribbe and Müller-Steinhagen (2000) found that the Müller-Steinhagen and Fig. 8

(17)

m

n

Re

0.137 0.172 0.161 0.195

2.99 2.99 3.15 2.99

16,000

Qualitative Pressure Drop Characteristics of Two-Phase Flow Regime

Fig. 8 Qualitative Pressure Drop Characteristics of Two-Phase Flow Regime (Wallis 1970)

5.14

2009 ASHRAE Handbook—Fundamentals

Pressure drop within the port holes is correlated as follows, treating the entire flow as saturated vapor: 'pport = 0.0076UV 2/2g

(18)

This equation accounts for pressure drop in both inlet and outlet refrigerant ports and gives the pressure drop in units of lb/in2 with input for U in lb/ft3, V in ft/s, and g in ft/s2.

ENHANCED SURFACES Enhanced heat transfer surfaces are used in heat exchangers to improve performance and decrease cost. Condensing heat transfer is often enhanced with circular fins attached to the external surfaces of tubes to increase the heat transfer area. Other enhancement methods (e.g., porous coatings, integral fins, reentrant cavities) are used to augment boiling heat transfer on external surfaces of evaporator tubes. Webb (1981) surveyed external boiling surfaces and compared performances of several enhanced surfaces with performance of smooth tubes. For heat exchangers, the heat transfer coefficient for the refrigerant side is often smaller than the coefficient for the water side. Thus, enhancing the refrigerant-side surface can reduce the size of the heat exchanger and improve its performance. Internal fins increase the heat transfer coefficients during evaporation or condensation in tubes. However, internal fins increase refrigerant pressure drop and reduce the heat transfer rate by decreasing the available temperature difference between hot and cold fluids. Designers should carefully determine the number of parallel refrigerant passes that give optimum loading for best overall heat transfer. For a review of internal enhancements for two-phase heat transfer, including the effects of oil, see Newell and Shah (2001). For additional information on enhancement methods in two-phase flow, consult Bergles (1976, 1985), Thome (1990), and Webb (1994).

SYMBOLS A = area, effective plate area a = local acceleration b = breadth of condensing surface. For vertical tube, b = Sd; for horizontal tube, b = 2L; flow channel gap in flat plate heat exchanger. Bo = boiling number C = coefficient or constant Co = convection number cp = specific heat at constant pressure cv = specific heat at constant volume D = diameter Do = outside tube diameter d = diameter; or prefix meaning differential (dp/dz) = pressure gradient (dp/dz)fric = frictional pressure gradient (dp/dz)l = frictional pressure gradient, assuming that liquid alone is flowing in pipe (dp/dz)mom= momentum pressure gradient (dp/dz)v = frictional pressure gradient, assuming that gas (or vapor) alone is flowing in pipe Fr = Froude number f = friction factor for single-phase flow (Fanning) G = mass velocity g = gravitational acceleration gc = gravitational constant Gr = Grashof number h = heat transfer coefficient hf = single-phase liquid heat transfer coefficient hfg = latent heat of vaporization or of condensation j = Colburn j-factor k = thermal conductivity KD = mass transfer coefficient, dimensionless coefficient (Table 1) L = length Lp = plate length M = mass; or molecular weight m = general exponent m· = mass flow rate

Mm Mv N n Nu P p pc pg Pr pr pv Qv q r Ra Re Rp t U V We x Xtt x, y, z Yg Yv

= = = = = = = = = = = = = = = = = = = = = = = = = = =

mean molecular weight of vapor/gas mixture molecular weight of condensing vapor number of tubes in vertical tier general exponent Nusselt number plate perimeter pressure critical thermodynamic pressure for coolant partial pressure of noncondensable gas Prandtl number reduced pressure = p/pc partial pressure of vapor volumetric flow rate heat transfer rate radius Rayleigh number Reynolds number surface roughness, Pm temperature overall heat transfer coefficient linear velocity Weber number quality (i.e., mass fraction of vapor); or distance in dt/dx Martinelli parameter lengths along principal coordinate axes mole fraction of noncondensable gas mole fraction of vapor

Greek D = thermal diffusivity = k/Ucp E = coefficient of thermal expansion, chevron angle * = mass rate of flow of condensate per unit of breadth (see section on Condensing) ' = difference between values H = roughness of interface Hv = vapor void fraction T = contact angle P = absolute (dynamic) viscosity Pl = dynamic viscosity of saturated liquid Pv = dynamic viscosity of saturated vapor Q = kinematic viscosity U = density Ul = density of saturated liquid Uv = density of saturated vapor phase V = surface tension ) = two-phase multiplier I = fin efficiency

Subscripts and Superscripts a b c e eff f fric g gv h i if l m mac max mic min mom ncb o r s sat t tot v w f *

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

exponent in Equation (1) bubble critical, cold (fluid), characteristic, coolant equivalent effective film or fin friction noncondensable gas noncondensable gas and vapor mixture horizontal, hot (fluid), hydraulic inlet or inside interface liquid mean convective mechanism maximum nucleation mechanism minimum momentum nucleate boiling outside, outlet, overall, reference root (fin) or reduced pressure surface or secondary heat transfer surface saturation temperature or terminal temperature of tip (fin) total vapor or vertical wall bulk or far-field reference

Two-Phase Flow

5.15 REFERENCES

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5.16 Howard, A.H. and I. Mudawar. 1999. Orientation effects on pool boiling critical heat flux (CHF) and modeling of CHF for near-vertical surfaces. International Journal of Heat and Mass Transfer 42:1665-1688. Hughmark, G.A. 1962. A statistical analysis of nucleate pool boiling data. International Journal of Heat and Mass Transfer 5:667. Incropera, F.P. and D.P. DeWitt. 2002. Fundamentals of heat and mass transfer, 5th ed. John Wiley & Sons, New York. Isrealachvili, J.N. 1991. Intermolecular surface forces. Academic Press, New York. Jakob, M. 1949, 1957. Heat transfer, vols. I and II. John Wiley & Sons, New York. Jonsson, I. 1985. Plate heat exchangers as evaporators and condensers for refrigerants. Australian Refrigeration, Air Conditioning and Heating 39(9):30-31, 33-35. Kandlikar, S.G., ed. 1999. Handbook of phase change: Boiling and condensation. Taylor and Francis, Philadelphia. Kandlikar, S.G. 2001. A theoretical model to predict pool boiling CHF incorporating effects of contact angle and orientation. Journal of Heat Transfer 123:1071-1079. Kattan, N., J.R. Thome, and D. Favrat. 1998a. Flow boiling in horizontal tubes, part 1: Development of diabatic two-phase flow pattern map. Journal of Heat Transfer 120(1):140-147. Kattan, N., J.R. Thome, and D. Favrat. 1998b. Flow boiling in horizontal tubes, part 3: Development of new heat transfer model based on flow patterns. Journal of Heat Transfer 120(1):156-165. Kumar, H. 1984. The plate heat exchanger: Construction and design. Institute of Chemical Engineering Symposium Series 86:1275-1288. Kutateladze, S.S. 1951. A hydrodynamic theory of changes in the boiling process under free convection. Izvestia Akademii Nauk, USSR, Otdelenie Tekhnicheski Nauk 4:529. Kutateladze, S.S. 1963. Fundamentals of heat transfer. E. Arnold Press, London. Lienhard, J.H. and V.E. Schrock. 1963. The effect of pressure, geometry and the equation of state upon peak and minimum boiling heat flux. ASME Journal of Heat Transfer 85:261. Lienhard, J.H. and P.T.Y. Wong. 1964. The dominant unstable wavelength and minimum heat flux during film boiling on a horizontal cylinder. Journal of Heat Transfer 86:220-226. Lockhart, R.W. and R.C. Martinelli. 1949. Proposed correlation of data for isothermal two-phase, two-component flow in pipes. Chemical Engineering Progress 45(1):39-48. Mandhane, J.M., G.A. Gregory, and K. Aziz. 1974. A flow pattern map for gas-liquid flow in horizontal pipes. International Journal of Multiphase Flow 1:537-553. Martinelli, R.C. and D.B. Nelson. 1948. Prediction of pressure drops during forced circulation boiling of water. ASME Transactions 70:695. McAdams, W.H. 1954. Heat transmission, 3rd ed. McGraw-Hill, New York. McGillis, W.R. and V.P. Carey. 1996. On the role of the Marangoni effects on the critical heat flux for pool boiling of binary mixture. Journal of Heat Transfer 118(1):103-109. Müller-Steinhagen, H. and K. Heck. 1986. A simple friction pressure drop correlation for two-phase flow in pipes. Chemical Engineering Progress 20:297-308. Newell, T.A. and R.K. Shah. 2001. An assessment of refrigerant heat transfer, pressure drop, and void fraction effects in microfin tubes. International Journal of HVAC&R Research 7(2):125-153. Nukiyama, S. 1934. The maximum and minimum values of heat transmitted from metal to boiling water under atmospheric pressure. Journal of the Japanese Society of Mechanical Engineers 37:367. Nusselt, W. 1916. Die Oberflächenkondensation des Wasserdampfes. Zeitung Verein Deutscher Ingenieure 60:541. Othmer, D.F. 1929. The condensation of steam. Industrial and Engineering Chemistry 21(June):576. Ould Didi, M.B., N. Kattan and J.R. Thome. 2002. Prediction of two-phase pressure gradients of refrigerants in horizontal tubes. International Journal of Refrigeration 25:935-947. Palen, J. and Z.H. Yang. 2001. Reflux condensation flooding prediction: A review of current status. Transactions of the Institute of Chemical Engineers 79(A):463-469. Panchal, C.B. 1985. Condensation heat transfer in plate heat exchangers. Two-Phase Heat Exchanger Symposium, HTD vol. 44, pp. 45-52. American Society of Mechanical Engineers, New York.

2009 ASHRAE Handbook—Fundamentals Panchal, C.B. 1990. Experimental investigation of condensation of steam in the presence of noncondensable gases using plate heat exchangers. Argonne National Laboratory Report CONF-900339-1. Panchal, C.B. and D.L. Hillis. 1984. OTEC Performance tests of the AlfaLaval plate heat exchanger as an ammonia evaporator. Argonne National Laboratory Report ANL-OTEC-PS-13. Panchal, C.B., D.L. Hillis, and A. Thomas. 1983. Convective boiling of ammonia and Freon 22 in plate heat exchangers. Argonne National Laboratory Report CONF-830301-13. Perry, J.H. 1950. Chemical engineers handbook, 3rd ed. McGraw-Hill, New York. Pierre, B. 1964. Flow resistance with boiling refrigerant. ASHRAE Journal (September/October). Reddy, R.P. and J.H. Lienhard. 1989. The peak heat flux in saturated ethanolwater mixtures. Journal of Heat Transfer 111:480-486. Rohsenow, W.M. 1963. Boiling heat transfer. In Modern developments in heat transfer, W. Ibele, ed. Academic Press, New York. Rohsenow, W.M. and P. Griffith. 1956. Correlation of maximum heat flux data for boiling of saturated liquids. Chemical Engineering Progress Symposium Series 52:47-49. Rohsenow, W.M., J.P. Hartnett, and Y.I. Cho. 1998. Handbook of heat transfer, 3rd ed., pp. 1570-1571. McGraw-Hill. Rose, J.W. 1969. Condensation of a vapour in the presence of a noncondensable gas. International Journal of Heat and Mass Transfer 12:233. Rose, J.W. 1998. Condensation heat transfer fundamentals. Transactions of the Institution of Chemical Engineers 76(A):143-152. Rouhani, Z. and E. Axelsson. 1970. Calculation of void volume fraction in the subcooled and quality boiling regions. International Journal of Heat and Mass Transfer 13:383-393. Schlager, L.M., M.B. Pate, and A.E. Bergles. 1987. Evaporation and condensation of refrigerant-oil mixtures in a smooth tube and micro-fin tube. ASHRAE Transactions 93:293-316. Sefiane, K. 2001. A new approach in the modeling of the critical heat flux and enhancement techniques. AIChE Journal 47(11):2402-2412. Shah, M.M. 1979. A general correlation for heat transfer during film condensation inside pipes. International Journal of Heat and Mass Transfer 22:547-556. Shah, M.M. 1982. A new correlation for saturated boiling heat transfer: Equations and further study. ASHRAE Transactions 88(1):185-196. Sparrow, E.M. and S.H. Lin. 1964. Condensation in the presence of a noncondensable gas. ASME Transactions, Journal of Heat Transfer 86C: 430. Sparrow, E.M., W.J. Minkowycz, and M. Saddy. 1967. Forced convection condensation in the presence of noncondensables and interfacial resistance. International Journal of Heat and Mass Transfer 10:1829. Spedding, P.L. and D.R. Spence. 1993. Flow regimes in two-phase gasliquid flow. International Journal of Multiphase Flow 19(2):245-280. Starczewski, J. 1965. Generalized design of evaporation heat transfer to nucleate boiling liquids. British Chemical Engineering (August). Steiner, D. 1993. VDI-Wärmeatlas (VDI Heat Atlas). Verein Deutscher Ingenieure, VDI-Gesellschaft Verfahrenstechnik und Chemieingenieurwesen (GCV), Düsseldorf, Chapter Hbb. Steiner, D. and J. Taborek. 1992. Flow boiling heat transfer in vertical tubes correlated by an asymptotic model. Heat Transfer Engineering 13(2): 43-69. Stephan, K. 1963. Influence of oil on heat transfer of boiling Freon-12 and Freon-22. Eleventh International Congress of Refrigeration, IIR Bulletin 3. Stephan, K. 1992. Heat transfer in condensation and boiling. SpringerVerlag, Berlin. Stephan, K. and M. Abdelsalam. 1980. Heat transfer correlations for natural convection boiling. International Journal of Heat and Mass Transfer 23:73-87. Syed, A. 1990. The use of plate heat exchangers as evaporators and condensers in process refrigeration. Symposium on Advanced Heat Exchanger Design. Institute of Chemical Engineers, Leeds, U.K. Thom, J.R.S. 1964. Prediction of pressure drop during forced circulation boiling water. International Journal of Heat and Mass Transfer 7: 709-724. Thome, J.R. 1990. Enhanced boiling heat transfer. Hemisphere (Taylor and Francis), New York. Thome, J.R. 2001. Flow regime based modeling of two-phase heat transfer. Multiphase Science and Technology 13(3-4):131-160.

Two-Phase Flow Thome, J.R. 2003. Update on the Kattan-Thome-Favrat flow boiling model and flow pattern map. Fifth International Conference on Boiling Heat Transfer, Montego Bay, Jamaica. Thome, J.R. and A.W. Shock. 1984. Boiling of multicomponent liquid mixtures. In Advances in heat transfer, vol. 16, pp. 59-156. Academic Press, New York. Thome, J.R., J. El Hajal, and A. Cavallini. 2003. Condensation in horizontal tubes, Part 2: New heat transfer model based on flow regimes. International Journal of Heat and Mass Transfer 46(18):3365-3387. Thonon, B. 1995. Design method for plate evaporators and condensers. 1st International Conference on Process Intensification for the Chemical Industry, BHR Group Conference Series Publication 18, pp. 37-47. Thonon, B., R. Vidil, and C. Marvillet. 1995. Recent research and developments in plate heat exchangers. Journal of Enhanced Heat Transfer 2(12):149-155. Tribbe, C. and H. Müller-Steinhagen. 2000. An evaluation of the performance of phenomenological models for predicting pressure gradient during gas-liquid flow in horizontal pipelines. International Journal of Multiphase Flow 26:1019-1036. Tschernobyiski, I. and G. Ratiani. 1955. Kholodilnaya Teknika 32. Turner, J.M. and G.B. Wallis. 1965. The separate-cylinders model of twophase flow. Report NYO-3114-6. Thayer’s School of Engineering, Dartmouth College, Hanover, NH. Van Stralen, S.J. 1959. Heat transfer to boiling binary liquid mixtures. British Chemical Engineering 4(January):78. Van Stralen, S.J. and R. Cole. 1979. Boiling phenomena, vol. 1. Hemisphere Publishing, Washington, D.C. Wallis, G.B. 1969. One-dimensional two-phase flow. McGraw-Hill, New York.

5.17 Wallis, G.C. 1970. Annular two-phase flow, part I: A simple theory, part II: Additional effect. ASME Transactions, Journal of Basic Engineering 92D:59 and 73. Webb, R.L. 1981. The evolution of enhanced surface geometrics for nucleate boiling. Heat Transfer Engineering 2(3-4):46-69. Webb, J.R. 1994. Enhanced boiling heat transfer. John Wiley & Sons, New York. Westwater, J.W. 1963. Things we don’t know about boiling. In Research in Heat Transfer, J. Clark, ed. Pergamon Press, New York. Worsoe-Schmidt, P. 1959. Some characteristics of flow-pattern and heat transfer of Freon-12 evaporating in horizontal tubes. Ingenieren, International edition, 3(3). Yan, Y.-Y. and T.-F. Lin. 1999. Evaporation heat transfer and pressure drop of refrigerant R-134a in a plate heat exchanger. Journal of Heat Transfer 121(1):118-127. Young, M. 1994. Plate heat exchangers as liquid cooling evaporators in ammonia refrigeration systems. Proceedings of the IIAR 16th Annual Meeting, St. Louis. Zeurcher O., J.R. Thome, and D. Favrat. 1998. In-tube flow boiling of R407C and R-407C/oil mixtures, part II: Plain tube results and predictions. International Journal of HVAC&R Research 4(4):373-399. Zivi, S.M. 1964. Estimation of steady-state steam void-fraction by means of the principle of minimum entropy production. Journal of Heat Transfer 86:247-252. Zuber, N. 1959. Hydrodynamic aspects of boiling heat transfer. U.S. Atomic Energy Commission, Technical Information Service, Report AECU 4439. Oak Ridge, TN. Zuber, N., M. Tribus, and J.W. Westwater. 1962. The hydrodynamic crisis in pool boiling of saturated and subcooled liquids. Proceedings of the International Heat Transfer Conference 2:230, and discussion of the papers, vol. 6.

CHAPTER 6

MASS TRANSFER Molecular Diffusion ........................................................................................................................ 6.1 Convection of Mass ......................................................................................................................... 6.5 Simultaneous Heat and Mass Transfer Between Water-Wetted Surfaces and Air.......................... 6.9 Symbols ......................................................................................................................................... 6.13

M

the mixture of gases A and B in a direction that reduces the concentration gradient.

ASS transfer by either molecular diffusion or convection is the transport of one component of a mixture relative to the motion of the mixture and is the result of a concentration gradient. Mass transfer can occur in liquids and solids as well as gases. For example, water on the wetted slats of a cooling tower evaporates into air in a cooling tower (liquid to gas mass transfer), and water vapor from a food product transfers to the dry air as it dries. A piece of solid CO2 (dry ice) also gets smaller and smaller over time as the CO2 molecules diffuse into air (solid to gas mass transfer). A piece of sugar added to a cup of coffee eventually dissolves and diffuses into the solution, sweetening the coffee, although the sugar molecules are much heavier than the water molecules (solid to liquid mass transfer). Air freshener does not just smell where sprayed, but rather the smell spreads throughout the room. The air freshener (matter) moves from an area of high concentration where sprayed to an area of low concentration far away. In an absorption chiller, lowpressure, low-temperature refrigerant vapor from the evaporator enters the thermal compressor in the absorber section, where the refrigerant vapor is absorbed by the strong absorbent (concentrated solution) and dilutes the solution. In air conditioning, water vapor is added or removed from the air by simultaneous transfer of heat and mass (water vapor) between the airstream and a wetted surface. The wetted surface can be water droplets in an air washer, condensate on the surface of a dehumidifying coil, a spray of liquid absorbent, or wetted surfaces of an evaporative condenser. Equipment performance with these phenomena must be calculated carefully because of simultaneous heat and mass transfer. This chapter addresses mass transfer principles and provides methods of solving a simultaneous heat and mass transfer problem involving air and water vapor, emphasizing air-conditioning processes. The formulations presented can help analyze performance of specific equipment. For discussion of performance of cooling coils, evaporative condensers, cooling towers, and air washers, see Chapters 22, 38, 39, and 40, respectively, of the 2008 ASHRAE Handbook—HVAC Systems and Equipment.

Fick’s Law The basic equation for molecular diffusion is Fick’s law. Expressing the concentration of component B of a binary mixture of components A and B in terms of the mass fraction UB/U or mole fraction CB /C, Fick’s law is d UB e U J B = – U D v --------------------= –JA dy

(1a)

d CB e C J B* = – CD v ---------------------- = – J A* dy

(1b)

where U = UA + UB and C = CA + CB. The minus sign indicates that the concentration gradient is negative in the direction of diffusion. The proportionality factor Dv is the mass diffusivity or the diffusion coefficient. The total mass flux m· Bs and molar flux m· Bs* are due to the average velocity of the mixture plus the diffusive flux: d UB e U m· Bs = U B v – UD v --------------------dy

(2a)

d CB e C m· Bs* = C B v * – CD v ---------------------dy

(2b)

where v is the mixture’s mass average velocity and v* is the molar average velocity. Bird et al. (1960) present an analysis of Equations (1a) and (1b). Equations (1a) and (1b) are equivalent forms of Fick’s law. The equation used depends on the problem and individual preference. This chapter emphasizes mass analysis rather than molar analysis. However, all results can be converted to the molar form using the relation CB { UB /MB.

MOLECULAR DIFFUSION

Fick’s Law for Dilute Mixtures

Most mass transfer problems can be analyzed by considering diffusion of a gas into a second gas, a liquid, or a solid. In this chapter, the diffusing or dilute component is designated as component B, and the other component as component A. For example, when water vapor diffuses into air, the water vapor is component B and dry air is component A. Properties with subscripts A or B are local properties of that component. Properties without subscripts are local properties of the mixture. The primary mechanism of mass diffusion at ordinary temperature and pressure conditions is molecular diffusion, a result of density gradient. In a binary gas mixture, the presence of a concentration gradient causes transport of matter by molecular diffusion; that is, because of random molecular motion, gas B diffuses through

In many mass diffusion problems, component B is dilute, with a density much smaller than the mixture’s. In this case, Equation (1a) can be written as dU B J B = – Dv dy

(3)

when UB 234 sin 68.62q + 68 @0.2 ------------------------------- = 29 Btu/h·ft 2 Example 8. Find the direct, diffuse and ground-reflected components of clear-sky solar irradiance on the skylight in Example 6. Solution: This example uses the same values as Example 7, except that the surface slope is 6 = 30° and the angle of incidence, calculated in Example 6, is T = 8.74°. The clear-sky irradiance components are then calculated from Equations (26), (29) and (31); the ratio Y is calculated for a vertical surface having the same azimuth as the receiving surface, so the value calculated in Example 7 is unchanged. Et,b = 234 cos(8.74°) = 231 Btu/h·ft2 Et,d = 68[0.750 sin(30°) + cos(30°)] = 84 Btu/h·ft2 1 – cos 30q 2 E t , r = > 234 sin 68.62q + 68 @0.2 ------------------------------- = 4 Btu/h·ft 2

(limiting by saturation in the case of the wet-bulb). This procedure is applicable to annual or monthly data and is illustrated in Example 9. Table 7 specifies the input values to be used for generation of several design-day types. Because daily temperature variation is driven by heat from the sun, the profile in Table 6 is, strictly speaking, specified in terms of solar time. Typical HVAC calculations (e.g., hourly cooling loads) are performed in local time, reflecting building operation schedules. The difference between local and solar time can easily be 1 or 2 h, depending on site longitude and whether daylight saving time is in effect. This difference can be included by accessing the temperature profile using apparent solar time (AST) calculated with Equation (7), as shown in the Example 9. Additional Moist-Air Properties. Once hourly dry-bulb and wet-bulb temperatures are known, additional moist air properties (e.g., dew-point temperature, humidity ratio, enthalpy) can be derived using the psychrometric chart, equations in Chapter 1, or psychrometric software. Example 9. Deriving Hourly Design-Day Temperatures. Calculate hourly temperatures for Atlanta, GA, for a July dry-bulb design day using the 5% design conditions. Solution: From Table 1, the July 5% dry-bulb design conditions for Atlanta are DB = 92.0°F and MCWB = 74.4°F. Daily range values are MCDBR = 20.7°F and MCWBR = 6.3°F. Daylight saving time is in effect for Atlanta in July. Apparent solar time (AST) for hour 1 local daylight saving time (LDT) is – 0.73. The nearest hour to the AST is 23, yielding a Table 6 profile value of 0.75. Then tdb,1 = 92.0 – 0.75 u 20.7 = 76.5°F. Similarly, twb,1 = 74.4 – 0.75 u 6.3 = 69.7°F. With psychrometric formulas, derive tdp,1 = 66.7 °F. Table 8 shows results of this procedure for all 24 h.

GENERATING DESIGN-DAY DATA This section provides procedures for generating 24 h temperature data sequences suitable as input to many HVAC analysis methods, including the radiant time series (RTS) cooling load calculation procedure described in Chapter 18. Temperatures. Table 6 gives a normalized daily temperature profile in fractions of daily temperature range. Recent research projects RP-1363 (Hedrick 2009) and RP-1453 (Thevenard 2009) have shown that this profile is representative of both dry-bulb and wetbulb temperature variation on typical design days. To calculate hourly temperatures, subtract the Table 6 fraction of the dry- or wet-bulb daily range from the dry- or wet-bulb design temperature Table 5 Ground Reflectance of Foreground Surfaces Foreground Surface

Reflectance

Water (large angle of incidences) Coniferous forest (winter) Bituminous and gravel roof Dry bare ground Weathered concrete Green grass Dry grassland Desert sand Light building surfaces Snow-covered surfaces: Typical city centre Typical urban site Typical rural site Isolated rural site

0.07 0.07 0.13 0.2 0.22 0.26 0.2 to 0.3 0.4 0.6

ESTIMATION OF DEGREE-DAYS Monthly Degree-Days The tables of climatic design conditions in this chapter list heating and cooling degree-days (bases 50 and 65°F). Although 50 and 65°F represent the most commonly used bases for the calculation of degree-days, calculation to other bases may be necessary. With that goal in mind, the tables also provide two parameters (monthly average temperature T, and standard deviation of daily average temperature sd) that enable estimation of degree-days to any base with reasonable accuracy. The calculation method was established by Schoenau and Kehrig (1990). Heating degree days HDDb to base Tb are expressed as Table 6

Fraction of Daily Temperature Range

Time, h

Fraction

Time, h

Fraction

Time, h

Fraction

1 2 3 4 5 6 7 8

0.88 0.92 0.95 0.98 1.00 0.98 0.91 0.74

9 10 11 12 13 14 15 16

0.55 0.38 0.23 0.13 0.05 0.00 0.00 0.06

17 18 19 20 21 22 23 24

0.14 0.24 0.39 0.50 0.59 0.68 0.75 0.82

0.2 0.4 0.5 0.7

Source: Adapted from Thevenard and Haddad (2006).

Table 7 Input Sources for Design-Day Generation Design Day Type

Design Conditions

Daily Ranges

Limits

Dry-bulb Annual Monthly

0.4, 1, or 2% annual cooling DB/MCWB 0.4, 2, 5, or 10% DB/MCWB for month

Hottest month 5% DB MCDBR/MCWBR 5% DB MCDBR/MCWBR for month

Hourly wet-bulb temp. = min(dry-bulb temp., wet-bulb temp.)

Wet-bulb Annual Monthly

0.4, 1, or 2% annual cooling WB/MCDB 0.4, 2, 5, or 10% WB/MCDB for month

Hottest month 5% WB MCDBR/MCWBR 5% WB MCDBR/MCWBR for month

Hourly dry-bulb temp. = max(dry-bulb temp. wet-bulb temp.)

14.12

2009 ASHRAE Handbook—Fundamentals

Table 8 Derived Hourly Temperatures for Atlanta, GA for July for 5% Design Conditions, °F Hour (LDT)

tdb

twb

tdp

Hour (LDT)

tdb

twb

tdp

1 2 3 4 5 6 7 8 9 10 11 12

76.5 75.0 73.8 73.0 72.3 71.7 71.3 71.7 73.2 76.7 80.6 84.1

69.7 69.2 68.9 68.6 68.4 68.2 68.1 68.2 68.7 69.7 70.9 72.0

66.7 66.7 66.7 66.7 66.7 66.7 66.7 66.7 66.7 66.8 66.9 67.0

13 14 15 16 17 18 19 20 21 22 23 24

87.2 89.3 91.0 92.0 92.0 90.8 89.1 87.0 83.9 81.7 79.8 77.9

73.0 73.6 74.1 74.4 74.4 74.0 73.5 72.9 71.9 71.2 70.7 70.1

67.1 67.3 67.4 67.4 67.4 67.3 67.2 67.1 67.0 66.9 66.8 66.8

LDT = Local daylight saving time

HDDb = Nsd [ZbF(Zb) + f (Zb)]

(32)

where N is the number of days in the month and Zb is the difference between monthly average temperature T and base temperature Tb , normalized by the standard deviation of the daily average temperature sd : Tb – T Z b = ---------------sd

(33)

Function f is the normal (Gaussian) probability density function with mean 0 and standard deviation 1, and function F is the equivalent cumulative normal probability function: § –Z 2 · 1 f Z = ----------exp ¨ --------- ¸ © 2 ¹ 2S F Z =

(34)

Z

¦ f z dz

(35)

–f

Both f and F are readily available as built-in functions in many scientific calculators or spreadsheet programs, so their manual calculation is rarely warranted. Cooling degree days CDDb to base Tb are calculated by the same equation: CDDb = Nsd [ZbF(Zb) + f (Zb)]

(36)

except that Zb is now expressed as T – Tb Z b = ---------------sd

(37)

Annual Degree-Days Annual degree-days are simply the sum of monthly degree days over the twelve months of the year. Example 10. Calculate heating and cooling degree-days (base 59°F) for Atlanta for the month of October. Solution: For October in Atlanta, Table 1 provides T = 63.5°F and sd = 7.08°F. For heating degree-days, Equation (33) provides Zb = (59 – 63.5)/7.08 = –0.636. From a scientific calculator or a spreadsheet program f (Zb) = 0.326, and F(Zb) = 0.263. Equation (32) then gives HDD59 = 31 × 7.08 [–0.636 × 0.263 + 0.326] = 34.9°F-day. For cooling degree-days, Zb = 0.636. Note that f (–Zb) = f (Zb) and F(–Zb) = 1 – F(Zb), hence

f (Zb) = 0.326

and

F(Zb) = 0.737

and CDD59 = 31 × 7.08 (–0.636 × 0.737 + 0.326) = 174.4°F-day. For most stations, the monthly degree days calculated with this method are within 9°F-day of the observed values.

REPRESENTATIVENESS OF DATA AND SOURCES OF UNCERTAINTY Representativeness of Data The climatic design information in this chapter was obtained by direct analysis of observations from the indicated locations. Design values reflect an estimate of the cumulative frequency of occurrence of the weather conditions at the recording station, either for single or jointly occurring elements, for several years into the future. Several sources of uncertainty affect the accuracy of using the design conditions to represent other locations or periods. The most important of these factors is spatial representativeness. Most of the observed data for which design conditions were calculated were collected from airport observing sites, the majority of which are flat, grassy, open areas, away from buildings and trees or other local influences. Temperatures recorded in these areas may be significantly different (5 to 8°F lower) compared to areas where the design conditions are being applied. Significant variations can also occur with changes in local elevation, across large metropolitan areas, or in the vicinity of large bodies of water. Judgment must always be exercised in assessing the representativeness of the design conditions. It is especially important to note the elevation of locations, because design conditions vary significantly for locations whose elevations differ by as little as a few hundred feet. Data representing psychrometric conditions are generally properties of air masses rather than local features, and tend to vary on regional scales. As a result, a particular value may reasonably represent an area extending several miles. Consult an applied climatologist regarding estimating design conditions for locations not listed in this chapter. For online references to applied climatologists, see http://www.ncdc.noaa.gov/oa/about/amscert.html. Also, GIScompatible files (KML format) are provided on the CD-ROM accompanying this book. This allows use of the data in a GIS environment such as Google Earth or ArcGIS, which provides capabilities to overlay various layers of information such as elevation, land-use, bodies of water, etc. This type of information can greatly assist in determining the most representative location to use for an application. The underlying data also depend on the method of observation. During the 1990s, most data gathering in the United States and Canada was converted to automated systems designated either an ASOS (Automated Surface Observation System) or an AWOS (Automated Weather Observing System). This change improved completeness and consistency of available data. However, changes have resulted from the inherent differences in type of instrumentation, instrumentation location, and processing procedures between the prior manual systems and ASOS. These effects were investigated in ASHRAE research project RP-1226 (Belcher and DeGaetano 2004). Comparison of one-year ASOS and manual records revealed some biases in dry-bulb temperature, dew-point temperature, and wind speed. These biases are judged to be negligible for HVAC engineering purposes; the tabulated design conditions in this chapter were derived from mixed automated and manual data as available. It has been recognized that changes in the location of the observing instruments often have a larger effect than the change in instrumentation. On the other hand, ASOS measurements of sky coverage and ceiling height differ markedly from manual observations and are incompatible with solar radiation models used in energy simulation software. An updated solar model, compatible with ASOS data, was developed as

Climatic Design Information Table 9

14.13

Locations Representing Various Climate Types

Cold Snow Forest Dry

Warm Rainy

Portland, ME Grand Island, NE Minot, ND Indianapolis, IN

Huntsville, AL Key West, FL Wilmington, NC West Palm Beach, FL Portland, OR Quillayute, WA

Amarillo, TX Bakersfield, CA Sacramento, CA Phoenix, AZ

Tropical Rainy

part of RP-1226. The ASOS-based model was found less accurate than models based on manually observed data when compared to measured solar radiation. Weather conditions vary from year to year and, to some extent, from decade to decade because of the inherent variability of climate. Similarly, values representing design conditions vary depending on the period of record used in the analysis. Thus, because of shortterm climatic variability, there is always some uncertainty in using design conditions from one period to represent another period. Typically, values of design dry-bulb temperature vary less than 2°F from decade to decade, but larger variations can occur. Differing periods used in the analysis can lead to differences in design conditions between nearby locations at similar elevations. Design conditions may show trends in areas of increasing urbanization or other regions experiencing extensive changes to land use. Longer-term climatic change brought by human or natural causes may also introduce trends into design conditions. This is discussed further in the section on Effects of Climate Change. Wind speed and direction are very sensitive to local exposure features such as terrain and surface cover. The original wind data used to calculate the wind speed and direction design conditions in Table 1 are often representative of a flat, open exposure, such as at airports. Wind engineering methods, as described in Chapter 24, can be used to account for exposure differences between airport and building sites. This is a complex procedure, best undertaken by an experienced applied climatologist or wind engineer with knowledge of the exposure of the observing and building sites and surrounding regions.

Uncertainty from Variation in Length of Record ASHRAE research project RP-1171 (Hubbard et al. 2004) investigated the uncertainty associated with the climatic design conditions in the 2001 ASHRAE Handbook—Fundamentals. The main objectives were to determine how many years are needed to calculate reliable design values and to look at the frequency and duration of episodes exceeding the design values. Design temperatures in the 1997 and 2001 editions were calculated for locations for which there were at least 8 years of sufficient data; the criterion for using 8 years was based on unpublished work by TC 4.2. RP-1171 analyzed data records from 14 U.S. locations (Table 9) representing four different climate types. The dry-bulb temperatures corresponding to the five annual percentile design temperatures (99.6, 99, 0.4, 1, and 2%) from the 33-year period 1961-1993 (period used for the 2001 edition’s U.S. stations) were calculated for each location. The temperatures corresponding to the same percentiles for each contiguous subperiod ranging from 1 to 33 years in length was calculated, and the standard deviation of the differences between the resulting design temperature from each subperiod and the entire 33-year period was calculated. For instance, for a 10-year period, the dry-bulb values corresponding to each of the 23 subperiods 1961-1970, 1962-1971, . . . , 1984-1993 were calculated and the standard deviation of differences with the dry-bulb value for the same percentile from the 33-year period calculated. The standard deviation values represent a measure of uncertainty of the design temperatures relative to the design temperature for the entire period of record. The results for the five annual percentiles are summarized in Figures 4A to 4E, each of which shows how the uncertainty (the average standard deviation for each of the locations in each climate type) varies with length of period.

To the degree that the differences used to calculate the standard deviations are distributed normally, the short-period design temperatures can be expected to lie within one standard deviation of the long-term design temperature 68% of the time. For example, from Figure 4A, the uncertainty for the Cold Snow Forest for a 1-year period is 6.5°F. This can be interpreted that the probability is 68% that the difference in a 99.6% dry-bulb in any given year will be within 6.5°F of the long-term 99.6% dry-bulb. Similarly, there is a 68% probability that the 99.6% dry-bulb from any 10-year period will be within 1.8°F of the long-term value for a location of the Cold Snow Forest climate type. The uncertainty for the cold season is higher than for the warm season. For example, the uncertainty for the 99.6% dry-bulb for a 10-year period ranges from 1.1 to 1.8°F for the five climate types, whereas the uncertainty for the 0.4% dry-bulb for a 10-year period ranges from 0.7 to 1.1°F. A variety of other general characteristics of uncertainty are evident from an inspection of Figure 4. For example, the highest uncertainty of any climate type for a 10-year period is 2.0°F for the Cold Snow Forest 99% dry-bulb case. The smallest uncertainty is 0.4°F for the Tropical Rainy 1% and 2% dry-bulb cases. Based on these results, it was concluded that using a minimum of 8 years of data would provide reliable (within ±1.8°F) climatic design calculations for most stations.

Effects of Climate Change The evidence is unequivocal that the climate system is warming globally (IPCC 2007). The most frequently observed effects relate to increases in average, and to some degree, extreme temperatures. This is partly illustrated by the results of an analysis of design conditions conducted as part of developing the updated values for this chapter (Thevenard 2009). For 1274 observing sites worldwide with suitably complete data from 1977 to 2006, selected design conditions were compared between the period 1977-1986 and 19972006. The results, averaged over all locations, are as follows: • • • • •

The 99.6% annual dry-bulb temperature increased 2.74°F The 0.4% annual dry-bulb increased 1.42°F Annual dew point increased by 0.99°F Heating-degree days (base 65°F) decreased by 427°F-days Cooling degree-days (base 50°F) increased by 245°F-days

Although these results are consistent with general warming of the world climate system, there are other effects that undoubtedly contribute, such as increased urbanization around many of the observing sites (airports, typically). There was no attempt in the analysis to determine the reasons for the changes. Regardless of the reasons for increases, the general approach of developing design conditions based on analysis of the recent record (25 years, in this case) was specifically adopted for updating the values in this chapter as a balance between accounting for longterm trends and the sampling variation caused by year-to-year variation. Although this does not necessarily provide the optimum predictive value for representing conditions over the next one or two decades, it at least has the effect of incorporating changes in climate and local conditions as they occur, as updates are conducted regularly using recent data. Meteorological services worldwide are considering the many aspects of this complex issue in the calculation of climate “normals” (averages, extremes, and other statistical summary information of climate elements typically calculated for a 30-year period at the end of each decade). Livezey et al. (2007) and WMO (2007) provide detailed analyses and recommendations in this regard. Extrapolating design conditions to the next few decades based on observed trends should only be done with attention to the particular climate element and the regional and temporal characteristics of observed trends (Livezey et al. 2007).

14.14 Fig. 4

2009 ASHRAE Handbook—Fundamentals Uncertainty versus Period Length for Various Dry-Bulb Temperatures, by Climate Type

Fig. 4

Uncertainty versus Period Length for Various Dry-Bulb Temperatures, by Climate Type

Episodes Exceeding the Design Dry-Bulb Temperature Design temperatures based on annual percentiles indicate how many hours each year on average the specific conditions will be exceeded, but do not provide any information on the length or frequency of such episodes. As reported by Hubbard et al. (2004), each episode and its duration for the locations in Table 9 during which the 2001 design conditions represented by the 99.6, 99, 0.4, 1, and 2% dry-bulb temperatures were exceeded (i.e., were more extreme) was tabulated and their frequency of occurrence analyzed. The measure of frequency is the average number of episodes per year or its reciprocal, the average period between episodes.

Cold- and warm-season results are presented in Figures 5A and 5B, respectively, for Indianapolis, IN, as a representative example. The duration for the 10-year period between episodes more extreme than the 99.6% design dry-bulb is 37 h, and 62 h for the 99% design dry-bulb. For the warm season, the 10-year period durations corresponding to the 0.4, 1, and 2% design dry-bulb, are about 10, 12, and 15 h, respectively. Although the results in Hubbard et al. (2004) varied somewhat among the locations analyzed, generally the longest cold-season episodes last days, whereas the longest warm-season episodes were always shorter than 24 h. These results were seen at almost

Climatic Design Information Fig. 1 Frequency and Duration of Episodes Exceeding Design Dry-Bulb Temperature for Indianapolis, IN

14.15 • Display frequency distribution and the cumulative frequency distribution functions in graphical form • Display joint frequency functions in graphical form • Display the table of years and months used for the calculation • Display hourly binned dry-bulb temperature data • Calculate heating and cooling degree-days to any base, using the method of Schoenau and Kehrig (1990) The Engineering Weather Data CD (NCDC 1999), an update of Air Force Manual 88-29, was compiled by the U.S. Air Force Combat Climatology Center. This CD contains several tabular and graphical summaries of temperature, humidity, and wind speed information for hundreds of locations in the United States and around the world. In particular, it contains detailed joint frequency tables of temperature and humidity for each month, binned at 1°F and 3 h local time-of-day intervals. This CD is available from NCDC: http: // ols.nndc.noaa.gov/ plolstore/ plsql/ olstore.prodspecific? prodnum=C00515-CDR-A0001. The International Station Meteorological Climate Summary (ISMCS) is a CD-ROM containing climatic summary information for over 7000 locations around the world (NCDC 1996). A table providing the joint frequency of dry-bulb temperature and wet-bulb temperature depression is provided for the locations with hourly observations. It can be used as an aid in estimating design conditions for locations for which no other information is available. The CD is available here: http://ols.nndc.noaa.gov/plolstore/plsql/olstore. prodspecific?prodnum=C00268-CDR-A0001. A Web version of this product is now available free of charge from NCDC: http://cdo.ncdc. noaa.gov/pls/plclimprod/poemain.accessrouter?datasetabbv= DS3505. Note that you should select the “advanced” option, then click on the “data summary” option. This service is also available via a GIS Web site: http://gis.ncdc.noaa.gov/website/ims-cdo/ish/viewer.htm. The monthly frequency distribution of dry-bulb temperatures and mean coincident wet-bulb temperatures for 134 Canadian locations is available from Environment Canada (1983-1987).

Degree Days and Climate Normals Fig. 5 Frequency and Duration of Episodes Exceeding Design Dry-Bulb Temperature for Indianapolis, IN all locations, and are general for the continental United States. The only exception was Phoenix, where the longest cold-season episodes were less than 24 h. This is likely the result of the southern latitude and dry climate, which produces a large daily temperature range, even in the cold season.

OTHER SOURCES OF CLIMATIC INFORMATION Joint Frequency Tables of Psychrometric Conditions Design values in this chapter were developed by ASHRAE research project RP-1453 (Thevenard 2009). The frequency vectors used to calculate the simple design conditions, and the joint frequency matrices used to calculate the coincident design conditions, are available in ASHRAE’s Weather Data Viewer 4.0 (WDView 4.0) (ASHRAE 2009). WDView 4.0 gives users full access to the frequency vectors and joint frequency matrices for all 5564 stations in the 2009 ASHRAE Handbook—Fundamentals via a spreadsheet. WDView 4.0 provides the following capabilities: • Select a station by WMO number or region/country/state/name or by proximity to a given latitude and longitude • Retrieve design climatic conditions for a specified station, in SI or I-P units • Display frequency vectors and joint frequency matrices in the form of numerical tables

Heating and cooling degree-day summary data for over 4000 U.S. stations are available online at no cost at http://cdo.ncdc.noaa.gov/ climatenormals/clim81_supp/CLIM81_Sup_02.pdf (NCDC 2002a, 2002b). This publication presents annual heating degree day normals to the following bases (°F): 65, 60, 57, 55, 50, 45, and 40; and annual cooling degree day normals to the following bases (°F): 70, 65, 60, 57, 55, 50, and 45. The 1971-2000 climate normals for over 6000 United States locations are available online (free of charge) and on CD from the National Climatic Data Center: http://cdo.ncdc.noaa.gov/cgi-bin/ climatenormals/climatenormals.pl. Also, users may generate normals/averages for any chosen period (dynamic normals) at http:// www7.ncdc.noaa.gov/CDO/normals. The Canadian Climate Normals for 1971-2000 are available from Environment Canada at http://climate.weatheroffice.ec.gc.ca (Environment Canada 2003). The Climatography of the United States No. 20 (CLIM20), monthly station climate summaries for 1971-2000 are climatic station summaries of particular interest to engineering, energy, industry, and agricultural applications (NCDC 2004). These summaries contain a variety of statistics for temperature, precipitation, snow, freeze dates, and degree-day elements for 4273 stations. The statistics include means, median (precipitation and snow elements), extremes, mean number of days exceeding threshold values, and heating, cooling, and growing degree-days for various temperature bases. Also included are probabilities for monthly precipitation and freeze data. Information on this product can be found at http:// www.ncdc.noaa.gov/oa/documentlibrary/pdf/eis/clim20eis.pdf. Heating and cooling degree-day and degree-hour data for 3677 locations from 115 countries were developed by Crawley (1994)

14.16 from the Global Daily Summary (GDS) version 1.0 and the International Station Meteorological Climate Summary (ISMCS) version 4.0 data.

Typical Year Data Sets Software is available to simulate the annual energy performance of buildings requiring a 1-year data set (8760 h) of weather conditions. Many data sets in different record formats have been developed to meet this requirement. The data represent a typical year with respect to weather-induced energy loads on a building. No explicit effort was made to represent extreme conditions, so these files do not represent design conditions. The National Renewable Energy Laboratory’s (NREL) TMY3 data set (Wilcox and Marion 2008) contains data for 1020 U.S. locations. TMY3, along with the 1991-2005 National Solar Radiation Data Base (NSRDB) (NREL 2007), contains hourly solar radiation [global, beam (direct), and diffuse} and meteorological data for 1454 stations, and is available at http://ols.nndc.noaa.gov/plolstore/plsql/ olstore.prodspecific?prodnum=C00668-TAP-A0001. These were produced using an objective statistical algorithm to select the most typical month from the long-term record. Canadian Weather Year for Energy Calculation (CWEC) files for 47 Canadian locations were developed for use with the Canadian National Energy Code, using the TMY algorithm and software (Environment Canada 1993). Files for 75 locations are now available. Examples of the use of these files for energy calculations in both residential and commercial buildings, including the differences among the files, are available in Crawley (1998) and Huang (1998).

Sequences of Extreme Temperature and Humidity Durations Colliver (1997) and Colliver et al. (1998) compiled extreme sequences of 1-, 3-, 5-, and 7-day duration for 239 U.S. and 144 Canadian locations based independently on the following five criteria: high dry-bulb temperature, high dew-point temperature, high enthalpy, low dry-bulb temperature, and low wet-bulb depression. For the criteria associated with high values, the sequences are selected according to annual percentiles of 0.4, 1.0, and 2.0. For the criteria corresponding to low values, annual percentiles of 99.6, 99.0, and 98.0 are reported. Although these percentiles are identical to those used to select annual heating and cooling design temperatures, the maximum or minimum temperatures within each sequence are significantly more extreme than the corresponding design temperatures. The data included for each hour of a sequence are solar radiation, dry-bulb and dew-point temperature, atmospheric pressure, and wind speed and direction. Accompanying information allows the user to go back to the source data and obtain sequences with different characteristics (i.e., different probability of occurrence, windy conditions, low or high solar radiation, etc.). These extreme sequences are available on CD (ASHRAE 1997). These sequences were developed primarily to assist the design of heating or cooling systems having a finite capacity before regeneration is required or of systems that rely on thermal mass to limit loads. The information is also useful where information on the hourly weather sequence during extreme episodes is required for design.

Global Weather Data Source Web Page Because of growing demand for more comprehensive global coverage of weather data for HVAC applications around the world, ASHRAE sponsored research project RP-1170 (Plantico 2001) to construct a Global Weather Data Sources (GWDS) Web page. With the growth of the World Wide Web, many national climate services and other climate data sources are making more information available over the Internet. The purpose of RP-1170 was to provide ASHRAE membership with easy access to major sources of international weather data through one consolidated system via the Web.

2009 ASHRAE Handbook—Fundamentals This Web page was recently updated to better use the resources of the World Meteorological Organization (WMO) and NCDC. The GWDS Web page is accessible at http://www.ncdc.noaa.gov/oa/ ashrae/gwds-title.html.

Observational Data Sets For detailed designs, custom analysis of the most appropriate long-term weather record is best. National weather services are generally the best source of long-term observational data. The National Climatic Data Center (NCDC), in conjunction with U.S. Air Force and Navy partners in Asheville’s Federal Climate Complex (FCC), developed the global Integrated Surface Data (Lott 2004; Lott et al. 2001) to address a pressing need for an integrated global database of hourly land surface climatological data. The database of over 20,000 stations contains hourly and some daily summary data from as early as 1900 (many stations beginning in the 1948-1973 timeframe), is operationally updated each day with the latest available data, and is now being further integrated with various data sets from the United States and other countries to further expand the spatial and temporal coverage of the data. For access to ISD, go to http:// cdo.ncdc.noaa.gov/ pls/plclimprod/ poemain.accessrouter?dataset abbv=DS3505 or, for a GIS interface, http://gis.ncdc.noaa.gov /website/ims-cdo/ish/viewer.htm. For a complete review of ISD and all of its products, go to http://www.ncdc.noaa.gov/oa/climate/isd/ index.php. The National Solar Radiation Database (NSRBD) (http://ols.nndc. noaa.gov/plolstore/plsql/olstore.prodspecific?prodnum=C00668TAP-A0001) and Canadian Weather Energy and Engineering Data Sets (CWEEDS) (Environment Canada 1993) provide long-term hourly data, including solar radiation values for the United States and Canada. A new solar model was required because of the implementation of automated observing systems that do not report traditional cloud elements. Considerable information about weather and climate services and data sets is available elsewhere through the World Wide Web. Information supplementary to this chapter may also be posted on the ASHRAE Technical Committee 4.2 Web site, the link to which is available from the ASHRAE Web site (www.ashrae.org).

REFERENCES ASHRAE. 1997. Design weather sequence viewer 2.1. (CD-ROM). ASHRAE. 2009. Weather Data Viewer, version 4.0. (CD-ROM). Belcher, B.N. and A.T. DeGaetano. 2004. Integration of ASOS weather data into building energy calculations with emphasis on model-derived solar radiation (RP-1226). ASHRAE Research Project, Final Report. Charlock T.P., F. Rose, D.A. Rutan, Z. Jin, D. Fillmore, and W.D. Collins. 2004. Global retrievals of the surface and atmosphere radiation budget and direct aerosol forcing. Proceedings, 13th Conference on Satellite Meteorology and Oceanography. American Meteorological Society, Norfolk, VA. Clarke A.D., W.G. Collins, P.J. Rasch, V.N. Kapustin, K. Moore, S. Howell, and H.E. Fuelberg. 2001. Dust and pollution transport on global scales: Aerosol measurements and model predictions. Journal of Geophysical Research 106 (D23): 32555-32569. Colliver, D.G. 1997. Sequences of extreme temperature and humidity for design calculations (RP-828). ASHRAE Research Project, Final Report. Colliver D.G., R.S. Gates, H. Zhang, and K.T. Priddy. 1998. Sequences of extreme temperature and humidity for design calculations. ASHRAE Transactions 104(1A):133-144. Colliver, D.G., R.S. Gates, T.F. Burkes, and H. Zhang. 2000. Development of the design climatic data for the 1997 ASHRAE Handbook—Fundamentals. ASHRAE Transactions 106(1). Crawley, D.B. 1994. Development of degree day and degree hour data for international locations. D.B. Crawley Consulting, Washington, D.C. Crawley, D.B. 1998. Which weather data should you use for energy simulations of commercial buildings? ASHRAE Transactions 104(2):498-515. Environment Canada. 1983-1987. Principal station data. PSD 1 to 134. Atmospheric Environment Service, Downsview, Ontario.

Climatic Design Information Environment Canada. 1993. Canadian weather for energy calculations (CWEC files) user’s manual. Atmospheric Environment Service, Downsview, Ontario. Environment Canada. 2003. Canadian 1971-2000 climate normals. Meteorological Service of Canada, Downsview, Ontario. (Available at http:// climate.weatheroffice.ec.gc.ca). Gueymard, C.A. 1987. An anisotropic solar irradiance model for tilted surfaces and its comparison with selected engineering algorithms. Solar Energy 38:367-386. Erratum, Solar Energy 40:175 (1988). Gueymard C.A. 2008. REST2: High performance solar radiation model for cloudless-sky irradiance, illuminance and photosynthetically active radiation—Validation with a benchmark dataset. Solar Energy 82:272-285. Harriman, L.G., D.G. Colliver, and H.K. Quinn. 1999. New weather data for energy calculations. ASHRAE Journal 41(3):31-38. Hedrick, R. 2009. Generation of hourly design-day weather data (RP-1363). ASHRAE Research Project, Final Report (Draft). Huang, J. 1998. The impact of different weather data on simulated residential heating and cooling loads. ASHRAE Transactions 104(2):516-527. Hubbard, K., K. Kunkel, A. DeGaetano, and K. Redmond. 2004. Sources of uncertainty in the calculation of the design weather conditions in the ASHRAE Handbook of Fundamentals (RP-1171). ASHRAE Research Project, Final Report. IPCC. 2007. Fourth assessment report: Summary for policy makers. International Panel on Climate Change, World Meteorological Organization, Geneva. (Available at http://ipcc.cac.es/pdf/assessment-report/ar4/syr/ ar4_syr_spm.pdf). Iqbal, M. 1983. An introduction to solar radiation. Academic Press, Toronto. Kasten, F. and T. Young. 1989. Revised optical air mass tables and approximation formula. Applied Optics 28:4735-4738. Lamming, S.D. and J.R. Salmon. 1996. Wind data for design of smoke control systems (RP-816). ASHRAE Research Project, Final Report. Lamming, S.D. and J.R. Salmon. 1998. Wind data for design of smoke control systems. ASHRAE Transactions 104(1A):742-751. Livezey, R.E., K.Y.Vinnikov, M.M. Timofeyeva, R. Tinker, and H.M. Van Den Dool. 2007. Estimation and extrapolation of climate normals and climatic trends. Journal of Applied Meteorology and Climatology 46: 1759-1776. Lott, J.N., R. Baldwin, and P. Jones. 2001. The FCC Integrated Surface Hourly Database, a new resource of global climate data. NCDC Technical Report 2001-01. National Climatic Data Center, Asheville, NC. (Available at ftp://ftp.ncdc.noaa.gov/pub/data/techrpts/tr200101/tr200101.pdf). Lott, J.N. 2004. The quality control of the integrated surface hourly database. 84th American Meteorological Society Annual Meeting, Seattle, WA. (Available at http://ams.confex.com/ams/pdfpapers/71929.pdf). Lowery, M.D. and J.E. Nash. 1970. A comparison of methods of fitting the double exponential distribution. Journal of Hydrology 10(3):259-275. Machler, M.A. and M. Iqbal. 1985. A modification of the ASHRAE clear sky irradiation model. ASHRAE Transactions 91(1A):106-115. NCDC. 1996. International station meteorological climate summary (ISMCS). National Climatic Data Center, Asheville, NC. NCDC. 1999. Engineering weather data. National Climatic Data Center, Asheville, NC.

14.17 NCDC. 2002a. Monthly normals of temperature, precipitation, and heating and cooling degree-days. In Climatography of the United States #81. National Climatic Data Center, Asheville, NC. NCDC. 2002b. Annual degree-days to selected bases (1971-2000). In Climatography of the United States #81. National Climatic Data Center, Asheville, NC. NCDC. 2003. Data documentation for data set 3505 (DSI-3505) integrated surface hourly (ISH) data. National Climatic Data Center, Asheville, NC. NCDC. 2004. Monthly station climate summaries. In Climatography of the U.S. #20. National Climatic Data Center, Asheville, NC. NREL. 2007. National solar radiation database, 1991-2005 update: User’s manual. Technical Report NREL/TP-581-41364. National Renewable Energy Laboratory, Golden, CO. (Available at http://www.nrel.gov/ docs/fy07osti/41364.pdf). Perez, R., P. Ineichen, R. Seals, J. Michalsky, and R. Stewart. 1990. Modeling daylight availability and irradiance components from direct and global irradiance. Solar Energy 44(5):271-289. Plantico, M. 2001. Identify and characterize international weather data sources (RP-1170). ASHRAE Research Project, Final Report. Randel, D.L., T.J. Greenwald, T.H. Vonder Haar, G.L. Stephens, M.A. Ringerud, and C.L. Combs. 1996. A new global water vapor dataset. Bulletin of the American Meteorological Society 77:1233-1246. Rasch, P.J., N.M. Mahowald, and B.E. Eaton. 1997. Representations of transport, convection, and the hydrologic cycle in chemical transport models: Implications for the modeling of short-lived and soluble species. Journal of Geophysical Research 102(D23):28127-28138. Schoenau, G.J. and R.A. Kehrig. 1990. A method for calculating degreedays to any base temperature. Energy and Buildings 14:299-302. Stephenson, D.G. 1965. Equations for solar heat gain through windows. Solar Energy 9(2):81-86. Thevenard, D. 2009. Updating the ASHRAE climatic data for design and standards (RP-1453). ASHRAE Research Project, Final Report. Thevenard, D., J. Lundgren, and R. Humphries. 2005. Updating the climatic design conditions in the ASHRAE Handbook of Fundamentals (RP1273). ASHRAE Research Project, Final Report. Thevenard, D. and K. Haddad. 2006. Ground reflectivity in the context of building energy simulation. Energy and Buildings 38(8):972-980. Thevenard, D. and R. Humphries. 2005. The calculation of climatic design conditions in the 2005 ASHRAE Handbook—Fundamentals. ASHRAE Transactions 111(1):457-466. Threlkeld, J.L. 1963. Solar irradiation of surfaces on clear days. ASHRAE Transactions 69:24. Wilcox, S. and W. Marion. 2008. Users manual for TMY3 data sets. Technical Report NREL/TP-581-43156. National Renewable Energy Laboratory, Golden, CO. (Available at http://www.nrel.gov/docs/fy08osti/ 43156.pdf). WMO. 2007. The role of climatological normals in a changing climate. Technical Document 1377. World Meteorological Organization, Geneva.

BIBLIOGRAPHY ASHRAE. 2006. Weather data for building design standards. ANSI/ ASHRAE Standard 169-2006.

