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INTERMODEL, ANALYTICAL, AND EXPERIMENTAL VALIDATION OF A HEAT BALANCE BASED RESIDENTIAL COOLING LOAD CALCULATION PROCEDURE By DONGYI XIAO Bachelor of Science in Thermal Engineering Shenyang Architectural and Civil Engineering Institute Shenyang, China 1995 Master of Science in Thermal Engineering Tongji University Shanghai, China 1998 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY December, 2006 ii INTERMODEL, ANALYTICAL, AND EXPERIMENTAL VALIDATION OF A HEAT BALANCE BASED RESIDENTIAL COOLING LOAD CALCULATION PROCEDURE Dissertation Approved: Dr. Jeffrey D. Spitler Dissertation Adviser Dr. Daniel E. Fisher Dr. Ronald D. Delahoussaye Dr. Khaled Mansy Dr. A. Gordon Emslie Dean of the Graduate College iii ACKNOWLEDGEMENTS I am so thankful to my dear husband, Xiaobing Liu, who accompanies me day and night, encourages me to continue during difficult times, and supports me all through the way. I cannot imagine how this work would have been finished without his love. I am so grateful that God gave us Rena, our daughter, who is two years old now. Bringing her up along the way was exhausting, but the joy and happiness she brings I will cherish for a lifetime. My thankfulness also goes to all my family in China, for their endless love and constant support. I would sincerely appreciate my advisor, Dr. Jeffrey D. Spitler. With the assistantship he offered, I was able to start this research work back in August 1999. Ever since then, I have learned a lot from him, not only in research but also in life. I thank him for his continuous support, constructive guidance, excellent leadership, and ceaseless understanding and patience during the seven years of my graduate study. My sincere appreciation also extends to the members of my doctoral committee: Drs. Daniel E. Fisher, Ronald D. Delahoussaye, and Khaled Mansy for their ideas and suggestions that helped me improve this dissertation. Mr. Charles S. Barnaby, currently Vice President of Research of the Wrightsoft Corporation, is one of the key personnel that developed RHB  the subject of this iv research work. He helped develop the automatic parametric run tool used for the intermodel comparison of RHB. He also assisted in the process of analytical testing and experimental validation of RHB. Dr. Simon J. Rees, currently senior research fellow in the Institute of Energy and Sustainable Development at De Montfort University, U.K., helped guide the development of the test suite used for the analytical verification of RHB. Mr. Bruce A. Wilcox, the manager and experimental designer of the Cardinal Fort Wayne Project, generously aided in providing measured data and corresponding information from the Fort Wayne house, which was used in the experimental validation of RHB. Dr. Jon W. Hand, currently senior research fellow in the Energy Systems Research Unit at the University of Strathclyde, U.K., gave useful advice on using ESPr, the reference model used for the intermodel comparison of RHB. To them I extend my sincere gratitude and appreciation. I would also like to thank my colleagues in the Building and Environment Thermal Systems Research Group at Oklahoma State University for their ideas, help, and friendship. Here, I only list a few: Andrew D. Chiasson, Mahadevan Ramamoorthy, David Eldridge, Hui Jin, Chanvit Chantrasrisalai, Calvin Iu, Weixiu Kong, Zheng Deng, Xia Xiao and Xiaowei Xu. Finally, support from ASHRAE under research projects RP1052 and RP1199, and in the form of a GrantinAid scholarship during 20052006 is gratefully acknowledged. Approval from Cardinal Glass Industries for using the experimental data is also gratefully acknowledged. v TABLE OF CONTENTS Chapter Page 1. INTRODUCTION .......................................................................................................... 1 1.1 Nonresidential Cooling Load Calculation Procedures ............................................ 2 1.2 Residential Cooling Load Calculation Procedures ................................................... 5 1.2.1 Characteristics of Residential Load Calculation................................................ 5 1.2.2 Prior Residential Cooling Load Calculation Procedures ................................... 8 1.2.3 Heat Balance Based Residential Cooling Load Calculation Procedure........... 12 1.3 Objective................................................................................................................. 14 2. LITERATURE REVIEW............................................................................................. 16 2.1 Heat Balance Based Residential Cooling Load Calculation Procedure ................. 16 2.1.1 Heat Balance Method for Cooling Load Calculation....................................... 17 2.1.2 Heat Balance for Residential Applications ...................................................... 28 2.1.3 Calculation Algorithms.................................................................................... 29 2.1.4 Component Models.......................................................................................... 34 2.1.5 Modeling Assumptions .................................................................................... 40 2.2 Validation Methods of Cooling Load Calculation Programs ................................. 43 2.2.1 Analytical Verification..................................................................................... 45 2.2.2 Comparative Testing........................................................................................ 46 2.2.3 Empirical Validation........................................................................................ 47 2.2.4 Application of the Validation Methods............................................................ 48 2.2.5 Summary of Prior Validation Work................................................................. 49 3. OBJECTIVES............................................................................................................... 52 4. INTERMODEL VALIDATION OF THE HEAT BALANCE BASED RESIDENTIAL COOLING LOAD CALCULATION PROCEDURE ........................... 54 4.1 Selecting the Comparison Tool............................................................................... 55 4.1.1 Basic Requirements of the Comparison Tool .................................................. 55 4.1.2 Review of Candidate Programs ....................................................................... 59 4.1.3 Selection of Comparison Tool ......................................................................... 71 vi Chapter Page 4.2 Methodology........................................................................................................... 77 4.2.1 Types of Comparison....................................................................................... 77 4.2.2 Parametric Code............................................................................................... 78 4.2.3 Combined Testing Process............................................................................... 79 4.2.4 RHBGen Parametric Generator ....................................................................... 80 4.2.5 ESPr System................................................................................................... 80 4.2.6 Design Evaluation Figure of Merit .................................................................. 85 4.2.7 Model Assumptions Used in the Comparison ................................................. 87 4.3 Results..................................................................................................................... 89 4.3.1 Description of Test Sets ................................................................................... 89 4.3.2 Ideal Load Comparison.................................................................................... 94 4.3.3 System Design Evaluations............................................................................ 125 4.4 Conclusions........................................................................................................... 147 5. ANALYTICAL VERIFICATION OF THE HEAT BALANCE BASED RESIDENTIAL COOLING LOAD CALCULATION PROCEDURE ......................... 151 5.1 Development of the Analytical Verification Test Suite........................................ 152 5.1.1 The Test Suite ................................................................................................ 153 5.1.2 The Test Suite Software................................................................................. 160 5.1.3 The Test Documentation................................................................................ 161 5.1.4 Evaluation of the Test Suite........................................................................... 163 5.2 Analytical Test of the Heat Balance Based Residential Cooling Load Calculation Procedure .................................................................................................................... 164 5.2.1 Testing ResHB............................................................................................... 164 5.2.2 The Analytical Tests and Testing Results...................................................... 168 5.3 Conclusions........................................................................................................... 193 6. EXPERIMENTAL VALIDATION OF THE HEAT BALANCE BASED RESIDENTIAL COOLING LOAD CALCULATION PROCEDURE ......................... 195 6.1 Experimental House.............................................................................................. 197 6.2 Instrumentation and Data Acquisition .................................................................. 201 6.3 Data Analysis........................................................................................................ 204 6.4 Simulation Approach ............................................................................................ 214 6.4.1 Simulation Inputs ........................................................................................... 214 6.4.2 Simulation Component Models ..................................................................... 225 6.4.3 Comparisons Made ........................................................................................ 227 6.5 Results................................................................................................................... 228 6.5.1 Interzone Airflow ......................................................................................... 228 6.5.2 Masterslave Control...................................................................................... 231 6.5.3 Ideal Control .................................................................................................. 239 6.5.4 ResHB and ESPr Result Comparison........................................................... 248 vii Chapter Page 6.5.5 Uncertainty Analysis...................................................................................... 251 6.6 Conclusions........................................................................................................... 256 7. CONCLUSIONS......................................................................................................... 259 REFERENCES ............................................................................................................... 267 APPENDIX A. ANALYTICAL VERIFICATION OF ESPR...................................... 279 A.1 Single Zone Tests................................................................................................. 281 A.2 Multizone Tests .................................................................................................. 287 APPENDIX B. PARAMETRIC CODE USED FOR THE INTERMODEL COMPARISON .............................................................................................................. 290 APPENDIX C. SAMPLE PERL AND SHELL SCRIPTS USED FOR THE INTERMODEL COMPARISON............................................................................................... 294 C.1 Sample Perl Scripts .............................................................................................. 294 C.2 Sample Shell Scripts ............................................................................................ 300 Shell script 1: Climate............................................................................................. 300 Shell script 2: Rotate............................................................................................... 301 Shell script 3: Simulate ........................................................................................... 302 Shell script 4: Analyse ............................................................................................ 303 viii LIST OF TABLES Table Page 21 The “sys off” and “sys on” values for default model of inside surface convection coefficients (W/m2K) in ResHB............................................................................... 34 22 Fractional components of internal heat sources incorporated in ResHB.................... 42 23 Advantages and Disadvantages of the three validation methods as from Judkoff (1988)........................................................................................................................ 44 41 Classification of basic requirements for candidate comparison tools ........................ 59 42 Summary of the features of the alternative programs................................................. 70 43 Main advantages and disadvantages of the candidate programs ................................ 71 44 Part 1 More detailed summaries of the candidate programs ...................................... 73 44 Part 2 More detailed summaries of the candidate programs ...................................... 74 45 Part 1 Model assumptions used in ESPr and RHB for the comparison .................... 88 45 Part 2 Model assumptions used in ESPr and RHB for the comparison .................... 89 46 Test parameters for the 576 test cases ........................................................................ 93 47 Algorithm for attributing the PPD Cause ................................................................. 127 51 Organization of the Test Suite.................................................................................. 155 52 Tests Selected for Testing ResHB............................................................................ 165 53 Convection Coefficients Used in Testing ResHB .................................................... 167 54 Differences in zone load between the ResHB program and analytically calculated loads for the convection and conduction cases ....................................................... 171 55 Test parameters used for the steady state convection and conduction tests ............. 171 56 Constructions used for the transient conduction tests .............................................. 172 57 Differences in zone load between ResHB and analytical result for the solar related cases ........................................................................................................................ 180 58 Parameters used for the ExtSolRad test.................................................................... 180 59 Parameters used for the SolRadGlazing and SolRadShade tests.............................. 181 510 Parameters used for the WinReveal and IntSolarDist tests .................................... 181 511 Differences in zone load between ResHB and analytical result for the interior longwave radiation tests.......................................................................................... 191 61 Construction materials of the Fort Wayne house ..................................................... 200 62 Windows of the Fort Wayne house .......................................................................... 200 63 Constants c, n and ELA values derived from blower door measurements.............. 209 64 Construction thermal properties input in ResHB/ESPr simulation......................... 217 65 Surface absorptances and emissivities input in ResHB/ESPr simulation ............... 217 ix Table Page 66 Solar Heat Gain Coefficient (SHGC), Solar Transmittance (T) and Layer Absorptances (A) for ResHB fenestration class FCA17c ..................................... 218 67 Component models used in ResHB and ESPr for experimental validation ............ 226 68 Uncertainties resulting from representative simulation inputs and experimental measurements.......................................................................................................... 252 A1 Analytical Verification Tests of ESPr .................................................................... 280 B1 Parametric Code....................................................................................................... 291 B2 Roof constructions ................................................................................................... 292 B3 Ceiling constructions ............................................................................................... 292 B4 Wall constructions ................................................................................................... 292 B5 Fenestration.............................................................................................................. 292 B6 Partition wall constructions...................................................................................... 293 B7 Partition floor/ceiling constructions......................................................................... 293 B8 Interior mass constructions ...................................................................................... 293 B9 Exterior floor constructions ..................................................................................... 293 x LIST OF FIGURES Figure Page 11. Schematic floor plan for a single family detached house with masterslave control .. 7 41. Overall intermodel testing process........................................................................... 79 42. Predicted Percentage of Dissatisfied (PPD) as a function of Predicted Mean Vote (PMV) ....................................................................................................................... 86 43. Schematic floor plan of the Shoebox prototype ( figure drawn with front side facing north; front, left, back, right as defined in RHBGen) ............................................... 90 44. Schematic floor plan of the 4bedroom house prototype ( figure drawn with front side facing north; front, left, back, right as defined in RHBGen)............................. 92 45. Peak cooling load comparison (Shoebox  Master)................................................... 95 46. Cooling load error percentage based on peak average Shoebox load (Master)......... 95 47. Peak cooling load comparison (4bedroom house – Family room)........................... 97 48. Peak cooling load comparison (4bedroom house – Laundry).................................. 98 49. Peak cooling load comparison (4bedroom house – Foyer 1) ................................... 98 410. Peak cooling load comparison (4bedroom house – Bedroom 1) ........................... 99 411. Peak cooling load comparison (4bedroom house – Total)..................................... 99 412. Cooling load error percentage based on peak average 4bedroom house load (Family room) ......................................................................................................... 100 413. Cooling load error percentage based on peak average 4bedroom house load (Total) ................................................................................................................................ 100 414. Outside ground surface temperatures from RHB and ESPr for Alamosa, CO .... 103 415. Comparison of the ambient dry bulb temperature and the outside surface temperatures calculated from ESPr (Shoebox  Master) ....................................... 104 416. Comparison of cooling load calculated by RHB and ESPr (Shoebox  Master): (a) with external long wave radiation (b) without external long wave radiation ......... 104 417. Comparison of cooling load error percentage between RHB and ESPr (4bedroom house – Family room): (a) with external long wave radiation (b) without external long wave radiation................................................................................................. 106 418. Comparison of cooling load calculated by RHB and ESPr (Shoebox – Master): (a) with internal thermal mass (b) without internal thermal mass................................ 108 419. Comparison of cooling load error percentage between RHB and ESPr (ESPr with simple solar distribution, Shoebox – Master): (a) with internal thermal mass (b) without internal thermal mass................................................................................. 109 420. Comparison of cooling load error percentage between RHB and ESPr (Shoebox – Master): (a) ESPr with detailed solar distribution, with internal thermal mass (b) ESPr with simple solar distribution, without internal thermal mass ..................... 110 xi Figure Page 421. ESPr simple solar distribution vs. detailed solar distribution (Shoebox – Master): (a) comparison of cooling load (b) comparison of cooling load error percentage.. 111 422. Comparison of cooling load calculated by RHB and ESPr (4bedroom house – Family room): (a) ESPr with interzone conduction (b) ESPr without interzone conduction............................................................................................................... 115 423. Comparison of cooling load calculated by RHB and ESPr (4bedroom house – Laundry): (a) ESPr with interzone conduction (b) ESPr without interzone conduction............................................................................................................... 115 424. Comparison of cooling load calculated by RHB and ESPr (4bedroom house – Foyer 1): (a) ESPr with interzone conduction (b) ESPr without interzone conduction............................................................................................................... 116 425. Comparison of ESPr calculated cooling loads (without interzone conduction vs. with interzone conduction): (a) 4bedroom house – Family room (b) 4bedroom house – Foyer 1....................................................................................................... 116 426. Comparison of cooling load calculated by RHB and ESPr (Shoebox – Master): (a) with internal longwave radiation (b) without internal longwave radiation............. 118 427. Comparison of cooling load calculated by RHB and ESPr (Shoebox – Master): without external long wave radiation, internal thermal mass, interzone conduction, internal long wave radiation and windows ............................................................. 120 428. (a) Ambient air temperatures used for Alamosa, CO in RHB and ESPr (b) Outside surface absorbed solar radiation in RHB and ESPr (Shoebox  Master, Alamosa, CO).......................................................................................................................... 121 429. Comparison of cooling load calculated by RHB and ESPr (Shoebox – Master, without external and internal longwave radiation, without thermal mass, interzone conduction, and windows) ...................................................................................... 122 430. Analytically calculated zone loads and those predicted by RHB and ESPr......... 124 431. Processed PPD showing night time ambient cooling, system designed with zero temperature swing (Shoebox) ................................................................................. 129 432. Processed PPD showing system undersizing and inadequate distribution, system designed with zero temperature swing (Shoebox) .................................................. 130 433. Hourly PPD vs. temperature, system designed with zero temperature swing (Shoebox  case 17)................................................................................................. 131 434. Hourly PPD vs. temperature, system designed with zero temperature swing (Shoebox  case 20)................................................................................................. 131 435. Processed PPD showing night time ambient cooling, system designed with zero temperature swing (4bedroom house) ................................................................... 133 436. Processed PPD showing system undersizing and inadequate distribution, system designed with zero temperature swing (4bedroom house) .................................... 135 437. Hourly PPD vs. temperature, system designed with zero temperature swing (4 bedroom house: case 121)...................................................................................... 135 438. Processed PPD showing night time ambient cooling, system designed with medium temperature swing (Shoebox) ................................................................................. 137 439. Processed PPD showing system undersizing and inadequate distribution, system designed with medium temperature swing (Shoebox)............................................ 137 xii Figure Page 440. Hourly PPD vs. temperature, system designed with medium temperature swing (Shoebox  case 355)............................................................................................... 138 441. Processed PPD showing night time ambient cooling, system designed with medium temperature swing (4bedroom house) ................................................................... 139 442. Processed PPD showing system undersizing and inadequate distribution, system designed with medium temperature swing (4bedroom house).............................. 139 443. Hourly PPD vs. temperature, system designed with medium temperature swing (4 bedroom house: case 144)....................................................................................... 141 444. Hourly PPD vs. temperature, system designed with medium temperature swing (4 bedroom house: case 451)....................................................................................... 141 445. Average degree hours for systems designed with zero or medium temperature swing (4bedroom house): (a) Family room (b) whole house ................................ 143 446. Average processed PPD values for systems designed with zero or medium temperature swing (4bedroom house): (a) night time ambient cooling (b) inadequate distribution .............................................................................................................. 145 447. Average processed PPD values for systems designed with zero or medium temperature swing (4bedroom house): (a) system undersizing (b) inadequate distribution and system undersizing ...................................................................... 146 51. Example parameter input screen (Test SSCond)..................................................... 161 52. Sinusoidal driving external dry bulb temperature profile used in the transient conduction test TC3 ................................................................................................ 169 53. Analytically calculated zone loads and those predicted by the ResHB program for the transient conduction test with sinusoidal driving temperature: Case 1................... 174 54. Analytically calculated zone loads and those predicted by the ResHB program for the transient conduction test with sinusoidal driving temperature: case 2. .................. 174 55. Analytically calculated zone loads and those predicted by the ResHB program for the transient conduction test with sinusoidal driving temperature: case 3. .................. 175 56: Zone geometry of the internal solar distribution test (a) plan view showing two vertical fins (b) vertical view showing horizontal fin at the top of the window. The dimensions W, Rv and Rh are 0.5m (1.64ft), and the dimensions H and B are 1.0m (3.28ft). ................................................................................................................... 178 57. Analytically calculated zone loads and those predicted by different versions of ResHB for the solar shading test: horizontal and right side vertical fin on a southfacing window......................................................................................................... 182 58. Analytically calculated zone loads and those predicted by different versions of ResHB for the solar shading test: horizontal and left side vertical fin on a southfacing window......................................................................................................... 183 59. Analytically calculated zone loads and those predicted by ResHB for the window reveal test: before reveal depth was added to the depths of vertical fins................ 184 510. Analytically calculated zone loads and those predicted by ResHB for the window reveal test: after reveal depth was added to the depths of vertical fins................... 184 511. Analytically calculated zone loads and those predicted by ResHB for the internal solar distribution test: Case 1, the floor in RHB test zone is heavy weight............ 185 xiii Figure Page 512. Analytically calculated zone loads and those predicted by ResHB for the internal solar distribution test: Case 2, the floor in RHB test zone is massless.................. 186 513: Zone load variation with zone aspect ratio and different surface emissivities. The emissivities are: Case 1, external surface 0.9, opposite surface 0.1, other surfaces 0.3; Case 2, external surface 0.9, all other surfaces 0.1; Case 3, all surfaces 0.9... 190 514. Analytical and ResHBpredicted zone load variation with zone aspect ratio and different surface emissivities. The emissivities are: Case 1, external surface 0.9, all other surfaces 0.1; Case 2, all surfaces 0.9; Case 3, external surface 0.9, opposite surface 0.1, other surfaces 0.3................................................................................. 191 61(a). Front view of the house in Ft. Wayne, Indiana (Wilcox 2004)........................... 198 61(b). Back view of the house in Ft. Wayne, Indiana (Wilcox 2004)........................... 198 62. Floor plans of the house in Ft. Wayne, Indiana (Wilcox 2004) .............................. 199 63. Campbell Scientific CR10X data logger: measurement and control module (left), wiring panel CR10XWP (right). (Picture from http://www.campbellsci.com) ...... 202 64. Aspirated temperature thermocouple (Wilcox 2004) .............................................. 202 65. Conceptual flow chart of the experimental validation............................................. 205 66. Hourly averaged outside drybulb and wetbulb temperature for 09/21/2005 ........ 207 67. Hourly averaged beam and diffuse solar radiation for 09/21/2005......................... 207 68. Hourly averaged internal heat gain for 09/21/2005................................................. 208 69. Hourly return air temperature and hourly flowweighted runtime supply air temperature for 09/21/2005, values shown only for hours when the system was on ................................................................................................................................ 211 610. Hourly air conditioning “on” fraction for 09/21/2005........................................... 212 611. Hourly basement duct gain (including runtime part and average T part) for 09/21/2005, values shown only for hours when the system was on ....................... 213 612. House total sensible cooling load for 09/21/2005 ................................................. 