INTERACTION BETWEEN THERMAL COMFORT AND HVAC ENERGY CONSUMPTION IN COMMERCIAL BUILDINGS by ALIREZA TAGHI NAZARI B.A.Sc., Khaje Nasir Toosi University of Technology, 2005 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) February 2008 ©Alireza Taghi Nazari, 2008 ii ABSTRACT The primary purpose of the current research was to implement a numerical model to investigate the interactions between the energy consumption in Heating, Ventilating, and Air Conditioning (HVAC) systems and occupants’ thermal comfort in commercial buildings. A numerical model was developed to perform a thermal analysis of a single zone and simultaneously investigate its occupants’ thermal sensations as a non-linear function of the thermal environmental (i.e. temperature, thermal radiation, humidity, and air speed) and personal factors (i.e. activity and clothing). The zone thermal analyses and thermal comfort calculations were carried out by applying the heat balance method and current thermal comfort standard (ASHRAE STANDARD 55-2004) respectively. The model was then validated and applied on a single generic zone, representing the perimeter office spaces of the Centre for Interactive Research on Sustainability (CIRS), to investigate the impacts of variation in occupants’ behaviors, building’s envelope, HVAC system, and climate on both energy consumption and thermal comfort. Regarding the large number of parameters involved, the initial summer and winter screening analyses were carried out to determine the measures that their impacts on the energy and/or thermal comfort were most significant. These analyses showed that, without any incremental cost, the energy consumption in both new and existing buildings may significantly be reduced with a broader range of setpoints, adaptive clothing for the occupants, and higher air exchange rate over the cooling season. The effects of these measures as well as their combination on the zone thermal performance were then studied in more detail with the whole year analyses. These analyses suggest that with the modest increase in the averaged occupants’ thermal dissatisfaction, the combination scenario can notably reduce the total annual energy consumption of the baseline zone. Considering the global warming and the life of a building, the impacts of climate change on the whole year modeling results were also investigated for the year 2050. According to these analyses, global warming reduced the energy consumption for both the baseline and combination scenario, thanks to the moderate and cold climate of Vancouver. iii TABLE OF CONTENTS Abstract ………………………………………………………………………………………..… ii Table of Contents ……………………………………………………………………………….. iii List of Tables …………………………………………………………………………………... vii List of Figures …………………………………………………………………………………. viii List of Abbreviations ………………………………………………………………………….... xi List of Symbols …………………………………………………………………………...…..... xii List of Greek Symbols ……………………………………………………………………….. xviii Acknowledgments …………………………………………………………………………….... xx 1. Introduction …………………………………………………………………………………… 1 1.1. Background and Hypothesis .………………………………………..………………. 1 1.2. Literature Review …………………………………………………………………… 2 1.2.1. Heat Balance Method ………………...…………………………………… 2 1.2.2. Thermal Comfort …………………………………………………….….… 4 1.2.3. Interactions of Energy Consumption and Thermal Comfort in Buildings ... 7 1.3. Objectives and Scope of Work ……………………………………………..…..…… 7 2. Formulation and Structure of the Numerical Model ………………………………...….…….. 9 2.1. Introduction …………………………………………………….………………..….. 9 2.2. Heat Balance Model …………………………………………………….……….….. 9 2.2.1. Heat Balance Method on the External Opaque Surfaces ……………….... 10 2.2.2. Heat Balance Method on the Transparent Surfaces …………………...…. 11 2.2.3. Heat Balance Method on the Internal Opaque Surfaces …...……….……. 13 2.2.4. Heat Balance Method on the Zone Air ….............................……….……. 13 2.2.4.1. Sensible Heat Balance on the Zone Air …...……….………..…. 14 2.2.4.2. Latent Heat Balance on the Zone Air ……………………….…. 15 2.3. Thermal Comfort Model ……………...……………………………………………. 16 2.4. Validations ….…………………………...…………………………………………. 17 3. Results and Discussion ………………………………………………………………………. 19 3.1. Introduction ………………………………………………………………………... 19 3.2. Screening Analyses …...……………………………………………………………. 22 iv 3.2.1. Increasing the Range of Setpoints ……………………………..………… 26 3.2.2. Floor Slab Cooling/Heating .……………………………………..……… 27 3.2.3. Increasing the Zone Air Speed ……………………………...…………… 28 3.2.4. Changing the Glazing System ….…………………...…………………… 29 3.2.5. Removing the Vertical Fins ….……………………………………..……. 31 3.2.6. Removing the Horizontal Overhang …………………………..………… 33 3.2.7. Increasing the Zone Thermal Mass ……………………………………… 33 3.2.8. Increasing the Insulation Thickness …………………………………...… 34 3.2.9. Increasing the Infiltration Rate ……………...…………...………………. 35 3.2.10. Relocating the Baseline Zone to the South Façade ……………..……… 36 3.2.11. Relocating the Baseline Zone to the West Façade .…………..………… 38 3.2.12. Relocating the Baseline Zone to the North Façade …………………….. 41 3.2.13. Adaptive Clothing ……………………………………………………… 42 3.2.14. Adjusting the Occupancy Period ………………………….……………. 43 3.3. Whole Year Analyses …………………………………...…………………………. 43 3.3.1. Increasing the Range of Setpoints ………………….……………………. 47 3.3.2. Adaptive Clothing ……………………………………………………..…. 48 3.3.3. Increasing the Air Exchange Rate over the Cooling Season ………….…. 49 3.3.4. Combination Scenario …………………………………………………… 51 3.4. Climate Change ……………………………………………………………………. 53 3.4.1. Combination Scenario …………………………………………………… 56 4. Conclusions and Future Work …………………………………….…………………………. 60 4.1. Conclusions ………………………………………………………………………... 60 4.2. Future Work ……………………………………………………………………..…. 63 References …………………………………………………….………………………..………. 65 Appendix One: Heat Balance Method on the External Opaque Surfaces …………………...…. 71 A1.1. Introduction ……………………………………………………………………… 71 A1.2. Case One: Grid Points inside Slabs ……………………………………………… 72 A1.3. Case Two: Grid Points on the Boundary of Two Adjacent Slabs …………..…… 74 A1.4. Case Three: Grid Point on the Exterior Surface …………………………………. 76 A1.4.1. External Shortwave Solar Radiation …………………...………………. 76 v A1.4.2. External Longwave Radiation …………………………….…………… 83 A1.4.3. External Convection …………………………………………………… 85 A1.5. Case Four: Grid Point on the Interior Surface …………………………...………. 89 A1.5.1. Longwave Radiation between Surfaces ………………..………………. 90 A1.5.2. Radiation from Internal Heat Gains …………………………………… 92 A1.5.3. Transmitted Solar Radiation ………………………...…………………. 92 A1.5.4. Internal Convection …………………………………….……………… 95 Appendix Two: Heat Balance Method on the Transparent Surfaces …………………...……… 98 Appendix Three: Heat Balance Method on the Internal Opaque Surfaces …………………… 104 Appendix Four: Heat Balance Method on the Zone Air ……………………………………… 107 A4.1. Sensible Heat Balance on the Zone Air ………………………...………………. 107 A4.1.1. Convection from the Zone Interior Surfaces ….……………………… 107 A4.1.2. Convection from the Internal Heat Gains ….…………………………. 108 A4.1.3. Sensible Infiltration …………………...……………………………… 108 A4.1.4. Sensible Heat Insertion Rate from the HVAC System …………….…. 110 A4.1.4.1. Maintaining a Fixed Zone Air Temperature …..……………. 111 A4.1.4.2. No Control on the Zone Air Temperature ……………..…… 111 A4.1.4.3. Maintaining the Zone Air Temperature between the Heating and Cooling Setpoints …………………………...………………………… 111 A4.2. Latent heat balance on the zone air …………………………………………..…. 113 A4.2.1. Latent Internal Heat Gain ………………………………..…………… 114 A4.2.2. Latent infiltration ……………………..………………………………. 114 A4.2.3. Humidification Rate from the HVAC System ………………………... 115 A4.2.3.1. Maintaining a fixed zone air Humidity Ratio …………….… 115 A4.2.3.2. No Control on the Zone Air Humidity Ratio ……………….. 115 A4.2.3.3. Maintaining the Zone Air Humidity Ratio in the Specific Range ……………………………………….………………………… 115 Appendix Five: Thermal Comfort Model …………………………………………...………... 118 A5.1. Heat Balance Method on a Body …………………………………………….… 118 A5.1.1 Sensible Heat Loss from Skin ………………………………………… 119 A5.1.2. Latent Heat Loss from Skin ………………………………………….. 123 vi A5.1.3. Total Heat Loss through Respiration …………………………………. 124 A5.2. PMV-PPD Model …………………………………………………………….… 125 A5.3. Local Thermal Discomfort …………………………………………………...… 127 A5.3.1. Radiant Temperature Asymmetry …………………………….……… 127 A5.3.2. Draft ……………………..