CHAPTER 15

FENESTRATION Fenestration Components ........................................................ 15.1 Determining Fenestration Energy Flow................................... 15.2 U-FACTOR (THERMAL TRANSMITTANCE) ......................... 15.4 Determining Fenestration U-Factors....................................... 15.4 Surface and Cavity Heat Transfer Coefficients........................ 15.5 Representative U-Factors for Doors...................................... 15.12 SOLAR HEAT GAIN AND VISIBLE TRANSMITTANCE ...... 15.13 Solar-Optical Properties of Glazing ...................................... 15.13 Solar Heat Gain Coefficient................................................... 15.17 Calculation of Solar Heat Gain ............................................. 15.28 SHADING AND FENESTRATION ATTACHMENTS ............ 15.29 Shading .................................................................................. 15.29 Fenestration Attachments....................................................... 15.30

VISUAL AND THERMAL CONTROLS.................................. AIR LEAKAGE ....................................................................... DAYLIGHTING ...................................................................... Daylight Prediction................................................................ Light Transmittance and Daylight Use .................................. SELECTING FENESTRATION.............................................. Annual Energy Performance .................................................. Condensation Resistance ....................................................... Occupant Comfort and Acceptance ....................................... Durability ............................................................................... Supply and Exhaust Airflow Windows ................................... Codes and Standards.............................................................. Symbols ..................................................................................

F

door slabs; and shading devices such as louvered blinds, drapes, roller shades, and awnings. In this chapter, fenestration and fenestration systems refer to the basic assemblies and components of exterior window, skylight, and door systems within the building envelope.

ENESTRATION is an architectural term that refers to the arrangement, proportion, and design of window, skylight, and door systems in a building. Fenestration can serve as a physical and/or visual connection to the outdoors, as well as a means to admit solar radiation for natural lighting (daylighting), and for heat gain to a space. Fenestration can be fixed or operable, and operable units can allow natural ventilation to a space and egress in low-rise buildings. Fenestration affects building energy use through four basic mechanisms: thermal heat transfer, solar heat gain, air leakage, and daylighting. The energy effects of fenestration can be minimized by (1) using daylight to offset lighting requirements, (2) using glazings and shading strategies to control solar heat gain to supplement heating through passive solar gain and minimize cooling requirements, (3) using glazing to minimize conductive heat loss, (4) specifying low-air-leakage fenestration products, and (5) integrating fenestration into natural ventilation strategies that can reduce energy use for cooling and fresh air requirements. Today’s designers, builders, energy codes, and energy-efficiency incentive programs [such as ENERGY STAR (www.energystar.gov) and the LEED Green Building Program (www.usgbc.org)] are asking more and more from fenestration systems. Window, skylight, and door manufacturers are responding with new and improved products to meet those demands. With the advent of computer simulation software, designing to improve thermal performance of fenestration products has become much easier. Through participation in rating and certification programs [such as those of the National Fenestration Rating Council (NFRC)] that require the use of this software, fenestration manufacturers can take credit for these improvements through certified ratings that are credible to designers, builders, and code officials. A designer should consider architectural requirements, thermal performance, economic criteria, and human comfort when selecting fenestration. Typically, a wide range of fenestration products are available that meet the specifications for a project. Refining the specifications to improve energy performance and enhance a living or work space can result in lower energy costs, increased productivity, and improved thermal and visual comfort. CEA (1995) provides guidance for carrying out these requirements.

15.49 15.50 15.51 15.51 15.52 15.54 15.54 15.54 15.56 15.58 15.58 15.59 15.60

Glazing Units A glazing unit may consist of a single glazing or multiple glazings. Units with multiple glazing layers, sometimes called insulating glazing units (IGUs), are hermetically sealed, multiple-pane assemblies consisting of two or more glazing layers held and bonded at their perimeter by a spacer bar typically containing a desiccant material. The desiccated spacer is surrounded on at least two sides by a sealant that adheres the glass to the spacer. Figure 1 shows the construction of a typical double-glazing unit. Glazing. The most common glazing material is glass, although plastic is also used. Both may be clear, tinted, coated, laminated, patterned, or obscured. Clear glass transmits more than 75% of the incident solar radiation and more than 85% of the visible light. Tinted glass is available in many colors, all of which differ in the amount of solar radiation and visible light they transmit and absorb. Coatings on glass affect the transmission of solar radiation, and visible light may affect the absorptance of room-temperature radiation. Fig. 1 Double Glazing Unit Construction Detail

FENESTRATION COMPONENTS Fenestration components include glazing material, either glass or plastic; framing, mullions, muntin bars, dividers, and opaque Fig. 1 Double-Glazing Unit Construction Detail

The preparation of this chapter is assigned to TC 4.5, Fenestration.

15.1

15.2 Some coatings are highly reflective (e.g., mirrors), whereas others have very low reflectance. Some coatings result in visible light transmittance as much as twice the solar heat gain coefficient (desirable for good daylighting while minimizing cooling loads). Laminated glass is made of two panes of glass adhered together. The interlayer between the two panes of glass is typically plastic and may be clear, tinted, or coated. Patterned glass is a durable ceramic frit applied to a glass surface in a decorative pattern. Obscured glass is translucent and is typically used in privacy applications. Because of its energy efficiency, daylighting, and comfort benefits, low-emissivity (low-e) coated glass is now used in more than 50% of all fenestration products installed in the United States. Tinted and reflective glazing can also be used to reduce solar heat gain through fenestration products. Low-e coatings can also be applied to thin plastic films for use as one of the middle layers in glazing units with three or more layers. There are two types of lowe coating: high-solar-gain coatings primarily reduce heat conduction through the glazing system, and are intended for cold climates. Low-solar-gain coatings, for hot climates, reduce solar heat gain by blocking admission of the infrared portion of the solar spectrum. There are two ways of achieving low-solar-gain low-e performance: (1) with a special, multilayer solar-infrared-reflecting coating, and (2) with a solar-infrared-absorbing outer glass. To protect the inner glazing and building interior from the absorbed heat from this outer glass, a cold-climate-type low-e coating is also used to reduce conduction of heat from the outer pane to the inner one. In addition, argon and krypton gas are used in lieu of air in the gap between the panes in combination with low-e glazing to further reduce energy transfer. Some manufacturers construct glazing units with one or more suspended, low-e coated plastic films between glazing layers and with a spacer that has better insulating properties and a dual sealant that improves the seal around the gas spaces. Spacer. The spacer separates the panes of glass and provides the surface for primary and secondary sealant adhesion. Several types of spacers are used today. Each type provides different heat transfer properties, depending on spacer material and geometry. Heat transfer at the edge of the glazing unit is greater than at its center because of greater heat flow through the spacer system. To minimize this heat flow, warm-edge spacers have been developed that reduce edge heat transfer by using spacer materials that have lower thermal conductivity than the typical aluminum (e.g., stainless steel, galvanized steel, tin-plated steel, polymers, foamed silicone) from which spacers have often been made. Fusing or bending the corners of the spacer minimizes moisture and hydrocarbon vapor transmission into the air space through the corners. Desiccants such as molecular sieve or silica gel are also used to absorb moisture initially trapped in the glazing unit during assembly or that gradually diffuses through the seals after construction. Sealant(s). Several different sealant configurations are used successfully in modern glazing unit construction. In all sealant configurations, the primary seal minimizes moisture and hydrocarbon transmission. In dual-seal construction, the secondary seal provides structural integrity between the lites of the glazing unit. A secondary seal ensures long-term adhesion and greater resistance to solvents, oils, and short-term water immersion. In typical dual-seal construction, the primary seal is made of compressed polyisobutylene (PIB), and the secondary seal is made of silicone, polysulfide, or polyurethane. Single-seal construction depends on a single sealant to provide adhesion of the glass to the spacer as well as minimizing moisture and hydrocarbon transmission. Single-seal construction is generally more cost efficient than dual-seal systems. A third type of sealant takes advantage of advanced cross-linking polymers that provide both low moisture transmission and structural properties equivalent to dual-seal systems; therefore, these sealants are typically called dual-seal-equivalent (DSE) materials. Desiccants. Typical desiccants include molecular sieve, silica gel, or a matrix of both materials. Desiccants are used to absorb

2009 ASHRAE Handbook—Fundamentals moisture initially trapped in the glazing unit during assembly or that gradually diffused through the seals after construction. Gas Fill. The hermetically sealed space between glass panes is most often filled with air. In some cases, argon and krypton gas are used instead, to further reduce energy transfer.

Framing The three main categories of window framing materials are wood, metal, and polymers. Wood has good structural integrity and insulating value but low resistance to weather, moisture, warpage, and organic degradation (from mold and insects). Metal is durable and has excellent structural characteristics, but it has very poor thermal performance. The metal of choice in windows is almost exclusively aluminum, because of its ease of manufacture, low cost, and low mass, but aluminum has a thermal conductivity roughly 1000 times that of wood or polymers. The poor thermal performance of metalframe windows can be improved with a thermal break (a nonmetal component that separates the metal frame exposed to the outside from the surfaces exposed to the inside). Polymer frames are made of extruded vinyl or poltruded fiberglass (glass-reinforced polyester). Their thermal and structural performance is similar to that of wood, although vinyl frames for large windows must be reinforced. Manufacturers sometimes combine these materials as clad units (e.g., vinyl-clad aluminum, aluminum-clad wood, vinyl-clad wood) to increase durability, improve thermal performance, or improve aesthetics. In addition, curtain wall systems for commercial buildings may be structurally glazed, and the outdoor “framing” is simply rubber gaskets or silicone. Residential windows can be categorized by operator type, as shown by the traditional basic types in Figure 2. The glazing system can be mounted either directly in the frame (a direct-glazed or directset window, which is not operable) or in a sash that moves in the frame (for an operating window). In operable windows, a weathersealing system between the frame and sash reduces air and water leakage.

Shading Shading can be located either outdoors or indoors, and in some cases, internal to the glazing system (between the glass). Materials used include metal, wood, plastic, and fabric. Shading devices are available in a wide range of products that differ greatly in their appearance and energy performance. They include indoor and outdoor blinds, integral blinds, indoor and outdoor screens, shutters, draperies, and roller shades. Shading devices on the outdoor side of the glazing reduce solar heat gain more effectively than indoor devices. However, indoor devices are easier to operate and adjust. Some products help insulate the indoors from the outdoors, whereas others redirect incoming solar radiation to minimize visual and thermal discomfort. Window reveals and side fins as well as awnings and overhangs can offer effective shading as well. Outdoor vegetative shading is particularly effective in reducing solar heat gain while enhancing the outdoor scene.

DETERMINING FENESTRATION ENERGY FLOW Energy flows through fenestration via (1) conductive and convective heat transfer caused by the temperature difference between outdoor and indoor air, (2) net long-wave (above 2500 nm) radiative exchange between the fenestration and its surroundings and between glazing layers, and (3) short-wave (below 2500 nm) solar radiation incident on the fenestration product, either directly from the sun or reflected from the ground or adjacent objects. Simplified calculations are based on the observation that temperatures of the sky, ground, and surrounding objects (and hence their radiant emission) correlate with the outdoor air temperature. The radiative interchanges are then approximated by assuming that all the radiating surfaces (including the sky) are at the same temperature as the

Fenestration

15.3 In this chapter, Q is divided into two parts:

Fig. 2 Types of Residential Windows

Q = Qth + Qsol

(2)

where Qth = steady-state heat transfer caused by indoor/outdoor temperature difference, Btu/h Qsol = steady-state heat transfer caused by solar radiation, Btu/h

The section on U-Factor (Thermal Transmittance) deals with Qth, and the section on Solar Heat Gain and Visible Transmittance discusses Qsol. In the latter section, the effects of both direct solar radiation and solar radiation scattered by the sky or ground are included. Equation (1) presents a fenestration as it might appear on a building plan: a featureless, planar object filling an opening in the building envelope. Real fenestrations, however, are composite three-dimensional objects that may consist of multiple complex assemblies. Heat transfer through such an assembly of elements is calculated by dividing the fenestration area into parts, each of which has an energy flow that is more simply calculated than the total: Q =

¦ Av qv

(3)

v

where qv = energy flux (energy flow per unit area) of vth part, Btu/h Av = area of vth part, ft2

This subdivision is applied to each term in Equation (2) separately; for example, heat transfer through glazings differs from that through frames, so it is useful to make the following separation: Qth = Af qf + Ag qg

(4)

where the subscript f refers to the frame, and g refers to the glazing (both for thermal energy flow). Similarly, solar radiation has different effects on the frame and the glazed area of a fenestration (because the frame is generally opaque), so that Fig. 2 Types of Residential Windows

Qsol = Aop qop + As qs

outdoor air. With this assumption, the basic equation for the steadystate energy flow Q through a fenestration is Q = UApf (tout – tin) + (SHGC)Apf Et

(1)

where Q = instantaneous energy flow, Btu/h U = overall coefficient of heat transfer (U-factor), Btu/h·ft2 ·°F Apf = total projected area of fenestration (the product’s rough opening in the wall or roof less installation clearances), ft 2 tin = indoor air temperature, °F tout = outdoor air temperature, °F SHGC = solar heat gain coefficient, dimensionless Et = incident total irradiance, Btu/h·ft2

U and SHGC are steady-state performance indices. The main justification for Equation (1) is its simplicity, achieved by collecting all the linked radiative, conductive, and convective energy transfer processes into U and SHGC. These quantities vary because (1) convective heat transfer rates vary as fractional powers of temperature differences or free-stream speeds, (2) variations in temperature caused by weather or climate are small on the absolute temperature scale (°R) that controls radiative heat transfer rates, (3) fenestration systems always involve at least two thermal resistances in series, and (4) solar heat gain coefficients depend on solar incident angle and spectral distribution.

(5)

where the subscript op refers to the (opaque) frame (for solar energy flow), and s refers to the (solar-transmitting) glazing. This division into frame and glazing areas can be and usually is different for the solar and other thermal energy flows. Subdivisions of this sort, when Equation (3) is compared with Equation (1), effectively make the overall U-factor and solar heat gain coefficient area-averaged quantities. This area averaging is described explicitly in the appropriate sections of this chapter. Note that, in more complicated fenestrations, where the glazing portion may contain opaque shading elements, the opaque portion by definition can never under any conditions admit directly transmitted solar energy. A window with a closed, perfectly opaque blind would not be considered an opaque element because sometimes the blind may be open. A section of curtain wall consisting of wall or frame elements with an outdoor cover of glass (for uniform appearance) would be an opaque element despite its transparent covering. A second type of subdivision occurs when, for a given part of the fenestration system, energy flow is driven by physical processes that are more complicated than those assumed in Equation (1). For example, heat transfer through a glazing consists of contact (i.e., glass-to-air) and radiative parts, and the latter (qR) may depend on radiant temperatures that differ from the air temperatures in Equation (1): q = qC + qR

(6)

15.4

2009 ASHRAE Handbook—Fundamentals

U-FACTOR (THERMAL TRANSMITTANCE) In the absence of sunlight, air infiltration, and moisture condensation, the first term in Equation (1) represents the heat transfer rate through a fenestration system. Most fenestration systems consist of transparent multipane glazing units and opaque elements comprising the sash and frame (hereafter called frame). The glazing unit’s heat transfer paths are subdivided into center-of-glass, edge-ofglass, and frame contributions (denoted by subscripts cg, eg, and f, respectively). Consequently, the total rate of heat transfer through a fenestration system can be calculated knowing the separate contributions of the these three paths. (When present, glazing dividers, such as decorative grilles and muntin bars, also affect heat transfer, and their contribution must be considered.) The overall U-factor is estimated using area-weighted U-factors for each contribution by Ucg A cg + Ueg A eg + Uf Af U o = -----------------------------------------------------------A pf

(7)

When a fenestration product has glazed surfaces in only one direction, the sum of the areas equals the projected area Apf . Skylights, greenhouse/garden windows, bay/bow windows, etc., because they extend beyond the plane of the wall/roof, have greater surface area for heat loss than a window with a similar glazing option and frame material; consequently, U-factors for such products are expected to be greater.

have no significant effect on Ucg . Greater glazing unit thicknesses decrease Uo because the length of the shortest heat flow path through the frame increases. A low-emissivity coating combined with krypton gas fill offers significant potential for reducing heat transfer in narrow-gap-width glazing units.

Edge-of-Glass U-Factor Glazing units usually have continuous spacer members around the glass perimeter to separate the glazing and provide an edge seal. Aluminum spacers greatly increase conductive heat transfer between the contacted inner and outer glazing, thereby degrading the thermal performance of the glazing unit locally. The edge-ofglass area is typically taken to be a band 2.5 in. wide around the sightline. The width of this area is determined from the extent of two-dimensional heat transfer effects in current computer models, which are based on conduction-only analysis. In reality, because of convective and radiative effects, this area may extend beyond 2.5 in. (Beck et al. 1995; Curcija and Goss 1994; Wright and Sullivan 1995b), and depends on the type of insulating glazing unit and its thickness. Fig. 3 Center-of-Glass U-Factor for Vertical Double- and Triple-Pane Glazing Units

DETERMINING FENESTRATION U-FACTORS Center-of-Glass U-Factor For single glass, U-factors depend strongly on indoor and outdoor film coefficients. The U-factor for single glass is 1 U = ---------------------------------------------1 e ho + 1 e hi + L e k

(8)

where ho, hi = outdoor and indoor respective glass surface heat transfer coefficients, Btu/h·ft2 ·°F L = glass thickness, ft k = thermal conductivity, Btu·in/h·ft2 ·°F

For other fenestration, values for Ucg at standard indoor and outdoor conditions depend on glazing construction features such as the number of glazing lights, gas space dimensions, orientation relative to vertical, emissivity of each surface, and composition of fill gas. Several computer programs can be used to estimate glazing unit heat transfer for a wide range of glazing construction. The NFRC calls for WINDOW 5 (LBL 2001) as a standard calculation method for center glazing. Heat flow across the central glazed portion of a multipane unit must consider both convective and radiative transfer in the gas space, and may be considered one-dimensional. Convective heat transfer is estimated based on high-aspect-ratio, natural convection correlations for vertical and inclined air layers (El Sherbiny et al. 1982; Shewen 1986; Wright 1996a). Radiative heat transfer (ignoring gas absorption) is quantified using a more fundamental approach. Computational methods solving the combined heat transfer problem have been devised (Hollands and Wright 1982; Rubin 1982a, 1982b). Figure 3 shows the effect of gas space width on Ucg for vertical double- and triple-paned glazing units. U-factors are plotted for air, argon, and krypton fill gases and for high (uncoated) and low (coated) values of surface emissivity. The optimum gas space width is 0.5 in. for air and argon, and 5/16 in. for krypton. Greater widths

Fig. 3

Center-of-Glass U-Factor for Vertical Double- and Triple-Pane Glazing Units

Fenestration

15.5 Table 1 Representative Fenestration Frame U-Factors in Btu/h· ft2 · °F, Vertical Orientation Product Type/Number of Glazing Layers Operable

Garden Window

Fixed

Plant-Assembled Skylight

Curtain Walle

Sloped/Overhead Glazinge

Type of Spacer

1b

2c

3d

1b

2c

3d

1b

2c

1b

2c

3d

1f

2g

3h

1f

2g

3h

All

2.38

2.27

2.20

1.92

1.80

1.74

1.88

1.83

7.85

7.02

6.87

3.01

2.96

2.83

3.05

3.00

2.87

Metal 1.20 Insulated N/A

0.92 0.88

0.83 0.77

1.32 N/A

1.13 1.04

1.11 1.02

6.95 N/A

5.05 4.75

4.58 4.12

1.80 N/A

1.75 1.63

1.65 1.51

1.82 N/A

1.76 1.64

1.66 1.52

Aluminum-clad wood/ Metal 0.60 reinforced vinyl Insulated N/A

0.58 0.55

0.51 0.48

0.55 N/A

0.51 0.48

0.48 0.44

4.86 N/A

3.93 3.75

3.66 3.43

Wood/vinyl

Metal 0.55 Insulated N/A

0.51 0.49

0.48 0.40

0.55 N/A

0.48 0.42

0.42 0.35

2.50 N/A

2.08 2.02

1.78 1.71

Insulated fiberglass/vinyl

Metal 0.37 Insulated N/A

0.33 0.32

0.32 0.26

0.37 N/A

0.33 0.32

0.32 0.26

Structural glazing

Metal Insulated

1.80 N/A

1.27 1.02

1.04 0.75

1.82 N/A

1.28 1.02

1.05 0.75

Frame Material Aluminum without thermal break Aluminum with thermal breaka

Note: This table should only be used as an estimating tool for early phases of design. aDepends strongly on width of thermal break. Value given is for 3/8 in. bSingle glazing corresponds to individual glazing unit thickness of 1/8 in. (nominal). cDouble glazing corresponds to individual glazing unit thickness of 3/4 in. (nominal). dTriple glazing corresponds to individual glazing unit thickness of 1 3/8 in. (nominal).

In low-conductivity frames, heat flow at the edge-of-glass and frame area is through the spacer, and so the type of spacer has a greater impact on the edge-of-glass and frame U-factor. In metal frames, the edge-of-glass and frame U-factor varies little with the type of spacer (metal or insulating) because there is a significant heat flow through the highly conductive frame near the edge-ofglass area.

Frame U-Factor Fenestration frame elements consist of all structural members exclusive of glazing units and include sash, jamb, head, and sill members; meeting rails and stiles; mullions; and other glazing dividers. Estimating the rate of heat transfer through the frame is complicated by the (1) variety of fenestration products and frame configurations, (2) different combinations of materials used for frames, (3) different sizes available, and, to a lesser extent, (4) glazing unit width and spacer type. Internal dividers or grilles have little effect on the fenestration U-factor, provided there is at least a 1/8 in. gap between the divider and each panel of glass. Computer simulations found that frame heat loss in most fenestration is controlled by a single component or controlling resistance, and only changes in this component significantly affect frame heat loss (EEL 1990). For example, the frame U-factor for thermally broken aluminum fenestration products is largely controlled by the depth of the thermal break material in the heat flow direction. For aluminum frames without a thermal break, the inside film coefficient provides most of the resistance to heat flow. For vinyl- and wood-framed fenestrations, the controlling resistance is the shortest distance between the inside and outside surfaces, which usually depends on the thickness of the sealed glazing unit. Carpenter and McGowan (1993) experimentally validated frame U-factors for a variety of fixed and operable fenestration product types, sizes, and materials using computer modeling techniques. Table 1 lists frame U-factors for a variety of frame and spacer materials and glazing unit thicknesses. Frame and edge U-factors are normally determined by two-dimensional computer simulation.

Curtain Wall Construction A curtain wall is an outdoor building wall that carries no roof or floor loads and consists entirely or principally of glass and other surfacing materials supported by a framework. A curtain wall typically has a metal frame. To improve the thermal performance of standard

0.90 N/A

0.85 0.83

eGlass

thickness in curtainwall and sloped/overhead glazing is 1/4 in. glazing corresponds to individual glazing unit thickness of 1/4 in. (nominal). glazing corresponds to individual glazing unit thickness of 1 in. (nominal). hTriple glazing corresponds to individual glazing unit thickness of 1 3/4 in. (nominal). N/A: Not applicable fSingle

gDouble

metal frames, manufacturers provide both traditional thermal breaks as well as thermally improved products. The traditional thermal break is poured and debridged (i.e., urethane is poured into a metal U-channel in the frame and then the bottom of the channel is removed by machine). For this system to work well, there must be a thermal break between indoors and outdoors for all frame components, including those in any operable sash. Skip debridging (incomplete pour and debridging used for increased structural strength) can significantly degrade the U-factor. Bolts that penetrate the thermal break also degrade performance, but to a lesser degree. Griffith et al. (1998) showed that stainless steel bolts spaced 12 in. on center increased the frame U-factor by 18%. The paper also concluded that, in general, the isothermal planes method referenced in Chapter 27 provides a conservative approach to determining Ufactors. Thermally improved curtain wall products are a more recent development. In these products, most of the metal frame tends to be located on the indoor side with only a metal cap exposed on the outdoor side. Plastic spacers isolate the glazing assembly from both the outdoor metal cap and the indoor metal frame. These products can have significantly better thermal performance than standard metal frames, but it is important to minimize the number and area of the bolts that penetrate from outdoor to indoor.

SURFACE AND CAVITY HEAT TRANSFER COEFFICIENTS Part of the overall thermal resistance of a fenestration system derives from convective and radiative heat transfer between the exposed surfaces and the environment, and in the cavity between panes of glass. Surface heat transfer coefficients ho , hi , and hc at the outer and inner glazing surfaces, and in the cavity, respectively, combine the effects of radiation and convection. Wind speed and building orientation are important in determining ho. This relationship has long been studied, and many correlations have been proposed for ho as a function of wind speed. However, no universal relationship has been accepted, and limited field measurements at low wind speeds by Klems (1989) differ significantly from values used by others. Convective heat transfer coefficients are usually determined at standard temperature and air velocity conditions on each side. Wind speed can vary from less than 0.5 mph for calm weather, free convection conditions, to over 65 mph for storm conditions. A nominal

15.6

2009 ASHRAE Handbook—Fundamentals Table 2

Indoor Surface Heat Transfer Coefficient hi in Btu/h· ft2 · °F, Vertical Orientation (Still Air Conditions)

Glazing IDa Glazing Type 1

Single glazing

5

Double glazing with 1/2 in. air space

23

43

Glazing Height, ft

Double glazing with e = 0.1 on surface 2 and 1/2 in. argon space Triple glazing with e = 0.1 on surfaces 2 and 5 and 1/2 in. argon spaces

Notes: aGlazing ID refers to fenestration assemblies in Table 4. bWinter conditions: room air temperature t = 70°F, outdoor air i temperature to = 0°F, no solar radiation

2 4 6 2 4 6 2 4 6 2 4 6

Winter Conditionsb

Summer Conditionsc

hi , Glass Temp., Temp. Diff., °F °F Btu/h· ft2 · °F

hi , Glass Temp., Temp. Diff., °F °F Btu/h· ft2 · °F

17 17 17 45 45 45 56 56 56 63 63 63

53 53 53 25 25 25 14 14 14 7 7 7

1.41 1.31 1.25 1.36 1.27 1.22 1.31 1.23 1.19 1.25 1.18 1.15

89 89 89 89 89 89 87 87 87 93 93 93

14 14 14 14 14 14 12 12 12 18 18 18

1.41 1.33 1.29 1.41 1.33 1.29 1.38 1.31 1.27 1.45 1.36 1.32

cSummer

conditions: room air temperature ti = 75°F, outdoor air temperature to = 89°F, direct solar irradiance ED = 248 Btu/h· ft2 hi = hic + hiR = 1.46('T/L)0.25 + HV(T i4 – T g4 )/'T, where 'T = Ti – Tg, °R; L = glazing height, ft; Tg = glass temperature, °R; V = Stefan-Boltzmann constant; and H = surface emissivity.

value of 5.1 Btu/h·ft2 ·°F corresponding to a 15 mph wind is often used to represent winter design conditions. At low wind speeds, ho varies with outside air and surface temperature, orientation to vertical, and air moisture content. The overall surface heat transfer coefficient can be as low as 1.2 Btu/h·ft2 ·°F (Yazdanian and Klems 1993). For natural convection and radiation at the indoor surface of a vertical fenestration product, surface coefficient hi depends on the indoor air and glass surface temperatures and on the emissivity of the glass surface. Table 2 shows the variation of hi for winter (ti = 70°F) and summer (ti = 75°F) design conditions, for a range of glass types and heights. Designers often use hi = 1.46 Btu/h·ft2 ·°F, which corresponds to ti = 70°F, glass temperature of 15°F, and uncoated glass with eg = 0.84. For summer conditions, the same value [hi = 1.46 Btu/h·ft2 ·°F] is normally used, and it corresponds approximately to glass temperature of 95°F, ti = 75°F, and eg = 0.84. For winter conditions, this most closely approximates single glazing with clear glass that is 2 ft tall, but it overestimates the value as the glazing unit conductance decreases and height increases. For summer conditions, this value approximates all types of glass that are 2 ft tall but, again, is less accurate as glass height increases. If the indoor surface of the glass has a low-e coating, hi values are about halved at both winter and summer conditions. Heat transfer between the glazing surface and its environment is driven not only by local air temperatures but also by radiant temperatures to which the surface is exposed. The radiant temperature of the indoor environment is generally assumed to be equal to the indoor air temperature. This is a safe assumption where a small fenestration is exposed to a large room with surface temperatures equal to the air temperature, but it is not valid in rooms where the fenestration is exposed to other large areas of glazing surfaces (e.g., greenhouse, atrium) or to other cooled or heated surfaces (Parmelee and Huebscher 1947). The radiant temperature of the outdoor environment is frequently assumed to be equal to the outdoor air temperature. This assumption may be in error, because additional radiative heat loss occurs between a fenestration and the clear sky (Berdahl and Martin 1984). Therefore, for clear-sky conditions, some effective outdoor temperature to,e should replace to in Equation (1). For methods of determining to,e , see, for example, work by AGSL (1992). Note that a fully cloudy sky is assumed in ASHRAE design conditions. The air space in a window constructed using glass with no reflective coating on the air space surfaces has a coefficient hs of 1.3 Btu/h· ft2 · °F. When a reflective coating is applied to an air space surface, hs can be selected from Table 3 by first calculating the effective air space emissivity es,e by Equation (9):

1 e s ,e = -------------------------------------1 e eo + 1 e ei – 1

(9)

where eo and ei are the hemispherical emissivities of the two air space surfaces. Hemispherical emissivity of ordinary uncoated glass is 0.84 over a wavelength range of 0.4 to 40 Pm. Table 4 lists computed U-factors, using winter design conditions, for a variety of generic fenestration products, based on ASHRAEsponsored research involving laboratory testing and computer simulations. In the past, test data were used to provide more accurate results for specific products (Hogan 1988). Computer simulations (with validation by testing) are now accepted as the standard method for accurate product-specific U-factor determination. The simulation methodologies are specified in the National Fenestration Rating Council’s NFRC Technical Document 100 (NFRC 2004a) and are based on algorithms published in ISO Standard 15099 (ISO 2000). The International Energy Conservation Code and various state energy codes in the United States, the National Energy Code in Canada, and ASHRAE Standards 90.1 and 90.2 all reference these standards. Fenestration must be rated in accordance with the NFRC standards for code compliance. Use of Table 4 should be limited to that of an estimating tool for the early phases of design. Values in Table 4 are for vertical installation and for skylights and other sloped installations with glazing surfaces sloped 20° from the horizontal. Data are based on center-of-glass and edge-of-glass component U-factors and assume that there are no dividers. However, they apply only to the specific design conditions described in the table’s footnotes, and are typically used only to determine peak load conditions for sizing heating equipment. Although these Ufactors have been determined for winter conditions, they can also be used to estimate heat gain during peak cooling conditions, because conductive gain, which is one of several variables, is usually a small portion of the total heat gain for fenestration in direct sunlight. Glazing designs and framing materials may be compared in choosing a fenestration system that needs a specific winter design U-factor. Table 4 lists 48 glazing types, with multiple glazing categories appropriate for sealed glazing units and the addition of storm sash to other glazing units. No distinction is made between flat and domed units such as skylights. For acrylic domes, use an average gas-space width to determine the U-factor. Note that garden window and sloped/pyramid/barrel vault skylight U-factors are approximately twice those of other similar products. Although this is partially due to the difference in slope in the case of sloped/pyramid/barrel vault skylights, it is largely because these products project out from the surface of the wall or roof. For instance, the skylight surface area,

Fenestration

15.7

Table 3 Air Space Coefficients for Horizontal Heat Flow Air Air Air Space Space Temp. Thickness, Temp., Diff., in. °F °F

Air Space Coefficient hs , Btu/h· ft2 · °F Effective Emissivity es,e 0.82

0.72

0.40

0.20

0.10

0.05

5

10 25 55 70 90

0.88 0.90 1.00 1.05 1.10

0.82 0.83 0.93 0.98 1.03

0.60 0.61 0.71 0.76 0.81

0.46 0.48 0.57 0.62 0.67

0.39 0.41 0.50 0.55 0.60

0.35 0.37 0.47 0.51 0.57

32

10 25 55 70 90

1.00 1.01 1.08 1.12 1.17

0.92 0.93 1.00 1.04 1.09

0.66 0.67 0.74 0.78 0.83

0.50 0.51 0.57 0.62 0.67

0.42 0.43 0.49 0.53 0.58

0.38 0.39 0.45 0.49 0.54

50

10 25 55 70 90

1.09 1.10 1.14 1.18 1.23

1.00 1.01 1.05 1.09 1.14

0.71 0.72 0.76 0.80 0.85

0.53 0.54 0.58 0.62 0.67

0.44 0.44 0.49 0.53 0.57

0.39 0.40 0.44 0.48 0.53

85

10 25 55 70 90

1.28 1.28 1.30 1.33 1.36

1.16 1.17 1.19 1.21 1.25

0.81 0.81 0.84 0.86 0.90

0.59 0.59 0.62 0.64 0.67

0.48 0.48 0.51 0.53 0.56

0.42 0.43 0.45 0.47 0.51

120

10 25 55 70 90

1.48 1.49 1.50 1.51 1.53

1.35 1.35 1.37 1.38 1.40

0.92 0.92 0.94 0.95 0.97

0.66 0.66 0.67 0.68 0.70

0.52 0.52 0.54 0.55 0.57

0.46 0.46 0.47 0.48 0.50

5

10 55 90

0.96 1.00 1.07

0.89 0.93 1.01

0.67 0.71 0.78

0.54 0.57 0.64

0.47 0.50 0.58

0.43 0.47 0.54

32

10 55 90

1.09 1.11 1.15

1.00 1.03 1.07

0.74 0.76 0.81

0.58 0.60 0.64

0.50 0.52 0.56

0.46 0.48 0.52

50

10 55 90

1.18 1.19 1.22

1.09 1.10 1.13

0.79 0.81 0.84

0.61 0.63 0.66

0.52 0.54 0.57

0.48 0.49 0.52

85

10 55 90

1.37 1.38 1.40

1.26 1.26 1.26

0.90 0.91 0.93

0.68 0.69 0.70

0.57 0.58 0.59

0.51 0.52 0.54

120

10 55 90

1.58 1.59 1.60

1.45 1.45 1.46

1.02 1.02 1.03

0.75 0.76 0.77

0.62 0.62 0.63

0.55 0.56 0.57

0.3

5 32 50 85 120

0.5) 0.46 (SHGC < 0.5)

0.54 0.40 0.67 (SHGC > 0.5) 0.54 (SHGC < 0.5)

1.00

0.00

0.00

1.00

Comments See Table 1 for other conditions. See Tables 6 to 12 for details of equipment heat gain and recommended radiative/convective splits for motors, cooking appliances, laboratory equipment, medical equipment, office equipment, etc. Varies; see Table 3.

Varies; see Tables 13A to 13G in Chapter 15.

Source: Nigusse (2007).

Table 15 Solar Absorptance Values of Various Surfaces Surface

Absorptance (Purdue) a

Brick, red Paint Redb Black, matteb Sandstoneb White acrylica Sheet metal, galvanized Newa Weathereda Shingles Grayb Brownb Blackb Whiteb Concretea,c

0.63 0.63 0.94 0.50 0.26 0.65 0.80 0.82 0.91 0.97 0.75 0.60 to 0.83

aIncropera

and DeWitt (1990). et al. (2000). cMiller (1971). bParker

Because vertical surfaces receive long-wave radiation from the ground and surrounding buildings as well as from the sky, accurate 'R values are difficult to determine. When solar radiation intensity is high, surfaces of terrestrial objects usually have a higher temperature than the outdoor air; thus, their long-wave radiation compensates to some extent for the sky’s low emittance. Therefore, it is common practice to assume H'R = 0 for vertical surfaces. Tabulated Temperature Values. The sol-air temperatures in Example Cooling and Heating Load Calculations section have been calculated based on H'R/ho values of 7°F for horizontal surfaces and 0°F for vertical surfaces; total solar intensity values used for the calculations were calculated using equations in Chapter 14. Surface Colors. Sol-air temperature values are given in the Example Cooling and Heating Load Calculations section for two values of the parameter D/ho; the value of 0.15 is appropriate for a light-colored surface, whereas 0.30 represents the usual maximum value for this parameter (i.e., for a dark-colored surface or any surface for which the permanent lightness cannot reliably be anticipated). Solar absorptance values of various surfaces are included in Table 15.

This procedure was used to calculate the sol-air temperatures included in the Examples section. Because of the tedious solar angle and intensity calculations, using a simple computer spreadsheet or other software for these calculations can reduce the effort involved.

Calculating Conductive Heat Gain Using Conduction Time Series In the RTS method, conduction through exterior walls and roofs is calculated using conduction time series (CTS). Wall and roof conductive heat input at the exterior is defined by the familiar conduction equation as qi,T-n = UA(te,T-n – trc)

(31)

where qi,T-n U A te,T-n trc

= = = = =

conductive heat input for the surface n hours ago, Btu/h overall heat transfer coefficient for the surface, Btu/h·ft2 ·°F surface area, ft2 sol-air temperature n hours ago, °F presumed constant room air temperature, °F

Conductive heat gain through walls or roofs can be calculated using conductive heat inputs for the current hours and past 23 h and conduction time series: qT = c0qi,T + c1qi,T-1 + c2qi,T-2 + c3qi,T-3 + … + c23qi,T-23

(32)

where qT = hourly conductive heat gain for the surface, Btu/h qi,T = heat input for the current hour qi,T-n = heat input n hours ago c0, c1, etc. = conduction time factors

Conduction time factors for representative wall and roof types are included in Tables 16 and 17. Those values were derived by first calculating conduction transfer functions for each example wall and roof construction. Assuming steady-periodic heat input conditions for design load calculations allows conduction transfer functions to be reformulated into periodic response factors, as demonstrated by Spitler and Fisher (1999a). The periodic response factors were further simplified by dividing the 24 periodic response factors by the respective overall wall or roof U-factor to form the conduction time series (CTS). The conduction time factors can then be used in Equation (32) and provide a way to compare time delay characteristics between different wall and roof constructions. Construction material

18.24

2009 ASHRAE Handbook—Fundamentals Table 16 CURTAIN WALLS Wall Number =

1

2

3

Wall Conduction Time Series (CTS)

STUD WALLS 4

5

6

EIFS 7

8

9

BRICK WALLS 10

11

12

13

14

15

U-Factor, Btu/h·ft2 ·°F 0.075 0.076 0.075 0.074 0.074 0.071 0.073 0.118 0.054 0.092 0.101 0.066 0.050 0.102 Total R 13.3 13.2 13.3 13.6 13.6 14.0 13.8 8.5 18.6 10.8 9.9 15.1 20.1 9.8 6.3 4.3 16.4 5.2 17.3 5.2 13.7 7.5 7.8 26.8 42.9 44.0 44.2 59.6 Mass, lb/ft2 1.5 1.0 3.3 1.2 3.6 1.6 3.0 1.8 1.9 5.9 8.7 8.7 8.7 11.7 Thermal Capacity, Btu/ft2 ·°F Hour

16

17

18

19

20

0.061 0.111 0.124 0.091 0.102 0.068 16.3 9.0 8.1 11.0 9.8 14.6 62.3 76.2 80.2 96.2 182.8 136.3 12.4 15.7 15.3 19.0 38.4 28.4

Conduction Time Factors, %

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

18 58 20 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

25 57 15 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

8 45 32 11 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

19 59 18 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

6 42 33 13 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

7 44 32 12 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

5 41 34 13 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

11 50 26 9 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

2 25 31 20 11 5 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 6 9 9 9 8 7 6 6 5 5 4 4 3 3 3 2 2 2 2 1 1 0

0 5 14 17 15 12 9 7 5 4 3 2 2 1 1 1 1 1 0 0 0 0 0 0

0 4 13 17 15 12 9 7 5 4 3 2 2 2 2 1 1 1 0 0 0 0 0 0

0 1 7 12 13 13 11 9 7 6 5 4 3 2 2 1 1 1 1 1 0 0 0 0

1 1 2 5 8 9 9 9 8 7 7 6 5 4 4 3 3 2 2 2 1 1 1 0

2 2 2 3 5 6 7 7 7 7 6 6 5 5 5 4 4 3 3 3 3 2 2 1

2 2 2 4 5 6 6 7 7 6 6 6 5 5 5 4 4 4 3 3 3 2 2 1

1 1 3 6 7 8 8 8 8 7 6 6 5 4 4 3 3 3 2 2 2 1 1 1

3 3 3 3 3 4 4 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 3

4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 4 4 4 4 4 4 4 4 4

3 3 3 4 4 4 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 3 3

Total Percentage

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

Layer ID from outside to inside (see Table 18)

F01 F09 F04 I02 F04 G01 F02 —

F01 F08 F04 I02 F04 G01 F02 —

F01 F01 F01 F01 F01 F01 F01 F01 F10 F08 F10 F11 F07 F06 F06 F06 F04 G03 G03 G02 G03 I01 I01 I01 I02 I04 I04 I04 I04 G03 G03 G03 F04 G01 G01 G04 G01 F04 I04 M03 G01 F02 F02 F02 F02 G01 G01 F04 F02 — — — — F02 F02 G01 — — — — — — — F02

F01 M01 F04 I01 G03 F04 G01 F02

F01 M01 F04 G03 I04 G01 F02 —

F01 M01 F04 I01 G03 I04 G01 F02

F01 M01 F04 I01 M03 F02 — —

F01 M01 F04 M03 I04 G01 F02 —

F01 F01 F01 F01 F01 M01 M01 M01 M01 M01 F04 F04 F04 F04 F04 I01 I01 I01 I01 M15 M05 M01 M13 M16 I04 G01 F02 F04 F04 G01 F02 — G01 G01 F02 — — F02 F02 —

Wall Number Descriptions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Spandrel glass, R-10 insulation board, gyp board Metal wall panel, R-10 insulation board, gyp board 1 in. stone, R-10 insulation board, gyp board Metal wall panel, sheathing, R-11 batt insulation, gyp board 1 in. stone, sheathing, R-11 batt insulation, gyp board Wood siding, sheathing, R-11 batt insulation, 1/2 in. wood 1 in. stucco, sheathing, R-11 batt insulation, gyp board EIFS finish, R-5 insulation board, sheathing, gyp board EIFS finish, R-5 insulation board, sheathing, R-11 batt insulation, gyp board EIFS finish, R-5 insulation board, sheathing, 8 in. LW CMU, gyp board

data used in the calculations for walls and roofs in Tables 16 and 17 are listed in Table 18. Heat gains calculated for walls or roofs using periodic response factors (and thus CTS) are identical to those calculated using conduction transfer functions for the steady periodic conditions assumed in design cooling load calculations. The methodology for calculating periodic response factors from conduction transfer functions was originally developed as part of ASHRAE research project RP-875 (Spitler and Fisher 1999b; Spitler et al. 1997). For walls and roofs that are not reasonably close to the representative constructions in Tables 16 and 17, CTS coefficients may be computed with a computer program such as that described by Iu and

11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Brick, R-5 insulation board, sheathing, gyp board Brick, sheathing, R-11 batt insulation, gyp board Brick, R-5 insulation board, sheathing, R-11 batt insulation, gyp board Brick, R-5 insulation board, 8 in. LW CMU Brick, 8 in. LW CMU, R-11 batt insulation, gyp board Brick, R-5 insulation board, 8 in. HW CMU, gyp board Brick, R-5 insulation board, brick Brick, R-5 insulation board, 8 in. LW concrete, gyp board Brick, R-5 insulation board, 12 in. HW concrete, gyp board Brick, 8 in. HW concrete, R-11 batt insulation, gyp board

Fisher (2004). For walls and roofs with thermal bridges, the procedure described by Karambakkam et al. (2005) may be used to determine an equivalent wall construction, which can then be used as the basis for finding the CTS coefficients. When considering the level of detail needed to make an adequate approximation, remember that, for buildings with windows and internal heat gains, the conduction heat gains make up a relatively small part of the cooling load. For heating load calculations, the conduction heat loss may be more significant. The tedious calculations involved make a simple computer spreadsheet or other computer software a useful labor saver.

Nonresidential Cooling and Heating Load Calculations

18.25

Table 16 Wall Conduction Time Series (CTS) (Concluded) CONCRETE BLOCK WALL Wall Number =

PRECAST AND CAST-IN-PLACE CONCRETE WALLS

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

0.067 14.8 22.3 4.8

0.059 16.9 22.3 4.8

0.073 13.7 46.0 10.0

0.186 5.4 19.3 4.1

0.147 6.8 21.9 4.7

0.121 8.2 34.6 7.4

0.118 8.4 29.5 6.1

0.074 13.6 29.6 6.1

0.076 13.1 53.8 10.8

0.115 8.7 59.8 12.1

0.068 14.7 56.3 11.4

0.082 12.2 100.0 21.6

0.076 13.1 96.3 20.8

0.047 21.4 143.2 30.9

0.550 1.8 140.0 30.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

0 4 13 16 14 11 9 7 6 4 3 3 2 2 2 1 1 1 1 0 0 0 0 0

1 1 5 9 11 10 9 8 7 6 5 4 4 3 3 3 2 2 2 1 1 1 1 1

0 2 8 12 12 11 9 8 7 6 5 4 3 2 2 2 1 1 1 1 1 1 1 0

1 11 21 20 15 10 7 5 3 2 2 1 1 1 0 0 0 0 0 0 0 0 0 0

0 3 12 16 15 12 10 8 6 4 3 3 2 2 1 1 1 1 0 0 0 0 0 0

1 1 2 5 7 9 9 8 8 7 6 6 5 4 4 3 3 2 2 2 2 2 1 1

1 10 20 18 14 10 7 5 4 3 2 2 1 1 1 1 0 0 0 0 0 0 0 0

0 8 18 18 14 11 8 6 4 3 2 2 2 1 1 1 1 0 0 0 0 0 0 0

1 1 3 6 8 9 9 9 8 7 7 6 5 4 4 3 2 2 1 1 1 1 1 1

2 2 3 5 6 6 6 6 6 6 5 5 5 5 4 4 4 3 3 3 3 3 3 2

1 2 3 6 7 8 8 7 7 6 6 5 5 4 4 3 3 3 2 2 2 2 2 2

3 3 4 5 6 6 6 5 5 5 5 5 4 4 4 4 4 4 4 3 3 3 3 2

1 2 5 8 9 9 8 7 6 6 5 5 4 4 3 3 3 2 2 2 2 2 1 1

2 2 3 3 5 5 6 6 6 6 6 5 5 5 4 4 4 4 4 3 3 3 3 3

1 2 4 7 8 8 8 8 7 6 6 5 4 4 4 3 3 3 2 2 2 1 1 1

Total Percentage

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

Layer ID from outside to inside (see Table 18)

F01 M03 I04 G01 F02 —

F01 M08 I04 G01 F02 —

F01 F07 M05 I04 G01 F02

F01 M08 F02 — — —

F01 M08 F04 G01 F02 —

F01 M09 F04 G01 F02 —

F01 M11 I01 F04 G01 F02

F01 M11 I04 G01 F02 —

F01 M11 I02 M11 F02 —

F01 F06 I01 M13 G01 F02

F01 M13 I04 G01 F02 —

F01 F06 I02 M15 G01 F02

F01 M15 I04 G01 F02 —

F01 M16 I05 G01 F02 —

F01 M16 F02 — — —

U-Factor, Btu/h·ft2 ·°F Total R Mass, lb/ft2 Thermal Capacity, Btu/ft2 ·°F Hour

Conduction Time Factors, %

Wall Number Descriptions 21. 22. 23. 24. 25. 26. 27. 28.

8 in. LW CMU, R-11 batt insulation, gyp board 8 in. LW CMU with fill insulation, R-11 batt insulation, gyp board 1 in. stucco, 8 in. HW CMU, R-11 batt insulation, gyp board 8 in. LW CMU with fill insulation 8 in. LW CMU with fill insulation, gyp board 12 in. LW CMU with fill insulation, gyp board 4 in. LW concrete, R-5 board insulation, gyp board 4 in. LW concrete, R-11 batt insulation, gyp board

29. 30. 31. 32. 33. 34. 35.

HEAT GAIN THROUGH INTERIOR SURFACES Whenever a conditioned space is adjacent to a space with a different temperature, heat transfer through the separating physical section must be considered. The heat transfer rate is given by q = UA(tb – ti)

(33)

where q = heat transfer rate, Btu/h U = coefficient of overall heat transfer between adjacent and conditioned space, Btu/h·ft2 ·°F A = area of separating section concerned, ft2 tb = average air temperature in adjacent space, °F ti = air temperature in conditioned space, °F

U-values can be obtained from Chapter 27. Temperature tb may differ greatly from ti. The temperature in a kitchen or boiler room, for

4 in. LW concrete, R-10 board insulation, 4 in. LW concrete EIFS finish, R-5 insulation board, 8 in. LW concrete, gyp board 8 in. LW concrete, R-11 batt insulation, gyp board EIFS finish, R-10 insulation board, 8 in. HW concrete, gyp board 8 in. HW concrete, R-11 batt insulation, gyp board 12 in. HW concrete, R-19 batt insulation, gyp board 12 in. HW concrete

example, may be as much as 15 to 50°F above the outdoor air temperature. Actual temperatures in adjoining spaces should be measured, when possible. Where nothing is known except that the adjacent space is of conventional construction, contains no heat sources, and itself receives no significant solar heat gain, tb – ti may be considered the difference between the outdoor air and conditioned space design dry-bulb temperatures minus 5°F. In some cases, air temperature in the adjacent space corresponds to the outdoor air temperature or higher.

Floors For floors directly in contact with the ground or over an underground basement that is neither ventilated nor conditioned, sensible heat transfer may be neglected for cooling load estimates because usually there is a heat loss rather than a gain. An exception is in hot climates (i.e., where average outdoor air temperature exceeds

18.26

2009 ASHRAE Handbook—Fundamentals Table 17 Roof Conduction Time Series (CTS) SLOPED FRAME ROOFS

Roof Number

1

2

3

4

5

WOOD DECK 6

7

8

METAL DECK ROOFS 9

10

11

12

CONCRETE ROOFS

13

14

15

16

17

18

19

U-Factor, 0.044 0.040 0.045 0.041 0.042 0.041 0.069 0.058 0.080 0.065 0.057 0.036 0.052 0.054 0.052 0.051 0.056 0.055 0.042 Btu/h·ft2 ·°F Total R 22.8 25.0 22.2 24.1 23.7 24.6 14.5 17.2 12.6 15.4 17.6 27.6 19.1 18.6 19.2 19.7 18.0 18.2 23.7 5.5 4.3 2.9 7.1 11.4 7.1 10.0 11.5 4.9 6.3 5.1 5.6 11.8 30.6 43.9 57.2 73.9 97.2 74.2 Mass, lb/ft2 1.3 0.8 0.6 2.3 3.6 2.3 3.7 3.9 1.4 1.6 1.4 1.6 2.8 6.6 9.3 12.0 16.3 21.4 16.2 Thermal Capacity, Btu/ft2 ·°F Hour 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Layer ID from outside to inside (see Table 18)

Conduction Time Factors, % 6 45 33 11 3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10 57 27 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

27 62 10 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 17 31 24 14 7 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 17 34 25 13 6 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 12 25 22 15 10 6 4 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0

0 7 18 18 15 11 8 6 5 3 3 2 1 1 1 1 0 0 0 0 0 0 0 0

1 3 8 10 10 9 8 7 6 5 5 4 4 3 3 3 2 2 2 2 1 1 1 0

18 61 18 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

4 41 35 14 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

8 53 30 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 23 38 22 10 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 10 22 20 14 10 7 5 4 3 2 1 1 1 0 0 0 0 0 0 0 0 0 0

1 2 8 11 11 10 9 7 6 5 5 4 3 3 3 2 2 2 1 1 1 1 1 1

2 2 3 6 7 8 8 7 7 6 5 5 5 4 4 3 3 3 3 2 2 2 2 1

2 2 3 4 5 6 6 6 6 6 6 5 5 5 4 4 4 4 3 3 3 3 3 2

2 2 5 6 7 7 6 6 6 5 5 5 4 4 4 4 3 3 3 3 3 3 2 2

3 3 3 5 6 6 6 6 6 5 5 5 5 4 4 4 4 4 3 3 3 3 2 2

1 2 6 8 8 8 7 7 6 5 5 5 4 4 3 3 3 3 2 2 2 2 2 2

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

F01 F01 F01 F01 F01 F01 F08 F08 F08 F12 F14 F15 G03 G03 G03 G05 G05 G05 F05 F05 F05 F05 F05 F05 I05 I05 I05 I05 I05 I05 G01 F05 F03 F05 F05 F05 F03 F16 — G01 G01 G01 — F03 — F03 F03 F03

F01 F13 G03 I02 G06 F03 — —

F01 F13 G03 I02 G06 F05 F16 F03

F01 F13 G03 I02 F08 F03 — —

F01 F13 G03 I02 F08 F05 F16 F03

F01 F13 G03 I03 F08 F03 — —

F01 F01 F01 F01 F01 F01 F01 F01 F13 M17 F13 F13 F13 F13 F13 F13 G03 F13 G03 G03 G03 G03 G03 M14 I02 G03 I03 I03 I03 I03 I03 F05 I03 I03 M11 M12 M13 M14 M15 I05 F08 F08 F03 F03 F03 F03 F03 F16 — F03 — — — — — F03 — — — — — — — —

Roof Number Descriptions 1. Metal roof, R-19 batt insulation, gyp board 11. 2. Metal roof, R-19 batt insulation, suspended acoustical ceiling 12. 3. Metal roof, R-19 batt insulation 13. 4. Asphalt shingles, wood sheathing, R-19 batt insulation, gyp board 14. 5. Slate or tile, wood sheathing, R-19 batt insulation, gyp board 15. 6. Wood shingles, wood sheathing, R-19 batt insulation, gyp board 16. 7. Membrane, sheathing, R-10 insulation board, wood deck 17. 8. Membrane, sheathing, R-10 insulation board, wood deck, suspended acoustical ceiling 18. 9. Membrane, sheathing, R-10 insulation board, metal deck 19. 10. Membrane, sheathing, R-10 insulation board, metal deck, suspended acoustical ceiling

indoor design condition), where the positive soil-to-indoor temperature difference causes sensible heat gains (Rock 2005). In many climates and for various temperatures and local soil conditions, moisture transport up through slabs-on-grade and basement floors is also significant, and contributes to the latent heat portion of the cooling load.