214 613. Minutely measured room air temperature during the systemoff hours for 09/21/2005: (a) kitchen and living room (b) master bedroom and master bathroom ................................................................................................................................ 219 614. Minutely measured room air temperature for 09/21/2005: dining room............... 222 615. Schematic representation of the ESPr airflow network for the first and second floor ................................................................................................................................ 224 616. Simulated and experimental total house cooling load comparison: ESPr with/without interzone airflow, ResHB with/without internal heat gain and ventilation distribution............................................................................................ 229 617. Simulated and experimental total house cooling load comparison: ResHB with dining room specified as master room, fixed set point of 23.89 oC with 0.0, 0.2, 0.4, 0.6, 0.8 oC temperature swing, with internal heat gain and ventilation distribution ................................................................................................................................ 232 618. Simulated and experimental room temperature comparison, ResHB with dining room specified as master room, fixed set point of 23.89 oC with 0.0, 0.2, 0.4, 0.6, 0.8 oC temperature swing, with internal heat gain and ventilation distribution: (a) Dining room (b) Living room ................................................................................. 233 xiv Figure Page 619. Simulated and experimental total house cooling load comparison: ResHB with master room specified as dining room, living room, Foyer 1 and bedroom 2, master room uses experimental hourly average room air temperature as set point without temperature swing, with internal heat gain and ventilation distribution................. 235 620. Simulated and experimental room temperature comparison, ResHB with master room specified as dining room, living room, Foyer 1 and bedroom 2, master room uses experimental hourly average room air temperature as set point without temperature swing, with internal heat gain and ventilation distribution: (a) Dining room (b) Living room ............................................................................................. 237 621. Simulated and experimental total house cooling load comparison: ResHB uses ideal control, every room uses fixed set point of 23.89 oC with 0.8 oC or 0.0 oC temperature swing, with internal heat gain and ventilation distribution................. 241 622. Simulated and experimental room temperature comparison, ResHB uses ideal control, every room uses fixed set point of 23.89 oC with 0.8 oC temperature swing, with internal heat gain and ventilation distribution: (a) Dining room (b) Kitchen (c) Bedroom 3............................................................................................................... 244 623. Simulated and experimental total house cooling load comparison: ResHB uses ideal control, every room uses fixed set point of 23.89 oC with 0.8 oC or 0.0 oC temperature swing or every room uses experimental hourly average room air temperature as set point without temperature swing, with internal heat gain and ventilation distribution............................................................................................ 245 624. Simulated and experimental room temperature comparison, ResHB uses ideal control, every room uses fixed set point of 23.89 oC with 0.8 oC temperature swing or every room uses experimental hourly average room air temperature as set point without temperature swing, with internal heat gain and ventilation distribution: (a) Dining room (b) Kitchen (c) Bedroom 3 ................................................................ 247 625. Simulated and experimental total house cooling load comparison: ResHB uses ideal control, every room uses fixed set point of 23.89 oC with 0.8 oC temperature swing, with internal heat gain and ventilation distribution; ESPr models system control with airflow network under masterslave onoff control ........................................ 249 626. Minutely ESPr simulated and experimental dining room (master) temperature comparison: ESPr models system control with airflow network under masterslave onoff control .......................................................................................................... 250 627. Simulated and experimental room temperature comparison: ResHB uses ideal control, every room uses fixed set point of 23.89 oC with 0.8 oC temperature swing, with internal heat gain and ventilation distribution; ESPr models system control with airflow network under masterslave onoff control: (a) Dining room (b) Kitchen (c) Attic ................................................................................................................... 251 628. Simulated and experimental total house cooling load comparison: ResHB uses ideal control, every room uses experimental hourly average room air temperature as set point without temperature swing, with internal heat gain and ventilation distribution, cases with infiltration rate of 0.2, 0.4, 0.6 and 0.8ACH ........................................ 254 xv Figure Page 629. Simulated and experimental room temperature comparison: ResHB uses ideal control, every room uses experimental hourly average room air temperature as set point without temperature swing, with internal heat gain and ventilation distribution, cases with infiltration rate of 0.2, 0.4, 0.6 and 0.8ACH: (a) Dining room (b) Master bedroom .................................................................................................................. 255 A1a Analytically calculated zone loads and those calculated by ESPr for Solar Radiation – Glazed Surfaces test: East, west and south facing window................. 282 A1b Analytically calculated zone loads and those calculated by ESPr for Solar Radiation – Glazed Surfaces test: East, west and south facing window (with hourly instantaneous weather data) .................................................................................... 283 A1c Comparison of solar beam irradiance used by ESPr and Analytical solution...... 283 A2 Analytically calculated zone loads and those calculated by ESPr for Solar Radiation – Window Shading test: south facing window with left side vertical fin ............... 284 A3 Analytically calculated zone loads and those calculated by ESPr for the Internal Long Wave Radiation test: emissivity of the external surface = 0.9, emissivity of other surfaces = 0.1 ................................................................................................. 285 A4 Analytically calculated zone loads and those calculated by ESPr for the Internal Long Wave Radiation test: emissivity of all surfaces = 0.9 ................................... 286 A5 The convective heat input profiles of the test zones used in the VAV and OnOff control tests with ESPr program............................................................................ 288 A6 Zone air temperatures predicted by ESPr program and analytical solution for the VAV control test ..................................................................................................... 288 A7 Zone air temperatures predicted by ESPr program and analytical solution for the OnOff control test.................................................................................................. 289 xvi NOMENCLATURE Symbols c p specific heat, Btu/(lbºF) or J/(kgºC) c, n empirical constants from regression analysis h convection coefficient, Btu/h.ft2 or W/m2K k thermal conductivity, Btu/(hftºF) or W/(mK) N the number of cases used in calculating mean bias error O observed value, equals the ESPr predicted loads in our case, Btu/h or W P predicted value, equals the RHB predicted loads in our case, Btu/h or W Q volume air flow rate, CFM or m3/s Tmaster master room temperature, ºF or ºC Tsetpoint room temperature set point, ºF or ºC Tslave slave room temperature, ºF or ºC U conductance, W/m2K or Btu/h.ft2 density, lbm /ft3 or kg/m3 p pressure difference across the house envelope, Pa T difference between the system supply and return air temperature, oC T temperature tolerance used in calculating integrated PPD values, ºF or ºC xvii Abbreviations CLF Cooling Load Factor CLTD Cooling Load Temperature Difference CTF Conduction Transfer Functions DH Degree Hours ELA Effective Leakage Area ETD Equivalent Temperature Difference GLF Glass Load Factors HVAC Heating, Ventilating and Air Conditioning MBE Mean Bias Error PMV Predicted Mean Vote PPD Predicted Percentage of Dissatisfied RHB Residential Heat Balance load calculation procedure SCL Solar Cooling Load SHGC Solar Heat Gain Coefficient TA Time Averaging TETD Total Equivalent Temperature Difference TFM Transfer Function Method 1 1. INTRODUCTION Properly designed residential heating, ventilating and air conditioning (HVAC) systems should provide good comfort and high efficiency at minimum cost. Oversized HVAC systems compromise indoor comfort, reduce system efficiency, and increase the initial investment and energy cost. (Khattar et al. 1987; Reddy and Claridge 1993; Neal and O’Neal 1994; Proctor et al. 1995; James et al. 1997). Since load calculation is the main factor affecting the selection of HVAC system capacities, it is essential to use a reliable heating and cooling load calculation procedure to obtain high efficiency and good quality both for the design and energy utilization of a residential HVAC system. It is important at the outset to define three interrelated but oftenconfused concepts: heat gain, cooling load, and heat extraction rate. Heat gain is the rate at which energy enters into or is generated within a space. Heat gains can occur in various forms such as solar radiation, heat conduction, internal heat gain, ventilation and infiltration air, etc. Cooling load is the rate at which energy must be removed from a space to maintain the temperature and humidity at the design values. The space heat gain usually does not equal the space cooling load. This is because the radiant heat gains must first be absorbed by the surfaces enclosing the space and the objects in the space. Only when the surfaces and objects receiving the radiant heat become warmer than the surrounding air, 2 will some of this energy be transferred to the air by convection and become a part of the cooling load. The heat extraction rate is the rate at which energy is removed from the space by the cooling and dehumidifying equipment. It equals the space cooling load only if the space conditions are kept constant by the operating equipment. Although the heat extraction rate is usually not calculated for commercial building equipment selection, permissible temperature swings in residential buildings require that this be considered in the development of a residential load calculation procedure. Since the subject of this validation work is a newly developed residential load calculation procedure based on the heat balance method, it is of interest to consider the background of this procedure. Accompanying the historical development of air conditioning, building heating and cooling load calculations have gone through a continuous development. Romine (1992) gave a short summary of the development of load calculations in ASHRAE (American Society of Heating, Refrigerating and Air Conditioning Engineers) until 1992. The load calculation development history both in ASHRAE and CIBSE (Chartered Institution of Building Services Engineers) is also reviewed by Rees, et al. (2000). 1.1 Nonresidential Cooling Load Calculation Procedures For nonresidential (commercial and industrial) applications, three methods were presented for calculating cooling loads in the 1997 ASHRAE Handbook of Fundamentals. These are the transfer function method (TFM), the cooling load temperature 3 difference/solar cooling load/ cooling load factor (CLTD/SCL/CLF) method, and the total equivalent temperature difference/time averaging (TETD/TA) method. The three methods are directly or indirectly an approximation of the heat balance method (to be discussed in more detail later). This is because calculating cooling load for a space inevitably involves the calculation of a conductive, convective, and radiative heat balance for each room surface and a convective heat balance for the room air. Exact solutions of space cooling load by heat balance procedures requires a rigorous and laborious calculation of the heat balance equations and is impractical for widespread or routine use without the speed of modern digital computers (ASHRAE 1997). Due to the limited computer capability available in earlier days, various simplified forms of the heat balance procedure were developed for routine cooling load calculation purposes. As an ongoing effort in developing cooling load calculation methods, ASHRAE funded a research project entitled “Advanced Methods for Calculating Peak Cooling Loads (RP875)” in 1996. As the goal of this project, two new methods  the Heat Balance (HB) method (Pedersen, et al. 1997) and the Radiant Time Series (RTS) method (Spitler, et al. 1997)  have been developed. As mentioned before, the heat balance concept is the foundation of the three simplified methods recommended by the 1997 ASHRAE Handbook of Fundamentals. It has been applied in many energy calculation programs in one form or another for many years. It was first implemented in NBSLD (Kusuda 1967), and has also been applied to BLAST and TARP by Walton (1981, 1983). The heat balance method is introduced for load calculation purposes because it has the potential to be the most accurate method for calculating space heating and cooling 4 loads and may be the most understandable method to practicing engineers. It accounts for all energy flows in their most basic, fundamental form and does not impose any simplifications on the solution technique (Strand et al., 1999). It calculates space heating or cooling load by solving the heat balance equations for each of the outside and inside zone surfaces and for the zone air. Transient conduction heat transfer through building fabric is estimated by applying conduction transfer functions. Radiant and convective heat exchanges at both external and internal surfaces are treated separately, with internal radiant exchange calculated by the method of mean radiant temperature with balance (Walton 1980). The heat balance method is also the first ASHRAE load calculation method that completely relies on computer implementation (Rees, et al. 2000). Derived from the heat balance method, the radiant time series method is the new ASHRAE simplified cooling load calculation method for nonresidential buildings, effectively replacing the TFM, TETD/TA and CLTD/SCL/CLF methods (Spitler, et al. 1997). Sharing many heat transfer submodels with the heat balance method, the radiant time series method is most similar to the transfer function method and can be shown equivalent in some aspects (Spitler and Fisher 1999). Experimental validation of both the heat balance method and the radiant time series method has been done in test cells at Oklahoma State University (Chantrasrisalai, et al. 2003; Iu, et al. 2003). As a result of the development and validation work, the heat balance method and the radiant time series method are presented in the 2001 ASHRAE Handbook of Fundamentals, superseding the TFM, TETD/TA and CLTD/SCL/CLF methods. 5 1.2 Residential Cooling Load Calculation Procedures 1.2.1 Characteristics of Residential Load Calculation In comparison to the nonresidential applications, the situation with the residential cooling load calculation is somewhat different because of some unique features inherent in residential buildings. Load patterns of residences differ significantly from those of commercial structures because of different building scale, construction, occupancy, and controls. Compared to commercial or industrial buildings, residential buildings are usually smaller, and their constructions usually have less thermal mass (product of mass and specific heat). Loads from the residential envelope usually compose a much greater fraction of the total building load. The internal heat gains of residences, especially those from occupants and lights, are relatively small. Current ASHRAE design procedure (ASHRAE 1997) assumes that residences usually will be occupied and conditioned for 24 hours a day, every day during the heating and cooling seasons. Residential load calculation usually must be done with a quick and simple method. This limits the usage of whole building energy analysis programs (such as DOE 2, BLAST and EnergyPlus) in the residential realm. Large, sophisticated programs usually allow the possibility of comprehensively describing the buildings. For example, an energy analysis program may allow the user to specify fairly detailed information on the cracks and openings of a building in order to compute the infiltration load. This level 6 of input can be overwhelming for the typical residential HVAC system designer. Instead, a method that allows simple input is usually preferred. In general, most singlefamily detached houses use constant air volume systems with one return and a single central thermostat to control the temperatures of all rooms (Figure 11). This type of temperature control necessarily allows temperatures to fluctuate through out the house. It usually results in temperature swings of several degrees Fahrenheit between different rooms of a house, which is generally considered acceptable from the standpoint of the occupants’ comfort. These temperature swings also result in interzone heat transfer and heat storage in building elements, which have the effect of moderating peak loads. Interzone airflow driven by the air distribution system or thermal buoyancy also produces loadmoderating effects in residences. These thermal interactions, including interzone heat transfer and interzone air flow, contribute to the result that the peak or peak total load of the building is significantly less than the sum of peak room loads. For individual units in multifamily buildings that do not have exposures facing all directions, the loadmoderating effect is not as significant as in the singlefamily detached houses, and the loads are usually closer to the sum of the room peak loads. With the interzone thermal communication as an important feature of residential buildings, the capability to simultaneously model all zones to reflect this feature becomes one of the primary requirements of the detailed reference tool used to evaluate a residential load calculation procedure (See Chapter 4). 7 Master zone Central Single air return Hallway thermostat Utility room Kitchen Bath room Bath room Bedroom 3 Air supply register Bedroom 2 Bedroom 1 Garage Great room Figure 11 Schematic floor plan for a single family detached house with masterslave control In addition to thermal communication, the control strategy becomes another important issue in this case. If the zone containing the central thermostat is called the “master” zone (Figure 11), and other zones are called “slave” zones accordingly, this problem can then be briefly described as the masterslave zone control problem. Because of the single thermostat control, the temperatures generally cannot be simultaneously controlled at the design set point in all rooms. The master zone temperature can be well controlled by the thermostat. The slave zone air temperatures will float depending on the relation between the zone load and the output of the air conditioning system. The slave zones may maintain reasonable temperatures if they have load profiles similar to that of the master zone. Poor zone configurations can result if the slave zones have load profiles significantly different than the master zone. This “masterslave” zone control problem is another unique feature of the residential load calculation. All the features discussed above make the residential load calculation a unique problem. The load calculation techniques developed for commercial buildings therefore cannot be applied directly to residential load calculation. 8 1.2.2 Prior Residential Cooling Load Calculation Procedures Prior to the development of the Residential Heat Balance (RHB) load calculation procedure, there were three common procedures in use for residential cooling load calculations. One is the procedure recommended by ASHRAE. Fully described in Chapter 28 of the ASHRAE 2001 Handbook of Fundamentals, this procedure is primarily based on research project RP342 of ASHRAE (McQuiston et al. 1984). The second is the procedure presented in Manual J, published by the Air Conditioning Contractors of America (ACCA), including the widely used Manual J Seventh Edition (Rutkowski 1986) and Manual J Eighth Edition (Rutkowski 2002). Sharing an ASHRAE heritage, Manual J is based on preRP342 data, and in some cases, techniques that date from the 1950s. The third is the procedure stated in Standard CAN/CSAF280M90 (CSA 1990). Maintained by the Heating, Refrigerating, and AirConditioning Institute of Canada (HRAI), it is actually an adaptation of the ASHRAE procedure to Canadian use. Though differing in many details, this family of methods uses the same general approach to residential load calculation. For cooling load calculations, cooling load temperature differences (CLTD, or equivalent temperature differences (ETD)) and glass load factors (GLF) are used since peak cooling conditions occur intermittently for different rooms during several hours of the day, and buildings do not reach steady state. Here, the CLTD is a purposely defined and precalculated effective temperature difference so that the steady state formulation can be used for cooling load from opaque surfaces. The GLF is the effective cooling load produced by a unit area of glazing. It is defined and generated for the same purpose as the CLTD. The values of CLTD and GLF vary with building construction, orientation, environmental climate, and residence type. 9 With CLTD and GLF precalculated, the cooling load for each opaque element is computed as the CLTD multiplied by its Ufactor and area. Cooling load from fenestration gain is computed as the GLF multiplied by the glazing area. The cooling load of the building fabric is then obtained by summing up cooling loads for opaque elements and glazing surfaces. The CLTD/GLF form of the cooling load calculation is actually an application of the CLTD/SCL/CLF method in residential buildings. It is not only conceptually clear but also simple to implement, in that each building element creates a load per unit area and only an accumulation of component loads is required. However, this “sum up the component loads” approach is an approximation considering the fact that the real load in the conditioned space is a combined effect of component gains. Although this approximation is generally accurate and conservative, consideration of radiant heat transfer, heat storage effects in the space and the possibility that some heat gains are reflected or conducted back out again (as explained by Rees, et al. 1998) may cause this approximation to be inordinately conservative. Except Manual J 8th edition (which requires an evaluation of the designday fenestration gain profiles), all prior methods use single design condition in the cooling load calculation. The single designcondition cooling load calculation has long been problematic. To avoid overpredicting zone loads with the “sum up the component loads” approach and account for heat gain diversity (heat gains generally occur at different times over the day), semiempirical adjustments such as multihour averaging were used to derive the cooling load factors in prior methods. However, for multifamily units with 10 limited exposure (apartments), it is more appropriate to use the “sum up the component loads” approach, as the dominant fenestration gains peak simultaneously in this case. To deal with such configurations, prior methods have used alternative factors and/or adjustments. User judgment is required to select the appropriate application. There is also concern about the accuracy in terms of the derivation of the CLTD/GLF values. The CLTD/GLF values are derived based on the cooling loads calculated by the transfer function method, which is already an approximation to the heat balance method. (The Heat Transfer Multipliers (HTM) in ACCA Manual J are derived from the ETD or CLTD values (which are based on the TFM method) recommended by the ASHRAE Handbook of Fundamentals (1985 for the 7th Edition, 1989 and 1997 for the 8th Edition), supplemented by information from other sources that the manual does not list.) The approximate nature of the transfer function method and its associated errors are therefore unavoidably brought into the results derived from this method. With the development of the computer based heat balance load calculation procedure, there is no apparent reason why this most fundamental method should not be used directly to derive the CLTD/GLF values (if it is still needed) instead of the transfer function method. It is also problematic to estimate other important component loads such as infiltration load. The documentation on airchange method of infiltration is nearly nonexistent (ASHRAE RP342, 1984). The widely used crack length methods require an unreasonably large amount of input for a simplified method (Spitler 2000). Its accuracy depends on the accuracy of the air leakage data for individual buildings and the designer’s experience. The ASHRAE method uses the simple mathematical linear model 11 (Bahnfleth et al. 1957; Coblentz and Achenbach 1963) to estimate the infiltration rate, which relates the air changes per hour as a linear function of the wind velocity and the indooroutdoor design temperature difference (Details can be found in ASHRAE RP342, 1984). Another concern regards the validation of the prior procedures. Although the evaluation of a load calculation procedure can be very comprehensive, timeconsuming and expensive (if empirical test is performed), the validity of a load calculation procedure is very important. Unfortunately, none of the prior procedures has been thoroughly evaluated and validated since their development. Systematic testing of the prior procedures is not documented in the literature. In summary, the formulation of the prior residential cooling load calculation procedures is satisfactory for most residential buildings. However, problems and questions exist concerning the accuracy of the resulting loads, the method of deriving the CLTD and GLF values, the method of estimating some important component loads, and the validity of the prior methods. A new heat balance based residential cooling load calculation procedure is highly desirable. In the development of the new procedure, attention must be paid to consider and model the interzone thermal interactions and masterslave zone controls. It is also desirable that the new procedure be well tested and the system design resulted from the new procedure be carefully evaluated. 12 1.2.3 Heat Balance Based Residential Cooling Load Calculation Procedure In response to the problems of the prior procedures, ASHRAE sponsored a research project (1199RP) “Updating the ASHRAE/ACCA Residential Heating and Cooling Load Calculation Procedures and Data” (Barnaby et. al. 2004). In this project, a new residential loads calculation procedure  Residential Heat Balance (RHB) – was developed. RHB is a detailed heat balance based procedure. It requires computer execution, as the roombyroom hourly designday simulation used in this procedure is computationally extensive. The hourly designday simulation eliminates issues of gain diversity that are problematic in prior procedures, which use single design condition. The average/peak distinction used in prior procedures is no longer necessary, as the design load is simply the peak hourly load. For calculation of sensible cooling load, RHB applies the general approach of the ASHRAE Heat Balance (HB) method. As the heat transfer equations are solved in their most basic, fundamental form in the heat balance method, prior concerns about the “sum up the component loads” approximation are eliminated. The concern regarding the approximate accuracy of the transfer function method, which is used in the derivation of the CLTD/GLF factors of the prior methods, is also eliminated. Considering the unique features of residential load calculation, RHB includes algorithms for calculating sensible cooling loads with temperature swing and addresses the masterslave zone control problem. 13 As part of 1199RP, the ResHB computer program was developed as the reference implementation of the RHB procedure. The ResHB source code is derived from the ASHRAE Loads Toolkit (Pedersen et. al. 2001). An additional utility program, RHBGen, was also developed to automatically generate and run parametrically varied ResHB cases for testing and research purposes. The RHB development also involved review, refinement, and extension of the ASHRAE Loads Toolkit models. Component models and assumptions used for RHB are considered appropriate for residential application. For example, the AIM2 infiltration model was selected for RHB (Walker and Wilson 1990, 1998, and “enhanced model” in Chapter 26, ASHRAE 2001). An algorithm was developed to derive a homogeneous layer that corresponds to a framed construction layer, which is common in residential buildings. Details of the component models and assumptions of RHB are documented in the project final report (Barnaby et. al. 2004) and are summarized in the literature review section (see Chapter 2). One concern left and deserving detailed investigation is the validity of RHB. As a newly developed cooling load calculation procedure, no validation has been conducted prior to the work described in this dissertation. Independent and objective assessment of RHB is clearly necessary in view of the important effect it will have on the residential HVAC system design. Theoretically, RHB includes the most fundamental heat balance method, which potentially is the most accurate method. However, individual heat transfer mechanisms implemented in ResHB need to be tested. The algorithms included in RHB to handle 14 temperature swing and masterslave zone control need to be checked. Cooling loads calculated by ResHB and hence the system capacity and design need to be evaluated. Integrated performance of the component models in ResHB also needs to be validated. In a word, a thorough validation of RHB is highly desirable and has not been done yet. 1.3 Objective Therefore, the objective of this research is to conduct a systematic validation and evaluation of the new heat balance based residential cooling load calculation procedure  RHB. Three types of testing methods will be applied to validate RHB: intermodel comparison, analytical verification and experimental validation. For intermodel comparison, a detailed heat balance based computer program will be selected as a reference tool to evaluate RHB. A parametric analysis tool will be developed for systematic and automatic implementation of large amounts of intermodel comparisons. Cooling loads calculated by ResHB will be compared to that calculated by the reference tool. System designs resulting from ResHB will also be evaluated by detailed simulations with the reference tool. Intermodel validation of RHB is discussed in detail in Chapter 4. For analytical verification, RHB will be tested against an analytical verification test suite that the author has previously developed together with other colleagues in Oklahoma State University: the Analytical Verification Test Suite for Whole Building Energy Simulation Programs  Building Fabric (ASHRAE 1052RP, Spitler, et al. 2001). The test suite consists of sixteen individual tests, each with the objective to test the ability of a building energy simulation program to model a particular heat transfer phenomena, including convection, conduction, solar radiation, long wave radiation and infiltration. 