……………………………………………. 128 A5.3.3. Vertical Air Temperature Difference …………………………………. 128 A5.3.4. Floor Surface Temperature ……………………………………...……. 128 Appendix Six: Validations of the Main Individual Modules ……………………………….… 130 A6.1. Conduction Process through the External Opaque Surfaces …………………… 130 A6.1.1. Transient Conduction with Heat Generation inside the Control Volume …………………………………………………………...…………… 130 A6.1.2. Transient Conduction in Semi-Infinite Solid …………………………. 132 A6.2. Calculations of the View Factors and the Mean Radiant Temperature ……….... 133 A6.3. Thermal Comfort Model …………………………………………..……………. 136 Appendix Seven: Whole Model Validation with IES<VE> …………………..……………… 138 vii LIST OF TABLES Table 3.1. General specifications of the baseline zone ………………...………………………. 20 Table 3.2. Thermal properties of the baseline zone opaque surfaces ………………...……….... 21 Table 3.3. Thermal and optical properties of the baseline glazing system ……………..……… 21 Table 3.4. The results of the screening analyses for the typical summer and winter days …….. 25 Table 3.5. Specifications of the alternative glazing system for the CIRS offices …………...… 30 Table 3.6. The results of the whole year analyses …………………………………………….... 46 Table 3.7. The results of the whole year analyses for the current time and 2050 ……………… 57 Table 4.1. Measures with the highest impact on energy and thermal comfort ………………… 61 Table 4.2. The final results of the whole year analyses ……………………………………...… 63 Table A1.1. Convection correlation coefficients ………………………………………………. 87 Table A1.2. Surface roughness multipliers …………………………………………………….. 87 Table A1.3. Convection heat transfer coefficients on interior surfaces ……………………...… 95 Table A5.1. Specification of the typical office clothing ensembles ………………………….. 122 Table A5.2. Allowable Radiant Temperature Asymmetry …………………………………… 127 Table A6.1. Computed grid points’ temperatures with different analyses …………………… 131 Table A6.2. Energy conservation analyses of the numerical model ………………………….. 132 Table A6.3. The effect of improving the size of the time-step on the results ………………… 133 Table A6.4. The Effect of refining the mesh on the results ………………………………...…. 133 Table A6.5. View factor and imaginary interior temperature of different zone surfaces …….. 135 Table A6.6. The plane and mean radiant temperatures ……………………………………….. 136 Table A6.7. Values used to generate the comfort envelope on the psychometric chart ……… 136 viii LIST OF FIGURES Figure 1.1. Commercial sector energy consumption by end use in Canada ………..…………… 1 Figure 2.1. Transient heat fluxes that affect the external opaque surfaces ……………..……… 11 Figure 2.2. Transient heat fluxes that affect a double-pane window ………………...………… 12 Figure 2.3. Transient heat fluxes that affect the internal opaque surfaces ……………...……… 13 Figure 2.4. Sensible transient heat fluxes that affect the zone air ………………...…….……… 14 Figure 2.5. Latent transient heat fluxes that affect the zone air ………………...………………. 16 Figure 3.1. The schematic of the baseline zone ………………...………………………………. 19 Figure 3.2. The climate data for the typical summer and winter days of Vancouver ……..…… 22 Figure 3.3. The baseline thermal performance over the typical summer and winter days …….. 23 Figure 3.4. Increasing the range of setpoints over the typical summer day ……………….…… 26 Figure 3.5. Increasing the range of setpoints over the typical winter day ………………...…… 27 Figure 3.6. Floor slab cooling over the typical summer day ….……………...……………...…. 28 Figure 3.7. Floor slab cooling over the typical winter day .………………...………………..… 29 Figure 3.8. Increasing the zone air speed ………………...…………………………………..… 30 Figure 3.9. Using the alternative glazing system over the typical winter day …………………. 31 Figure 3.10. Removing the vertical fins over the typical summer day ………………………… 32 Figure 3.11. The lower glazing system thermal performance without the vertical fins over the typical summer day ………………...………………………………………………………...… 32 Figure 3.12. Increasing the zone thermal mass over the typical summer day …...…………….. 34 Figure 3.13. Increasing the air exchange rate over the typical summer day (zone air temperature) ……………...…………………………………………………………………….. 35 Figure 3.14. Increasing the air exchange rate over the typical summer day (occupants’ thermal sensations) ………………...……………………………………………………………………. 36 Figure 3.15. Increasing the air infiltration rate over the typical winter day ……………………. 37 Figure 3.16. Having the zone on the south facade over the typical summer day ……………..... 38 Figure 3.17. Having the zone on the south facade over the typical winter day ……………….... 39 Figure 3.18. Having the zone on the west facade over the typical summer day ……………….. 40 Figure 3.19. Having the zone on the west facade over the typical winter day …………………. 40 Figure 3.20. Having the zone on the north facade over the typical summer day …………….… 41 ix Figure 3.21. Adaptive clothing over the typical summer and winter days ……………..……… 42 Figure 3.22. The monthly averaged CWEC climate data of Vancouver .……………………… 44 Figure 3.23. Baseline slab energy consumption over the whole year (Histogram) ……………. 44 Figure 3.24. Baseline slab energy consumption over the whole year (Daily) ……………….… 45 Figure 3.25. Baseline thermal comfort indicators over the whole year (Histogram) ………..… 46 Figure 3.26. Energy consumption with a broader range of setpoints over the whole year (Histogram) …………………………………………………………………………………….. 47 Figure 3.27. Energy consumption with a broader range of setpoints over the whole year (Daily) ………………...………………………………………………………………………... 48 Figure 3.28. Thermal comfort indicators with a broader range of setpoints over the whole year (Histogram) ………………...…………………………………………………………………... 48 Figure 3.29. Thermal comfort indicators with adaptive clothing over the whole year (Histogram) ………………...………………………………………………………………...… 49 Figure 3.30. Energy consumption with higher air exchange rate (Histogram) ……………….... 50 Figure 3.31. Energy consumption with higher air exchange rate (Daily) ……………………… 50 Figure 3.32. Thermal comfort indicators with higher air exchange rate (Histogram) ……….… 51 Figure 3.33. Energy consumption with the combination scenario over the whole year (Histogram) ………………...………………………………………………………………...… 52 Figure 3.34. Energy consumption with the combination scenario over the whole year (Daily) .. 52 Figure 3.35. Thermal comfort indicators with the combination scenario over the whole year (Histogram) ………………...………………………………………………………………….... 53 Figure 3.36. Increase in the effective CO2 concentration, based on the IPCC IS92a scenario … 54 Figure 3.37. The effects of climate change on the amount of solar radiation and dry-bulb temperature ………………...…………………………………………………………………... 55 Figure 3.38. Energy consumption with climate change over the whole year (Histogram) ……. 55 Figure 3.39. Energy consumption with climate change over the whole year (Daily) …………. 56 Figure 3.40. Thermal comfort indicators with climate change over the whole year (Histogram) ………………………………………………………...………………...………… 57 Figure 3.41. Energy consumption with climate change and combination scenario over the whole year (Histogram) ………………...……………………………………………………………... 58 x Figure 3.42. Energy consumption with climate change and combination scenario over the whole year (Daily) ………………...…………………………………………………………………... 58 Figure 3.43. Thermal comfort indicators with climate change and combination scenario (Histogram) ………………...…………………………………………………………………... 59 Figure A1.1. Case One: Grid points inside slabs .………………...……………………………. 72 Figure A1.2. Case Two: Grid points on the boundary of two adjacent slabs ………………….. 75 Figure A1.3. Transient heat fluxes on the exterior surfaces of a building ……………………... 77 Figure A1.4. Different solar angles between the sun and a surface in an arbitrary direction ….. 78 Figure A1.5. Vancouver CWEC climate data for January 1st ………………………………..… 83 Figure A1.6. Case Three: Grid point on the exterior surface of a building ……………………. 88 Figure A1.7. Transient heat fluxes on the interior surfaces of a building …………………….... 89 Figure A1.8. Glazing system with external shadings ………………...……………………….... 94 Figure A1.9. Case Four: Grid point on the interior surface of a building ……………………… 96 Figure A2.1. Heat fluxes on the exterior pane of a glazing system …………………………... 