CALCULATING COOLING LOAD The instantaneous cooling load is the rate at which heat energy is convected to the zone air at a given point in time. Computation of cooling load is complicated by the radiant exchange between

Membrane, sheathing, R-15 insulation board, metal deck Membrane, sheathing, R-10 plus R-15 insulation boards, metal deck 2 in. concrete roof ballast, membrane, sheathing, R-15 insulation board, metal deck Membrane, sheathing, R-15 insulation board, 4 in. LW concrete Membrane, sheathing, R-15 insulation board, 6 in. LW concrete Membrane, sheathing, R-15 insulation board, 8 in. LW concrete Membrane, sheathing, R-15 insulation board, 6 in. HW concrete Membrane, sheathing, R-15 insulation board, 8 in. HW concrete Membrane, 6-in HW concrete, R-19 batt insulation, suspended acoustical ceiling

surfaces, furniture, partitions, and other mass in the zone. Most heat gain sources transfer energy by both convection and radiation. Radiative heat transfer introduces a time dependency to the process that is not easily quantified. Radiation is absorbed by thermal masses in the zone and then later transferred by convection into the space. This process creates a time lag and dampening effect. The convective portion, on the other hand, is assumed to immediately become cooling load in the hour in which that heat gain occurs. Heat balance procedures calculate the radiant exchange between surfaces based on their surface temperatures and emissivities, but they typically rely on estimated “radiative/convective splits” to determine the contribution of internal loads, including people, lighting,

Nonresidential Cooling and Heating Load Calculations

18.27

Table 18 Thermal Properties and Code Numbers of Layers Used in Wall and Roof Descriptions for Tables 16 and 17 Layer ID Description F01 F02 F03 F04 F05 F06 F07 F08 F09 F10 F11 F12 F13 F14 F15 F16 F17 F18 G01 G02 G03 G04 G05 G06 G07 I01 I02 I03 I04 I05 I06 M01 M02 M03 M04 M05 M06 M07 M08 M09 M10 M11 M12 M13 M14 M15 M16 M17

Outside surface resistance Inside vertical surface resistance Inside horizontal surface resistance Wall air space resistance Ceiling air space resistance EIFS finish 1 in. stucco Metal surface Opaque spandrel glass 1 in. stone Wood siding Asphalt shingles Built-up roofing Slate or tile Wood shingles Acoustic tile Carpet Terrazzo 5/8 in. gyp board 5/8 in. plywood 1/2 in. fiberboard sheathing 1/2 in. wood 1 in. wood 2 in. wood 4 in. wood R-5, 1 in. insulation board R-10, 2 in. insulation board R-15, 3 in. insulation board R-11, 3-1/2 in. batt insulation R-19, 6-1/4 in. batt insulation R-30, 9-1/2 in. batt insulation 4 in. brick 6 in. LW concrete block 8 in. LW concrete block 12 in. LW concrete block 8 in. concrete block 12 in. concrete block 6 in. LW concrete block (filled) 8 in. LW concrete block (filled) 12 in. LW concrete block (filled) 8 in. concrete block (filled) 4 in. lightweight concrete 6 in. lightweight concrete 8 in. lightweight concrete 6 in. heavyweight concrete 8 in. heavyweight concrete 12 in. heavyweight concrete 2 in. LW concrete roof ballast

Specific Thickness, Conductivity, Density, Heat, Resistance, 2 3 in. Btu·in/h·ft ·°F lb/ft Btu/lb·°F ft2 ·°F·h/Btu — — — — — 0.375 1.000 0.030 0.250 1.000 0.500 0.125 0.375 0.500 0.250 0.750 0.500 1.000 0.625 0.625 0.500 0.500 1.000 2.000 4.000 1.000 2.000 3.000 3.520 6.080 9.600 4.000 6.000 8.000 12.000 8.000 12.000 6.000 8.000 12.000 8.000 4.000 6.000 8.000 6.000 8.000 12.000 2.000

— — — — — 5.00 5.00 314.00 6.90 22.00 0.62 0.28 1.13 11.00 0.27 0.42 0.41 12.50 1.11 0.80 0.47 1.06 1.06 1.06 1.06 0.20 0.20 0.20 0.32 0.32 0.32 6.20 3.39 3.44 4.92 7.72 9.72 1.98 1.80 2.04 5.00 3.70 3.70 3.70 13.50 13.50 13.50 1.30

Notes: The following notes give sources for the data in this table. 1. Chapter 26, Table 1 for 7.5 mph wind 2. Chapter 26, Table 1 for still air, horizontal heat flow 3. Chapter 26, Table 1 for still air, downward heat flow 4. Chapter 26, Table 3 for 1.5 in. space, 90°F, horizontal heat flow, 0.82 emittance 5. Chapter 26, Table 3 for 3.5 in. space, 90°F, downward heat flow, 0.82 emittance 6. EIFS finish layers approximated by Chapter 26, Table 4 for 3/8 in. cement plaster, sand aggregate 7. Chapter 33, Table 3 for steel (mild) 8. Chapter 26, Table 4 for architectural glass 9. Chapter 26, Table 4 for marble and granite 10. Chapter 26, Table 4, density assumed same as Southern pine 11. Chapter 26, Table 4 for mineral fiberboard, wet molded, acoustical tile 12. Chapter 26, Table 4 for carpet and rubber pad, density assumed same as fiberboard 13. Chapter 26, Table 4, density assumed same as stone

— — — — — 116.0 116.0 489.0 158.0 160.0 37.0 70.0 70.0 120.0 37.0 23.0 18.0 160.0 50.0 34.0 25.0 38.0 38.0 38.0 38.0 2.7 2.7 2.7 1.2 1.2 1.2 120.0 32.0 29.0 32.0 50.0 50.0 32.0 29.0 32.0 50.0 80.0 80.0 80.0 140.0 140.0 140.0 40 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

— — — — — 0.20 0.20 0.12 0.21 0.19 0.28 0.30 0.35 0.30 0.31 0.14 0.33 0.19 0.26 0.29 0.31 0.39 0.39 0.39 0.39 0.29 0.29 0.29 0.23 0.23 0.23 0.19 0.21 0.21 0.21 0.22 0.22 0.21 0.21 0.21 0.22 0.20 0.20 0.20 0.22 0.22 0.22 0.20

0.25 0.68 0.92 0.87 1.00 — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

R

Mass, lb/ft2

0.25 — 0.68 — 0.92 — 0.87 — 1.00 — 0.08 3.63 0.20 9.67 0.00 1.22 0.04 3.29 0.05 13.33 0.81 1.54 0.44 0.73 0.33 2.19 0.05 5.00 0.94 0.77 1.79 1.44 1.23 0.75 0.08 13.33 0.56 2.60 0.78 1.77 1.06 1.04 0.47 1.58 0.94 3.17 1.89 6.33 3.77 12.67 5.00 0.23 10.00 0.45 15.00 0.68 11.00 0.35 19.00 0.61 30.00 0.96 0.65 40.00 1.77 16.00 2.33 19.33 2.44 32.00 1.04 33.33 1.23 50.00 3.03 16.00 4.44 19.33 5.88 32.00 1.60 33.33 1.08 26.67 1.62 40.00 2.16 53.33 0.44 70.00 0.48 93.33 0.89 140.0 1.54 6.7

Thermal Capacity, Btu/ft2 ·°F Notes — — — — — 0.73 1.93 0.15 0.69 2.53 0.43 0.22 0.77 1.50 0.24 0.20 0.25 2.53 0.68 0.51 0.32 0.62 1.24 2.47 4.94 0.07 0.13 0.20 0.08 0.14 0.22 7.60 3.36 4.06 6.72 7.33 11.00 3.36 4.06 6.72 7.33 5.33 8.00 10.67 15.05 20.07 30.10 1.33

1 2 3 4 5 6 6 7 8 9 10

11 12 13

14 15 15 15 15 16 16 16 17 17 17 18 19 20 21 22 23 24 25 26 27

28

Chapter 26, Table 4 for nail-base sheathing Chapter 26, Table 4 for Southern pine Chapter 26, Table 4 for expanded polystyrene Chapter 26, Table 4 for glass fiber batt, specific heat per glass fiber board Chapter 26, Table 4 for clay fired brick Chapter 26, Table 4, 16 lb block, 8 u16 in. face Chapter 26, Table 4, 19 lb block, 8 u16 in. face Chapter 26, Table 4, 32 lb block, 8 u16 in. face Chapter 26, Table 4, 33 lb normal weight block, 8 u 16 in. face Chapter 26, Table 4, 50 lb normal weight block, 8 u16 in. face Chapter 26, Table 4, 16 lb block, vermiculite fill Chapter 26, Table 4, 19 lb block, 8 u16 in. face, vermiculite fill Chapter 26, Table 4, 32 lb block, 8 u16 in. face, vermiculite fill Chapter 26, Table 4, 33 lb normal weight block, 8 u16 in. face, vermiculite fill Chapter 26, Table 4 for 40 lb/ft3 LW concrete

18.28 appliances, and equipment, to the radiant exchange. RTS further simplifies the HB procedure by also relying on an estimated radiative/convective split of wall and roof conductive heat gain instead of simultaneously solving for the instantaneous convective and radiative heat transfer from each surface, as is done in the HB procedure. Thus, the cooling load for each load component (lights, people, walls, roofs, windows, appliances, etc.) for a particular hour is the sum of the convective portion of the heat gain for that hour plus the time-delayed portion of radiant heat gains for that hour and the previous 23 h. Table 14 contains recommendations for splitting each of the heat gain components into convective and radiant portions. RTS converts the radiant portion of hourly heat gains to hourly cooling loads using radiant time factors, the coefficients of the radiant time series. Radiant time factors are used to calculate the cooling load for the current hour on the basis of current and past heat gains. The radiant time series for a particular zone gives the time-dependent response of the zone to a single pulse of radiant energy. The series shows the portion of the radiant pulse that is convected to zone air for each hour. Thus, r0 represents the fraction of the radiant pulse convected to the zone air in the current hour r1 in the previous hour, and so on. The radiant time series thus generated is used to convert the radiant portion of hourly heat gains to hourly cooling loads according to the following equation: Qr,T = r0qr,T + r1qr,T –1 + r2 qr,T –2 + r3qr,T –3 + … + r23qr,T –23 (34) where Qr, T =radiant cooling load Qr for current hour T, Btu/h qr, T =radiant heat gain for current hour, Btu/h qr,Tn =radiant heat gain n hours ago, Btu/h r0, r1, etc.=radiant time factors

The radiant cooling load for the current hour, which is calculated using RTS and Equation (34), is added to the convective portion to determine the total cooling load for that component for that hour. Radiant time factors are generated by a heat balance based procedure. A separate series of radiant time factors is theoretically required for each unique zone and for each unique radiant energy distribution function assumption. For most common design applications, RTS variation depends primarily on the overall massiveness of the construction and the thermal responsiveness of the surfaces the radiant heat gains strike. One goal in developing RTS was to provide a simplified method based directly on the HB method; thus, it was deemed desirable to generate RTS coefficients directly from a heat balance. A heat balance computer program was developed to do this: Hbfort, which is included as part of Cooling and Heating Load Calculation Principles (Pedersen et al. 1998). The RTS procedure is described by Spitler et al. (1997). The procedure for generating RTS coefficients may be thought of as analogous to the custom weighting factor generation procedure used by DOE 2.1 (Kerrisk et al. 1981; Sowell 1988a, 1988b). In both cases, a zone model is pulsed with a heat gain. With DOE 2.1, the resulting loads are used to estimate the best values of the transfer function method weighting factors to most closely match the load profile. In the procedure described here, a unit periodic heat gain pulse is used to generate loads for a 24 h period. As long as the heat gain pulse is a unit pulse, the resulting loads are equivalent to the RTS coefficients. Two different radiant time series are used: Solar, for direct transmitted solar heat gain (radiant energy assumed to be distributed to the floor and furnishings only) and nonsolar, for all other types of heat gains (radiant energy assumed to be uniformly distributed on all internal surfaces). Nonsolar RTS apply to radiant heat gains from people, lights, appliances, walls, roofs, and floors. Also, for diffuse solar heat gain and direct solar heat gain from fenestration with inside shading (blinds, drapes, etc.), the nonsolar RTS should be used. Radiation from those sources is assumed to be more uniformly

2009 ASHRAE Handbook—Fundamentals distributed onto all room surfaces. Effect of beam solar radiation distribution assumptions is addressed by Hittle (1999). Representative solar and nonsolar RTS data for light, medium, and heavyweight constructions are provided in Tables 19 and 20. Those were calculated using the Hbfort computer program (Pedersen et al. 1998) with zone characteristics listed in Table 21. Customized RTS values may be calculated using the HB method where the zone is not reasonably similar to these typical zones or where more precision is desired. ASHRAE research project RP-942 compared HB and RTS results over a wide range of zone types and input variables (Rees et al. 2000; Spitler et al. 1998). In general, total cooling loads calculated using RTS closely agreed with or were slightly higher than those of the HB method with the same inputs. The project examined more than 5000 test cases of varying zone parameters. The dominating variable was overall thermal mass, and results were grouped into lightweight, U.S. medium-weight, U.K. medium-weight, and heavyweight construction. Best agreement between RTS and HB results was obtained for light- and medium-weight construction. Greater differences occurred in heavyweight cases, with RTS generally predicting slightly higher peak cooling loads than HB. Greater differences also were observed in zones with extremely high internal radiant loads and large glazing areas or with a very lightweight exterior envelope. In this case, heat balance calculations predict that some of the internal radiant load will be transmitted to the outdoor environment and never becomes cooling load within the space. RTS does not account for energy transfer out of the space to the environment, and thus predicted higher cooling loads. ASHRAE research project RP-1117 constructed two model rooms for which cooling loads were physically measured using extensive instrumentation. The results agreed with previous simulations (Chantrasrisalai et al. 2003; Eldridge et al. 2003; Iu et al. 2003). HB calculations closely approximated the measured cooling loads when provided with detailed data for the test rooms. RTS overpredicted measured cooling loads in tests with large, clear, single-glazed window areas with bare concrete floor and no furnishings or internal loads. Tests under more typical conditions (venetian blinds, carpeted floor, office-type furnishings, and normal internal loads) provided good agreement between HB, RTS, and measured loads.

HEATING LOAD CALCULATIONS Techniques for estimating design heating load for commercial, institutional, and industrial applications are essentially the same as for those estimating design cooling loads for such uses, with the following exceptions: • Temperatures outside conditioned spaces are generally lower than maintained space temperatures. • Credit for solar or internal heat gains is not included • Thermal storage effect of building structure or content is ignored. • Thermal bridging effects on wall and roof conduction are greater for heating loads than for cooling loads, and greater care must be taken to account for bridging effects on U-factors used in heating load calculations. Heat losses (negative heat gains) are thus considered to be instantaneous, heat transfer essentially conductive, and latent heat treated only as a function of replacing space humidity lost to the exterior environment. This simplified approach is justified because it evaluates worstcase conditions that can reasonably occur during a heating season. Therefore, the near-worst-case load is based on the following: • • • •

Design interior and exterior conditions Including infiltration and/or ventilation No solar effect (at night or on cloudy winter days) Before the periodic presence of people, lights, and appliances has an offsetting effect

Nonresidential Cooling and Heating Load Calculations Table 19

18.29

Representative Nonsolar RTS Values for Light to Heavy Construction Interior Zones

% Glass Hour 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

With Carpet

Medium No Carpet

With Carpet

Heavy

No Carpet

With Carpet

Light No Carpet

10% 50% 90% 10% 50% 90% 10% 50% 90% 10% 50% 90% 10% 50% 90% 10% 50% 90% 47 19 11 6 4 3 2 2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0

50 18 10 6 4 3 2 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0

53 17 9 5 3 2 2 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0

41 20 12 8 5 4 3 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0

43 19 11 7 5 3 3 2 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0

46 19 11 7 5 3 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0

100 100 100 100 100 100

46 18 10 6 4 2 2 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0

49 17 9 5 3 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0

Radiant Time Factor, % 31 33 35 34 38 17 16 15 9 9 11 10 10 6 6 8 7 7 4 4 6 5 5 4 4 4 4 4 4 3 4 3 3 3 3 3 3 3 3 3 3 2 2 3 3 2 2 2 3 3 2 2 2 3 2 2 2 2 2 2 1 1 1 2 2 1 1 1 2 2 1 1 1 2 2 1 1 1 2 2 1 1 1 2 2 1 1 1 2 2 1 1 1 2 2 0 1 1 2 2 0 1 1 2 1 0 1 1 2 1 0 1 0 1 1 0 0 0 1 1

52 16 8 5 3 2 2 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0

100 100 100 100 100 100

42 9 5 4 4 3 3 3 3 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1

22 10 6 5 5 4 4 4 4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2

25 9 6 5 5 4 4 4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2

28 9 6 5 4 4 4 4 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 1

100 100 100 100 100 100

Medium

Heavy

With Carpet No Carpet With Carpet No Carpet With Carpet No Carpet

Light

46 19 11 6 4 3 2 2 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0

40 20 12 8 5 4 3 2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0

46 18 10 6 3 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0

31 17 11 8 6 4 4 3 3 2 2 2 1 1 1 1 1 1 1 0 0 0 0 0

33 9 6 5 4 4 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 1 1

21 9 6 5 5 4 4 4 4 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2

100 100 100 100 100 100

Table 20 Representative Solar RTS Values for Light to Heavy Construction Light % Glass Hour 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

With Carpet 10% 53 17 9 5 3 2 2 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 100

50% 55 17 9 5 3 2 2 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 100

Medium No Carpet

90% 56 17 9 5 3 2 2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 100

10% 44 19 11 7 5 3 3 2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 100

50% 45 20 11 7 5 3 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 100

With Carpet

90% 46 20 11 7 5 3 2 2 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 100

10% 52 16 8 5 3 2 2 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 100

50%

90%

Heavy No Carpet

10%

With Carpet

No Carpet

50%

90%

10%

50%

90%

10%

50%

90%

Radiant Time Factor, % 54 55 28 29 16 15 15 15 8 8 10 10 4 4 7 7 3 3 6 6 2 2 5 5 1 1 4 4 1 1 4 3 1 1 3 3 1 1 3 3 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 100 100 100 100

29 15 10 7 6 5 4 3 3 3 2 2 2 2 1 1 1 1 1 1 1 0 0 0 100

47 11 6 4 3 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 100

49 12 6 4 3 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 100

51 12 6 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 100

26 12 7 5 4 4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 100

27 13 7 5 4 4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 1 1 100

28 13 7 5 4 4 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 1 1 100

18.30

2009 ASHRAE Handbook—Fundamentals Table 21 RTS Representative Zone Construction for Tables 19 and 20

Construction Class Exterior Wall

Roof/Ceiling

Partitions

Floor

Furnishings

4 in. LW concrete, ceiling air space, acoustic tile

3/4 in. gyp, air space, 3/4 in. gyp

acoustic tile, ceiling air space, 4 in. LW concrete

1 in. wood @ 50% of floor area

Medium

4 in. face brick, 2 in. insulation, 4 in. HW concrete, ceiling air space, 3/4 in. gyp air space, acoustic tile

3/4 in. gyp, air space, 3/4 in. gyp

acoustic tile, ceiling air space, 4 in. HW concrete

1 in. wood @ 50% of floor area

Heavy

4 in. face brick, 8 in. HW concrete air space, 2 in. insulation, 3/4 in. gyp

3/4 in. gyp, 8 in. HW concrete block, 3/4 in. gyp

acoustic tile, ceiling air space, 8 in. HW concrete

1 in. wood @ 50% of floor area

Light

steel siding, 2 in. insulation, air space, 3/4 in. gyp

8 in. HW concrete, ceiling air space, acoustic tile

Typical commercial and retail spaces have nighttime unoccupied periods at a setback temperature where little to no ventilation is required, building lights and equipment are off, and heat loss is primarily through conduction and infiltration. Before being occupied, buildings are warmed to the occupied temperature (see the following discussion). During occupied time, building lights, equipment, and people cooling loads can offset conduction heat loss, although some perimeter heat may be required, leaving the infiltration and ventilation loads as the primary heating loads. Ventilation heat load may be offset with heat recovery equipment. These loads (conduction loss, warm-up load, and ventilation load) may not be additive when sizing building heating equipment, and it is prudent to analyze each load and their interactions to arrive at final equipment sizing for heating.

Fig. 12 Heat Flow from Below-Grade Surface

HEAT LOSS CALCULATIONS The general procedure for calculation of design heat losses of a structure is as follows: 1. Select outdoor design conditions: temperature, humidity, and wind direction and speed. 2. Select indoor design conditions to be maintained. 3. Estimate temperature in any adjacent unheated spaces. 4. Select transmission coefficients and compute heat losses for walls, floors, ceilings, windows, doors, and foundation elements. 5. Compute heat load through infiltration and any other outdoor air introduced directly to the space. 6. Sum the losses caused by transmission and infiltration.

Outdoor Design Conditions The ideal heating system would provide enough heat to match the structure’s heat loss. However, weather conditions vary considerably from year to year, and heating systems designed for the worst weather conditions on record would have a great excess of capacity most of the time. A system’s failure to maintain design conditions during brief periods of severe weather usually is not critical. However, close regulation of indoor temperature may be critical for some occupancies or industrial processes. Design temperature data and discussion of their application are given in Chapter 14. Generally, the 99% temperature values given in the tabulated weather data be used. However, caution should be used, and local conditions always investigated. In some locations, outdoor temperatures are commonly much lower and wind velocities higher than those given in the tabulated weather data.

Indoor Design Conditions The main purpose of the heating system is to maintain indoor conditions that make most of the occupants comfortable. It should be kept in mind, however, that the purpose of heating load calculations is to obtain data for sizing the heating system components. In many cases, the system will rarely be called upon to operate at the design conditions. Therefore, the use and occupancy of the space are general considerations from the design temperature point of view. Later, when the building’s energy requirements are computed, the actual conditions in the space and outdoor environment, including internal heat gains, must be considered.

Fig. 12 Heat Flow from Below-Grade Surface The indoor design temperature should be selected at the lower end of the acceptable temperature range, so that the heating equipment will not be oversized. Even properly sized equipment operates under partial load, at reduced efficiency, most of the time; therefore, any oversizing aggravates this condition and lowers overall system efficiency. A maximum design dry-bulb temperature of 70°F is recommended for most occupancies. The indoor design value of relative humidity should be compatible with a healthful environment and the thermal and moisture integrity of the building envelope. A minimum relative humidity of 30% is recommended for most situations.

Calculation of Transmission Heat Losses Exterior Surface Above Grade. All above-grade surfaces exposed to outdoor conditions (walls, doors, ceilings, fenestration, and raised floors) are treated identically, as follows: q = A u HF

(35)

HF = U 't

(36) Btu/h·ft2.

where HF is the heating load factor in Below-Grade Surfaces. An approximate method for estimating below-grade heat loss [based on the work of Latta and Boileau (1969)] assumes that the heat flow paths shown in Figure 12 can be used to find the steady-state heat loss to the ground surface, as follows: HF = U avg t in – t gr

(37)

where Uavg = average U-factor for below-grade surface from Equation (39) or (40), Btu/h·ft2·°F tin = below-grade space air temperature, °F tgr = design ground surface temperature from Equation (38), °F

Nonresidential Cooling and Heating Load Calculations

18.31 Table 22

Fig. 13 Ground Temperature Amplitude

Average U-Factor for Basement Walls with Uniform Insulation Uavg,bw from Grade to Depth, Btu/h·ft2·°F

Depth, ft Uninsulated 1 2.6 3 4 5 6 7 8

0.432 0.331 0.273 0.235 0.208 0.187 0.170 0.157

R-5

R-10

R-15

0.135 0.121 0.110 0.101 0.094 0.088 0.083 0.078

0.080 0.075 0.070 0.066 0.063 0.060 0.057 0.055

0.057 0.054 0.052 0.050 0.048 0.046 0.044 0.043

Soil conductivity = 0.8 Btu/h·ft·°F; insulation is over entire depth. For other soil conductivities and partial insulation, use Equation (39).

Table 23 Average U-Factor for Basement Floors Uavg,bf , Btu/h·ft2·°F

Fig. 13 Fig. 14

Ground Temperature Amplitude

wb (Shortest Width of Basement), ft

zf (Depth of Floor Below Grade), ft

20

24

28

32

1 2 3 4 5 6 7

0.064 0.054 0.047 0.042 0.038 0.035 0.032

0.057 0.048 0.042 0.038 0.035 0.032 0.030

0.052 0.044 0.039 0.035 0.032 0.030 0.028

0.047 0.040 0.036 0.033 0.030 0.028 0.026

Below-Grade Parameters

Soil conductivity is 0.8 Btu/h·ft·°F; floor is uninsulated. For other soil conductivities and insulation, use Equation (39).

Fig. 14

Below-Grade Parameters

The effect of soil heat capacity means that none of the usual external design air temperatures are suitable values for tgr. Ground surface temperature fluctuates about an annual mean value by amplitude A, which varies with geographic location and surface cover. The minimum ground surface temperature, suitable for heat loss estimates, is therefore t gr = t gr – A

(38)

where t gr = mean ground temperature, °F, estimated from the annual average air temperature or from well-water temperatures, shown in Figure 17 of Chapter 32 in the 2007 ASHRAE Handbook—HVAC Applications A = ground surface temperature amplitude, °F, from Figure 13 for North America

Figure 14 shows depth parameters used in determining Uavg. For walls, the region defined by z1 and z2 may be the entire wall or any portion of it, allowing partially insulated configurations to be analyzed piecewise. The below-grade wall average U-factor is given by 2k soil U avg,bw = -----------------------S z1 – z2 ×

The value of soil thermal conductivity k varies widely with soil type and moisture content. A typical value of 0.8 Btu/h·ft·°F has been used previously to tabulate U-factors, and Rother is approximately 1.47 h·ft2 ·°F/Btu for uninsulated concrete walls. For these parameters, representative values for Uavg,bw are shown in Table 22. The average below-grade floor U-factor (where the entire basement floor is uninsulated or has uniform insulation) is given by

(39)

2k soil R other· 2k soil R other· § § ln ¨ z 2 + -----------------------------¸ – ln ¨ z 1 + -----------------------------¸ S S © ¹ © ¹

2k soil U avg,bf = ------------Sw b × where wb = basement width (shortest dimension), ft zf = floor depth below grade, ft (see Figure 14)

Representative values of Uavg,bf for uninsulated basement floors are shown in Table 23. At-Grade Surfaces. Concrete slab floors may be (1) unheated, relying for warmth on heat delivered above floor level by the heating system, or (2) heated, containing heated pipes or ducts that constitute a radiant slab or portion of it for complete or partial heating of the house. The simplified approach that treats heat loss as proportional to slab perimeter allows slab heat loss to be estimated for both unheated and heated slab floors:

where Uavg,bw = average U-factor for wall region defined by z1 and z2, Btu/h·ft2 ·°F ksoil = soil thermal conductivity, Btu/h·ft·°F Rother = total resistance of wall, insulation, and inside surface resistance, h·ft2 ·°F/Btu z1, z2 = depths of top and bottom of wall segment under consideration, ft (Figure 14)

(40) §w § k soil R other· z k soil R other· ln ¨ -----b- + ---f + -------------------------¸ – ln ¨ --------------------------¸ ©2 2 S ¹ © S ¹

q = p u HF

(41)

HF = F p 't

(42)

where q = heat loss through perimeter, Btu/h Fp = heat loss coefficient per foot of perimeter, Btu/h·ft·°F, Table 24 p = perimeter (exposed edge) of floor, ft

18.32

2009 ASHRAE Handbook—Fundamentals

Table 24 Heat Loss Coefficient Fp of Slab Floor Construction Construction

Insulation

Fp, Btu/h·ft·°F

8 in. block wall, brick facing Uninsulated R-5.4 from edge to footer 4 in. block wall, brick facing Uninsulated R-5.4 from edge to footer Metal stud wall, stucco Uninsulated R-5.4 from edge to footer Poured concrete wall with duct Uninsulated near perimeter* R-5.4 from edge to footer

0.68 0.50 0.84 0.49 1.20 0.53 2.12 0.72

*Weighted average temperature of heating duct was assumed at 110ºF during heating season (outdoor air temperature less than 65ºF).

Surfaces Adjacent to Buffer Space. Heat loss to adjacent unconditioned or semiconditioned spaces can be calculated using a heating factor based on the partition temperature difference: HF = U t in – t b

(43)

Infiltration All structures have some air leakage or infiltration. This means a heat loss because the cold, dry outdoor air must be heated to the inside design temperature and moisture must be added to increase the humidity to the design value. Procedures for estimating the infiltration rate are discussed in Chapter 16. Once the infiltration rate has been calculated, the resulting sensible heat loss, equivalent to the sensible heating load from infiltration, is given by q s = 60 cfm e v c p t in – t o

(44)

where cfm = volume flow rate of infiltrating air cp = specific heat capacity of air, Btu/lbm ·ºF v = specific volume of infiltrating air, ft3/lbm

Assuming standard air conditions (59°F and sea-level conditions) for v and cp , Equation (44) may be written as q s = 1.10 cfm t in – t o

(45)

The infiltrating air also introduces a latent heating load given by q l = 60 cfm e v W in – W o D h

(46)

where Win = humidity ratio for inside space air, lbw /lba Wo = humidity ratio for outdoor air, lbw /lba Dh = change in enthalpy to convert 1 lb water from vapor to liquid, Btu/lbw

For standard air and nominal indoor comfort conditions, the latent load may be expressed as q l = 4840 cfm W in – W o

(47)

The coefficients 1.10 in Equation (45) and 4840 in Equation (47) are given for standard conditions. They depend on temperature and altitude (and, consequently, pressure).

Table 25 Common Sizing Calculations in Other Chapters Subject

Volume/Chapter

Duct heat transfer Piping heat transfer Fan heat transfer Pump heat transfer Moist-air sensible heating and cooling Moist-air cooling and dehumidification Air mixing Space heat absorption and moist-air moisture gains Adiabatic mixing of water injected into moist air

ASTM Standard C680 Fundamentals Ch. 3 (35) Fundamentals Ch. 19 (22) Systems Ch. 43 (3), (4), (5) Fundamentals Ch. 1 (43) Fundamentals Ch. 1 (45) Fundamentals Ch. 1 (46) Fundamentals Ch. 1 (48)

Equation(s)

Fundamentals Ch. 1

(47)

infiltration-prone assemblies than the energy-efficient and much tighter buildings typical of today. Allowances of 10 to 20% of the net calculated heating load for piping losses to unheated spaces, and 10 to 20% more for a warm-up load, were common practice, along with other occasional safety factors reflecting the experience and/or concern of the individual designer. Such measures are less conservatively applied today with newer construction. A combined warm-up/safety allowance of 20 to 25% is fairly common but varies depending on the particular climate, building use, and type of construction. Engineering judgment must be applied for the particular project. Armstrong et al. (1992a, 1992b) provide a design method to deal with warm-up and cooldown load.

OTHER HEATING CONSIDERATIONS Calculation of design heating load estimates has essentially become a subset of the more involved and complex estimation of cooling loads for such spaces. Chapter 19 discusses using the heating load estimate to predict or analyze energy consumption over time. Special provisions to deal with particular applications are covered in the 2007 ASHRAE Handbook—HVAC Applications and the 2008 ASHRAE Handbook—HVAC Systems and Equipment. The 1989 ASHRAE Handbook—Fundamentals was the last edition to contain a chapter dedicated only to heating load. Its contents were incorporated into this volume’s Chapter 17, which describes steady-state conduction and convection heat transfer and provides, among other data, information on losses through basement floors and slabs.

SYSTEM HEATING AND COOLING LOAD EFFECTS The heat balance (HB) or radiant time series (RTS) methods are used to determine cooling loads of rooms within a building, but they do not address the plant size necessary to reject the heat. Principal factors to consider in determining the plant size are ventilation, heat transport equipment, and air distribution systems. Some of these factors vary as a function of room load, ambient temperature, and control strategies, so it is often necessary to evaluate the factors and strategies dynamically and simultaneously with the heat loss or gain calculations. The detailed analysis of system components and methods calculating their contribution to equipment sizing are beyond the scope of this chapter, which is general in nature. Table 25 lists the most frequently used calculations in other chapters and volumes.

HEATING SAFETY FACTORS AND LOAD ALLOWANCES

ZONING

Before mechanical cooling became common in the second half of the 1900s, and when energy was less expensive, buildings included much less insulation; large, operable windows; and generally more

The organization of building rooms as defined for load calculations into zones and air-handling units has no effect on room cooling loads. However, specific grouping and ungrouping of rooms into

Nonresidential Cooling and Heating Load Calculations zones may cause peak system loads to occur at different times during the day or year and may significantly affected heat removal equipment sizes. For example, if each room is cooled by a separate heat removal system, the total capacity of the heat transport systems equals the sum of peak room loads. Conditioning all rooms by a single heat transport system (e.g., a variable-volume air handler) requires less capacity (equal to the simultaneous peak of the combined rooms load, which includes some rooms at off-peak loads). This may significantly reduce equipment capacity, depending on the configuration of the building.

VENTILATION Consult ASHRAE Standard 62.1 and building codes to determine the required quantity of ventilation air for an application, and the various methods of achieving acceptable indoor air quality. The following discussion is confined to the effect of mechanical ventilation on sizing heat removal equipment. Where natural ventilation is used, through operable windows or other means, it is considered as infiltration and is part of the direct-to-room heat gain. Where ventilation air is conditioned and supplied through the mechanical system its sensible and latent loads are applied directly to heat transport and central equipment, and do not affect room heating and cooling loads. If the mechanical ventilation rate sufficiently exceeds exhaust airflows, air pressure may be positive and infiltration from envelope openings and outside wind may not be included in the load calculations. Chapter 16 includes more information on ventilating commercial buildings.

18.33 for picking up the sensible load. The quantity of heat added can be determined by Equation (9). With a constant-volume reheat system, heat transport system load does not vary with changes in room load, unless the cooling coil discharge temperature is allowed to vary. Where a minimum circulation rate requires a supply air temperature greater than the available design supply air temperature, reheat adds to the cooling load on the heat transport system. This makes the cooling load on the heat transport system larger than the room peak load.

Mixed Air Systems Mixed air systems change the supply air temperature to match the cooling capacity by mixing airstreams of different temperatures; examples include multizone and dual-duct systems. Systems that cool the entire airstream to remove moisture and to reheat some of the air before mixing with the cooling airstream influence load on the heat transport system in the same way a reheat system does. Other systems separate the air paths so that mixing of hot- and colddeck airstreams does not occur. For systems that mix hot and cold airstreams, the contribution to the heat transport system load is determined as follows. 1. Determine the ratio of cold-deck flow to hot-deck flow from Qh ------ = T c – T r e T r – T h Qc 2. From Equation (10), the hot-deck contribution to room load during off-peak cooling is qrh = 1.1Qh (Th – Tr)

AIR HEAT TRANSPORT SYSTEMS Heat transport equipment is usually selected to provide adequate heating or cooling for the peak load condition. However, selection must also consider maintaining desired inside conditions during all occupied hours, which requires matching the rate of heat transport to room peak heating and cooling loads. Automatic control systems normally vary the heating and cooling system capacity during these off-peak hours of operation.

where Qh Qc Tc Th Th qrh

= = = = = =

heating airflow, cfm cooling airflow, cfm cooling air temperature, °F heating air temperature, °F room or return air temperature, °F heating airflow contribution to room load at off-peak hours, Btu/h

On/Off Control Systems

Heat Gain from Fans

On/off control systems, common in residential and light commercial applications, cycle equipment on and off to match room load. They are adaptable to heating or cooling because they can cycle both heating and cooling equipment. In their purest form, their heat transport matches the combined room and ventilation load over a series of cycles.

Fans that circulate air through HVAC systems add energy to the system through the following processes:

Variable-Air-Volume Systems Variable-air-volume (VAV) systems have airflow controls that adjust cooling airflow to match the room cooling load. Damper leakage or minimum airflow settings may cause overcooling, so most VAV systems are used in conjunction with separate heating systems. These may be duct-mounted heating coils, or separate radiant or convective heating systems. The amount of heat added by the heating systems during cooling becomes part of the room cooling load. Calculations must determine the minimum airflow relative to off-peak cooling loads. The quantity of heat added to the cooling load can be determined for each terminal by Equation (9) using the minimum required supply airflow rate and the difference between supply air temperature and the room inside heating design temperature.

Constant-Air-Volume Reheat Systems In constant-air-volume (CAV) reheat systems, all supply air is cooled to remove moisture and then heated to avoid overcooling rooms. Reheat refers to the amount of heat added to cooling supply air to raise the supply air temperature to the temperature necessary

• Increasing velocity and static pressure adds kinetic and potential energy • Fan inefficiency in producing airflow and static pressure adds sensible heat (fan heat) to the airflow • Inefficiency of motor and drive dissipates sensible heat The power required to provide airflow and static pressure can be determined from the first law of thermodynamics with the following equation: PA = 0.000157Vp where PA = air power, hp V = flow rate, cfm p = pressure, in. of water

at standard air conditions with air density = 0.075 lb/ft3 built into the multiplier 0.000157. The power necessary at the fan shaft must account for fan inefficiencies, which may vary from 50 to 70%. This may be determined from PF = PA /KF where PF = power required at fan shaft, hp KF = fan efficiency, dimensionless

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2009 ASHRAE Handbook—Fundamentals

The power necessary at the input to the fan motor must account for fan motor inefficiencies and drive losses. Fan motor efficiencies generally vary from 80 to 95%, and drive losses for a belt drive are 3% of the fan power. This may be determined from PM = (1 + DL) PF /EM ED where PM ED EM PF DL

= = = = =

power required at input to motor, hp belt drive efficiency, dimensionless fan motor efficiency, dimensionless power required at fan shaft, hp drive loss, dimensionless

Almost all the energy required to generate airflow and static pressure is ultimately dissipated as heat within the building and HVAC system; a small portion is discharged with any exhaust air. Generally, it is assumed that all the heat is released at the fan rather than dispersed to the remainder of the system. The portion of fan heat released to the airstream depends on the location of the fan motor and drive: if they are within the airstream, all the energy input to the fan motor is released to the airstream. If the fan motor and drive are outside the airstream, the energy is split between the airstream and the room housing the motor and drive. Therefore, the following equations may be used to calculate heat generated by fans and motors: If motor and drive are outside the airstream, qf s = 2545PF qfr = 2545(PM – PF ) If motor and drive are inside the airstream, qf s = 2545PM qfr = 0.0 where PF PM qf s qfr 2545

= = = = =

power required at fan shaft, hp power required at input to motor, hp heat release to airstream, Btu/h heat release to room housing motor and drive, Btu/h conversion factor, Btu/h·hp

Supply airstream temperature rise may be determined from psychrometric formulas or Equation (9). Variable- or adjustable-frequency drives (VFDs or AFDs) often drive fan motors in VAV air-handling units. These devices release heat to the surrounding space. Refer to manufacturers’ data for heat released or efficiencies. The disposition of heat released is determined by the drive’s location: in the conditioned space, in the return air path, or in a nonconditioned equipment room. These drives, and other electronic equipment such as building control, data processing, and communications devices, are temperature sensitive, so the rooms in which they are housed require cooling, frequently yearround.

Duct Surface Heat Transfer Heat transfer across the duct surface is one mechanism for energy transfer to or from air inside a duct. It involves conduction through the duct wall and insulation, convection at inner and outer surfaces, and radiation between the duct and its surroundings. Chapter 4 presents a rigorous analysis of duct heat loss and gain, and Chapter 23 addresses application of analysis to insulated duct systems. The effect of duct heat loss or gain depends on the duct routing, duct insulation, and its surrounding environment. Consider the following conditions:

• For duct run within the area cooled or heated by air in the duct, heat transfer from the space to the duct has no effect on heating or cooling load, but beware of the potential for condensation on cold ducts. • For duct run through unconditioned spaces or outdoors, heat transfer adds to the cooling or heating load for the air transport system but not for the conditioned space. • For duct run through conditioned space not served by the duct, heat transfer affects the conditioned space as well as the air transport system serving the duct. • For an extensive duct system, heat transfer reduces the effective supply air differential temperature, requiring adjustment through air balancing to increase airflow to extremities of the distribution system.

Duct Leakage Air leakage from supply ducts can considerably affect HVAC system energy use. Leakage reduces cooling and/or dehumidifying capacity for the conditioned space, and must be offset by increased airflow (sometimes reduced supply air temperatures), unless leaked air enters the conditioned space directly. Supply air leakage into a ceiling return plenum or leakage from unconditioned spaces into return ducts also affects return air temperature and/or humidity. Determining leakage from a duct system is complex because of the variables in paths, fabrication, and installation methods. Refer to Chapter 21 and publications from the Sheet Metal and Air Conditioning Contractors’ National Association (SMACNA) for methods of determining leakage. In general, good-quality ducts and postinstallation duct sealing provide highly cost-effective energy savings, with improved thermal comfort and delivery of ventilation air.

Ceiling Return Air Plenum Temperatures The space above a ceiling, when used as a return air path, is a ceiling return air plenum, or simply a return plenum. Unlike a traditional ducted return, the plenum may have multiple heat sources in the air path. These heat sources may be radiant and convective loads from lighting and transformers; conduction loads from adjacent walls, roofs, or glazing; or duct and piping systems within the plenum. As heat from these sources is picked up by the unducted return air, the temperature differential between the ceiling cavity and conditioned space is small. Most return plenum temperatures do not rise more than 1 to 3°F above space temperature, thus generating only a relatively small thermal gradient for heat transfer through plenum surfaces, except to the outdoors. This yields a relatively largepercentage reduction in space cooling load by shifting plenum loads to the system. Another reason plenum temperatures do not rise more is leakage into the plenum from supply air ducts, and, if exposed to the roof, increasing levels of insulation. Where the ceiling space is used as a return air plenum, energy balance requires that heat picked up from the lights into the return air (1) become part of the cooling load to the return air (represented by a temperature rise of return air as it passes through the ceiling space), (2) be partially transferred back into the conditioned space through the ceiling material below, and/or (3) be partially lost from the space through floor surfaces above the plenum. If the plenum has one or more exterior surfaces, heat gains through them must be considered; if adjacent to spaces with different indoor temperatures, partition loads must be considered, too. In a multistory building, the conditioned space frequently gains heat through its floor from a similar plenum below, offsetting the floor loss. The radiant component of heat leaving the ceiling or floor surface of a plenum is normally so small, because of relatively small temperature differences, that all such heat transfer is considered convective for calculation purposes (Rock and Wolfe 1997). Figure 15 shows a schematic of a typical return air plenum. The following equations, using the heat flow directions shown in Figure

Nonresidential Cooling and Heating Load Calculations

18.35 return air is small and may be considered as convective for calculation purposes.

Fig. 15 Schematic Diagram of Typical Return Air Plenum

Fig. 15

Schematic Diagram of Typical Return Air Plenum

15, represent the heat balance of a return air plenum design for a typical interior room in a multifloor building: q1 = Uc Ac(tp – tr)

(48)

q2 = Uf Af (tp – tfa )

(49)

q3 = 1.1Q(tp – tr)

(50)

qlp – q2 – q1 – q3 = 0

(51)

qr + q1 Q = -------------------------1.1 t r – t s

(52)

where q1 q2 q3 Q qlp qlr qf qw qr

= = = = = = = = =

tp tr tfa ts

= = = =

heat gain to space from plenum through ceiling, Btu/h heat loss from plenum through floor above, Btu/h heat gain “pickup” by return air, Btu/h return airflow, cfm light heat gain to plenum via return air, Btu/h light heat gain to space, Btu/h heat gain from plenum below, through floor, Btu/h heat gain from exterior wall, Btu/h space cooling load, including appropriate treatment of qlr, qf , and/or qw , Btu/h plenum air temperature, °F space air temperature, °F space air temperature of floor above, °F supply air temperature, °F

By substituting Equations (48), (49), (50), and (52) into heat balance Equation (51), tp can be found as the resultant return air temperature or plenum temperature. The results, although rigorous and best solved by computer, are important in determining the cooling load, which affects equipment size selection, future energy consumption, and other factors. Equations (48) to (52) are simplified to illustrate the heat balance relationship. Heat gain into a return air plenum is not limited to heat from lights. Exterior walls directly exposed to the ceiling space can transfer heat directly to or from return air. For single-story buildings or the top floor of a multistory building, roof heat gain or loss enters or leaves the ceiling plenum rather than the conditioned space directly. The supply air quantity calculated by Equation (52) is only for the conditioned space under consideration, and is assumed to equal the return air quantity. The amount of airflow through a return plenum above a conditioned space may not be limited to that supplied into the space; it will, however, have no noticeable effect on plenum temperature if the surplus comes from an adjacent plenum operating under similar conditions. Where special conditions exist, Equations (48) to (52) must be modified appropriately. Finally, although the building’s thermal storage has some effect, the amount of heat entering the

Ceiling Plenums with Ducted Returns Compared to those in unducted plenum returns, temperatures in ceiling plenums that have well-sealed return or exhaust air ducts float considerably. In cooling mode, heat from lights and other equipment raises the ceiling plenum’s temperature considerably. Solar heat gain through a poorly insulated roof can drive the ceiling plenum temperature to extreme levels, so much so that heat gains to uninsulated supply air ducts in the plenum can dramatically decrease available cooling capacity to the rooms below. In cold weather, much heat is lost from warm supply ducts. Thus, insulating supply air ducts and sealing them well to minimize air leaks are highly desirable, if not essential. Appropriately insulating roofs and plenums’ exterior walls and minimizing infiltration are also key to lowering total building loads and improving HVAC system performance.

Floor Plenum Distribution Systems Underfloor air distribution (UFAD) systems are designed to provide comfort conditions in the occupied level and allow stratification to occur above this level of the space. In contrast, room cooling loads determined by methods in this chapter assume uniform temperatures and complete mixing of air within the conditioned space, typically by conventional overhead air distribution systems. Ongoing research projects have identified several factors relating to the load calculation process: • Heat transfer from a conditioned space with a conventional air distribution system is by convection; radiant loads are converted to convection and transferred to the airstream within the conditioned space. • A significant fraction of heat transfer with a UFAD system is by radiation directly to the floor surface and, from there, by convection to the airstream in the supply plenum. • Load at the cooling coil is similar for identical spaces with alternative distribution systems.

Plenums in Load Calculations Currently, most designers include ceiling and floor plenums within neighboring occupied spaces when thermally zoning a building. However, temperatures in these plenums, and the way that they behave, are significantly different from those of occupied spaces. Thus, they should be defined as a separate thermal zone. However, most hand and computer-based load calculation routines currently do not allow floating air temperatures or humidities; assuming a constant air temperature in plenums, attics, and other unconditioned spaces is a poor, but often necessary, assumption. The heat balance method does allow floating space conditions, and when fully implemented in design load software, should allow more accurate modeling of plenums and other complex spaces.

CENTRAL PLANT Piping Losses must be considered for piping systems that transport heat. For water or hydronic piping systems, heat is transferred through the piping and insulation (see Chapter 23 for ways to determine this transfer). However, distribution of this transferred heat depends on the fluid in the pipe and the surrounding environment. Consider a heating hot-water pipe. If the pipe serves a room heater and is routed through the heated space, any heat loss from the pipe adds heat to the room. Heat transfer to the heated space and heat loss from the piping system is null. If the piping is exposed to ambient conditions en route to the heater, the loss must be considered when selecting the heating equipment; if the pipe is routed

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2009 ASHRAE Handbook—Fundamentals

through a space requiring cooling, heat loss from the piping also becomes a load on the cooling system. In summary, the designer must evaluate both the magnitude of the pipe heat transfer and the routing of the piping.

Fig. 16

Single-Room Example Conference Room

Pumps Calculating heat gain from pumps is addressed in the section on Electric Motors. For pumps serving hydronic systems, disposition of heat from the pumps depends on the service. For chilled-water systems, energy applied to the fluid to generate flow and pressure becomes a chiller load. For condenser water pumps, pumping energy must be rejected through the cooling tower. The magnitude of pumping energy relative to cooling load is generally small.

EXAMPLE COOLING AND HEATING LOAD CALCULATIONS To illustrate the cooling and heating load calculation procedures discussed in this chapter, an example problem has been developed based on building located in Atlanta, Georgia. This example is a two-story office building of approximately 30,000 ft2, including a variety of common office functions and occupancies. In addition to demonstrating calculation procedures, a hypothetical design/construction process is discussed to illustrate (1) application of load calculations and (2) the need to develop reasonable assumptions when specific data is not yet available, as often occurs in everyday design processes.

SINGLE-ROOM EXAMPLE Calculate the peak heating and cooling loads for the conference room shown in Figure 16, for Atlanta, Georgia. The room is on the second floor of a two-story building and has two vertical exterior exposures, with a flat roof above.

Room Characteristics Area: 274 ft2 Floor: Carpeted 5 in. concrete slab on metal deck above a conditioned space. Roof: Flat metal deck topped with rigid mineral fiber insulation and perlite board (R = 12.5), felt, and light-colored membrane roofing. Space above 9 ft suspended acoustical tile ceiling is used as a return air plenum. Assume 30% of the cooling load from the roof is directly absorbed in the return airstream without becoming room load. Use roof U = 0.07 Btu/h·ft2 ·°F. Spandrel wall: Spandrel bronze-tinted glass, opaque, backed with air space, rigid mineral fiber insulation (R = 5.0), mineral fiber batt insulation (R = 5.0), and 5/8 in. gypsum wall board. Use spandrel wall U = 0.08 Btu/h·ft2 ·°F. Brick wall: Light-brown-colored face brick (4 in.), mineral fiber batt insulation (R = 10), lightweight concrete block (6 in.) and gypsum wall board (5/8 in.). Use brick wall U = 0.08 Btu/h·ft2 ·°F. Windows: Double glazed, 1/4 in. bronze-tinted outside pane, 1/2 in. air space and 1/4 in. clear inside pane with light-colored interior miniblinds. Window normal solar heat gain coefficient (SHGC) = 0.49. Windows are nonoperable and mounted in aluminum frames with thermal breaks having overall combined U = 0.56 Btu/h·ft2 ·°F (based on Type 5d from Tables 4 and 10 of Chapter 15). Inside attenuation coefficients (IACs) for inside miniblinds are based on light venetian blinds (assumed louver reflectance = 0.8 and louvers positioned at 45° angle) with heat-absorbing double glazing (Type 5d from Table 13B of Chapter 15), IAC(0) = 0.74, IAC(60) = 0.65, IAD(diff) = 0.79, and radiant fraction = 0.54. Each window is 6.25 ft wide by 6.4 ft tall for an area per window = 40 ft2. South exposure:

Orientation Window area

= 30° east of true south = 40 ft2

Fig. 16

Single-Room Example Conference Room

Spandrel wall area = 60 ft2 Brick wall area = 60 ft2 West exposure: Orientation = 60° west of south Window area = 80 ft2 Spandrel wall area = 120 ft2 Brick wall area = 75 ft2 Occupancy: 12 people from 8:00 AM to 5:00 PM. Lighting: Four 3-lamp recessed fluorescent 2 by 4 ft parabolic reflector (without lens) type with side slot return-air-type fixtures. Each fixture has three 32 W T-8 lamps plus electronic ballasts, for a total of 110 W per fixture or 440 W total for the room. Operation is from 7:00 AM to 7:00 PM. Assume 26% of the cooling load from lighting is directly absorbed in the return air stream without becoming room load, per Table 3. Equipment: Several computers and a video projector may used, for which an allowance of 1 W/ft2 is to be accommodated by the cooling system, for a total of 274 W for the room. Operation is from 8:00 AM to 5:00 PM. Infiltration: For purposes of this example, assume the building is maintained under positive pressure during peak cooling conditions and therefore has no infiltration. Assume that infiltration during peak heating conditions is equivalent to one air change per hour. Weather data: Per Chapter 14, for Atlanta, Georgia, latitude = 33.64, longitude = 84.43, elevation = 1027 ft above sea level, 99.6% heating design dry-bulb temperature = 20.7°F. For cooling load calculations, use 5% dry-bulb/coincident wet-bulb monthly design day profile calculated per Chapter 14. See Table 26 for temperature profiles used in these examples. Inside design conditions: 72°F for heating; 75°F with 50% rh for cooling.

Cooling Loads Using RTS Method Traditionally, simplified cooling load calculation methods have estimated the total cooling load at a particular design condition by independently calculating and then summing the load from each component (walls, windows, people, lights, etc). Although the actual heat transfer processes for each component do affect each other, this simplification is appropriate for design load calculations and useful

Nonresidential Cooling and Heating Load Calculations to the designer in understanding the relative contribution of each component to the total cooling load. Cooling loads are calculated with the RTS method on a component basis similar to previous methods. The following example parts illustrate cooling load calculations for individual components of this single room for a particular hour and month. Part 1. Internal cooling load using radiant time series. Calculate the cooling load from lighting at 3:00 PM for the previously described conference room. Solution: First calculate the 24 h heat gain profile for lighting, then split those heat gains into radiant and convective portions, apply the appropriate RTS to the radiant portion, and sum the convective and radiant cooling load components to determine total cooling load at the designated time. Using Equation (1), the lighting heat gain profile, based on the occupancy schedule indicated is q1 = (440 W)3.41(0%) = 0

q13 = (440 W)3.41(100%) = 1500

q2 = (440 W)3.41(0%) = 0

q14 = (440 W)3.41(100%) = 1500

q3 = (440 W)3.41(0%) = 0

q15 = (440 W)3.41(100%) = 1500

q4 = (440 W)3.41(0%) = 0

q16 = (440 W)3.41(100%) = 1500

q5 = (440 W)3.41(0%) = 0

q17 = (440 W)3.41(100%) = 1500

q6 = (440 W)3.41(0%) = 0

q18 = (440 W)3.41(100%) = 1500

q7 = (440 W)3.41(100%) = 1500 q19 = (440 W)3.41(0%) = 0 q8 = (440 W)3.41(100%) = 1500 q20 = (440 W)3.41(0%) = 0 q9 = (440 W)3.41(100%) = 1500 q21 = (440 W)3.41(0%) = 0 q10 = (440 W)3.41(100%) = 1500 q22 = (440 W)3.41(0%) = 0 q11 = (440 W)3.41(100%) = 1500 q23 = (440 W)3.41(0%) = 0 q12 = (440 W)3.41(100%) = 1500 q24 = (440 W)3.41(0%) = 0 The convective portion is simply the lighting heat gain for the hour being calculated times the convective fraction for recessed fluorescent lighting fixtures without lens and with side slot return air, from Table 3: Qc,15 = (1500)(52%) = 780 Btu/h The radiant portion of the cooling load is calculated using lighting heat gains for the current hour and past 23 h, the radiant fraction from Table 3 (48%), and radiant time series from Table 19, in accordance with Equation (34). From Table 19, select the RTS for medium-weight construction, assuming 50% glass and carpeted floors as representative of the described construction. Thus, the radiant cooling load for lighting is Qr,15 = r0(0.48)q15 + r1(0.48)q14 + r2(0.48)q13 + r3(0.48)q12 + … + r23(0.48)q16 = (0.49)(0.48)(1500) + (0.17)(0.48)(1500) + (0.09)(0.48)(1500) + (0.05)(0.48)(1500) + (0.03)(0.48)(1500) + (0.02)(0.48)(1500) + (0.02)(0.48)(1500) + (0.01)(0.48)(1500) + (0.01)(0.48)(1500) + (0.01)(0.48)(0) + (0.01)(0.48)(0) + (0.01)(0.48)(0) + (0.01)(0.48)(0) + (0.01)(0.48)(0) + (0.01)(0.48)(0) + (0.01)(0.48)(0) + (0.01)(0.48)(0) + (0.01)(0.48)(0) + (0.01)(0.48)(0)+ (0.01)(0.48)(0) + (0.00)(0.48)(0) + (0.00)(0.48)(1500) + (0.00)(0.48)(1500) + (0.00)(0.48)(1500) = 641 Btu/h The total lighting cooling load at the designated hour is thus Qlight = Qc,15 + Qr,15 = 780 + 641 = 1421 Btu/h As noted in the example definition, if it is assumed that 26% of the total lighting load is absorbed by the return air stream, the net lighting cooling load to the room is Qlight-room, 15 = Qlight,15 (74%) = 1421(0.74) = 1052 Btu/h

18.37 See Table 27 for the conference room’s lighting usage, heat gain, and cooling load profiles. Part 2. Wall cooling load using sol-air temperature, conduction time series and radiant time series. Calculate the cooling load contribution from the spandrel wall section facing 60° west of south at 3:00 PM local standard time in July for the previously described conference room. Solution: Determine the wall cooling load by calculating (1) sol-air temperatures at the exterior surface, (2) heat input based on sol-air temperature, (3) delayed heat gain through the mass of the wall to the interior surface using conduction time series, and (4) delayed space cooling load from heat gain using radiant time series. First, calculate the sol-air temperature at 3:00 PM local standard time (LST) (4:00 PM daylight saving time) on July 21 for a vertical, dark-colored wall surface, facing 60° west of south, located in Atlanta, Georgia (latitude = 33.64, longitude = 84.43), solar taub = 0.556 and taud = 1.779 from monthly Atlanta weather data for July (Table 1 in Chapter 14). From Table 26, the calculated outdoor design temperature for that month and time is 92°F. The ground reflectivity is assumed Ug = 0.2. Sol-air temperature is calculated using Equation (30). For the darkcolored wall, D/ho = 0.30, and for vertical surfaces, H'R/ho = 0. The solar irradiance Et on the wall must be determined using the equations in Chapter 14: Solar Angles: \ = southwest orientation = +60° 6 = surface tilt from horizontal (where horizontal = 0°) = 90° for vertical wall surface 3:00 PM LST = hour 15 Calculate solar altitude, solar azimuth, surface solar azimuth, and incident angle as follows: From Table 2 in Chapter 14, solar position data and constants for July 21 are ET = –6.4 min G = 20.4° Eo = 419.8 Btu/h·ft2 Local standard meridian (LSM) for Eastern Time Zone = 75°. Apparent solar time AST AST = LST + ET/60 + (LSM – LON)/15 = 15 + (–6.4/60) + [(75 – 84.43)/15] = 14.2647 Hour angle H, degrees H = 15(AST – 12) = 15(14.2647 – 12) = 33.97° Solar altitude E sin E = cos L cos G cos H + sin L sin G = cos (33.64) cos (20.4) cos (33.97) + sin (33.64) sin (20.4) = 0.841 E = sin–1(0.841) = 57.2° Solar azimuth I cos I = (sin E sin L – sin G)/(cos E cos L) = [(sin (57.2)sin (33.64) – sin (20.4)]/[cos (57.2) cos (33.64)] = 0.258 I = cos–1(0.253) = 75.05° Surface-solar azimuth J J = I–\ = 75.05 – 60 = 15.05° Incident angle T cos T = cos E cos g sin 6 + sin E cos 6 = cos (57.2) cos (15.05) sin (90) + sin (57.2) cos (90) = 0.523 T = cos–1(0.523) = 58.5° Beam normal irradiance Eb Eb = Eo exp(–Wbmab) m = relative air mass = 1/[sin E +0.50572(6.07995 + E)–1.6364], E expressed in degrees = 1.18905

18.38

2009 ASHRAE Handbook—Fundamentals Table 26 Monthly/Hourly Design Temperatures (5% Conditions) for Atlanta, GA, °F

Hour

January

February

March

db

db

db

wb

wb

wb

April db

wb

May db

wb

June db

wb

July db

wb

August db

wb

September October db

wb

db

wb

November December db

wb

db

wb

1

44.1 43.0 47.2 45.9 52.8 48.3 59.2 54.2 66.3 61.9 71.3 66.3 73.8 68.9 73.2 68.9 69.4 65.4 60.9 57.6 53.3 51.8 47.1 46.9

2

43.3 42.5 46.4 45.4 51.9 47.9 58.2 53.8 65.5 61.6 70.4 66.0 73.0 68.6 72.5 68.7 68.6 65.1 60.1 57.3 52.5 51.3 46.3 46.3

3

42.6 42.0 45.8 45.0 51.2 47.5 57.6 53.5 64.9 61.4 69.8 65.8 72.3 68.4 71.9 68.5 68.0 64.9 59.5 57.0 51.9 51.0 45.7 45.7

4

42.0 41.6 45.1 44.7 50.5 47.1 56.9 53.2 64.3 61.2 69.2 65.6 71.7 68.2 71.3 68.3 67.5 64.7 58.9 56.8 51.3 50.6 45.1 45.1

5

41.6 41.3 44.7 44.4 50.0 46.9 56.4 53.0 63.9 61.0 68.8 65.5 71.3 68.1 70.9 68.2 67.1 64.6 58.5 56.6 50.9 50.4 44.7 44.7

6

42.0 41.6 45.1 44.7 50.5 47.1 56.9 53.2 64.3 61.2 69.2 65.6 71.7 68.2 71.3 68.3 67.5 64.7 58.9 56.8 51.3 50.6 45.1 45.1

7

43.5 42.6 46.6 45.6 52.1 48.0 58.5 53.9 65.7 61.7 70.6 66.1 73.2 68.7 72.6 68.7 68.8 65.2 60.3 57.4 52.7 51.4 46.5 46.5

8

47.0 45.1 50.2 47.8 56.1 50.0 62.4 55.5 69.2 63.1 74.1 67.2 76.7 69.7 75.9 69.8 72.0 66.3 63.6 58.9 56.2 53.4 49.8 48.8

9

51.0 47.8 54.2 50.2 60.5 52.3 66.8 57.4 73.1 64.6 78.0 68.5 80.6 70.9 79.6 70.9 75.6 67.6 67.4 60.5 60.0 55.6 53.5 51.3

10

54.5 50.3 57.8 52.4 64.4 54.3 70.7 59.1 76.5 65.9 81.5 69.6 84.1 72.0 82.9 72.0 78.8 68.8 70.7 62.0 63.4 57.5 56.9 53.6

11

57.6 52.5 61.0 54.3 67.9 56.1 74.1 60.5 79.6 67.1 84.6 70.6 87.2 73.0 85.8 72.9 81.7 69.8 73.7 63.3 66.5 59.3 59.8 55.6

12

59.7 53.9 63.1 55.6 70.3 57.3 76.4 61.5 81.6 67.9 86.6 71.2 89.3 73.6 87.8 73.5 83.5 70.4 75.6 64.2 68.5 60.4 61.8 57.0

13

61.4 55.1 64.8 56.7 72.1 58.2 78.3 62.3 83.3 68.5 88.3 71.8 91.0 74.1 89.3 74.0 85.1 71.0 77.2 64.9 70.1 61.3 63.3 58.0

14

62.4 55.8 65.9 57.3 73.3 58.8 79.4 62.8 84.3 68.9 89.3 72.1 92.0 74.4 90.3 74.3 86.0 71.3 78.2 65.3 71.1 61.9 64.3 58.7

15

62.4 55.8 65.9 57.3 73.3 58.8 79.4 62.8 84.3 68.9 89.3 72.1 92.0 74.4 90.3 74.3 86.0 71.3 78.2 65.3 71.1 61.9 64.3 58.7