15 Tests appropriate for application to RHB will be done and analysis and diagnosis will be made based on the test results. Analytical verification of RHB is presented in Chapter 5. Finally, appropriate residential experimental data will be used to validate RHB. Experimental data will be obtained from a wellinstrumented house located in Fort Wayne, IN. ResHB input files will be created for the house and ResHBcalculated cooling loads and room temperatures will be compared to measured data. Experimental validation of RHB is discussed in Chapter 6. 16 2. LITERATURE REVIEW The literature review in this chapter includes two parts. First, a review is given for the subject of this research work – the heat balance based residential cooling load calculation procedure. The purpose is to gain a full knowledge and familiarity of RHB, with regards to its basic structure and algorithm, theoretical principles and assumptions, and component models. Second, a review is given for the general validation methods of building thermal simulation programs. The purpose is to identify possible methodologies and available tools for validating cooling load calculation programs. 2.1 Heat Balance Based Residential Cooling Load Calculation Procedure The recent ASHRAE research project (1199RP) “Updating the ASHRAE/ACCA Residential Heating and Cooling Load Calculation Procedures and Data” (Barnaby et al. 2004) developed a new detailed heat balance based residential loads calculation procedure: Residential Heat Balance (RHB). For calculation of sensible cooling load, RHB applies the general approach of the ASHRAE Heat Balance (HB) method, based on roombyroom 24hour designday simulation. RHB includes algorithms for calculating sensible cooling loads with temperature swing and addresses the master / slave zone control problem that is unique for residential load calculation. 17 As part of 1199RP, the ResHB computer program was developed as the reference implementation of the RHB procedure. The ResHB source code is derived from the ASHRAE Loads Toolkit (Pedersen et. al. 2001). An additional utility program, RHBGen, was also developed to automatically generate and run parametrically varied ResHB cases for testing and research purposes. As will be described later in Chapter 4, RHBGen helps running all the intermodel comparison cases on the ResHB side. Documentation of ResHB and RHBGen is included in the 1199RP final report (Barnaby et al. 2004). In this section, theoretical principles of RHB  the heat balance method – are summarized first. Calculation algorithms, modeling assumptions and component models of RHB and their implementation in ResHB are described second. 2.1.1 Heat Balance Method for Cooling Load Calculation As mentioned in the introduction section, heat balance method has been applied in many energy calculation programs in one form or another for many years. It was first implemented in NBSLD (Kusuda 1967), and has also been applied to BLAST and TARP by Walton (1981, 1983). In ASHRAE Research Project 875, the heat balance method was first described in a form applicable to cooling load calculations. Details of the method are described in Pedersen et al. (1997, 1998, 2001), and Chapter 29 of ASHRAE Handbook of Fundamentals (2001). It is summarized here for completeness. 18 2.1.1.1 Heat Balance Model Elements The heat balance method is first of all based on some model assumptions, which assume that: • The zone air is well mixed and has a uniform temperature • The surfaces of the zone have uniform surface temperatures, uniform longwave (LW) and shortwave (SW) irradiation, diffuse radiating surfaces and onedimensional heat conduction within. Based on these assumptions, the heat balance model involves four distinct elements: Outside heat balance, wall conduction process (for transparent surfaces, the conduction process is accompanied by solar absorption and transmission), inside heat balance and air heat balance. Each of these elements is briefly discussed below. Note that each element has several heat transfer processes, to which particular models can be applied. These models are not to be enumerated here. Details of available models can be found in the ASHRAE Loads Toolkit (Pedersen, et al. 2001), from which the residential heat balance cooling load calculation procedure is derived. Outside Heat Balance The outside heat balance for opaque surfaces has four heat exchange processes, of which the summation of the heat fluxes should be zero: " " " " 0 sol LWR conv ko q q q q + + = (2.1) where: 19 " sol q = absorbed direct and diffuse solar radiation heat flux, W/m2 " LWR q = net longwave radiation flux exchange with the air and surroundings, W/m2 " conv q = convective flux exchange with outside air, W/m2 " ko q = conductive heat flux into the wall, W/m2 All terms are positive for net flux to the surface except the conduction term, which is traditionally taken to be positive in the direction from outside to inside of the wall. For transparent surfaces, the absorbed solar component would appear in the conduction process (to be discussed next) instead of at the outside surface. It would also split into an inward and an outward flowing fraction and participate in the inside and outside surface heat balance. Wall Conduction Process For building load calculation purpose, it is usually appropriate to assume the wall conduction process as a onedimensional transient process through multilayer construction, with each layer material considered homogeneous and having constant thermal properties. The governing equation for transient onedimensional heat conduction, assuming constant thermal properties, is expressed as: 2 2 T(x,t) 1 T(x,t) x t = (2.2) where T = the wall temperature as a function of position (x) and time (t), K 20 p k C = is the thermal diffusivity of the layer material, m2/s k = thermal conductivity of the layer material, W/(mK) = density of the layer material, Kg/m3 p C = specific heat of the layer material, J/(kgK) This equation is typically coupled with Fourier’s law of conduction that relates the heat flux at any position and time to temperature as follows: q" (x,t) k T(x,t) x = (2.3) Analytical solutions to equation (2.2) and (2.3) exist for a single homogeneous layer. For a multilayer slab, the solution becomes extremely tedious. Possible ways to model this process are: • Numerical finite difference • Numerical finite element • Transform methods • Time series methods While each of these methods has advantages over the others in various applications, traditionally, building thermal simulations have used either time series based or finite difference based methods. In the ASHRAE Loads Toolkit (Pedersen, et al. 2001), from which the residential heat balance cooling load calculation procedure is 21 derived, a time series method using conduction transfer functions is used because of the computational time advantage. Inside Heat Balance The inside heat balance involves four coupled heat transfer components: 1) wall conduction, 2) convection to the inside air, 3) shortwave radiation absorption and reflectance and 4) longwave radiant interchange. The shortwave radiation includes transmitted solar radiation from windows and emittance from internal sources such as lights. The longwave radiation interchange includes those from all other zone surfaces and those from internal sources such as equipment and people. The inside heat balance for each surface is written as (all terms are positive for net flux to the surface): " " " " " " 0 qLWX + qSW + qLWS + qki + qsol + qconv = (2.4) where: " LWX q = net long wave radiant exchange flux between zone surfaces, W/m2 " SW q = net short wave radiation flux to surface from lights, W/m2 " LWS q = long wave radiation flux from equipment in zone, W/m2 " ki q = conduction flux through the wall, W/m2 " sol q = transmitted solar radiation flux absorbed at surface, W/m2 " conv q = convective heat flux to inside air, W/m2 22 Air Heat Balance In the air heat balance formulated for cooling load calculation purposes, it is usually assumed that the capacitance of the zone air can be ignored and the zone air is at quasisteady state at each simulation time step such as an hour. Therefore, the air heat balance reduces to a form similar to that of the surface heat balances—a summation of four heat transfer terms equal to zero (all terms are positive for net heat flow to the air): qconv + qCE + qIV + qsys = 0 (2.5) where: conv q = convection heat transfer from the inside zone surfaces, W CE q = convection from internal sources, i.e. people, lights, equipment, etc., W IV q = sensible load due to infiltration and ventilation, W sys q = heat transfer to/from the HVAC system, W 2.1.1.2 Mathematical Description of Heat Balance Procedure The above section describes the physical process of the heat balance model conceptually. This section introduces the basic equations used in the heat balance procedure mathematically. All information is based on the ASHRAE Loads Toolkit (Pedersen, et al. 2001), from which the residential heat balance cooling load calculation procedure is derived. 23 Conduction Process As mentioned above, the ASHRAE Loads Toolkit formulates the wall conduction process using Conduction Transfer Functions (CTFs), which relate conductive heat fluxes to the current and past surface temperatures and the past heat fluxes. The basic form for the inside heat flux is as follows: " " 0 , , 0 , , , 1 1 1 ( ) nz nz nq ki si t j si t j so t j so t j j ki t j j j j q t ZT ZT YT YT q = = = = + + + (2.6) For the outside heat flux, the form is: " " 0 , , 0 , , , 1 1 1 ( ) nz nz nq ko si t j si t j sot j sot j j kot j j j j q t YT YT XT XT q = = = = + + + (2.7) where: j X = Outside CTF coefficient, j= 0,1,...nz, W/m2K j Y = Cross CTF coefficient, j= 0,1,...nz, W/m2K j Z = Inside CTF coefficient, j= 0,1,...nz, W/m2K j = Flux CTF coefficient, j = 1,2,...nq t = time, s = time step, s si T = Inside face temperature, oC so T = Outside face temperature, oC " ki q = conduction heat flux on outside face, W/m2 " ko q = conduction heat flux on inside face, W/m2 24 The subscript following the comma indicates the time period for the quantity in terms of the time step P. Note that the first terms in the series (those with subscript 0) have been separated from the rest in order to facilitate solving for the current temperature in the solution scheme. There are two main methods for calculating conduction transfer functions: the Laplace Transform method and the State Space method. Detailed documentation and Fortran Modules are available for both methods in the ASHRAE Loads Toolkit. Heat Balance Equations The heat balance processes for the thermal zone are formulated for a 24hour steady periodic condition. The primary variables in the heat balance equations are the inside face temperatures, the outside face temperatures, and the sensible cooling load at each of the 24 hours. Assigning i as the surface index and j as the hour index, then, the primary variables are: soi , j T = outside face temperature, (i=1, 2, ... number of surfaces; j=1, 2, ... 24) , oC sii , j T = inside face temperature, (i=1, 2, ... number of surfaces; j=1, 2, ... 24) , oC sys j q = sensible cooling load, (j=1,2, ... 24), W Equation (2.1) is combined with equation (2.7) to solve for so T to produce equations applicable at each time step for each surface: 25 , , , , , , , , , " " " , , , ,0 1 1 1 ,0 i j k i j k i j k i j i j i j j i j i j i j nz nz nq si ik so ik ik ko sol LWR si i o co k k k so i co T Y T X q q q T Y T h T X h = = = + + + + = + (2.8) where: o T = outside air temperature, oC co h = outside convection coefficient, obtained from " ( ) conv co o so q = h T T , W/(m2K) Equation (2.4) is combined with equation (2.6) to solve for si T to produce equations applicable at each time step for each surface: , , , , , , , " " " " " ,0 , , , 1 1 1 ,0 i j i j k i j k i j k j i j i j i j nz nz nq so i so i k si i k i k ki a ci LWS LWX SW sol k k k si i ci T Y T Y T Z q T h q q q q T Z h = = = + + + + + + + = + (2.9) where: a T = zone air temperature, oC ci h = inside convection coefficient, obtained from " ( ) conv ci a si q = h T T , W/(m2K) Note that in Equations (2.8) and (2.9), the opposite surface temperature at the current time appears on the right hand side. The two equations can be solved simultaneously to eliminate that variable. Depending on the order of updating the other terms in the equations, this can have a beneficial effect on the solution stability. The remaining equation comes from the air heat balance, Equation (2.5). It determines the cooling load sys q at each hour: 26 , 12 , 1 sys j i c i ( sii j a j ) CE IV i q AhT T q q = = + + (2.10) where: A = surface area, m2 The convective heat transfer term in equation (2.10) is expanded to show the relationship between the surface temperatures and the cooling load. Note that equation (2.10) is formulated this way in the cooling load calculation procedure implemented in the ASHRAE Loads Toolkit. But, it may also be formulated other ways. For example, it may be formulated to give zone air temperature with or without system input, as in the case when temperature swing is considered in RHB. 2.1.1.3 Solution Method of Heat Balance Procedure The solution method of the heat balance procedure implemented in the ASHRAE Loads Tookit is a basic iterative, or successive substitution method, which is inherited in the residential heat balance cooling load calculation procedure with some modifications and extensions. The Toolkit implementation consists of a series of initial calculations that proceed sequentially, followed by a double iteration loop. The initial calculations include the following: • Initialize the areas, thermal properties, and surface temperatures for all surfaces for 24 hours. • Calculate incident and transmitted solar flux for all surfaces for 24 hours. • Distribute transmitted solar energy to all inside surfaces for 24 hours in a prescribed manner. 27 • Calculate internal load quantities for 24 hours. • Distribute longwave, shortwave, and convective energy from internal loads to all surfaces for 24 hours in a prescribed manner. • Calculate infiltration and ventilation loads for 24 hours. After the above initial calculations, the iterative solution scheme is as follows: Repeat Day For Hour = 1 to 24 For Iteration = 1 to Maximum Iterations per Hour For Surface = 1 to Number of Surfaces Evaluate Equation (2.8) Evaluate Equation (2.9) Next Surface Evaluate Equation (2.10) Next Iteration (or until Hour results converge) Next Hour Until day converged There are two iteration loops in this solution scheme. The outer loop, or the day iteration, is necessary to arrive at the steady periodic response and thus eliminate any initial condition influence on the solution. This is a result of the fact that conduction is transient and inherently slower than other thermal processes. The inner loop, or the hour 28 iteration, is necessary to allow the radiation balance between surfaces. This is a result of the fact that not all surfaces are solved simultaneously but successively. It should be noted that the heat balance procedure requires a fair amount of input information for the thermal zone, such as the design conditions, details about the walls and windows, roof and floor information, thermal mass, internal heat gains, etc. A more detailed list can be found in Pedersen et al. (1997) and in Chapter 29 of ASHRAE Handbook of Fundamentals (2001) and will not be repeated here. 2.1.2 Heat Balance for Residential Applications The Residential Heat Balance method is a specialized application of the ASHRAE Heat Balance method. Compared to the ASHRAE Heat Balance method, RHB has the following changes: • Multiroom, multizone, and multisystem. Independent heat balances are performed for each room. Because of the simplified geometric input (where surface areas and orientations are known but their positions are not), room adjacencies required by a detailed interroom heat transfer calculation are not available. However, as shown in the calculation sequence below, interroom references are available for the current hour during a simulation, allowing room temperatures in one room being used as the boundary condition for another room. Zones and systems are accounting structures to which loads are accumulated to provide overall results. 29 • Specialized algorithms. Specialized algorithm was implemented to handle temperature swing and master / slave control. • Residential models and assumptions. Component models and assumptions used for RHB are considered appropriate for residential application. • Simple latent cooling procedures. Latent load can be estimated from moisture gain from infiltration, ventilation, duct leakage, and occupants. The remaining parts of this section briefly describe the above aspects of RHB. More details can be found in Barnaby et al. (2004). 2.1.3 Calculation Algorithms As discussed in the introduction section, residential air conditioning applications use constant volume systems controlled by a single thermostat (master/slave control). Typically a thermostat located in one room (master room) controls system output for multiple rooms (slave rooms). As a result, the temperature of the master room can be well controlled. The temperatures of the slave rooms will float depending on the relation between their particular load profiles and the output of the air conditioning system. Usually their temperatures will not be held at the set point even when the system is operating. This hourtohour temperature variation, or temperature swing, has a significant moderating effect on peak loads, due to heat storage in building components. The level of the load moderating effect caused by the master/slave control and temperature swing varies in different residence categories. It is more significant in single 30 family detached houses that have exposed walls in four directions than in multifamily houses that have exposures in only one or two directions. The master/slave control and the resulting temperature swing have long been recognized as a major consideration in residential cooling load calculations. In prior methods, load factors were derived using semiempirical adjustments such as multihour averaging to account for the peak load moderating effects. In RHB, specialized algorithms were developed to model master/slave control and temperature swing. As an application of the heat balance method, RHB basically is a design day procedure that requires iteration to find the steadyperiodic solution at which all heat flows correctly balance. In order to handle temperature swing and master/slave control, RHB has the additional requirement of finding loads under floating temperature conditions, as described below. 2.1.3.1 Calculation Sequence and Convergence Criteria The basic RHB load calculation sequence is: repeat swing repeat day for hour = 1 to 24 for all rooms repeat for all surfaces perform surface heat balance 31 end for surfaces perform air heat balance until room convergence for current hour end for rooms end for hours until day convergence determine room supply air flow rates for next swing iteration until swing convergence Note that the goal of the RHB procedure is to find the roombyroom capacity required to meet the combination of design condition with permitted temperature swing. (The cooling load used for sizing the capacity of the central air conditioning system is the sum of all peak room loads. The roombyroom capacities are also used to design the air distribution system.) Temperature swing occurs when the cooling capacity for a particular room is less than that required to hold that room at the set point. (The cooling capacity could be less than that required in two cases: 1. When the system is operating but does not have enough capacity. 2. When the system is turned off by the thermostat located in the master room, but the slave rooms still need cooling.) In the calculation sequence shown above, the outer loop handles temperature swing (discussed below). The swing search algorithm adjusts the supply air flow rate to each room and repeats the entire calculation until the permitted temperature swing is reached. Note that the hour loop is outside the room loop, so that current hour conditions are available for all rooms for interroom references. 32 The following criteria were used in ResHB to determine whether the solution has converged: • Hour. The convergence criterion of the hour calculation is: For each room, the sum of the absolute change in surface and air temperatures is less than 0.0005 °K (0.0009 °F). • Day. The convergence criteria of the day calculation are: For all rooms, a) the fractional difference between inside and outside surface flux summed over the day is less than 0.005 and b) the areaweighted total absolute temperature change for all surfaces plus air is less than 0.0002 °K (0.00036 °F). Note that the allroom requirement means that some rooms will be iterated beyond this point. • Swing. The convergence criterion of the swing search is: For all rooms, swings are within 0.01 °K (0.018 °F) of specified. (RHB allows a different swing specified for each room.) Again, the allroom requirement means extra iteration for some rooms. 2.1.3.2 Temperature Swing When temperature swing is permitted, ResHB uses a secant method search algorithm to search for the load. The calculations are based on varying system air volume flow rate with an assumed supply air temperature. The calculation sequence for the swing search is: 33 • The required cooling air flow rate is found first for the 0 swing situation (that is, maximum available air supply volume is unlimited and room temperature held at the setpoint or floating below it with no supply air flow). • This maximum supply air flow rate is then reduced by 20% per °K (11% per °F) of target swing and the room is calculated again. • The supply air flow rate is iteratively adjusted in proportion to the error in temperature swing, as indicated by the secant method. This algorithm is reported to be extremely efficient. Convergence to within 0.01 °K (0.018 °F) of the target swing usually occurs in less than 10 cycles. However, it is also reported that specific room characteristics can cause the search to fail. 2.1.3.3 Master/slave Control RHB models master/slave control with the temperature swing algorithm. The problem is to find the peak slave room supply air volume flow rate so that the maximum room temperature is the set point plus permitted temperature swing (the swing could be zero). At each swing iteration, the peak flow rate is adjusted using the temperature swing search described above (the search is used even if the specified swing is zero). Then the flow rates for all hours are set by applying the master room profile. (By definition, a slave room has the same supply air flow rate profile as the master room). The next day iteration proceeds without any further adjustment of air flow rate. It is reported that when the master and slave rooms have significantly different load profiles, subcooling can occur in the slave rooms. 34 2.1.4 Component Models This section describes the main component models that were refined or extended during the RHB development. Other component models are inherited from the ASHRAE Loads Toolkit and can be found in its documentation (Pedersen et al. 2001). 2.1.4.1 Inside Surface Convection Coefficients The choice of inside surface convection coefficients is very important as it directly affects the cooling load. (The cooling load is the total convective heat transfer from all internal surfaces plus convective gain from other sources). The default model for inside surface convection coefficients in ResHB is a variant of the TARP simple model (Walton 1983). For each hour, the coefficient used is the systemrunfractionweighted combination of the “sys off” and “sys on” values. The “sys off” values are those from the TARP simple model. To improve convergence stability, the transition between heat flow up and down values is made linearly over 2°C (3.6°F), rather than abruptly. The “sys on” value was chosen to be 5 W/m2K (0.88 Btu/hft2F) for all surfaces, based on analysis of experimental data from ASHRAE research projects 529RP and 664RP for air change rates of approximately 8 ACH (typical for residential systems). Table 21 shows the “sys off” and “sys on” values for the default model. Table 21. The “sys off” and “sys on” values for default model of inside surface convection coefficients (W/m2K) in ResHB Ceiling Floor Heat flow up Heat flow down Wall Heat flow up Heat flow down Sys on 5.000 5.000 5.000 5.000 5.000 Sys off 4.043 0.920 3.078 4.043 0.920 35 In addition to the default model, ResHB also has optional models of fixed convection coefficients (1.250 ceiling, 4.679 wall, 4.370 floor (all W/m2K)), TARP detailed model and Fisher model (documented in Pedersen et al. 2001). 2.1.4.2 Elevation Effects on Convective Heat Transfer During the development of RHB, efforts have been made to study the effect of elevation on convection coefficients. The investigation showed that applying an elevation correction to convection coefficients has a significant effect on predicted loads for high elevation locations (about 13% for Denver). A simple linear approximation was developed and used in RHB: 0 0 0.24 0.76 P h h P = + (2.11) where h = convective coefficient at pressure P (units consistent with h0) h0 = convective coefficient at sea level pressure P = atmosphere pressure at site elevation (units consistent with P0) P0 = sea level atmospheric pressure 2.1.4.3 Buffer Spaces Taking advantage of the heat balance approach, buffer space temperatures are predicted by modeling an unconditioned room in ResHB. These temperatures are then used as outside boundary conditions for surfaces of adjacent conditioned spaces. Although this treatment maintains the single zone methodology, it deviates from the real heat balance approach. The interroom reference in ResHB is different from those 36 available in a detailed interroom heat transfer analysis. In ResHB, the unconditioned rooms do not take the actual variations in the adjacent conditioned room temperatures into account, while in a detailed interroom heat transfer analysis, it does. 2.1.4.4 Infiltration The default infiltration model for RHB is the AIM2 model (Walker and Wilson 1990, Walker and Wilson 1998, and “enhanced model” in Chapter 26, ASHRAE 2001). AIM2 is a single zone model in which infiltration is determined for the whole building. In RHB, the overall infiltration rate is allocated to rooms in proportion to volume – that is, the same air change rate is assumed for all rooms. RHB provides typical default values for several required inputs of the AIM2 model that are difficult to determine, including effective leakage area, leakage area distribution, and wind shelter parameters. Leakage area can be specified based on pressurization test or defaulted based on leakage classes defined by ANSI/ASHRAE Standard 119 (ASHRAE 1994). Modeling of the interaction between mechanical ventilation and infiltration in RHB follows Palmiter and Bond (1991) and Sherman (1992). First, overall supply and exhaust flow rates must be determined and then divided into “balanced” and “unbalanced” components. Qbal = MIN(Qsup ,Qexh ) (2.12) ( , ) unbal sup exh bal Q = MAX Q Q Q (2.13) where bal Q = balanced air flow rate, L/s or cfm 37 sup Q = total ventilation supply air flow rate, L/s or cfm exh Q = total ventilation exhaust air flow rate (including any combustion air requirements), L/s or cfm unbal Q = unbalanced air flow rate, L/s or cfm The air flow components are combined with infiltration leakage as follows: ( , 0.5 ) vi bal unbal inf unbal Q = Q +MAX Q Q + Q (2.14) where vi Q = combined infiltration/ventilation flow rate (not including balanced component), L/s or cfm inf Q = infiltration leakage rate determined assuming no mechanical pressurization, L/s or cfm 2.1.4.5 Distribution Losses ResHB duct losses are calculated using models specified in ANSI/ASHRAE 152 2004, Method of Test for Determining the Design and Seasonal Efficiencies of Residential Thermal Distribution Systems and Palmiter and Francisco 1997. The method estimates the overall steadystate thermal efficiency of residential forcedair distribution systems by accounting for the conduction loss through the duct walls to the buffer zones and air leakage out of the supply ducts or into the return ducts. The conduction efficiency is calculated as: exp p UPL mc = (2.15) 38 where = the conduction efficiency of the pipe U = the overall duct wall conductance, W/m2K P = the inside perimeter of the pipe, m L = the length of the pipe, m m = the mass flow rate of the air in the pipe, Kg/s p C = the specific heat of the air, KJ/kgK The air leakage efficiency of the pipe is defined as: = 1 Leak Fraction (2.16) The overall duct efficiency with combined conduction and air leakage is (the subscripts s and r refer to the supply and return ducts respectively): ( ) ( ) 0 1 r 1 s s s s s r r s s e e T T T T = (2.17) where 0 = the overall duct system efficiency r T = the difference between the temperature of the air in the pipe at the return register and the temperature of the air around the return duct, K s T = the difference between the temperature of the air in the pipe at the return register and the temperature of the air around the supply duct, K e T = the temperature rise across the equipment, it equals the difference between the temperature of the air in the pipe at the supply plenum and the temperature of the air in the pipe at return plenum, K 39 Impacts of duct interaction with natural infiltration on efficiency are considered by subtracting the efficiency loss in due to the interaction from the overall efficiency. in is calculated as: 1 ( ) in 2 r s e T T = (2.18) where T = the difference between the temperature of the air in the pipe at the return register and the temperature of infiltration air, K 2.1.4.6 Framed Constructions Framed constructions are common in residential buildings. As from the ASHRAE Loads Toolkit, the CTFbased conduction model in ResHB assumes onedimensional conduction heat flow and requires layerbylayer construction input. ResHB includes an algorithm that derives fictitious material properties for a homogeneous layer that corresponds to a framed layer. The resistance of the layer is chosen to preserve the overall Ufactor of the construction. Density and specific heat of the layer are the volumetric averages of the framed layer components. 2.1.4.7 Fenestration and Solar Gain Distribution ResHB implements fenestration class and includes builtin fenestration class definitions for common residential glazing types. The fenestration class embodies the ratio of transmission to absorption and the angular characteristics of the fenestration system. An actual fenestration is specified by its Ufactor, SHGC, and its fenestration class. The required angular characteristics of a specified fenestration are taken from the 40 specified fenestration class and are scaled by the ratio of specified SHGC to nominal (fenestration class) SHGC. Interior and exterior shading treatments in ResHB are represented by the ASHRAE Interior Attenuation Coefficient (IAC) and Exterior Attenuation Coefficient (EAC) models (Chapter 30, 2001 ASHRAE Handbook of Fundamentals). Overhang and fin shading is modeled with ASHRAE Loads Toolkit methods. Hourly scheduled shading is also allowed in ResHB. For internal solar distribution, a modified version of the Loads Toolkit BLAST model is used. It distributes radiative gains in proportion to surface areaabsorptance product. Beam solar gain is assumed to hit floor surfaces. One refinement to this model in RHB is that internal mass surfaces are assumed to be “half floor” with respect to beam radiation, as furnishings typically intercept some of the incoming beam. 2.1.4.8 Ground Heat Transfer RHB models slabs as 300 mm (1 ft) of earth with adiabatic boundary conditions. This construction captures some of the diurnal heat storage effects of slab construction, but not net conduction to the ground. 