101 Figure A2.2. Heat fluxes on the interior pane of a glazing system …………………………… 102 Figure A5.1. Analytical formulas for calculating angle factor for small plane element …….... 121 Figure A6.1. The thermal properties and the convection boundary conditions of the plane wall ………………...………………………………………………………………………….. 131 Figure A6.2. Grid study on the explicit finite difference method …………………………….. 134 Figure A6.3. The schematic of the generic zone ………………...……………………………. 134 Figure A6.4. View factors of the south and east windows ………………...………………….. 135 Figure A6.5. The numerical model vs. the current thermal comfort standard ……………...… 137 Figure A7.1. The hourly climate data for the 15th of August and January ……………………. 139 Figure A7.2. The numerical model vs. IES<VE> ………………...…………………………... 140 xi LIST OF ABBREVIATIONS ACH Air Change per Hour ANSI American National Standards Institute ASHRAE American Society of Heating, Refrigerating and Air-Conditioning Engineers BLAST Building Loads Analysis and System Thermodynamics CFM Cubic Feet per Minute CIRS Centre for Interactive Research on Sustainability CERL Construction Engineering Research Laboratory CRCM Canadian Regional Climate Model CWEEDS Canadian Energy and Engineering Data Sets CWEC Canadian Weather for Energy Calculations DOE Department of Energy EOT Equation of Time HVAC Heating, Ventilation and Air Conditioning IPCC Intergovernmental Panel on Climate Change LST Local Solar Time LCT Local Civil Time NBSLD National Bureau of Standards Load Determination PMV Predicted Mean Vote PPD Predicted Percentage of Dissatisfaction TARP Thermal Analysis Research Program xii LIST OF SYMBOLS DA Nude body surface area [m 2] eosA Area of an external opaque surface [m 2] fsA Area of the fictitious surface [m 2] gA Area of a glazing system [m 2] iA Area of an internal surface [m 2] skyA Area of the Sky [m 2] ,sl gA Sunlit Area of a glazing system [m 2] c Specific heat capacity [J/kg.K] C Ratio of diffuse solar irradiation to direct normal solar irradiation, dimensionless NC Atmospheric clearness number, dimensionless ,p outC Specific heat capacity of the outdoor air [J/kg.K] , ,p out airC Specific heat capacity of dry air at constant pressure, 1000 [J/kg.K] , ,p out waterC Specific heat capacity of water vapor at constant pressure, 1860 [J/kg.K] clo Clothing level clf Clothing area factor, dimensionless convF Convective fraction, dimensionless seF View factor of the sky to the external opaque surface, dimensionless esF View factor of the external opaque surface to the sky, dimensionless egF View factor of the external opaque surface to the ground, dimensionless radF Radiative fraction, dimensionless dG Diffuse solar irradiation [W/m 2] DG Direct solar irradiation [W/m 2] NDG Normal direct solar irradiation [W/m 2] RG Reflected solar irradiation [W/m 2] xiii tG Total solar irradiation [W/m 2] H Hour angle [deg] k Thermal conductivity [W/m.K] cclh Convective heat transfer coefficient on the outer clothing surface [W/ m 2.K] ,conv exth Exterior convection heat transfer coefficient [W/m 2.K] , ,conv in sh Interior convection heat transfer coefficient [W/m 2.K] eh Evaporative heat transfer coefficient [W/m 2.kPa] nh Natural convection component [W/m 2.K] fh Forced convection component [W/m 2.K] 2,fg H O h Enthalpy of the evaporation of water at 0˚ C, 2.5e6 [J/kg] ,LWrad inh Longwave radiation coefficient on an interior surface [W/m 2.K] rclh Radiative heat transfer coefficient on the outer clothing surface [W/ m 2.K] cli Clothing vapor permeation efficiency, dimensionless exi Exhaust air enthalpy [J/kg] ini Zone air enthalpy [J/kg] l Height [m] L Latitude [deg] iosL Thickness of the internal opaque surface [m] LL Longitude [deg] SL Standard Meridian [deg] LR Lewis ratio constant, dimensionless m Weight [kg] am Mass of dry air [kg] am Mass flow rate of the infiltrating air [kg/s] vm Mass of water vapor [kg] resm Pulmonary ventilation rate [kg/s] M Rate of metabolic heat production [W/m2] xiv aM Molecular weight of dry air, equal to 28.97 [kg/kmol] vM Molecular weight of water vapor, equal to 18.02 [kg/kmol] p Indicator of time P Atmospheric pressure from the CWEC weather files [Pa] aP Partial pressure of dry air [Pa] HP Horizontal projection [m] ,sk sP Water vapor pressure at skin [kPa] vP Vertical projection [m] ,v aP Water vapor pressure in the outdoor air [kPa] ,v inP Partial pressure of water vapor in the zone air [kPa] ,v outP Partial pressure of water vapor in the outdoor air [Pa] draftPD Percent dissatisfied due to draft, percentage ,conv extq Convection heat flux from the exterior surface to the outdoor air [W/m 2] , ,conv in sq Convection heat flux from the indoor air to the interior of surface [W/m 2] groundq The net longwave radiation heat flux from the surface to the ground [W/m 2] , ,LW rad extq Net longwave radiation heat flux from the exterior surface [W/m 2] , ,LW rad inq Net longwave radiation to the interior of surface [W/m 2] ,rad Sihgq Total radiation heat flux from internal heat gains [W/m 2] skyq The net longwave radiation heat flux from the surface to the sky [W/m 2] ,solar floorq Solar radiation absorbed by the floor [W/m 2] ,solar inq Solar radiation absorbed by the zone interior surfaces (except the floor) [W/m 2] , ,SW solar extq Absorbed shortwave solar radiation [W/m 2] ,TSHG Dq Total transmitted direct solar radiation [W] ,TSHG dq Total transmitted diffuse solar radiation [W] ,Wsolar eq Total solar radiation absorbed by the exterior pane [W/m 2] xv ,Wsolar iq Total solar radiation absorbed by the interior pane [W/m 2] ,Wsolar pq Total solar radiation absorbed by a single pane glazing system [W/m 2] ,Wsolarb eq Inside-to-outside solar radiation absorbed by the exterior pane [W/m 2] ,Wsolarf eq Outside-to-inside solar radiation absorbed by the exterior pane [W/m 2] ,Wsolarf iq Inside-to-outside solar radiation absorbed by the interior pane [W/m 2] ,Wsolarf iq Outside-to-inside solar radiation absorbed by the interior pane [W/m 2] q Internal heat generation [W/m3] ,conv inQ Total convection heat fluxes from all the interior surfaces [W] ,L ihgQ Total humidification rate from internal heat gains [W] ,L infiltrationQ Total humidification rate due to infiltration [W] ,L systemQ Total humidification rate from the HVAC system to the zone air [W] ,L equipmentQ Total latent heat gain from equipment [W] ,L peopleQ Total latent heat gain from people [W] LresQ Latent respiration heat loss [W/m 2] LskinQ Latent heat loss from skin [W/m 2] maxLskinQ Maximum latent heat loss from the skin [W/m 2] LsweatQ Evaporative heat loss by regulatory sweating [W/m 2] resQ Total heat loss through respiration [W/m 2] ,S infiltrationQ Total sensible infiltration load [W] ,S peopleQ Total sensible heat gain from people [W] lightingQ Total heat gain from lighting [W] ,S equipmentQ Total sensible heat gain from equipment [W] ,S systemQ Heat insertion from the HVAC system to the zone air [W] ,Sihg convQ Total convection heat flux from internal heat gains [W] ,Sihg convQ Total sensible convection heat flux from internal heat gains [W] xvi SresQ Sensible respiration heat loss [W/m 2] SskinQ Sensible heat loss from skin [W/m 2] aR Dry air gas constant, 287 [J/kg.K] clR Thermal resistance of clothing [m 2.K/W] ,e clR Evaporative heat transfer resistance of clothing layer [m 2.kPa/W] fR Surface roughness multiplier, dimensionless WS Shadow width [m] HS Shadow height [m] clT Clothing surface temperature [K] dT θ Diffuse transmissivity, dimensionless DT θ Direct transmissivity at incident angle ofθ , dimensionless esT Exterior surface temperature [K] fsT Temperature of the fictitious surface [K] gT Ground surface temperature [K] inT Indoor air temperature [K] isT Interior surface temperature [K] IACT Interior solar attenuation coefficient, dimensionless outT Outdoor air temperature [K] rT Mean radiant temperature [K] setCT Cooling setpoint temperature [K] setHT Heating setpoint temperature [K] skT Skin surface temperature [K] skyT Effective sky temperature [K] ,sky HorzT Effective sky temperature for a horizontal surface [K] ,skyT Σ Effective sky temperature for a tilt surface [K] xvii Tu Turbulence intensity, percentage airspaceU Thermal conductance of the air spaces [W/m 2.K] V Air velocity inside the zone [m/s] windV Wind speed at standard condition [m/s] zoneV Zone volume [m 3] outw Outdoor air humidity ratio [kgwater/kgDryair] inw Zone air humidity ratio [kgwater/kgDryair] minw Minimum zone air humidity ratio [kgwater/kgDryair] maxw Maximum zone air humidity ratio [kgwater/kgDryair] W Rate of mechanical work accomplished [W/m2] xviii LIST OF GREEK SYMBOLS α Thermal diffusivity [m2/s] ,df eα Diffuse absorptivity of an exterior pane, dimensionless ,df iα Diffuse absorptivity of an interior pane, dimensionless ,D f eθα Direct absorptivity of an exterior pane at the incident angle ofθ , dimensionless ,D f iθα Direct absorptivity of an interior pane at the incident angle ofθ , dimensionless solα Solar absorptivity, dimensionless β Solar altitude angle [deg] δ Sun’s declination angle [deg] ε Exterior surface emissivity, dimensionless iε Interior surface emissivity, dimensionless fsε Emissivity of the fictitious surface, dimensionless φ Solar azimuth angle [deg] γ Surface-solar azimuth angle [deg] λ Angle between the normal of the fin and the normal of the glazing surface [deg] θ Solar incident angle [deg] ρ Density [kg/m3] airρ Density of the outdoor air [kg/m3] gρ Reflectance of the ground, dimensionless σ Stefan-Boltzmann constant [W/m2K4] siς Kronecker delta ,df eτ Diffuse transmissivity of an exterior pane, dimensionless ,D f eθτ Direct transmissivity of an exterior pane at the incident angle ofθ , dimensionless Γ Thermal load on a body [W/m2] LΛ Latent proportional constant [W/K] SΛ Sensible proportional constant [W/K] xix Σ Surface tilt angle [deg] Ψ Surface azimuth angle [deg] xx ACKNOWLEDMENTS First and foremost, I would like to take this opportunity to express my sincere gratitude and appreciation to Dr. Steven Rogak for taking me under his wing during the past two years. His invaluable technical and editorial advice, suggestions, discussions and guidance were a real support to complete this thesis. I would also like to thank Dr. Nima Atabaki for generously sharing his knowledge of heating, ventilation and air conditioning. I am also thankful to Dr. John Robinson, the Professor in the Institute for Environment, Resources and Sustainability, for his warm support on the Centre for Interactive Research on Sustainability (CIRS) project. Furthermore, special thanks to BC Hydro and NSERC for their financial support and their endorsement of the project. Thanks to Steve Cao, Graham Henderson, Bojan Andjelkovic, and Elizabeth Johnston at BC Hydro, Power Smart Engineering. Finally, I would like to express my love to my parents Maryam and Nader for their support and encouragement. They had more faith in me than could ever be justified by logical argument. 1 Chapter One: Introduction 1.1. Background and Hypothesis Some of the major impacts of excessive energy use are: escalating cost of fuel, rapid increase in greenhouse gas emissions, climate change, acid rain, and poor air quality. These are all among the imminent threats to humanity and need urgent consideration by governments, businesses, and individuals. Energy Information Administration (2007) reported that with 460 [GJ/year/person] Canada was among the major energy consumers per capita in the world in 2005. The total energy consumption in Canada in 2005 was 15 [EJ] (Energy Information Administration 2007). Approximately, 13% of this amount is allocated to the commercial sector (Cuddihy et al. 2005). The breakdown of energy consumption in this sector is shown in Figure 1.1. Figure 1.1. Commercial sector energy consumption by end use in Canada (Cuddihy et al. 2005). The energy consumption for space heating/cooling in the commercial sector in Canada is just about the annual energy consumption of over 25 million vehicles. Space Cooling 5% Lighting 15% Auxiliary Motor and Equipment 20% Water Heating 7% Space Heating 53% 2 As illustrated in the previous Figure, roughly 60% of the total energy consumption in the commercial sector in Canada is being used by Heating, Ventilation and Air Conditioning (HVAC) systems to provide what is now regarded as an acceptable standard of thermal comfort. The current comfort standard (ANSI/ASHRAE STANDARD 55-2004) specifies the combinations of indoor thermal environmental and personal factors that will produce interior thermal environments acceptable to at least 80% of the occupants within the space. The environmental factors addressed in this standard are temperature, thermal radiation, humidity, and air speed; the personal factors are those of activity and clothing. Based on this standard, the occupants’ satisfaction with the thermal environment responds to the interactions of all these factors, rather than just the zone air temperature, which is usually the only parameter used in sizing the HVAC equipment. Therefore, it is expected that understanding these interactions may result in a significant reduction in HVAC energy consumption while still producing thermally comfortable conditions for the occupants. To investigate these interactions in detail, an accurate computational model is required. The model not only needs to do the detailed thermal analysis of a building but it should also be capable of calculating occupants’ thermal sensations as a non-linear function of the thermal environmental and personal factors. The next section discusses the previous work that has been conducted in each of these two fields and ultimately on their interactions. 1.2. Literature Review 1.2.1. Heat Balance Method Among various approaches for building thermal analysis, the heat balance method has the potential to be the most accurate one because it accounts for all energy flows in their most fundamental form and has the least number of simplifications on the solution technique (Strand et al. 1999). The application of the heat balance method to building thermal physics requires that the First Law of Thermodynamics be enforced at each building element/air interface and on a control volume around the zone air mass (Pedersen et al.1997). 3 The concept of applying this method to buildings is certainly not a new approach in the field of building thermal simulations. The first implementation of the heat balance method was in National Bureau of Standards Load Determination (NBSLD) program (Kusuda 1976). This program implemented the heat balance technique to perform a thermal analysis for a single zone, which might represent a room or an entire building. With this analysis it was possible to determine the cooling load when the zone air temperature was kept constant, as well as to determine the zone air temperature when the cooling system was turned off or when the cooling system capacity was excessive or short of the cooling requirements. Although NBSLD was originally developed to calculate the design cooling load, it was modified in the early 1980’s, for the annual energy calculation of a single zone with a simple HVAC system (Kusuda 2001). Later, Walton (1983) applied the detailed heat balance method and developed the Thermal Analysis Research Program (TARP) to investigate the thermal performance of a building with more than one zone. Walton (1981) also implemented a novel extension of an air infiltration prediction technique in this research tool to model the air-movement between the adjacent zones. One of the main applications of the heat balance method was in the Building Loads Analysis and System Thermodynamics (BLAST) program (Building Systems Laboratory. 1999; Hittle 1977). Originating from NBSLD and TARP, this program was developed by the U.S. Army Construction Engineering Research Laboratory (CERL) in 1977. It was then sponsored by the U.S. Department of Defense for two decades. The last version of BLAST, released in 1997, was a comprehensive set of programs capable of performing the design load calculations as well as predicting energy consumption and energy system performance of a building with any type, size and design (Building Systems Laboratory. 