16

61.2 54.9 64.6 56.5 71.9 58.1 78.0 62.2 83.1 68.4 88.1 71.7 90.8 74.0 89.1 73.9 84.9 70.9 77.0 64.8 69.9 61.2 63.1 57.9

17

59.5 53.8 62.9 55.5 70.0 57.1 76.2 61.4 81.4 67.8 86.4 71.2 89.1 73.5 87.6 73.4 83.4 70.4 75.4 64.1 68.3 60.3 61.6 56.8

18

57.4 52.3 60.8 54.2 67.7 55.9 73.9 60.4 79.4 67.0 84.4 70.5 87.0 72.9 85.6 72.8 81.5 69.7 73.5 63.2 66.3 59.1 59.6 55.5

19

54.3 50.1 57.6 52.3 64.2 54.2 70.4 59.0 76.3 65.8 81.3 69.5 83.9 71.9 82.7 71.9 78.6 68.7 70.5 61.9 63.2 57.4 56.7 53.5

20

52.0 48.6 55.3 50.9 61.7 52.9 67.9 57.9 74.1 65.0 79.1 68.8 81.7 71.3 80.6 71.3 76.6 68.0 68.4 61.0 61.0 56.2 54.5 52.0

21

50.1 47.2 53.4 49.7 59.6 51.8 65.8 57.0 72.3 64.2 77.2 68.2 79.8 70.7 78.9 70.7 74.8 67.3 66.6 60.2 59.2 55.1 52.7 50.8

22

48.3 45.9 51.5 48.5 57.5 50.7 63.8 56.1 70.4 63.5 75.4 67.6 77.9 70.1 77.1 70.2 73.1 66.7 64.8 59.4 57.4 54.1 51.0 49.6

23

46.6 44.8 49.8 47.5 55.6 49.8 61.9 55.4 68.8 62.9 73.7 67.1 76.3 69.6 75.6 69.7 71.6 66.2 63.2 58.7 55.7 53.2 49.4 48.5

24

45.3 43.9 48.5 46.7 54.2 49.0 60.5 54.8 67.6 62.4 72.5 66.7 75.0 69.2 74.4 69.3 70.5 65.8 62.0 58.2 54.5 52.5 48.2 47.7

Table 27 Cooling Load Component: Lighting, Btu/h Heat Gain, Btu/h Hour

Usage Profile, %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0 0 0 0 0 0 100 100 100 100 100 100 100 100 100 100 100 100 0 0 0 0 0 0

Total

48%

Nonsolar RTS Zone Type 8, %

Radiant Cooling Load

Total Sensible Cooling Load

% Lighting to Return 26%

Room Sensible Cooling Load

— — — — — — 780 780 780 780 780 780 780 780 780 780 780 780 — — — — — —

— — — — — — 720 720 720 720 720 720 720 720 720 720 720 720 — — — — — —

49 17 9 5 3 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0

86 86 79 72 65 58 403 519 576 605 619 627 634 634 641 648 655 663 317 202 144 115 101 94

86 86 79 72 65 58 1,184 1,299 1,356 1,385 1,400 1,407 1,414 1,414 1,421 1,428 1,436 1,443 317 202 144 115 101 94

22 22 21 19 17 15 308 338 353 360 364 366 368 368 370 371 373 375 82 52 37 30 26 24

64 64 59 53 48 43 876 961 1,004 1,025 1,036 1,041 1,046 1,046 1,052 1,057 1,062 1,068 234 149 107 85 75 69

9,362

8,642

1

8,642

18,005

4,681

13,324

Convective

Radiant

Total

52%

— — — — — — 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 — — — — — — 18,005

Nonresidential Cooling and Heating Load Calculations ab = = = Eb = =

beam air mass exponent 1.219 – 0.043Wb – 0.151Wd – 0.204WbWd 0.72468 419.8 exp[–0.556(1.89050.72468)] 223.5 Btu/h·ft2

Surface beam irradiance Et,b Et,b = Eb cos T = (223.5) cos (58.5) = 117 Btu/h·ft2 Ratio Y of sky diffuse radiation on vertical surface to sky diffuse radiation on horizontal surface Y = 0.55 + 0.437 cos T + 0.313 cos 2 T = 0.55 + 0.437 cos (58.5) + 0.313 cos2 (58.5) = 0.864 Diffuse irradiance Ed – Horizontal surfaces Ed = Eo exp(–Wd mad) ad = diffuse air mass exponent = 0.202 + 0.852Wb – 0.007Wd – 0.357WbWd = 0.3101417 Ed = Eo exp(–Wd mad) = 419.8 exp(–1.779(1.89050.3101)] = 64.24 Btu/h·ft2 Diffuse irradiance Ed – Vertical surfaces Et,d = EdY = (64.24)(0.864) = 55.5 Btu/h·ft2 Ground reflected irradiance Et,r Et,r = (Eb sin E + Ed)U g (l – cos 6 = [ sin (57.2) + 64.24](0.2)[1 – cos (90)]/2 = 25.2 Btu/h·ft2 Total surface irradiance Et Et = ED + Ed + Er = 117 + 55.5 + 25.2 = 197.7 Btu/h·ft2 Sol–air temperature [from Equation (30)]: Te = to + DEt /ho – H'R/ho = 92 + (0.30)(197.7) – 0 = 151°F This procedure is used to calculate the sol-air temperatures for each hour on each surface. Because of the tedious solar angle and intensity calculations, using a simple computer spreadsheet or other computer software can reduce the effort involved. A spreadsheet was used to calculate a 24 h sol-air temperature profile for the data of this example. See Table 28A for the solar angle and intensity calculations and Table 28B for the sol-air temperatures for this wall surface and orientation. Conductive heat gain is calculated using Equations (31) and (32). First, calculate the 24 h heat input profile using Equation (31) and the sol-air temperatures for a southwest-facing wall with dark exterior color: qi,1 qi,2 qi,3 qi,4 qi,5 qi,6 qi,7 qi,8 qi,9 qi,10 qi,11 qi,12 qi,13 qi,14 qi,15 qi,16 qi,17 qi,18 qi,19 qi,20 qi,21 qi,22

= = = = = = = = = = = = = = = = = = = = = =

(0.08)(120)(73.8 – 75) (0.08)(120)(73 – 75) (0.08)(120)(72.3 – 75) (0.08)(120)(71.7 – 75) (0.08)(120)(71.3 – 75) (0.08)(120)(72.7 – 75) (0.08)(120)(78.4 – 75) (0.08)(120)(85.9 – 75) (0.08)(120)(93.1 – 75) (0.08)(120)(99.3 – 75) (0.08)(120)(104.5 – 75) (0.08)(120)(109.2 – 75) (0.08)(120)(125.4 – 75) (0.08)(120)(141.4 – 75) (0.08)(120)(151.3 – 75) (0.08)(120)(152.7 – 75) (0.08)(120)(144.8 – 75) (0.08)(120)(126.6 – 75) (0.08)(120)(98 – 75) (0.08)(120)(81.7 – 75) (0.08)(120)(79.8 – 75) (0.08)(120)(77.9 – 75)

= = = = = = = = = = = = = = = = = = = = = =

–12 Btu/h –19 –26 –32 –36 –22 33 104 174 234 283 328 484 638 733 746 670 495 221 064 046 028

18.39 qi,23 = (0.08)(120)(76.3 – 75) qi,24 = (0.08)(120)(75 – 75)

= 12 = 00

Next, calculate wall heat gain using conduction time series. The preceding heat input profile is used with conduction time series to calculate the wall heat gain. From Table 16, the most similar wall construction is wall number 1. This is a spandrel glass wall that has similar mass and thermal capacity. Using Equation (32), the conduction time factors for wall 1 can be used in conjunction with the 24 h heat input profile to determine the wall heat gain at 3:00 PM LST: q15 = c0qi,15 + c1qi,14 + c2qi,13 + c3qi,12 + … + c23qi,14 = (0.18)(733) + (0.58)(638) + (0.20)(484) + (0.04)(328) + (0.00)(283) + (0.00)(234) + (0.00)(174) + (0.00)(104) + (0.00)(33) + (0.00)(–22) + (0.00)(–36) + (0.00)(–32) + (0.00)(–26) + (0.00)(–19) + (0.00)(–12) + (0.00)(0) + (0.00)(12) + (0.00)(28) + (0.00)(46) + (0.00)(64) + (0.00)(221) + (0.00)(495) + (0.00)(670) + (0.00)(746) = 612 Btu/h Because of the tedious calculations involved, a spreadsheet is used to calculate the remainder of a 24 h heat gain profile indicated in Table 28B for the data of this example. Finally, calculate wall cooling load using radiant time series. Total cooling load for the wall is calculated by summing the convective and radiant portions. The convective portion is simply the wall heat gain for the hour being calculated times the convective fraction for walls from Table 14 (54%): Qc = (612)(0.54) = 330 Btu/h The radiant portion of the cooling load is calculated using conductive heat gains for the current and past 23 h, the radiant fraction for walls from Table 14 (46%), and radiant time series from Table 19, in accordance with Equation (34). From Table 19, select the RTS for medium-weight construction, assuming 50% glass and carpeted floors as representative for the described construction. Use the wall heat gains from Table 28B for 24 h design conditions in July. Thus, the radiant cooling load for the wall at 3:00 PM is Qr,15 = r0(0.46)qi,15 + r1(0.46) qi,14 + r2(0.46) qi,13 + r3(0.46) qi,12 + … + r23(0.46) qi,16 = (0.49)(0.46)(612) + (0.17)(0.46)(472) + (0.09)(0.46)(344) + (0.05)(0.46)(277) + (0.03)(0.46)(225) + (0.02)(0.46)(165) + (0.02)(0.46)(97) + (0.01)(0.46)(32) + (0.01)(0.46)(–15) + (0.01)(0.46)(–32) + (0.01)(0.46)(–31) + (0.01)(0.46)(–25) + (0.01)(0.46)(–18) + (0.01)(0.46)(–10) + (0.01)(0.46)(2) + (0.01)(0.46)(15) + (0.01)(0.46)(30) + (0.01)(0.46)(53) + (0.01)(0.46)(110) + (0.01)(0.46)(266) + (0.00)(0.46)(491) + (0.00)(0.46)(656) + (0.00)(0.46)(725) + (0.00)(0.46)(706) = 203 Btu/h The total wall cooling load at the designated hour is thus Qwall = Qc + Qr15 = 330 + 203 = 533 Btu/h Again, a simple computer spreadsheet or other software is necessary to reduce the effort involved. A spreadsheet was used with the heat gain profile to split the heat gain into convective and radiant portions, apply RTS to the radiant portion, and total the convective and radiant loads to determine a 24 h cooling load profile for this example, with results in Table 28B. Part 3. Window cooling load using radiant time series. Calculate the cooling load contribution, with and without inside shading (venetian blinds) for the window area facing 60° west of south at 3:00 PM in July for the conference room example. Solution: First, calculate the 24 h heat gain profile for the window, then split those heat gains into radiant and convective portions, apply the appropriate RTS to the radiant portion, then sum the convective and radiant cooling load components to determine total window cooling load for the time. The window heat gain components are calculated using Equations (13) to (15). From Part 2, at hour 15 LST (3:00 PM): Et,b Et,d Er T

= = = =

117 Btu/h·ft2 55.5 Btu/h·ft2 25.2 Btu/h·ft2 58.5°

18.40

2009 ASHRAE Handbook—Fundamentals Table 28A Wall Component of Solar Irradiance Direct Beam Solar

Diffuse Solar Heat Gain

Local Apparent Hour Solar Solar Eb , Direct Surface Surface Ed, Diffuse Ground Standard Solar Angle Altitude Azimuth Normal Incident Direct Horizontal, Diffuse Hour Time H E M Btu/h·ft2 Angle T Btu/h·ft2 Btu/h·ft2 Btu/h·ft2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0.26 1.26 2.26 3.26 4.26 5.26 6.26 7.26 8.26 9.26 10.26 11.26 12.26 13.26 14.26 15.26 16.26 17.26 18.26 19.26 20.26 21.26 22.26 23.26

–176 –161 –146 –131 –116 –101 –86 –71 –56 –41 –26 –11 4 19 34 49 64 79 94 109 124 139 154 169

–36 –33 –27 –19 –9 3 14 27 39 51 63 74 76 69 57 45 32 20 8 –3 –14 –23 –30 –35

–175 –159 –144 –132 –122 –113 –105 –98 –90 –81 –67 –39 16 57 75 86 94 102 109 117 127 138 151 167

0.0 0.0 0.0 0.0 0.0 5.6 92.4 155.4 193.1 216.1 229.8 236.7 238.0 233.8 223.5 205.3 175.5 126.2 44.7 0.0 0.0 0.0 0.0 0.0

117.4 130.9 144.5 158.1 171.3 172.5 159.5 145.9 132.3 118.8 105.6 92.6 80.2 68.7 58.4 50.4 45.8 45.5 49.7 57.5 67.5 79.0 91.3 104.2

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 40.4 85.1 117.0 130.8 122.4 88.4 28.9 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 5.8 27.4 42.9 53.9 61.6 66.6 69.3 69.8 68.1 64.2 57.9 48.5 35.4 16.6 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.6 5.0 11.2 17.5 23.1 27.2 29.6 30.1 28.6 25.2 20.3 14.3 7.9 2.3 0.0 0.0 0.0 0.0 0.0

Y Ratio 0.4500 0.4500 0.4500 0.4500 0.4500 0.4500 0.4500 0.4500 0.4500 0.4500 0.4553 0.5306 0.6332 0.7505 0.8644 0.9555 1.0073 1.0100 0.9631 0.8755 0.7630 0.6452 0.5403 0.4618

Total Sky Subtotal Surface Diffuse Diffuse Irradiance Btu/h·ft2 Btu/h·ft2 Btu/h·ft2 0.0 0.0 0.0 0.0 0.0 2.6 12.3 19.3 24.3 27.7 30.3 36.8 44.2 51.1 55.5 55.3 48.9 35.7 16.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 3.2 17.3 30.5 41.8 50.8 57.5 66.4 74.3 79.7 80.7 75.6 63.2 43.6 18.3 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 3.2 17.3 30.5 41.8 50.8 57.5 66.4 114.7 164.8 197.7 206.4 185.6 132.0 47.1 0.0 0.0 0.0 0.0 0.0

Table 28B Wall Component of Sol-Air Temperatures, Heat Input, Heat Gain, Cooling Load Total Local Surface Outside Standard Irradiance Temp., Hour Btu/h·ft2 °F 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0.0 0.0 0.0 0.0 0.0 3.2 17.3 30.5 41.8 50.8 57.5 66.4 114.7 164.8 197.7 206.4 185.6 132.0 47.1 0.0 0.0 0.0 0.0 0.0

73.8 73.0 72.3 71.7 71.3 71.7 73.2 76.7 80.6 84.1 87.2 89.3 91.0 92.0 92.0 90.8 89.1 87.0 83.9 81.7 79.8 77.9 76.3 75.0

Heat Gain, Btu/h Sol-Air Inside Temp., Temp., °F °F 74 73 72 72 71 73 78 86 93 99 104 109 125 141 151 153 145 127 98 82 80 78 76 75

75 75 75 75 75 75 75 75 75 75 75 75 75 75 75 75 75 75 75 75 75 75 75 75

Heat Input, Btu/h –12 –19 –26 –32 –36 –22 33 104 174 234 283 328 484 638 733 746 670 495 221 64 46 28 12 0

CTS Type 1, % 18 58 20 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Convective

Radiant

Total

54%

46%

2 –10 –18 –25 –31 –32 –15 32 97 165 225 277 344 472 612 706 725 656 491 266 110 53 30 15

1 –5 –10 –14 –17 –17 –8 17 53 89 122 149 185 255 330 381 392 354 265 143 59 29 16 8

1 –4 –8 –12 –14 –15 –7 15 45 76 104 127 158 217 281 325 334 302 226 122 50 25 14 7

Nonsolar RTS Zone Type 8, %

Radiant Cooling Load, Btu/h

Total Cooling Load, Btu/h

49 17 9 5 3 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0

32 25 21 17 14 12 14 24 41 62 81 100 121 157 203 243 265 262 227 167 110 75 54 41

33 20 11 4 –3 –5 5 41 94 151 203 249 306 412 533 624 657 617 492 310 169 104 70 49

Nonresidential Cooling and Heating Load Calculations

18.41

Table 29 Window Component of Heat Gain (No Blinds or Overhang) Beam Solar Heat Gain

Diffuse Solar Heat Gain

Beam Adjus- Solar Beam Surface Surface Local Normal, Inci- Beam, ted Heat Beam Beam Gain, Std. dent Btu/ Btu/ Hour h·ft2 Angle h·ft2 SHGC IAC Btu/h 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0.0 0.0 0.0 0.0 0.0 5.6 92.4 155.4 193.1 216.1 229.8 236.7 238.0 233.8 223.5 205.3 175.5 126.2 44.7 0.0 0.0 0.0 0.0 0.0

117.4 130.9 144.5 158.1 171.3 172.5 159.5 145.9 132.3 118.8 105.6 92.6 80.2 68.7 58.4 50.4 45.8 45.5 49.7 57.5 67.5 79.0 91.3 104.2

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 40.4 85.1 117.0 130.8 122.4 88.4 28.9 0.0 0.0 0.0 0.0 0.0

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.166 0.321 0.398 0.438 0.448 0.449 0.441 0.403 0.330 0.185 0.000 0.000

1.000 1.000 1.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.000 0.000 0.000 1.000 1.000

Diffuse Ground Horiz. Diffuse, Y Ed, Btu/ Btu/ h·ft2 h·ft2 Ratio

0 0 0 0 0 0 0 0 0 0 0 0 537 2183 3722 4583 4392 3177 1017 0 0 0 0 0

0.0 0.0 0.0 0.0 0.0 5.8 27.4 42.9 53.9 61.6 66.6 69.3 69.8 68.1 64.2 57.9 48.5 35.4 16.6 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.6 5.0 11.2 17.5 23.1 27.2 29.6 30.1 28.6 25.2 20.3 14.3 7.9 2.3 0.0 0.0 0.0 0.0 0.0

From Chapter 15, Table 10, for glass type 5d, SHGC(T) = SHGC(58.5) = 0.3978 (interpolated) ¢SHGC²D = 0.41 From Chapter 15, Table 13B, for light-colored blinds (assumed louver reflectance = 0.8 and louvers positioned at 45° angle) on doubleglazed, heat-absorbing windows (Type 5d from Table 13B of Chapter 15), IAC(0) = 0.74, IAC(60) = 0.65, IAC(diff) = 0.79, and radiant fraction = 0.54. Without blinds, IAC = 1.0. Therefore, window heat gain components for hour 15, without blinds, are qb15 = AEt,b SHGC(T)(IAC) = (80)(117)(0.3978)(1.00) = 3722 Btu/h qd15 = A(Et,d + Er)¢SHGC²D(IAC) = (80)(55.5 + 25.2)(0.41)(1.00) = 2648 Btu/h qc15 = UA(tout – tin) = (0.56)(80)(92 – 75) = 762 Btu/h This procedure is repeated to determine these values for a 24 h heat gain profile, shown in Table 29. Total cooling load for the window is calculated by summing the convective and radiant portions. For windows with inside shading (blinds, drapes, etc.), the direct beam, diffuse, and conductive heat gains may be summed and treated together in calculating cooling loads. However, in this example, the window does not have inside shading, and the direct beam solar heat gain should be treated separately from the diffuse and conductive heat gains. The direct beam heat gain, without inside shading, is treated as 100% radiant, and solar RTS factors from Table 20 are used to convert the beam heat gains to cooling loads. The diffuse and conductive heat gains can be totaled and split into radiant and convective portions according to Table 14, and nonsolar RTS factors from Table 19 are used to convert the radiant portion to cooling load. The solar beam cooling load is calculated using heat gains for the current hour and past 23 h and radiant time series from Table 20, in accordance with Equation (39). From Table 20, select the solar RTS for medium-weight construction, assuming 50% glass and carpeted floors

0.4500 0.4500 0.4500 0.4500 0.4500 0.4500 0.4500 0.4500 0.4500 0.4500 0.4553 0.5306 0.6332 0.7505 0.8644 0.9555 1.0073 1.0100 0.9631 0.8755 0.7630 0.6452 0.5403 0.4618

Conduction

Diff. Total ConSubtotal Sky Solar Out- duction Window Diffuse, Diffuse, Heat side Heat Heat Hemis. Gain, Temp., Gain, Btu/ Btu/ Gain, SHGC Btu/h h·ft2 h·ft2 °F Btu/h Btu/h 0.0 0.0 0.0 0.0 0.0 2.6 12.3 19.3 24.3 27.7 30.3 36.8 44.2 51.1 55.5 55.3 48.9 35.7 16.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 3.2 17.3 30.5 41.8 50.8 57.5 66.4 74.3 79.7 80.7 75.6 63.2 43.6 18.3 0.0 0.0 0.0 0.0 0.0

0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410

0 0 0 0 0 31 167 294 402 488 553 638 714 766 776 727 607 419 176 0 0 0 0 0

73.8 73.0 72.3 71.7 71.3 71.7 73.2 76.7 80.6 84.1 87.2 89.3 91.0 92.0 92.0 90.8 89.1 87.0 83.9 81.7 79.8 77.9 76.3 75.0

–54 –90 –121 –148 –166 –148 –81 76 251 408 547 641 717 762 762 708 632 538 399 300 215 130 58 0

–54 –90 –121 –148 –166 –42 488 1078 1622 2073 2434 2818 3690 5559 7132 7770 7096 5143 2015 300 215 130 58 0

for this example. Using Table 29 values for direct solar heat gain, the radiant cooling load for the window direct beam solar component is Qb,15 = r0qb,15 + r1qb,14 + r2qb,13 + r3qb,12 + … + r23qb,14 = (0.54)(3722) + (0.16)(2183) + (0.08)(537) + (0.04)(0) + (0.03)(0) + (0.02)(0) + (0.01)(0) + (0.01)(0) + (0.01)(0) + (0.01)(0) + (0.01)(0) + (0.01)(0) + (0.01)(0) + (0.01)(0) + (0.01)(0) + (0.01)(0) + (0.01)(0) + (0.01)(0) + (0.01)(0) + (0.00)(0) + (0.00)(1017) + (0.00)(3177) + (0.00)(4392) + (0.00)(4583) = 2402 Btu/h This process is repeated for other hours; results are listed in Table 30. For diffuse and conductive heat gains, the radiant fraction according to Table 14 is 46%. The radiant portion is processed using nonsolar RTS coefficients from Table 19. The results are listed in Tables 29 and 30. For 3:00 PM, the diffuse and conductive cooling load is 3144 Btu/h. The total window cooling load at the designated hour is thus Qwindow = Qb + Qdiff + cond = 2402 + 3144 = 5546 Btu/h Again, a computer spreadsheet or other software is commonly used to reduce the effort involved in calculations. The spreadsheet illustrated in Table 29 is expanded in Table 30 to include splitting the heat gain into convective and radiant portions, applying RTS to the radiant portion, and totaling the convective and radiant loads to determine a 24 h cooling load profile for a window without inside shading. If the window has an inside shading device, it is accounted for with the inside attenuation coefficients (IAC), the radiant fraction, and the RTS type used. If a window has no inside shading, 100% of the direct beam energy is assumed to be radiant and solar RTS factors are used. However, if an inside shading device is present, the direct beam is assumed to be interrupted by the shading device, and a portion immediately becomes cooling load by convection. Also, the energy is assumed to be radiated to all surfaces of the room, therefore nonsolar RTS values are used to convert the radiant load into cooling load. IAC values depend on several factors: (1) type of shading device, (2) position of shading device relative to window, (3) reflectivity of shading device, (4) angular adjustment of shading device, as well as (5) solar position relative to the shading device. These factors are discussed

18.42

2009 ASHRAE Handbook—Fundamentals Table 30 Window Component of Cooling Load (No Blinds or Overhang) Unshaded Direct Beam Solar (if AC = 1)

Local Beam Stan- Heat dard Gain, Hour Btu/h 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0 0 0 0 0 0 0 0 0 0 0 0 537 2183 3722 4583 4392 3177 1017 0 0 0 0 0

Solar ConRTS, vective Radiant Zone Cooling 0%, 100%, Type 8, Radiant Load, Btu/h Btu/h % Btu/h Btu/h 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 537 2183 3722 4583 4392 3177 1017 0 0 0 0 0

54 16 8 4 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0

196 196 196 196 196 196 196 191 169 132 86 42 300 1265 2402 3266 3506 3010 1753 832 496 334 248 206

196 196 196 196 196 196 196 191 169 132 86 42 300 1265 2402 3266 3506 3010 1753 832 496 334 248 206

Shaded Direct Beam (AC < 1.0) + Diffuse + Conduction ConBeam Diffuse duction Heat Heat Heat Gain, Gain, Gain, Btu/h Btu/h Btu/h 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

in detail in Chapter 15. For this example with venetian blinds, the IAC for beam radiation is treated separately from the diffuse solar gain. The direct beam IAC must be adjusted based on the profile angle of the sun. At 3:00 PM in July, the profile angle of the sun relative to the window surface is 58°. Calculated using Equation (45) from Chapter 15, the beam IAC = 0.653. The diffuse IAC is 0.79. Thus, the window heat gains, with light-colored blinds, at 3:00 PM are qb15 = AED SHGC(T)(IAC) = (80)(117)(0.3978)(0.653) = 2430 Btu/h qd15 = A(Ed + Er)¢SHGC²D(IAC)D= (80)(55.5 + 25.2)(0.41)(0.79) = 2092 Btu/h qc15 = UA(tout – tin) = (0.56)(80)(92 – 75) = 762 Btu/h Because the same radiant fraction and nonsolar RTS are applied to all parts of the window heat gain when inside shading is present, those loads can be totaled and the cooling load calculated after splitting the radiant portion for processing with nonsolar RTS. This is illustrated by the spreadsheet results in Table 31. The total window cooling load with venetian blinds at 3:00 PM = 4500 Btu/h . Part 4. Window cooling load using radiant time series for window with overhang shading. Calculate the cooling load contribution for the previous example with the addition of a 10 ft overhang shading the window. Solution: In Chapter 15, methods are described and examples provided for calculating the area of a window shaded by attached vertical or horizontal projections. For 3:00 PM LST IN July, the solar position calculated in previous examples is Solar altitude E = 57.2° Solar azimuth I 75.1° Surface-solar azimuth J = 15.1° From Chapter 15, Equation (106), profile angle : is calculated by tan : = tan E/cos J = tan(57.2)/cos(15.1) = 1.6087

0 0 0 0 0 106 569 1002 1371 1665 1887 2177 2436 2614 2648 2479 2072 1429 599 0 0 0 0 0

–54 –90 –121 –148 –166 –148 –81 76 251 408 547 641 717 762 762 708 632 538 399 300 215 130 58 0

Total Heat Gain, Btu/h –54 –90 –121 –148 –166 –42 488 1078 1622 2073 2434 2818 3153 3376 3410 3187 2703 1967 998 300 215 130 58 0

Window NonCoolCon- Radi- solar vective ant RTS, Radi- Cooling ing 54%, 46%, Zone ant Load, Load, Btu/h Btu/h Type 8 Btu/h Btu/h Btu/h –29 –48 –65 –80 –90 –23 263 582 876 1119 1314 1522 1703 1823 1841 1721 1460 1062 539 162 116 70 31 0

–25 –41 –56 –68 –76 –19 224 496 746 953 1119 1296 1450 1553 1569 1466 1243 905 459 138 99 60 27 0

49 17 9 5 3 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0

138 118 101 84 67 81 196 361 539 705 849 994 1130 1241 1303 1291 1191 999 717 456 332 255 203 167

109 70 36 4 –23 58 460 943 1415 1824 2164 2516 2833 3064 3144 3012 2651 2061 1256 618 448 325 234 167

305 266 232 200 174 254 656 1134 1583 1956 2249 2558 3133 4329 5547 6278 6157 5071 3008 1449 945 659 483 373

: = 58.1° From Chapter 15, Equation (40), shadow height SH is SH = PH tan : = 10(1.6087) = 16.1 ft Because the window is 6.4 ft tall, at 3:00 PM the window is completely shaded by the 10 ft deep overhang. Thus, the shaded window heat gain includes only diffuse solar and conduction gains. This is converted to cooling load by separating the radiant portion, applying RTS, and adding the resulting radiant cooling load to the convective portion to determine total cooling load. Those results are in Table 32. The total window cooling load = 2631 Btu/h. Part 5. Room cooling load total. Calculate the sensible cooling loads for the previously described conference room at 3:00 PM in July. Solution: The steps in the previous example parts are repeated for each of the internal and external loads components, including the southeast facing window, spandrel and brick walls, the southwest facing brick wall, the roof, people, and equipment loads. The results are tabulated in Table 33. The total room sensible cooling load for the conference room is 10,022 Btu/h at 3:00 PM in July. When this calculation process is repeated for a 24 h design day for each month, it is found that the peak room sensible cooling load actually occurs in August at hour 15 (3:00 PM solar time) at 10,126 Btu/h as indicated in Table 34.

Although simple in concept, these steps involved in calculating cooling loads are tedious and repetitive, even using the “simplified” RTS method; practically, they should be performed using a computer spreadsheet or other program. The calculations should be repeated for multiple design conditions (i.e., times of day, other months) to determine the maximum cooling load for mechanical equipment sizing. Example spreadsheets for computing each cooling load component using conduction and radiant time series have been compiled and are available from ASHRAE. To illustrate the full building example discussed previously, those individual component spreadsheets have been compiled to allow calculation of

Nonresidential Cooling and Heating Load Calculations Table 31

Window Component of Cooling Load (With Blinds, No Overhang)

Unshaded Direct Beam Solar (if AC = 1) Beam Local Heat Standard Gain, Hour Btu/h 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Shaded Direct Beam (AC < 1.0) + Diffuse + Conduction

Solar ConRTS, vective Radiant Zone Cooling 0%, 100%, Type 8, Radiant Load, Btu/h Btu/h % Btu/h Btu/h 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Table 32

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

52 40 29 19 9 –3 –15 –28 –43 –58 –73 –87 80 69 58 48 38 26 12 –6 –32 –64 87 67

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 0 0 0 0 84 449 791 1083 1315 1491 1720 1925 2065 2092 1958 1637 1129 473 0 0 0 0 0

–54 –90 –121 –148 –166 –148 –81 76 251 408 547 641 717 762 762 708 632 538 399 300 215 130 58 0

–54 –90 –121 –148 –166 –64 368 868 1334 1723 2037 2361 2990 4246 5284 5728 5271 3893 1606 300 215 130 58 0

–25 –41 –56 –68 –76 –29 169 399 614 793 937 1086 1376 1953 2431 2635 2425 1791 739 138 99 60 27 0

–29 –48 –65 –80 –90 –35 199 469 720 930 1100 1275 1615 2293 2853 3093 2847 2102 867 162 116 70 31 0

NonWindow solar RTS, Cooling Cooling Zone Radiant Load, Load, Type 8 Btu/h Btu/h Btu/h 49% 17% 9% 5% 3% 2% 2% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 0% 0% 0% 0%

211 184 165 146 127 140 249 411 587 746 880 1008 1219 1630 2070 2379 2409 2093 1400 814 555 406 314 254

186 143 109 78 51 110 419 810 1200 1539 1817 2094 2594 3583 4500 5014 4834 3883 2139 952 654 466 341 254

186 143 109 78 51 110 419 810 1200 1539 1817 2094 2594 3583 4500 5014 4834 3883 2139 952 654 466 341 254

Window Component of Cooling Load (With Blinds and Overhang) Shaded Direct Beam (AC < 1.0) + Diffuse + Conduction

Direct Local Surface Shadow Shadow Sunlit Standard Solar Profile Width, Height, Area, Hour Azimuth Angle ft ft ft2 –235 –219 –204 –192 –182 –173 –165 –158 –150 –141 –127 –99 –44 –3 15 26 34 42 49 57 67 78 91 107

ConBeam Diffuse duction Total ConHeat Heat Heat Heat vective Radiant Gain, Gain, Gain, Gain, 54%, 46%, Btu/h Btu/h Btu/h Btu/h Btu/h Btu/h 0 0 0 0 0 0 0 0 0 0 0 0 349 1419 2430 3062 3003 2227 734 0 0 0 0 0

Overhang and Fins Shading

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

18.43

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.4 6.4 6.4 6.4 6.4 4.9 2.2 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 18.9 53.0 0.0 0.0 0.0 0.0 0.0

ConBeam Diffuse duction Heat Heat Heat Gain, Gain, Gain, Btu/h Btu/h Btu/h 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 525 486 0 0 0 0 0

0 0 0 0 0 84 449 791 1083 1315 1491 1720 1925 2065 2092 1958 1637 1129 473 0 0 0 0 0

–54 –90 –121 –148 –166 –148 –81 76 251 408 547 641 717 762 762 708 632 538 399 300 215 130 58 0

Total Heat Gain, Btu/h –54 –90 –121 –148 –166 –64 368 868 1334 1723 2037 2361 2641 2827 2854 2666 2268 2192 1359 300 215 130 58 0

NonWindow Consolar vective Radiant RTS, Cooling Cooling 54%, 46%, Zone Radiant Load, Load, Btu/h Btu/h Btu/h Type 8 Btu/h Btu/h –29 –48 –65 –80 –90 –35 199 469 720 930 1100 1275 1426 1527 1541 1440 1225 1184 734 162 116 70 31 0

–25 –41 –56 –68 –76 –29 169 399 614 793 937 1086 1215 1300 1313 1226 1043 1008 625 138 99 60 27 0

49% 17% 9% 5% 3% 2% 2% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 0% 0% 0% 0%

122 101 84 68 52 63 156 294 445 587 712 836 950 1041 1090 1080 997 959 760 455 323 241 188 152

93 52 19 –12 –37 28 355 763 1166 1518 1813 2110 2377 2567 2631 2520 2222 2142 1493 617 439 312 219 152

93 52 19 –12 –37 28 355 763 1166 1518 1813 2110 2377 2567 2631 2520 2222 2142 1493 617 439 312 219 152

18.44

2009 ASHRAE Handbook—Fundamentals Table 33

Single-Room Example Cooling Load (July 3:00 PM) for ASHRAE Example Office Building, Atlanta, GA Room Sensible Return Air Cooling, Sensible Btu/h Cooling, Btu/h

Per Unit Cooling

Room Latent Cooling, Btu/h

Room Sensible Heating, Btu/h

Internal Loads:

274 W

Btu/h·person 234 Btu/h·ft2 3.8 1.3 3.3

Roof area, ft2 274

Btu/h·ft2 2.3

Wall area, ft2

Btu/h·ft2

0 60 0 75

0.0 1.8 0.0 1.2

— 108 — 93

— — — —

— — — —

— 246 — 308

0 60 0 120

0.0 3.2 0.0 4.4

— 193 — 533

— — — —

— — — —

— 246 — 492

Windows: Window Type 1 North South East West Window Type 2 North South East West

Window area, ft2

Btu/h·ft2

Infiltration Loads: Cooling, sensible: Cooling, latent: Heating:

People: Lighting: Lighting 26% to RA: Equipment: Envelope Loads: Roof: Area, ft2: Roof 30% to RA: Walls: Wall Type 1: Brick North South East West Wall Type 2: Spandrel North South East West

No. 12 440 W

2802

2400

1052 — 904

— 370 —

— — —

— — —

627 —

— 269

— —

984 —

0 0 0 0

0.0 0.0 0.0 0.0

— — — —

— — — —

— — — —

— — — —

0 40 0 80

0.0 27.0 0.0 32.9

— 1079 — 2631

— — — —

— — — —

— 1149 — 2314

Airflow, cfm 0 0 41

Btu/h·cfm 0.0 0.0 56.4

— — —

— — —

— — —

— — 2314

10,022 506 1.8

638

2400 Heating cfm:

8038 261

Room Load Totals: Cooling cfm: cfm/ft2:

cooling and heating loads on a room by room basis as well as for a “block” calculation for analysis of overall areas or buildings where detailed room-by-room data is not available.

SINGLE-ROOM EXAMPLE PEAK HEATING LOAD Although the physics of heat transfer that creates a heating load is identical to that for cooling loads, a number of traditionally used simplifying assumptions facilitate a much simpler calculation procedure. As described in the Heating Load Calculations section, design heating load calculations typically assume a single outside temperature, with no heat gain from solar or internal sources, under steady-state conditions. Thus, space heating load is determined by computing the heat transfer rate through building envelope elements (UA'T) plus heat required because of outside air infiltration. Part 6. Room heating load. Calculate the room heating load for the previous described conference room, including infiltration airflow at one air change per hour.

Solution: Because solar heat gain is not considered in calculating design heating loads, orientation of similar envelope elements may be ignored and total areas of each wall or window type combined. Thus, the total spandrel wall area = 60 + 120 = 180 ft2, total brick wall area = 60 + 75 = 135 ft2, and total window area = 40 + 80 = 120 ft2. For this example, use the U-factors that were used for cooling load conditions. In some climates, higher prevalent winds in winter should be considered in calculating U-factors (see Chapter 25 for information on calculating U-factors and surface heat transfer coefficients appropriate for local wind conditions). The 99.6% heating design dry-bulb temperature for Atlanta is 20.7°F and the inside design temperature is 72°F. The room volume with a 9 ft ceiling = 9u274 = 2466 ft3. At one air change per hour, the infiltration airflow = 1 u 2466/60 = 41 cfm. Thus, the heating load is Windows: Spandrel Wall: Brick Wall: Roof: Infiltration: Total Room Heating Load:

0.56u120u(72 – 20.7) 0.09u180u(72 – 20.7) 0.08u135u(72 – 20.7) 0.07u274u(72 – 20.7) 41u1.1u(72 – 20.7)

= = = = =

3447 Btu/h 831 554 984 2314 8130 Btu/h

Nonresidential Cooling and Heating Load Calculations

18.45

Table 34 Single-Room Example Peak Cooling Load (September 5:00 PM) for ASHRAE Example Office Building, Atlanta, GA Per Unit Cooling

Room Sensible Return Air Cooling, Sensible Btu/h Cooling, Btu/h

Room Latent Cooling, Btu/h

Room Sensible Heating, Btu/h

Internal Loads: No. 12

274 W

Btu/h·person 234 Btu/h·ft2 3.8 1.3 3.3

Roof area, ft2 274

Btu/h·ft2 2.1

Wall area, ft2

Btu/h·ft2

0 60 0 75

0.0 1.9 0.0 1.2

— 116 — 90

— — — —

— — — —

— 246 — 308

0 60 0 120

0.0 3.7 0.0 4.8

— 220 — 570

— — — —

— — — —

— 246 — 492

Windows: Window Type 1 North South East West Window Type 2 North South East West

Window area, ft2

Btu/h·ft2

Infiltration Loads: Cooling, sensible: Cooling, latent: Heating:

People: Lighting: Lighting 20% to RA: Equipment: Envelope Loads: Roof: Area, ft2: Roof 30% to RA: Walls: Wall Type 1: Brick North South East West Wall Type 2: Spandrel North South East West

440 W

2802

2400

1052 — 904

— 370 —

— — —

— — —

573 —

— 246

— —

984 —

0 0 0 0

0.0 0.0 0.0 0.0

— — — —

— — — —

— — — —

— — — —

0 40 0 80

0.0 27.1 0.0 33.9

— 1084 — 2715

— — — —

— — — —

— 1149 — 2298

Airflow, cfm 0 0 41

Btu/h·cfm 0.0 0.0 56.4

— — —

— — —

— — —

— — 2314

10,126 511 1.9

615

2400 Heating cfm:

8038 261

Room Load Totals: Cooling cfm: cfm/ft2:

WHOLE-BUILDING EXAMPLE Because a single-room example does not illustrate the full application of load calculations, a multistory, multiple-room example building has been developed to show a more realistic case. A hypothetical project development process is described to illustrate its effect on the application of load calculations.

Design Process and Shell Building Definition A development company has acquired a piece of property in Atlanta, GA, to construct an office building. Although no tenant or end user has yet been identified, the owner/developer has decided to proceed with the project on a speculative basis. They select an architectural design firm, who retains an engineering firm for the mechanical and electrical design. At the first meeting, the developer indicates the project is to proceed on a fast-track basis to take advantage of market conditions; he is negotiating with several potential tenants who will need to occupy the new building within a year. This requires preparing

shell-and-core construction documents to obtain a building permit, order equipment, and begin construction to meet the schedule. The shell-and-core design documents will include finished design of the building exterior (the shell), as well as permanent interior elements such as stairs, restrooms, elevator, electrical rooms and mechanical spaces (the core). The primary mechanical equipment must be sized and installed as part of the shell-and-core package in order for the project to meet the schedule, even though the building occupant is not yet known. The architect selects a two-story design with an exterior skin of tinted, double-glazed vision glass; opaque, insulated spandrel glass, and brick pilasters. The roof area extends beyond the building edge to form a substantial overhang, shading the second floor windows. Architectural drawings for the shell-and-core package (see Figures 17 to 22) include plans, elevations, and skin construction details, and are furnished to the engineer for use in “block” heating and cooling load calculations. Mechanical systems and equipment must be specified and installed based on those calculations. (Note: Fullsize, scalable electronic versions of the drawings in Figures 17 to

18.46

2009 ASHRAE Handbook—Fundamentals Table 35

Block Load Example: Envelope Area Summary, ft2

Brick Areas

Spandrel/Soffit Areas

Floor Area

North

South

East

West

First Floor

15,050

680

680

400

400

Second Floor

15,050

510

510

300

300

Building Total

30,100

1190

1190

700

700

1740

North

Window Areas

South

East

West

North

South

East

West

700

700

360

360

600

560

360

360

1040

1000

540

540

560

600

360

360

1700

900

900

1160

1160

720

720

22, as well as detailed lighting plans, are available from ASHRAE at www.ashrae.org.) The HVAC design engineer meets with the developer’s operations staff to agree on the basic HVAC systems for the project. Based on their experience operating other buildings and the lack of specific information on the tenant(s), the team decides on two variablevolume air-handling units (AHUs), one per floor, to provide operating flexibility if one floor is leased to one tenant and the other floor to someone else. Cooling will be provided by an air-cooled chiller located on grade across the parking lot. Heating will be provided by electric resistance heaters in parallel-type fan-powered variable-airvolume (VAV) terminal units. The AHUs must be sized quickly to confirm the size of the mechanical rooms on the architectural plans. The AHUs and chiller must be ordered by the mechanical subcontractor within 10 days to meet the construction schedule. Likewise, the electric heating loads must be provided to the electrical engineers to size the electrical service and for the utility company to extend services to the site. The mechanical engineer must determine the (1) peak airflow and cooling coil capacity for each AHU, (2) peak cooling capacity required for the chiller, and (3) total heating capacity for sizing the electrical service. Solution: First, calculate “block” heating and cooling loads for each floor to size the AHUs, then calculate a block load for the whole building determine chiller and electric heating capacity. Based on the architectural drawings, the HVAC engineer assembles basic data on the building as follows: Location: Atlanta, GA. Per Chapter 14, latitude = 33.64, longitude = 84.43, elevation = 1027 ft above sea level, 99.6% heating design dry-bulb temperature = 20.7°F. For cooling load calculations, use 5% dry-bulb/coincident wet-bulb monthly design day profile from Chapter 14 (on CD-ROM). See Table 26 for temperature profiles used in these examples. Inside design conditions: 72°F for heating; 75°F with 50% rh for cooling. Building orientation: Plan north is 30° west of true north. Gross area per floor: 15,050 ft2 Total building gross area: 30,100 ft2 Windows: Bronze-tinted, double-glazed. Solar heat gain coefficients, U-factors are as in the single-room example. Walls: Part insulated spandrel glass and part brick-and-block clad columns. The insulation barrier in the soffit at the second floor is similar to that of the spandrel glass and is of lightweight construction; for simplicity, that surface is assumed to have similar thermal heat gain/loss to the spandrel glass. Construction and insulation values are as in single-room example. Roof: Metal deck, topped with board insulation and membrane roofing. Construction and insulation values are as in the singleroom example. Floor: 5 in. lightweight concrete slab on grade for first floor and 5 in. lightweight concrete on metal deck for second floor Total areas of building exterior skin, as measured from the architectural plans, are listed in Table 35. The engineer needs additional data to estimate the building loads. Thus far, no tenant has yet been signed, so no interior layouts for population counts, lighting layouts or equipment loads are available.

To meet the schedule, assumptions must be made on these load components. The owner requires that the system design must be flexible enough to provide for a variety of tenants over the life of the building. Based on similar office buildings, the team agrees to base the block load calculations on the following assumptions: Occupancy: 7 people per 1000 ft2 = 143 ft2/person Lighting: 1.5 W/ft2 Tenant’s office equipment: 1 W/ft2 Normal use schedule is assumed at 100% from 7:00 AM to 7:00 PM and unoccupied/off during other hours. With interior finishes not finalized, the owner commits to using light-colored interior blinds on all windows. The tenant interior design could include carpeted flooring or acoustical tile ceilings in all areas, but the more conservative assumption, from a peak load standpoint, is chosen: carpeted flooring and no acoustical tile ceilings (no ceiling return plenum). For block loads, the engineer assumes that the building is maintained under positive pressure during peak cooling conditions and that infiltration during peak heating conditions is equivalent to one air change per hour in a 12 ft deep perimeter zone around the building. To maintain indoor air quality, outside air must be introduced into the building. Air will be ducted from roof intake hoods to the AHUs where it will be mixed with return air before being cooled and dehumidified by the AHU’s cooling coil. ASHRAE Standard 62.1 is the design basis for ventilation rates; however, no interior tenant layout is available for application of Standard 62.1 procedures. Based on past experience, the engineer decides to use 20 cfm of outside air per person for sizing the cooling coils and chiller. Block load calculations were performed using the RTS method, and results for the first and second floors and the entire building are summarized in Tables 36, 37, and 38. Based on these results, the engineer performs psychrometric coil analysis, checks capacities versus vendor catalog data, and prepares specifications and schedules for the equipment. This information is released to the contractor with the shell-and-core design documents. The air-handling units and chiller are purchased, and construction proceeds.

Tenant Fit Design Process and Definition About halfway through construction, a tenant agrees to lease the entire building. The tenant will require a combination of open and enclosed office space with a few common areas, such as conference/ training rooms, and a small computer room that will operate on a 24 h basis. Based on the tenant’s space program, the architect prepares interior floor plans and furniture layout plans (Figures 23 and 24), and the electrical engineer prepares lighting design plans. Those drawings are furnished to the HVAC engineer to prepare detailed design documents. The first step in this process is to prepare room-by-room peak heating and cooling load calculations, which will then be used for design of the air distribution systems from each of the VAV air handlers already installed. The HVAC engineer must perform a room-by-room “takeoff” of the architect’s drawings. For each room, this effort identifies the floor area, room function, exterior envelope elements and areas, number of occupants, and lighting and equipment loads. The tenant layout calls for a dropped acoustical tile ceiling throughout, which will be used as a return air plenum. Typical 2 by 4 ft fluorescent, recessed, return-air-type lighting fixtures are

Nonresidential Cooling and Heating Load Calculations

18.47

Table 36 Block Load Example—First Floor Loads for ASHRAE Example Office Building, Atlanta, GA

Room

Per Unit Cooling

Loads:a

Room Sensible Return Air Cooling, Sensible Btu/h Cooling, Btu/h

Room Latent Cooling, Btu/h

Room Sensible Heating, Btu/h

Internal Loads: No. 105

15,050 W

Btu/h·person 238 Btu/h·ft2 4.9 0.0 3.3

Roof area, ft2 —

Btu/h· ft2 0.0

Wall area, ft2

Btu/h· ft2

680 680 400 400

1.3 1.9 1.9 1.6

894 1297 743 639

— — — —

— — — —

2791 2791 1642 1642

700 700 360 360

3.2 2.8 2.6 5.2

2264 1966 943 1872

— — — —

— — — —

2873 2873 1477 1477

Windows: Window Type 1: North South East West Window Type 2: North South East West

Window area, ft2

Btu/h· ft2

600 560 360 360

36.5 24.4 24.3 64.0

21,924 13,665 8755 23,040

— — — —

— — — —

17,237 16,088 10,342 10,342

0 0 0 0

0.0 0.0 0.0 0.0

— — — —

— — — —

— — — —

— — — —

Infiltration Loads: Cooling, sensible: Cooling, latent: Heating:

Airflow, cfm 0 0 863

Btu/h·cfm 0.0 0.0 56.4

— — —

— — —

— — —

— — 48,499

Room Load Totals: Cooling cfm: cfm/ft2:

225,741 11,401 0.8

21,000 Heating cfm:

120,273 3905

Total Room Sensible + RA + Latent: Outside air (OA) sensible: OA cfm: 2100 OA latent: Fan hp: 10 Fan heat to supply air: Pump hp: 0 Pump heat to chilled water:

246,741 36,498 50,267 25,461 —

People: Lighting: Lighting 0% to RA: Equipment: Envelope Loads: Roof: Area, ft2: Roof 0% to RA:

22,575 W

Walls: Wall Type 1: Brick North South East West Wall Type 2: Spandrel North South East West

Block Loads:b

Total Block Cooling Load, Btu/h:

24,675

21,000

73,284 — 49,780

— — —

— — —

— — —

— —

— — —

— —

— —

358,967

Room heating: OA heating: Total heating, Btu/h: Heating Btu/h·ft2: tons 29.9

120,273 118,503 238,776 15.9 ft2/ton 503

aPeak

room sensible load occurs in month 7 at hour 16. bPeak block load occurs in month 7 at hour 16.

selected. Based on this, the engineer assumes that 20% of the heat gain from lighting will be to the return air plenum and not enter rooms directly. Likewise, some portion of the heat gain from the roof will be extracted via the ceiling return air plenum. From experience, the engineer understands that return air plenum paths are not always predictable, and decides to credit only 30% of the roof heat gain to the return air, with the balance included in the room cooling load. For the open office areas, some areas along the building perimeter will have different load characteristics from purely interior spaces because of heat gains and losses through the building skin.

Although those perimeter areas are not separated from other open office spaces by walls, the engineer knows from experience that they must be served by separate control zones to maintain comfort conditions. The data compiled from the room-by-room takeoff are included in Tables 39 and 40.

Room by Room Cooling and Heating Loads The room by room results of RTS method calculations, including the month and time of day of each room’s peak cooling load, are tabulated in supplemental Tables 41 and 42 (available at

18.48

2009 ASHRAE Handbook—Fundamentals Table 37 Block Load Example—Second Floor Loads for ASHRAE Example Office Building, Atlanta, GA

Room

Per Unit Cooling

Loads:a

Room Sensible Return Air Cooling, Sensible Btu/h Cooling, Btu/h

Room Latent Cooling, Btu/h

Room Sensible Heating, Btu/h

Internal Loads: No. 105

15,050 W

Btu/h·person 234 Btu/h·ft2 4.8 0.0 3.4

Roof area, ft2 15,050

Btu/h· ft2 3.3

Wall area, ft2

Btu/h· ft2

People: Lighting: Lighting 0% to RA: Equipment: Envelope Loads: Roof: Area, ft2: Roof 0% to RA:

22,575 W

Walls: Wall Type 1: Brick North South East West Wall Type 2: Spandrel North South East West

72,915 49,626

— — —

— — —

— — —

49,202 —

— —

— —

54,045 —

565 915 545 373

— — — —

— — — —

2093 2093 1231 1231

1040 1000 540 540

2.8 3.2 2.8 4.4

2865 3224 1491 2398

— — — —

— — — —

4268 4104 2216 2216

— — — —

— — — —

— — — —

— — — —

— — — —

— — — —

16,088 17,237 10,342 10,342

— — —

— — —

— — —

— — 48,699

Room Load Totals: Cooling cfm: cfm/ft2:

261,968 13,231 0.9

21,000 Heating cfm:

176,205 5721

Total Room Sensible + RA + Latent: Outside air (OA) sensible: OA latent: OA cfm: 2100 Fan hp: 10 Fan heat to supply air: Pump hp: 0 Pump heat to chilled water:

282,968 39,270 50,908 25,461 —

Total Block Cooling Load, Btu/h:

398,607

560 600 360 360

28.4 27.0 26.1 32.9

Infiltration Loads: Cooling, sensible: Cooling, latent: Heating:

Airflow, cfm 0 0 863

Btu/h·cfm 0.0 0.0 56.4

bPeak

21,000

1.1 1.8 1.8 1.2

Window area, ft2

aPeak

510 510 300 300

Windows: Window Type 1: North South East West Window Type 2: North South East West

Block Loads:b

24,518

Btu/h· ft2

0 0 0 0

0 0 0 0

15,916 16,188 9,389 11,840

Room heating: OA heating: Total heating, Btu/h: Heating Btu/h·ft2: tons 33.2

176,205 118,503 294,708 19.6 ft2/ton 453

room sensible load occurs in month 7 at hour 15. block load occurs in month 7 at hour 15.

www.ashrae.org), as well as peak heating loads for each room. These results are used by the HVAC engineer to select and design room air distribution devices and to schedule airflow rates for each space. That information is incorporated into the tenant fit drawings and specifications issued to the contractor.

Conclusions The example results illustrate issues which should be understood and accounted for in calculating heating and cooling loads:

• First, peak room cooling loads occur at different months and times depending on the exterior exposure of the room. Calculation of cooling loads for a single point in time may miss the peak and result in inadequate cooling for that room. • Often, in real design processes, all data is not known. Reasonable assumptions based on past experience must be made. • Heating and air-conditioning systems often serve spaces whose use changes over the life of a building. Assumptions used in heating and cooling load calculations should consider reasonable possible uses over the life of the building, not just the first use of the space.

Nonresidential Cooling and Heating Load Calculations

18.49

Table 38 Block Load Example—Overall Building Loads for ASHRAE Example Office Building, Atlanta, GA Room Sensible Return Air Cooling, Sensible Btu/h Cooling, Btu/h Room Loadsa

Room Load Totals: Cooling cfm: cfm/ft2:

483,550 24,422 0.8

Block Loads:b

Total Room Sensible + RA + Latent: Outside air (OA) sensible: 4200 OA latent: 20 Fan heat to supply air: 5 Pump heat to chilled water:

525,550 91,540 101,816 50,922 12,730

Total Block Cooling Load, Btu/h:

782,558

OA cfm: Fan hp: Pump hp:

aPeak bPeak

Room Latent Cooling, Btu/h

Room Sensible Heating, Btu/h

42,000 Heating cfm:

296,478 9626

Room heating: OA heating: Total heating, Btu/h: Heating Btu/h·ft2: tons 65.2

296,478 237,006 533,484 17.7 ft2/ton 462

room sensible load occurs in month 7 at hour 15. block load occurs in month 7 at hour 15.

• The relative importance of each cooling and heating load component varies depending on the portion of the building being considered. Characteristics of a particular window may have little effect on the entire building load, but could have a significant effect on the supply airflow to the room where the window is located and thus on the comfort of the occupants of that space.

PREVIOUS COOLING LOAD CALCULATION METHODS Procedures described in this chapter are the most current and scientifically derived means for estimating cooling load for a defined building space, but methods in earlier editions of the ASHRAE Handbook are valid for many applications. These earlier procedures are simplifications of the heat balance principles, and their use requires experience to deal with atypical or unusual circumstances. In fact, any cooling or heating load estimate is no better than the assumptions used to define conditions and parameters such as physical makeup of the various envelope surfaces, conditions of occupancy and use, and ambient weather conditions. Experience of the practitioner can never be ignored. The primary difference between the HB and RTS methods and the older methods is the newer methods’ direct approach, compared to the simplifications necessitated by the limited computer capability available previously. The transfer function method (TFM), for example, required many calculation steps. It was originally designed for energy analysis with emphasis on daily, monthly, and annual energy use, and thus was more oriented to average hourly cooling loads than peak design loads. The total equivalent temperature differential method with time averaging (TETD/TA) has been a highly reliable (if subjective) method of load estimating since its initial presentation in the 1967 Handbook of Fundamentals. Originally intended as a manual method of calculation, it proved suitable only as a computer application because of the need to calculate an extended profile of hourly heat gain values, from which radiant components had to be averaged over a time representative of the general mass of the building involved. Because perception of thermal storage characteristics of a given building is almost entirely subjective, with little specific information for the user to judge variations, the TETD/TA method’s primary usefulness has always been to the experienced engineer. The cooling load temperature differential method with solar cooling load factors (CLTD/CLF) attempted to simplify the twostep TFM and TETD/TA methods into a single-step technique that proceeded directly from raw data to cooling load without intermediate conversion of radiant heat gain to cooling load. A series of factors were taken from cooling load calculation results (produced

by more sophisticated methods) as “cooling load temperature differences” and “cooling load factors” for use in traditional conduction (q = UA't) equations. The results are approximate cooling load values rather than simple heat gain values. The simplifications and assumptions used in the original work to derive those factors limit this method’s applicability to those building types and conditions for which the CLTD/CLF factors were derived; the method should not be used beyond the range of applicability. Although the TFM, TETD/TA, and CLTD/CLF procedures are not republished in this chapter, those methods are not invalidated or discredited. Experienced engineers have successfully used them in millions of buildings around the world. The accuracy of cooling load calculations in practice depends primarily on the availability of accurate information and the design engineer’s judgment in the assumptions made in interpreting the available data. Those factors have much greater influence on a project’s success than does the choice of a particular cooling load calculation method. The primary benefit of HB and RTS calculations is their somewhat reduced dependency on purely subjective input (e.g., determining a proper time-averaging period for TETD/TA; ascertaining appropriate safety factors to add to the rounded-off TFM results; determining whether CLTD/CLF factors are applicable to a specific unique application). However, using the most up-to-date techniques in real-world design still requires judgment on the part of the design engineer and care in choosing appropriate assumptions, just as in applying older calculation methods.

REFERENCES Abushakra, B., J.S. Haberl, and D.E. Claridge. 2004. Overview of literature on diversity factors and schedules for energy and cooling load calculations (1093-RP). ASHRAE Transactions 110(1):164-176. Armstrong, P.R., C.E. Hancock, III, and J.E. Seem. 1992a. Commercial building temperature recovery—Part I: Design procedure based on a step response model. ASHRAE Transactions 98(1):381-396. Armstrong, P.R., C.E. Hancock, III, and J.E. Seem. 1992b. Commercial building temperature recovery—Part II: Experiments to verify the step response model. ASHRAE Transactions 98(1):397-410. ASHRAE. 2004. Thermal environmental conditions for human occupancy. ANSI/ASHRAE Standard 55-2004. ASHRAE. 2001. Ventilation for acceptable indoor air quality. ANSI/ ASHRAE Standard 62-2001. ASHRAE. 2007. Energy standard for building except low-rise residential buildings. ANSI/ASHRAE/IESNA Standard 90.1-2007. ASHRAE. 2004. Updating the climatic design conditions in the ASHRAE Handbook—Fundamentals (RP-1273). ASHRAE Research Project, Final Report. ASTM. 2008. Practice for estimate of the heat gain or loss and the surface temperatures of insulated flat, cylindrical, and spherical systems by use of computer programs. Standard C680-08. American Society for Testing and Materials, West Conshohocken, PA.