2.1.5 Modeling Assumptions The following sections describe the modeling assumptions of RHB. 41 2.1.5.1 Outdoor Design Conditions RHB requires hourly design day outdoor conditions. In addition to the ability of accepting 24hour profiles from user input, ResHB can also automatically generate 24 hour profiles from design drybulb temperature and its daily range, coincident wetbulb temperature, site coordinates, and site elevation, as follows: • Drybulb temperature. The design dry bulb and daily range are expanded to 24 hours using the generic profile from Table 17, Chapter 29 of the 2001 ASHRAE Handbook of Fundamentals. The generic profile is shifted 1 hour later when daylight savings time is specified. • Wetbulb temperature and other moisturerelated values. The design dry bulb and coincident wet bulb are used to determine the design dew point temperature. The hourly dew point is the minimum of the design dew point and the hourly dry bulb (that is, constant absolute humidity is assumed, limited by saturation). Other hourly psychrometric values (wet bulb temperature, humidity ratio, and enthalpy) are derived from the hourly dry bulb and dew point temperatures. • Solar radiation. Hourly incident solar is derived using the ASHRAE clear sky model (Chapters 29 and 30, 2001 ASHRAE Handbook of Fundamentals) with updated coefficients from Machler and Iqbal (1985). • Sky temperature. Sky temperature is required for calculation of exterior surface long wave radiant exchange. The model of Berdahl and Martin (1984) is used to calculate hourly sky temperature from hourly drybulb and dew point temperatures (cloud cover assumed to be 0). 42 All psychrometric calculations are done with ASHRAE Loads Toolkit procedures (originally from Brandemuehl et al. 1993) assuming a constant barometric pressure determined from site elevation according to a standard atmosphere relationship (Eqn (3), Chapter 6, 2001 ASHRAE Handbook of Fundamentals). 2.1.5.2 Internal Gain Internal gain assumptions in RHB are based on Building America (2003), which provides gain intensities and schedules for significant residential end uses as a function of building floor area and number of occupants. Also, RHB requires the radiant/convective/latent split for each gain source, which Building America (2003) does not fully define. Estimates were developed from 2001 ASHRAE Handbook of Fundamentals and other sources as needed, as shown in Table 22. Table 22. Fractional components of internal heat sources incorporated in ResHB Internal gain (to space) Source Radiant Convective Latent Exhausted Refrigerator 0 1 0 0 Range .24 .16 .30 .30 Dishwasher .51 .34 .15 0 Clothes washer .40 .60 0 0 Clothes dryer .09 .06 .05 .80 Lighting .79 .21 0 0 Other appliances and plug loads .54 .36 .1 0 People (living) .33 .22 .45 0 People (sleeping) .30 .30 .40 0 2.1.5.3 Internal Mass In RHB, the recommended assumption regarding internal mass is: each room should be modeled including internal mass having surface area equal to room floor area and consisting of 12 mm (0.5 in) wood exposed on one side (adiabatic outside surface 43 conditions). This surface should be radiantly coupled to all room internal surfaces. ResHB implements a special surface type “IM” for internal thermal mass. 2.1.5.4 Other Assumptions Surface absorptance. Surface absorptance values in ResHB can either be the defaults (documented in Barnaby et al. 2004) or specified by the user. Material properties. ResHB includes default material properties as documented in Barnaby et al. (2004). Again the user can also specify material properties. 2.2 Validation Methods of Cooling Load Calculation Programs The word validation has been widely used with a variety of meanings. Strachan (1993) gave the following definition of validation: “The rigorous testing of a program – comprising its theoretical basis, software implementation and user interface – under a range of conditions which typify its expected use.” In practice, it is impossible and also unnecessary to conduct an absolute validation of a simulation program. The aim instead is to apply a developed validation method so that the simulation program is good enough to predict building performance for most situations with specific purposes. In this section, three validation methods are introduced along with a discussion of the advantages and disadvantages of each method. Some general ideas about the application of the validation methods are described. Finally, a brief summary is given for prior validation work. 44 In view of the increased use of building energy simulation programs, it has been long recognized that some form of validation is needed for the purpose of objective quality control. A number of attempts have been made over the last two decades to identify suitable validation procedures for building energy simulation programs. However, no standard validation procedures have been universally accepted. Judkoff et al. (1983) first attempted to document the three most commonly used validation methods of building energy simulation programs. These are analytical verification, comparative testing and empirical validation. In each method, results from one program are compared with results from other sources, as will be discussed in the following sections. Judkoff (1988) also summarized the advantages and disadvantages of the three validation methods, as shown in Table 23. Table 23. Advantages and Disadvantages of the three validation methods as from Judkoff (1988) Technique Advantages Disadvantages Comparative Relative test of model and solution process No input uncertainty Any level of complexity Inexpensive Quick, many comparisons possible No truth standard Analytical Test of numerical solution No input uncertainty Exact truth standard given the simplicity of the model Inexpensive No test of model Limited to cases for which analytical solutions can be derived Empirical Test of model and solution process Approximate truth standard within experimental accuracy Any level of complexity Measurement involves some degree of input uncertainty Detailed measurements of high quality are expensive and timeconsuming A limited number of data sites are economically practical 45 2.2.1 Analytical Verification In analytical verification, the output from a program, subroutine, or algorithm is compared to the result from a known analytical solution for isolated heat transfer mechanisms, under very simple boundary conditions. (Here, the term “analytical” means a mathematical model of reality that has an analytically determinable solution for a given set of parameters and boundary conditions.) Where test specifications have to be interpreted in some way by a user in the form of input data for a particular test program, differences may arise from different interpretations of the specifications. This has been shown in the past on several projects (Allen et al. 1985). Fortunately, these problems can be minimized in the case of analytical tests due to the simplified nature of the building zone specifications and the possibility of using idealized zone constructions. Analytical tests are (partly by necessity) simplified in nature and should usually be designed to allow only one particular feature to be tested at a time. This should allow not only the ability of the program to model particular features to be verified, but also the identification of particular model components or algorithms as the source of any problems. As noted above, in testing a building energy analysis program it is both the underlying algorithms of the code and their implementation that are tested. Inadequacies in both the algorithms or in their implementation (code bugs) can be the source of discrepancies. It is not possible to test the algorithms without implicitly testing their coding. Therefore developers can use analytical tests as a diagnostic tool to find bugs in the implementation as well as verify the operation of the various component models. 46 Being most abstracted from the full complexities of real building simulation problems, analytical testing has the advantage of offering the most certain form of reference or ‘truth’ model with which comparisons can be made. The nature of analytical testing also makes it only applicable to limited cases for which analytical solutions can be derived. Errors arising from the integrated performance of all the submodels and algorithms in a program are beyond the scope of an analytical test. 2.2.2 Comparative Testing In comparative testing, a program is compared to itself or to other programs that may be considered better validated or more detailed and, presumably, more physically correct. The comparative approach includes “sensitivity testing” and “intermodel comparisons”. Comparative testing cannot directly address the issue of a truth standard, but can be a very powerful way of identifying errors by doing many comparisons quickly and inexpensively. One comparative testing approach is parametric sensitivity analysis. It provides information on the influence of the uncertainties in the program’s input parameters. The other comparative testing approach is intermodel comparison. It involves checking the agreement of several different programs with different thermal solution and modeling approaches in a variety of representative cases. Cases for which the program predictions diverge indicate areas for further investigation. (Judkoff and Neymark 1995) Intermodel comparisons are useful in two aspects. Firstly, they provide a “useful” 47 evaluation in the case where one of the programs has already been the subject of rigorous validation. Secondly, they often highlight serious shortcomings in one or more of the programs. An important consideration in an intermodel comparison is the requirement for input equivalence. (Strachan 1993) 2.2.3 Empirical Validation In empirical validation, calculated results from a program, subroutine, or algorithm are compared to monitored data from a real structure, test cell, or laboratory experiment. Empirical validation is the most widely used technique for testing a simulation program, as it can be considered to be a conclusive test of whether model predictions reflect reality. In particular, whole model empirical validation ensures that the overall performance of the simulation program is tested. In this case, it is not only an individual process, but also the interaction of those processes that are tested. (Strachan 1993) Empirical validation offers an approximate truth standard within the accuracy of the data acquisition system and many parameter values that are on measurement. Also, empirical validation can be applied with any level of complexity. However, detailed, high quality measurements are usually expensive, difficult and timeconsuming, even for one or a few cases. Even if highquality experimental data sets are available for performing empirical validation and a program has performed satisfactorily, it is still difficult to generalize results from one particular combination of building type, climate and operating conditions to others. In addition, measurements of both building performance parameters 48 and program input parameters have a finite accuracy. The uncertainty in program input parameters (air change rates, material properties, occupant behavior etc.) leads to uncertainty in the program predictions that may be quite apart from the adequacy of the algorithms employed by the program. (Bloomfield 1989, 1999) 2.2.4 Application of the Validation Methods In any type of validation, three things are implicitly tested, each of which may contribute to the overall ‘error’ in the results (Rees, et al. 2002): • The interpretation of the input data • The model(s) or algorithm(s) • The computer implementation of the algorithm(s) A general principle applies to any type of validation method: the more realistic the test case, the more difficult it is to establish cause and effect, and to diagnose problems. The simpler and more controlled the test case, the easier it is to pinpoint the sources of error or inaccuracy. (Judkoff and Neymark 1995) In fact, the three validation methods may be used together in a number of ways. For example, analytical verification can be conducted at first to check the mathematical solution of major heat transfer models of a program. If discrepancy occurs, the source of the difference must be corrected before any further validation is done. Then, intermodel comparisons may be done in advance of an empirical validation to better define the experiment and to help estimate experimental uncertainty by propagating all known sources of uncertainty through one or several wholebuilding energy simulation programs. 49 2.2.5 Summary of Prior Validation Work Independent work on model validation started in the late seventies and early eighties, after the growth of popularity of energy simulation because of the 1973 energy crisis. Examples of the early work include Judkoff et al. (1980, 1981), IEA (1981), and Hoellwarth (1980), which showed significant disagreements between codes for very simple test cases. Over the last two decades, a number of organizations have attempted to identify suitable validation procedures for building energy simulation programs, e.g. NREL (Judkoff, et al. 1983; Judkoff and Neymark 1995), BRE (BRE 1988) and the IEA (Bloomfield et al. 1988). A good summary overview is found in Judkoff (1988) and Judkoff and Neymark (1995). Further updated validation/testing literature review is included in Ahmad (1997), Bloomfield (1999), and Judkoff and Neymark (2002). Much less emphasis has been placed on design load calculation procedures, perhaps since design load calculation methods have historically relied less heavily on computer implementation than annual energy calculation (Rees and Spitler 1999). A brief overview of published intermodel comparisons of cooling load calculation procedures is found in Spitler and Rees (1998). The Comité Européen De Normalisation (CEN) (1997) has developed a standard approach to load calculations. It consists of a set of heat balance equations and a set of qualification tests against which particular computer codes can be evaluated. The purpose of the tests is qualification to a certain standard of accuracy and not diagnosis of particular faults. The tests are based on a single test zone that is exposed to a combination of loads. The tests are varied by changing shading, internal loads, wall construction, 50 system controls, etc. In each case a number of submodels of the load calculation method are tested together. One notable attempt of intermodel comparison for design cooling load calculation methods has been completed as part of ASHRAE 942RP (Rees et al. 1998; Spitler and Rees 1998), which consists of a large number of test cases (of the order one thousand) where certain parameters are systematically varied. The comparison was primarily organized as a parametric study for three cooling load calculation procedures: the ASHRAE heat balance procedure, the ASHRAE radiant time series procedure, and the CIBSE admittance procedure. 18 different parameters describing different constructions, internal heat gains, zone dimensions and weather data were systematically varied for the comparison. Rees and Spitler (1999) also proposed a diagnostic test procedure for building loads, named BUILDTEST, in which the ASHRAE heat balance method is used as a reference model. A series of 25 simplified tests were devised to be used in intermodel comparisons with the reference model. The purpose of the tests is diagnosing deficiencies in the load calculation method and/or its implementation. This was done by subjecting the test zone to a particular type of heat gain or use a particular heat transfer path in turn, rather than using different combinations of loads. Thus the results are functions of either individual (or at most only a few) submodels alone and not the whole zone heat transfer model. As will be discussed in detail later in Chapter 5, Spitler et al. (2001) have developed an analytical verification test suite for building fabric models in whole 51 building energy simulation programs — ASHRAE 1052RP. The tests are intended to be used in support of ASHRAE Standard 140 ‘Standard Method of Test for Building Energy Analysis Software’ (ASHRAE 1998). The test suite consists of sixteen individual tests, each with the objective to test the ability of a building energy simulation program to model a particular heat transfer phenomena. The test is applied by comparing the output of the energy simulation program to be tested with the analytical solution for a special test zone. The data to be compared may be a single zone load, heat flux, temperature, or hourly loads over one or more days of output. More recently, experimental validation of both the ASHRAE heat balance method and radiant time series method has been done in test cells at Oklahoma State University (Chantrasrisalai, et al. 2003; Iu, et al. 2003). For the RHB method, no validation work has been done prior to this dissertation as it has just been developed in 2004. Analytical, intermodel, and experimental validation of RHB is highly desirable and therefore is the objective of this research. 52 3. OBJECTIVES The objectives of this research have been briefly outlined in the Introduction. In more detail, the task of validating a heat balance based residential cooling load calculation procedure is discussed below. Firstly, a literature review will be done for the RHB cooling load calculation procedure and validation methods of cooling load calculation program. For RHB, the subject of the validation work, the goal is to obtain an indepth comprehension of its basic structure and algorithm, theoretical principles and assumptions, and component models. This is very important as the testing, analyzing and diagnosing process involved in the validation work requires a full knowledge and familiarity of RHB. For validation methods, the goal is to identify possible methods and available tools for validating cooling load calculation programs. The literature review section has attempted to do this by introducing the RHB procedure and general validation methods. Another part of the literature review is a systematic review of candidate programs that could be used as intermodel comparison tool. This is covered under the section of selecting comparison tool in Chapter 4. Secondly, intermodel validation of ResHB, the reference computer implementation of the RHB procedure, will be performed. Intermodel validation requires the selection of a comparison tool. Therefore, a systematic review and comparison of 53 candidate building simulation programs, with regard to their capabilities of modeling residential buildings, will be made. Based on the review results, one program will be selected as the comparison tool. Modifications will be made to the selected comparison tool if necessary. A parametric analysis tool will be developed for systematic and automatic implementation of large amounts of intermodel comparisons for typical residences. The parametric analysis tool should be able to create input files, run simulations and process outputs of interest for the comparison tool automatically. Cooling loads calculated by ResHB will be compared to that calculated by the comparison tool. System design resulted from ResHB will also be evaluated by the detailed simulation with the comparison tool. Thirdly, analytical verification of ResHB will be conducted. The ResHB program will be tested with the Analytical Verification Test Suite for Whole Building Energy Simulation Programs  Building Fabric (ASHRAE 1052RP, Spitler, et al. 2001). Applicable analytical tests from the test suite will be applied and modifications of the input structure of ResHB will be made as needed. All the analytical tests completed will be used as a set of reference tests that can be run after each revision of ResHB, assisting diagnosis of any new problems that could possibly be introduced. Finally, experimental validation of the ResHB program will be done. Experimental data will be obtained from a wellinstrumented house located in Fort Wayne, IN. ResHB input files will be created for the house and ResHBcalculated cooling loads and room temperatures will be compared to measured data. 54 4. INTERMODEL VALIDATION OF THE HEAT BALANCE BASED RESIDENTIAL COOLING LOAD CALCULATION PROCEDURE As mentioned in the literature review, of the three types of validation methods, intermodel comparison cannot directly address the issue of a truth standard, but can be a very powerful way of identifying errors by doing many comparisons quickly and inexpensively. The intermodel validation desired and conducted for the Residential Heat Balance (RHB) cooling load calculation procedure is similar to the study performed by (Rees et al. 1998; Spitler and Rees 1998). It consists of a large number of test cases (of the order one thousand) where certain parameters are systematically varied. It is desirable that this type of intermodel comparison be made in a highlyautomated fashion, so that the RHB procedure can be tested and evaluated throughout the development cycle. How has this been implemented for the RHB procedure is discussed in the following sections, which include the selection of the comparison tool, the methodology employed and the comparison results obtained. 55 4.1 Selecting the Comparison Tool 4.1.1 Basic Requirements of the Comparison Tool In choosing the comparison tool, the following basic requirements regarding the code robustness, required features and/or feasibility of extension are considered. 1. Heat balance method The heat balance method is generally considered as the most scientifically rigorous method. It accounts for every energy flow in the most basic, fundamental way and does not impose any simplification on the solution technique (Strand et al. 1999), while other methods make many simplifying assumptions along the way from the initial model to the final procedure that the basic processes are essentially lost (Pedersen et al. 1997). Therefore, to supply intermodel validation of the new heat balance based residential cooling load calculation procedure, a heat balance based comparison tool is the best choice. A comparison tool with an approximate method will not be accurate and fundamental enough to serve as a reference in the intermodel validation. 2. Include welldeveloped models for most aspects of building load calculation Although modification and extension is expected if necessary, it would be best to choose a tool that requires a minimum amount of modification. Therefore, welldeveloped models for most aspects of building load calculation are desired in the selected tool. These aspects include: 56 • Transient heat conduction: Obviously, the detailed heat balance method needs a transient heat conduction model to account for the dynamic effects of the thermal mass on the zone loads. This is necessary for both exterior and interior/interzone walls. This requirement exists because the typical central located thermostat in residences cannot simultaneously control the temperatures in all rooms and the resultant temperature swings lead to interzone conduction. • Detailed convection model: Although there is sensitivity analysis showing that the effect of the outside convection coefficient on the cooling load is very low (McClellan and Pedersen 1997), the inside convection coefficient can be important (BeausoleilMorrison 2000). The comparison tool should be able to deal with a detailed convection model and permit variable convection coefficients. • Solar radiation/window shading: Solar gain is an important part of the cooling load, both that absorbed by opaque surfaces and that transmitted through fenestration. It may become even more important for residential buildings because the loads in residences are primarily from the building envelope and are greatly affected by outside conditions. Therefore, accurate models for solar radiation, fenestration and window shading are required in the comparison tool. • Detailed inside/outside long wave radiation: The simplified approaches that use a combined coefficient to predict the total convective and radiative gain on a surface mask their respective effects on zone loads and depart from the 57 heat balance principle. These models therefore should not be used in the comparison tool. Instead, a detailed inside/outside long wave radiation model is recommended. Long wave radiation from internal sources may have to be dealt with in the traditional way by defining a radiant/convective split. Although the surface temperature of the internal sources could be calculated based on the heat balance principle, it is difficult to predict their locations since occupants of the space may move them from time to time. • Infiltration and interzone airflow and mixing: In comparison to those in commercial or industrial buildings, zone load from infiltration is important for residential buildings because the internal heat gains in residences are relatively low. Interzone airflow and mixing is also an important feature required to model interzone thermal interaction. 3. Short time step Usually, onehour time steps are used in energy simulation programs. But short time steps may be necessary in the comparison tool if system on/off behavior is modeled. Shorter time steps are already available in several simulation tools. 4. Flexible HVAC system simulation/control tool The comparison tool should permit the “masterslave” zone control feature of residences. From the HVAC system simulation concept, it would be good to realize an integrated simultaneous simulation, so that feedback from system response can be seen by the zone load procedure. But for the validation of a load calculation method that aims to be the basis of system design and equipment sizing, this may not be necessary. Instead, 58 an idealized representation of the system may be sufficient. E.g., a system control profile based on zone temperature and system capacity may be satisfactory for this application. 5. Convenient to be modified or extended If necessary, extension or modification of the selected comparison tool is expected. Therefore, a welldocumented and wellorganized source code of the selected program is desired. As to the program language, Fortran 90 is preferred, with Fortran 77 being a second choice. 6. Source code availability The status of the source code availability, or the cost to obtain the source code is another condition that limits the choice of the programs. Since the research project funding is limited, it is preferred to keep the cost of the source code reasonably low. 7. Status of the program validation The comparison tool needs to be validated as it is used as a reference. With everything else being equal, the program that has been best validated should be chosen. Even with other advantages, fatal errors that cannot be fixed will eliminate the program from consideration. 8. Support It’s important that technical support of the selected comparison tool is available since help from the original developer usually saves time. 59 Among the basic requirements discussed above, some features are necessary, some features may be necessary, while other features are desirable. Table 41 summarizes the classification of these features. Consideration should be given to distinguish these features in choosing the comparison tool. Table 41 Classification of basic requirements for candidate comparison tools Basic requirements Necessary May be necessary Desirable Heat balance method X Transient, insideoutside/interzone heat conduction X Detailed convection model X Solar radiation/window shading X Detailed inside/outside long wave radiation X Include welldeveloped model for most aspects of building load calculation Infiltration and interzone airflow/mixing X Short time step X Flexible HVAC system simulation/control tool X Convenient to be modified or extended X Source code availability X Program validation X Support X 4.1.2 Review of Candidate Programs With the basic requirements for the comparison tool discussed above, a systematic review of candidate computer programs is needed. Although we are looking for a detailed load calculation program, the unique features of residential load calculation and hence the specific requirements of the comparison tool make it necessary to look into a range of whole building simulation tools in terms of their system simulation and control possibilities. 60 Generally speaking, two types of building simulation tools are in use today: generalpurpose tools and special purpose tool
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Title  Intermodel, Analytical, and Experimental Validation of a Heat Balance Based Residential Cooling Load Calculation Procedure 
Date  20061201 
Author  Xiao, Dongyi 
Department  Mechanical Engineering 
Document Type  
Full Text Type  Open Access 
Abstract  A systematic validation of the ASHRAE heat balance based residential cooling load calculation procedure (RHB) has been performed with intermodel comparison, analytical verification and experimental validation. The intermodel validation was performed using ESPr as the reference model. The testing process was automated through parametric generation and simulation of large sets of test cases for both RHB and ESPr. The house prototypes covered include a simple Shoebox prototype and a real 4bedroom house prototype. An analytical verification test suite for building fabric models of whole building energy simulation programs has been developed. The test suite consists of a series of sixteen tests covering convection, conduction, solar irradiation, longwave radiation, infiltration and groundcoupled floors. Using the test suite, a total of twelve analytical tests have been done with the RHB procedure. The experimental validation has been conducted using experimental data collected from a Cardinal Project house located in Fort Wayne, Indiana. During the diagnostic process of the experimental validation, comparisons have also been made between ESPr simulation results and experimental data. It is concluded RHB is acceptable as a design tool on a typical North American house. Analytical tests confirmed the underlying mechanisms for modeling basic heat transfer phenomena in building fabric. The intermodel comparison showed that the differences found between RHB and ESPr can be traced to the differences in submodels used by RHB and ESPr. It also showed that the RHBdesigned systems can meet the design criteria and that the RHB temperature swing option is helpful in reducing system oversizing. The experimental validation demonstrated that the systems designed with the method will have adequate size to meet the room temperatures specified in the design, whether or not swing is utilized. However, actual system operation may cause deviations in the room temperatures, particularly in the slave rooms. For better prediction of these deviations, simulation or a better approximation for interzone airflows and heat transfers would be needed. The RHB procedure may be said to give cooling loads that are as accurate as the inputs and reallife uncertainties inputs will be more significant than errors that caused by the method. 