1999; Crawley et al. 2005). After twenty years of expanding BLAST capabilities, its further improvement became difficult, time-consuming, and expensive. Thus, in 1996, the U.S. federal agencies began developing EnergyPlus as a new building energy simulation program based on the most popular features and capabilities of BLAST. The main priority of EnergyPlus over BLAST was its integrated (simultaneous loads and systems) simulation model for accurate temperature prediction. This was crucial for system and plant sizing as well as occupants’ comfort and health calculations 4 (Crawley et al. 2001, 2004; Strand et al. 2001). The integrated simulation model also allowed users to investigate a number of processes that were not possible to simulate with BLAST. Some of the more important ones are: realistic system controls, moisture adsorption and desorption in building elements, radiant heating and cooling systems, and interzone air flow. The first version of EnergyPlus was released in April 2001. In addition to the previous building energy simulation programs, the heat balance technique has also been applied in BSim, DeST, Ener-Win, ESP-r, HEED, IES <VE>, TAS, and TRANSYS to perform buildings’ thermal analysis, design load and energy calculations, economic cost assessment, and a life-cycle cost analysis (Jiang 1982, Hong and Jiang 1997, Chen and Jiang 1999, Zhu and Jiang 2003, Rode and Grau 2003, Degelman 1990, ESRU 2005, Clarke 2001, IES <VE>, EDSL 1989, Klein et al. 2004, Crawley et al. 2005). These programs have been developed, enhanced, validated, and used throughout the building energy community for many years. 1.2.2. Thermal Comfort Fanger (1967) developed the first thermal comfort model by applying the heat balance theories on the human body. Based on these theories, the human body applies physiological processes (e.g. sweating, shivering, regulating blood flow to the skin) to balance the heat produced by metabolism with the heat lost from the body. Maintaining this heat balance is the first condition for achieving a neutral thermal sensation. Investigating the body’s physiological processes when it is close to neutral, Fanger (1967) determined that the sweat rate and mean skin temperature were the only physiological processes influencing the heat balance on the human body. Fanger (1967) derived a linear empirical relationship for both of these processes as a function of activity level and implemented these relationships in the heat balance equations to produce a comfort equation. The comfort equation described all combinations of the four physical variables (air temperature, air velocity, mean radiant temperature, and relative humidity), and two personal variables (clothing insulation and activity level) that resulted in a neutral thermal sensation. 5 Fanger (1970) combined data from Nevins et al. (1966), McNall et al. (1967), and his own studies, to expand the comfort equation for situations where subjects did not feel neutral. The expanded equation predicted thermal comfort, using ASHRAE thermal sensation scale (Figure 1.2), by comparing the actual heat flow from the body in a given thermal environment with the heat flow required for neutral comfort for a given activity. This expanded equation was known as the Predicted Mean Vote (PMV) model. -3 -2 -1 0 1 2 3 cold cool slightly cool neutral slightly warm warm hot Figure 1.2. ASHRAE Thermal Sensation Scale Since the initial development of the PMV model, a large number of experimental laboratory and field studies have been conducted to validate the PMV model. These studies led to identifying the range of conditions in which the thermal sensation, predicted by the PMV model, had the least discrepancy from that given by an actual group of participants voting on the ASHRAE thermal sensation scale. In a review of laboratory studies, Humphreys (1994) concluded that the results of the early laboratory studies compared well with the predictions of the PMV model. However, the more recent laboratory studies that applied a wider range of conditions for the personal factors (Doherty and Arens 1988), showed greater discrepancies from the PMV model. Based on these studies Humphreys (1994) found that the PMV model was most accurate when the participants had sedentary activities and light clothing, but it lost its accuracy for heavier clothing and higher activity levels. Field studies on thermal comfort were mostly focused on comparing the neutral temperature given from actual thermal sensations against that predicted by the PMV model (Humphreys 1975, 1976, 1978, Auliciems 1981 de Dear and Auliciems 1985, Schiller 1990, Oseland 1996). These studies showed that the PMV model overestimates the neutral temperature between 2.2˚C and 3.6˚C. The more recent field studies (Humphreys 1994, Brager and de Dear 1998) that were 6 conducted in the wider range of countries and climates, showed that the PMV model not only overestimates the neutral temperature but also underestimates it by up to 3.4˚C. In addition to comparing the actual neutral temperature with the one predicted by the PMV model, several field studies (Schiller 1990, Busch 1992, Croome et al. 1992, de Dear et al. 1993, Oseland, 1995) investigated the occupants’ sensitivity away from neutral thermal sensation. These studies showed that the PMV model underpredicted the sensitivity of the occupants to the change in temperature. This underprediction got larger the further away from the occupants’ neutral thermal sensation. The previous laboratory and field studies proved that the PMV model is not always a good predictor of actual thermal sensation. Therefore, in 1995, a large database of thermal comfort studies was created and analyzed to determine the bias-free range of the PMV model (de Dear 1998, Jones 2002, and Humphreys & Nicol 2002). This database comprised the results of the thermal comfort field studies on 22,346 participants from 160 buildings in different climates around the world. These analyses showed that the PMV model predicted the actual thermal sensation most accurately for zone temperatures below 27˚C, for relative humidity below 60%, for air velocities less than 0.2 m/s, for clothing insulation in the range 0.3 to 1.2 clo (1 clo = 0.155 m2K/W), for activity levels below 1.4 met (1 met = 58.2 W/m2), and for air-conditioned buildings. Therefore, although these analyses restricted the use of the PMV model, the conditions found in air-conditioned office buildings typically fall outside those associated with serious PMV bias (Charles 2003). As a result, the Fanger’s PMV model was applied to develop the current thermal comfort standard (ANSI/ASHRAE STANDARD 55-2004) for the evaluation of thermal environments in air-conditioned office buildings. This standard specifies the combinations of indoor thermal environmental factors (i.e. temperature, thermal radiation, humidity, and air speed) and personal factors (i.e. activity and clothing) that will produce thermal environmental conditions acceptable to at least 80% of the occupants within the space. 7 1.2.3. Interactions of Energy Consumption and Thermal Comfort in Buildings Thermal comfort in indoor environments is a non-linear function of the thermal environmental and personal factors. Therefore, the overall thermal satisfaction experienced by occupants responds to the interactions of all of these factors. However, these interactions can hardly be captured by the existing building energy simulation programs that are capable of evaluating occupants’ thermal sensations (i.e. BLAST, Tas, TRNSYS, EnergyPlus, and IES <VE>). First, due to the inaccuracy of their results, caused by their inherent assumptions, approximations, and simplifications on the solution technique; and second, due to the difficulties associated with modifying the source code and structure of these black box programs for all different scenarios of interest. This explains why despite the significant efforts that have been made towards the development of the heat balance method and the current comfort standard, no numerical study has been carried out to directly investigate their interactions. The current research filled this gap by applying the heat balance method and the current comfort standard to develop a single zone numerical model. The model was then validated and applied to the office spaces of the Centre for Interactive Research on Sustainability (CIRS), as one of the greenest buildings in North America, to analyze the interactions between the environmental and personal factors, the occupants’ thermal comfort, and the associated HVAC energy consumption. This analysis answered the major research questions and defined guidelines for the optimum combinations of these factors that could produce occupants’ thermal satisfaction with less energy consumption. 