18.50

2009 ASHRAE Handbook—Fundamentals Table 39

Tenant Fit Example: First Floor Room Data Spandrel/Soffit Area (Wall), ft2

Room No. Room Name

Brick Area (Wall), ft2 Area, 2 ft North South East West

101 102 103 104 105 106 107 108 109 109A 110 111 112 113 114 115 116 117 118 119 120 121 122 122A 123 123A 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151

147 314 9 128 128 128 128 271 1,908 281 135 313 254 218 1,464 77 175 461 397 43 30 129 1,812 255 123 123 123 253 128 128 128 128 225 26 244 132 128 14 311 14 255 590 580 236 170 55 107 174 174 57 220 766 120 120

60 0 0 40 40 40 40 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 60 40 40 0 0 0 0 80 80 60 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 240 20 80 0 0 0 0 40 0 120 40 40 40 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 80 0 140 40 0 0 40 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 40 40 40 40 40 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

20 0 0 40 40 40 40 80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 40 40 40 0 0 0 0 80 80 160 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 200 20 160 0 0 0 0 40 0 120 40 40 40 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 40 0 160 40 0 0 40 80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 80 40 40 40 40 40 0 80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

80 0 0 40 40 40 40 80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 40 40 40 0 0 0 0 80 80 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 160 80 0 0 0 0 0 40 0 120 40 40 40 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 40 0 160 40 0 0 40 80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 80 40 40 40 40 40 0 80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

15,050

680

680

400

400

700

700

360

360

600

560

360

360

Total

Vestibule Reception Coats Meeting Room Mgr. Mtgs./Conf. Mgr. Ed./Ch. Prog. Admin. Asst. Director Open Office E. Open Office Member Mgr. Member. Files Prod./Misc./Stor. Storage Mailroom Vestibule Stair 2 Elevator Lobby Computer/Tel. Electrical Equip. Storage Data Proc. Mgr. Open Office S. Open Office Comm. Mgr. Acct. Supervisor Acct. Mgr. Director Admin. Asst. Meeting Room Assist. B.O.D. President Conference Storage Ex. Director Ex. Secretary Asst. Ex. Dir. Storage Waiting Storage Open Office Sec’y Conf. A Conf. B Stair 1 Conf. C Janitor Storage Men Women Electrical Mechanical Hall of Fame Personnel Mgr. Personnel Clerk

North South East

Window Area, ft2

West

North South

East

No. of Lights, Equip., West People W W 0 4 0 6 3 1 1 9 12 3 1 0 0 0 2 0 0 0 2 0 0 1 7 4 1 2 2 5 1 6 1 1 8 0 5 1 1 0 2 0 3 28 20 0 8 0 0 0 0 0 0 0 1 2

210 540 0 220 220 220 220 440 2850 390 220 660 300 150 2090 60 0 610 880 30 30 220 2860 660 220 220 220 440 220 220 220 220 220 0 440 220 220 0 390 0 770 780 750 90 440 75 150 420 420 0 0 900 220 220

0 314 0 128 128 128 128 271 1908 281 135 313 254 0 2928 0 0 0 397 0 0 129 1812 255 123 123 123 253 128 128 128 128 225 0 244 132 128 0 311 0 255 590 580 0 170 0 0 0 0 0 0 766 120 120

154 22,785 14,279

Nonresidential Cooling and Heating Load Calculations Table 40 Room No. Room Name 201 201A 202 203 204 205 206 207 208 209 220 211 212 213 214 215 216 217 218 219 220 221 222 223 224 226 227 228 229 229A 229 230 231 232 233 234 235 235A 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 Total

Mgr. Stds. Admin. Asst. Stds. Admin. Asst. Mgr. Stds. Asst. Mgr. Stds. Mgr. Tech. Serv. Admin. Asst./Dir. Director Open Office Mgr. Research Mgr. Res. Prom. Future Copy/Storage Rare Books Arch. Library Corridor Conf. Room Storage Breakroom Stair 2 Elevator Lobby Supplies Cam./Darkroom Open Office S. Open Office Prod. Mgr. Graphics Mgr. Editor (Handbook) Open Office S. Open Office W. Open Office Conf. Room Editor Editor Director Admin. Asst. Adv. Sales Mgr. Adv. Prod. Mgr. Comm/P.R. Mgr. Conf. Room Marketing Mgr. Open Office Storage Stair 1 Corridor Hall of Fame Janitor Storage Men Women Electrical Mechanical Storage

18.51

Tenant Fit Example: Second Floor Room Data

Brick Area (Wall), ft2 Area, 2 ft North South East West

Spandrel/Soffit Area (Wall), ft2 North South East

West

Window Area, ft2 North South East

No. of Lights, Equip. West People W W

131 170 128 128 128 128 128 252 1357 128 128 128 115 111 802 791 255 560 470 175 124 160 150 1,146 179 128 128 128 1,664 159 233 274 128 128 252 128 128 128 128 128 128 1,001 230 252 111 545 55 107 174 174 57 220 173

30 0 30 30 30 30 30 45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 45 30 30 30 30 30 30 0 0 60 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 105 60 0 0 0 0 60 30 30 30 0 45 0 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 75 0 30 30 30 0 0 0 0 60 75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 75 30 30 75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

60 0 60 60 60 60 60 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 60 60 60 60 60 60 60 0 0 200 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 180 180 160 0 0 0 0 120 60 60 60 0 120 0 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 120 0 60 60 60 0 0 0 0 120 120 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 180 120 60 60 120 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

40 0 40 40 40 40 40 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 40 40 40 40 40 40 40 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 120 120 40 0 0 0 0 80 40 40 40 0 80 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 80 0 40 40 40 0 0 0 0 80 80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 120 80 40 40 80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

15,050

510

510

300

300

1040

1000

540

540

560

600

360

360

1 3 1 1 2 2 1 5 8 2 2 2 0 0 13 0 12 0 16 0 0 0 1 8 6 2 1 2 7 5 5 12 1 2 7 1 1 1 1 6 1 6 0 0 0 0 0 0 0 0 0 0 0

220 330 220 220 220 220 220 440 2480 220 220 220 150 150 1430 1480 440 550 770 220 120 150 150 1760 440 220 220 220 2750 440 660 440 220 220 440 220 220 220 220 220 220 2200 225 440 90 690 75 75 420 420 0 0 225

131 170 128 128 128 128 128 252 1357 128 128 128 115 111 802 791 255 560 470 0 0 160 150 1146 179 128 128 128 1664 159 233 274 128 128 252 128 128 128 128 128 128 1001 0 0 0 0 0 0 0 0 0 0 0

147 25,050 12,654

18.52 Bliss, R.J.V. 1961. Atmospheric radiation near the surface of the ground. Solar Energy 5(3):103. Chantrasrisalai, C., D.E. Fisher, I. Iu, and D. Eldridge. 2003. Experimental validation of design cooling load procedures: The heat balance method. ASHRAE Transactions 109(2):160-173. Claridge, D.E., B. Abushakra, J.S. Haberl, and A. Sreshthaputra. 2004. Electricity diversity profiles for energy simulation of office buildings (RP-1093). ASHRAE Transactions 110(1):365-377. Eldridge, D., D.E. Fisher, I. Iu, and C. Chantrasrisalai. 2003. Experimental validation of design cooling load procedures: Facility design (RP-1117). ASHRAE Transactions 109(2):151-159. Fisher, D.R. 1998. New recommended heat gains for commercial cooking equipment. ASHRAE Transactions 104(2):953-960. Fisher, D.E. and C. Chantrasrisalai. 2006. Lighting heat gain distribution in buildings (RP-1282). ASHRAE Research Project, Final Report. Fisher, D.E. and C.O. Pedersen. 1997. Convective heat transfer in building energy and thermal load calculations. ASHRAE Transactions 103(2): 137-148. Gordon, E.B., D.J. Horton, and F.A. Parvin. 1994. Development and application of a standard test method for the performance of exhaust hoods with commercial cooking appliances. ASHRAE Transactions 100(2). Hittle, D.C. 1999. The effect of beam solar radiation on peak cooling loads. ASHRAE Transactions 105(2):510-513. Hittle, D.C. and C.O. Pedersen. 1981. Calculating building heating loads using the frequency of multi-layered slabs. ASHRAE Transactions 87(2):545-568. Hosni, M.H. and B.T. Beck. 2008. Update to measurements of office equipment heat gain data (RP-1482). ASHRAE Research Project, Progress Report. Hosni, M.H., B.W. Jones, J.M. Sipes, and Y. Xu. 1998. Total heat gain and the split between radiant and convective heat gain from office and laboratory equipment in buildings. ASHRAE Transactions 104(1A):356-365. Hosni, M.H., B.W. Jones, and H. Xu. 1999. Experimental results for heat gain and radiant/convective split from equipment in buildings. ASHRAE Transactions 105(2):527-539. Incropera, F.P. and D.P DeWitt. 1990. Fundamentals of heat and mass transfer, 3rd ed. Wiley, New York. Iu, I. and D.E. Fisher. 2004. Application of conduction transfer functions and periodic response factors in cooling load calculation procedures. ASHRAE Transactions 110(2):829-841. Iu, I., C. Chantrasrisalai, D.S. Eldridge, and D.E. Fisher. 2003. experimental validation of design cooling load procedures: The radiant time series method (RP-1117). ASHRAE Transactions 109(2):139-150. Jones, B.W., M.H. Hosni, and J.M. Sipes. 1998. Measurement of radiant heat gain from office equipment using a scanning radiometer. ASHRAE Transactions 104(1B):1775-1783. Karambakkam, B.K., B. Nigusse, and J.D. Spitler. 2005. A one-dimensional approximation for transient multi-dimensional conduction heat transfer in building envelopes. Proceedings of the 7th Symposium on Building Physics in the Nordic Countries, The Icelandic Building Research Institute, Reykjavik, vol. 1, pp. 340-347. Kerrisk, J.F., N.M. Schnurr, J.E. Moore, and B.D. Hunn. 1981. The custom weighting-factor method for thermal load calculations in the DOE-2 computer program. ASHRAE Transactions 87(2):569-584. Komor, P. 1997. Space cooling demands from office plug loads. ASHRAE Journal 39(12):41-44. Kusuda, T. 1967. NBSLD, the computer program for heating and cooling loads for buildings. BSS 69 and NBSIR 74-574. National Bureau of Standards. Latta, J.K. and G.G. Boileau. 1969. Heat losses from house basements. Canadian Building 19(10):39. LBL. 2003. WINDOW 5.2: A PC program for analyzing window thermal performance for fenestration products. LBL-44789. Windows and Daylighting Group. Lawrence Berkeley Laboratory, Berkeley. Liesen, R.J. and C.O. Pedersen. 1997. An evaluation of inside surface heat balance models for cooling load calculations. ASHRAE Transactions 103(2):485-502. Marn, W.L. 1962. Commercial gas kitchen ventilation studies. Research Bulletin 90(March). Gas Association Laboratories, Cleveland, OH. McClellan, T.M. and C.O. Pedersen. 1997. Investigation of outside heat balance models for use in a heat balance cooling load calculation procedure. ASHRAE Transactions 103(2):469-484. McQuiston, F.C. and J.D. Spitler. 1992. Cooling and heating load calculation manual, 2nd ed. ASHRAE.

2009 ASHRAE Handbook—Fundamentals Miller, A. 1971. Meteorology, 2nd ed. Charles E. Merrill, Columbus. Nigusse, B.A. 2007. Improvements to the radiant time series method cooling load calculation procedure. Ph.D. dissertation, Oklahoma State University. Parker, D.S., J.E.R. McIlvaine, S.F. Barkaszi, D.J. Beal, and M.T. Anello. 2000. Laboratory testing of the reflectance properties of roofing material. FSEC-CR670-00. Florida Solar Energy Center, Cocoa. Pedersen, C.O., D.E. Fisher, and R.J. Liesen. 1997. Development of a heat balance procedure for calculating cooling loads. ASHRAE Transactions 103(2):459-468. Pedersen, C.O., D.E. Fisher, J.D. Spitler, and R.J. Liesen. 1998. Cooling and heating load calculation principles. ASHRAE. Rees, S.J., J.D. Spitler, M.G. Davies, and P. Haves. 2000. Qualitative comparison of North American and U.K. cooling load calculation methods. International Journal of Heating, Ventilating, Air-Conditioning and Refrigerating Research 6(1):75-99. Rock, B.A. 2005. A user-friendly model and coefficients for slab-on-grade load and energy calculation. ASHRAE Transactions 111(2):122-136. Rock, B.A. and D.J. Wolfe. 1997. A sensitivity study of floor and ceiling plenum energy model parameters. ASHRAE Transactions 103(1):16-30. Smith, V.A., R.T. Swierczyna, and C.N. Claar. 1995. Application and enhancement of the standard test method for the performance of commercial kitchen ventilation systems. ASHRAE Transactions 101(2). Sowell, E.F. 1988a. Cross-check and modification of the DOE-2 program for calculation of zone weighting factors. ASHRAE Transactions 94(2). Sowell, E.F. 1988b. Load calculations for 200,640 zones. ASHRAE Transactions 94(2):716-736. Spitler, J.D. and D.E. Fisher. 1999a. Development of periodic response factors for use with the radiant time series method. ASHRAE Transactions 105(2):491-509. Spitler, J.D. and D.E. Fisher. 1999b. On the relationship between the radiant time series and transfer function methods for design cooling load calculations. International Journal of Heating, Ventilating, Air-Conditioning and Refrigerating Research (now HVAC&R Research) 5(2):125-138. Spitler, J.D., D.E. Fisher, and C.O. Pedersen. 1997. The radiant time series cooling load calculation procedure. ASHRAE Transactions 103(2). Spitler, J.D., S.J. Rees, and P. Haves. 1998. Quantitive comparison of North American and U.K. cooling load calculation procedures—Part 1: Methodology, Part II: Results. ASHRAE Transactions 104(2):36-46, 47-61. Sun, T.-Y. 1968. Shadow area equations for window overhangs and side-fins and their application in computer calculation. ASHRAE Transactions 74(1):I-1.1 to I-1.9. Swierczyna, R., P. Sobiski, and D. Fisher. 2008. Revised heat gain and capture and containment exhaust rates from typical commercial cooking appliances (RP-1362). ASHRAE Research Project, Final Report. Swierczyna, R., P.A. Sobiski, and D.R. Fisher. 2009 (forthcoming). Revised heat gain rates from typical commercial cooking appliances from RP1362. ASHRAE Transactions 115(2). Talbert, S.G., L.J. Canigan, and J.A. Eibling. 1973. An experimental study of ventilation requirements of commercial electric kitchens. ASHRAE Transactions 79(1):34. Walton, G. 1983. Thermal analysis research program reference manual. National Bureau of Standards. Wilkins, C.K. and M.R. Cook. 1999. Cooling loads in laboratories. ASHRAE Transactions 105(1):744-749. Wilkins, C.K. and M.H. Hosni. 2000. Heat gain from office equipment. ASHRAE Journal 42(6):33-44. Wilkins, C.K. and N. McGaffin. 1994. Measuring computer equipment loads in office buildings. ASHRAE Journal 36(8):21-24. Wilkins, C.K., R. Kosonen, and T. Laine. 1991. An analysis of office equipment load factors. ASHRAE Journal 33(9):38-44.

BIBLIOGRAPHY Alereza, T. and J.P. Breen, III. 1984. Estimates of recommended heat gain due to commercial appliances and equipment. ASHRAE Transactions 90(2A):25-58. Alford, J.S., J.E. Ryan, and F.O. Urban. 1939. Effect of heat storage and variation in outdoor temperature and solar intensity on heat transfer through walls. ASHVE Transactions 45:387. American Gas Association. 1948. A comparison of gas and electric use for commercial cooking. Cleveland, OH. American Gas Association. 1950. Gas and electric consumption in two college cafeterias. Cleveland, OH.

Nonresidential Cooling and Heating Load Calculations ASHRAE. 1975. Procedure for determining heating and cooling loads for computerized energy calculations, algorithms for building heat transfer subroutines. ASHRAE. 1979. Cooling and heating load calculation manual. BLAST Support Office. 1991. BLAST user reference. University of Illinois, Urbana–Champaign. Brisken, W.R. and G.E. Reque. 1956. Thermal circuit and analog computer methods, thermal response. ASHAE Transactions 62:391. Buchberg, H. 1958. Cooling load from thermal network solutions. ASHAE Standard 64:111. Buchberg, H. 1955. Electric analog prediction of the thermal behavior of an inhabitable enclosure. ASHAE Transactions 61:339-386. Buffington, D.E. 1975. Heat gain by conduction through exterior walls and roofs—Transmission matrix method. ASHRAE Transactions 81(2):89. Burch, D.M., B.A. Peavy, and F.J. Powell. 1974. Experimental validation of the NBS load and indoor temperature prediction model. ASHRAE Transactions 80(2):291. Burch, D.M., J.E. Seem, G.N. Walton, and B.A. Licitra. 1992. Dynamic evaluation of thermal bridges in a typical office building. ASHRAE Transactions 98:291-304. Butler, R. 1984. The computation of heat flows through multi-layer slabs. Building and Environment 19(3):197-206. Ceylan, H.T. and G.E. Myers. 1985. Application of response-coefficient method to heat-conduction transients. ASHRAE Transactions 91:30-39. Chiles, D.C. and E.F. Sowell. 1984. A counter-intuitive effect of mass on zone cooling load response. ASHRAE Transactions 91(2A):201-208. Chorpening, B.T. 1997. The sensitivity of cooling load calculations to window solar transmission models. ASHRAE Transactions 103(1). Clarke, J.A. 1985. Energy simulation in building design. Adam Hilger Ltd., Boston. Consolazio, W. and L.J. Pecora. 1947. Minimal replenishment air required for living spaces. ASHVE Standard 53:127. Colliver, D.G., H. Zhang, R.S. Gates, and K.T. Priddy. 1995. Determination of the 1%, 2.5%, and 5% occurrences of extreme dew-point temperatures and mean coincident dry-bulb temperatures. ASHRAE Transactions 101(2):265-286. Colliver, D.G., R.S. Gates, H. Zhang, and K.T. Priddy. 1998. Sequences of extreme temperature and humidity for design calculations. ASHRAE Transactions 104(1A):133-144. Colliver, D.G., R.S. Gates, T.F. Burke, and H. Zhang. 2000. Development of the design climatic data for the 1997 ASHRAE Handbook—Fundamentals. ASHRAE Transactions 106(1):3-14. Davies, M.G. 1996. A time-domain estimation of wall conduction transfer function coefficients. ASHRAE Transactions 102(1):328-208. DeAlbuquerque, A.J. 1972. Equipment loads in laboratories. ASHRAE Journal 14(10):59. Falconer, D.R., E.F. Sowell, J.D. Spitler, and B.B. Todorovich. 1993. Electronic tables for the ASHRAE load calculation manual. ASHRAE Transactions 99(1):193-200. Harris, S.M. and F.C. McQuiston. 1988. A study to categorize walls and roofs on the basis of thermal response. ASHRAE Transactions 94(2): 688-714. Headrick, J.B. and D.P. Jordan. 1969. Analog computer simulation of heat gain through a flat composite roof section. ASHRAE Transactions 75(2):21. Hittle, D.C. 1981. Calculating building heating and cooling loads using the frequency response of multilayered slabs, Ph.D. dissertation, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana-Champaign. Hittle, D.C. and R. Bishop. 1983. An improved root-finding procedure for use in calculating transient heat flow through multilayered slabs. International Journal of Heat and Mass Transfer 26:1685-1693. Houghton, D.G., C. Gutherlet, and A.J. Wahl. 1935. ASHVE Research Report No. 1001—Cooling requirements of single rooms in a modern office building. ASHVE Transactions 41:53. Kimura and Stephenson. 1968. Theoretical study of cooling loads caused by lights. ASHRAE Transactions 74(2):189-197. Kusuda, T. 1969. Thermal response factors for multilayer structures of various heat conduction systems. ASHRAE Transactions 75(1):246. Leopold, C.S. 1947. The mechanism of heat transfer, panel cooling, heat storage. Refrigerating Engineering 7:33. Leopold, C.S. 1948. Hydraulic analogue for the solution of problems of thermal storage, radiation, convection, and conduction. ASHVE Transactions 54:3-9.

18.53 Livermore, J.N. 1943. Study of actual vs predicted cooling load on an air conditioning system. ASHVE Transactions 49:287. Mackey, C.O. and N.R. Gay. 1949. Heat gains are not cooling loads. ASHVE Transactions 55:413. Mackey, C.O. and N.R. Gay. 1952. Cooling load from sunlit glass. ASHVE Transactions 58:321. Mackey, C.O. and N.R. Gay. 1954. Cooling load from sunlit glass and wall. ASHVE Transactions 60:469. Mackey, C.O. and L.T. Wright, Jr. 1944. Periodic heat flow—homogeneous walls or roofs. ASHVE Transactions 50:293. Mackey, C.O. and L.T. Wright, Jr. 1946. Periodic heat flow—composite walls or roofs. ASHVE Transactions 52:283. Mast, W.D. 1972. Comparison between measured and calculated hour heating and cooling loads for an instrumented building. ASHRAE Symposium Bulletin 72(2). McBridge, M.F., C.D. Jones, W.D. Mast, and C.F. Sepsey. 1975. Field validation test of the hourly load program developed from the ASHRAE algorithms. ASHRAE Transactions 1(1):291. Mitalas, G.P. 1968. Calculations of transient heat flow through walls and roofs. ASHRAE Transactions 74(2):182-188. Mitalas, G.P. 1969. An experimental check on the weighting factor method of calculating room cooling load. ASHRAE Transactions 75(2):22. Mitalas, G.P. 1972. Transfer function method of calculating cooling loads, heat extraction rate, and space temperature. ASHRAE Journal 14(12):52. Mitalas, G.P. 1973. Calculating cooling load caused by lights. ASHRAE Transactions 75(6):7. Mitalas, G.P. 1978. Comments on the Z-transfer function method for calculating heat transfer in buildings. ASHRAE Transactions 84(1):667-674. Mitalas, G.P. and J.G. Arsenault. 1970. Fortran IV program to calculate Ztransfer functions for the calculation of transient heat transfer through walls and roofs. Use of Computers for Environmental Engineering Related to Buildings, pp. 633-668. National Bureau of Standards, Gaithersburg, MD. Mitalas, G.P. and K. Kimura. 1971. A calorimeter to determine cooling load caused by lights. ASHRAE Transactions 77(2):65. Mitalas, G.P. and D.G. Stephenson. 1967. Room thermal response factors. ASHRAE Transactions 73(2): III.2.1. Nevins, R.G., H.E. Straub, and H.D. Ball. 1971. Thermal analysis of heat removal troffers. ASHRAE Transactions 77(2):58-72. NFPA. 1999. Standard for health care facilities. Standard 99-99. National Fire Protection Association, Quincy, MA. Nottage, H.B. and G.V. Parmelee. 1954. Circuit analysis applied to load estimating. ASHVE Transactions 60:59. Nottage, H.B. and G.V. Parmelee. 1955. Circuit analysis applied to load estimating. ASHAE Transactions 61(2):125. Ouyang, K. and F. Haghighat. 1991. A procedure for calculating thermal response factors of multi-layer walls—State space method. Building and Environment 26(2):173-177. Parmelee, G.V., P. Vance, and A.N. Cherny. 1957. Analysis of an air conditioning thermal circuit by an electronic differential analyzer. ASHAE Transactions 63:129. Paschkis, V. 1942. Periodic heat flow in building walls determined by electric analog method. ASHVE Transactions 48:75. Peavy, B.A. 1978. A note on response factors and conduction transfer functions. ASHRAE Transactions 84(1):688-690. Peavy, B.A., F.J. Powell, and D.M. Burch. 1975. Dynamic thermal performance of an experimental masonry building. NBS Building Science Series 45 (July). Romine, T.B., Jr. 1992. Cooling load calculation: Art or science? ASHRAE Journal, 34(1):14. Rudoy, W. 1979. Don’t turn the tables. ASHRAE Journal 21(7):62. Rudoy, W. and F. Duran. 1975. Development of an improved cooling load calculation method. ASHRAE Transactions 81(2):19-69. Seem, J.E., S.A. Klein, W.A. Beckman, and J.W. Mitchell. 1989. Transfer functions for efficient calculation of multidimensional transient heat transfer. Journal of Heat Transfer 111:5-12. Sowell, E.F. and D.C. Chiles. 1984a. Characterization of zone dynamic response for CLF/CLTD tables. ASHRAE Transactions 91(2A):162-178. Sowell, E.F. and D.C. Chiles. 1984b. Zone descriptions and response characterization for CLF/CLTD calculations. ASHRAE Transactions 91(2A): 179-200. Spitler, J.D. 1996. Annotated guide to load calculation models and algorithms. ASHRAE.

18.54 Spitler, J.D., F.C. McQuiston, and K.L. Lindsey. 1993. The CLTD/SCL/CLF cooling load calculation method. ASHRAE Transactions 99(1):183-192. Spitler, J.D. and F.C. McQuiston. 1993. Development of a revised cooling and heating calculation manual. ASHRAE Transactions 99(1):175-182. Stephenson, D.G. 1962. Method of determining non-steady-state heat flow through walls and roofs at buildings. Journal of the Institution of Heating and Ventilating Engineers 30:5. Stephenson, D.G. and G.P. Mitalas. 1967. Cooling load calculation by thermal response factor method. ASHRAE Transactions 73(2):III.1.1. Stephenson, D.G. and G.P. Mitalas. 1971. Calculation of heat transfer functions for multi-layer slabs. ASHRAE Transactions 77(2):117-126. Stewart, J.P. 1948. Solar heat gain through walls and roofs for cooling load calculations. ASHVE Transactions 54:361. Sun, T.-Y. 1968. Computer evaluation of the shadow area on a window cast by the adjacent building. ASHRAE Journal (September). Todorovic, B. 1982. Cooling load from solar radiation through partially shaded windows, taking heat storage effect into account. ASHRAE Transactions 88(2):924-937. Todorovic, B. 1984. Distribution of solar energy following its transmittal through window panes. ASHRAE Transactions 90(1B):806-815.

2009 ASHRAE Handbook—Fundamentals Todorovic, B. 1987. The effect of the changing shade line on the cooling load calculations. In ASHRAE videotape, Practical applications for cooling load calculations. Todorovic, B. 1989. Heat storage in building structure and its effect on cooling load; Heat and mass transfer in building materials and structure. Hemisphere Publishing, New York. Todorovic, B. and D. Curcija. 1984. Calculative procedure for estimating cooling loads influenced by window shading, using negative cooling load method. ASHRAE Transactions 2:662. Todorovic, B., L. Marjanovic, and D. Kovacevic. 1993. Comparison of different calculation procedures for cooling load from solar radiation through a window. ASHRAE Transactions 99(2):559-564. Vild, D.J. 1964. Solar heat gain factors and shading coefficients. ASHRAE Journal 6(10):47. Wilkins, C.K. 1998. Electronic equipment heat gains in buildings. ASHRAE Transactions 104(1B):1784-1789. York, D.A. and C.C. Cappiello. 1981. DOE-2 engineers manual (Version 2.1A). Lawrence Berkeley Laboratory and Los Alamos National Laboratory.

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Fig. 17 First Floor Shell and Core Plan

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Fig. 18 Second Floor Shell and Core Plan

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Fig. 18 Second Floor Shell and Core Plan

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Fig. 19 Second Floor Shell and Core Plan

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Fig. 20 Second Floor Shell and Core Plan

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Fig. 20 North/South Elevations

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Fig. 21 Second Floor Shell and Core Plan

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Fig. 21 East/West Elevations, Elevation Details, and Perimeter Section

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Fig. 22 Second Floor Shell and Core Plan

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Fig. 23 Second Floor Shell and Core Plan

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Fig. 24 Second Floor Shell and Core Plan

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CHAPTER 19

ENERGY ESTIMATING AND MODELING METHODS GENERAL CONSIDERATIONS .............................................. 19.1 Models and Approaches........................................................... 19.1 Characteristics of Models ........................................................ 19.1 Choosing an Analysis Method ................................................. 19.3 COMPONENT MODELING AND LOADS ............................. 19.3 Calculating Space Sensible Loads ........................................... 19.3 Ground Heat Transfer .............................................................. 19.7 Secondary System Components................................................ 19.9 Primary System Components ................................................. 19.12 SYSTEM MODELING............................................................ 19.17 Overall Modeling Strategies .................................................. 19.17 Degree-Day and Bin Methods................................................ 19.17

Correlation Methods .............................................................. Simulating Secondary and Primary Systems ......................... Modeling of System Controls ................................................. Integration of System Models ................................................. DATA-DRIVEN MODELING ................................................. Categories of Data-Driven Methods ...................................... Types of Data-Driven Models ................................................ Examples Using Data-Driven Methods ................................. Model Selection...................................................................... MODEL VALIDATION AND TESTING................................. Methodological Basis............................................................. Summary of Previous Testing and Validation Work ...............

E

Forward modeling of building energy use begins with a physical description of the building system or component of interest. For example, building geometry, geographical location, physical characteristics (e.g., wall material and thickness), type of equipment and operating schedules, type of HVAC system, building operating schedules, plant equipment, etc., are specified. The peak and average energy use of such a building can then be predicted or simulated by the forward simulation model. The primary benefits of this method are that it is based on sound engineering principles usually taught in colleges and universities, and consequently has gained widespread acceptance by the design and professional community. Major government-developed simulation codes, such as BLAST, DOE-2, and EnergyPlus, are based on forward simulation models. Figure 1 illustrates the ordering of the analysis typically performed by a building energy simulation program. Data-Driven (Inverse) Approach. In this case, input and output variables are known and measured, and the objective is to determine a mathematical description of the system and to estimate system parameters. In contrast to the forward approach, the data-driven approach is relevant when the system has already been built and actual performance data are available for model development and/or identification. Two types of performance data can be used: nonintrusive and intrusive. Intrusive data are gathered under conditions of predetermined or planned experiments on the system to elicit system response under a wider range of system performance than would have occurred under normal system operation. These performance data allow more accurate model specification and identification. When constraints on system operation do not permit such tests to be performed, the model must be identified from nonintrusive data obtained under normal operation. Data-driven modeling often allows identification of system models that are not only simpler to use but also are more accurate predictors of future system performance than forward models. The data-driven approach arises in many fields, such as physics, biology, engineering, and economics. Although several monographs, textbooks, and even specialized technical journals are available in this area, the approach has not yet been widely adopted in energy-related curricula and by the building professional community.

NERGY requirements and fuel consumption of HVAC systems directly affect a building’s operating cost and indirectly affect the environment. This chapter discusses methods for estimating energy use for two purposes: modeling for building and HVAC system design and associated design optimization (forward modeling), and modeling energy use of existing buildings for establishing baselines and calculating retrofit savings (data-driven modeling).

GENERAL CONSIDERATIONS MODELS AND APPROACHES A mathematical model is a description of the behavior of a system. It is made up of three components (Beck and Arnold 1977): 1. Input variables (statisticians call these regressor variables, whereas physicists call them forcing variables), which act on the system. There are two types: controllable by the experimenter, and uncontrollable (e.g., climate). 2. System structure and parameters/properties, which provide the necessary physical description of the system (e.g., thermal mass or mechanical properties of the elements). 3. Output (response, or dependent) variables, which describe the reaction of the system to the input variables. Energy use is often a response variable. The science of mathematical modeling as applied to physical systems involves determining the third component of a system when the other two components are given or specified. There are two broad but distinct approaches to modeling; which to use is dictated by the objective or purpose of the investigation (Rabl 1988). Forward (Classical) Approach. The objective is to predict the output variables of a specified model with known structure and known parameters when subject to specified input variables. To ensure accuracy, models have tended to become increasingly complex, especially with the advent of cheap and powerful computing power. This approach presumes detailed knowledge not only of the various natural phenomena affecting system behavior but also of the magnitude of various interactions (e.g., effective thermal mass, heat and mass transfer coefficients, etc.). The main advantage of this approach is that the system need not be physically built to predict its behavior. Thus, this approach is ideal in the preliminary design and analysis stage and is most often used then. The preparation of this chapter is assigned to TC 4.7, Energy Calculations.

19.22 19.22 19.23 19.23 19.24 19.24 19.25 19.30 19.31 19.31 19.32 19.33

CHARACTERISTICS OF MODELS Forward Models Although procedures for estimating energy requirements vary considerably in their degree of complexity, they all have three common elements: calculation of (1) space load, (2) secondary

19.1

19.2

2009 ASHRAE Handbook—Fundamentals

Fig. 1 Flow Chart for Building Energy Simulation Program

resource consumed, as opposed to energy delivered to the building boundary. Often, energy calculations lead to an economic analysis to establish the cost-effectiveness of conservation measures (ASHRAE Standard 90.1). Thus, thorough energy analysis provides intermediate data, such as time of energy usage and maximum demand, so that utility charges can be accurately estimated. Although not part of the energy calculations, estimated capital equipment costs should be included. Complex and often unexpected interactions can occur between systems or between various modes of heat transfer. For example, radiant heating panels affect space loads by raising the mean radiant temperature in the space (Howell and Suryanarayana 1990). As a result, air temperature can be lowered while maintaining comfort. Compared to a conventional heated-air system, radiant panels create a greater temperature difference from the inside surface to the outside air. Thus, conduction losses through the walls and roof increase because the inside surface temperatures are greater. At the same time, the heating load caused by infiltration or ventilation decreases because of the reduced indoor-to-outdoor-air temperature difference. The infiltration rate may also decrease because the reduced air temperature difference reduces the stack effect.

Data-Driven Models

Fig. 1 Flow Chart for Building Energy Simulation Program (Ayres and Stamper 1995)

equipment load, and (3) primary equipment energy requirements. Here, secondary refers to equipment that distributes the heating, cooling, or ventilating medium to conditioned spaces, whereas primary refers to central plant equipment that converts fuel or electric energy to heating or cooling effect. The first step in calculating energy requirements is to determine the space load, which is the amount of energy that must be added to or extracted from a space to maintain thermal comfort. The simplest procedures assume that the energy required to maintain comfort is only a function of the outdoor dry-bulb temperature. More detailed methods consider solar effects, internal gains, heat storage in the walls and interiors, and the effects of wind on both building envelope heat transfer and infiltration. Chapters 17 and 18 discuss load calculation in detail. Although energy calculations are similar to the heating and cooling load calculations used to size equipment, they are not the same. Energy calculations are based on average use and typical weather conditions rather than on maximum use and worst-case weather. Currently, the most sophisticated procedures are based on hourly profiles for climatic conditions and operational characteristics for a number of typical days of the year or on 8760 h of operation per year. The second step translates the space load to a load on the secondary equipment. This can be a simple estimate of duct or piping losses or gains or a complex hour-by-hour simulation of an air system, such as variable-air-volume with outdoor-air cooling. This step must include calculation of all forms of energy required by the secondary system (e.g., electrical energy to operate fans and/or pumps, as well as energy in the form of heated or chilled water). The third step calculates the fuel and energy required by the primary equipment to meet these loads and the peak demand on the utility system. It considers equipment efficiencies and part-load characteristics. It is often necessary to keep track of the different forms of energy, such as electrical, natural gas, or oil. In some cases, where calculations are required to ensure compliance with codes or standards, these energies must be converted to source energy or

The data-driven model has to meet requirements very different from the forward model. The data-driven model can only contain a relatively small number of parameters because of the limited and often repetitive information contained in the performance data. (For example, building operation from one day to the next is fairly repetitive.) It is thus a much simpler model that contains fewer terms representative of aggregated or macroscopic parameters (e.g., overall building heat loss coefficient and time constants). Because model parameters are deduced from actual building performance, it is much more likely to accurately capture as-built system performance, thus allowing more accurate prediction of future system behavior under certain specific circumstances. Performance data collection and model formulation need to be appropriately tailored for the specific circumstance, which often requires a higher level of user skill and expertise. In general, data-driven models are less flexible than forward models in evaluating energy implications of different design and operational alternatives, and so are not a substitute in this regard. To better understand the uses of data-driven models, consider some of the questions that a building professional may ask about an existing building with known energy consumption (Rabl 1988): • How does consumption compare with design predictions (and, in case of discrepancies, are they caused by anomalous weather, unintended building operation, improper operation, or other causes)? • How would consumption change if thermostat settings, ventilation rates, or indoor lighting levels were changed? • How much energy could be saved by retrofits to the building shell, changes to air handler operation from CV to VAV, or changes in the various control settings? • If retrofits are implemented, can one verify that the savings are due to the retrofit and not to other causes (e.g., the weather)? • How can one detect faults in HVAC equipment and optimize control and operation? All these questions are better addressed by the data-driven approach. The forward approach could also be used, for example, by going back to the blueprints of the building and of the HVAC system, and repeating the analysis performed at the design stage using actual building schedules and operating modes, but this is tedious and labor-intensive, and materials and equipment often perform differently in reality than as specified. Tuning the forward-simulation model is often awkward and labor intensive, although it is still an option (as adopted in the calibrated data-driven approach).

Energy Estimating and Modeling Methods CHOOSING AN ANALYSIS METHOD The most important step in selecting an energy analysis method is matching method capabilities with project requirements. The method must be capable of evaluating all design options with sufficient accuracy to make correct choices. The following factors apply generally (Sonderegger 1985): • Accuracy. The method should be sufficiently accurate to allow correct choices. Because of the many parameters involved in energy estimation, absolutely accurate energy prediction is not possible (Waltz 1992). ANSI/ASHRAE Standard 140, Method of Test for the Evaluation of Building Energy Analysis Computer Programs, was developed to identify and diagnose differences in predictions that may be caused by algorithmic differences, modeling limitations, coding errors, or input errors. More information on model validation and testing can be found in the Model Validation and Testing section of this chapter and in ANSI/ASHRAE Standard 140. • Sensitivity. The method should be sensitive to the design options being considered. The difference in energy use between two choices should be adequately reflected. • Versatility. The method should allow analysis of all options under consideration. When different methods must be used to consider different options, an accurate estimate of the differential energy use cannot be made. • Speed and cost. The total time (gathering data, preparing input, calculations, and analysis of output) to make an analysis should be appropriate to the potential benefits gained. With greater speed, more options can be considered in a given time. The cost of analysis is largely determined by the total time of analysis. • Reproducibility. The method should not allow so many vaguely defined choices that different analysts would get completely different results (Corson 1992). • Ease of use. This affects both the economics of analysis (speed) and the reproducibility of results.

Selecting Energy Analysis Computer Programs Selecting a building energy analysis program depends on its application, number of times it will be used, experience of the user, and hardware available to run it. The first criterion is the capability of the program to deal with the application. For example, if the effect of a shading device is to be analyzed on a building that is also shaded by other buildings part of the time, the ability to analyze detached shading is an absolute requirement, regardless of any other factors. Because almost all manual methods are now implemented on a computer, selection of an energy analysis method is the selection of a computer program. The cost of the computer facilities and the software itself are typically a small part of running a building energy analysis; the major costs are of learning to use the program and of using it. Major issues that influence the cost of learning a program include (1) complexity of input procedures, (2) quality of the user’s manual, and (3) availability of a good support system to answer questions. As the user becomes more experienced, the cost of learning becomes less important, but the need to obtain and enter a complex set of input data continues to consume the time of even an experienced user until data are readily available in electronic form compatible with simulation programs. Complexity of input is largely influenced by the availability of default values for the input variables. Default values can be used as a simple set of input data when detail is not needed or when building design is very conventional, but additional complexity can be supplied when needed. Secondary defaults, which can be supplied by the user, are also useful in the same way. Some programs allow the user to specify a level of detail. Then the program requests only the information appropriate to that level of detail, using default values for all others.

19.3 Quality of output is another factor to consider. Reports should be easy to read and uncluttered. Titles and headings should be unambiguous. Units should be stated explicitly. The user’s manual should explain the meanings of data presented. Graphic output can be very helpful. In most cases, simple summaries of overall results are the most useful, but very detailed output is needed for certain studies and also for debugging program input during the early stages of analysis. Before a final decision is made, manuals for the most suitable programs should be obtained and reviewed, and, if possible, demonstration versions of the programs should be obtained and run, and support from the software supplier should be tested. The availability of training should be considered when choosing a more complex program. Availability of weather data and a weather data processing subroutine or program are major features of a program. Some programs include subroutine or supplementary programs that allow the user to create a weather file for any site for which weather data are available. Programs that do not have this capability must have weather files for various sites created by the program supplier. In that case, the available weather data and the terms on which the supplier will create new weather data files must be checked. More information on weather data can be found in Chapter 14. Auxiliary capabilities, such as economic analysis and design calculations, are a final concern in selecting a program. An economic analysis may include only the ability to calculate annual energy bills from utility rates, or it might extend to calculations or even to life-cycle cost optimization. An integrated program may save time because some input data have been entered already for other purposes. The results of computer calculations should be accepted with caution, because the software vendor does not accept responsibility for the correctness of calculations or use of the program. Manual calculation should be done to develop a good understanding of underlying physical processes and building behavior. In addition, the user should (1) review the computer program documentation to determine what calculation procedures are used, (2) compare results with manual calculations and measured data, and (3) conduct sample tests to confirm that the program delivers acceptable results.

Tools for Energy Analysis The most accurate methods for calculating building energy consumption are the most costly because of their intense computational requirements and the expertise needed by the designer or analyst. Simulation programs that assemble component models into system models and then exercise those models with weather and occupancy data are preferred by experts for determining energy use in buildings. Often, energy consumption at a system or whole-building level must be estimated quickly to study trends, compare systems, or study building effects such as envelope characteristics. For these purposes, simpler methods, such as degree-day and bin, may be used. Table 1 classifies methods for analyzing building energy use as either forward or data-driven, and either steady-state or dynamic. The U.S. Department of Energy maintains an up-to-date listing of building energy software with links to other sites that describe energy modeling tools at http://www.energytoolsdirectory.gov.

COMPONENT MODELING AND LOADS CALCULATING SPACE SENSIBLE LOADS Calculating instantaneous space sensible load is a key step in any building energy simulation. The heat balance and weightingfactor methods are used for these calculations. A third method, the thermal-network method, is not widely used but shows promise. The instantaneous space sensible load is the rate of heat flow into the space air mass. This quantity, sometimes called the cooling load, differs from heat gain, which usually contains a radiative

19.4

2009 ASHRAE Handbook—Fundamentals Table 1 Classification of Analysis Methods For Building Energy Use Data-Driven

Method

Empirical or Calibrated Physical or Forward Black-Box Simulation Gray-Box

Comments

Steady-State Methods Simple linear regression (Kissock et al. 1998; Ruch and Claridge 1991) Multiple linear regression (Dhar 1995; Dhar et al. 1998, 1999a, 1999b; Katipamula et al. 1998; Sonderegger 1998) Modified degree-day method Variable-base degree-day method, or 3-P change point models (Fels 1986; Reddy et al. 1997; Sonderegger 1998) Change-point models: 4-P, 5-P (Fels 1986; Kissock et al. 1998) ASHRAE bin method and data-driven bin method (Thamilseran and Haberl 1995) ASHRAE TC 4.7 modified bin method (Knebel 1983) Multistep parameter identification (Reddy et al. 1999)

X

One dependent parameter, one independent parameter. May have slope and y-intercept. One dependent parameter, multiple independent parameters.

X

X X

— X

— —

— X

Based on fixed reference temperature of 65°F. Variable base reference temperatures.

X

X

X

X

Uses daily or monthly utility billing data and average period temperatures. Hours in temperature bin times load for that bin.

X

Modified bin method with cooling load factors.

X

Uses daily data to determine overall heat loss and ventilation of large buildings.

X

X

X

Uses equivalent thermal parameters (data-driven mode). Tabulated or as used in simulation programs.

X

X

X

X

X

X

X

X

X

X

X

X

Hourly and subhourly simulation programs with system models.

X

Subhourly simulation programs.

X

Connectionist models.

Dynamic Methods Thermal network (Rabl 1988; Reddy 1989; Sonderegger 1977) Response factors (Kusuda 1969; Mitalas 1968; Mitalas and Stephenson 1967; Stephenson and Mitalas 1967) Fourier analysis (Shurcliff 1984; Subbarao 1988) ARMA model (Rabl 1988; Reddy 1989; Subbarao 1986) PSTAR (Subbarao 1988) Modal analysis (Bacot et al. 1984; Rabl 1988) Differential equation (Rabl 1988) Computer simulation: DOE-2, BLAST, EnergyPlus (Crawley et al. 2001; Haberl and Bou-Saada 1998; Manke et al. 1996; Norford et al. 1994) Computer emulation (HVACSIM+, TRNSYS) (Clark 1985; Klein et al. 1994) Artificial neural networks (Kreider and Haberl 1994; Kreider and Wang 1991)

component that passes through the air and is absorbed by other bounding surfaces. Instantaneous space sensible load is entirely convective; even loads from internal equipment, lights, and occupants enter the air by convection from the surface of such objects or by convection from room surfaces that have absorbed the radiant component of energy emitted from these sources. However, some adjustment must be made when radiant cooling and heating systems are evaluated because some of the space load is offset directly by radiant transfer without convective transfer to the air mass. For equilibrium, the instantaneous space sensible load must match the heat removal rate of the conditioning equipment. Any imbalance in these rates changes the energy stored in the air mass. Customarily, however, the thermal mass (heat capacity) of the air itself is ignored in analysis, so the air is always assumed to be in thermal equilibrium. Under these assumptions, the instantaneous space sensible load and rate of heat removal are equal in magnitude and opposite in sign. The weighting-factor and heat balance methods use conduction transfer functions (or their equivalents) to calculate transmission heat gain or loss. The main difference is in the methods used to

Frequency domain analysis convertible to time domain. Autoregressive moving average (ARMA) model. Combination of ARMA and Fourier series; includes loads in time domain. Building described by diagonalized differential equation using nodes. Analytical linear differential equation.

calculate the subsequent internal heat transfers to the room. Experience with both methods has indicated largely the same results, provided the weighting factors are determined for the specific building under analysis.

Heat Balance Method The heat balance method for calculating net space sensible loads, as described in the ASHRAE Toolkit for Building Load Calculations (Pedersen et al. 2001, 2003), is more fundamental than the weighting-factor method. Its development relies on the first law of thermodynamics (conservation of energy) and the principles of matrix algebra. Because it requires fewer assumptions than the weighting-factor method, it is also more flexible. However, the heat balance method requires more calculations at each point in the simulation process, using more computer time. The weighting factors used are determined with a heat balance procedure. Although not necessary, linearization is commonly used to simplify the radiative transfer formulation. The heat balance method allows the net instantaneous sensible heating and/or cooling load to be calculated on the space air mass.

Energy Estimating and Modeling Methods

19.5

Generally, a heat balance equation is written for each enclosing surface, plus one equation for room air. This set of equations can then be solved for the unknown surface and air temperatures. Once these temperatures are known, they can be used to calculate the convective heat flow to or from the space air mass. The heat balance method is developed in Chapter 18 for use in design cooling load calculations, so a fuller description is omitted here. However, the heat balance procedure described in Chapter 18 is aimed at obtaining the design cooling load for a fixed zone air temperature. For building energy analysis purposes, it is preferable to know the actual heat extraction rate. This may be determined by recasting Equation (27) of Chapter 18 so that the system heat transfer is determined simultaneously with the zone air temperature. The system heat transfer is the rate at which heat is transferred to the space by the system. Although this can be done by simultaneously modeling the zone and the system (Taylor et al. 1990, 1991), it is convenient to make a simple, piecewise-linear representation of the system known as a control profile. This usually takes the form q sys = a + bt a j

(1)

j

where q sysj = system heat transfer at time step j, Btu/h a, b = coefficients that apply over a certain range of zone air temperatures t a j = zone air temperature at time step j, °F

System heat transfer q sysj may be considered positive when heating is provided to the space and negative when cooling is provided. It is equal in magnitude but opposite in sign to the zone cooling load, as defined in Chapter 18, when zone air temperature is fixed. Substituting Equation (1) into Equation (27) of Chapter 18 and solving for zone air temperature, N

a + ¦ A i h ci t si + UcV infil t o + UcV vent t v + q c ,int i=1

i,j

j

j

j

j

j

t a = --------------------------------------------------------------------------------------------------------------------------j

N

– b + ¦ A i h ci + UcV infil + UcV vent j

(2)

j

i=1

where N = number of zone surfaces Ai = area of ith surface, ft2 hci = convection coefficient for ith surface, Btu/h·ft2 ·°F t si = surface temperature for ith surface at time step j, °F i, j U = density, lbm/ft3 c = specific heat of air, Btu/lbm ·°F V = volumetric flow rate of air, ft3/h t o = outdoor air temperature at time step j, °F j t v = ventilation air temperature at time step j, °F j q c int = sum of convective portions of all internal heat gains at time j step j, Btu/h

The zone air heat balance equation [Equation (2)] must be solved simultaneously with the interior and exterior surface heat balance equations [Equations (26) and (25) in Chapter 18]. Also, the correct temperature range must be found to use the proper set of a and b coefficients; this may be done iteratively. Once the zone air temperature is found, the actual system heat transfer rate may be found directly from Equation (1). Beyond treatment of system heat transfer, other considerations that may be important in building energy analysis programs include simulations over periods as long as a year, treatment of radiant cooling and heating systems, treatment of interzone heat transfer, modeling convection heat transfer, and modeling radiation heat transfer. The heat balance method in Chapter 18 assumes the use of a single design day. In a building energy analysis program, it is most

commonly used with a year’s worth of design weather data. In this case, the first day of the year is usually simulated several times until a steady-periodic response is obtained. Then, each day is simulated sequentially, and, where needed, historical data for surface temperatures and heat fluxes from the previous day are used. When radiant cooling and heating systems are evaluated, the radiant source should be identified as a room surface. The calculation procedure considers the radiant source in the heat balance analysis. Therefore, the heat balance method is preferred over the weighting-factor method for evaluating radiant systems. Strand and Pedersen (1997) describe implementation of heat source conduction transfer functions, which may be used for modeling radiant panels, into a heat balance-based building simulation program. In principle, this method extends directly to multiple spaces, with heat transfer between zones. In this case, some surface temperatures appear in the surface heat balance equations for two different zones. In practice, however, the size of the coefficient array required for solving the simultaneous equations becomes prohibitively large, and the solution time excessive. For this reason, many programs solve only one space at a time and assume that adjacent space temperatures are either the same as the space in question or some assigned, constant value. Other approaches may remove this limitation (Walton 1980). Relatively simple exterior and interior convection models may be used for design cooling load calculation procedures. However, more sophisticated exterior convection models (Cooper and Tree 1973; Fracastoro et al. 1982; Melo and Hammond 1991; Walton 1983; Yazdanian and Klems 1994) that incorporate the effects of wind speed, wind direction, surface orientation, etc., may be preferable. More detailed interior convection correlations for use in buildings are also available (Alamdari and Hammond 1982, 1983; Altmayer et al. 1983; Bauman et al. 1983; Bohn et al. 1984; Chandra and Kerestecioglu 1984; Khalifa and Marshall 1990; Spitler et al. 1991; Walton 1983). Also, more detailed models of exterior [e.g., Cole (1976); Walton (1983)] and interior [e.g., Carroll (1980); Davies (1988); Kamal and Novak (1991); Steinman et al. (1989); Walton (1980)] long-wave radiation transfer have been implemented in detailed building simulation programs.

Weighting-Factor Method The weighting-factor method of calculating instantaneous space sensible load is a compromise between simpler methods (e.g., steady-state calculation) that ignore the ability of building mass to store energy, and more complex methods (e.g., complete energy balance calculations). With this method, space heat gains at constant space temperature are determined from a physical description of the building, ambient weather conditions, and internal load profiles. Along with the characteristics and availability of heating and cooling systems for the building, space heat gains are used to calculate air temperatures and heat extraction rates. This discussion is in terms of heat gains, cooling loads, and heat extraction rates. Heat losses, heating loads, and heat addition rates are merely different terms for the same quantities, depending on the direction of the heat flow. The weighting factors represent Z-transfer functions (Kerrisk et al. 1981; York and Cappiello 1982). The Z-transform is a method for solving differential equations with discrete data. Two groups of weighting factors are used: heat gain and air temperature. Heat gain weighting factors represent transfer functions that relate space cooling load to instantaneous heat gains. A set of weighting factors is calculated for each group of heat sources that differ significantly in the (1) relative amounts of energy appearing as convection to the air versus radiation, and (2) distribution of radiant energy intensities on different surfaces. Air temperature weighting factors represent a transfer function that relates room air temperature to the net energy load of the room. Weighting factors for a particular heat source are determined by

19.6

2009 ASHRAE Handbook—Fundamentals

introducing a unit pulse of energy from that source into the room’s network. The network is a set of equations that represents a heat balance for the room. At each time step (1 h intervals), including the initial introduction, the energy flow to the room air represents the amount of the pulse that becomes a cooling load. Thus, a long sequence of cooling loads can be generated, from which weighting factors are calculated. Similarly, a unit pulse change in room air temperature can be used to produce a sequence of cooling loads. A two-step process is used to determine the air temperature and heat extraction rate of a room or building zone for a given set of conditions. First, the room air temperature is assumed to be fixed at some reference value, usually the average air temperature expected for the room over the simulation period. Instantaneous heat gains are calculated based on this constant air temperature. Various types of heat gains are considered. Some, such as solar energy entering through windows or energy from lighting, people, or equipment, are independent of the reference temperature. Others, such as conduction through walls, depend directly on the reference temperature. A space sensible cooling load for the room, defined as the rate at which energy must be removed from the room to maintain the reference value of the air temperature, is calculated for each type of instantaneous heat gain. The cooling load generally differs from the instantaneous heat gain because some energy from heat gain is absorbed by walls or furniture and stored for later release to the air. At time T, the calculation uses present and past values of the instantaneous heat gain (qT, qT–1), past values of the cooling load (QT–1, QT–2, ...), and the heat gain weighting factors (v0, v1, v2, ..., w1, w2, ...) for the type of heat gain under consideration. Thus, for each type of heat gain qT, cooling load QT is calculated as QT = v0 qT + v1 qT –1 + } – w1 QT –1 – w2 QT –2 – }

(3)

The heat gain weighting factors are a set of parameters that determine how much of the energy entering a room is stored and how rapidly stored energy is released later. Mathematically, the weighting factors are parameters in a Z-transfer function relating the heat gain to the cooling load. These weighting factors differ for different heat gain sources because the relative amounts of convective and radiative energy leaving various sources differ and because the distribution of radiative energy can differ. Heat gain weighting factors also differ for different rooms because room construction affects the amount of incoming energy stored by walls or furniture and the rate at which it is released. Sowell (1988) showed the effects of 14 zone design parameters on zone dynamic response. After the first step, cooling loads from various heat gains are added to give a total cooling load for the room. In the second step, the total cooling load is used (with information on the room’s HVAC system and a set of air temperature weighting factors) to calculate the actual heat extraction rate and air temperature. The actual heat extraction rate differs from the cooling load (1) because, in practice, air temperature can vary from the reference value used to calculate the cooling load, or (2) because of HVAC system characteristics. Deviation of air temperature tT from the reference value at hour T is calculated as t T = 1 e g 0 + > Q T – ER T + P 1 Q T – 1 – ER T –1 + P 2 Q T – 2 – ER T – 2 + } – g 1 t T – 1 – g 2 t T – 2 – } @

(4)

where ERT is the energy removal rate of the HVAC system at hour T, and g0, g1, g2, …, P1, P2, … are air temperature weighting factors, which incorporate information about the room, particularly thermal coupling between the air and the storage capacity of the building mass. Values of weighting factors for typical building rooms are presented in the following table. One of the three groups of weighting

factors, for light, medium, and heavy construction rooms, can be used to approximate the behavior of any room. Some automated simulation techniques allow weighting factors to be calculated specifically for the building under consideration. This option improves the accuracy of the calculated results, particularly for a building with an unconventional design. McQuiston and Spitler (1992) provided electronic tables of weighting factors for a large number of parametrically defined zones. Normalized Coefficients of Space Air Transfer Functions Room Envelope Construction

g 0*

g 1*

g 2*

Btu/h·ft· °F

p0

p1

Dimensionless

Light

1.68

–1.73

0.05

1.0

–0.82

Medium

1.81

–1.89

0.08

1.0

–0.87

Heavy

1.85

–1.95

0.10

1.0

–0.93

Two assumptions are made in the weighting-factor method. First, the processes modeled are linear. This assumption is necessary because heat gains from various sources are calculated independently and summed to obtain the overall result (i.e., the superposition principle is used). Therefore, nonlinear processes such as radiation or natural convection must be approximated linearly. This assumption is not a significant limitation because these processes can be linearly approximated with sufficient accuracy for most calculations. The second assumption is that system properties influencing the weighting factors are constant (i.e., they are not functions of time). This assumption is necessary because only one set of weighting factors is used during the entire simulation period. This assumption can limit the use of weighting factors in situations where important room properties vary during the calculation (e.g., the distribution of solar radiation incident on the interior walls of a room, which can vary hourly, and inside surface heat transfer coefficients). When the weighting-factor method is used, a combined radiative/ convective heat transfer coefficient is used as the inside surface heat transfer coefficient. This value is assumed constant even though, in a real room, (1) radiant heat transferred from a surface depends on the temperature of other room surfaces (not on room air temperature) and (2) the combined heat transfer coefficient is not constant. Under these circumstances, an average value of the property must be used to determine the weighting factors. Cumali et al. (1979) investigated extensions to the weighting-factor method to eliminate this limitation.