Note  Dissertation 
Rights  © Oklahoma Agricultural and Mechanical Board of Regents 
Transcript  INTERMODEL, ANALYTICAL, AND EXPERIMENTAL VALIDATION OF A HEAT BALANCE BASED RESIDENTIAL COOLING LOAD CALCULATION PROCEDURE By DONGYI XIAO Bachelor of Science in Thermal Engineering Shenyang Architectural and Civil Engineering Institute Shenyang, China 1995 Master of Science in Thermal Engineering Tongji University Shanghai, China 1998 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY December, 2006 ii INTERMODEL, ANALYTICAL, AND EXPERIMENTAL VALIDATION OF A HEAT BALANCE BASED RESIDENTIAL COOLING LOAD CALCULATION PROCEDURE Dissertation Approved: Dr. Jeffrey D. Spitler Dissertation Adviser Dr. Daniel E. Fisher Dr. Ronald D. Delahoussaye Dr. Khaled Mansy Dr. A. Gordon Emslie Dean of the Graduate College iii ACKNOWLEDGEMENTS I am so thankful to my dear husband, Xiaobing Liu, who accompanies me day and night, encourages me to continue during difficult times, and supports me all through the way. I cannot imagine how this work would have been finished without his love. I am so grateful that God gave us Rena, our daughter, who is two years old now. Bringing her up along the way was exhausting, but the joy and happiness she brings I will cherish for a lifetime. My thankfulness also goes to all my family in China, for their endless love and constant support. I would sincerely appreciate my advisor, Dr. Jeffrey D. Spitler. With the assistantship he offered, I was able to start this research work back in August 1999. Ever since then, I have learned a lot from him, not only in research but also in life. I thank him for his continuous support, constructive guidance, excellent leadership, and ceaseless understanding and patience during the seven years of my graduate study. My sincere appreciation also extends to the members of my doctoral committee: Drs. Daniel E. Fisher, Ronald D. Delahoussaye, and Khaled Mansy for their ideas and suggestions that helped me improve this dissertation. Mr. Charles S. Barnaby, currently Vice President of Research of the Wrightsoft Corporation, is one of the key personnel that developed RHB  the subject of this iv research work. He helped develop the automatic parametric run tool used for the intermodel comparison of RHB. He also assisted in the process of analytical testing and experimental validation of RHB. Dr. Simon J. Rees, currently senior research fellow in the Institute of Energy and Sustainable Development at De Montfort University, U.K., helped guide the development of the test suite used for the analytical verification of RHB. Mr. Bruce A. Wilcox, the manager and experimental designer of the Cardinal Fort Wayne Project, generously aided in providing measured data and corresponding information from the Fort Wayne house, which was used in the experimental validation of RHB. Dr. Jon W. Hand, currently senior research fellow in the Energy Systems Research Unit at the University of Strathclyde, U.K., gave useful advice on using ESPr, the reference model used for the intermodel comparison of RHB. To them I extend my sincere gratitude and appreciation. I would also like to thank my colleagues in the Building and Environment Thermal Systems Research Group at Oklahoma State University for their ideas, help, and friendship. Here, I only list a few: Andrew D. Chiasson, Mahadevan Ramamoorthy, David Eldridge, Hui Jin, Chanvit Chantrasrisalai, Calvin Iu, Weixiu Kong, Zheng Deng, Xia Xiao and Xiaowei Xu. Finally, support from ASHRAE under research projects RP1052 and RP1199, and in the form of a GrantinAid scholarship during 20052006 is gratefully acknowledged. Approval from Cardinal Glass Industries for using the experimental data is also gratefully acknowledged. v TABLE OF CONTENTS Chapter Page 1. INTRODUCTION .......................................................................................................... 1 1.1 Nonresidential Cooling Load Calculation Procedures ............................................ 2 1.2 Residential Cooling Load Calculation Procedures ................................................... 5 1.2.1 Characteristics of Residential Load Calculation................................................ 5 1.2.2 Prior Residential Cooling Load Calculation Procedures ................................... 8 1.2.3 Heat Balance Based Residential Cooling Load Calculation Procedure........... 12 1.3 Objective................................................................................................................. 14 2. LITERATURE REVIEW............................................................................................. 16 2.1 Heat Balance Based Residential Cooling Load Calculation Procedure ................. 16 2.1.1 Heat Balance Method for Cooling Load Calculation....................................... 17 2.1.2 Heat Balance for Residential Applications ...................................................... 28 2.1.3 Calculation Algorithms.................................................................................... 29 2.1.4 Component Models.......................................................................................... 34 2.1.5 Modeling Assumptions .................................................................................... 40 2.2 Validation Methods of Cooling Load Calculation Programs ................................. 43 2.2.1 Analytical Verification..................................................................................... 45 2.2.2 Comparative Testing........................................................................................ 46 2.2.3 Empirical Validation........................................................................................ 47 2.2.4 Application of the Validation Methods............................................................ 48 2.2.5 Summary of Prior Validation Work................................................................. 49 3. OBJECTIVES............................................................................................................... 52 4. INTERMODEL VALIDATION OF THE HEAT BALANCE BASED RESIDENTIAL COOLING LOAD CALCULATION PROCEDURE ........................... 54 4.1 Selecting the Comparison Tool............................................................................... 55 4.1.1 Basic Requirements of the Comparison Tool .................................................. 55 4.1.2 Review of Candidate Programs ....................................................................... 59 4.1.3 Selection of Comparison Tool ......................................................................... 71 vi Chapter Page 4.2 Methodology........................................................................................................... 77 4.2.1 Types of Comparison....................................................................................... 77 4.2.2 Parametric Code............................................................................................... 78 4.2.3 Combined Testing Process............................................................................... 79 4.2.4 RHBGen Parametric Generator ....................................................................... 80 4.2.5 ESPr System................................................................................................... 80 4.2.6 Design Evaluation Figure of Merit .................................................................. 85 4.2.7 Model Assumptions Used in the Comparison ................................................. 87 4.3 Results..................................................................................................................... 89 4.3.1 Description of Test Sets ................................................................................... 89 4.3.2 Ideal Load Comparison.................................................................................... 94 4.3.3 System Design Evaluations............................................................................ 125 4.4 Conclusions........................................................................................................... 147 5. ANALYTICAL VERIFICATION OF THE HEAT BALANCE BASED RESIDENTIAL COOLING LOAD CALCULATION PROCEDURE ......................... 151 5.1 Development of the Analytical Verification Test Suite........................................ 152 5.1.1 The Test Suite ................................................................................................ 153 5.1.2 The Test Suite Software................................................................................. 160 5.1.3 The Test Documentation................................................................................ 161 5.1.4 Evaluation of the Test Suite........................................................................... 163 5.2 Analytical Test of the Heat Balance Based Residential Cooling Load Calculation Procedure .................................................................................................................... 164 5.2.1 Testing ResHB............................................................................................... 164 5.2.2 The Analytical Tests and Testing Results...................................................... 168 5.3 Conclusions........................................................................................................... 193 6. EXPERIMENTAL VALIDATION OF THE HEAT BALANCE BASED RESIDENTIAL COOLING LOAD CALCULATION PROCEDURE ......................... 195 6.1 Experimental House.............................................................................................. 197 6.2 Instrumentation and Data Acquisition .................................................................. 201 6.3 Data Analysis........................................................................................................ 204 6.4 Simulation Approach ............................................................................................ 214 6.4.1 Simulation Inputs ........................................................................................... 214 6.4.2 Simulation Component Models ..................................................................... 225 6.4.3 Comparisons Made ........................................................................................ 227 6.5 Results................................................................................................................... 228 6.5.1 Interzone Airflow ......................................................................................... 228 6.5.2 Masterslave Control...................................................................................... 231 6.5.3 Ideal Control .................................................................................................. 239 6.5.4 ResHB and ESPr Result Comparison........................................................... 248 vii Chapter Page 6.5.5 Uncertainty Analysis...................................................................................... 251 6.6 Conclusions........................................................................................................... 256 7. CONCLUSIONS......................................................................................................... 259 REFERENCES ............................................................................................................... 267 APPENDIX A. ANALYTICAL VERIFICATION OF ESPR...................................... 279 A.1 Single Zone Tests................................................................................................. 281 A.2 Multizone Tests .................................................................................................. 287 APPENDIX B. PARAMETRIC CODE USED FOR THE INTERMODEL COMPARISON .............................................................................................................. 290 APPENDIX C. SAMPLE PERL AND SHELL SCRIPTS USED FOR THE INTERMODEL COMPARISON............................................................................................... 294 C.1 Sample Perl Scripts .............................................................................................. 294 C.2 Sample Shell Scripts ............................................................................................ 300 Shell script 1: Climate............................................................................................. 300 Shell script 2: Rotate............................................................................................... 301 Shell script 3: Simulate ........................................................................................... 302 Shell script 4: Analyse ............................................................................................ 303 viii LIST OF TABLES Table Page 21 The “sys off” and “sys on” values for default model of inside surface convection coefficients (W/m2K) in ResHB............................................................................... 34 22 Fractional components of internal heat sources incorporated in ResHB.................... 42 23 Advantages and Disadvantages of the three validation methods as from Judkoff (1988)........................................................................................................................ 44 41 Classification of basic requirements for candidate comparison tools ........................ 59 42 Summary of the features of the alternative programs................................................. 70 43 Main advantages and disadvantages of the candidate programs ................................ 71 44 Part 1 More detailed summaries of the candidate programs ...................................... 73 44 Part 2 More detailed summaries of the candidate programs ...................................... 74 45 Part 1 Model assumptions used in ESPr and RHB for the comparison .................... 88 45 Part 2 Model assumptions used in ESPr and RHB for the comparison .................... 89 46 Test parameters for the 576 test cases ........................................................................ 93 47 Algorithm for attributing the PPD Cause ................................................................. 127 51 Organization of the Test Suite.................................................................................. 155 52 Tests Selected for Testing ResHB............................................................................ 165 53 Convection Coefficients Used in Testing ResHB .................................................... 167 54 Differences in zone load between the ResHB program and analytically calculated loads for the convection and conduction cases ....................................................... 171 55 Test parameters used for the steady state convection and conduction tests ............. 171 56 Constructions used for the transient conduction tests .............................................. 172 57 Differences in zone load between ResHB and analytical result for the solar related cases ........................................................................................................................ 180 58 Parameters used for the ExtSolRad test.................................................................... 180 59 Parameters used for the SolRadGlazing and SolRadShade tests.............................. 181 510 Parameters used for the WinReveal and IntSolarDist tests .................................... 181 511 Differences in zone load between ResHB and analytical result for the interior longwave radiation tests.......................................................................................... 191 61 Construction materials of the Fort Wayne house ..................................................... 200 62 Windows of the Fort Wayne house .......................................................................... 200 63 Constants c, n and ELA values derived from blower door measurements.............. 209 64 Construction thermal properties input in ResHB/ESPr simulation......................... 217 65 Surface absorptances and emissivities input in ResHB/ESPr simulation ............... 217 ix Table Page 66 Solar Heat Gain Coefficient (SHGC), Solar Transmittance (T) and Layer Absorptances (A) for ResHB fenestration class FCA17c ..................................... 218 67 Component models used in ResHB and ESPr for experimental validation ............ 226 68 Uncertainties resulting from representative simulation inputs and experimental measurements.......................................................................................................... 252 A1 Analytical Verification Tests of ESPr .................................................................... 280 B1 Parametric Code....................................................................................................... 291 B2 Roof constructions ................................................................................................... 292 B3 Ceiling constructions ............................................................................................... 292 B4 Wall constructions ................................................................................................... 292 B5 Fenestration.............................................................................................................. 292 B6 Partition wall constructions...................................................................................... 293 B7 Partition floor/ceiling constructions......................................................................... 293 B8 Interior mass constructions ...................................................................................... 293 B9 Exterior floor constructions ..................................................................................... 293 x LIST OF FIGURES Figure Page 11. Schematic floor plan for a single family detached house with masterslave control .. 7 41. Overall intermodel testing process........................................................................... 79 42. Predicted Percentage of Dissatisfied (PPD) as a function of Predicted Mean Vote (PMV) ....................................................................................................................... 86 43. Schematic floor plan of the Shoebox prototype ( figure drawn with front side facing north; front, left, back, right as defined in RHBGen) ............................................... 90 44. Schematic floor plan of the 4bedroom house prototype ( figure drawn with front side facing north; front, left, back, right as defined in RHBGen)............................. 92 45. Peak cooling load comparison (Shoebox  Master)................................................... 95 46. Cooling load error percentage based on peak average Shoebox load (Master)......... 95 47. Peak cooling load comparison (4bedroom house – Family room)........................... 97 48. Peak cooling load comparison (4bedroom house – Laundry).................................. 98 49. Peak cooling load comparison (4bedroom house – Foyer 1) ................................... 98 410. Peak cooling load comparison (4bedroom house – Bedroom 1) ........................... 99 411. Peak cooling load comparison (4bedroom house – Total)..................................... 99 412. Cooling load error percentage based on peak average 4bedroom house load (Family room) ......................................................................................................... 100 413. Cooling load error percentage based on peak average 4bedroom house load (Total) ................................................................................................................................ 100 414. Outside ground surface temperatures from RHB and ESPr for Alamosa, CO .... 103 415. Comparison of the ambient dry bulb temperature and the outside surface temperatures calculated from ESPr (Shoebox  Master) ....................................... 104 416. Comparison of cooling load calculated by RHB and ESPr (Shoebox  Master): (a) with external long wave radiation (b) without external long wave radiation ......... 104 417. Comparison of cooling load error percentage between RHB and ESPr (4bedroom house – Family room): (a) with external long wave radiation (b) without external long wave radiation................................................................................................. 106 418. Comparison of cooling load calculated by RHB and ESPr (Shoebox – Master): (a) with internal thermal mass (b) without internal thermal mass................................ 108 419. Comparison of cooling load error percentage between RHB and ESPr (ESPr with simple solar distribution, Shoebox – Master): (a) with internal thermal mass (b) without internal thermal mass................................................................................. 109 420. Comparison of cooling load error percentage between RHB and ESPr (Shoebox – Master): (a) ESPr with detailed solar distribution, with internal thermal mass (b) ESPr with simple solar distribution, without internal thermal mass ..................... 110 xi Figure Page 421. ESPr simple solar distribution vs. detailed solar distribution (Shoebox – Master): (a) comparison of cooling load (b) comparison of cooling load error percentage.. 111 422. Comparison of cooling load calculated by RHB and ESPr (4bedroom house – Family room): (a) ESPr with interzone conduction (b) ESPr without interzone conduction............................................................................................................... 115 423. Comparison of cooling load calculated by RHB and ESPr (4bedroom house – Laundry): (a) ESPr with interzone conduction (b) ESPr without interzone conduction............................................................................................................... 115 424. Comparison of cooling load calculated by RHB and ESPr (4bedroom house – Foyer 1): (a) ESPr with interzone conduction (b) ESPr without interzone conduction............................................................................................................... 116 425. Comparison of ESPr calculated cooling loads (without interzone conduction vs. with interzone conduction): (a) 4bedroom house – Family room (b) 4bedroom house – Foyer 1....................................................................................................... 116 426. Comparison of cooling load calculated by RHB and ESPr (Shoebox – Master): (a) with internal longwave radiation (b) without internal longwave radiation............. 118 427. Comparison of cooling load calculated by RHB and ESPr (Shoebox – Master): without external long wave radiation, internal thermal mass, interzone conduction, internal long wave radiation and windows ............................................................. 120 428. (a) Ambient air temperatures used for Alamosa, CO in RHB and ESPr (b) Outside surface absorbed solar radiation in RHB and ESPr (Shoebox  Master, Alamosa, CO).......................................................................................................................... 121 429. Comparison of cooling load calculated by RHB and ESPr (Shoebox – Master, without external and internal longwave radiation, without thermal mass, interzone conduction, and windows) ...................................................................................... 122 430. Analytically calculated zone loads and those predicted by RHB and ESPr......... 124 431. Processed PPD showing night time ambient cooling, system designed with zero temperature swing (Shoebox) ................................................................................. 129 432. Processed PPD showing system undersizing and inadequate distribution, system designed with zero temperature swing (Shoebox) .................................................. 130 433. Hourly PPD vs. temperature, system designed with zero temperature swing (Shoebox  case 17)................................................................................................. 131 434. Hourly PPD vs. temperature, system designed with zero temperature swing (Shoebox  case 20)................................................................................................. 131 435. Processed PPD showing night time ambient cooling, system designed with zero temperature swing (4bedroom house) ................................................................... 133 436. Processed PPD showing system undersizing and inadequate distribution, system designed with zero temperature swing (4bedroom house) .................................... 135 437. Hourly PPD vs. temperature, system designed with zero temperature swing (4 bedroom house: case 121)...................................................................................... 135 438. Processed PPD showing night time ambient cooling, system designed with medium temperature swing (Shoebox) ................................................................................. 137 439. Processed PPD showing system undersizing and inadequate distribution, system designed with medium temperature swing (Shoebox)............................................ 137 xii Figure Page 440. Hourly PPD vs. temperature, system designed with medium temperature swing (Shoebox  case 355)............................................................................................... 138 441. Processed PPD showing night time ambient cooling, system designed with medium temperature swing (4bedroom house) ................................................................... 139 442. Processed PPD showing system undersizing and inadequate distribution, system designed with medium temperature swing (4bedroom house).............................. 139 443. Hourly PPD vs. temperature, system designed with medium temperature swing (4 bedroom house: case 144)....................................................................................... 141 444. Hourly PPD vs. temperature, system designed with medium temperature swing (4 bedroom house: case 451)....................................................................................... 141 445. Average degree hours for systems designed with zero or medium temperature swing (4bedroom house): (a) Family room (b) whole house ................................ 143 446. Average processed PPD values for systems designed with zero or medium temperature swing (4bedroom house): (a) night time ambient cooling (b) inadequate distribution .............................................................................................................. 145 447. Average processed PPD values for systems designed with zero or medium temperature swing (4bedroom house): (a) system undersizing (b) inadequate distribution and system undersizing ...................................................................... 146 51. Example parameter input screen (Test SSCond)..................................................... 161 52. Sinusoidal driving external dry bulb temperature profile used in the transient conduction test TC3 ................................................................................................ 169 53. Analytically calculated zone loads and those predicted by the ResHB program for the transient conduction test with sinusoidal driving temperature: Case 1................... 174 54. Analytically calculated zone loads and those predicted by the ResHB program for the transient conduction test with sinusoidal driving temperature: case 2. .................. 174 55. Analytically calculated zone loads and those predicted by the ResHB program for the transient conduction test with sinusoidal driving temperature: case 3. .................. 175 56: Zone geometry of the internal solar distribution test (a) plan view showing two vertical fins (b) vertical view showing horizontal fin at the top of the window. The dimensions W, Rv and Rh are 0.5m (1.64ft), and the dimensions H and B are 1.0m (3.28ft). ................................................................................................................... 178 57. Analytically calculated zone loads and those predicted by different versions of ResHB for the solar shading test: horizontal and right side vertical fin on a southfacing window......................................................................................................... 182 58. Analytically calculated zone loads and those predicted by different versions of ResHB for the solar shading test: horizontal and left side vertical fin on a southfacing window......................................................................................................... 183 59. Analytically calculated zone loads and those predicted by ResHB for the window reveal test: before reveal depth was added to the depths of vertical fins................ 184 510. Analytically calculated zone loads and those predicted by ResHB for the window reveal test: after reveal depth was added to the depths of vertical fins................... 184 511. Analytically calculated zone loads and those predicted by ResHB for the internal solar distribution test: Case 1, the floor in RHB test zone is heavy weight............ 185 xiii Figure Page 512. Analytically calculated zone loads and those predicted by ResHB for the internal solar distribution test: Case 2, the floor in RHB test zone is massless.................. 186 513: Zone load variation with zone aspect ratio and different surface emissivities. The emissivities are: Case 1, external surface 0.9, opposite surface 0.1, other surfaces 0.3; Case 2, external surface 0.9, all other surfaces 0.1; Case 3, all surfaces 0.9... 190 514. Analytical and ResHBpredicted zone load variation with zone aspect ratio and different surface emissivities. The emissivities are: Case 1, external surface 0.9, all other surfaces 0.1; Case 2, all surfaces 0.9; Case 3, external surface 0.9, opposite surface 0.1, other surfaces 0.3................................................................................. 191 61(a). Front view of the house in Ft. Wayne, Indiana (Wilcox 2004)........................... 198 61(b). Back view of the house in Ft. Wayne, Indiana (Wilcox 2004)........................... 198 62. Floor plans of the house in Ft. Wayne, Indiana (Wilcox 2004) .............................. 199 63. Campbell Scientific CR10X data logger: measurement and control module (left), wiring panel CR10XWP (right). (Picture from http://www.campbellsci.com) ...... 202 64. Aspirated temperature thermocouple (Wilcox 2004) .............................................. 202 65. Conceptual flow chart of the experimental validation............................................. 205 66. Hourly averaged outside drybulb and wetbulb temperature for 09/21/2005 ........ 207 67. Hourly averaged beam and diffuse solar radiation for 09/21/2005......................... 207 68. Hourly averaged internal heat gain for 09/21/2005................................................. 