1.3. Objectives and Scope of Work The principal objective of this thesis work was to develop and use a numerical model to investigate the interactions between the HVAC energy consumption and the occupants’ thermal comfort in commercial buildings. The model uses the heat balance method to perform building thermal analysis and applies the current comfort standard to evaluate occupant thermal sensations as a non-linear function of thermal environmental and personal factors. A 8 comprehensive discussion on the development and validation of this model is presented in Chapter 2. Chapter 3 is the application of the model to the CIRS office spaces to investigate the impacts of variations in occupant behaviors, building envelope, HVAC system, and climate on both energy consumption and thermal comfort. Conclusions drawn from this study are implemented to find the optimum combination of these variations that minimizes the HVAC energy consumption with respect to occupant thermal comfort. The final conclusions and future work are outlined in chapter 4. 9 Chapter Two: Formulation and Structure of the Numerical Model 2.1. Introduction A numerical model was developed to investigate the interactions of the building’s HVAC energy consumption and occupants’ thermal comfort. The model comprises the following two major components: • The heat balance model • The thermal comfort model The heat balance model performs the thermal analysis of a building at each time step to calculate the thermal environmental parameters (i.e. temperature, thermal radiation, humidity, and air speed) and the required HVAC energy consumption. The thermal parameters are then passed to the thermal comfort model at the same time step to investigate the occupants’ thermal sensation. This chapter presents a comprehensive discussion on the formulation, structure, development, and validation of this numerical model. 2.2. Heat Balance Model The implementation of the heat balance method in the model may be viewed as involving four distinct parts: • External opaque surfaces (i.e. walls and roof). • Transparent surfaces (i.e. fenestrations). • Internal surfaces (i.e. partitions, floor, and ceiling). • Zone air. The first three parts result in determining the interior surface temperatures of different zone surfaces. These temperatures are then used to calculate the convective heat fluxes from the 10 surfaces to the zone air. The sum of the convective heat fluxes is balanced with the convective portion of the sensible internal heat gain, sensible heat gain/loss due to infiltration, and sensible heat insertion rate (i.e. the rate at which the HVAC system supplies heat into the thermal zone) over the zone air control volume. Likewise, latent internal heat gain, latent infiltration heat gain/loss, and latent heat insertion rate into the thermal zone (i.e. the rate at which the HVAC system humidifies the zone air) are also balanced over the zone air control volume. This analysis produces the required inputs for the thermal comfort model and also calculates the associated HVAC energy consumption. The most fundamental assumptions of the heat balance model are: • The thermal properties of the air are uniform throughout the entire zone. • All the surfaces of the zone have uniform surface temperatures. • One-dimensional conduction heat transfer in the zone’s surfaces. 2.2.1. Heat Balance Method on the External Opaque Surfaces The transient heat fluxes that change the temperature distribution inside the external opaque surfaces are shown in Figure 2.1. To capture these changes, with respect to the assumptions of the heat balance model and thermal mass of the external opaque surfaces, a one dimensional transient conduction formulation was applied and solved with the explicit finite difference method. This requires that the thickness of these surfaces be divided into a known number of grids. Depending on the location of the grid points four different cases may occur: • Case One: Grid points inside the slab. • Case Two: Grid points on the boundary of two adjacent slabs. • Case Three: Grid point on the exterior surface. • Case Four: Grid point on the interior surface. The application of the heat balance method on all of these cases results in calculating the temperature distribution inside the external opaque surfaces for the next time step by knowing 11 their values at the current time. The main outputs of this application, however, are only the interior surface temperatures of these external opaque surfaces. A detail explanation of this application is presented in Appendix One. Figure 2.1. Transient heat fluxes that affect the external opaque surfaces. 2.2.2. Heat Balance Method on the Transparent Surfaces The transient heat fluxes that affect the control volume around a double-pane window are shown in Figure 2.2. The primary difference of this thermal network with the external opaque surfaces’ is that the solar radiation is absorbed throughout the window rather than just at the interior and exterior surfaces. This results in some rather arduous calculations, which were simplified by the following assumptions: • Because a window contains very little thermal mass, it was assumed that it behaves in a quasi-steady-state mode. k1&α1 H eat Panel Case 1Case 4 Case 3Case 1 L2 LhpL1 L4 Q gen (w /m 3) Interior Surface Exterior Surface Shortwave Solar Radiation Net Longwave Radiation from/to the Sky and Surroundings Convection Transmitted Solar Radiation Convection Radiation from Internal Heat Gains IN Tin Case 2 OUT Tout Net Longwave Radiation from/to the Other Interior Surfaces k2&α2 k4&α4 Control Volume 12 • The conductive resistance of each pane is so small that it was neglected in comparison to the convective and radiative resistances at the interior and exterior surfaces and (if a multiple-pane window) between the panes. • Neglecting the conductive thermal resistance causes each layer to have a uniform temperature, which was calculated by a single heat balance equation for each pane. • For a multiple pane window, the radiation and convection thermal resistances between the panes were combined. The total thermal resistance for air spaces may be obtained from ASHRAE (2005) as a function of orientation, direction of heat flow, and air temperature of the space. Figure 2.2. Transient heat fluxes that affect a double-pane window. Radiation from Internal Heat Gains Convection Net Longwave Radiation from the Other Interior Surfaces Convection Net Longwave Radiation from the Sky and Surroundings Interior Pane Radiation & Convection Outside-To-Inside Shortwave Solar Radiation Air Space Exterior Pane OUT Tout IN Tin Inside-To-Outside Transmitted Solar Radiation piT peT 13 Considering the previous assumptions, the heat balance method was applied to each pane to calculate the interior surface temperature of glazing systems. Appendix Two provides a detailed explanation of this application. 2.2.3. Heat Balance Method on the Internal Opaque Surfaces Internal opaque surfaces divide the internal zones of a building. Regarding of the fact that the model developed in this study is only able to perform the thermal analysis for a single zone; the boundary conditions on the exterior of these surfaces were assumed to be adiabatic. This assumption was made to avoid violating the first law of thermodynamics. Because the internal opaque surfaces are not exposed to the outside heat fluxes, their temperature fluctuations are considerably smaller in comparison to the external surfaces. Therefore, the lumped heat capacity method was a reasonably simple model with an acceptable accuracy for capturing these fluctuations. Figure 2.3 illustrates the transient heat fluxes that affect the control volume around the internal opaque surfaces. The detailed explanation of the application of the heat balance method to these surfaces is presented in Appendix Three. Figure 2.3. Transient heat fluxes that affect the internal opaque surfaces. 