Thermal-Network Methods Although implementations of the thermal-network method vary, they all have in common the discretization of the building into a network of nodes, with interconnecting paths through which energy flows. In many respects, thermal-network models may be considered a refinement of the heat balance method. Where the heat balance model generally uses one node for zone air, the thermalnetwork method might use multiple nodes. For each heat transfer element (wall, roof, floor, etc.), the heat balance model generally has one interior and one exterior surface node; the thermal-network model may include additional nodes. Heat balance models generally use simple methods for distributing radiation from lights; thermalnetwork models may model the lamp, ballast, and luminaire housing separately. Furthermore, thermal-network models depend on a heat balance at each node to determine node temperature and energy flow between all connected nodes. Energy flows may include conduction, convection, and short- or long-wave radiation. For any mode of energy flow, a range of techniques may be used to model the energy flow between two nodes. Taking conduction heat transfer as an example, the simplest thermal-network model would be a resistance/capacitance network (Sowell 1990). By refining network discretization, the models become what are commonly

Energy Estimating and Modeling Methods

19.7

thought of as finite-difference or finite-volume models (Clarke 2001; Lewis and Alexander 1990; Walton 1993). Thermal-network models generally use a set of algebraic and differential equations. In most implementations, the solution procedure is separated from the models so that, in theory, different solvers might be used to perform the simulation. In contrast, most heat balance and weighting factor programs interweave the solution technique with the models. Various solution techniques have been used in conjunction with thermal-network models. Examples include graph theory combined with Newton-Raphson and predictor/corrector ordinary differential equation integration (Buhl et al. 1990) and the use of Euler explicit integration combined with sparse matrix techniques (Walton 1993). Of the three zone models discussed, thermal-network models are the most flexible and have the greatest potential for high accuracy. However, they also require the most computation time, and, in current implementations, require more user effort to take advantage of the flexibility.

Z = annual angular frequency (Z = 1.992 u 10–7 rad/s) I = phase lag between total slab heat loss/gain and soil surface temperature, radians

Equation (5) is convenient and flexible because it can be used to calculate the foundation heat loss/gain not only at any time but also at design conditions and for any time period (such as a heating season or 1 year). In particular, the design heat loss/gain load qdes for a slab foundation is obtained as follows: q des = q mean + q amp

Parameters qmean and qamp are functions of variables such as building dimensions, soil properties, and insulation R-values. Expressions developed by nondimensional analysis allow calculation of qmean and qamp. The soil conductivity is normalized to form four parameters (Uo, G, H, and D): ks U o = ------------------------ A e P eff, b

GROUND HEAT TRANSFER The thermal performance of building foundations, including guidelines for placement of insulation, is described in Chapter 25 of this volume and Chapter 43 of the 2007 ASHRAE Handbook— HVAC Applications. Chapter 18 provides information for calculating transmission heat losses through slab foundations and through basement walls and floors. These calculations are appropriate for design loads but are not intended for estimating annual energy usage. This section provides simplified calculation methods suitable for energy estimates over time periods of arbitrary length. Thermal performance of building foundations has been largely ignored. It is estimated that, in the early 1970s, only 10% of the total energy use of a typical U.S. home was attributed to heat transfer from its foundation (Labs et al. 1988). Since then, thermal performance of above-grade building elements has improved significantly, and the contribution of ground-coupled heat transfer to total energy use in a typical U.S. home has increased. Shipp and Broderick (1983) estimated that heat transfer from an uninsulated basement in Columbus, Ohio, can represent up to 67% of the total building envelope heating load. Earth-contact heat transfer, rated at 1 to 3 quadrillion Btu of energy annually in U.S. buildings, has an effect similar to infiltration on annual heating and cooling loads in residential buildings (Claridge 1988a). Adding insulation to building foundations is estimated to save up to 0.5 quadrillion Btu of annual energy use in the U.S. (Labs et al. 1988).

q T = q mean + q amp sin Z T + I where qmean = annual-mean heat loss/gain, Btu/h qamp = heat loss/gain amplitude, Btu/h T = time, s

(5)

(7)

where ks = soil thermal conductivity, Btu·ft/h·ft2 ·°F P = slab perimeter, ft A = slab area, ft2

For mean calculations, A e P eff b mean = > 1 + b eff – 0.4 + e

– Hb

@ A e P b

(8)

For annual calculations, A e P eff b amp = 1 + b eff e

– Hb

A e P b

(9)

where A e P H b = -----------------bk s R eq

(10)

B b eff = ----------------- A e P b

(11)

where B = basement depth, ft (0 ft for slab). Z G = k s R eq ----Ds

Simplified Calculation Method for Slab Foundations and Basements The design tool for slab-on-grade floors developed by Krarti and Chuangchid (1999) can be modified to a simplified design tool for calculating heat loss for slabs and basements. The design tool is easy to use and requires straightforward input parameters with continuously variable values, including foundation size, insulation R-values, soil thermal properties, and indoor and outdoor temperatures. The simplified method provides a set of equations suitable for estimating the design, seasonal, and annual total heat loss of a slab or a basement as a function of a wide range of variables. When the indoor temperature of the building is maintained constant, the ground-coupled heat transfer q(T) varies with time according to the following equation:

(6)

(12)

where Req = equivalent thermal resistance for entire slab, ft2 ·h·°F/Btu Ds = soil thermal diffusivity, ft2/s

For uniform insulation configurations (placed horizontally beneath the slab floor), R eq = R f + R i

(13)

where Rf = thermal resistance of floor, ft2 ·h·°F/Btu Ri = thermal resistance of insulation, ft2 ·h·°F/Btu

For partial insulation configurations (both horizontal and vertical), Rf R eq = -------------------------------------------------------Ri c 1 – § ----------- ---------------------- · © A e P Ri + Rf ¹

(14)

19.8

2009 ASHRAE Handbook—Fundamentals

Table 2 Coefficients m and a for Slab-Foundation Heat Transfer Calculations Insulation Placement

m

a

Uniform horizontal

0.40

0.25

Partial horizontal

0.34

0.20

Vertical

0.28

0.13

Temperatures Indoor temperature tr = 68°F Annual average ambient temperature ta = 43°F Annual amplitude ambient temperature tamp = 36°F Annual angular frequency Z = 1.992 u 10–7 rad/s Step 2. Calculate qmean and qamp values. The various normalized parameters are first calculated using Equations (7) to (18). Then, the annual mean and amplitude of the foundation slab heat loss/gain are determined using Equations (19) and (20).

where c = insulation length of slab, ft. A e P eff, b H = ------------------------k s R eq

(15)

1- · H D = ln 1 + H § 1 + --© H¹

(16)

ks U o = --------------- = 0.70 ---------- = 0.0711 A e P 9.84 A e P 9.84 H = ---------------- = ------------------------------------- = 0.6155 k s R eq 0.70 2.84 + 20 1- · H = 1.074 D = ln 1 + H § 1 + --© H¹

The effective heat-transfer coefficients for mean heat flow Ueff,mean and heat-flow amplitude Ueff,amp, Btu/h·ft2 ·°F, are U eff , mean = mU o D

–7

Z 1.992 u10 G = k s R eq ----- = 0.70 2.84 + 20 --------------------------- = 2.8141 –6 Ds 6.43 u10

(17)

Therefore,

U eff , amp = aU o D

0.16

G

– 0.6

(18)

where the dimensionless coefficients m and a depend on the insulation placement configurations and are provided in Table 2. The annual-mean slab foundation and basement heat loss/gain can now be defined as

q mean = U eff mean A t r – t a = 0.40 u 0.0711 u 1.074 u 1615 u 68 – 43 = 1233 Btu/h and q amp = U eff amp At amp

q mean = U eff, mean A t a – t r

(19)

= 0.25 u 0.0711 u 1.074

0.16

u 2.8141

– 0.6

u 1615 u 36

= 562 Btu/h

where ta = annual average ambient dry-bulb temperature, °F tr = annual average indoor dry-bulb temperature, °F

The heat loss/gain amplitude for slab foundations and basements is

Example 2. Calculation for Basements. Determine the annual mean and amplitude of total basement heat loss for a building located in Denver, Colorado. Solution:

q amp = U eff, amp At amp

(20)

Step 1. Provide the required input data. Dimensions Basement width = 32.81 ft Basement length = 49.22 ft Basement wall height B = 4.92 ft Basement slab and wall total area = 2422 ft2 Ratio of slab and wall area to slab and wall perimeter, (A/P )b = 11.91 ft 4 in. thick reinforced concrete slab, thermal resistance Rf = 2.84 h·ft2 ·°F/Btu

where tamp = annual amplitude ambient temperature, °F. This simplified model for slab-foundation and basement heat flows provides accurate predictions when A/P is larger than 1.5 ft. To illustrate the use of the simplified models, two examples are presented: one for a slab-on-grade floor for a building insulated with uniform horizontal insulation, and one for a basement structure insulated with uniform insulation. Example 1. Calculation for Slab Foundations. Determine the annual mean and annual amplitude of total slab heat loss for the slab foundation illustrated in Figure 2. The building is located in Denver, Colorado.

Soil Thermal Properties Soil thermal conductivity Soil thermal diffusivity

ks = 0.70 Btu·ft/h·ft2 ·°F Ds = 4.812 u 10–6 ft2/s

Solution: Step 1. Provide the required input data.

Fig. 2

Slab Foundation for Example 1

Dimensions Slab width = 32.81 ft Slab length = 49.22 ft Ratio of slab area to slab perimeter, A/P = 9.84 ft 4 in. thick reinforced concrete slab, thermal resistance Rf = 2.84 h·ft2 ·°F/Btu Soil Thermal Properties Soil thermal conductivity Soil density Soil thermal diffusivity

ks = 0.70 Btu/h·ft·°F U = 168.56 lbm/ft3 Ds = 6.43 u 10–6 ft2/s

Insulation Uniform insulation R-value Ri = 20.0 h·ft2 ·°F/Btu

Fig. 2 Slab Foundation for Example 1

Energy Estimating and Modeling Methods SECONDARY SYSTEM COMPONENTS

Insulation Uniform insulation R-value Ri = 6.54 h·ft2 ·°F/Btu Temperatures Indoor temperature, tr = 71.6°F Annual average ambient temperature, ta = 50°F Annual amplitude ambient temperature, tamp = 23°F Annual angular frequency, Z = 1.992 u 10–7 rad/s Step 2. Calculate qmean and qamp values. The normalized parameters are first calculated using Equations (7) to (18). Then, the annual mean and amplitude of the basement heat loss are determined using Equations (19) and (20). A e P 11.91 H b = -----------------b- = ------------------------------------------- = 1.8139 0.70 2.84 + 6.54 k s R eq 4.92 B b eff = ------------------ = ------------- = 0.4131 11.91 A e P b A e P eff b mean = > 1 + 0.4131 – 0.4 + e A e P eff b amp = 1 + 0.4131 e

– 1.8139

– 1.8139

@ u 11.91 = 10.7440

u 11.91 = 12.7120

ks 0.70 - = ------------------- = 0.0652 U o mean = -------------------------------------10.7440 A e P eff b mean ks 0.70 = 0.0551 U o amp = -----------------------------------= ----------------- A e P eff b amp 12.7120 A e P eff b mean 10.7440 H mean = -------------------------------------- = ------------------------------------------- = 1.6363 0.70 2.84 + 6.54 k s R eq A e P eff b amp 12.7120 = -----------------------------------------H amp = ------------------------------------ = 1.9360 0.70 2.84 + 6.54 k s R eq 1 D mean = ln 1 + H mean § 1 + ----------------· © ¹ H

H mean

H amp

= 1.8832

–7

1.992 u 10 Z G = k s R eq ----- = 0.70 2.84 + 6.54 ------------------------------- = 1.3359 –7 Ds 48.12 u 10 Therefore, q mean = U eff mean A t a – t r = 0.4 u 0.0652 u 1.7498 u 2422 u 71.6 – 50 = 2387 Btu/h and q amp = U eff amp At amp = 0.25 u 0.0551 u 1.8832 u 1.3359

– 0.6

0.16

u 2422 u 23 = 714 Btu/h

Table 3 compares results of the simplified method presented here and the more exact interzone temperature profile estimation (ITPE) (Krarti 1994a, 1994b; Krarti et al. 1988a, 1988b).

Table 3 Method Simplified ITPE solution

Secondary HVAC systems generally include all elements of the overall building energy system between a central heating and cooling plant and the building zones. The precise definition depends heavily on the building design. A secondary system typically includes air-handling equipment; air distribution systems with associated ductwork; dampers; fans; and heating, cooling, and humidity-conditioning equipment. They also include liquid distribution systems between the central plant and the zone and airhandling equipment, including piping, valves, and pumps. Although the exact design of secondary systems varies dramatically among buildings, they are composed of a relatively small set of generic HVAC components. These components include distribution components (e.g., pumps/fans, pipes/ducts, valves/dampers, headers/plenums, fittings) and heat and mass transfer components (e.g., heating coils, cooling and dehumidifying coils, liquid heat exchangers, air heat exchangers, evaporative coolers, steam injectors). Most secondary systems can be described by simply connecting these components to form the complete system. Energy estimation through computer simulation often mimics the modular construction of secondary systems by using modular simulation elements [e.g., the ASHRAE HVAC2 Toolkit (Brandemuehl 1993; Brandemuehl and Gabel 1994), the simulation program TRNSYS (Klein et al. 1994), and Annex 10 activities of the International Energy Agency]. To the extent that the secondary system consumes energy and transfers energy between the building and central plant, an energy analysis can be performed by characterizing the energy consumption of the individual components and the energy transferred among system components. In fact, few secondary components consume energy directly, except fans, pumps, furnaces, direct-expansion air-conditioning package units with gasfired heaters, and inline heaters. In this chapter, secondary components are divided into two categories: distribution components and heat and mass transfer components.

Fans, Pumps, and Distribution Systems = 1.7498

mean

1 D amp = ln 1 + H amp § 1 + ------------- · © H amp ¹

19.9

Example 2 Heat Loss per Unit Area for Simplified and ITPE Methods Mean (qmean), Btu/h

Amplitude (qamp ), Btu/h

2387 2245

714 724

The distribution system of an HVAC system affects energy consumption in two ways. First, fans and pumps consume electrical energy directly, based on the flow and pressures under which the device operates. Ducts and dampers, or pipes and valves, and the system control strategies affect the flow and pressures at the fan or pump. Second, thermal energy is often transferred to (or from) the fluid by (1) heat transfer through pipes and ducts and (2) electrical input to fans and pumps. Analysis of system components should, therefore, account for both direct electrical energy consumption and thermal energy transfer. Fan and pump performance are discussed in Chapters 20 and 43 of the 2008 ASHRAE Handbook—HVAC Systems and Equipment. In addition, Chapter 21 of this volume covers pressure loss calculations for airflow in ducts and duct fittings. Chapter 22 presents a similar discussion for fluid flow in pipes. Although these chapters do not specifically focus on energy estimation, energy use is governed by the same performance characteristics and engineering relationships. Strictly speaking, performance calculations of a building’s fan and air distribution systems require a detailed pressure balance on the entire network. For example, in an air distribution system, airflow through the fan depends on its physical characteristics, operating speed, and pressure differential across the fan. Pressure drop through the duct system depends on duct design, position of all dampers, and airflow through the fan. Interaction between the fan and duct system results in a set of coupled, nonlinear algebraic equations. Models and subroutines for performing these calculations are available in the ASHRAE HVAC2 Toolkit (Brandemuehl 1993). Detailed analysis of a distribution system requires flow and pressure balancing among the components, but nearly all commercially

19.10

2009 ASHRAE Handbook—Fundamentals

available energy analysis methods approximate the effect of the interactions with part-load performance curves. This eliminates the need to calculate pressure drop through the distribution system at off-design conditions. Part-load curves are often expressed in terms of a power input ratio as a function of the part-load ratio, defined as the ratio of part-load flow to design flow: Q W PIR = ----------- = f plr § -------------· © Q full ¹ Wfull

(21)

where PIR W Wfull Q Qfull fplr

= = = = = =

power input ratio fan motor power at part load, W fan motor power at full load or design, W fan airflow rate at part load, cfm fan airflow rate at full load or design, cfm regression function, typically polynomial

The exact shape of the part-load curve depends on the effect of flow control on the pressure and fan efficiency and may be calculated using a detailed analysis or measured field data. Figure 3 shows the relationship for three typical fan control strategies, as represented in a simulation program (York and Cappiello 1982). In the simulation program, the curves are represented by polynomial regression equations. Models and subroutines for performing these calculations are also available in the ASHRAE HVAC2 Toolkit (Brandemuehl 1993). Figure 4 shows an example of a similar curve for the part-load operation of a fan system in a monitored building (Brandemuehl and Bradford 1999). In this particular case, the fan system represents ten separate air handlers, each with supply and return fans, operating with variable-speed fan control to maintain a set duct static pressure. Notice that, although the shape of the curve is similar to the variablespeed curve of Figure 3, the measured data for this particular system exhibit a more linear relationship between power and flow. Heat transferred to the airstream because of fan operation increases air temperature. Although fan shaft power directly affects heat transfer, motor inefficiencies also heat the air if the motor is mounted inside the airstream. For pumps, this contribution is typically assumed to be zero. The following equation provides a convenient and general model to calculate the heat transferred to the fluid: q fluid = > K m + 1 – K m f m, loss @W

(22)

where qfluid = heat transferred to fluid, Btu/h

Fig. 3

Part-Load Curves for Typical Fan Operating Strategies

fm, loss = fraction of motor heat loss transferred to fluid stream, dimensionless (= 1 if fan mounted in airstream, = 0 if fan mounted outside airstream) W = fan motor power, Btu/h Km = motor efficiency

Heat and Mass Transfer Components Secondary HVAC systems comprise heat and mass transfer components (e.g., steam-based air-heating coils, chilled-water cooling and dehumidifying coils, shell-and-tube liquid heat exchangers, air-to-air heat exchangers, evaporative coolers, steam injectors). Although these components do not consume energy directly, their thermal performance dictates interactions between building loads and energy-consuming primary components (e.g., chillers, boilers). In particular, secondary component performance determines the entering fluid conditions for primary components, which in turn determine energy efficiencies of primary equipment. Accurate energy calculations cannot be performed without appropriate models of the system heat and mass transfer components. For example, load on a chiller is typically described as the sum of zone sensible and latent loads, plus any heat gain from ducts, plenums, fans, pumps, and piping. However, the chiller’s energy consumption is determined not only by the load but also by the return chilled-water temperature and flow rate. The return water condition is determined by cooling coil performance and part-load operating strategy of the air and water distribution system. The cooling coil might typically be controlled to maintain a constant leaving air temperature by modulating water flow through the coil. In such a scenario, the cooling coil model must be able to calculate the leaving air humidity, water temperature, and water flow rate given the cooling coil design characteristics and entering air temperature and humidity, airflow, and water temperature. Virtually all building energy simulation programs include, and require, models of heat and mass transfer components. These models are generally relatively simple. Whereas a coil designer might use a detailed tube-by-tube analysis of conduction and convection heat transfer and condensation on fin surfaces to develop an optimal combination of fin and tube geometry, an energy analyst is more interested in determining changes in leaving fluid states as operating conditions vary during the year. In addition, the energy analyst is likely to have limited design data on the equipment and, therefore, requires a model with very few parameters that depend on equipment geometry and detailed design characteristics. A typical approach to modeling heat and mass transfer components for energy calculations is based on an effectivenessNTU heat exchanger model (Kays and London 1984). The effectiveness-NTU (number of transfer units) model is described in most heat transfer textbooks and briefly discussed in Chapter 4.

Fig. 4 Fan Part-Load Curve Obtained from Measured Field Data under ASHRAE 823-RP

Fig. 3 Part-Load Curves for Typical Fan Operating Strategies

Fig. 4 Fan Part-Load Curve Obtained from Measured Field Data under ASHRAE RP-823

(York and Cappiello 1982)

(Brandemuehl and Bradford 1999)

Energy Estimating and Modeling Methods It is particularly appropriate for describing leaving fluid conditions when entering fluid conditions and equipment design characteristics are known. Also, this model requires only a single parameter to describe the characteristics of the exchanger: the overall transfer coefficient UA, which can be determined from limited design performance data. Because the classical effectiveness methods were developed for sensible heat exchangers, they are used to perform energy calculations for a variety of sensible heat exchangers in HVAC systems. For typical finned-tube air-heating coils, the crossflow configuration with both fluid streams unmixed is most appropriate. The same configuration typically applies to air-to-air heat exchangers. For liquidto-liquid exchangers, tube-in-tube equipment can be modeled as parallel or counterflow, depending on flow directions; shell-andtube equipment can be modeled as either counter- or crossflow, depending on the extent of baffling and the number of tube passes. The energy analyst must determine the UA to describe the operations of a specific heat exchanger. There are typically two approaches to determine this important parameter: direct calculation and manufacturers’ data. Given detailed information about the materials, geometry, and construction of the heat exchanger, fundamental heat transfer principles can be applied to calculate the overall heat transfer coefficient. However, the method most appropriate for energy estimation is using manufacturers’ performance data or direct measurements of installed performance. In reporting the design performance of a heat exchanger, a manufacturer typically gives the heat transfer rate under various operating conditions, with operating conditions described in terms of entering fluid flow rates and temperatures. The effectiveness and UA can be calculated from the given heat transfer rate and entering fluid conditions. Example 3. An energy analyst seeks evaluate a hot-water heating system that includes a hot-water heating coil. The energy analysis program uses an effectiveness-NTU model of the coil and requires the UA of the coil as an input parameter. Although detailed information on the coil geometry and heat transfer surfaces is not available, the manufacturer states that the one-row hot-water heating coil delivers 818,000 Btu/h of heat under the following design conditions: Design Performance Entering water temperature thi = 175°F Water mass flow rate m· h = 661 lb/min Entering air temperature tci = 68°F Air mass flow rate m· c = 1058 lb/min Design heat transfer q = 818,000 Btu/h Solution: First determine the heat exchanger UA from design data, then use UA to predict performance at off-design conditions. EffectivenessNTU relationships are used for both steps. The key assumption is that the UA is constant for both operating conditions. a) An examination of flow rates and fluid specific heats allows calculation of the hot-fluid capacity rate Ch and the cold-fluid capacity rate Cc at design conditions, and the capacity rate ratio Z. C h = m· c p h = 661 1.00 60 = 39 ,660 Btu/h · °F C c = m· c p c = 1058 0.24 60 = 15 ,235 Btu/h · °F C max = C h

C min = C c

C min - = 0.384 Z = ----------C max where cp is specific heat and cmax and cmin are the larger and smaller of the capacity rates, respectively, b) Effectiveness can be directly calculated from the heat transfer definition. t co – t ci q e Cc 818 ,000 e 15 ,235 = --------------------- = --------------------------------------------- = 0.502 H = --------------------- t hi – t ci t hi – t ci 175 – 68 where tco is the leaving air temperature.

19.11 c) The effectiveness-NTU relationships for a crossflow heat exchanger with both fluids unmixed allow calculation of the effectiveness in terms of the capacity rate ratio Z and the NTU [the relationships are available from most heat transfer textbooks and, specifically, in Kays and London (1984)]. Given the effectiveness and capacity rate ratio, NTU = 0.804. d) The heat transfer UA is then determined from the definition of the NTU. UA = C min NTU = 15 ,235 0.804 = 12 ,250 Btu/h · °F

Application to Cooling and Dehumidifying Coils Analysis of air-cooling and dehumidifying coils requires coupled, nonlinear heat and mass transfer relationships. These relationships form the basis for all HVAC components with moisture transfer, including cooling coils, cooling towers, air washers, and evaporative coolers. Although the complex heat and mass transfer theory presented in many textbooks is often required for cooling coil design, simpler models based on effectiveness concepts are usually more appropriate for energy estimation. For example, the bypass factor is a form of effectiveness in the approach of the leaving air temperature to the apparatus dew-point, or coil surface, temperature. The effectiveness-NTU method is typically developed and applied in analysis of sensible heat exchangers, but it can also be used to analyze other types of exchangers, such as cooling and dehumidifying coils, that couple heat and mass transfer. By redefining the state variables, capacity rates, and overall exchange coefficient of these enthalpy exchangers, the effectiveness concept may be used to calculate heat transfer rates and leaving fluid states. For sensible heat exchangers, the state variable is temperature, the capacity is the product of mass flow and fluid specific heat, and the overall transfer coefficient is the conventional overall heat transfer coefficient. For cooling and dehumidifying coils, the state variable becomes moist air enthalpy, the capacity has units of mass flow, and the overall heat transfer coefficient is modified to reflect enthalpy exchange. This approach is the basis for models by Brandemuehl (1993), Braun (1988), Elmahdy and Mitalas (1977), and Threlkeld (1970). The same principles also underlie the coil model described in Chapter 22 of the 2008 ASHRAE Handbook—HVAC Systems and Equipment. The effectiveness model is based on the observation that, for a given set of entering air and liquid conditions, the heat and mass transfer are bounded by thermodynamic maximum values. Figure 5 shows the limits for leaving air states on a psychrometric chart. Specifically, the leaving chilled-water temperature cannot be warmer than the entering air temperature, and the leaving air temperature and humidity cannot be lower than the conditions of saturated moist air at the temperature of the entering chilled water. Figure 5 also shows that performance of a cooling coil requires evaluating two different effectivenesses to identify the leaving air temperature and humidity. An overall effectiveness can be used to describe the approach of the leaving air enthalpy to the minimum possible value. An air-side effectiveness, related to the coil bypass factor, describes the approach of the leaving air temperature to the effective wet-coil surface temperature. Effectiveness analysis is accomplished for wet coils by establishing a common state variable for both the moist air and liquid streams. As implied by the lower limit of the entering chilled-water temperature, this common state variable is the moist air enthalpy. In other words, all liquid and coil temperatures are transformed to the enthalpy of saturated moist air at the liquid or coil temperature. Changes in liquid temperature can similarly be expressed in terms of changes in saturated moist air enthalpy through a saturation specific heat cp,sat defined by the following: 'h l sat c p sat = ---------------'t l

(23)

19.12

2009 ASHRAE Handbook—Fundamentals

Fig. 5 Psychrometric Schematic of Cooling Coil Processes

coil properties or from manufacturers’ performance data. A sensible heat exchanger is modeled with a single effectiveness and can be described by a single parameter UA, but a wet cooling and dehumidifying coil requires two parameters to describe the two effectivenesses shown in Figure 5. These parameters are the internal and external UAs: one describes heat transfer between the chilled water and the air-side surface through the pipe wall, and the other between the surface and the moist air. UA values can be determined from the sensible and latent capacity of a cooling coil at a single rating condition. A significant advantage of the effectiveness-NTU method is that the component can be described with as little as one measured data point or one manufacturer’s design calculation.

PRIMARY SYSTEM COMPONENTS Fig. 5

Psychrometric Schematic of Cooling Coil Processes

Using the definition of Equation (23), the basic effectiveness relationships discussed in Chapter 4 can be written as q = C a h a, ent – h a, lvg = C l h l, sat, lvg – h l, sat, ent

(24)

q = HC min h a ent – h l sat ent

(25)

C a = m· a

(26)

m· c p l C l = ---------------c p, sat

(27)

C min = min C a, C l

(28)

where q C m· a m·

= = = l = cp,l = cp,sat = ha = hl,sat =

heat transfer from air to water, Btu/h fluid capacity, lb/h dry air mass flow rate, lb/h liquid mass flow rate, lb/h liquid specific heat, Btu/lb· °F saturation specific heat, defined by Equation (23), Btu/lb· °F enthalpy of moist air, Btu/lb enthalpy of saturated moist air at the temperature of the liquid, Btu/lb

The cooling coil effectiveness of Equation (25) is defined, then, as the ratio of moist air enthalpies in Figure 5. As with sensible heat exchangers, effectiveness is also a function of the physical coil characteristics and can be obtained by modeling the coil as a counterflow heat exchanger. However, because heat transfer calculations are performed based on enthalpies, the overall transfer coefficient must be based on enthalpy potential rather than temperature potential. The enthalpy-based heat transfer coefficient UAh is related to the conventional temperature-based coefficient by the specific heat:

Primary HVAC systems consume energy and deliver heating and cooling to a building, usually through secondary systems. Primary equipment generally includes chillers, boilers, cooling towers, cogeneration equipment, and plant-level thermal-storage equipment. In particular, primary equipment generally represents the major energy-consuming equipment of a building, so accurate characterization of building energy use relies on accurate modeling of primary equipment energy consumption.

Modeling Strategies Energy consumption characteristics of primary equipment generally depend on equipment design, load conditions, environmental conditions, and equipment control strategies. For example, chiller performance depends on the basic equipment design features (e.g., heat exchange surfaces, compressor design), temperatures and flow through the condenser and evaporator, and methods for controlling the chiller at different loads and operating conditions (e.g., inlet guide vane control on centrifugal chillers to maintain leaving chilled-water temperature set point). In general, these variables vary constantly and require calculations on an hourly basis. Regression Models. Although many secondary components (e.g., heat exchangers, valves) are readily described by fundamental engineering principles, the complex nature of most primary equipment has discouraged the use of first-principle models for energy calculations. Instead, energy consumption characteristics of primary equipment have traditionally been modeled using simple equations developed by regression analysis of manufacturers’ published design data. Because published data are often available only for full-load design conditions, additional correction functions are used to correct the full-load data to part-load conditions. The functional form of the regression equations and correction functions takes many forms, including exponentials, Fourier series, and, most of the time, second- or third-order polynomials. Selection of an appropriate functional form depends on the behavior of the equipment. In some cases, energy consumption is calculated using direct interpolation from tables of data, but this often requires excessive data input and computer memory. The typical approach to modeling primary equipment in energy simulation programs is to assume the following functional form for equipment power consumption:

q = UA 't = UA h 'h UA 't UA UA h = -------------- = -------'h cp

P = PIR u Load PIR = PIR nom f 1 t a, t b, } f 2 PLR

(29)

A similar analysis can be performed to evaluate the air-side effectiveness, which identifies the leaving air temperature. Whereas the overall enthalpy-based effectiveness is based on an overall heat transfer coefficient between the chilled water and air, air-side effectiveness is based on a heat transfer coefficient between the coil surface and air. As with sensible heat exchangers, the overall heat transfer coefficients UA can be determined either from direct calculation from

(30)

C avail = C nom f 3 t a t b } LoadPLR = -------------C avail where P = equipment power, kW PIR = energy input ratio PIRnom = energy input ratio under nominal full-load conditions

(31)

Energy Estimating and Modeling Methods Load Cavail Cnom f1

= = = =

f2 = f3 = ta, tb = PLR =

19.13

power delivered to load, kW available equipment capacity, kW nominal equipment capacity, kW function relating full-load power at off-design conditions (ta, tb , ...) to full-load power at design conditions fraction full-load power function, relating part-load power to full-load power function relating available capacity at off-design conditions (ta, tb, ...) to nominal capacity various operating temperatures that affect power part-load ratio

The part-load ratio is the ratio of the load to the available equipment capacity at given off-design operating conditions. Like the power, the available, or full-load, capacity is a function of operating conditions. The particular forms of off-design functions f1 and f3 depend on the specific type of primary equipment. For example, for fossil-fuel boilers, full-load capacity and power (or fuel use) can be affected by thermal losses to ambient temperature. However, these off-design functions are typically considered to be unity in most building simulation programs. For chillers, both capacity and power are affected by condenser and evaporator temperatures, which are often characterized in terms of their secondary fluids. For direct-expansion aircooled chillers, operating temperatures are typically the wet-bulb temperature of air entering the evaporator and the dry-bulb temperature of air entering the condenser. For liquid chillers, the temperatures are usually the leaving chilled-water temperature and the entering condenser water temperature. As an example, consider the performance of a direct-expansion (DX) packaged single-zone rooftop unit. The nominal rated performance of these units is typically given for an outdoor air temperature of 95°F and evaporator entering coil conditions of 80°F db and 67°F wb. However, performance changes as outdoor temperature and entering coil conditions vary. To account for these effects, the DOE-2.1E simulation program expresses the off-design functions f1 and f3 with biquadratic functions of the outdoor dry-bulb temperature and the coil entering wet-bulb temperature. f 1 t wb ent t oa 2

2

(32)

2

2

(33)

= a 0 + a 1 t wb, ent + a 2 t wb, ent + a 3 t oa + a 4 t oa + a 5 t wb, ent t oa f 3 t wb ent t oa = c 0 + c 1 t wb, ent + c 2 t wb, ent + c 3 t oa + c 4 t oa + c 5 t wb, ent t oa The constants in Equations (32) and (33) are given in Table 4. The fraction full-load power function f2 represents the change in equipment efficiency at part-load conditions and depends heavily on the control strategies used to match load and capacity. Figure 6 shows several possible shapes of these functional relationships. (Notice that these curves are similar to the fan part-load curves of Figure 3.) Curve 1 represents equipment with constant efficiency, independent of load. Curve 2 represents equipment that is most efficient in the middle of its operating range. Curve 3 represents equipment that is most efficient at full load. Note that these types of curves apply to both boilers and chillers. First-Principle Models. As with the secondary components, engineering first principles can also be used to develop models of primary equipment. Gordon and Ng (1994, 1995), Gordon et al. (1995), Lebrun et al. (1999), and others have sought to develop such models in which unknown model parameters are extracted from measured or published manufacturers’ data. The energy analyst often must choose the appropriate model for the job. For example, a complex boiler model is not appropriate if the boiler operates at virtually constant efficiency. Similarly, a regression-based model might be appropriate when the user has a

Table 4 Correlation Coefficients for Off-Design Relationships Corr.

1

2

3

4

5

f1 –1.063931 0.0306584 0.0001269 0.0154213 0.0000497 0.0002096 f3

0.8740302 0.0011416 0.0001711–0.002957 0.0000102 0.0000592

Fig. 6 Possible Part-Load Power Curves

Fig. 6 Possible Part-Load Power Curves full dataset of reliable in-situ measurements of the plant. However, first-principle physical models generally have several advantages over pure regression models: • Physical models allow confident extrapolation outside the range of available data. • Regression is still required to obtain values for unknown physical parameters. However, the values of these parameters usually have physical significance, which can be used to estimate default parameter values, diagnose errors in data analysis through checks for realistic parameter values, and even evaluate potential performance improvements. • The number of unknown parameters is generally much smaller than the number of unknown coefficients in the typical regression model. For example, the standard ARI compressor model requires as many as 30 coefficients, 10 each for regressions of capacity, power, and refrigerant flow. By comparison, a physical compressor model may have as few as four or five unknown parameters. Thus, physical models require fewer measured data. • Data on part-load operation of chillers and boilers are notoriously difficult to obtain. Part-load corrections often represent the greatest uncertainty in the regression models, while causing the greatest effect on annual energy predictions. By comparison, physical models of full-load operation often allow direct extension to partload operation with little additional required data. Physical models of primary HVAC equipment are generally based on fundamental engineering analysis and found in many HVAC textbooks, but the models described here are specifically based on the work of Bourdouxhe et al. (1994a, 1994b, 1994c) in developing the ASHRAE HVAC 1 Toolkit (Lebrun et al. 1999). Each elementary component’s behavior is characterized by a limited number of physical parameters, such as heat exchanger heat transfer area or centrifugal compressor impeller blade angle. Values of these parameters are identified, or tuned, based on regression fits of overall performance compared to measured or published data. Although physical models are based on physical characteristics, values obtained through a regression analysis of manufacturers’

19.14

2009 ASHRAE Handbook—Fundamentals

Fig. 7 Boiler Modeled with Elementary Components

Fig. 7

Boiler Steady-State Modeling

Modern boilers are airtight, so there is almost no air circulation across the combustion chamber when the burner is off. In this case, the boiler behaves as a simple water/environment heat exchanger (i.e., HEX1 and HEX2 are combined) and the thermal model is reduced to that of a simple heat exchanger. Combustion Chamber Model. Mathematical description of this model allows the flue gas mass flow rate and enthalpy hfg,in1 (in Btu/lbfg) at the flue gas/water heat exchanger (HEX1) inlet to be calculated. The calculated flue gas mass flow rate is not necessarily the one associated with the specified value of the flue gas/water heat transfer coefficient/area product. Therefore, the following empirical relationship is used to adjust the value of this coefficient to the calculated value of the flue gas mass flow rate.

data are not necessarily representative of the actual measured values. Strictly speaking, the parameter values are regression coefficients with estimated values, identified to minimize the error in overall system performance. In other words, errors in the fundamental models of equipment are offset by over- or under-estimation of the parameter values.

Boiler Model The literature on boiler models is extensive, ranging from steadystate performance models (DeCicco 1990; Lebrun 1993) to detailed dynamic simulation models (Bonne and Jansen 1985; Lebrun et al. 1985), to a combination of these two schemes (Laret 1991; Malmström et al. 1985). Dynamic models are meant to describe transient behavior of the equipment. Consequently, these models need to accurately capture the combustion process and the complex energy exchange that occurs inside the combustion chamber. Usually, this kind of model is very detailed and demanding to formulate and use. Hence, a dynamic boiler model should be considered only in more complex situations (e.g., large boilers in large buildings, district heating systems, cogeneration systems), where a complete, detailed representation of heat distribution, emission, and operation and control under varying external conditions is warranted. Although all major variables of a boiler may vary with load and environmental conditions, assuming steady-state conditions during burner-on and burner-off times results in a relationship between input and output variables that is much simpler than those in dynamic models. Model evaluation against actual measurements shows that the steady-state model can be sufficiently accurate for energy calculations over relatively long time periods (e.g., weeks or months) with regard to the measuring accuracy. In steady-state modeling, it is assumed that, during continuous operation, the boiler can be disaggregated into one adiabatic combustion chamber and two heat exchangers (Figure 7). The following fluid streams flow across the • Combustion chamber (CC): air (subscript a) and fuel (subscript f ) streams at the inlet, and combustion gas (subscript fg) at the outlet • First heat exchanger (HEX1): combustion gas outlet and supply water streams (subscript in) • Second heat exchanger (HEX2): heated water stream (subscript out) and a fluid representing the environment The boiler model is characterized by three parameters, which represent the following heat transfer coefficients: • UAge: between the flue gas and the environment in CC • UAgw: between the flue gas and the water in HEX1 • UAwe: between the water and the environment in HEX2 Primary model inputs to the model are the leaving water set-point temperature (Tw,out ) and control model and the load characteristics (i.e., entering water temperature Tw,in and water flow rate m· w ). Secondary model inputs include the air, fuel, and ambient temperatures (Ta, Tf , and Te) as well as the fuel/air ratio f.

m· fg = 1 + --1- m· f f

(34)

h fg ,in1 h fg ,in = --------------1 + 1--f

(35)

m· fg UA gw calc = UA gw ------------------------· m fg rated

0.65

(36)

where hfg,in1 = known function of composition of combustion products and flue gas temperature at inlet of gas/water heat exchanger, Btu/lbfg hfg,in = gas enthalpy at outlet of gas/water heat exchanger, Btu/lbf m· fg rated =flue gas mass flow rate associated with specified value of gas/water heat transfer coefficient/area product, lb/min

Flue Gas-Water Heat Exchanger Model. The first step is to calculate the heat transfer rate qgw across HEX1: qgw = Hgw Cfg (Tfg,in – Tw,in)

(37)

where

Cfg = cp,fg m· fg = heat capacity flow rate of flue gas

1 – exp > – NTU 1 – C @ Hgw = ------------------------------------------------------------- = effectiveness for HEX1 1 – C exp > – NTU 1 – C @

For a counterflow heat exchanger, UA gw NTU = -------------C fg

and

C fg C = -------Cw

(38)

where Cfg d Cw and Cw = cp,w m· w . The temperature of flue gas leaving HEX1 (Tfg,out) can be calculated from Hgw(Tfg,in – Tw,in) = (Tfg,in – Tfg,out)

(39)

Other unknowns need also to be calculated. In HEX1, heat is transferred from hot flue gas to the water q gw = C w T w* ,out – T w ,in

(40)

from which the temperature of water leaving HEX1 and entering HEX2 is q gw T w* ,out = --------- + T w ,in Cw

(41)

Energy Estimating and Modeling Methods

19.15

Water-Environment Heat Exchanger Model. In HEX2, H we T w* ,out – T e = T w* ,out – T w ,out

Fig. 8 Chiller Model Using Elementary Components (42)

where Hwe = 1 – exp(– UAwe /Cw). Then water temperature at the outlet of HEX2 is T w* ,out – T e T w ,out = T e + ----------------------------§ UA we· exp ¨ --------------¸ © Cw ¹

(43)

Consequently, heat loss from hot water in HEX2 is q we = C w T w* ,out – T w ,out

(44)

Useful heat given to the water stream is qb = qgw – qwe

Fig. 8

Chiller Model Using Elementary Components (See Figure 10 for description of points 1 to 4)

Fig. 9 General Schematic of Compressor (45)

Finally, boiler efficiency is given by qb K = --------------------------· m f u FLHV

(46)

where FLHV is fuel lower heating value. The main outputs of this model are • The “useful” boiler output: its leaving water temperature (to be compared with its set point), or its corresponding “useful” power (i.e., net rate of heat transfer qb by the heated water) • Its energy consumption: burner fuel flow rate m· f or corresponding efficiency K Secondary model outputs include • Flue gas temperature, specific heat, and corresponding enthalpy flow in the chimney • Environmental loss qwe in boiler room The three-parameter model allows simulation of boilers using most conventional fuels under a wide range of operating conditions with less than 1% error. A two-exchanger model appears to be flexible enough to describe boiler behavior at different load conditions and water temperatures. This simple model is stated to accurately predict the sensitivity of a boiler to variations of burner fuel rate and airflow rates as well as water/environment losses.

Vapor Compression Chiller Models Figure 8 shows a schematic of a vapor compression chiller. In this case, the components include two heat exchangers, an expansion valve, and a compressor with a motor and transmission. Chiller components are linked through the refrigerant. For energy estimating, a simplified approach is sufficient to represent the refrigerant as a “perfect” fluid with fictitious property values. That is, refrigerant liquid is modeled as incompressible, and vapor properties are described by ideal gas laws with effective average values of property parameters, such as specific heat. Condenser and Evaporator Modeling. Both condensers and evaporators are modeled as classical heat exchangers. The two heat exchangers are each assumed to have a constant overall heat transfer coefficient. In addition, the models used in chiller systems suffer from one additional assumption: the refrigerant fluid is assumed to be isothermal for both heat exchangers, which effectively ignores the superheated and subcooled regions of the heat exchanger. The assumption of an isothermal refrigerant is particularly crude for the condenser, which sees very high refrigerant

Fig. 9 General Schematic of Compressor temperatures from the compressor discharge; thus, the mean temperature difference between refrigerant and water in the heat exchanger is significantly underestimated. Fortunately, this systematic error is offset by a significant overestimate of the corresponding heat transfer coefficient. General Compressor Modeling. Modeling real compressors requires description of many thermomechanical losses (e.g., heat loss, fluid friction, throttling losses in valves, motor and transmission inefficiencies) within the compressor. Some of these losses can be modeled within the compressor, but others are too complex or unknown to describe in a model for energy calculations. The general approach used here for compressor modeling is described in Figure 9. The compressor is described by two distinct internal elements: an idealized internal compressor and a motortransmission element to account for unknown losses. Schematically, the motor-transmission subsystem represents an inefficiency of energy conversion. Losses from these inefficiencies are assumed to heat the fluid before compression. Mathematically, it can be modeled by the following linear relationship: W = Wlo + (1 + D)Wint

(47)

where W = electrical power for a hermetic or semihermetic compressor, or shaft power for an open compressor Wlo = constant electromechanical loss Wint = idealized internal compressor power (depends on type of compressor) D = proportional power loss factor

Wlo and D are empirical parameters determined by performing a regression analysis on manufacturers’ data. Other parameters are also required to model Wint , depending on the type of compressor.

19.16

2009 ASHRAE Handbook—Fundamentals involve additional parameters. For example, the effect of cylinder unloading can be modeled by the following relationship:

Fig. 10 Schematic of Reciprocating Compressor Model

Nc Wint = Ws + § 1 – ---------------· Wpump © ¹ N

(49)

c, F L

where Wint Nc Nc,FL Wpump

idealized internal compressor power number of cylinders in use number of cylinders in use in full-load regime internal power of the compressor when all the cylinders are unloaded (pumping power) Ws = isentropic power

Fig. 10 Schematic of Reciprocating Compressor Model The following sections describe different modeling techniques for reciprocating, screw, and centrifugal compressors. Detailed modeling techniques are available in the ASHRAE HVAC 1 Toolkit (Lebrun et al. 1999) and associated references. Modeling the Reciprocating Compressor. The schematic for a reciprocating compressor, for use with the general model, is shown in Figure 10. Refrigerant enters the compressor at state 1 and is heated to state 1a by thermomechanical losses of the motortransmission model in Figure 9. The refrigerant undergoes isentropic compression to state 2s, followed by throttling to the compressor discharge at state 2. The throttling valve is a simplified approach to model known losses within the compressor caused by pressure drops across the suction and discharge valves. A more accurate model might include pressure losses at both the compressor inlet and outlet, but analysis of compressor data reveals that the simpler model is adequate for modeling of typical reciprocating compressors. In fact, many compressors can be adequately modeled with no throttling valve at all. The refrigerant flow rate through the system must be determined to predict chiller and compressor performance. In general, volumetric flow depends on the pressure difference across the compressor. The compressor refrigerant flow rate is a decreasing function of the pressure ratio because of vapor re-expansion in the clearance volume. With refrigerant vapor modeled as an ideal gas, the volumetric flow rate is given by p ex ·1 e J V = V s 1 + C f – C f § --------©p ¹ suc

(48)

where V = volumetric flow rate Vs = swept volumetric flow rate (geometric displacement of the compressor) Cf = clearance factor = Vclearance /Vs pex /psuc = cylinder pressure ratio J = specific heat ratio

Vs and Cf must be identified using data for the actual reciprocating compressor. Although the models discussed apply to full-load operation, Equation (48) is also valid at part-load conditions. However, the internal power use can be different at part load depending on the particular strategy for capacity modulation, such as on-off cycling, cylinder unloading, hot-gas bypass, or variable-speed motor. In most cases, simple physical models can be developed to describe these methods, which generally vary the swept volumetric rate. Additional thermomechanical losses can also be modeled but often

= = = =

The variable Wpump characterizes the part-load regime of the reciprocating compressor, and is assumed to be constant throughout the entire part-load range. In summary, a realistic physical model of a reciprocating compressor, covering both full- and part-load operations, can be developed based on six parameters: the constant and proportional loss terms of the motor-transmission model Wlo and D, the swept volumetric flow rate Vs of the compressor cylinders, the cylinder clearance volume factor Cf , the fictitious exhaust valve flow area Aex, and the zero-load pumping power of the unloaded compressor Wpump. The entire chiller can then be modeled with two additional parameters for the overall heat transfer coefficients of the condenser and evaporator. Modeling Other Compressors and Chillers. From a modeling perspective, the thermodynamic processes of a screw compressor are similar to those of a reciprocating compressor. Physically, the screw compressor transports an initial volumetric flow rate of refrigerant vapor to a higher pressure and density by squeezing it into a smaller space. A realistic physical model of a variablevolume-ratio, twin-screw compressor, covering both full- and part-load operations, can be developed based on five parameters: the (1) constant and (2) proportional loss terms of the motor-transmission model of Equation (47), (3) swept volumetric flow rate of the compressor screw, (4) internal leakage area, and (5) pumped pressure differential for diverted flow at part load (Lebrun et al. 1999). The entire chiller can then be modeled with two additional parameters for the overall heat transfer coefficients of the condenser and evaporator. An idealized internal model of a centrifugal compressor, to be used in conjunction with Equation (47) and Figure 9, can be based on an ideal analysis of a single-stage compressor composed of an isentropic impeller and isentropic diffuser. In addition to the thermomechanical loss parameters of Equation (47), only three additional parameters are required: the (1) peripheral speed of the impeller, (2) vane inclination at the impeller exhaust, and (3) impeller exhaust area. The refrigerant cycle of an absorption chiller is the same as for a vapor compression cycle, except for the absorption-generation subsystem in place of the compressor (see Chapter 2 for more information). The absorption-generation subsystem includes an absorber, steam-fired generator, recovery heat exchanger, pump, and control valve. All components except the pump and control valve can be modeled as heat exchangers.

Cooling Tower Model A cooling tower is used in primary systems to reject heat from the chiller condenser. Controls typically manage tower fans and pumps to maintain a desired water temperature entering the condenser. Like cooling and dehumidifying coils in secondary systems, cooling tower performance has a strong influence on the chiller’s energy consumption. In addition, tower fans consume electrical energy directly. Fundamentally, a cooling tower is a direct contact heat and mass exchanger. Equations describing the basic processes are given in

Energy Estimating and Modeling Methods Chapter 6 and in many HVAC textbooks. Chapter 39 of the 2008 ASHRAE Handbook—HVAC Systems and Equipment describes the specific performance of cooling towers. Performance subroutines are also available in Klein et al. (1994) and Lebrun et al. (1999). For energy calculations, cooling tower performance is typically described in terms of the outdoor wet-bulb temperature, temperature drop of water flowing through the tower (range), and difference between leaving water and air wet-bulb temperatures (approach). Simple models assume constant range and approach, but more sophisticated models use rating performance data to relate leaving water temperature to the outdoor wet-bulb temperature, water flow, and airflow. Simple cooling tower models, such as those based on a single overall transfer coefficient that can be directly inferred from a single tower rating point, are often appropriate for energy calculations.

SYSTEM MODELING OVERALL MODELING STRATEGIES In developing a simulation model for building energy prediction, two basic issues must be considered: (1) modeling components or subsystems and (2) overall modeling strategy. Modeling components, discussed in the section on Component Modeling and Loads, results in sets of equations describing the individual components. The overall modeling strategy refers to the sequence and procedures used to solve these equations. The accuracy of results and the computer resources required to achieve these results depend on the modeling strategy. In most building energy programs, load models are executed for every space for every hour of the simulation period. (Practically all models use 1 h as the time step, which excludes any information on phenomena occurring in a shorter time span.) The load model is followed by running models for every secondary system, one at a time, for every hour of the simulation. Finally, the plant simulation model is executed again for the entire period. Each sequential execution processes the fixed output of the preceding step. This procedure is illustrated in Figure 11. Solid lines represent data passed from one model to the next; dashed lines represent information, usually provided by the user, about one model passed to the preceding model. For example, the system information consists of a piecewise-linear function of zone temperature that gives the system capacity. Because of this loads-systems-plants sequence, certain phenomena cannot be modeled precisely. For example, if the heat balance method for computing loads is used, and some component in the system simulation model cannot meet the load, the program can only report the current load. In actuality, the space temperature should readjust until the load matches equipment capacity, but this cannot be modeled because loads have been precalculated and fixed. If the weighting-factor method is used for loads, this problem is partially overcome, because loads are continually readjusted during the system simulation. However, the weighting factor technique is based on linear mathematics, and wide departures of room temperatures from those used during execution of the load program can introduce errors.

Fig. 11 Overall Modeling Strategy

Fig. 11

Overall Modeling Strategy

19.17 A similar problem arises in plant simulation. For example, in an actual building, as the load on the central plant varies, the supply chilled-water temperature also varies. This variation in turn affects the capacity of secondary system equipment. In an actual building, when the central plant becomes overloaded, space temperatures should rise to reduce load. However, in most energy estimating programs, this condition cannot occur; thus, only the overload condition can be reported. These are some of the penalties associated with decoupling of the load, system, and plant models. An alternative strategy, in which all calculations are performed at each time step, is possible. Here, the load, system, and plant equations are solved simultaneously at each time interval. With this strategy, unmet loads and imbalances cannot occur; conditions at the plant are immediately reflected to the secondary system and then to the load model, forcing them to readjust to the instantaneous conditions throughout the building. The results of this modeling strategy are superior, although the magnitude and importance of the improvement are uncertain. The principal disadvantage of this approach, and the reason that it was not widely used in the past, is that it demands more computing resources. However, most current desktop computers can now run programs using the alternative approach in a reasonable amount of time. Programs that, to one degree or another, implement simultaneous solution of the loads, system, and plant models have been developed by Clarke (2001), Crawley et al. (2001), Klein et al. (1994), Park et al. (1985), and Taylor et al. (1990, 1991). Some of these programs simulate the loads, systems, and plants using subhourly time steps. An economic model, as shown in Figure 11, calculates energy costs (and sometimes capital costs) based on the estimated required input energy. Thus, the simulation model calculates energy use and cost for any given input weather and internal loads. By applying this model (i.e., determining output for given inputs) at each hour (or other suitable interval), the hour-by-hour energy consumption and cost can be determined. Maintaining running sums of these quantities yields monthly or annual energy usage and costs. These models only compare design alternatives; a large number of uncontrolled and unknown factors usually rule out such models for accurate prediction of utility bills. For example, Miller (1980) found that the dynamics of control of components may have at least minor effects on predicted energy use. The Bibliography lists several models, which are also described in Walton (1983) and York and Cappiello (1982). Generally, load models tend to be the most complex and time-consuming, whereas the central plant model is the least complex. Because detailed models are computationally intensive, several simplified methods have been developed, including the degree-day, bin, and correlation methods.

DEGREE-DAY AND BIN METHODS Degree-day methods are the simplest methods for energy analysis and are appropriate if building use and HVAC equipment efficiency are constant. Where efficiency or conditions of use vary with outdoor temperature, consumption can be calculated for different values of the outdoor temperature and multiplied by the corresponding number of hours; this approach is used in various bin methods. When the indoor temperature is allowed to fluctuate or when interior gains vary, simple steady-state models must not be used. Although computers can easily calculate the energy consumption of a building, the concepts of degree-days and balance point temperature remain valuable tools. A climate’s severity can be characterized concisely in terms of degree-days. Also, the degree-day method and its generalizations can provide a simple estimate of annual loads, which can be accurate if the indoor temperature and internal gains are relatively constant and if the heating or cooling systems operate for a complete season.

19.18

2009 ASHRAE Handbook—Fundamentals

Balance Point Temperature The balance point temperature tbal of a building is defined as that value of the outdoor temperature to at which, for the specified value of the interior temperature ti, the total heat loss qgain is equal to the heat gain from sun, occupants, lights, and so forth. qgain = Ktot (ti – tbal )

(50)

where Ktot is the total heat loss coefficient of the building in Btu/h·°F. For any steady-state method described in this section, heat gains must be the average for the period in question, not for the peak values. In particular, solar radiation must be based on averages, not peak values. The balance point temperature is therefore t bal

q gain = t i – -----------K tot

(51)

Heating is needed only when to drops below tbal . The rate of energy consumption of the heating system is K tot + >t – t T @ q h = --------K h bal o

(52)

where Kh is the efficiency of the heating system, also designated on an annual basis as the annual fuel use efficiency (AFUE), T is time, and the plus sign above the bracket indicates that only positive values are counted. If tbal, Ktot , and Kh are constant, the annual heating consumption can be written as an integral: K tot + Q h yr = --------- > t bal – t o T @ dT Kh

³

(53)

This integral of the temperature difference conveniently summarizes the effect of outdoor temperatures on a building. In practice, it is approximated by summing averages over short time intervals (daily or hourly); the results are called degree-days or degreehours.

DD c t bal = 1 day ¦ t o – t bal

+

Although the definition of the balance point temperature is the same as that for heating, in a given building its numerical value for cooling is generally different from that for heating because qi , Ktot , and ti can be different. According to Claridge et al. (1987), tbal can include both solar and internal gains as well as losses to the ground. Calculating cooling energy consumption using degree-days is more difficult than heating. For cooling, the equation analogous to Equation (55) is K tot Q c yr = ---------DD c t bal Kh

Annual Degree-Days. If daily average values of outdoor temperature are used for evaluating the integral, the degree-days for heating DDh(tbal ) are obtained as DD h t bal = 1 day ¦ t bal – t o

+

(54)

(57)

for a building with static Ktot . That assumption is generally acceptable during the heating season, when windows are closed and the air exchange rate is fairly constant. However, during the intermediate or cooling season, heat gains can be eliminated, and the onset of mechanical cooling can be postponed by opening windows or increasing the ventilation. (In buildings with mechanical ventilation, this is called the economizer mode.) Mechanical air conditioning is needed only when the outdoor temperature exceeds the threshold tmax. This threshold is given by an equation analogous to Equation (51), replacing the closed-window heat transmission coefficient Ktot with Kmax for open windows: q gain t max = t i – -----------K max

(58)

Kmax varies considerably with wind speed, but a constant value can be assumed for simple cases. The resulting sensible cooling load is shown schematically in Figure 12 as a function of to. The solid line is the load with open windows or increased ventilation; the dashed line shows the load if Kmax were kept constant. The annual cooling load for this mode can be calculated by breaking the area under the solid line into a rectangle and a triangle, or Qc = Ktot [DDc (tmax) + (tmax – tbal)Nmax]

Annual Degree-Day Method

(56)

days

(59)

where DDc(tmax) are the cooling degree-days for base tmax , and Nmax is the number of days during the season when to rises above tmax. This is merely a schematic model of air conditioning. In practice, heat gains and ventilation rates vary, as does occupant behavior in using the windows and air conditioner. Also, in commercial buildings with economizers, the extra fan energy for increased ventila-

days

Fig. 12 Cooling Load as Function of Outdoor Temperature to with dimensions of °F ·days. Here the summation is to extend over the entire year or over the heating season. It is a function of tbal, reflecting the roles of ti, heat gain, and loss coefficient. The balance point temperature tbal is also known as the base of the degree-days. In terms of degree-days, the annual heating consumption is K tot Q h yr = --------- DD h t bal Kh

(55)

Heating degree-days or degree-hours for a balance point temperature of 65°F have been widely tabulated (this temperature represents average conditions in typical buildings in the past). The 65°F base is assumed whenever tbal is not indicated explicitly. The extension of degree-day data to different bases is discussed later. Cooling degree-days can be calculated using an equation analogous to Equation (54) for heating degree-days as

Fig. 12 Cooling Load as Function of Outdoor Temperature to

Energy Estimating and Modeling Methods

19.19

tion must be added to the calculations. Finally, air-conditioning systems are often turned off during unoccupied periods. Therefore, cooling degree-hours better represent the period when equipment is operating than cooling degree-days because degree-days assume uninterrupted equipment operation as long as there is a cooling load. Latent loads can form an appreciable part of a building’s cooling load. The degree-day method can be used to estimate the latent load during the cooling season on a monthly basis by adding the following term to Equation (59): q latent = m· h fg W o – W i

(60)

where qlatent m· hfg Wo Wi

= = = = =

monthly latent cooling load, Btu/h monthly infiltration (total airflow), lb/h heat of vaporization of water, Btu/lb outdoor humidity ratio (monthly averaged) indoor humidity ratio (monthly averaged)

The degree-day method assumes that tbal is constant, which is not well satisfied in practice. Solar gains are zero at night, and internal gains tend to be highest during the evening. The pattern for a typical house is shown in Figure 13. As long as to always stays below tbal, variations average out without changing consumption. But for the situation in Figure 13, to rises above tbal from shortly after 1000 h to 2200 h; the consequences for energy consumption depend on thermal inertia and HVAC system control. If this building had low inertia and temperature control were critical, heating would be needed at night and cooling during the day. In practice, this effect is reduced by thermal inertia and by the dead band of the thermostat, which allows ti to float. The closer to is to tbal, the greater the uncertainty. If occupants keep windows closed during mild weather, ti will rise above the set point. If they open windows, the potential benefit of heat gains is reduced. In either case, the true values of tbal become uncertain. Therefore, the degree-day method, like any steady-state method, is unreliable for estimating consumption during mild weather. In fact, consumption becomes most sensitive to occupant behavior and cannot be predicted with certainty. Despite these problems, the degree-day method (using an appropriate base temperature) can give remarkably accurate results for the annual heating energy of single-zone buildings dominated by losses through the walls and roof and/or ventilation. Typical buildings have time constants that are about 1 day, and a building’s thermal inertia essentially averages over the diurnal variations, especially if

Fig. 13 Variation of Balance Point Temperature and Internal Gains for a Typical House

ti is allowed to float. Furthermore, energy consumption in mild weather is small; hence, a relatively large error here has only a small effect on the total for the season. Variable-Base Annual Degree-Days. Calculating Qh from degree-days DDh(tbal) depends on the value of tbal . This value varies widely from one building to another because of widely differing personal preferences for thermostat settings and setbacks and because of different building characteristics. In response to the fuel crises of the 1970s, heat transmission coefficients have been reduced, and thermostat setback has become common. At the same time, energy use by appliances has increased. These trends all reduce tbal (Fels and Goldberg 1986). Hence, in general, degree-days with the traditional base 65°F are not to be used. Figure 14A shows how heating degree-days vary with tbal for a particular site (New York). The plot is obtained by evaluating Equation (54) with data for the number of hours per year during which to is within 5°F temperature intervals centered at 77°F, 72°F, 67°F, 62°F, …, 7°F. Data for the number of hours in each interval, or bin, are included as labels in this plot. Analogous curves, without these labels, are shown in Figure 14B for Houston, Washington, D.C., and Denver. If the annual average of to is known, the cooling degreedays to any base below 72 r 2.5°F can also be found. Seasonal Efficiency. The seasonal efficiency Kh of heating equipment depends on factors such as steady-state efficiency, sizing, cycling effects, and energy conservation devices. It can be much lower than or comparable to steady-state efficiency. Alereza and Kusuda (1982) developed expressions to estimate seasonal efficiency for a variety of furnaces, if information on rated input and output is available. These expressions correlate seasonal efficiency with variables determined by using the equipment simulation capabilities of a large hourly simulation program and typical equipment performance curves supplied by the National Institute of Standards and Technology (NIST): K ss CF pl K = ------------------1 + DD

(61)

where Kss = steady-state efficiency (rated output/input) CFpl = part-load correction factor DD = fraction of heat loss from ducts

The dimensionless term CFpl is a characteristic of the part-load efficiency of the heating equipment, which may be calculated as follows: Gas Forced-Air Furnaces With pilot CFpl = 0.6328 + 0.5738(RLC) 0.3323(RLC)2 With intermittent ignition CFpl = 0.7791 + 0.1983(RLC) 0.0711(RLC)2 With intermittent ignition and loose stack damper CFpl = 0.9276 + 0.0732(RLC) 0.0284(RLC)2 Oil Furnaces Without Stack Damper CFpl = 0.7092 + 0.6515(RLC) 0.4711(RLC)2 Resistance Electric Furnaces CFpl = 1.0

Fig. 13 Variation of Balance Point Temperature and Internal Gains for a Typical House (Nisson and Dutt 1985)

These equations are based on many annual simulations for the equipment. The dimensionless ratio RLC of building design load to the capacity (rated output) of the equipment is defined as follows:

19.20

2009 ASHRAE Handbook—Fundamentals This is a dimensional equation with t and V in °F; V yr is the standard deviation of the monthly average temperatures about the annual average t o yr :

BLC- t – t 1 + D RLC = ----------D CHT bal od where BLC = building loss coefficient, Btu/h·°F tod = outside design temperature, °F CHT = capacity (rated output) of heating equipment, Btu/h

12

V yr =

2 1- t – t ----o o, yr 12 ¦

BLC can be defined as design-day heat loss/(tbal – tod). The design-day heat loss includes both infiltration and ground losses. Duct losses as a percentage of the design-day heat loss are added using the factor (1 + DD). RLC assumes values in the range 0 to 1.0, appropriate for typical cases when heating equipment is oversized. Seasonal efficiency is also discussed by Chi and Kelly (1978), Mitchell (1983), and Parker et al. (1980).