208 69. Hourly return air temperature and hourly flowweighted runtime supply air temperature for 09/21/2005, values shown only for hours when the system was on ................................................................................................................................ 211 610. Hourly air conditioning “on” fraction for 09/21/2005........................................... 212 611. Hourly basement duct gain (including runtime part and average T part) for 09/21/2005, values shown only for hours when the system was on ....................... 213 612. House total sensible cooling load for 09/21/2005 ................................................. 214 613. Minutely measured room air temperature during the systemoff hours for 09/21/2005: (a) kitchen and living room (b) master bedroom and master bathroom ................................................................................................................................ 219 614. Minutely measured room air temperature for 09/21/2005: dining room............... 222 615. Schematic representation of the ESPr airflow network for the first and second floor ................................................................................................................................ 224 616. Simulated and experimental total house cooling load comparison: ESPr with/without interzone airflow, ResHB with/without internal heat gain and ventilation distribution............................................................................................ 229 617. Simulated and experimental total house cooling load comparison: ResHB with dining room specified as master room, fixed set point of 23.89 oC with 0.0, 0.2, 0.4, 0.6, 0.8 oC temperature swing, with internal heat gain and ventilation distribution ................................................................................................................................ 232 618. Simulated and experimental room temperature comparison, ResHB with dining room specified as master room, fixed set point of 23.89 oC with 0.0, 0.2, 0.4, 0.6, 0.8 oC temperature swing, with internal heat gain and ventilation distribution: (a) Dining room (b) Living room ................................................................................. 233 xiv Figure Page 619. Simulated and experimental total house cooling load comparison: ResHB with master room specified as dining room, living room, Foyer 1 and bedroom 2, master room uses experimental hourly average room air temperature as set point without temperature swing, with internal heat gain and ventilation distribution................. 235 620. Simulated and experimental room temperature comparison, ResHB with master room specified as dining room, living room, Foyer 1 and bedroom 2, master room uses experimental hourly average room air temperature as set point without temperature swing, with internal heat gain and ventilation distribution: (a) Dining room (b) Living room ............................................................................................. 237 621. Simulated and experimental total house cooling load comparison: ResHB uses ideal control, every room uses fixed set point of 23.89 oC with 0.8 oC or 0.0 oC temperature swing, with internal heat gain and ventilation distribution................. 241 622. Simulated and experimental room temperature comparison, ResHB uses ideal control, every room uses fixed set point of 23.89 oC with 0.8 oC temperature swing, with internal heat gain and ventilation distribution: (a) Dining room (b) Kitchen (c) Bedroom 3............................................................................................................... 244 623. Simulated and experimental total house cooling load comparison: ResHB uses ideal control, every room uses fixed set point of 23.89 oC with 0.8 oC or 0.0 oC temperature swing or every room uses experimental hourly average room air temperature as set point without temperature swing, with internal heat gain and ventilation distribution............................................................................................ 245 624. Simulated and experimental room temperature comparison, ResHB uses ideal control, every room uses fixed set point of 23.89 oC with 0.8 oC temperature swing or every room uses experimental hourly average room air temperature as set point without temperature swing, with internal heat gain and ventilation distribution: (a) Dining room (b) Kitchen (c) Bedroom 3 ................................................................ 247 625. Simulated and experimental total house cooling load comparison: ResHB uses ideal control, every room uses fixed set point of 23.89 oC with 0.8 oC temperature swing, with internal heat gain and ventilation distribution; ESPr models system control with airflow network under masterslave onoff control ........................................ 249 626. Minutely ESPr simulated and experimental dining room (master) temperature comparison: ESPr models system control with airflow network under masterslave onoff control .......................................................................................................... 250 627. Simulated and experimental room temperature comparison: ResHB uses ideal control, every room uses fixed set point of 23.89 oC with 0.8 oC temperature swing, with internal heat gain and ventilation distribution; ESPr models system control with airflow network under masterslave onoff control: (a) Dining room (b) Kitchen (c) Attic ................................................................................................................... 251 628. Simulated and experimental total house cooling load comparison: ResHB uses ideal control, every room uses experimental hourly average room air temperature as set point without temperature swing, with internal heat gain and ventilation distribution, cases with infiltration rate of 0.2, 0.4, 0.6 and 0.8ACH ........................................ 254 xv Figure Page 629. Simulated and experimental room temperature comparison: ResHB uses ideal control, every room uses experimental hourly average room air temperature as set point without temperature swing, with internal heat gain and ventilation distribution, cases with infiltration rate of 0.2, 0.4, 0.6 and 0.8ACH: (a) Dining room (b) Master bedroom .................................................................................................................. 255 A1a Analytically calculated zone loads and those calculated by ESPr for Solar Radiation – Glazed Surfaces test: East, west and south facing window................. 282 A1b Analytically calculated zone loads and those calculated by ESPr for Solar Radiation – Glazed Surfaces test: East, west and south facing window (with hourly instantaneous weather data) .................................................................................... 283 A1c Comparison of solar beam irradiance used by ESPr and Analytical solution...... 283 A2 Analytically calculated zone loads and those calculated by ESPr for Solar Radiation – Window Shading test: south facing window with left side vertical fin ............... 284 A3 Analytically calculated zone loads and those calculated by ESPr for the Internal Long Wave Radiation test: emissivity of the external surface = 0.9, emissivity of other surfaces = 0.1 ................................................................................................. 285 A4 Analytically calculated zone loads and those calculated by ESPr for the Internal Long Wave Radiation test: emissivity of all surfaces = 0.9 ................................... 286 A5 The convective heat input profiles of the test zones used in the VAV and OnOff control tests with ESPr program............................................................................ 288 A6 Zone air temperatures predicted by ESPr program and analytical solution for the VAV control test ..................................................................................................... 288 A7 Zone air temperatures predicted by ESPr program and analytical solution for the OnOff control test.................................................................................................. 289 xvi NOMENCLATURE Symbols c p specific heat, Btu/(lbºF) or J/(kgºC) c, n empirical constants from regression analysis h convection coefficient, Btu/h.ft2 or W/m2K k thermal conductivity, Btu/(hftºF) or W/(mK) N the number of cases used in calculating mean bias error O observed value, equals the ESPr predicted loads in our case, Btu/h or W P predicted value, equals the RHB predicted loads in our case, Btu/h or W Q volume air flow rate, CFM or m3/s Tmaster master room temperature, ºF or ºC Tsetpoint room temperature set point, ºF or ºC Tslave slave room temperature, ºF or ºC U conductance, W/m2K or Btu/h.ft2 density, lbm /ft3 or kg/m3 p pressure difference across the house envelope, Pa T difference between the system supply and return air temperature, oC T temperature tolerance used in calculating integrated PPD values, ºF or ºC xvii Abbreviations CLF Cooling Load Factor CLTD Cooling Load Temperature Difference CTF Conduction Transfer Functions DH Degree Hours ELA Effective Leakage Area ETD Equivalent Temperature Difference GLF Glass Load Factors HVAC Heating, Ventilating and Air Conditioning MBE Mean Bias Error PMV Predicted Mean Vote PPD Predicted Percentage of Dissatisfied RHB Residential Heat Balance load calculation procedure SCL Solar Cooling Load SHGC Solar Heat Gain Coefficient TA Time Averaging TETD Total Equivalent Temperature Difference TFM Transfer Function Method 1 1. INTRODUCTION Properly designed residential heating, ventilating and air conditioning (HVAC) systems should provide good comfort and high efficiency at minimum cost. Oversized HVAC systems compromise indoor comfort, reduce system efficiency, and increase the initial investment and energy cost. (Khattar et al. 1987; Reddy and Claridge 1993; Neal and O’Neal 1994; Proctor et al. 1995; James et al. 1997). Since load calculation is the main factor affecting the selection of HVAC system capacities, it is essential to use a reliable heating and cooling load calculation procedure to obtain high efficiency and good quality both for the design and energy utilization of a residential HVAC system. It is important at the outset to define three interrelated but oftenconfused concepts: heat gain, cooling load, and heat extraction rate. Heat gain is the rate at which energy enters into or is generated within a space. Heat gains can occur in various forms such as solar radiation, heat conduction, internal heat gain, ventilation and infiltration air, etc. Cooling load is the rate at which energy must be removed from a space to maintain the temperature and humidity at the design values. The space heat gain usually does not equal the space cooling load. This is because the radiant heat gains must first be absorbed by the surfaces enclosing the space and the objects in the space. Only when the surfaces and objects receiving the radiant heat become warmer than the surrounding air, 2 will some of this energy be transferred to the air by convection and become a part of the cooling load. The heat extraction rate is the rate at which energy is removed from the space by the cooling and dehumidifying equipment. It equals the space cooling load only if the space conditions are kept constant by the operating equipment. Although the heat extraction rate is usually not calculated for commercial building equipment selection, permissible temperature swings in residential buildings require that this be considered in the development of a residential load calculation procedure. Since the subject of this validation work is a newly developed residential load calculation procedure based on the heat balance method, it is of interest to consider the background of this procedure. Accompanying the historical development of air conditioning, building heating and cooling load calculations have gone through a continuous development. Romine (1992) gave a short summary of the development of load calculations in ASHRAE (American Society of Heating, Refrigerating and Air Conditioning Engineers) until 1992. The load calculation development history both in ASHRAE and CIBSE (Chartered Institution of Building Services Engineers) is also reviewed by Rees, et al. (2000). 1.1 Nonresidential Cooling Load Calculation Procedures For nonresidential (commercial and industrial) applications, three methods were presented for calculating cooling loads in the 1997 ASHRAE Handbook of Fundamentals. These are the transfer function method (TFM), the cooling load temperature 3 difference/solar cooling load/ cooling load factor (CLTD/SCL/CLF) method, and the total equivalent temperature difference/time averaging (TETD/TA) method. The three methods are directly or indirectly an approximation of the heat balance method (to be discussed in more detail later). This is because calculating cooling load for a space inevitably involves the calculation of a conductive, convective, and radiative heat balance for each room surface and a convective heat balance for the room air. Exact solutions of space cooling load by heat balance procedures requires a rigorous and laborious calculation of the heat balance equations and is impractical for widespread or routine use without the speed of modern digital computers (ASHRAE 1997). Due to the limited computer capability available in earlier days, various simplified forms of the heat balance procedure were developed for routine cooling load calculation purposes. As an ongoing effort in developing cooling load calculation methods, ASHRAE funded a research project entitled “Advanced Methods for Calculating Peak Cooling Loads (RP875)” in 1996. As the goal of this project, two new methods  the Heat Balance (HB) method (Pedersen, et al. 1997) and the Radiant Time Series (RTS) method (Spitler, et al. 1997)  have been developed. As mentioned before, the heat balance concept is the foundation of the three simplified methods recommended by the 1997 ASHRAE Handbook of Fundamentals. It has been applied in many energy calculation programs in one form or another for many years. It was first implemented in NBSLD (Kusuda 1967), and has also been applied to BLAST and TARP by Walton (1981, 1983). The heat balance method is introduced for load calculation purposes because it has the potential to be the most accurate method for calculating space heating and cooling 4 loads and may be the most understandable method to practicing engineers. It accounts for all energy flows in their most basic, fundamental form and does not impose any simplifications on the solution technique (Strand et al., 1999). It calculates space heating or cooling load by solving the heat balance equations for each of the outside and inside zone surfaces and for the zone air. Transient conduction heat transfer through building fabric is estimated by applying conduction transfer functions. Radiant and convective heat exchanges at both external and internal surfaces are treated separately, with internal radiant exchange calculated by the method of mean radiant temperature with balance (Walton 1980). The heat balance method is also the first ASHRAE load calculation method that completely relies on computer implementation (Rees, et al. 2000). Derived from the heat balance method, the radiant time series method is the new ASHRAE simplified cooling load calculation method for nonresidential buildings, effectively replacing the TFM, TETD/TA and CLTD/SCL/CLF methods (Spitler, et al. 1997). Sharing many heat transfer submodels with the heat balance method, the radiant time series method is most similar to the transfer function method and can be shown equivalent in some aspects (Spitler and Fisher 1999). Experimental validation of both the heat balance method and the radiant time series method has been done in test cells at Oklahoma State University (Chantrasrisalai, et al. 2003; Iu, et al. 2003). As a result of the development and validation work, the heat balance method and the radiant time series method are presented in the 2001 ASHRAE Handbook of Fundamentals, superseding the TFM, TETD/TA and CLTD/SCL/CLF methods. 5 1.2 Residential Cooling Load Calculation Procedures 1.2.1 Characteristics of Residential Load Calculation In comparison to the nonresidential applications, the situation with the residential cooling load calculation is somewhat different because of some unique features inherent in residential buildings. Load patterns of residences differ significantly from those of commercial structures because of different building scale, construction, occupancy, and controls. Compared to commercial or industrial buildings, residential buildings are usually smaller, and their constructions usually have less thermal mass (product of mass and specific heat). Loads from the residential envelope usually compose a much greater fraction of the total building load. The internal heat gains of residences, especially those from occupants and lights, are relatively small. Current ASHRAE design procedure (ASHRAE 1997) assumes that residences usually will be occupied and conditioned for 24 hours a day, every day during the heating and cooling seasons. Residential load calculation usually must be done with a quick and simple method. This limits the usage of whole building energy analysis programs (such as DOE 2, BLAST and EnergyPlus) in the residential realm. Large, sophisticated programs usually allow the possibility of comprehensively describing the buildings. For example, an energy analysis program may allow the user to specify fairly detailed information on the cracks and openings of a building in order to compute the infiltration load. This level 6 of input can be overwhelming for the typical residential HVAC system designer. Instead, a method that allows simple input is usually preferred. In general, most singlefamily detached houses use constant air volume systems with one return and a single central thermostat to control the temperatures of all rooms (Figure 11). This type of temperature control necessarily allows temperatures to fluctuate through out the house. It usually results in temperature swings of several degrees Fahrenheit between different rooms of a house, which is generally considered acceptable from the standpoint of the occupants’ comfort. These temperature swings also result in interzone heat transfer and heat storage in building elements, which have the effect of moderating peak loads. Interzone airflow driven by the air distribution system or thermal buoyancy also produces loadmoderating effects in residences. These thermal interactions, including interzone heat transfer and interzone air flow, contribute to the result that the peak or peak total load of the building is significantly less than the sum of peak room loads. For individual units in multifamily buildings that do not have exposures facing all directions, the loadmoderating effect is not as significant as in the singlefamily detached houses, and the loads are usually closer to the sum of the room peak loads. With the interzone thermal communication as an important feature of residential buildings, the capability to simultaneously model all zones to reflect this feature becomes one of the primary requirements of the detailed reference tool used to evaluate a residential load calculation procedure (See Chapter 4). 7 Master zone Central Single air return Hallway thermostat Utility room Kitchen Bath room Bath room Bedroom 3 Air supply register Bedroom 2 Bedroom 1 Garage Great room Figure 11 Schematic floor plan for a single family detached house with masterslave control In addition to thermal communication, the control strategy becomes another important issue in this case. If the zone containing the central thermostat is called the “master” zone (Figure 11), and other zones are called “slave” zones accordingly, this problem can then be briefly described as the masterslave zone control problem. Because of the single thermostat control, the temperatures generally cannot be simultaneously controlled at the design set point in all rooms. The master zone temperature can be well controlled by the thermostat. The slave zone air temperatures will float depending on the relation between the zone load and the output of the air conditioning system. The slave zones may maintain reasonable temperatures if they have load profiles similar to that of the master zone. Poor zone configurations can result if the slave zones have load profiles significantly different than the master zone. This “masterslave” zone control problem is another unique feature of the residential load calculation. All the features discussed above make the residential load calculation a unique problem. The load calculation techniques developed for commercial buildings therefore cannot be applied directly to residential load calculation. 8 1.2.2 Prior Residential Cooling Load Calculation Procedures Prior to the development of the Residential Heat Balance (RHB) load calculation procedure, there were three common procedures in use for residential cooling load calculations. One is the procedure recommended by ASHRAE. Fully described in Chapter 28 of the ASHRAE 2001 Handbook of Fundamentals, this procedure is primarily based on research project RP342 of ASHRAE (McQuiston et al. 1984). The second is the procedure presented in Manual J, published by the Air Conditioning Contractors of America (ACCA), including the widely used Manual J Seventh Edition (Rutkowski 1986) and Manual J Eighth Edition (Rutkowski 2002). Sharing an ASHRAE heritage, Manual J is based on preRP342 data, and in some cases, techniques that date from the 1950s. The third is the procedure stated in Standard CAN/CSAF280M90 (CSA 1990). Maintained by the Heating, Refrigerating, and AirConditioning Institute of Canada (HRAI), it is actually an adaptation of the ASHRAE procedure to Canadian use. Though differing in many details, this family of methods uses the same general approach to residential load calculation. For cooling load calculations, cooling load temperature differences (CLTD, or equivalent temperature differences (ETD)) and glass load factors (GLF) are used since peak cooling conditions occur intermittently for different rooms during several hours of the day, and buildings do not reach steady state. Here, the CLTD is a purposely defined and precalculated effective temperature difference so that the steady state formulation can be used for cooling load from opaque surfaces. The GLF is the effective cooling load produced by a unit area of glazing. It is defined and generated for the same purpose as the CLTD. The values of CLTD and GLF vary with building construction, orientation, environmental climate, and residence type. 9 With CLTD and GLF precalculated, the cooling load for each opaque element is computed as the CLTD multiplied by its Ufactor and area. Cooling load from fenestration gain is computed as the GLF multiplied by the glazing area. The cooling load of the building fabric is then obtained by summing up cooling loads for opaque elements and glazing surfaces. The CLTD/GLF form of the cooling load calculation is actually an application of the CLTD/SCL/CLF method in residential buildings. It is not only conceptually clear but also simple to implement, in that each building element creates a load per unit area and only an accumulation of component loads is required. However, this “sum up the component loads” approach is an approximation considering the fact that the real load in the conditioned space is a combined effect of component gains. Although this approximation is generally accurate and conservative, consideration of radiant heat transfer, heat storage effects in the space and the possibility that some heat gains are reflected or conducted back out again (as explained by Rees, et al. 1998) may cause this approximation to be inordinately conservative. Except Manual J 8th edition (which requires an evaluation of the designday fenestration gain profiles), all prior methods use single design condition in the cooling load calculation. The single designcondition cooling load calculation has long been problematic. To avoid overpredicting zone loads with the “sum up the component loads” approach and account for heat gain diversity (heat gains generally occur at different times over the day), semiempirical adjustments such as multihour averaging were used to derive the cooling load factors in prior methods. However, for multifamily units with 10 limited exposure (apartments), it is more appropriate to use the “sum up the component loads” approach, as the dominant fenestration gains peak simultaneously in this case. To deal with such configurations, prior methods have used alternative factors and/or adjustments. User judgment is required to select the appropriate application. There is also concern about the accuracy in terms of the derivation of the CLTD/GLF values. The CLTD/GLF values are derived based on the cooling loads calculated by the transfer function method, which is already an approximation to the heat balance method. (The Heat Transfer Multipliers (HTM) in ACCA Manual J are derived from the ETD or CLTD values (which are based on the TFM method) recommended by the ASHRAE Handbook of Fundamentals (1985 for the 7th Edition, 1989 and 1997 for the 8th Edition), supplemented by information from other sources that the manual does not list.) The approximate nature of the transfer function method and its associated errors are therefore unavoidably brought into the results derived from this method. With the development of the computer based heat balance load calculation procedure, there is no apparent reason why this most fundamental method should not be used directly to derive the CLTD/GLF values (if it is still needed) instead of the transfer function method. It is also problematic to estimate other important component loads such as infiltration load. The documentation on airchange method of infiltration is nearly nonexistent (ASHRAE RP342, 1984). The widely used crack length methods require an unreasonably large amount of input for a simplified method (Spitler 2000). Its accuracy depends on the accuracy of the air leakage data for individual buildings and the designer’s experience. The ASHRAE method uses the simple mathematical linear model 11 (Bahnfleth et al. 1957; Coblentz and Achenbach 1963) to estimate the infiltration rate, which relates the air changes per hour as a linear function of the wind velocity and the indooroutdoor design temperature difference (Details can be found in ASHRAE RP342, 1984). Another concern regards the validation of the prior procedures. Although the evaluation of a load calculation procedure can be very comprehensive, timeconsuming and expensive (if empirical test is performed), the validity of a load calculation procedure is very important. Unfortunately, none of the prior procedures has been thoroughly evaluated and validated since their development. Systematic testing of the prior procedures is not documented in the literature. In summary, the formulation of the prior residential cooling load calculation procedures is satisfactory for most residential buildings. However, problems and questions exist concerning the accuracy of the resulting loads, the method of deriving the CLTD and GLF values, the method of estimating some important component loads, and the validity of the prior methods. A new heat balance based residential cooling load calculation procedure is highly desirable. In the development of the new procedure, attention must be paid to consider and model the interzone thermal interactions and masterslave zone controls. It is also desirable that the new procedure be well tested and the system design resulted from the new procedure be carefully evaluated. 12 1.2.3 Heat Balance Based Residential Cooling Load Calculation Procedure In response to the problems of the prior procedures, ASHRAE sponsored a research project (1199RP) “Updating the ASHRAE/ACCA Residential Heating and Cooling Load Calculation Procedures and Data” (Barnaby et. al. 2004). In this project, a new residential loads calculation procedure  Residential Heat Balance (RHB) – was developed. RHB is a detailed heat balance based procedure. It requires computer execution, as the roombyroom hourly designday simulation used in this procedure is computationally extensive. The hourly designday simulation eliminates issues of gain diversity that are problematic in prior procedures, which use single design condition. The average/peak distinction used in prior procedures is no longer necessary, as the design load is simply the peak hourly load. For calculation of sensible cooling load, RHB applies the general approach of the ASHRAE Heat Balance (HB) method. As the heat transfer equations are solved in their most basic, fundamental form in the heat balance method, prior concerns about the “sum up the component loads” approximation are eliminated. The concern regarding the approximate accuracy of the transfer function method, which is used in the derivation of the CLTD/GLF factors of the prior methods, is also eliminated. Considering the unique features of residential load calculation, RHB includes algorithms for calculating sensible cooling loads with temperature swing and addresses the masterslave zone control problem. 13 As part of 1199RP, the ResHB computer program was developed as the reference implementation of the RHB procedure. The ResHB source code is derived from the ASHRAE Loads Toolkit (Pedersen et. al. 2001). An additional utility program, RHBGen, was also developed to automatically generate and run parametrically varied ResHB cases for testing and research purposes. The RHB development also involved review, refinement, and extension of the ASHRAE Loads Toolkit models. Component models and assumptions used for RHB are considered appropriate for residential application. For example, the AIM2 infiltration model was selected for RHB (Walker and Wilson 1990, 1998, and “enhanced model” in Chapter 26, ASHRAE 2001). An algorithm was developed to derive a homogeneous layer that corresponds to a framed construction layer, which is common in residential buildings. Details of the component models and assumptions of RHB are documented in the project final report (Barnaby et. al. 2004) and are summarized in the literature review section (see Chapter 2). One concern left and deserving detailed investigation is the validity of RHB. As a newly developed cooling load calculation procedure, no validation has been conducted prior to the work described in this dissertation. Independent and objective assessment of RHB is clearly necessary in view of the important effect it will have on the residential HVAC system design. Theoretically, RHB includes the most fundamental heat balance method, which potentially is the most accurate method. However, individual heat transfer mechanisms implemented in ResHB need to be tested. The algorithms included in RHB to handle 14 temperature swing and masterslave zone control need to be checked. Cooling loads calculated by ResHB and hence the system capacity and design need to be evaluated. Integrated performance of the component models in ResHB also needs to be validated. In a word, a thorough validation of RHB is highly desirable and has not been done yet. 1.3 Objective Therefore, the objective of this research is to conduct a systematic validation and evaluation of the new heat balance based residential cooling load calculation procedure  RHB. Three types of testing methods will be applied to validate RHB: intermodel comparison, analytical verification and experimental validation. For intermodel comparison, a detailed heat balance based computer program will be selected as a reference tool to evaluate RHB. A parametric analysis tool will be developed for systematic and automatic implementation of large amounts of intermodel comparisons. Cooling loads calculated by ResHB will be compared to that calculated by the reference tool. System designs resulting from ResHB will also be evaluated by detailed simulations with the reference tool. Intermodel validation of RHB is discussed in detail in Chapter 4. For analytical verification, RHB will be tested against an analytical verification test suite that the author has previously developed together with other colleagues in Oklahoma State University: the Analytical Verification Test Suite for Whole Building Energy Simulation Programs  Building Fabric (ASHRAE 1052RP, Spitler, et al. 2001). The test suite consists of sixteen individual tests, each with the objective to test the ability of a building energy simulation program to model a particular heat transfer phenomena, including convection, conduction, solar radiation, long wave radiation and infiltration. 