2.2.4. Heat Balance Method on the Zone Air The application of the heat balance method to the zone air may be viewed as two distinct processes: Internal Convection Radiation from Internal Heat Gains , ,k cρ Net Longwave Radiation from the Other Interior Surfaces Control Volume Transmitted Solar radiation from windows iosL 14 • The sensible heat balance. • The latent heat balance. In addition to the main assumptions of the heat balance method, it was assumed that in both of the previous cases, the zone air has a negligible thermal mass and it behaves in a quasi-steady- state mode. 2.2.4.1. Sensible Heat Balance on the Zone Air The application of the heat balance method to different zone surfaces resulted in calculating their interior surface temperatures. These temperatures are used to determine the convection heat fluxes from these surfaces to the zone air. By applying the heat balance method to the control volume around the zone air, the sum of these heat fluxes is balanced with the convective portion of the sensible internal heat gain, sensible heat gain/loss due to infiltration, and sensible heat insertion rate from the HVAC system. These sensible transient heat fluxes that affect the zone air control volume are shown in Figure 2.4. Figure 2.4. Sensible transient heat fluxes that affect the zone air. Zone AirConvection from the Zone Interior Surfaces Sensible Infiltration Sensible Heat Insertion Rate from the HVAC System Convection from the Internal Heat Gains (i.e. People, Lighting, And Equipment) Control Volume 15 Depending on the purpose of modeling, the sensible heat balance on the zone air may be cast in three different forms: • Solving for the required sensible HVAC energy consumption to maintain a fixed zone air temperature (i.e. used for design load calculations). • Solving for the zone air temperature when the HVAC system is off (i.e. used for modeling naturally ventilated buildings). • Solving for the required sensible HVAC energy consumption and zone air temperature, when the zone air temperature is varying between the heating and cooling setpoints (i.e. the most general formulations, used for building HVAC energy modeling). The detailed explanation of the application of the sensible heat balance to the zone air for all the previous three scenarios is provided in Appendix Four. 2.2.4.2. Latent Heat Balance on the Zone Air The latent heat gains in the zone air control volume are shown in Figure 2.5. These heat fluxes directly affect the humidity ratio inside the zone air. Similar to the sensible heat balance, the latent heat balance may also be cast in several forms, depending on the control strategy used for the zone air humidity ratio: • Solving for the required latent HVAC energy consumption to maintain a fixed zone air humidity ratio. • Solving for the zone air humidity ratio when the HVAC system does not participate in humidification/dehumidification of the zone air. • Solving for the required latent HVAC energy consumption and zone air humidity ratio, when the zone air humidity ratio is varying in the specific range. Appendix Four provides a detailed explanation on the zone air latent heat balance. 16 Figure 2.5. Latent transient heat fluxes that affect the zone air. 2.3. Thermal Comfort Model The thermal comfort model was developed by applying the heat balance method on the control volume around a body. Assuming that the body behaves in a quasi-steady-state condition, the total heat production within the body (i.e. caused by metabolic activities) was balanced with the total dissipated heat from the body to the surrounding environment. This dissipation may occur by different modes of heat exchange: • Sensible heat flow from the skin. • Latent heat flow from the evaporation of sweat. • Latent heat flow from the evaporation of moisture diffused through the skin. • Sensible heat flow during respiration. • Latent heat flow due to evaporation of moisture during respiration. Zone Air Latent Infiltration Control Volume Latent Internal Heat Gain (i.e. People and Some Equipment) Humidification Rate from the HVAC System 17 The detailed calculations of the previous heat fluxes are provided in Appendix Five. Applying the heat balance method to the control volume around the body leads to evaluating a neutral thermal sensation for steady state conditions by a single equation as a function of the indoor thermal environmental and personal factors. The environmental factors addressed in this standard are temperature, thermal radiation, humidity, and air speed. These factors are determined from the previous applications of the heat balance method to different zone surfaces and to the zone air. The personal factors are those of activity and clothing. The thermal comfort equation was expanded for situations where subjects were not at a neutral thermal sensation. This resulted in developing the PMV-PPD model, which predicts the mean response of a large group of occupants on their thermal sensations according to the ASHRAE thermal sensation scale, and estimates the percentage of the zone occupants that are dissatisfied with their thermal environment. In addition to the evaluation of thermal comfort for the body as a whole, the effects of local thermal discomfort are also considered in the thermal comfort model. Local thermal discomfort may be caused by an asymmetric radiant field, draft, zone air temperature stratification, or contact with a hot or cold floor. These factors are described in Appendix Five. 2.4. Validation The main individual modules of the numerical model were validated using the analytical solutions. The detailed explanations on these validations are provided in the Appendix Six. These validations were on the: • Conduction formulation for the heat transfer through the external opaque surfaces. • Calculations of the view factors and the mean radiant temperature. • Thermal comfort model. The previous validations showed that the numerical model conserves energy and predicts the results with an acceptable accuracy. 18 Once the main modules of the model were validated, the numerical model was applied to the single zone, representing the perimeter office spaces of the Centre for Interactive Research on Sustainability (CIRS) to investigate the zone thermal performance as well as the occupants’ thermal sensations over the summer and winter days. The results were then validated against those predicted by IES<VE>. The whole model validation showed that the numerical model is computing solutions that are reasonable compared to IES<VE>. The detailed explanation of this validation is given in Appendix Seven. 19 5m 0.8m 1.25m 1.15m 0.25m 5m PLAN VIEW SOUTH VIEW EAST VIEW AXONOMETRIC VIEW South Partition North Partition West Partition East External Surface 5m 3.45m Ceiling Floor West Partition East External Surface Upper Window Lower Window External Wall External Wall North Chapter Three: Results and Discussion 3.1. Introduction The numerical model was applied to a single generic zone, shown in Figure 3.1, to investigate the impacts of variation in occupants’ behaviors, building’s envelope, HVAC system, and climate on both HVAC energy consumption and thermal comfort. This zone represents the perimeter office spaces of the Centre for Interactive Research on Sustainability (CIRS). CIRS, which will be built in the Lower Mainland of BC, will be among the most innovative buildings in North America. Figure 3.1. The schematic of the baseline zone. 20 The current design specifications of the CIRS office spaces, summarized in Table 3.1, were applied to define the baseline for the analyses. Baseline Specifications Location Vancouver HVAC System Hydronic radiant ceiling Setpoint 20˚C-24˚C Minimum Required Fresh Air 15 CFM/Person Infiltration 0.15 ACH Internal Shading - Clothing Level 0.96 clo (i.e. trousers, long-sleeve shirt, suit jacket) Occupancy Period 8AM-5PM People 6.25 m2/Person (Office Work) Lighting 5.4 W/m2 Table 3.1. General specifications of the baseline zone. The control strategy for the baseline zone was to maintain the zone air temperature at the desired range of setpoints only over the occupancy period. For the zone air temperature higher than the cooling setpoint or less than the heating setpoint, over this period, a geothermal heat pump introduced cooled or heated water, respectively, into the tubing laid in a pattern inside the hydronic (i.e. liquid) radiant ceiling slab to bring back the zone air temperature into the desired range of setpoints. It should be noted that, while the zone air temperature was within this range, no cooling/heating was provided from the ceiling slab into the zone air. According to the zone air and outdoor air temperature differences, the controlling system might also turn on the HVAC system, if needed, to preheat the zone air two hours before the occupancy period in winter. This preconditioning provided an acceptable level of thermal comfort over the early hours of occupancy and eliminated the HVAC energy consumption over the unoccupied hours. To calculate the energy consumption for treating the minimum required fresh air for