Monthly Degree-Days Many formulas have been proposed for estimating degree-days relative to an arbitrary base when detailed data are not available. The basic idea is to assume a typical probability distribution of temperature data, characterized by its average t o and by its standard deviation V. Erbs et al. (1983) developed a model that needs as input only the average t o for each month of the year. The standard deviations V m for each month are then estimated from the correlation

To obtain a simple expression for degree-days, a normalized temperature variable I is defined as t bal – t o I = --------------------Vm N

(62)

Fig. 14 Annual Heating Days DDh(tbal) as Function of Balance Temperature tbal

(64)

where N = number of days in the month (N has units of day/month and I has units of month e day ). Although temperature distributions can be different from month to month and location to location, most of this variability can be accounted for by the average and standard deviation of t o . Being centered around t o and scaled by V m, Ieliminates these effects. In terms of I, the monthly heating degreedays for any location are well approximated by DD h t bal = V m N

V m = 3.54 – 0.0290 t o + 0.0664 Vyr

(63)

1

1.5

I ln e –aI + e aI ---- + ---------------------------------2 2a

(65)

where a = 1.698 day e month . For nine locations spanning most climatic zones of the United States, Erbs et al. (1983) verified that the annual heating degreedays can be estimated with a maximum error of 315°F·days if Equation (65) is used for each month. For cooling degree-days, the largest error is 270°F·days. Such errors are quite acceptable, representing less than 5% of the total. Table 5 lists monthly heating degree-days for New York City, using the model of Erbs et al. (1983), given monthly averages of to as reproduced in column 2 of Table 5. The degree-days are based on a balance temperature of 60°F. Table 6 contains degree-day data for several sites and monthly averaged outdoor temperatures needed for the algorithm. More complete tabulations of the latter are contained in Cinquemani et al. (1978) and in local climatological data summaries available from the National Climatic Data Center, Asheville, NC (NOAA 1973; www. ncdc.noaa.gov). Monthly degree-day data at various bases, as well as other climatic information for 209 U.S. and 14 Canadian cities, may be found in Appendix 3 to Balcomb et al. (1982). Table 5 Degree-Day Calculation for New York City from Monthly Averaged Data

Fig. 14

Annual Heating Days DDh(tbal) as Function of Balance Temperature tbal

Month

t o qF N, day/mo.

January February March April May June July August September October November December

32.2 33.4 41.1 52.1 62.3 71.6 76.6 74.9 68.4 58.7 46.4 35.5

to,yr

54.4

Vyr

15.8

31 28 31 30 31 30 31 31 30 31 30 31

V m qF 3.65 3.62 3.40 3.08 2.79 2.52 2.38 2.41 2.61 2.88 3.22 3.56

Note: Use Equation (65) to calculate DDh(tbal).

I

mo./day

DDh(tbal), °F·day

1.37 1.39 1.00 0.47 –0.15 –0.84 –1.26 –1.11 –0.59 0.08 0.72 1.24

864 746 592 265 67 7 2 3 16 123 391 762

Sum

3837

Energy Estimating and Modeling Methods

19.21

Table 6 Degree-Day and Monthly Average Temperatures for Various Locations Variable-Base Heating Degree-Day, °F·daysa Site Los Angeles, CA Denver, CO Miami, FL Chicago, IL Albuquerque, NM New York, NY Bismarck, ND Nashville, TN Dallas/Ft. Worth, TX Seattle, WA a Source:

65

60

55

50

45

1245 6016 206 6127 4292 4909 9044 3696 2290 4727

522 4723 54 4952 3234 3787 7656 2758 1544 3269

158 3601 8 3912 2330 2806 6425 1964 949 2091

26 2653 0 2998 1557 1980 5326 1338 526 1194

0 1852 0 2219 963 1311 4374 852 250 602

Monthly Average Outdoor Temperature t o , °Fb Jan

Feb

Mar Apr May

54.5 55.6 56.5 29.9 32.8 37.0 67.2 67.8 71.3 24.3 27.4 36.8 35.2 40.0 45.8 32.2 33.4 41.1 8.2 13.5 25.1 38.3 41.0 48.7 45.4 49.4 55.8 39.7 43.5 45.5 b Source:

NOAA (1973).

58.8 47.5 75.0 49.9 55.8 52.1 43.0 60.1 66.4 50.4

61.9 57.0 78.0 60.0 65.3 62.3 54.4 68.5 73.8 56.5

Jul

Aug

Sep

Oct

Nov

Dec

64.5 68.5 66.0 73.0 81.0 82.3 70.5 74.7 74.6 78.7 71.6 76.6 63.8 70.8 76.6 79.6 81.6 85.7 61.3 65.7

Jun

69.6 71.6 82.9 73.7 76.6 74.9 69.2 78.5 85.8 64.9

68.7 62.8 81.7 65.9 70.1 68.4 57.5 72.0 78.2 60.6

65.2 60.5 52.0 39.4 77.8 72.2 55.4 40.4 58.2 44.5 58.7 47.4 46.8 28.9 60.9 48.4 68.0 55.9 54.2 45.7

56.9 32.6 68.3 28.5 36.2 35.5 15.6 40.4 48.2 42.0

Cinquemani et al. (1978).

Table 7 Sample Annual Bin Data Bin 100/ 104

Site Chicago, IL Dallas/Ft. Worth, TX Denver, CO Los Angeles, CA Miami, FL Nashville, TN Seattle, WA

95/ 99

90/ 94

85/ 89

80/ 84

75/ 79

70/ 74

65/ 69

60/ 64

55/ 59

50/ 54

45/ 49

40/ 44

35/ 39

97 222 27 210 351 527 3 118 235 8 8 9 17 45 864 7 137 407 16

362 804 348 53 1900 616 62

512 1100 390 194 2561 756 139

805 947 472 632 1605 1100 256

667 705 697 1583 871 866 450

615 826 699 234 442 706 769

622 761 762 2055 222 692 1353

585 615 783 1181 105 650 1436

577 615 718 394 77 670 1461

636 523 665 74 36 720 1413

720 364 758 4 12 582 915

Bin Method For many applications, the degree-day method should not be used, even with the variable-base method, because the heat loss coefficient Ktot , the efficiency Kh of the HVAC system, or the balance point temperature tbal may not be sufficiently constant. Heat pump efficiency, for example, varies strongly with outdoor temperature; efficiency of HVAC equipment may be affected indirectly by to when efficiency varies with load (common for boilers and chillers). Furthermore, in most commercial buildings, occupancy has a pronounced pattern, which affects heat gain, indoor temperature, and ventilation rate. In such cases, steady-state calculation can yield good results for annual energy consumption if different temperature intervals and time periods are evaluated separately. This approach is known as the bin method because consumption is calculated for several values of the outdoor temperature to and multiplied by the number of hours Nbin in the temperature interval (bin) centered around that temperature: K tot + Q bin = N bin --------- >t – t @ K h bal o

(66)

The superscript plus sign indicates that only positive values are counted; no heating is needed when to is above tbal. Equation (66) is evaluated for each bin, and the total consumption is the sum of the Qbin over all bins. In the United States, the necessary weather data are available in ASHRAE (1995) and USAF (1978). Bins are usually in 5°F increments and are often collected in three daily 8 h shifts. Mean coincident wet-bulb temperature data (for each dry-bulb bin) are used to calculate latent cooling loads from infiltration and ventilation. The bin method considers both occupied and unoccupied building conditions and gives credit for internal loads by adjusting the balance point. For example, a calculation could be performed for 42°F outdoors (representing all occurrences from 39.5 to 44.5°F) and with building operation during the midnight to 0800 shift. Because

30/ 34

25/ 29

20/ 24

10/ 14

5/ 9

0/ 4

–5/ –1

957 511 354 243 125 289 57 29 713 565 399 164 106

66

58

6

65

80

22

342 280 107 358 51 43

15/ 19

71 15

29 1

there are 23 5°F bins between –10 and 105°F and 3 8 h shifts, 69 separate operating points are calculated. For many applications, the number of calculations can be reduced. A residential heat pump (heating mode), for example, could be calculated for just the bins below 65°F without the three-shift breakdown. The data in Table 7 are samples of annual totals for a few sites, but ASHRAE (1995) and USAF (1978) include monthly data and data further separated into time intervals during the day. Equipment performance may vary with load. For heat pumps, the U.S. Department of Energy adopted test procedures to determine the effect of dynamic operations. The bin method uses these results for a specific heat pump to adjust the integrated capacity for the effect of part-load operation. Figure 15 compares adjusted heat pump capacity to building heat loss in Example 4. This type of curve must be developed for each model heat pump as applied to an individual profile. The heat pump cycles on and off above the balance point temperature to meet the house load; supplemental heat is required at lower temperatures. This cycling can reduce performance, depending on the part-load factor at a given temperature. The cycling capacity adjustment factors used in this example to account for cycling degradation can be calculated from the equation in footnote a of Table 8. Frosting and the necessary defrost cycle can reduce performance over steady-state conditions that do not include frosting. The effects of frosting and defrosting are already integrated into many (but not all) manufacturer’s published performance data. Example 4 assumes that the manufacturer’s data already account for frosting/defrosting losses (as indicated by the characteristic notch of the capacity curve in Figure 15) and shows how to adjust an integrated performance curve for cycling losses. Example 4. Estimate the energy requirements for a residence with a design heat loss of 40,000 Btu at 53°F design temperature difference. The inside design temperature is 70°F. Average internal heat gains are estimated to be 4280 Btu/h. Assume a 3 ton heat pump with the characteristics given in Columns E and H of Table 8 and in Figure 15.

19.22

2009 ASHRAE Handbook—Fundamentals Table 8 Calculation of Annual Heating Energy Consumption for Example 4 Climate

A

B

C

Temp. Temp. Bin, Diff., °F tbal – tbin 62 57 52 47 42 37 32 27 22 17 12 7 2

2.3 7.3 12.3 17.3 22.3 27.3 32.3 37.3 42.3 47.3 52.3 57.3 62.3

House D

Heat Pump E

Heat Heat Pump Weather Loss Integrated Data Rate, Heating Bin, 1000 Capacity, h Btu/h 1000 Btu/h 740 673 690 684 790 744 542 254 138 54 17 2 0

1.8 5.5 9.3 13.1 16.9 20.6 24.4 28.2 31.9 35.7 39.5 43.3 47.0

F

G

H

Supplemental I

J

K

L

M

N

Cycling Adjusted Heat Seasonal SuppleTotal Rated OperaCapacity Heat Pump Heat Pump mental Electric Space Heating Electric ting AdjustPump Supplied Electric Energy Time Heating, Consump- Load, Required, Consumpment Capacity, Input, Factora 1000 Btu/hb kW Fractionc 106 Btud tion, KWhe 106 Btuf kWhg tionh

44.3 41.8 39.3 36.8 29.9 28.3 26.6 25.0 23.4 21.8 19.3 16.8 14.3

0.760 0.783 0.809 0.839 0.891 0.932 0.979 1.000 1.000 1.000 1.000 1.000 1.000

33.7 32.7 31.8 30.9 26.6 26.4 26.0 25.0 23.4 21.8 19.3 16.8 —

a Cycling

3.77 3.67 3.56 3.46 3.23 3.15 3.07 3.00 2.92 2.84 2.74 2.63 —

Capacity Adjustment Factor = 1 Cd (1 x), where Cd = degradation coefficient (default = 0.25 unless part load factor is known) and x = building heat loss per unit capacity at temperature bin. Cycling capacity = 1 at the balance point and below. The cycling capacity adjustment factor should be 1.0 at all temperature bins if the manufacturer includes cycling effects in the heat pump capacity (Column E) and associated electrical input (Column H). bColumn G = Column E u Column F

Fig. 15 Heat Pump Capacity and Building Load

Fig. 15 Heat Pump Capacity and Building Load Solution: The design heat loss is based on no internal heat generation. The heat pump system energy input is the net heat requirement of the space (i.e., envelope loss minus internal heat generation). The net heat loss per degree and the heating/cooling balance temperature may be computed: Ktot = HL /'t = 40,000/53 = 755 Btu/h·°F From Equation (51), tbal = 70 – (4280/755) = 64.3°F Table 8 is then computed, resulting in 9578 kWh.

The modified bin method (Knebel 1983) extends the basic bin method to account for weekday/weekend and partial-day occupancy effects, to calculate net building loads (conduction, infiltration, internal loads, and solar loads) at four temperatures, rather than interpolate from design values, and to better describe secondary and primary equipment performance.

CORRELATION METHODS One way to simplify energy analyses is to correlate energy requirements to various inputs. Typically, the result of a correlation is a simple equation that may be used in a calculator or small computer

0.05 0.17 0.29 0.42 0.63 0.78 0.94 1.00 1.00 1.00 1.00 1.00 — Totals:

1.30 3.72 6.42 8.95 13.31 15.35 13.22 6.35 3.23 1.18 0.33 0.03 — 73.39

146 417 719 1002 1614 1833 1559 762 403 153 47 5 — 8660

1.30 3.72 6.42 8.95 13.31 15.35 13.22 7.16 4.41 1.93 0.67 0.09 — 76.52

— — — — — — — 236 345 220 101 16 — 917

146 417 719 1002 1614 1833 1559 998 748 373 147 21 — 9578

cOperating

Time Factor equals smaller of 1 or Column D/Column G J = (Column I u Column G u Column C)/1000 K = Column I u Column H u Column C fColumn L = Column C u Column D/1000 gColumn M = (Column L – Column J) u 106/3413 hColumn N = Column K + Column M dColumn eColumn

program, or to develop a graph that provides quick insight into the energy requirements. Examples are in ASHRAE Standard 90.1, which includes several empirical equations that may be used to predict energy consumption by many types of buildings. The accuracy of correlation methods depends on the size and accuracy of the database and the statistical means used to develop the correlation. A database generated from measured data can lead to accurate correlations (Lachal et al. 1992). The key to proper use of a correlation is ensuring that the case being studied matches the cases used in developing the database. Inputs to the correlation (independent variables) indicate factors that are considered to significantly affect energy consumption. A correlation is invalid either when an input parameter is used beyond its valid range (corresponding to extrapolation rather than interpolation) or when some important feature of the building/system is not included in the available inputs to the correlation.

SIMULATING SECONDARY AND PRIMARY SYSTEMS Traditionally, most energy analysis programs include a set of preprogrammed models that represent various systems (e.g., variable-air-volume, terminal reheat, multizone). In this scheme, the equations for each system are arranged so they can be solved sequentially. If this is not possible, then the smallest number of equations that must be solved simultaneously is solved using an appropriate technique. Furthermore, individual equations may vary from hour to hour in the simulation, depending on controls and operating conditions. For example, a dry coil uses different equations than a wet coil. The primary disadvantage of this scheme is that it is relatively inflexible: to modify a system, the program source code may have to be modified and recompiled. Alternative strategies (Klein et al. 1994; Park et al. 1985) view the system as a series of components (e.g., fan, coil, pump, duct, pipe, damper, thermostat) that may be organized in a component library. Users of the program specify the connections between the components. The program then resolves the specification of components and connections into a set of simultaneous equations. A refinement of component-based modeling is known as equation-based modeling (Buhl et al. 1993; Sowell and Moshier

Energy Estimating and Modeling Methods 1995). These models do not follow predetermined rules for a solution, and the user can specify which variables are inputs and which are outputs.

MODELING OF SYSTEM CONTROLS Building control systems are typically hierarchical: higher-level, supervisory controls generate set points for lower-level, local loop controls. Supervisory-level controls, which include reset and optimal control, directly influence energy consumption. Local loop controllers may also affect energy performance; for example, proportional-only room temperature control results in a tradeoff between energy use and comfort. Faults in control systems and devices can also affect energy consumption (e.g., leaking valves and dampers can significantly increase energy use). It is particularly important to account for these departures from ideal behavior when simulating performance of real buildings using calibrated models. Modeling and simulation of supervisory control are increasingly handled by whole-building simulation programs. Simulation of local loop controls requires more specialized, component- or equation-based modeling environments. Modern control systems, particularly direct digital controls (DDC), typically use integral action to drive the controlled variable to its set point. For energy modeling purposes, the controlled variable (e.g., supply air temperature) can be treated as being at the set point unless system capacity is insufficient. The simulation must determine whether the capacity required to meet set point exceeds available capacity. If it does, the available capacity is used to determine the actual value of the controlled variable. Where there is only proportional action, the resulting relationship between the controlled variable and the output of the system can be used to determine both values. For example, the action of a conventional pneumatic room temperature controller can be represented by a function relating heating and cooling delivery to space temperature. Similarly, supply air temperature reset control can be modeled as a relationship between outside or zone temperature and coil or fan discharge temperature. An accurate secondary system model must ensure that all controls are properly represented and that the governing equations are satisfied at each simulation time step. This often creates a need for iteration or for use of values from an earlier solution point. Controls on space temperature affect the interaction between loads calculations and the secondary system simulation. A realistic model might require a dead band in space temperature in which no heating or cooling is called for; within this range, the true space sensible load is zero, and the true space temperature must be adjusted

19.23 accordingly. If the thermostat has proportional control between zero and full capacity, the space temperature rises in proportion to the load during cooling and falls similarly during heating. Capacity to heat or cool also varies with space temperature after the control device has reached its maximum because capacity is proportional to the difference between supply and space temperatures. Failure to properly model these phenomena results in overestimating required energy.

INTEGRATION OF SYSTEM MODELS Energy calculations for secondary systems involve construction of the complete system from the set of HVAC components. For example, a variable-air-volume (VAV) system is a single-path system that controls zone temperature by modulating airflow while maintaining constant supply air temperature. VAV terminal units, located at each zone, adjust the quantity of air reaching each zone depending on its load requirements. Reheat coils may be included to provide required heating for perimeter zones. This VAV system simulation consists of a central air-handling unit and a VAV terminal unit with reheat coil located at each zone, as shown in Figure 16. The central air-handling unit includes a fan, cooling coil, preheat coil, and outside air economizer. Supply air leaving the air-handling unit is controlled to a fixed set point. The VAV terminal unit at each zone varies airflow to meet the cooling load. As zone cooling load decreases, the VAV terminal unit decreases zone airflow until the unit reaches its minimum position. If the cooling load continues to decrease, the reheat coil is activated to meet the zone load. As supply air volume leaving the unit decreases, fan power consumption also reduces. A variable-speed drive is used to control the supply fan. The simulation is based on system characteristics and zone design requirements. For each zone, the inputs include sensible and latent loads, zone set-point temperature, and minimum zone supplyair mass flow. System characteristics include supply air temperature set point; entering water temperature of reheat, preheat, and cooling coils; minimum mass flow of outside air; and economizer temperature/enthalpy set point for minimum airflow. The algorithm for performing calculations for this VAV system is shown in Figure 17. The algorithm directs sequential calculations of system performance. Calculations proceed from the zones along the return air path to the cooling coil inlet and back through the supply air path to the cooling coil discharge.

Fig. 16 variable-air-volumeSchematic of Variable-air-volume System with Reheat

Fig. 16 Schematic of Variable-Air-Volume System with Reheat

19.24

2009 ASHRAE Handbook—Fundamentals

Fig. 17 Algorithm for Calculating Performance BEGIN LOOP Calculate of VAV with System Reheatzone related design requirements

• Calculate required supply airflow to meet zone load • Sum actual zone mass airflow rate • Sum zone latent loads IF zone equals last zone THEN Exit Loop END LOOP • Calculate system return air temperature from zone temps • Assume an initial cooling coil leaving air humidity ratio

BEGIN LOOP Iterate on cooling coil leaving air humidity ratio • Calculate return air humidity ratio from latent loads • Calculate supply fan power consumption and entering fan air temperature • Calculate mixed air temperature and humidity ratio using an economizer cycle IF mixed air temperature is less than design supply air temperature THEN • Calculate preheat coil load ELSE • Calculate cooling coil load and leaving air humidity ratio ENDIF IF cooling coil leaving air humidity ratio converged THEN Exit Loop END LOOP BEGIN LOOP Calculate the zone reheat coil loads IF zone supply air temperature is greater than system design supply air temperature THEN • Calculate reheat coil load (Subroutine: COILINV/HCDET) ENDIF • Sum reheat coil loads for all zones IF zone equals last zone THEN Exit Loop END LOOP

Fig. 17 Algorithm for Calculating Performance of VAV with System Reheat Moving back along the supply air path, the fan entering air temperature is calculated by setting fan outlet air temperature to the system design supply air temperature. The known fan inlet air temperature is then used as both the cooling coil and preheat coil discharge air temperature set point. Moving along the return air path, the cooling coil entering air temperature can be determined by sequentially moving through the economizer cycle and preheat coil. Unlike temperature, the humidity ratio at any point in a system cannot be explicitly determined because of the dependence of cooling coil performance on the mixed air humidity ratio. The latent load defines the difference between zone humidity and supply air humidity. However, the humidity ratio of supply air depends on the humidity ratio entering the coil, which in turn depends on that of the return air. This calculation must be performed either by solving simultaneous equations or, as in this case, iteration. Assuming a trial value for the humidity ratio at the cooling coil discharge (e.g., 55°F, 90% rh), the humidity ratio at all other points throughout the system can be calculated. With known cooling coil inlet air conditions and a design discharge air temperature, the inverted cooling coil subroutine iterates on the coil fluid mass flow to converge on the discharge air temperature with the discharge air humidity ratio as an output. The cooling coil discharge air humidity ratio is then compared to the previous discharge humidity ratio. Iteration continues through the loop several times until the values of the cooling coil discharge air humidity ratio stabilize within a specified tolerance. This basic algorithm for simulation of a VAV system might be used in conjunction with a heat balance type of load calculation. For

a weighting factor approach, it would have to be modified to allow zone temperatures to vary and consequently zone loads to be readjusted. It should also be enhanced to allow possible limits on reheat temperature and/or cooling coil limits, zone humidity limits, outside air control (economizers), and/or heat-recovery devices, zone exhaust, return air fan, heat gain in the return air path because of lights, the presence of baseboard heaters, and more realistic control profiles. Most current building energy programs incorporate these and other features as user options, as well as algorithms for other types of systems.

DATA-DRIVEN MODELING CATEGORIES OF DATA-DRIVEN METHODS Data-driven methods for energy-use estimation in buildings and related HVAC&R equipment can be classified into three broad categories. These approaches differ widely in data requirements, time and effort needed to develop the associated models, user skill demands, and sophistication and reliability provided.

Empirical or “Black-Box” Approach With this approach, a simple or multivariate regression model is identified between measured energy use and the various influential parameters (e.g., climatic variables, building occupancy). The form of the regression models can be either purely statistical or loosely based on some basic engineering formulation of energy use in the building. In any case, the identified model coefficients are such that no (or very little) physical meaning can be assigned to them. This approach can be used with any time scale (monthly, daily, hourly or subhourly) if appropriate data are available. Single-variate, multivariate, change point, Fourier series, and artificial neural network (ANN) models fall under this category, as noted in Table 1. Model identification is relatively straightforward, usually requires little effort, and can be used in several diverse circumstances. The empirical approach is thus the most widely used data-driven approach. Although more sophisticated regression techniques such as maximum likelihood and two-stage regression schemes can be used for model identification, least-squares regression is most common. The purely statistical approach is usually adequate for evaluating demand-side management (DSM) programs to identify simple and conventional energy conservation measures in an actual building (lighting retrofits, air handler retrofits such as CV to VAV retrofits) and for baseline model development in energy conservation measurement and verification (M&V) projects (Claridge 1998b; Dhar 1995; Dhar et al. 1998, 1999a, 1999b; Fels 1986; Katipamula et al. 1998; Kissock et al. 1998; Krarti et al. 1998; Kreider and Wang 1991; MacDonald and Wasserman 1989; Miller and Seem 1991; Reddy et al. 1997; Ruch and Claridge 1991). It is also appropriate for modeling equipment such as pumps and fans, and even more elaborate equipment such as chillers and boilers, if the necessary performance data are available (Braun 1992; Englander and Norford 1992; Lorenzetti and Norford 1993; Phelan et al. 1996). Although this approach allows detection or flagging of equipment or system faults, it is usually of limited value for diagnosis and on-line control (with ANN as a possible exception).

Calibrated Simulation Approach This approach uses an existing building simulation computer program and “tunes” or calibrates the various physical inputs to the program so that observed energy use matches closely with that predicted by the simulation program. Once that is achieved, more reliable predictions can be made than with statistical approaches. Calibrated simulation is advocated where only whole-building metering is available and M&V calls for estimating energy savings of individual retrofits. Practitioners tend to use common forwardsimulation programs such as DOE-2 to calibrate with performance

Energy Estimating and Modeling Methods data. Hourly subaggregated monitored energy data (most compatible with the time step adopted by most building energy simulation programs) allow development of the most accurate calibrated model, but analysts usually must work with less data. Tuning can be done with monthly data or data that span only a few weeks or months over the year, but the resulting model is very likely to be increasingly less accurate with decrease in performance data. The main challenges of calibrated simulation are that it is laborintensive, requires a high level of user skill and knowledge in both simulation and practical building operation, is time-consuming, and often depends on the person doing the calibration. Several practical difficulties prevent achieving a calibrated simulation or a simulation that closely reflects actual building performance, including (1) measurement and adaptation of weather data for use by simulation programs (e.g., converting global horizontal solar into beam and diffuse solar radiation), (2) choice of methods used to calibrate the model, and (3) choice of methods used to measure required input parameters for the simulation (i.e., building mass, infiltration coefficients, and shading coefficients). Truly “calibrated” models have been achieved in only a few applications because they require a very large number of input parameters, a high degree of expertise, and enormous amounts of computing time, patience, and financial resources. Bou-Saada and Haberl (1995a, 1995b), Bronson et al. (1992), Corson (1992), Haberl and Bou-Saada (1998), Kaplan et al. (1990) Manke et al. (1996), and Norford et al. (1994) provide examples of different methods used to calibrate simulation models. Katipamula and Claridge (1993) and Liu and Claridge (1998) suggested that simpler models could also work, and allow model calibration to be done much faster. Typically, the building is divided into two zones: an exterior or perimeter zone and an interior or a core zone. The core zone is assumed to be insulated from envelope heat losses/gains, and solar heat gains, infiltration heat loss/gain, and conduction gains/losses from the roof are taken as loads on the external zone only. Given the internal load schedule, building description, type of HVAC system, and climatic parameters, HVAC system loads can be estimated for each hour of the day and for as many days of the year as needed by the simplified systems model. Because there are fewer parameters to vary, calibration is much faster. Therefore, these models have a significant advantage over general-purpose models in buildings where the HVAC systems can be adequately modeled. These studies, based on the ASHRAE Simplified Energy Analysis Procedure (Knebel 1983), illustrate the applicability of this method both to baseline model development for M&V purposes and as a diagnostic tool for identifying potential operational problems and for estimating potential savings from optimized operating parameters.

Gray-Box Approach This approach first formulates a physical model to represent the structure or physical configuration of the building or HVAC&R equipment or system, and then identifies important parameters representative of certain key and aggregated physical parameters and characteristics by statistical analysis (Rabl and Riahle 1992). This requires a high level of user expertise both in setting up the appropriate modeling equations and in estimating these parameters. Often an intrusive experimental protocol is necessary for proper parameter estimation, which also requires skill. This approach has great potential, especially for fault detection and diagnosis (FDD) and online control, but its applicability to whole-building energy use is limited. Examples of parameter estimation studies applied to building energy use are Andersen and Brandemuehl (1992), Braun (1990), Gordon and Ng (1995), Guyon and Palomo (1999a), Hammersten (1984), Rabl (1988), Reddy (1989), Reddy et al. (1999), Sonderegger (1977), and Subbarao (1988).

19.25 TYPES OF DATA-DRIVEN MODELS Steady-state models do not consider effects such as thermal mass or capacitance that cause short-term temperature transients. Generally, these models are appropriate for monthly, weekly, or daily data and are often used for baseline model development. Dynamic models capture effects such as building warm-up or cooldown periods and peak loads, and are appropriate for building load control, FDD, and equipment control. A simple criterion to determine whether a model is steady-state or dynamic is to look for the presence of time-lagged variables, either in the response or regressor variables. Steady-state models do not contain time-lagged variables.

Steady-State Models Several types of steady-state models are used for both building and equipment energy use: single-variate, multivariate, polynomial, and physical. Single-Variate Models. Single-variate models (i.e., models with one regressor variable only) are perhaps the most widely used. They formulate energy use in a building as a function of one driving force that affects building energy use. An important aspect in identifying statistical models of baseline energy use is the choice of the functional form and the independent (or regressor) variables. Extensive studies (Fels 1986; Katipamula et al. 1994; Kissock et al. 1993; Reddy et al. 1997) have clearly indicated that the outdoor dry-bulb temperature is the most important regressor variable, especially at monthly time scales but also at daily time scales. The simplest steady-state data-driven model is one developed by regressing monthly utility consumption data against average billing-period temperatures. The model must identify the balancepoint temperatures (or change points) at which energy use switches from weather-dependent to weather-independent behavior. In its simplest form, the 65°F degree-day model is a change-point model that has a fixed change point at 65°F. Other examples include threeand five-parameter Princeton Scorekeeping Methods (PRISM) based on the variable-base degree-day concept (Fels 1986). An allied modeling approach for commercial buildings is the fourparameter (4-P) model developed by Ruch and Claridge (1991), which is based on the monthly mean temperature (and not degreedays). Table 9 shows the appropriate model functional forms. The three parameters are a weather-independent base-level use, a change point, and a temperature-dependent energy use, characterized as a slope of a line that is determined by regression. The four parameters include a change point, a slope above the change point, a slope below the change point, and the energy use associated with the change point. An data-driven bin method has also been proposed to handle more than four change points (Thamilseran and Haberl 1995). Figure 18 shows several types of steady-state, single-variate data-driven models. Figure 18A shows a simple one-parameter, or constant, model, and Table 9 gives the equivalent notation for calculating the constant energy use using this model. Figure 18B shows a steady-state two-parameter (2-P) model where b0 is the y-axis intercept and b1 is the slope of the regression line for positive values of x, where x represents the ambient air temperature. The 2-P model represents cases when either heating or cooling is always required. Figure 18C shows a three-parameter change-point model, typical of natural gas energy use in a single-family residence that uses gas for space heating and domestic water heating. In the notation of Table 9 for the three-parameter model, b0 represents the baseline energy use and b1 is the slope of the regression line for values of ambient temperature less than the change point b2. In this type of notation, the superscripted plus sign indicates that only positive values of the parenthetical expression are considered. Figure 18D shows a three-parameter model for cooling energy use, and Table 9 provides the appropriate analytic expression. Figures 18E and 18F illustrate four-parameter models for heating and cooling, respectively. The appropriate expressions for

19.26

2009 ASHRAE Handbook—Fundamentals

Fig. 18 Steady-State, Single-Variate Models for Modeling Energy Use in Residential and Commercial Buildings

Fig. 18 Steady-State, Single-Variate Models for Modeling Energy Use in Residential and Commercial Buildings

Table 9 Single-Variate Models Applied to Utility Billing Data Model Type

Independent Variable(s)

Form

Examples

One-parameter or constant (1-P)

None

E = b0

Non-weather-sensitive demand

Two-parameter (2-P)

Temperature

E = b0 +b1(T )

Three-parameter (3-P)

Degree-days/ Temperature

E = b0 + b1(DDBT) E = b0 + b1(b2 T )+ E = b0 + b1(T b2)+

Seasonal weather-sensitive use (fuel in winter, electricity in summer for cooling)

Four-parameter change point (4-P)

Temperature

E = b0 + b1(b3 T )+ b2 (T b3)+ E = b0 – b1(b3 T )+ + b2 (T b3)+

Energy use in commercial buildings

Five-parameter (5-P)

Degree-days/ Monthly mean temperature

E = b0 b1(DDTH) + b2 (DDTC) E = b0 + b1(b3 T )+ + b (T – b4)+

Heating and cooling supplied by same meter

Note: DD denotes degree-days and T is monthly mean daily outdoor dry-bulb temperature.

Energy Estimating and Modeling Methods calculating the heating and cooling energy consumption are found in Table 9: b0 represents the baseline energy exactly at the change point b3, and b1 and b2 are the lower and upper region regression slopes for ambient air temperature below and above the change point b3. Figure 18G illustrates a 5-P model (Fels 1986), which is useful for modeling buildings that are electrically heated and cooled. The 5-P model has two change points and a base level consumption value. The advantage of these steady-state data-driven models is that their use can be easily automated and applied to large numbers of buildings where monthly utility billing data and average daily temperatures for the billing period are available. Steady-state singlevariate data-driven models have also been applied with success to daily data (Kissock et al. 1998). In such a case, the variable-base degree-day method and monthly mean temperature models described earlier for utility billing data analysis become identical in their functional form. Single-variate models can also be applied to daily data to compensate for differences such as weekday and weekend use by separating the data accordingly and identifying models for each period separately. Disadvantages of steady-state single-variate data-driven models include insensitivity to dynamic effects (e.g., thermal mass) and to variables other than temperature (e.g., humidity and solar gain), and inappropriateness for some buildings (e.g., buildings with strong on/off schedule-dependent loads or buildings with multiple change points). Moreover, a single-variable, 3-P model such as the PRISM model (Fels 1986) has a physical basis only when energy use above a base level is linearly proportional to degree-days. This is a good approximation in the case of heating energy use in residential buildings where heating load never exceeds the heating system’s capacity. However, commercial buildings generally have higher internal heat generation with simultaneous heating and cooling energy use and are strongly influenced by HVAC system type and control strategy. This makes energy use in commercial buildings less strongly influenced by outdoor air temperature alone. Therefore, it is not surprising that blind use of single-variate models has had mixed success at modeling energy use in commercial buildings (MacDonald and Wasserman 1989). Change-point regression models work best with heating data from buildings with systems that have few or no part-load nonlinearities (i.e., systems that become less efficient as they begin to cycle on/off with part loads). In general, change-point regression models do not predict cooling loads as well because outdoor humidity has a large influence on latent loads on the cooling coil. Other factors that decrease the accuracy of change-point models include solar effects, thermal lags, and on/off HVAC schedules. Four-parameter models are a better statistical fit than threeparameter models in buildings with continuous, year-round cooling or heating (e.g., grocery stores and office buildings with high internal loads). However, every model should be checked to ensure that the regression does not falsely indicate an unreasonable relationship. A major advantage of using a steady-state data-driven model to evaluate the effectiveness of energy conservation retrofits is its ability to factor out year-to-year weather variations by using a normalized annual consumption (NAC) (Fels 1986). Basically, annual energy conservation savings can be calculated by comparing the difference obtained by multiplying the pre- and postretrofit parameters by the weather conditions for the average year. Typically, 10 to 20 years of average daily weather data from a nearby weather service site are used to calculate 365 days of average weather conditions, which are then used to calculate the average pre- and postretrofit conditions. Utilities and government agencies have found it advantageous to prescreen many buildings against test regression models. These data-driven models can be used to develop comparative figures of merit for buildings in a similar standard industrial code (SIC)

19.27 classification. A minimum goodness of fit is usually established that determines whether the monthly utility billing data are well fitted by the one-, two-, three-, four-, or five-parameter model being tested. Comparative figures of merit can then be determined by dividing the parameters by the conditioned floor area to yield average daily energy use per unit area of conditioned space. For example, an areanormalized comparison of base-level parameters across residential buildings would be used to analyze weather-independent energy use. This information can be used by energy auditors to focus their efforts on those systems needing assistance (Haberl and Komor 1990a, 1990b). Multivariate Models. Two types of steady-state, multivariate models have been reported: • Standard multiple-linear or change-point regression models, where the set of data observations is treated without retaining the time-series nature of the data (Katipamula et al. 1998). • Fourier series models that retain the time-series nature of building energy use data and capture the diurnal and seasonal cycles according to which buildings are operated (Dhar 1995; Dhar et al. 1998, 1999a, 1999b; Seem and Braun 1991). These models are a logical extension of single-variate models, provided that the choice of variables to be included and their functional forms are based on the engineering principles on which HVAC systems and other systems in commercial buildings operate. The goal of modeling energy use by the multivariate approach is to characterize building energy use with a few readily available and reliable input variables. These input variables should be selected with care. The model should contain variables not affected by the retrofit and likely to change (for example, climatic variables) from preretrofit to postretrofit periods. Other less obvious variables, such as changes in operating hours, base load, and occupancy levels, should be included in the model if these are not energy conservation measures (ECMs) but variables that may change during the postretrofit period. Environmental variables that meet these criteria for modeling heating and cooling energy use include outdoor air dry-bulb temperature, solar radiation, and outdoor specific humidity. Some of these are difficult to estimate or measure in an actual building and hence are not good candidates for regressor variables. Further, some of the variables vary little. Although their effect on energy use may be important, a data-driven model will implicitly lump their effect into the parameter that represents constant load. In commercial buildings, internally generated loads, such as the heat given off by people, lights, and electrical equipment, also affect heating and cooling energy use. These internal loads are difficult to measure in their entirety given the ambiguous nature of occupant and latent loads. However, monitored electricity used by internal lights and equipment is a good surrogate for total internal sensible loads (Reddy et al. 1999). For example, when the building is fully occupied, it is also likely to be experiencing high internal electric loads, and vice versa. The effect of environmental variables is important for buildings such as offices but may be less so for mixed-use buildings (e.g., hotels and hospitals) and buildings such as retail buildings, schools, and assembly buildings. Differences in HVAC system behavior during occupied and unoccupied periods can be modeled by a dummy or indicator variable (Draper and Smith 1981). For some office buildings, there seems to be little need to include a dummy variable, but its inclusion in the general functional form adds flexibility. Several standard statistical tests evaluate the goodness-of-fit of the model and the degree of influence that each independent variable exerts on the response variable (Draper and Smith 1981; Neter et al. 1989). Although energy use in fact depends on several variables, there are strong practical incentives for identifying the simplest model that results in acceptable accuracy. Multivariate models require more metering and are unusable if even one of the variables becomes unavailable. In addition, some regressor variables may be

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2009 ASHRAE Handbook—Fundamentals

linearly correlated. This condition, called multicollinearity, can result in large uncertainty in the estimates of the regression coefficients (i.e., unintended error) and can also lead to poorer model prediction accuracy compared to a model where the regressors are not linearly correlated. Several authors recommend using principal component analysis (PCA) to overcome multicollinearity effects. PCA was one of the strongest analysis methods in the ASHRAE Predictor Shootout I and II contests (Haberl and Thamilseran 1996; Kreider and Haberl 1994). Analysis of multiyear monitored daily energy use in a grocery store found a clear superiority of PCA over multivariate regression models (Ruch et al. 1993), but this conclusion is unproven for commercial building energy use in general. A more general evaluation by Reddy and Claridge (1994) of both analysis techniques using synthetic data from four different U.S. locations found that injudicious use of PCA may exacerbate rather than overcome problems associated with multicollinearity. Draper and Smith (1981) also caution against indiscriminate use of PCA. The functional basis of air-side heating and cooling use in various HVAC system types has been addressed by Reddy et al. (1995) and subsequently applied to monitored data in commercial buildings (Katipamula et al. 1994, 1998). Because quadratic and crossproduct terms of engineering equations are not usually picked up by multivariate models, strictly linear energy use models are often the only option. In addition to To, internal electric equipment and lighting load Eint , solar loads qsol , and latent effects via the outdoor dew-point temperature Tdp are candidate regressor variables. In commercial buildings, a major portion of the latent load derives from fresh air ventilation. However, this load appears only when the outdoor air dew-point temperature exceeds the cooling coil temperature. Hence, the term (Tdp – Ts)+ (where the + sign indicates that the term is to be set to zero if negative, and Ts is the mean surface temperature of the cooling coil, typically about 51 to 55°F) is a more realistic descriptor of the latent loads than is Tdp alone. Using (Tdp – Ts)+ as a regressor in the model is a simplification that seems to yield good accuracy. Therefore, a multivariate linear regression model with an engineering basis has the following structure: –

+

Q bldg = E 0 + E 1 T o – E 3 + E 2 T o – E 3 + E 4 T dp – E 6 +

+ E 5 T dp – E 6 + E 7 q sol + E 8 E int

– in

(67)

+

(68)

where the indicator variable I is introduced to handle the change in slope of the energy use due to To. The variable I is set equal to 1 for To values to the right of the change point (i.e., for high To range) and set equal to 0 for low To values. As with the single-variate segmented models (i.e., 3-P and 4-P models), a search method is used to determine the change point that minimizes the total sum of squares of residuals (Fels 1986; Kissock et al. 1993). Katipamula et al. (1994) found that Equation (68), appropriate for VAV systems, could be simplified for constant-volume HVAC systems: +

Q bldg = a + bT o + eT dp + f q sol + gE int

(69)

Note that instead of using (Tdp – Ts)+, the absolute humidity potential (W0 – Ws)+ could also be used, where W0 is the outdoor absolute humidity, and Ws is the absolute humidity level at the dew

out

E comp = a + bQ evap + cT cond + dT evap + eQ evap in

Based on the preceding discussion, E4 = 0. Introducing indicator variable terminology (Draper and Smith 1981), Equation (67) becomes Q bldg = a + bT o + cI + dIT o + eT dp + f q sol + gE int

point of the cooling coil (typically about 0.198 lb/lb). A final aspect + to keep in mind is that the term T dp should be omitted from the regressor variable set when regressing heating energy use, because there are no latent loads on a heating coil. These multivariate models are very accurate for daily time scales and slightly less so for hourly time scales. This is because changes in the way the building is operated during the day and the night lead to different relative effects of the various regressors on energy use, which cannot be accurately modeled by one single hourly model. Breaking up energy use data into hourly bins corresponding to each hour of the day and then identifying 24 individual hourly models leads to appreciably greater accuracy (Katipamula et al. 1994). Polynomial Models. Historically, polynomial models have been widely used as pure statistical models to model the behavior of equipment such as pumps, fans, and chillers (Stoecker and Jones 1982). The theoretical aspects of calculating pump performance are well understood and documented. Pump capacity and efficiency are calculated from measurements of pump head, flow rate, and pump electrical power input. Phelan et al. (1996) studied the predictive ability of linear and quadratic models for electricity consumed by pumps and water mass flow rate, and concluded that quadratic models are superior to linear models. For fans, Phelan et al. (1996) studied the predictive ability of linear and quadratic polynomial single-variate models of fan electricity consumption as a function of supply air mass flow rate, and concluded that, although quadratic models are superior in terms of predicting energy use, the linear model seems to be the better overall predictor of both energy use and demand (i.e., maximum monthly power consumed by the fan). This is a noteworthy conclusion given that a third-order polynomial is warranted analytically as well as from monitored field data presented by previous authors (e.g., Englander and Norford 1992; Lorenzetti and Norford 1993). Polynomial models have been used to correlate chiller (or evaporator) thermal cooling capacity or load Q evap and the electrical power consumed by the chiller (or compressor) E comp with the relevant number of influential physical parameters. For example, based on the functional form of the DOE-2 building simulation software (York and Cappiello 1982), models for part-load performance of energy equipment and plant, Ecomp, can be modeled as the following triquadratic polynomial:

2

out 2

in

2 out

+ f T cond + gT evap + hQ evap T cond + iT evap Q evap in

out

in

out

+ j T cond T evap + kQ evap T cond T evap

(70)

In this model, there are 11 model parameters to identify. However, because all of them are unlikely to be statistically significant, a step-wise regression to the sample data set yields the optimal set of parameters to retain in a given model. Other authors, such as Braun (1992), have used slightly different polynomial forms. Physical Models. In contrast to polynomial models, which have no physical basis (merely a convenient statistical one), physical models are based on fundamental thermodynamic or heat transfer considerations. These types of models are usually associated with the parameter estimation approach. Often, physical models are preferred because they generally have fewer parameters, and their mathematical formulation can be traced to actual physical principles that govern the performance of the building or equipment. Hence, model coefficients tend to be more robust, leading to sounder model predictions. Only a few studies have used steady-state physical models for parameter estimation relating to commercial building energy use [e.g., Reddy et al. (1999)]. Unlike in single-family residences, it is difficult to perform elaborately planned experiments in large buildings and obtain representative values of indoor fluctuations.

Energy Estimating and Modeling Methods

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The generalized Gordon and Ng (GN) model (Gordon and Ng 2000) is a simple, analytical, universal model for chiller performance based on first principles of thermodynamics and linearized heat losses. The model predicts the dependent chiller coefficient of performance (COP) [the ratio of chiller (or evaporator) thermal cooling capacity Qch to electrical power E consumed by the chiller] with specially chosen independent, easily measurable parameters such as the fluid (water or air) temperature entering the condenser Tcdi, fluid temperature entering the evaporator Tcdi, and the thermal cooling capacity of the evaporator. The GN model is a three-parameter model in the following form: T chi T cdi – T chi chi 1 § ---------·T --------- – 1 = a 1 --------- + a 2 -----------------------------© COP- + 1¹ T Q ch T cdi Q ch cdi 1 e COP + 1 Q ch + a 3 -----------------------------------------T cdi

(71a)

where temperatures are in absolute units. Substituting the following,

T chi x 1 = -------- Q ch and

T cdi – T chi x 2 = ------------------------------ T cdi Q ch

x3

1 e COP + 1 Q ch -----------------------------------------T cdi

T chi 1 - + 1· --------–1 y = §© ---------¹T COP

(71b)

cdi

the model given by Equation (71a) becomes y = a1 x1 + a2 x2 + a3 x3

(71c)

which is a three-parameter linear model with no intercept term. The parameters of the model in Equation (71c) have the following physical meaning: a1 = 'S = total internal entropy production in chiller a2 = Qleak = heat losses (or gains) from (or into) chiller a3 = R = total heat exchanger thermal resistance = 1/Ccd + 1/Cch, where C is effective thermal conductance Gordon and Ng (2000) point out that Qleak is typically an order of magnitude smaller than the other terms, but it is not negligible for accurate modeling, and should be retained in the model if the other two parameters identified are to be used for chiller diagnostics. The same linear model structure as Equation (71c) can be used if the fluid temperature leaving the evaporator Tcho is used instead of Tchi. However, the physical interpretation of the term a3 is modified accordingly. Reddy and Anderson (2002) and Sreedharan and Haves (2001) found that the GN and multivariate polynomial (MP) models were comparable in their predictive abilities. The GN model requires much less data if selected judiciously [even four well-chosen data points can yield accurate models, as demonstrated by Corcoran and Reddy (2003)]. Jiang and Reddy (2003) tested the GN model against more than 50 data sets covering various generic types and sizes of water-cooled chillers (single- and double-stage centrifugal chillers with inlet guide vanes and variable-speed drives, screw, scroll), and found excellent predictive ability (coefficient of variation of RMSE in the range of 2 to 5%).

Dynamic Models In general, steady-state data-driven models are used with monthly and daily data containing one or more independent variables. Dynamic data-driven models are usually used with hourly or subhourly data in cases where the building’s thermal mass is signifi-

cant enough to delay heat gains or losses. Dynamic models traditionally required solving a set of differential equations. Disadvantages of dynamic data-driven models include their complexity and the need for more detailed measurements to tune the model. More information on measurements, including whole-building metering, retrofit isolation metering, and whole-building calibrated simulation, can be found in ASHRAE Guideline 14, Measurement of Energy and Demand Savings, and the International Performance Measurement and Verification Protocol (IPMVP) (U.S. Department of Energy 2001a, 2001b, 2003). Unlike steadystate data-driven models, dynamic data-driven models usually require a high degree of user interaction and knowledge of the building or system being modeled. Several residential energy studies have used dynamic data-driven models based on parameter estimation approaches, usually involving intrusive data gathering. Rabl (1988) classified the various types of dynamic data-driven models used for whole-building energy use identified the common underlying features of these models. There are essentially four different types of model formulations: thermalnetwork, time series, differential equation, and modal, all of which qualify as parameter-estimation approaches. Table 1 lists several pertinent studies in each category. A few studies (Hammersten 1984; Rabl 1988; Reddy 1989) evaluated these different approaches with the same data set. A number of papers reported results of applying different techniques, such as thermal-network and ARMA models, to residential and commercial building energy use (see Table 1). Examples of dynamic data-driven models for commercial building are found in Andersen and Brandemuehl (1992), Braun (1990), and Rabl (1988). Dynamic data-driven models based on pure statistical approaches have also been reported. Two examples are machine learning (Miller and Seem 1991) and artificial neural networks (Kreider and Haberl 1994; Kreider and Wang 1991; Miller and Seem 1991). Neural networks are considered to be intuitive because they learn by example rather than by following programmed rules. The ability to “learn” is one of their key aspects. A neural network consists of one input layer (which can contain one or more inputs), one or more hidden layers, and an output or target layer. One challenge of this technology is to construct a net with sufficient complexity to learn accurately without imposing excessive computational time. The weights of a net are initiated with small random numbers. Then, the weights are adjusted iteratively or “trained” so that applying a set of inputs produces the desired set of outputs. Usually, a network is trained with a training data set that consists of many input/ output pairs. Artificial neural networks have been trained by a wide variety of methods (McClelland and Rumelhart 1988, Wasserman 1989), including back propagation. Neural networks have been useful in modeling energy use in commercial buildings for • Predicting what a properly operating building should be doing compared to actual operation. If there is a difference, it can be used in an expert system to produce early diagnoses of building operation problems. • Predicting what a building, before an energy retrofit, would have consumed under present conditions. When compared to the measured consumption of the retrofitted building, the difference represents a good estimate of the energy savings due to the retrofit. This represents one of the few ways that actual energy savings can be determined after the preretrofit building configuration has ceased to exist.

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2009 ASHRAE Handbook—Fundamentals

EXAMPLES USING DATA-DRIVEN METHODS Modeling Utility Bill Data The following example (taken from Sonderegger 1998) illustrates a utility bill analysis. Assume that values of utility bills over an entire year have been measured. To obtain the equation coefficients through regression, the utility bills must be normalized by the length of the time interval between utility bills. This is equivalent to expressing all utility bills, degree-days, and other independent variables by their daily averages. Appropriate modeling software is used in which values are assumed for heating and cooling balance points; from these, the corresponding heating and cooling degree-days for each utility bill period are determined. Repeated regression is done till the regression equation represents the best fit to the meter data. The model coefficients are then assumed to be tuned. Some programs allow direct determination of these optimal model parameters without the user’s manual tuning of the parameters. A widely used statistic to gage the goodness-of-fit of the model is the coefficient of determination R2. A value of R2 = 1 indicates a perfect correlation between actual data and the regression equation; a value of R2 = 0 indicates no correlation. For tuning for a performance contract, as a rule of thumb the value of R2 should never be less than 0.75. When more than one independent variable is included in the regression, R2 is no longer sufficient to determine the goodness-offit. The standard error of the estimate of the coefficients becomes the more important determinant. The smaller the standard error compared to the coefficient’s magnitude, the more reliable the coefficient estimate. To identify the significance of individual coefficients, t-statistics (or t-values) are used. These are simply the ratio of the coefficient estimate divided by the standard error of the estimate. The coefficient of each variable included in the regression has a t-statistic. For a coefficient to be statistically meaningful, the absolute value of its t-statistic must be at least 2.0. In other words, under no circumstances should a variable be included in a regression if the standard error of its coefficient estimate is greater than half the magnitude of the coefficient (even when including a variable that increases the R2). Generally, including more variables in a regression results in a higher R2, but the significance of most individual coefficients is likely to decrease.

Fig. 19

Figure 19 illustrates how well a regression fit captures measured baseline energy use in a hospital building. Cooling degree-days are found to be a significant variable, with the best fit for a base temperature of 54°F. Individual utility bills may be unsuitable to develop a baseline and should be excluded from the regression. For example, a bill may be atypically high because of a one-time equipment malfunction that was subsequently repaired. However, it is often tempting to look for reasons to exclude bills that fall far from “the line” and not question those that are close to it. For example, bills for periods containing vacations or production shutdowns may look anomalously low, but excluding them from the regression would result in a chronic overestimate of the future baseline during the same period.

Neural Network Models Figure 20 shows results for a single neural network typical of several hundred networks constructed for an academic engineering center located in central Texas. The cooling load is created by solar gains, internal gains, outdoor air sensible heat, and outdoor air humidity loads. The neural network is used to predict the preretrofit energy consumption for comparison with measured consumption of the retrofitted building. Six months of preretrofit data were available to train the network. Solid lines show the known building consumption data, and dashed lines show the neural network predictions. This figure shows that a neural network trained for one period (September 1989) can predict energy consumption well into the future (in this case, January 1990). The network used for this prediction had two hidden layers. The input layer contained eight neurons that receive eight different types of input data as listed below. The output layer consisted of one neuron that gave the output datum (chilled-water consumption). Each training fact (i.e., training data set), therefore, contained eight input data (independent variables) and one pattern datum (dependent variable). The eight hourly input data used in each hour’s data vector were selected on physical bases (Kreider and Rabl 1994) and were as follows: • • • • • •

Hour number (0 to 2300) Ambient dry-bulb temperature Horizontal insolation Humidity ratio Wind speed Weekday/weekend binary flag (0, 1)

Variable-Base Degree-Day Model Identification Using Electricity Utility Bills at a Hospital

Fig. 19 Variable-Base Degree-Day Model Identification Using Electricity Utility Bills at Hospital (Sonderegger 1998)

Energy Estimating and Modeling Methods

19.31

• Past hour’s chilled-water consumption • Second past hour’s chilled-water consumption These measured independent variables were able to predict chilledwater use to an RMS error of less than 4% (JCEM 1992). Choosing an optimal network’s configuration for a given problem remains an art. The number of hidden neurons and layers must be sufficient to meet the requirement of the given application. However, if too many neurons and layers are used, the network tends to memorize data rather than learning (i.e., finding the underlying patterns in the data). Further, choosing an excessively large number of hidden layers significantly increases the required training time for certain learning algorithms. Anstett and Kreider (1993), Krarti et al. (1998), Kreider and Wang (1991), and Wang and Kreider (1992) report additional case studies for commercial buildings.

the possible cause of the malfunction if sufficient historical information has been previously gathered (Haberl and Claridge 1987). Hourly systems that use artificial neural networks have also been constructed (Kreider and Wang 1991). More information on data-driven models can be found in the ASHRAE Inverse Modeling Toolkit (Haberl et al. 2003; Kissock et al. 2003). This toolkit contains FORTRAN 90 and executable code for performing linear and change-point linear regressions, variable-based degree-days, multilinear regression, and combined regressions. It also includes a complete test suite of data sets for testing all models. Table 10 presents a decision diagram for selecting a forward or data-driven model where use of the model, degree of difficulty in understanding and applying the model, time scale for data used by the model, calculation time, and input variables used by the models are the criteria used to choose a particular model.