15 Tests appropriate for application to RHB will be done and analysis and diagnosis will be made based on the test results. Analytical verification of RHB is presented in Chapter 5. Finally, appropriate residential experimental data will be used to validate RHB. Experimental data will be obtained from a wellinstrumented house located in Fort Wayne, IN. ResHB input files will be created for the house and ResHBcalculated cooling loads and room temperatures will be compared to measured data. Experimental validation of RHB is discussed in Chapter 6. 16 2. LITERATURE REVIEW The literature review in this chapter includes two parts. First, a review is given for the subject of this research work – the heat balance based residential cooling load calculation procedure. The purpose is to gain a full knowledge and familiarity of RHB, with regards to its basic structure and algorithm, theoretical principles and assumptions, and component models. Second, a review is given for the general validation methods of building thermal simulation programs. The purpose is to identify possible methodologies and available tools for validating cooling load calculation programs. 2.1 Heat Balance Based Residential Cooling Load Calculation Procedure The recent ASHRAE research project (1199RP) “Updating the ASHRAE/ACCA Residential Heating and Cooling Load Calculation Procedures and Data” (Barnaby et al. 2004) developed a new detailed heat balance based residential loads calculation procedure: Residential Heat Balance (RHB). For calculation of sensible cooling load, RHB applies the general approach of the ASHRAE Heat Balance (HB) method, based on roombyroom 24hour designday simulation. RHB includes algorithms for calculating sensible cooling loads with temperature swing and addresses the master / slave zone control problem that is unique for residential load calculation. 17 As part of 1199RP, the ResHB computer program was developed as the reference implementation of the RHB procedure. The ResHB source code is derived from the ASHRAE Loads Toolkit (Pedersen et. al. 2001). An additional utility program, RHBGen, was also developed to automatically generate and run parametrically varied ResHB cases for testing and research purposes. As will be described later in Chapter 4, RHBGen helps running all the intermodel comparison cases on the ResHB side. Documentation of ResHB and RHBGen is included in the 1199RP final report (Barnaby et al. 2004). In this section, theoretical principles of RHB  the heat balance method – are summarized first. Calculation algorithms, modeling assumptions and component models of RHB and their implementation in ResHB are described second. 2.1.1 Heat Balance Method for Cooling Load Calculation As mentioned in the introduction section, heat balance method has been applied in many energy calculation programs in one form or another for many years. It was first implemented in NBSLD (Kusuda 1967), and has also been applied to BLAST and TARP by Walton (1981, 1983). In ASHRAE Research Project 875, the heat balance method was first described in a form applicable to cooling load calculations. Details of the method are described in Pedersen et al. (1997, 1998, 2001), and Chapter 29 of ASHRAE Handbook of Fundamentals (2001). It is summarized here for completeness. 18 2.1.1.1 Heat Balance Model Elements The heat balance method is first of all based on some model assumptions, which assume that: • The zone air is well mixed and has a uniform temperature • The surfaces of the zone have uniform surface temperatures, uniform longwave (LW) and shortwave (SW) irradiation, diffuse radiating surfaces and onedimensional heat conduction within. Based on these assumptions, the heat balance model involves four distinct elements: Outside heat balance, wall conduction process (for transparent surfaces, the conduction process is accompanied by solar absorption and transmission), inside heat balance and air heat balance. Each of these elements is briefly discussed below. Note that each element has several heat transfer processes, to which particular models can be applied. These models are not to be enumerated here. Details of available models can be found in the ASHRAE Loads Toolkit (Pedersen, et al. 2001), from which the residential heat balance cooling load calculation procedure is derived. Outside Heat Balance The outside heat balance for opaque surfaces has four heat exchange processes, of which the summation of the heat fluxes should be zero: " " " " 0 sol LWR conv ko q q q q + + = (2.1) where: 19 " sol q = absorbed direct and diffuse solar radiation heat flux, W/m2 " LWR q = net longwave radiation flux exchange with the air and surroundings, W/m2 " conv q = convective flux exchange with outside air, W/m2 " ko q = conductive heat flux into the wall, W/m2 All terms are positive for net flux to the surface except the conduction term, which is traditionally taken to be positive in the direction from outside to inside of the wall. For transparent surfaces, the absorbed solar component would appear in the conduction process (to be discussed next) instead of at the outside surface. It would also split into an inward and an outward flowing fraction and participate in the inside and outside surface heat balance. Wall Conduction Process For building load calculation purpose, it is usually appropriate to assume the wall conduction process as a onedimensional transient process through multilayer construction, with each layer material considered homogeneous and having constant thermal properties. The governing equation for transient onedimensional heat conduction, assuming constant thermal properties, is expressed as: 2 2 T(x,t) 1 T(x,t) x t = (2.2) where T = the wall temperature as a function of position (x) and time (t), K 20 p k C = is the thermal diffusivity of the layer material, m2/s k = thermal conductivity of the layer material, W/(mK) = density of the layer material, Kg/m3 p C = specific heat of the layer material, J/(kgK) This equation is typically coupled with Fourier’s law of conduction that relates the heat flux at any position and time to temperature as follows: q" (x,t) k T(x,t) x = (2.3) Analytical solutions to equation (2.2) and (2.3) exist for a single homogeneous layer. For a multilayer slab, the solution becomes extremely tedious. Possible ways to model this process are: • Numerical finite difference • Numerical finite element • Transform methods • Time series methods While each of these methods has advantages over the others in various applications, traditionally, building thermal simulations have used either time series based or finite difference based methods. In the ASHRAE Loads Toolkit (Pedersen, et al. 2001), from which the residential heat balance cooling load calculation procedure is 21 derived, a time series method using conduction transfer functions is used because of the computational time advantage. Inside Heat Balance The inside heat balance involves four coupled heat transfer components: 1) wall conduction, 2) convection to the inside air, 3) shortwave radiation absorption and reflectance and 4) longwave radiant interchange. The shortwave radiation includes transmitted solar radiation from windows and emittance from internal sources such as lights. The longwave radiation interchange includes those from all other zone surfaces and those from internal sources such as equipment and people. The inside heat balance for each surface is written as (all terms are positive for net flux to the surface): " " " " " " 0 qLWX + qSW + qLWS + qki + qsol + qconv = (2.4) where: " LWX q = net long wave radiant exchange flux between zone surfaces, W/m2 " SW q = net short wave radiation flux to surface from lights, W/m2 " LWS q = long wave radiation flux from equipment in zone, W/m2 " ki q = conduction flux through the wall, W/m2 " sol q = transmitted solar radiation flux absorbed at surface, W/m2 " conv q = convective heat flux to inside air, W/m2 22 Air Heat Balance In the air heat balance formulated for cooling load calculation purposes, it is usually assumed that the capacitance of the zone air can be ignored and the zone air is at quasisteady state at each simulation time step such as an hour. Therefore, the air heat balance reduces to a form similar to that of the surface heat balances—a summation of four heat transfer terms equal to zero (all terms are positive for net heat flow to the air): qconv + qCE + qIV + qsys = 0 (2.5) where: conv q = convection heat transfer from the inside zone surfaces, W CE q = convection from internal sources, i.e. people, lights, equipment, etc., W IV q = sensible load due to infiltration and ventilation, W sys q = heat transfer to/from the HVAC system, W 2.1.1.2 Mathematical Description of Heat Balance Procedure The above section describes the physical process of the heat balance model conceptually. This section introduces the basic equations used in the heat balance procedure mathematically. All information is based on the ASHRAE Loads Toolkit (Pedersen, et al. 2001), from which the residential heat balance cooling load calculation procedure is derived. 23 Conduction Process As mentioned above, the ASHRAE Loads Toolkit formulates the wall conduction process using Conduction Transfer Functions (CTFs), which relate conductive heat fluxes to the current and past surface temperatures and the past heat fluxes. The basic form for the inside heat flux is as follows: " " 0 , , 0 , , , 1 1 1 ( ) nz nz nq ki si t j si t j so t j so t j j ki t j j j j q t ZT ZT YT YT q = = = = + + + (2.6) For the outside heat flux, the form is: " " 0 , , 0 , , , 1 1 1 ( ) nz nz nq ko si t j si t j sot j sot j j kot j j j j q t YT YT XT XT q = = = = + + + (2.7) where: j X = Outside CTF coefficient, j= 0,1,...nz, W/m2K j Y = Cross CTF coefficient, j= 0,1,...nz, W/m2K j Z = Inside CTF coefficient, j= 0,1,...nz, W/m2K j = Flux CTF coefficient, j = 1,2,...nq t = time, s = time step, s si T = Inside face temperature, oC so T = Outside face temperature, oC " ki q = conduction heat flux on outside face, W/m2 " ko q = conduction heat flux on inside face, W/m2 24 The subscript following the comma indicates the time period for the quantity in terms of the time step P. Note that the first terms in the series (those with subscript 0) have been separated from the rest in order to facilitate solving for the current temperature in the solution scheme. There are two main methods for calculating conduction transfer functions: the Laplace Transform method and the State Space method. Detailed documentation and Fortran Modules are available for both methods in the ASHRAE Loads Toolkit. Heat Balance Equations The heat balance processes for the thermal zone are formulated for a 24hour steady periodic condition. The primary variables in the heat balance equations are the inside face temperatures, the outside face temperatures, and the sensible cooling load at each of the 24 hours. Assigning i as the surface index and j as the hour index, then, the primary variables are: soi , j T = outside face temperature, (i=1, 2, ... number of surfaces; j=1, 2, ... 24) , oC sii , j T = inside face temperature, (i=1, 2, ... number of surfaces; j=1, 2, ... 24) , oC sys j q = sensible cooling load, (j=1,2, ... 24), W Equation (2.1) is combined with equation (2.7) to solve for so T to produce equations applicable at each time step for each surface: 25 , , , , , , , , , " " " , , , ,0 1 1 1 ,0 i j k i j k i j k i j i j i j j i j i j i j nz nz nq si ik so ik ik ko sol LWR si i o co k k k so i co T Y T X q q q T Y T h T X h = = = + + + + = + (2.8) where: o T = outside air temperature, oC co h = outside convection coefficient, obtained from " ( ) conv co o so q = h T T , W/(m2K) Equation (2.4) is combined with equation (2.6) to solve for si T to produce equations applicable at each time step for each surface: , , , , , , , " " " " " ,0 , , , 1 1 1 ,0 i j i j k i j k i j k j i j i j i j nz nz nq so i so i k si i k i k ki a ci LWS LWX SW sol k k k si i ci T Y T Y T Z q T h q q q q T Z h = = = + + + + + + + = + (2.9) where: a T = zone air temperature, oC ci h = inside convection coefficient, obtained from " ( ) conv ci a si q = h T T , W/(m2K) Note that in Equations (2.8) and (2.9), the opposite surface temperature at the current time appears on the right hand side. The two equations can be solved simultaneously to eliminate that variable. Depending on the order of updating the other terms in the equations, this can have a beneficial effect on the solution stability. The remaining equation comes from the air heat balance, Equation (2.5). It determines the cooling load sys q at each hour: 26 , 12 , 1 sys j i c i ( sii j a j ) CE IV i q AhT T q q = = + + (2.10) where: A = surface area, m2 The convective heat transfer term in equation (2.10) is expanded to show the relationship between the surface temperatures and the cooling load. Note that equation (2.10) is formulated this way in the cooling load calculation procedure implemented in the ASHRAE Loads Toolkit. But, it may also be formulated other ways. For example, it may be formulated to give zone air temperature with or without system input, as in the case when temperature swing is considered in RHB. 2.1.1.3 Solution Method of Heat Balance Procedure The solution method of the heat balance procedure implemented in the ASHRAE Loads Tookit is a basic iterative, or successive substitution method, which is inherited in the residential heat balance cooling load calculation procedure with some modifications and extensions. The Toolkit implementation consists of a series of initial calculations that proceed sequentially, followed by a double iteration loop. The initial calculations include the following: • Initialize the areas, thermal properties, and surface temperatures for all surfaces for 24 hours. • Calculate incident and transmitted solar flux for all surfaces for 24 hours. • Distribute transmitted solar energy to all inside surfaces for 24 hours in a prescribed manner. 27 • Calculate internal load quantities for 24 hours. • Distribute longwave, shortwave, and convective energy from internal loads to all surfaces for 24 hours in a prescribed manner. • Calculate infiltration and ventilation loads for 24 hours. After the above initial calculations, the iterative solution scheme is as follows: Repeat Day For Hour = 1 to 24 For Iteration = 1 to Maximum Iterations per Hour For Surface = 1 to Number of Surfaces Evaluate Equation (2.8) Evaluate Equation (2.9) Next Surface Evaluate Equation (2.10) Next Iteration (or until Hour results converge) Next Hour Until day converged There are two iteration loops in this solution scheme. The outer loop, or the day iteration, is necessary to arrive at the steady periodic response and thus eliminate any initial condition influence on the solution. This is a result of the fact that conduction is transient and inherently slower than other thermal processes. The inner loop, or the hour 28 iteration, is necessary to allow the radiation balance between surfaces. This is a result of the fact that not all surfaces are solved simultaneously but successively. It should be noted that the heat balance procedure requires a fair amount of input information for the thermal zone, such as the design conditions, details about the walls and windows, roof and floor information, thermal mass, internal heat gains, etc. A more detailed list can be found in Pedersen et al. (1997) and in Chapter 29 of ASHRAE Handbook of Fundamentals (2001) and will not be repeated here. 2.1.2 Heat Balance for Residential Applications The Residential Heat Balance method is a specialized application of the ASHRAE Heat Balance method. Compared to the ASHRAE Heat Balance method, RHB has the following changes: • Multiroom, multizone, and multisystem. Independent heat balances are performed for each room. Because of the simplified geometric input (where surface areas and orientations are known but their positions are not), room adjacencies required by a detailed interroom heat transfer calculation are not available. However, as shown in the calculation sequence below, interroom references are available for the current hour during a simulation, allowing room temperatures in one room being used as the boundary condition for another room. Zones and systems are accounting structures to which loads are accumulated to provide overall results. 29 • Specialized algorithms. Specialized algorithm was implemented to handle temperature swing and master / slave control. • Residential models and assumptions. Component models and assumptions used for RHB are considered appropriate for residential application. • Simple latent cooling procedures. Latent load can be estimated from moisture gain from infiltration, ventilation, duct leakage, and occupants. The remaining parts of this section briefly describe the above aspects of RHB. More details can be found in Barnaby et al. (2004). 2.1.3 Calculation Algorithms As discussed in the introduction section, residential air conditioning applications use constant volume systems controlled by a single thermostat (master/slave control). Typically a thermostat located in one room (master room) controls system output for multiple rooms (slave rooms). As a result, the temperature of the master room can be well controlled. The temperatures of the slave rooms will float depending on the relation between their particular load profiles and the output of the air conditioning system. Usually their temperatures will not be held at the set point even when the system is operating. This hourtohour temperature variation, or temperature swing, has a significant moderating effect on peak loads, due to heat storage in building components. The level of the load moderating effect caused by the master/slave control and temperature swing varies in different residence categories. It is more significant in single 30 family detached houses that have exposed walls in four directions than in multifamily houses that have exposures in only one or two directions. The master/slave control and the resulting temperature swing have long been recognized as a major consideration in residential cooling load calculations. In prior methods, load factors were derived using semiempirical adjustments such as multihour averaging to account for the peak load moderating effects. In RHB, specialized algorithms were developed to model master/slave control and temperature swing. As an application of the heat balance method, RHB basically is a design day procedure that requires iteration to find the steadyperiodic solution at which all heat flows correctly balance. In order to handle temperature swing and master/slave control, RHB has the additional requirement of finding loads under floating temperature conditions, as described below. 2.1.3.1 Calculation Sequence and Convergence Criteria The basic RHB load calculation sequence is: repeat swing repeat day for hour = 1 to 24 for all rooms repeat for all surfaces perform surface heat balance 31 end for surfaces perform air heat balance until room convergence for current hour end for rooms end for hours until day convergence determine room supply air flow rates for next swing iteration until swing convergence Note that the goal of the RHB procedure is to find the roombyroom capacity required to meet the combination of design condition with permitted temperature swing. (The cooling load used for sizing the capacity of the central air conditioning system is the sum of all peak room loads. The roombyroom capacities are also used to design the air distribution system.) Temperature swing occurs when the cooling capacity for a particular room is less than that required to hold that room at the set point. (The cooling capacity could be less than that required in two cases: 1. When the system is operating but does not have enough capacity. 2. When the system is turned off by the thermostat located in the master room, but the slave rooms still need cooling.) In the calculation sequence shown above, the outer loop handles temperature swing (discussed below). The swing search algorithm adjusts the supply air flow rate to each room and repeats the entire calculation until the permitted temperature swing is reached. Note that the hour loop is outside the room loop, so that current hour conditions are available for all rooms for interroom references. 32 The following criteria were used in ResHB to determine whether the solution has converged: • Hour. The convergence criterion of the hour calculation is: For each room, the sum of the absolute change in surface and air temperatures is less than 0.0005 °K (0.0009 °F). • Day. The convergence criteria of the day calculation are: For all rooms, a) the fractional difference between inside and outside surface flux summed over the day is less than 0.005 and b) the areaweighted total absolute temperature change for all surfaces plus air is less than 0.0002 °K (0.00036 °F). Note that the allroom requirement means that some rooms will be iterated beyond this point. • Swing. The convergence criterion of the swing search is: For all rooms, swings are within 0.01 °K (0.018 °F) of specified. (RHB allows a different swing specified for each room.) Again, the allroom requirement means extra iteration for some rooms. 2.1.3.2 Temperature Swing When temperature swing is permitted, ResHB uses a secant method search algorithm to search for the load. The calculations are based on varying system air volume flow rate with an assumed supply air temperature. The calculation sequence for the swing search is: 33 • The required cooling air flow rate is found first for the 0 swing situation (that is, maximum available air supply volume is unlimited and room temperature held at the setpoint or floating below it with no supply air flow). • This maximum supply air flow rate is then reduced by 20% per °K (11% per °F) of target swing and the room is calculated again. • The supply air flow rate is iteratively adjusted in proportion to the error in temperature swing, as indicated by the secant method. This algorithm is reported to be extremely efficient. Convergence to within 0.01 °K (0.018 °F) of the target swing usually occurs in less than 10 cycles. However, it is also reported that specific room characteristics can cause the search to fail. 2.1.3.3 Master/slave Control RHB models master/slave control with the temperature swing algorithm. The problem is to find the peak slave room supply air volume flow rate so that the maximum room temperature is the set point plus permitted temperature swing (the swing could be zero). At each swing iteration, the peak flow rate is adjusted using the temperature swing search described above (the search is used even if the specified swing is zero). Then the flow rates for all hours are set by applying the master room profile. (By definition, a slave room has the same supply air flow rate profile as the master room). The next day iteration proceeds without any further adjustment of air flow rate. It is reported that when the master and slave rooms have significantly different load profiles, subcooling can occur in the slave rooms. 34 2.1.4 Component Models This section describes the main component models that were refined or extended during the RHB development. Other component models are inherited from the ASHRAE Loads Toolkit and can be found in its documentation (Pedersen et al. 2001). 2.1.4.1 Inside Surface Convection Coefficients The choice of inside surface convection coefficients is very important as it directly affects the cooling load. (The cooling load is the total convective heat transfer from all internal surfaces plus convective gain from other sources). The default model for inside surface convection coefficients in ResHB is a variant of the TARP simple model (Walton 1983). For each hour, the coefficient used is the systemrunfractionweighted combination of the “sys off” and “sys on” values. The “sys off” values are those from the TARP simple model. To improve convergence stability, the transition between heat flow up and down values is made linearly over 2°C (3.6°F), rather than abruptly. The “sys on” value was chosen to be 5 W/m2K (0.88 Btu/hft2F) for all surfaces, based on analysis of experimental data from ASHRAE research projects 529RP and 664RP for air change rates of approximately 8 ACH (typical for residential systems). Table 21 shows the “sys off” and “sys on” values for the default model. Table 21. The “sys off” and “sys on” values for default model of inside surface convection coefficients (W/m2K) in ResHB Ceiling Floor Heat flow up Heat flow down Wall Heat flow up Heat flow down Sys on 5.000 5.000 5.000 5.000 5.000 Sys off 4.043 0.920 3.078 4.043 0.920 35 In addition to the default model, ResHB also has optional models of fixed convection coefficients (1.250 ceiling, 4.679 wall, 4.370 floor (all W/m2K)), TARP detailed model and Fisher model (documented in Pedersen et al. 2001). 2.1.4.2 Elevation Effects on Convective Heat Transfer During the development of RHB, efforts have been made to study the effect of elevation on convection coefficients. The investigation showed that applying an elevation correction to convection coefficients has a significant effect on predicted loads for high elevation locations (about 13% for Denver). A simple linear approximation was developed and used in RHB: 0 0 0.24 0.76 P h h P = + (2.11) where h = convective coefficient at pressure P (units consistent with h0) h0 = convective coefficient at sea level pressure P = atmosphere pressure at site elevation (units consistent with P0) P0 = sea level atmospheric pressure 2.1.4.3 Buffer Spaces Taking advantage of the heat balance approach, buffer space temperatures are predicted by modeling an unconditioned room in ResHB. These temperatures are then used as outside boundary conditions for surfaces of adjacent conditioned spaces. Although this treatment maintains the single zone methodology, it deviates from the real heat balance approach. The interroom reference in ResHB is different from those 36 available in a detailed interroom heat transfer analysis. In ResHB, the unconditioned rooms do not take the actual variations in the adjacent conditioned room temperatures into account, while in a detailed interroom heat transfer analysis, it does. 2.1.4.4 Infiltration The default infiltration model for RHB is the AIM2 model (Walker and Wilson 1990, Walker and Wilson 1998, and “enhanced model” in Chapter 26, ASHRAE 2001). AIM2 is a single zone model in which infiltration is determined for the whole building. In RHB, the overall infiltration rate is allocated to rooms in proportion to volume – that is, the same air change rate is assumed for all rooms. RHB provides typical default values for several required inputs of the AIM2 model that are difficult to determine, including effective leakage area, leakage area distribution, and wind shelter parameters. Leakage area can be specified based on pressurization test or defaulted based on leakage classes defined by ANSI/ASHRAE Standard 119 (ASHRAE 1994). Modeling of the interaction between mechanical ventilation and infiltration in RHB follows Palmiter and Bond (1991) and Sherman (1992). First, overall supply and exhaust flow rates must be determined and then divided into “balanced” and “unbalanced” components. Qbal = MIN(Qsup ,Qexh ) (2.12) ( , ) unbal sup exh bal Q = MAX Q Q Q (2.13) where bal Q = balanced air flow rate, L/s or cfm 37 sup Q = total ventilation supply air flow rate, L/s or cfm exh Q = total ventilation exhaust air flow rate (including any combustion air requirements), L/s or cfm unbal Q = unbalanced air flow rate, L/s or cfm The air flow components are combined with infiltration leakage as follows: ( , 0.5 ) vi bal unbal inf unbal Q = Q +MAX Q Q + Q (2.14) where vi Q = combined infiltration/ventilation flow rate (not including balanced component), L/s or cfm inf Q = infiltration leakage rate determined assuming no mechanical pressurization, L/s or cfm 2.1.4.5 Distribution Losses ResHB duct losses are calculated using models specified in ANSI/ASHRAE 152 2004, Method of Test for Determining the Design and Seasonal Efficiencies of Residential Thermal Distribution Systems and Palmiter and Francisco 1997. The method estimates the overall steadystate thermal efficiency of residential forcedair distribution systems by accounting for the conduction loss through the duct walls to the buffer zones and air leakage out of the supply ducts or into the return ducts. The conduction efficiency is calculated as: exp p UPL mc = (2.15) 38 where = the conduction efficiency of the pipe U = the overall duct wall conductance, W/m2K P = the inside perimeter of the pipe, m L = the length of the pipe, m m = the mass flow rate of the air in the pipe, Kg/s p C = the specific heat of the air, KJ/kgK The air leakage efficiency of the pipe is defined as: = 1 Leak Fraction (2.16) The overall duct efficiency with combined conduction and air leakage is (the subscripts s and r refer to the supply and return ducts respectively): ( ) ( ) 0 1 r 1 s s s s s r r s s e e T T T T = (2.17) where 0 = the overall duct system efficiency r T = the difference between the temperature of the air in the pipe at the return register and the temperature of the air around the return duct, K s T = the difference between the temperature of the air in the pipe at the return register and the temperature of the air around the supply duct, K e T = the temperature rise across the equipment, it equals the difference between the temperature of the air in the pipe at the supply plenum and the temperature of the air in the pipe at return plenum, K 39 Impacts of duct interaction with natural infiltration on efficiency are considered by subtracting the efficiency loss in due to the interaction from the overall efficiency. in is calculated as: 1 ( ) in 2 r s e T T = (2.18) where T = the difference between the temperature of the air in the pipe at the return register and the temperature of infiltration air, K 2.1.4.6 Framed Constructions Framed constructions are common in residential buildings. As from the ASHRAE Loads Toolkit, the CTFbased conduction model in ResHB assumes onedimensional conduction heat flow and requires layerbylayer construction input. ResHB includes an algorithm that derives fictitious material properties for a homogeneous layer that corresponds to a framed layer. The resistance of the layer is chosen to preserve the overall Ufactor of the construction. Density and specific heat of the layer are the volumetric averages of the framed layer components. 2.1.4.7 Fenestration and Solar Gain Distribution ResHB implements fenestration class and includes builtin fenestration class definitions for common residential glazing types. The fenestration class embodies the ratio of transmission to absorption and the angular characteristics of the fenestration system. An actual fenestration is specified by its Ufactor, SHGC, and its fenestration class. The required angular characteristics of a specified fenestration are taken from the 40 specified fenestration class and are scaled by the ratio of specified SHGC to nominal (fenestration class) SHGC. Interior and exterior shading treatments in ResHB are represented by the ASHRAE Interior Attenuation Coefficient (IAC) and Exterior Attenuation Coefficient (EAC) models (Chapter 30, 2001 ASHRAE Handbook of Fundamentals). Overhang and fin shading is modeled with ASHRAE Loads Toolkit methods. Hourly scheduled shading is also allowed in ResHB. For internal solar distribution, a modified version of the Loads Toolkit BLAST model is used. It distributes radiative gains in proportion to surface areaabsorptance product. Beam solar gain is assumed to hit floor surfaces. One refinement to this model in RHB is that internal mass surfaces are assumed to be “half floor” with respect to beam radiation, as furnishings typically intercept some of the incoming beam. 2.1.4.8 Ground Heat Transfer RHB models slabs as 300 mm (1 ft) of earth with adiabatic boundary conditions. This construction captures some of the diurnal heat storage effects of slab construction, but not net conduction to the ground. 2.1.5 Modeling Assumptions The following sections describe the modeling assumptions of RHB. 41 2.1.5.1 Outdoor Design Conditions RHB requires hourly design day outdoor conditions. In addition to the ability of accepting 24hour profiles from user input, ResHB can also automatically generate 24 hour profiles from design drybulb temperature and its daily range, coincident wetbulb temperature, site coordinates, and site elevation, as follows: • Drybulb temperature. The design dry bulb and daily range are expanded to 24 hours using the generic profile from Table 17, Chapter 29 of the 2001 ASHRAE Handbook of Fundamentals. The generic profile is shifted 1 hour later when daylight savings time is specified. • Wetbulb temperature and other moisturerelated values. The design dry bulb and coincident wet bulb are used to determine the design dew point temperature. The hourly dew point is the minimum of the design dew point and the hourly dry bulb (that is, constant absolute humidity is assumed, limited by saturation). Other hourly psychrometric values (wet bulb temperature, humidity ratio, and enthalpy) are derived from the hourly dry bulb and dew point temperatures. • Solar radiation. Hourly incident solar is derived using the ASHRAE clear sky model (Chapters 29 and 30, 2001 ASHRAE Handbook of Fundamentals) with updated coefficients from Machler and Iqbal (1985). • Sky temperature. Sky temperature is required for calculation of exterior surface long wave radiant exchange. The model of Berdahl and Martin (1984) is used to calculate hourly sky temperature from hourly drybulb and dew point temperatures (cloud cover assumed to be 0). 42 All psychrometric calculations are done with ASHRAE Loads Toolkit procedures (originally from Brandemuehl et al. 1993) assuming a constant barometric pressure determined from site elevation according to a standard atmosphere relationship (Eqn (3), Chapter 6, 2001 ASHRAE Handbook of Fundamentals). 2.1.5.2 Internal Gain Internal gain assumptions in RHB are based on Building America (2003), which provides gain intensities and schedules for significant residential end uses as a function of building floor area and number of occupants. Also, RHB requires the radiant/convective/latent split for each gain source, which Building America (2003) does not fully define. Estimates were developed from 2001 ASHRAE Handbook of Fundamentals and other sources as needed, as shown in Table 22. Table 22. Fractional components of internal heat sources incorporated in ResHB Internal gain (to space) Source Radiant Convective Latent Exhausted Refrigerator 0 1 0 0 Range .24 .16 .30 .30 Dishwasher .51 .34 .15 0 Clothes washer .40 .60 0 0 Clothes dryer .09 .06 .05 .80 Lighting .79 .21 0 0 Other appliances and plug loads .54 .36 .1 0 People (living) .33 .22 .45 0 People (sleeping) .30 .30 .40 0 2.1.5.3 Internal Mass In RHB, the recommended assumption regarding internal mass is: each room should be modeled including internal mass having surface area equal to room floor area and consisting of 12 mm (0.5 in) wood exposed on one side (adiabatic outside surface 43 conditions). This surface should be radiantly coupled to all room internal surfaces. ResHB implements a special surface type “IM” for internal thermal mass. 2.1.5.4 Other Assumptions Surface absorptance. Surface absorptance values in ResHB can either be the defaults (documented in Barnaby et al. 2004) or specified by the user. Material properties. ResHB includes default material properties as documented in Barnaby et al. (2004). Again the user can also specify material properties. 2.2 Validation Methods of Cooling Load Calculation Programs The word validation has been widely used with a variety of meanings. Strachan (1993) gave the following definition of validation: “The rigorous testing of a program – comprising its theoretical basis, software implementation and user interface – under a range of conditions which typify its expected use.” In practice, it is impossible and also unnecessary to conduct an absolute validation of a simulation program. The aim instead is to apply a developed validation method so that the simulation program is good enough to predict building performance for most situations with specific purposes. In this section, three validation methods are introduced along with a discussion of the advantages and disadvantages of each method. Some general ideas about the application of the validation methods are described. Finally, a brief summary is given for prior validation work. 44 In view of the increased use of building energy simulation programs, it has been long recognized that some form of validation is needed for the purpose of objective quality control. A number of attempts have been made over the last two decades to identify suitable validation procedures for building energy simulation programs. However, no standard validation procedures have been universally accepted. Judkoff et al. (1983) first attempted to document the three most commonly used validation methods of building energy simulation programs. These are analytical verification, comparative testing and empirical validation. In each method, results from one program are compared with results from other sources, as will be discussed in the following sections. Judkoff (1988) also summarized the advantages and disadvantages of the three validation methods, as shown in Table 23. Table 23. Advantages and Disadvantages of the three validation methods as from Judkoff (1988) Technique Advantages Disadvantages Comparative Relative test of model and solution process No input uncertainty Any level of complexity Inexpensive Quick, many comparisons possible No truth standard Analytical Test of numerical solution No input uncertainty Exact truth standard given the simplicity of the model Inexpensive No test of model Limited to cases for which analytical solutions can be derived Empirical Test of model and solution process Approximate truth standard within experimental accuracy Any level of complexity Measurement involves some degree of input uncertainty Detailed measurements of high quality are expensive and timeconsuming A limited number of data sites are economically practical 45 2.2.1 Analytical Verification In analytical verification, the output from a program, subroutine, or algorithm is compared to the result from a known analytical solution for isolated heat transfer mechanisms, under very simple boundary conditions. (Here, the term “analytical” means a mathematical model of reality that has an analytically determinable solution for a given set of parameters and boundary conditions.) Where test specifications have to be interpreted in some way by a user in the form of input data for a particular test program, differences may arise from different interpretations of the specifications. This has been shown in the past on several projects (Allen et al. 1985). Fortunately, these problems can be minimized in the case of analytical tests due to the simplified nature of the building zone specifications and the possibility of using idealized zone constructions. Analytical tests are (partly by necessity) simplified in nature and should usually be designed to allow only one particular feature to be tested at a time. This should allow not only the ability of the program to model particular features to be verified, but also the identification of particular model components or algorithms as the source of any problems. As noted above, in testing a building energy analysis program it is both the underlying algorithms of the code and their implementation that are tested. Inadequacies in both the algorithms or in their implementation (code bugs) can be the source of discrepancies. It is not possible to test the algorithms without implicitly testing their coding. Therefore developers can use analytical tests as a diagnostic tool to find bugs in the implementation as well as verify the operation of the various component models. 46 Being most abstracted from the full complexities of real building simulation problems, analytical testing has the advantage of offering the most certain form of reference or ‘truth’ model with which comparisons can be made. The nature of analytical testing also makes it only applicable to limited cases for which analytical solutions can be derived. Errors arising from the integrated performance of all the submodels and algorithms in a program are beyond the scope of an analytical test. 2.2.2 Comparative Testing In comparative testing, a program is compared to itself or to other programs that may be considered better validated or more detailed and, presumably, more physically correct. The comparative approach includes “sensitivity testing” and “intermodel comparisons”. Comparative testing cannot directly address the issue of a truth standard, but can be a very powerful way of identifying errors by doing many comparisons quickly and inexpensively. One comparative testing approach is parametric sensitivity analysis. It provides information on the influence of the uncertainties in the program’s input parameters. The other comparative testing approach is intermodel comparison. It involves checking the agreement of several different programs with different thermal solution and modeling approaches in a variety of representative cases. Cases for which the program predictions diverge indicate areas for further investigation. (Judkoff and Neymark 1995) Intermodel comparisons are useful in two aspects. Firstly, they provide a “useful” 47 evaluation in the case where one of the programs has already been the subject of rigorous validation. Secondly, they often highlight serious shortcomings in one or more of the programs. An important consideration in an intermodel comparison is the requirement for input equivalence. (Strachan 1993) 2.2.3 Empirical Validation In empirical validation, calculated results from a program, subroutine, or algorithm are compared to monitored data from a real structure, test cell, or laboratory experiment. Empirical validation is the most widely used technique for testing a simulation program, as it can be considered to be a conclusive test of whether model predictions reflect reality. In particular, whole model empirical validation ensures that the overall performance of the simulation program is tested. In this case, it is not only an individual process, but also the interaction of those processes that are tested. (Strachan 1993) Empirical validation offers an approximate truth standard within the accuracy of the data acquisition system and many parameter values that are on measurement. Also, empirical validation can be applied with any level of complexity. However, detailed, high quality measurements are usually expensive, difficult and timeconsuming, even for one or a few cases. Even if highquality experimental data sets are available for performing empirical validation and a program has performed satisfactorily, it is still difficult to generalize results from one particular combination of building type, climate and operating conditions to others. In addition, measurements of both building performance parameters 48 and program input parameters have a finite accuracy. The uncertainty in program input parameters (air change rates, material properties, occupant behavior etc.) leads to uncertainty in the program predictions that may be quite apart from the adequacy of the algorithms employed by the program. (Bloomfield 1989, 1999) 2.2.4 Application of the Validation Methods In any type of validation, three things are implicitly tested, each of which may contribute to the overall ‘error’ in the results (Rees, et al. 2002): • The interpretation of the input data • The model(s) or algorithm(s) • The computer implementation of the algorithm(s) A general principle applies to any type of validation method: the more realistic the test case, the more difficult it is to establish cause and effect, and to diagnose problems. The simpler and more controlled the test case, the easier it is to pinpoint the sources of error or inaccuracy. (Judkoff and Neymark 1995) In fact, the three validation methods may be used together in a number of ways. For example, analytical verification can be conducted at first to check the mathematical solution of major heat transfer models of a program. If discrepancy occurs, the source of the difference must be corrected before any further validation is done. Then, intermodel comparisons may be done in advance of an empirical validation to better define the experiment and to help estimate experimental uncertainty by propagating all known sources of uncertainty through one or several wholebuilding energy simulation programs. 49 2.2.5 Summary of Prior Validation Work Independent work on model validation started in the late seventies and early eighties, after the growth of popularity of energy simulation because of the 1973 energy crisis. Examples of the early work include Judkoff et al. (1980, 1981), IEA (1981), and Hoellwarth (1980), which showed significant disagreements between codes for very simple test cases. Over the last two decades, a number of organizations have attempted to identify suitable validation procedures for building energy simulation programs, e.g. NREL (Judkoff, et al. 1983; Judkoff and Neymark 1995), BRE (BRE 1988) and the IEA (Bloomfield et al. 1988). A good summary overview is found in Judkoff (1988) and Judkoff and Neymark (1995). Further updated validation/testing literature review is included in Ahmad (1997), Bloomfield (1999), and Judkoff and Neymark (2002). Much less emphasis has been placed on design load calculation procedures, perhaps since design load calculation methods have historically relied less heavily on computer implementation than annual energy calculation (Rees and Spitler 1999). A brief overview of published intermodel comparisons of cooling load calculation procedures is found in Spitler and Rees (1998). The Comité Européen De Normalisation (CEN) (1997) has developed a standard approach to load calculations. It consists of a set of heat balance equations and a set of qualification tests against which particular computer codes can be evaluated. The purpose of the tests is qualification to a certain standard of accuracy and not diagnosis of particular faults. The tests are based on a single test zone that is exposed to a combination of loads. The tests are varied by changing shading, internal loads, wall construction, 50 system controls, etc. In each case a number of submodels of the load calculation method are tested together. One notable attempt of intermodel comparison for design cooling load calculation methods has been completed as part of ASHRAE 942RP (Rees et al. 1998; Spitler and Rees 1998), which consists of a large number of test cases (of the order one thousand) where certain parameters are systematically varied. The comparison was primarily organized as a parametric study for three cooling load calculation procedures: the ASHRAE heat balance procedure, the ASHRAE radiant time series procedure, and the CIBSE admittance procedure. 18 different parameters describing different constructions, internal heat gains, zone dimensions and weather data were systematically varied for the comparison. Rees and Spitler (1999) also proposed a diagnostic test procedure for building loads, named BUILDTEST, in which the ASHRAE heat balance method is used as a reference model. A series of 25 simplified tests were devised to be used in intermodel comparisons with the reference model. The purpose of the tests is diagnosing deficiencies in the load calculation method and/or its implementation. This was done by subjecting the test zone to a particular type of heat gain or use a particular heat transfer path in turn, rather than using different combinations of loads. Thus the results are functions of either individual (or at most only a few) submodels alone and not the whole zone heat transfer model. As will be discussed in detail later in Chapter 5, Spitler et al. (2001) have developed an analytical verification test suite for building fabric models in whole 51 building energy simulation programs — ASHRAE 1052RP. The tests are intended to be used in support of ASHRAE Standard 140 ‘Standard Method of Test for Building Energy Analysis Software’ (ASHRAE 1998). The test suite consists of sixteen individual tests, each with the objective to test the ability of a building energy simulation program to model a particular heat transfer phenomena. The test is applied by comparing the output of the energy simulation program to be tested with the analytical solution for a special test zone. The data to be compared may be a single zone load, heat flux, temperature, or hourly loads over one or more days of output. More recently, experimental validation of both the ASHRAE heat balance method and radiant time series method has been done in test cells at Oklahoma State University (Chantrasrisalai, et al. 2003; Iu, et al. 2003). For the RHB method, no validation work has been done prior to this dissertation as it has just been developed in 2004. Analytical, intermodel, and experimental validation of RHB is highly desirable and therefore is the objective of this research. 52 3. OBJECTIVES The objectives of this research have been briefly outlined in the Introduction. In more detail, the task of validating a heat balance based residential cooling load calculation procedure is discussed below. Firstly, a literature review will be done for the RHB cooling load calculation procedure and validation methods of cooling load calculation program. For RHB, the subject of the validation work, the goal is to obtain an indepth comprehension of its basic structure and algorithm, theoretical principles and assumptions, and component models. This is very important as the testing, analyzing and diagnosing process involved in the validation work requires a full knowledge and familiarity of RHB. For validation methods, the goal is to identify possible methods and available tools for validating cooling load calculation programs. The literature review section has attempted to do this by introducing the RHB procedure and general validation methods. Another part of the literature review is a systematic review of candidate programs that could be used as intermodel comparison tool. This is covered under the section of selecting comparison tool in Chapter 4. Secondly, intermodel validation of ResHB, the reference computer implementation of the RHB procedure, will be performed. Intermodel validation requires the selection of a comparison tool. Therefore, a systematic review and comparison of 53 candidate building simulation programs, with regard to their capabilities of modeling residential buildings, will be made. Based on the review results, one program will be selected as the comparison tool. Modifications will be made to the selected comparison tool if necessary. A parametric analysis tool will be developed for systematic and automatic implementation of large amounts of intermodel comparisons for typical residences. The parametric analysis tool should be able to create input files, run simulations and process outputs of interest for the comparison tool automatically. Cooling loads calculated by ResHB will be compared to that calculated by the comparison tool. System design resulted from ResHB will also be evaluated by the detailed simulation with the comparison tool. Thirdly, analytical verification of ResHB will be conducted. The ResHB program will be tested with the Analytical Verification Test Suite for Whole Building Energy Simulation Programs  Building Fabric (ASHRAE 1052RP, Spitler, et al. 2001). Applicable analytical tests from the test suite will be applied and modifications of the input structure of ResHB will be made as needed. All the analytical tests completed will be used as a set of reference tests that can be run after each revision of ResHB, assisting diagnosis of any new problems that could possibly be introduced. Finally, experimental validation of the ResHB program will be done. Experimental data will be obtained from a wellinstrumented house located in Fort Wayne, IN. ResHB input files will be created for the house and ResHBcalculated cooling loads and room temperatures will be compared to measured data. 54 4. INTERMODEL VALIDATION OF THE HEAT BALANCE BASED RESIDENTIAL COOLING LOAD CALCULATION PROCEDURE As mentioned in the literature review, of the three types of validation methods, intermodel comparison cannot directly address the issue of a truth standard, but can be a very powerful way of identifying errors by doing many comparisons quickly and inexpensively. The intermodel validation desired and conducted for the Residential Heat Balance (RHB) cooling load calculation procedure is similar to the study performed by (Rees et al. 1998; Spitler and Rees 1998). It consists of a large number of test cases (of the order one thousand) where certain parameters are systematically varied. It is desirable that this type of intermodel comparison be made in a highlyautomated fashion, so that the RHB procedure can be tested and evaluated throughout the development cycle. How has this been implemented for the RHB procedure is discussed in the following sections, which include the selection of the comparison tool, the methodology employed and the comparison results obtained. 55 4.1 Selecting the Comparison Tool 4.1.1 Basic Requirements of the Comparison Tool In choosing the comparison tool, the following basic requirements regarding the code robustness, required features and/or feasibility of extension are considered. 1. Heat balance method The heat balance method is generally considered as the most scientifically rigorous method. It accounts for every energy flow in the most basic, fundamental way and does not impose any simplification on the solution technique (Strand et al. 1999), while other methods make many simplifying assumptions along the way from the initial model to the final procedure that the basic processes are essentially lost (Pedersen et al. 1997). Therefore, to supply intermodel validation of the new heat balance based residential cooling load calculation procedure, a heat balance based comparison tool is the best choice. A comparison tool with an approximate method will not be accurate and fundamental enough to serve as a reference in the intermodel validation. 2. Include welldeveloped models for most aspects of building load calculation Although modification and extension is expected if necessary, it would be best to choose a tool that requires a minimum amount of modification. Therefore, welldeveloped models for most aspects of building load calculation are desired in the selected tool. These aspects include: 56 • Transient heat conduction: Obviously, the detailed heat balance method needs a transient heat conduction model to account for the dynamic effects of the thermal mass on the zone loads. This is necessary for both exterior and interior/interzone walls. This requirement exists because the typical central located thermostat in residences cannot simultaneously control the temperatures in all rooms and the resultant temperature swings lead to interzone conduction. • Detailed convection model: Although there is sensitivity analysis showing that the effect of the outside convection coefficient on the cooling load is very low (McClellan and Pedersen 1997), the inside convection coefficient can be important (BeausoleilMorrison 2000). The comparison tool should be able to deal with a detailed convection model and permit variable convection coefficients. • Solar radiation/window shading: Solar gain is an important part of the cooling load, both that absorbed by opaque surfaces and that transmitted through fenestration. It may become even more important for residential buildings because the loads in residences are primarily from the building envelope and are greatly affected by outside conditions. Therefore, accurate models for solar radiation, fenestration and window shading are required in the comparison tool. • Detailed inside/outside long wave radiation: The simplified approaches that use a combined coefficient to predict the total convective and radiative gain on a surface mask their respective effects on zone loads and depart from the 57 heat balance principle. These models therefore should not be used in the comparison tool. Instead, a detailed inside/outside long wave radiation model is recommended. Long wave radiation from internal sources may have to be dealt with in the traditional way by defining a radiant/convective split. Although the surface temperature of the internal sources could be calculated based on the heat balance principle, it is difficult to predict their locations since occupants of the space may move them from time to time. • Infiltration and interzone airflow and mixing: In comparison to those in commercial or industrial buildings, zone load from infiltration is important for residential buildings because the internal heat gains in residences are relatively low. Interzone airflow and mixing is also an important feature required to model interzone thermal interaction. 3. Short time step Usually, onehour time steps are used in energy simulation programs. But short time steps may be necessary in the comparison tool if system on/off behavior is modeled. Shorter time steps are already available in several simulation tools. 4. Flexible HVAC system simulation/control tool The comparison tool should permit the “masterslave” zone control feature of residences. From the HVAC system simulation concept, it would be good to realize an integrated simultaneous simulation, so that feedback from system response can be seen by the zone load procedure. But for the validation of a load calculation method that aims to be the basis of system design and equipment sizing, this may not be necessary. Instead, 58 an idealized representation of the system may be sufficient. E.g., a system control profile based on zone temperature and system capacity may be satisfactory for this application. 5. Convenient to be modified or extended If necessary, extension or modification of the selected comparison tool is expected. Therefore, a welldocumented and wellorganized source code of the selected program is desired. As to the program language, Fortran 90 is preferred, with Fortran 77 being a second choice. 6. Source code availability The status of the source code availability, or the cost to obtain the source code is another condition that limits the choice of the programs. Since the research project funding is limited, it is preferred to keep the cost of the source code reasonably low. 7. Status of the program validation The comparison tool needs to be validated as it is used as a reference. With everything else being equal, the program that has been best validated should be chosen. Even with other advantages, fatal errors that cannot be fixed will eliminate the program from consideration. 8. Support It’s important that technical support of the selected comparison tool is available since help from the original developer usually saves time. 59 Among the basic requirements discussed above, some features are necessary, some features may be necessary, while other features are desirable. Table 41 summarizes the classification of these features. Consideration should be given to distinguish these features in choosing the comparison tool. Table 41 Classification of basic requirements for candidate comparison tools Basic requirements Necessary May be necessary Desirable Heat balance method X Transient, insideoutside/interzone heat conduction X Detailed convection model X Solar radiation/window shading X Detailed inside/outside long wave radiation X Include welldeveloped model for most aspects of building load calculation Infiltration and interzone airflow/mixing X Short time step X Flexible HVAC system simulation/control tool X Convenient to be modified or extended X Source code availability X Program validation X Support X 4.1.2 Review of Candidate Programs With the basic requirements for the comparison tool discussed above, a systematic review of candidate computer programs is needed. Although we are looking for a detailed load calculation program, the unique features of residential load calculation and hence the specific requirements of the comparison tool make it necessary to look into a range of whole building simulation tools in terms of their system simulation and control possibilities. 60 Generally speaking, two types of building simulation tools are in use today: generalpurpose tools and special purpose tool 



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