MODEL SELECTION Steady-state and dynamic data-driven models can be used with energy management and control systems to predict energy use (Kreider and Haberl 1994). Hourly or daily comparisons of measured versus predicted energy use can be used to determine whether systems are being left on unnecessarily or are in need of maintenance. Combinations of predicted energy use and a knowledgebased system can indicate above-normal energy use and diagnose Fig. 20 Neural Network Prediction of Whole-Building, Hourly Chilled Water Consumption for a Commercial Building

MODEL VALIDATION AND TESTING ANSI/ASHRAE Standard 140, Method of Test for the Evaluation of Building Energy Analysis Computer Programs, was developed to identify and diagnose differences in predictions that may be caused by algorithmic differences, modeling limitations, or coding or input errors. Standard 140 allows all elements of a complete validation approach to be added as they become available. This structure corresponds to the following validation methodology, with subdivisions creating a matrix of six areas for testing: 1. 2. 3. 4. 5. 6.

Fig. 20 Neural Network Prediction of Whole-Building, Hourly Chilled-Water Consumption for Commercial Building

Comparative tests—building envelope Comparative tests—mechanical equipment Analytical verification—building envelope Analytical verification—mechanical equipment Empirical validation—building envelope Empirical validation—mechanical equipment

The current set of tests focus on categories 1 and 4. These tests are based on procedures developed by the National Renewable Energy Laboratory and field-tested by the International Energy Agency (IEA) over three IEA research tasks (Judkoff and Neymark 1995a; Neymark and Judkoff 2002). Additional tests are being developed under ASHRAE research projects (Spitler et al. 2001; Yuill and Haberl 2002) and under joint IEA Solar Heating and Cooling Programme/Energy Conservation in Buildings and Community Systems Task 34/Annex 43 (Judkoff and Neymark 2004) that are intended to fill in other categories of the validation matrix.

Table 10 Capabilities of Different Forward and Data-Driven Modeling Methods Methods

Usea

Difficulty

Time Scaleb

Calc. Time

Variablesc

Accuracy

Simple linear regression Multiple linear regression ASHRAE bin method and data-driven bin method Change-point models ASHRAE TC 4.7 modified bin method Artificial neural networks Thermal network Fourier series analysis ARMA model Modal analysis Differential equation Computer simulation (component-based) (fixed schematic) Computer emulation

ES D, ES ES D, ES ES, DE D, ES, C D, ES, C D, ES, C D, ES, C D, ES, C D, ES, C D, ES, C, DE D, ES, DE D, C

Simple Simple Moderate Simple Moderate Complex Complex Moderate Moderate Complex Complex Very complex Very complex Very complex

D, M D, M H H, D, M H S, H S, H S, H S, H S, H S, H S, H H S, H

Very fast Fast Fast Fast Medium Fast Fast Medium Medium Medium Fast Slow Slow Very slow

T T, H, S, W, t T T T, S, tm T, H, S, W, t, tm T, S, tm T, H, S, W, t, tm T, H, S, W, t, tm T, H, S, W, t, tm T, H, S, W, t, tm T, H, S, W, t, tm T, H, S, W, t, tm T, H, S, W, t, tm

Low Medium Medium Medium Medium High High High High High High Medium Medium High

Notes: a Use shown includes diagnostics (D), energy savings calculations (ES), design (DE), and control (C).

bTime

scales shown are hourly (H), daily (D), monthly (M), and subhourly (S).

cVariables include temperature (T ), humidity (H), solar (S), wind (W), time (t),

and thermal mass (tm).

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There are three ways to evaluate a whole-building energy simulation program’s accuracy (Judkoff et al. 1983; Neymark and Judkoff 2002): • Empirical validation, which compares calculated results from a program, subroutine, algorithm, or software object to monitored data from a real building, test cell, or laboratory experiment • Analytical verification, which compares outputs from a program, subroutine, algorithm, or software object to results from a known analytical solution or a generally accepted numerical method calculation for isolated heat transfer under very simple, highly constrained boundary conditions • Comparative testing, which compares a program to itself or to other programs Table 11 compares these techniques (Judkoff 1988). In this table, the term “model” is the representation of reality for a given physical behavior. For example, heat transfer may be simulated with one-, two-, or three-dimensional thermal conduction models. The term “solution process” encompasses the mathematics and computer coding to solve a given model. The solution process for a model can be perfect, while the model remains inappropriate for a given physical situation, such as using a one-dimensional conduction model where two-dimensional conduction dominates. The term “truth standard” represents the standard of accuracy for predicting real behavior. An analytical solution is a “mathematical truth standard,” but only tests the solution process for a model, not the appropriateness of the model. An approximate truth standard from an experiment tests both the solution process and appropriateness of the model within experimental uncertainty. The ultimate (or “absolute”) validation truth standard would be comparison of simulation results with a perfectly performed empirical experiment, with all simulation inputs perfectly defined. Establishing an absolute truth standard for evaluating a program’s ability to analyze physical behavior requires empirical validation, but this is only possible within the range of measurement uncertainty, including that related to instruments, spatial and temporal discretization, and the overall experimental design. Test cells and buildings are large, relatively complex experimental objects. The exact design details, material properties, and construction in the field may not be known, so there is some uncertainty about the simulation model inputs that accurately represent the experimental object. Meticulous care is required to describe the experimental apparatus as clearly as possible to modelers to minimize this uncertainty. This includes experimental determination of as many material properties as possible, including overall building parameters such as overall steady-state heat transmission coefficient, infiltration rate, and thermal capacitance. Also required are detailed meteorological measurements. For Table 11

example, many experiments measure global horizontal solar radiation, but very few experiments measure the splits between direct, diffuse, and ground reflected radiation, all of which are inputs to many whole-building energy simulation programs. The National Renewable Energy Laboratory (NREL) divides empirical validation into different levels, because many validation studies produced inconclusive results. The levels of validation depend on the degree of control over possible sources of error in a simulation. These error sources consist of seven types, divided into two groups:

External Error Types • Differences between actual building microclimate versus weather input used by the program • Differences between actual schedules, control strategies, effects of occupant behavior, and other effects from the real building versus those assumed by the program user • User error deriving building input files • Differences between actual physical properties of the building (including HVAC systems) versus those input by the user

Internal Error Types • Differences between actual thermal transfer mechanisms in the real building and its HVAC systems versus the simplified model of those processes in the simulation (all models, no matter how detailed, are simplifications of reality) • Errors or inaccuracies in the mathematical solution of the models • Coding errors The simplest level of empirical validation compares a building’s actual long-term energy use to that calculated by a computer program, with no attempt to eliminate sources of discrepancy. Because this is similar to how a simulation tool is used in practice, it is favored by many in the building industry. However, it is difficult to interpret the results because all possible error sources are acting simultaneously. Even if there is good agreement between measured and calculated performance, possible offsetting errors prevent a definitive conclusion about the model’s accuracy. More informative levels of validation involve controlling or eliminating various combinations of error types and increasing the density of output-to-data comparisons (e.g., comparing temperature and energy results at time scales ranging from subhourly to annual). At the most detailed level, all known sources of error are controlled to identify and quantify unknown error sources and to reveal causal relationships associated with error sources. This principle also applies to intermodel comparative testing and analytical verification. The more realistic the test case, the more difficult it is to establish causality and diagnose problems; the simpler

Validation Techniques

Technique

Advantages

Disadvantages

Empirical (test of model and solution process)

• Approximate truth standard within experimental accuracy • Any level of complexity

Analytical (test of solution process)

• No input uncertainty • Exact mathematical truth standard for given model • Inexpensive • No input uncertainty • Any level of complexity • Many diagnostic comparisons possible • Inexpensive and quick

• Experimental uncertainties: • Instrument calibration, spatial/temporal discretization • Imperfect knowledge/specification of experimental object (building) being simulated • High-quality, detailed measurements are expensive and time-consuming • Only a limited number of test conditions are practical • No test of model validity • Limited to highly constrained cases for which analytical solutions can be derived

Comparative (relative test of model and solution process)

Source: Neymark and Judkoff (2002).

• No absolute truth standard (only statistically based acceptance ranges are possible)

Energy Estimating and Modeling Methods Table 12 Types of Extrapolation Obtainable Data Points

19.33 Fig. 21 Validation Method

Extrapolation

A few climates Short-term total energy use

Many climates Long-term total energy use, or vice versa Short-term (hourly) temperatures Long-term total energy use, or vice and/or fluxes versa A few equipment performance points Many equipment performance points A few buildings representing a few Many buildings representing many sets of variable and parameter sets of variable and parameter combinations combinations, or vice versa Small-scale: simple test cells, Large-scale complex buildings with buildings, and mechanical systems; complex HVAC systems, or vice laboratory experiments versa Source: Neymark and Judkoff (2002).

and more controlled the test case, the easier it is to pinpoint sources of error or inaccuracy. Methodically building up to realistic cases is useful for testing interactions between algorithms modeling linked mechanisms. A comparison between measured and calculated performance represents a small region in an immense N-dimensional parameter space. Investigators are constrained to exploring relatively few regions in this space, yet would like to be assured that the results are not coincidental (e.g., not a result of offsetting errors) and do represent the validity of the simulation elsewhere in the parameter space. Analytical and comparative techniques minimize the uncertainty of extrapolations around the limited number of sampled empirical domains. Table 12 classifies these extrapolations. Use of the term “vice versa” in Table 12 is intended to mean that the extrapolation can go both ways (e.g., from short-term to long-term data and from long-term to short-term data). This does not mean that such extrapolations are correct, but only that researchers and practitioners have either explicitly or implicitly made such inferences in the past. Figure 21 shows one process to combine analytical, empirical, and comparative techniques. These three techniques may also be used together in other ways; for example, intermodel comparisons may be done before an empirical validation exercise, to better define the experiment and to help estimate experimental uncertainty by propagating all known error sources through one or more whole-building energy simulation programs (Hunn et al. 1982; Lomas et al. 1994). For the path shown in Figure 21, the first step is running the code against analytical verification test cases to check its mathematical solution. Discrepancies must be corrected before proceeding further. Second, the code is run against high-quality empirical validation data, and errors are corrected. Diagnosing error sources can be quite difficult and is an area of research in itself. Comparative techniques can be used to create diagnostics procedures (Judkoff 1988; Judkoff and Neymark 1995a, 1995b; Judkoff et al. 1980, 1983; Morck 1986; Neymark and Judkoff 2002; Spitler et al. 2001) and better define the experiments. The third step is to check agreement of several different thermal solution and modeling approaches (that have passed through steps 1 and 2) in a variety of representative cases. This uses the comparative technique as an extrapolation tool. Deviations in the program predictions indicate areas for further investigation. When programs successfully complete these three stages, they are considered validated for cases where acceptable agreement was achieved (i.e., for the range of building, climate, and mechanical system types represented by the test cases). Once several detailed simulation programs have satisfactorily completed the procedure, other programs and simplified design tools can be tested against them. A validation code does not necessarily represent truth. It does represent a set of algorithms that have been shown, through a repeatable procedure, to perform according to the current state of the art. NREL methodology for validating building energy simulation programs has been generally accepted by the International Energy

Fig. 21 Validation Method (Neymark and Judkoff 2002)

Agency (Irving 1988), ASHRAE Standard 140 and Addendum p to ASHRAE Standard 90.1, and elsewhere, with refinements suggested by other researchers (Bland 1992; Bloomfield 1988, 1999; Guyon and Palomo 1999b; Irving 1988; Lomas 1991; Lomas and Bowman 1987; Lomas and Eppel 1992). Additionally, the Commission of European Communities has conducted considerable work under the PASSYS program (Jensen 1989; Jensen and van de Perre 1991).

SUMMARY OF PREVIOUS TESTING AND VALIDATION WORK Neymark and Judkoff (2002) summarize approximately 100 articles and research papers on analytical, empirical, and comparative testing, from 1980 to 2004. Some of these works are listed by subject in the Bibliography.

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Analytical Verification Bland, B. 1993. Conduction tests for the validation of dynamic thermal models of buildings. Building Research Establishment, Garston, U.K. Bland, B.H. and D.P. Bloomfield. 1986. Validation of conduction algorithms in dynamic thermal models. Proceedings of the CIBSE 5th International Symposium on the Use of Computers for Environmental Engineering Related to Buildings, Bath, U.K. CEN. 2004. PrEN ISO 13791. Thermal performance of buildings—Calculation of internal temperatures of a room in summer without mechanical cooling—General criteria and validation procedures. Final draft. Comité Européen de la Normalisation, Brussels. Judkoff, R., D. Wortman, and B. O’Doherty. 1981. A comparative study of four building energy simulations, Phase II: DOE-2.1, BLAST-3.0, SUNCAT-2.4, and DEROB-4. Solar Energy Research Institute (now National Renewable Energy Laboratory), Golden, CO. Pinney, A. and M. Bean. 1988. A set of analytical tests for internal longwave radiation and view factor calculations. Final Report of the BRE/SERC Collaboration, vol. II, Appendix II.2. Building Research Establishment, Garston, U.K. Purdy, J. and I. Beausoleil-Morrison. 2003. Building Energy Simulation Test and diagnostic method for heating, ventilating, and air-conditioning equipment models (HVAC BESTEST), fuel-fired furnace. Natural Resources Canada CANMET Energy Technology Centre, Ottawa. http://www.iea-shc.org/task22/deliverables.htm. Rodriguez, E. and S. Alvarez. 1991. Solar shading analytical tests (I). Universidad de Savilla, Seville. San Isidro, M. 2000. Validating the solar shading test of IEA. Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, Madrid. Stefanizzi, P., A. Wilson, and A. Pinney. 1988. The internal longwave radiation exchange in thermal models, vol. II, Chapter 9. Final Report of the BRE/SERC Collaboration. Building Research Establishment, Garston, U.K. Tuomaala, P., ed. 1999. IEA task 22: A working document of subtask A.1, analytical tests. VTT Building Technology, Espoo, Finland. Tuomaala, P., K. Piira, J. Piippo, and C. Simonson. 1999. A validation test set for building energy simulation tools results obtained by BUS++. VTT Building Technology, Espoo, Finland. Walton, G. 1989. AIRNET—A computer program for building airflow network modeling. Appendix B: AIRNET Validation Tests. NISTIR 894072. National Institute of Standards and Technology, Gaithersburg, MD Wortman, D., B. O’Doherty, and R. Judkoff. 1981. The implementation of an analytical verification technique on three building energy analysis codes: SUNCAT 2.4, DOE 2.1, and DEROB III. SERI/TP-721-1008, UL-59c. Solar Energy Research Institute (now National Renewable Energy Laboratory), Golden, CO.

Empirical Validation Ahmad, Q. and S. Szokolay. 1993. Thermal design tools in Australia: A comparative study of TEMPER, CHEETAH, ARCHIPAK and QUICK. Building Simulation’93, Adelaide, Australia. International Building Performance Simulation Association. Barakat, S. 1983. Passive solar heating studies at the Division of Building Research. Building Research Note 181. Division of Building Research, Ottawa. Beausoleil-Morrison, I. and P. Strachan. 1999. On the significance of modeling internal surface convection in dynamic whole-building simulation programs. ASHRAE Transactions 105(2). Bloomfield, D., Y. Candau, P. Dalicieux, S. DeLille, S. Hammond, K. Lomas, C. Martin, F. Parand, J. Patronis, and N. Ramdani. 1995. New techniques for validating building energy simulation programs. Proceedings of Building Simulation’95, Madison, WI. International Building Performance Simulation Association.

2009 ASHRAE Handbook—Fundamentals Boulkroune, K., Y. Candau, G. Piar, and A. Jeandel. 1993. Modeling and simulation of the thermal behavior of a dwelling under ALLAN. Building Simulation’93, Adelaide, Australia. International Building Performance Simulation Association. Bowman, N. and K. Lomas. 1985. Empirical validation of dynamic thermal computer models of buildings. Building Service Engineering Research and Technology 6(4):153-162. Bowman, N. and K. Lomas. 1985. Building energy evaluation. Proceedings of the CICA Conference on Computers in Building Services Design, Nottingham, pp. 99-110. Construction Industry Computer Association. Burch, J., D. Wortman, R. Judkoff, and B. Hunn. 1985. Solar Energy Research Institute validation test house site handbook. LA-10333-MS and SERI/PR-254-2028. Solar Energy Research Institute (now National Renewable Energy Laboratory), Golden, CO, and Los Alamos National Laboratory, NM. David, G. 1991. Sensitivity analysis and empirical validation of HLITE using data from the NIST indoor test cell. Proceedings of Building Simulation’91, Nice, France. International Building Performance Simulation Association. Eppel, H. and K. Lomas. 1995. Empirical validation of three thermal simulation programs using data from a passive solar building. Proceedings of Building Simulation’95, Madison, WI. International Building Performance Simulation Association. Fisher, D.E. and C.O. Pedersen. 1997. Convective heat transfer in building energy and thermal load calculations. ASHRAE Transactions 103(2): 137-148. Guyon, G., and N. Rahni. 1997. Validation of a building thermal model in CLIM2000 simulation software using full-scale experimental data, sensitivity analysis and uncertainty analysis. Proceedings of Building Simulation’97, Prague. International Building Performance Simulation Association. Guyon, G., S. Moinard, and N. Ramdani. 1999. Empirical validation of building energy analysis tools by using tests carried out in small cells. Proceedings of Building Simulation’99, Kyoto. International Building Performance Simulation Association. Izquierdo, M., G. LeFebvre, E. Palomo, F. Boudaud, and A. Jeandel. 1995. A statistical methodology for model validation in the ALLAN• simulation environment. Proceedings of Building Simulation’95, Madison, WI. International Building Performance Simulation Association. Jensen, S. 1993. Empirical whole model validation case study: The PASSYS reference wall. Proceedings of Building Simulation’93, Adelaide, Australia. International Building Performance Simulation Association. Judkoff, R. and D. Wortman. 1984. Validation of building energy analysis simulations using 1983 data from the SERI Class A test house (draft). SERI/TR-253-2806. Solar Energy Research Institute (now National Renewable Energy Laboratory), Golden, CO. Judkoff, R., D. Wortman, and J. Burch. 1983. Measured versus predicted performance of the SERI test house: A validation study. SERI/TP-2541953. Solar Energy Research Institute (now National Renewable Energy Laboratory), Golden, CO. LeRoy, J., E. Groll, and J. Braun. 1997. Capacity and power demand of unitary air conditioners and heat pumps under extreme temperature and humidity conditions. Final Report, ASHRAE Research Project RP-859. LeRoy, J., E. Groll, and J. Braun. 1998. Computer model predictions of dehumidification performance of unitary air conditioners and heat pumps under extreme operating conditions. ASHRAE Transactions 104(2). Lomas, K. and N. Bowman. 1986. The evaluation and use of existing data sets for validating dynamic thermal models of buildings. Proceedings of the CIBSE 5th International Symposium on the Use of Computers for Environmental Engineering Related to Buildings, Bath, U.K. Martin, C. 1991. Detailed model comparisons: An empirical validation exercise using SERI-RES. Contractor Report to U.K. Department of Energy, ETSU S 1197-p9. Maxwell, G., P. Loutzenhiser, and C. Klaassen. 2003. Daylighting—HVAC interaction tests for the empirical validation of building energy analysis tools. Iowa State University, Department of Mechanical Engineering, Ames. http://www.iea-shc.org/task22/deliverables.htm. McFarland, R. 1982. Passive test cell data for the solar laboratory winter 1980-81. LA-9300-MS. Los Alamos National Laboratory, NM. Moinard, S. and G. Guyon. 1999. Empirical validation of EDF ETNA and GENEC test-cell models. Final Report, IEA SHC Task 22, Building Energy Analysis Tools, Project A.3. Electricité de France, Moret sur Loing. http://www.iea-shc.org/task22/deliverables.htm.

Energy Estimating and Modeling Methods Nishitani, Y., M. Zheng, H. Niwa, and N. Nakahara. 1999. A comparative study of HVAC dynamic behavior between actual measurements and simulated results by HVACSIM+(J). Proceedings of Building Simulation’99, Kyoto. International Building Performance Simulation Association. Rahni, N., N. Ramdani, Y. Candau, and G. Guyon. 1999. New experimental validation and model improvement tools for the CLIM2000 energy simulation software program. Proceedings of Building Simulation’99, Kyoto. International Building Performance Simulation Association. Sullivan, R. 1998. Validation studies of the DOE-2 building energy simulation program. Final Report. LBNL-42241. Lawrence Berkeley National Laboratory, CA. Travesi, J., G. Maxwell, C. Klaassen, M. Holtz, G. Knabe, C. Felsmann, M. Achermann, and M. Behne. 2001. Empirical validation of Iowa Energy Resource Station building energy analysis simulation models. Report, IEA SHC Task 22, Subtask A, Building Energy Analysis Tools, Project A.1 Empirical Validation. Centro de Investigaciones Energeticas, Medioambientales y Technologicas, Madrid. http://www.iea-shc.org/ task22/reports/Iowa_Energy_Report.pdf. Trombe, A., L. Serres, and A. Mavroulakis. 1993. Simulation study of coupled energy saving systems included in real site building. Proceedings of Building Simulation’93, Adelaide, Australia. International Building Performance Simulation Association. Walker, I., J. Siegel, and G. Degenetais. 2001. Simulation of residential HVAC system performance. Proceedings of eSim 2001, Natural Resources Canada, Ottawa. Yazdanian, M. and J. Klems. 1994. Measurement of the exterior convective film coefficient for windows in low-rise buildings. ASHRAE Transactions 100(1):1087-1096. Zheng, M., Y. Nishitani, S. Hayashi, and N. Nakahara. 1999. Comparison of reproducibility of a real CAV system by dynamic simulation HVACSIM+ and TRNSYS. Proceedings of Building Simulation’99, Kyoto. International Building Performance Simulation Association. See also Guyon and Palomo (1999a), Spitler et al. (1991), and U.S. Department of Energy (2004) in the References.

Intermodel Comparative Testing Achermann, M. and G. Zweifel. 2003. RADTEST—Radiant heating and cooling test cases. University of Applied Sciences of Central Switzerland, Lucerne School of Engineering and Architecture. http://www.ieashc.org/task22/deliverables.htm. Deru, M., R. Judkoff, and J. Neymark. 2003. Proposed IEA BESTEST ground-coupled cases. International Energy Agency, Solar Heating and Cooling Programme Task 22, Working Document. Fairey, P., M. Anello, L. Gu, D. Parker, M. Swami, and R. Vieira. 1998. Comparison of EnGauge 2.0 heating and cooling load predictions with the HERS BESTEST criteria. FSEC-CR-983-98. Florida Solar Energy Center, Cocoa. Haddad, K. and I. Beausoleil-Morrison. 2001. Results of the HERS BESTEST on an energy simulation computer program. ASHRAE Transactions 107(2). Haltrecht, D. and K. Fraser. 1997. Validation of HOT2000• using HERS BESTEST. Proceedings of Building Simulation’97, Prague. International Building Performance Simulation Association. ISSO. 2003. Energie Diagnose Referentie Versie 3.0. Institut voor Studie en Stimulering van Onderzoekop Het Gebied van Gebouwinstallaties, Rotterdam, The Netherlands. Judkoff, R. 1985. A comparative validation study of the BLAST-3.0, SERIRES-1.0, and DOE-2.1 A computer programs using the Canadian direct gain test building (draft). SERI/TR-253-2652. Solar Energy Research Institute (now National Renewable Energy Laboratory), Golden, CO. Judkoff, R. 1985. International Energy Agency building simulation comparison and validation study. Proceedings of the Building Energy Simulation Conference, Seattle. Judkoff, R. 1986. International Energy Agency sunspace intermodel comparison (draft). SERI/TR-254-2977. Solar Energy Research Institute (now National Renewable Energy Laboratory), Golden, CO.

19.39 Judkoff, R. and J. Neymark. 1997. Home Energy Rating System Building Energy Simulation Test for Florida (Florida-HERS BESTEST). NREL/ TP-550-23124. National Renewable Energy Laboratory, Golden, CO. http://www.nrel.gov/docs/legosti/fy97/23124a.pdf and http:// www.nrel.gov/docs/legosti/fy97/23124b.pdf. Judkoff, R. and J. Neymark. 1998. The BESTEST method for evaluating and diagnosing building energy software. Proceedings of the ACEEE Summer Study 1998, Washington, D.C. American Council for an EnergyEfficient Economy. Judkoff, R. and J. Neymark. 1999. Adaptation of the BESTEST intermodel comparison method for proposed ASHRAE Standard 140P: Method of test for building energy simulation programs. ASHRAE Transactions 105(2). Mathew, P. and A. Mahdavi. 1998. High-resolution thermal modeling for computational building design assistance. Proceedings of the International Computing Congress, Computing in Civil Engineering, Boston. Natural Resources Canada. 2000. Benchmark test for the evaluation of building energy analysis computer programs. Natural Resources Canada, Ottawa. (Translation of original Japanese version, approved by the Japanese Ministry of Construction.) Neymark, J. and R. Judkoff. 1997. A comparative validation based certification test for home energy rating system software. Proceedings of Building Simulation’97, Prague. International Building Performance Simulation Association. Neymark, J. and R. Judkoff. 2004. International Energy Agency Building Energy Simulation Test and diagnostic method for heating, ventilating, and air-conditioning equipment models (HVAC BESTEST), vol. 2: Cases E300-E545. NREL/TP-550-36754. National Renewable Energy Laboratory, Golden, CO. http://www.nrel.gov/docs/fy05osti/36754.pdf. Sakamoto, Y. 2000. Determination of standard values of benchmark test to evaluate annual heating and cooling load computer program. Natural Resources Canada, Ottawa. Soubdhan, T., T. Mara, H. Boyer, and A. Younes. 1999. Use of BESTEST procedure to improve a building thermal simulation program. Université de la Réunion, St Denis, La Reunion, France.

General Testing and Validation Allen, E., D. Bloomfield, N. Bowman, K. Lomas, J. Allen, J. Whittle, and A. Irving. 1985. Analytical and empirical validation of dynamic thermal building models. Proceedings of the First Building Energy Simulation Conference, Seattle, pp. 274-280. Beausoleil-Morrison, I. 2000. The adaptive coupling of heat and air flow modelling within dynamic whole-building simulation. Ph.D. dissertation. Energy Systems Research Unit, Department of Mechanical Engineering, University of Strathclyde, Glasgow. Bloomfield, D. 1985. Appraisal techniques for methods of calculating the thermal performance of buildings. Building Services Engineering Research & Technology. 6(1):13-20. Bloomfield, D., ed. 1989. Design tool evaluation: Benchmark cases. IEA T8B4. Solar Heating and Cooling Program, Task VIII: Passive and Hybrid Solar Low-Energy Buildings. Building Research Establishment, Garston, U.K. Bloomfield, D., K. Lomas, and C. Martin. 1992. Assessing programs which predict the thermal performance of buildings. BRE Information Paper, IP7/92. Building Research Establishment, Garston, U.K. Gough, M. 1999. A review of new techniques in building energy and environmental modelling. Final Report. BRE Contract No. BREA-42. Building Research Establishment, Garston, U.K. Judkoff, R., S. Barakat, D. Bloomfield, B. Poel, R. Stricker, P. van Haaster, and D. Wortman. 1988. International Energy Agency design tool evaluation procedure. SERI/TP-254-3371. Solar Energy Research Institute (now National Renewable Energy Laboratory), Golden, CO. Palomo, E. and G. Guyon. 2002. Using parameters space analysis techniques for diagnostic purposes in the framework of empirical model validation. LEPT-ENSAM, Talance, France. Electricité de France, Moret sur Loing.

CHAPTER 20

SPACE AIR DIFFUSION Indoor Air Quality and Sustainability ..................................... Applicable Standards and Codes ............................................. Terminology ............................................................................. Principles of Jet Behavior........................................................ SYSTEM DESIGN ....................................................................

20.1 20.2 20.2 20.3 20.7

Mixed-Air Systems.................................................................... 20.7 Fully Stratified Systems.......................................................... 20.14 Partially Mixed Systems ......................................................... 20.17 Task/Ambient Conditioning (TAC) ......................................... 20.19 Symbols .................................................................................. 20.20

OOM air distribution systems are intended to provide thermal comfort and ventilation for space occupants and processes. Although air terminals (inlets and outlets), terminal units, local ducts, and rooms themselves may affect room air diffusion, this chapter addresses only air terminals and their direct effect on occupant comfort. This chapter is intended to present HVAC designers the fundamental characteristics of air distribution devices. For information on naturally ventilated spaces, see Chapter 16. For a discussion of various air distribution strategies, tools, and guidelines for design and application, see Chapter 56 in the 2007 ASHRAE Handbook—HVAC Applications. Chapter 19 in the 2008 ASHRAE Handbook—HVAC Systems and Equipment provides descriptions of the characteristics of various air terminals (inlets and outlets) and terminal units, as well as selection tools and guidelines. Other fundamental references include Bauman and Daly (2003), Chen and Glicksman (2003), Kirkpatrick and Elleson (1996), Rock and Zhu (2002), and Skistad et al. (2002). Room air diffusion methods can be classified as one of the following:

the characteristics of the room supply airflow and heat load configuration. For room supply airflow, the major factors are

R

• Mixed systems produce little or no thermal stratification of air within the space. Overhead air distribution is an example of this type of system. • Fully (thermally) stratified systems produce little or no mixing of air within the occupied space. Thermal displacement ventilation is an example of this type of system. • Partially mixed systems provide some mixing within the occupied and/or process space while creating stratified conditions in the volume above. Most underfloor air distribution designs are examples of this type of system. • Task/ambient conditioning systems focus on conditioning only a certain portion of the space for thermal comfort and/or process control. Examples of task/ambient systems are personally controlled desk outlets (sometimes referred to as personal ventilation systems) and spot-conditioning systems. Air distribution systems, such as displacement ventilation (DV) and underfloor air distribution (UFAD), that deliver air in cooling mode at or near floor level and return air at or near ceiling level produce varying amounts of room air stratification. Figure 1 presents a series of simplified vertical profiles of temperature and pollutant concentration representing the spectrum of stratified conditions that may exist under cooling operation, from fully stratified (e.g., DV systems) to fully mixed (e.g., conventional overhead systems). For floor-level supply, thermal plumes that develop over heat sources in the room play a major role in driving overall floor-to-ceiling air motion. The amount of stratification in the room is primarily determined by the balance between total room airflow and heat load. In practice, the actual temperature (or concentration) profile depends on the combined effects of various factors, but is largely driven by The preparation of this chapter is assigned to TC 5.3, Room Air Distribution.

• • • •

Total room supply airflow quantity Room supply air temperature Diffuser type Diffuser throw height (or outlet velocity); this is associated with the amount of mixing provided by a floor diffuser (or room conditions near a low-sidewall DV diffuser) For room heat loads, the major factors are

• Magnitude and number of loads in space • Load type (point or distributed source) • Elevation of load (e.g., overhead lighting, person standing on floor, floor-to-ceiling glazing) • Radiative/convective split • For pollutant concentration profiles, whether pollutants are associated with heat sources

INDOOR AIR QUALITY AND SUSTAINABILITY Air diffusion methods affect not only indoor air quality (IAQ) and thermal comfort, but also energy consumption over the building’s life. Choices made early in the design process are important. The U.S. Green Building Council’s (USGBC 2005) Leadership in Energy and Environmental Design (LEED®) rating system, which was originally created in response to indoor air quality concerns, now includes prerequisites and credits for increasing ventilation effectiveness and improving thermal comfort. These requirements and optional points are relatively easy to achieve if good room air diffusion design principles, methods, and standards are followed. Environmental tobacco smoke (ETS) control is a LEED prerequisite. Banning indoor smoking is a common approach, but if indoor smoking is to be allowed, ANSI/ASHRAE Standard 62.1 requires that more than the base non-ETS ventilation air be provided where ETS is present in all or part of a building. Rock (2006) provides additional guidance on dealing with ETS. The air change effectiveness is affected directly by the room air distribution system’s design, construction, and operation, but is very difficult to predict. Many attempts have been made to quantify air change effectiveness, including ASHRAE Standard 129. However, this standard is only for experimental tests in well-controlled laboratories, and should not be applied directly to real buildings. ANSI/ASHRAE Standard 62.1-2007 provides a table of typical values to help predict ventilation effectiveness. For example, welldesigned ceiling-based air distribution systems produce near-perfect air mixing in cooling mode, and yield an air change effectiveness of almost 1.0. Displacement and underfloor air distribution (UFAD) systems have the potential for values greater than 1.0. More information on ceiling- and wall-mounted air inlets and outlets can be found in Rock and Zhu (2002). Displacement system performance is described in Chen and Glicksman (2003). Bauman and Daly (2003)

20.1

20.2

2009 ASHRAE Handbook—Fundamentals Fig. 1 Classification of Air Distribution Strategies

Fig. 1 Classification of Air Diffusion Methods discuss UFAD in detail. (These three ASHRAE books were produced by research projects for Technical Committee 5.3.) More information on ANSI/ASHRAE Standard 62.1-2007 is available in its user’s manual (ASHRAE 2007).

APPLICABLE STANDARDS AND CODES The following standards and codes should be reviewed when applying various room air diffusion methods: • ASHRAE Standard 55 specifies the combination of indoor thermal environmental factors and personal factors that will produce thermal acceptability to a majority of space occupants. • ASHRAE Standard 62.1 establishes the ventilation requirements for acceptable indoor environmental quality. This standard is adopted as part of many building codes. • ASHRAE/IESNA Standard 90.1 provides energy efficiency requirements that affect supply air characteristics. • ASHRAE Standard 113 describes a method for evaluating the effectiveness of various room air distribution systems in achieving thermal comfort. • ASHRAE Standard 129 specifies a method for measuring airchange effectiveness in mechanically ventilated spaces. Local codes should also be checked to see how they apply to each of these subjects.

TERMINOLOGY Adjacent zone. Area adjacent to an outlet in which long term occupancy is not recommended because of potential discomfort. Also called clear or near zone. Aspect ratio. Ratio of length to width of opening or core of a grille. Axial flow jet. Stream of air with motion approximately symmetrical along a line, although some spreading and drop or rise can occur from diffusion and buoyancy effects. CAV. Constant air volume. Coanda effect. Effect of a moving jet attaching to a parallel surface because of negative pressure developed between jet and surface. Coefficient of discharge. Ratio of area at vena contracta to area of opening. Cold air. General term for supply air, typically between 35 to 45°F.

Core area. Area of a register, grille, or linear slot pertaining to the frame or border, whichever is less. Damper. Device used to vary the volume flow rate of air passing through a confined cross section by varying the cross-sectional area. Diffuser. Outlet discharging supply air in various directions and planes. Diffusion. Dispersion of air within a space. Distribution. Moving air to or in a space by an outlet discharging supply air. Draft. Undesired or excessive local cooling of a person caused by low temperature and air movement. Drop. Vertical distance that the lower edge of a horizontally projected airstream descends between the outlet and the end of its throw. Effective area. Net area of an outlet or inlet device through which air can pass; equal to the free area times the coefficient of discharge. Entrainment. Movement of space air into the jet caused by the airstream discharged from the outlet (also known as secondary air motion). Entrainment (or induction) ratio. Volume flow rate of total air (primary plus entrained air) divided by the volume flow rate of primary air at a given distance from the outlet. Envelope. Outer boundary of an airstream moving at a perceptible velocity. Exhaust opening or inlet. Any opening through which air is removed from a space. Free area. Total minimum area of openings in an air outlet or inlet through which air can pass. Grille. Functional or decorative device covering any area through which air passes. Induction. See Entrainment. Isothermal jet. Air jet with same temperature as surrounding air. Lower (mixed) zone. In partially mixed systems, zone directly adjacent to floor, in which air is relatively well mixed. Neck area. Nominal area of duct connection to air outlet or inlet. Nonisothermal jet. Air jet with a discharge temperature different from surrounding air. Occupied zone. Room volume where occupants are located (typically 6 ft above floor level and 1 ft from walls). Outlet velocity. Average velocity of air emerging from outlet, measured in plane of opening. Primary air. Air delivered to an outlet by a supply duct.

Space Air Diffusion Radius of diffusion. Horizontal axial distance an airstream travels after leaving an air outlet before the maximum stream velocity is reduced to a specified terminal level (e.g., 50, 100, 150, or 200 fpm). Register. Grille equipped with a flow control damper. Spread. Divergence of airstream in horizontal and/or vertical plane after it leaves an outlet. Stagnant zone. Area characterized by stratification and little air motion. This term does not necessarily imply poor air quality. Stratification height. Vertical distance from floor to horizontal plane that defines lower boundary of upper mixed zone (in a fully stratified or partially mixed system). Stratified zone. Zone in which air movement is entirely driven by buoyancy caused by convective heat sources. Typically found in fully stratified or partially mixed systems Supply opening or outlet. Any opening or device through which supply air is delivered into a ventilated space being heated, cooled, humidified, or dehumidified. Supply outlets are classified according to their location in a room as sidewall, ceiling, baseboard, or floor outlets. However, because numerous designs exist, they are more accurately described by their construction features. (See Chapter 19 of the 2008 ASHRAE Handbook—HVAC Systems and Equipment.) Terminal velocity. Maximum airstream velocity at end of throw. Throw. Horizontal or vertical axial distance an airstream travels after leaving an air outlet before maximum stream velocity is reduced to a specified terminal velocity (e.g., 50, 100, 150, or 200 fpm), defined by ASHRAE Standard 70. Total air. Mixture of discharged and entrained air. Upper (mixed) zone. Zone in which air is relatively well mixed, with generally low average air velocities caused by the momentum of thermal plumes penetrating its lower boundary. Typically found in fully stratified or partially mixed systems. Vane. Component of supply air outlet that imparts direction to the discharge jet. Vane ratio. Ratio of depth of a vane to the space between two adjacent vanes. VAV. Variable air volume. Vena contracta. Smallest cross-sectional area of a fluid stream leaving an orifice.

PRINCIPLES OF JET BEHAVIOR Air Jet Fundamentals Air supplied to rooms through various types of outlets (e.g., grilles, ceiling diffusers, perforated panels) can be distributed by turbulent air jets (mixed and partially mixed systems) or in a lowvelocity, unidirectional manner (stratified systems). The air jet discharged from an outlet is the primary factor affecting room air motion. Baturin (1972), Christianson (1989), and Murakami (1992) have further information on the relationship between the air jet and occupied zone. If an air jet is not obstructed or affected by walls, ceiling, or other surfaces, it is considered a free jet. Characteristics of the air jet in a room might be influenced by reverse flows created by the same jet entraining ambient air. If the supply air temperature is equal to the ambient room air temperature, the air jet is called an isothermal jet. A jet with an initial temperature different from the ambient air temperature is called a nonisothermal jet. The air temperature differential between supplied and ambient room air generates thermal forces (buoyancy) in jets, affecting the jet’s (1) trajectory, (2) location at which it attaches to and separates from the ceiling/floor, and (3) throw. The significance of these effects depends on the ratio between the thermal buoyancy of the air and inertial forces. Angle of Divergence. The angle of divergence is well defined near the outlet face, but the boundary contours are billowy and easily affected by external influences. Near the outlet, as in the room, air movement has local eddies, vortices, and surges. Internal forces

20.3 governing this air motion are extremely delicate (Nottage et al. 1952a). Measured angles of divergence (spread) for discharge into large open spaces usually range from 20 to 24°, with an average of 22°. Coalescing jets for closely spaced multiple outlets expand at smaller angles, averaging 18°, and jets discharging into relatively small spaces show even smaller angles of expansion (McElroy 1943). When outlet area is small compared to the dimensions of the space normal to the jet, the jet may be considered free as long as X d 1.5 A R

(1)

where X = distance from face of outlet, ft AR = cross-sectional area of confined space normal to jet, ft2

Jet Expansion Zones. The full length of an air jet, in terms of the maximum or centerline velocity and temperature differential at the cross section, can be divided into four zones: • Zone 1, a short core zone extending about four diameters or widths from the outlet face, in which the maximum velocity (temperature) of the airstream remains practically unchanged. • Zone 2, a transition zone, with its length determined by the type of outlet, aspect ratio of the outlet, initial airflow turbulence, etc. • Zone 3, a zone of fully established turbulent flow that may be 25 to 100 equivalent air outlet diameters (widths for slot air diffusers) long. • Zone 4, a zone of diffuser jet degradation, where maximum air velocity and temperature decrease rapidly. Distance to this zone and its length depend on the velocities and turbulence characteristics of ambient air. In a few diameters or widths, air velocity becomes less than 50 fpm. Characteristics of this zone are still not well understood. Zone 3 is of major engineering importance because, in most cases, the diffuser jet enters the occupied area within this zone. Centerline Velocities in Zones 1 and 2. In zone 1, the ratio Vx /Vo is constant and equal to the ratio of the center velocity of the jet at the start of expansion to the average velocity. The ratio Vx /Vo varies from approximately 1.0 for rounded entrance nozzles to about 1.2 for straight pipe discharges; it has much higher values for diverging discharge outlets. Experimental evidence indicates that, in zone 2, Vx ------ = Vo

K c Ho ------------X

(2)

where Vx = centerline velocity at distance X from outlet, fpm Vo = Vc /Cd Rf a = average initial velocity at discharge from open-ended duct or across contracted stream at vena contracta of orifice or multiple-opening outlet, fpm Vc = nominal velocity of discharge based on core area, fpm Cd = discharge coefficient (usually between 0.65 and 0.90) Rfa = ratio of free area to gross (core) area Ho = width of jet at outlet or at vena contracta, ft Kc = centerline velocity constant, depending on outlet type and discharge pattern (see Table 1) X = distance from outlet to measurement of centerline velocity Vx, ft

The aspect ratio (Tuve 1953) and turbulence (Nottage et al. 1952a) primarily affect centerline velocities in zones 1 and 2. Aspect ratio has little effect on the terminal zone of the jet when Ho is greater than 4 in. This is particularly true of nonisothermal jets. When Ho is very small, induced air can penetrate the core of the jet, thus reducing centerline velocities. The difference in performance between a radial outlet with small Ho and an axial outlet with large Ho shows the importance of jet thickness.

20.4

2009 ASHRAE Handbook—Fundamentals Fig. 1 Airflow Patterns of Different Diffusers

Fig. 2

Airflow Patterns of Different Diffusers

Table 1 Recommended Values for Centerline Velocity Constant Kc for Commercial Supply Outlets Outlet Type

Discharge Pattern

High sidewall grilles (Figure 2A) High sidewall linear (Figure 2B) Low sidewall (Figure 2C) Baseboard (Figure 2C) Floor grille (Figure 2C) Ceiling (Figure 2D)

0° deflectiona Wide deflection Core less than 4 in. highb Core more than 4 in. high Up and on wall, no spread Wide spreadb Up and on wall, no spread Wide spread No spreadb Wide spread 360° horizontalc Four-way; little spread One-way; horizontal along ceilingb

Ceiling linear slot (Figure 2E) aFree

area is about 80% of core area. bFree area is about 50% of core area.

c Cone

area.

Ao

Kc

Free Free Free Free Free Free Core Core Free Free Neck Neck Free

5.7 4.2 4.4 5.0 4.5 3.0 4.0 2.0 4.7 1.6 1.1 3.8 5.5

free area is greater than duct

When air is discharged from relatively large perforated panels, the constant-velocity core formed by coalescence of individual jets extends a considerable distance from the panel face. In zone 1, when the ratio is less than 5, use the following equation for estimating centerline velocities (Koestel et al. 1949): V x = 1.2V o C d R fa

(3)

Centerline Velocity in Zone 3. In zone 3, maximum or centerline velocities of straight-flow isothermal jets can be determined accurately from the following equations: Kc Ao Kc Ho V - = ----------------------x- = -----------Vo X X

(4)

Kc Qo K c Vo A o V x = ------------------------ = --------------X X Ao

(5)

Space Air Diffusion

20.5 Solving for 50 fpm throw,

Fig. 2 Chart for Determining Centerline Velocities of Axial and Radial Jets

X = 2920/50 = 58.4 ft But, according to Figure 3, 50 fpm is in zone 4, which is typically 20% less than calculated in Equation (4), or X = 58.4 u 0.80 = 47 ft Solving for 100 fpm throw, X = 2920/100 = 29 ft Solving for 150 fpm throw, X = 2920/150 = 19 ft

Velocity Profiles of Jets. In zone 3 of both axial and radial jets, the velocity distribution may be expressed by a single curve (Figure 3) in terms of dimensionless coordinates; this same curve can be used as a good approximation for adjacent portions of zones 2 and 4. Temperature and density differences have little effect on crosssectional velocity profiles. Velocity distribution in zone 3 can be expressed by the Gauss error function or probability curve, which is approximated by the following equation: § r · -¸ ¨ ---------© r 0.5V¹

Fig. 3 Chart for Determining Centerline Velocities of Axial and Radial Jets

2

Vx = 3.3 log ----V

(7)

where

where

r = radial distance of point under consideration from centerline of jet r0.5V = radial distance in same cross-sectional plane from axis to point where velocity is one-half centerline velocity (i.e., V = 0.5Vx) Vx = centerline velocity in same cross-sectional plane V = actual velocity at point being considered

Kc = centerline velocity constant Ho = effective or equivalent diameter of stream at discharge from open-ended duct or at contracted section, ft Ao = core area or neck area as shown in Table 1, ft2 Ac = measured gross (core) area of outlet, ft2 Qo = discharge from outlet, cfm

Because Ao equals the effective area of the stream, the flow area for commercial registers and diffusers, according to ASHRAE Standard 70, can be used in Equation (4) with the appropriate value of K. Determining Centerline Velocities. To correlate data from all four zones, centerline velocity ratios are plotted against distance from the outlet in Figure 3. Airflow patterns of diffusers are related to the throw K-factors and throw distance. In general, diffusers with a circular airflow pattern have a shorter throw than those with a directional or cross-flow pattern. During cooling, the circular pattern tends to curl back from the end of the throw toward the diffuser, reducing the drop and ensuring that the cool air remains near the ceiling. Cross-flow airflow patterns have a longer throw, and the individual side jets react similarly to jets from sidewall grilles. Jets with this pattern have a longer throw, and airflow does not roll back to the diffuser at the end of the throw, but continues to move away from the diffuser at low velocities. Throw. Equation (5) can be transposed to determine the throw X of an outlet if the discharge volume and the centerline velocity are known: Kc Qo X = ----------------Vx Ao

Experiments show that the conical angle for r0.5V is approximately one-half the total angle of divergence of a jet. The velocity profile curve for one-half of a straight-flow turbulent jet (the other half being a symmetrical duplicate) is shown in Figure 4. For multiple-opening outlets, such as grilles or perforated panels, the velocity profiles are similar, but the angles of divergence are smaller. Entrainment Ratios. The following equations are for entrainment of circular jets and of jets from long slots. For third-zone expansion of circular jets, Qx 2X ------ = ----------------Qo Kc Ao By substituting from Equation (4), Qx V ------ = 2 -----oQo Vx

Qx 2------ = ----Qo Kc

The following example illustrates the use of Table 1 and Figure 3.

or, substituting from Equation (2), Qx ------ = Qo

Example 1. A 12 by 18 in. high sidewall grille with an 11.25 by 17.25 in. core area is selected. From Table 1, Kc = 5 for zone 3. If the airflow is 600 cfm, what is the throw to 50, 100, and 150 fpm?

Kc Qo 2920 5 u 600 X = ----------------- = ---------------------------------------------------------- = -----------Vx Vx Ao V x 11.25 u 17.25 e 144

(9)

For a continuous slot with active sections up to 10 ft and separated by 2 ft,

(6)

Solution: From Equation (6),

(8)

X----Hs

V 2 -----oVx

(10)

(11)

where Qx Qo X Kc

= = = =

total volumetric flow rate at distance X from face of outlet, cfm discharge from outlet, cfm distance from face of outlet, ft centerline velocity constant

20.6

2009 ASHRAE Handbook—Fundamentals

Fig. 3 Cross-Sectional Velocity Profiles for Straight-Flow Turbulent Jets

for outlet characteristics that affect the downthrow of heated air. Koestel (1954, 1955) developed equations for temperatures and velocities in heated and chilled jets. Kirkpatrick and Elleson (1996) and Li et al. (1993, 1995) provide additional information on nonisothermal jets.

Nonisothermal Horizontal Free Jet A horizontal free jet rises or falls according to the temperature difference between it and the ambient environment. The horizontal jet throw to a given distance follows an arc, rising for heated air and falling for cooled air. The distance from the diffuser to a given terminal velocity along the discharge jet remains essentially the same.

Comparison of Free Jet to Attached Jet Fig. 4

Cross-Sectional Velocity Profiles for Straight-Flow Turbulent Jets

Ao = core area or neck area free (see Table 1), ft Hs = width of slot, ft

The entrainment ratio Qx /Qo is important in determining total air movement at a given distance from an outlet. For a given outlet, the entrainment ratio is proportional to the distance X [Equation (8)] or to the square root of the distance X [Equation (10)] from the outlet. Equations (9) and (11) show that, for a fixed centerline velocity Vx, the entrainment ratio is proportional to outlet velocity. Equations (9) and (11) also show that, at a given centerline and outlet velocity, a circular jet has greater entrainment and total air movement than a long slot. Comparing Equations (8) and (10), the long slot should have a greater rate of entrainment. The entrainment ratio at a given distance is less with a large K than with a small K.

Isothermal Radial Flow Jets In a radial jet, as with an axial jet, the cross-sectional area at any distance from the outlet varies as the square of this distance. Centerline velocity gradients and cross-sectional velocity profiles are similar to those of zone 3 of axial jets, and the angles of divergence are about the same. A jet from a ceiling plaque has the same form as half of a free radial jet. The jet is wider and longer than a free jet, with maximum velocity close to the surface. Koestel (1957) provides an equation for radial flow outlets.

Nonisothermal Jets When the temperature of introduced air is different from the room air temperature, the diffuser air jet is affected by thermal buoyancy caused by air density difference. The trajectory of a nonisothermal jet introduced horizontally is determined by the Archimedes number (Baturin 1972): gL o T o – T A Ar = -------------------------------2 Vo TA

(12)

where g = gravitational acceleration rate, ft/min2 Lo = length scale of diffuser outlet equal to hydraulic diameter of outlet, ft (To – TA)= initial temperature of jet – temperature of ambient air, °F Vo = initial air velocity of jet, fpm TA = room air temperature, °R

The influence of buoyant forces on horizontally projected heated and chilled jets is significant in heating and cooling with wall outlets. Koestel’s (1955) equation describes the behavior of these jets. Helander and Jakowatz (1948), Helander et al. (1953, 1954, 1957), Knaak (1957), and Yen et al. (1956) developed equations

Most manufacturers’ throw data obtained in accordance with ASHRAE Standard 70 assume the discharge is attached to a surface. An attached jet induces air along the exposed side of the jet, whereas a free jet can induce air on all its surfaces. Because a free jet’s induction rate is larger compared to that of an attached jet, a free jet’s throw distance will be shorter. To calculate the throw distance X for a noncircular free jet from catalog data for an attached jet, the following estimate can be used. Xfree = Xattached × 0.707

(13)

Circular free jets generally have longer throws compared to noncircular jets. Jets from ceiling diffusers initially tend to attach to the ceiling surface, because of the force exerted by the Coanda effect. However, cold air jets will detach from the ceiling if the airstream’s buoyancy forces are greater than the inertia of the moving air stream. With separation, a cold draft may enter the occupied space, resulting in thermal discomfort. The thermal discomfort is caused by two factors: the cold draft of the separated jet in the occupied space, and the lack of adequate mixing in areas of the room not reached by the separated jet. The separation distance parameter xs is the distance from the diffuser at which a jet separates from the ceiling. Separation distance correlates with outlet jet conditions. Separation distance depends on the velocity constant K, outlet temperature, flow rate, and static pressure drop. For slot and round diffusers, xs = (11.91)(1.2)K 1/2 ('T/T )–1/2 Qo 1/4 'P 3/8

(14)

where xs Kc 'T T Qo 'P

= = = = = =

jet separation distance, ft centerline velocity constant room-jet temperature difference, °F average absolute room temperature, °R outlet flow rate, cfm diffuser static pressure drop, in. of water

A representative value of Cs that has been found to best match the results of analyses and experiments of a wide variety of diffusers is 1.2.

Surface Jets (Wall and Ceiling) Attached jets travel at a higher velocity and entrain less air than a free jet. Values of centerline velocity constant K are approximately those for a free jet multiplied by 2 ; that is, the normal maximum of 6.2 for K for free jets becomes 8.8 for a similar jet discharged parallel to an adjacent surface. When a jet is discharged parallel to but at some distance from a solid surface (wall, ceiling, or floor), its expansion in the direction of the surface is reduced, and entrained air must be obtained by recirculation from the jet instead of from ambient air (McElroy 1943; Nottage et al. 1952b; Zhang et al. 1990). The restriction to entrainment caused by the solid surface induces the Coanda effect, which makes the jet attach to a surface a short distance after

Space Air Diffusion it leaves the diffuser outlet. The jet then remains attached to the surface for some distance before separating again. In nonisothermal cases, the jet’s trajectory is determined by the balance between thermal buoyancy and the Coanda effect, which depends on jet momentum and distance between the jet exit and solid surface. The behavior of such nonisothermal surface jets has been studied by Kirkpatrick et al. (1991), Oakes (1987), Wilson et al. (1970), and Zhang et al. (1990), each addressing different factors. More systematic study of these jets in room ventilation flows is needed to provide reliable guidelines for designing air distribution systems.

Multiple Jets Twin parallel air jets act independently until they interfere. The point of interference and its distance from outlets vary with the distance between outlets. From outlets to the point of interference, maximum velocity, as for a single jet, is on the centerline of each jet. After interference, velocity on a line midway between and parallel to the two jet centerlines increases until it equals jet centerline velocity. From this point, maximum velocity of the combined jet stream is on the midway line, and the profile seems to emanate from a single outlet of twice the area of one of the two outlets.

Airflow in Occupied Zone Mixing Systems. Laboratory experiments on jets usually involve recirculated air with negligible resistance to flow on the return path. Experiments in small-cross-sectional mine tunnels, where return flow meets considerable resistance, show that jet expansion terminates abruptly at a distance that is independent of discharge velocity and is only slightly affected by outlet size. These distances are determined primarily by the return path’s size and length. In a long tunnel with a cross section of 5 by 6 ft, a jet may not travel more than 25 ft; in a tunnel with a relatively large section (25 by 60 ft), the jet may travel more than 250 ft. McElroy (1943) provides data on this phase of jet expansion. Zhang et al. (1990) found that, for a given heat load and room air supply rate, air velocity in the occupied zone increases when outlet discharge velocity increases. Therefore, the design supply air velocity should be high enough to maintain the jet traveling in the desired direction, to ensure good mixing before it reaches the occupied zone. Excessively high outlet air velocity induces high air velocity in the occupied zone and results in thermal discomfort. Turbulence Production and Transport. Air turbulence in a room is mainly produced at the diffuser jet region by interaction of supply air with room air and with solid surfaces (walls or ceiling) in the vicinity. It is then transported to other parts of the room, including the occupied zone (Zhang et al. 1992). Turbulence is also damped by viscous effect. Air in the occupied zone usually contains very small amounts of turbulent kinetic energy compared to the jet region. Because turbulence may cause thermal discomfort (Fanger et al. 1989), air distribution systems should be designed so that stationary occupants are not subjected to the region where primary mixing between supply and room air occurs (except in specialized applications such as task ambient or spot-conditioning systems).

SYSTEM DESIGN MIXED-AIR SYSTEMS In mixed-air systems, high-velocity supply jets from air outlets maintain comfort by mixing room air with supply air. This air mixing, heat transfer, and resultant velocity reduction should occur outside the occupied zone. Occupant comfort is maintained not directly by motion of air from the outlets, but from secondary air motion that results from mixing in the unoccupied zone. Comfort is maximized when uniform temperature distribution and room air velocities of less than 50 fpm are maintained in the occupied zone.

20.7 Outlet Types Straub and Chen (1957) and Straub et al. (1956) classified outlets into five groups: Group A. Outlets mounted in or near the ceiling that discharge air horizontally. Group B. Outlets mounted in or near the floor that discharge air vertically in a nonspreading jet. Group C. Outlets mounted in or near the floor that discharge air vertically in a spreading jet. Group D. Outlets mounted in or near the floor that discharge air horizontally. Group E. Outlets mounted in or near the ceiling that project primary air vertically. Analysis of outlet performance was based on primary air pattern, total air pattern, stagnant air layer, natural convection currents, return air pattern, and room air motion. Figures 5 to 9 show room air motion characteristics of the five outlet groups; exterior walls are depicted by heavy lines. The principles of air diffusion emphasized by these figures are as follows: • Primary air (shown by dark envelopes in Figures 5 to 9) from the outlet down to a velocity of about 150 fpm can be treated analytically. Heating or cooling load has a strong effect on the characteristics of primary air. • Total air, shown by light gray envelopes in Figures 5 to 9, is influenced by primary air and is of relatively high velocity (but less than 150 fpm). Total air is also influenced by the environment and drops during cooling or rises during heating; it is not subject to precise analytical treatment. • Natural convection currents form a stagnant zone from the ceiling down during cooling, and from the floor up during heating. This zone forms below the terminal point of the total air during heating and above the terminal point during cooling. Because this zone results from natural convection currents, its air velocities are usually low (approximately 20 fpm), and the air stratifies in layers of increasing temperatures. The concept of a stagnant zone is important in properly applying and selecting outlets because it considers the natural convection currents from warm and cold surfaces and internal loads. • A return inlet affects room air motion only in its immediate vicinity. The intake should be located in the stagnant zone to return the warmest room air during cooling or the coolest room air during heating. The importance of the location depends on the relative size of the stagnant zone, which depends on the type of outlet. • The general room air motion (shown by arrows in white areas in Figures 5 to 9) is a gentle drift toward the total air. Room conditions are maintained by entraining room air into the total airstream. The room air motion between the stagnant zone and the total air is relatively slow and uniform. The highest air motion occurs in and near the total airstreams. Group A Outlets. This group includes high sidewall grilles, sidewall diffusers, ceiling diffusers, linear ceiling diffusers, and similar outlets. High sidewall grilles and ceiling diffusers are illustrated in Figure 5. Primary air envelopes (isovels) show a horizontal, two-jet pattern for the high sidewall and a 360° diffusion pattern for the ceiling outlet. Although variation of vane settings might cause a discharge in one, two, or three jets in the case of the sidewall outlet, or have a smaller diffusion angle for the ceiling outlet, the general effect in each is the same. During cooling, the total air drops into the occupied zone at a distance from the outlet that depends on air quantity, supply velocity, temperature differential between supply and room air, deflection setting, ceiling effect, and type of loading within the space. Analytical

20.8

2009 ASHRAE Handbook—Fundamentals Fig. 4

Air Motion Characteristics of Group A Outlets

Fig. 5

Ai