the occupants, the initial modeling was carried out, assuming that a separate air handling unit introduced the fresh air into the thermal zone at the zone air temperature. However, because the zone air temperature was higher than that of the outdoor air during the cooling season, there was a heating requirement by the air handling unit, while the slab was cooling the zone air. 21 Therefore, this strategy was altered by assuming that the minimum required fresh air was directly introduced into the thermal zone at the outdoor air temperature and conditioned with the slab. The construction materials that were used in different opaque surfaces of the baseline zone are summarized in Table 3.2. The materials of the external wall are listed from inside to outside. Thermal Properties Surfaces/Materials Thermal Diffusivity [m2/s] Thermal Conductivity [W/m.K] Thickness [m] Floor/Ceiling 150 mm Reinforced Concrete 7.94e-07 1.4 0.15 Partitions 105 mm Brick (13mm Light Plaster Both Sides) 4.56e-07 0.62 0.13 External Wall Gypsum Plastering 4.18e-07 0.42 0.015 Medium Concrete Block 3.64e-07 0.51 0.1 Dense EPS Slab Insulation - Like Styrofoam 5.95e-07 0.025 0.06 Brickwork (Outer Leaf) 6.18e-07 0.84 0.1 Table 3.2. Thermal properties of the baseline zone opaque surfaces. The thermal and optical properties of the baseline zone glazing system are given in Table 3.3. Incidence Angles [Deg] Glazing System R = 0.95 [m2.K/W] GRN LE N or m al 0 40 50 60 70 80 H em is ., D iff us e Solar Transmittance 0.24 0.21 0.19 0.16 0.11 0.05 0.18 Front Reflectance 0.11 0.10 0.11 0.14 0.22 0.43 0.14 Back Reflectance 0.19 0.20 0.22 0.25 0.34 0.55 0.24 Outer Layer Absorptance 0.56 0.59 0.61 0.61 0.59 0.48 0.58 Inner Layer Absorptance 0.09 0.09 0.09 0.08 0.08 0.04 0.08 Table 3.3. Thermal and optical properties of the baseline glazing system. Due to the large number of parameters that might affect the thermal performance of the baseline zone, the initial summer and winter screening analyses were conducted to identify those for which the impacts on HVAC energy consumption and/or occupants’ thermal comfort were most significant. The whole year analyses were then carried out over those specific parameters to 22 0 4 8 12 16 20 240 8 16 24 Hour D ry -b ul b Te m pe ra tu re [C ] Summer Winter 0 4 8 12 16 20 242 5 8 11 Hour H um id ity R at io [g w at er /k g d ry ai r] Summer Winter 0 4 8 12 16 20 242 3 4 5 Hour W in d Sp ee d [m /s ] Summer Winter 0 4 8 12 16 20 240 200 400 600 Hour N or m al D ir ec t S ol ar R ad ia tio n [W /m 2 ] Summer Winter investigate their impacts on the annual HVAC energy consumption and the averaged occupants’ thermal sensations over the whole year. 3.2. Screening Analyses The screening analyses were carried out over the typical summer and winter days of Vancouver. Based on ASHRAE design weather data for Vancouver international Airport, the hottest and the coldest months of the year are respectively August and January. Therefore, to produce the climate data for the typical summer and winter days, the hourly weather data of these two months were averaged at each specific hour over the length of the month. The solar angles were also calculated for the middle day of these months. The climate data, used for the screening analyses is shown in Figure 3.2. Figure 3.2. The climate data for the typical summer and winter days of Vancouver. Implementing this climate data, the numerical model was applied to the baseline zone to investigate its thermal performance over the typical summer and winter days. The results are shown in Figure 3.3. 23 Figure 3.3. The baseline thermal performance over the typical summer and winter days. For the typical summer day, the zone air temperature decreased from midnight to sunrise, mainly because of the heat loss through the building envelope. With a higher outdoor air temperature and an increase in the amount of the solar radiation, the zone air temperature started to increase from sunrise. The increase in the zone air temperature continued and intensified by the internal heat gains from the start of the occupancy period until it reached the cooling setpoint. At this point, the ceiling slab started to provide cooling into the zone air to bring its temperature back into the desired range of setpoints. With only one external surface on the east façade, the baseline zone was only affected by the direct solar radiation in the morning. Therefore, with the elimination of the direct solar radiation and the reduction in the ceiling and outdoor air temperatures, the required cooling load was reduced in the afternoon. This turned off the cooling system at 3PM. At the end of the occupancy period, the zone air temperature dropped due to the elimination of the internal heat gains. With the reduction in the outdoor air temperature and the amount of solar radiation, the zone air temperature reduced from the end of the occupancy period until midnight. 0 4 8 12 16 20 2418 20 22 24 26 28 Hour C Zone Air Temp. Mean Radiant Temp. Ceiling Temp. 0 4 8 12 16 20 24-0.6 -0.5 -0.4 -0.3 PM V 6% 8% 10% 12% Hour PP D PPDPMV 0 4 8 12 16 20 240 0.2 0.4 0.6 PM V 6% 8% 10% 12% PP D Hour PPDPMV 0 4 8 12 16 20 2422 22.5 23 23.5 24 24.5 Hour C Zone Air Temp. Mean Radiant Temp. Ceiling Temp. SUMMER DAY WINTER DAY 24 According to the Predicted Mean Vote (PMV) values, shown in Figure 3.3, the occupants were feeling slightly warm over the typical summer day. Therefore, reduction in the zone air and/or mean radiant temperatures improved their thermal sensations. It should be noted that the higher Predicted Percentage of Dissatisfaction (PPD) over the occupancy period was caused by the internal heat gains that increased the zone air temperature over this period. For the typical winter day, there was a large difference between the zone air and outdoor air temperatures. Therefore, the minimum required fresh air, which was introduced at the outdoor air temperature directly into the thermal zone, notably dropped the zone air temperature over the occupancy period. To prevent the zone air temperature from exceeding the desired range of setpoints over the occupancy period, the ceiling slab started to preheat the zone air two hours in advance. From the start of the occupancy period the internal heat gains, solar radiation and the heat flux from the slab increased the zone air temperature and turned off the heating system at 9AM. The reduction in the outdoor air and slab temperatures as well as the amount solar radiation decreased the zone air temperature from noon to midnight. Because of the small convection heat transfer coefficient on horizontal surfaces for downward heat flow, the slab temperature was considerably increased to maintain the zone air temperature above the heating setpoint. Regarding the negative PMV values over the typical winter day, shown in Figure 3.3, the warmer slab improved the occupants’ thermal sensations by increasing both the zone air and/or mean radiant temperatures, while they were feeling slightly cool. Determining the thermal performance of the baseline zone for the typical summer and winter days, the screening analyses were carried out over the main parameters that were expected to affect the HVAC energy consumption and/or occupants’ thermal comfort. The results are summarized in Table 3.4. It is important to note that the thermal comfort indicators in this Table were weighted and averaged by the number of occupants. Also, the slab energy consumption refers to the total heat (or if negative, cooling) that should be supplied to the slab to maintain the zone air temperature 25 between the heating and cooling setpoints over the occupancy period. The detailed explanation on the impacts of these parameters is provided in the following subsections. TYPICAL SUMMER DAY TYPICAL WINTER DAY A N A L Y SE S PARAMETERS Slab Energy Consumption [kW.hr] Mean PPD Mean PMV Slab Energy Consumption [kW.hr] Mean PPD Mean PMV B A SE LI N E - -5.8 9.8% 0.48 10.8 7.8% -0.36 Setpoint Range Increased To 18˚C-26˚C 0.0 12.3% 0.58 8.5 19.7% -0.84 Floor Slab Cooling/Heating -9.6 8.1% 0.38 10.0 9.4% -0.46 SY ST EM Zone Air Speed Doubled -5.8 8.1% 0.38 10.8 9.5% -0.46 Glazing HI-P GRN W/LE CLR -5.8 9.8% 0.48 8.0 8.1% -0.38 Vertical Shading Fins Removed -7.0 10.0% 0.49 10.7 7.7% -0.36 G LA ZI N G / SH A D IN G S Horizontal Overhang Removed -5.8 9.8% 0.48 10.8 7.8% -0.36 Zone Thermal Mass Increased by 20% -3.7 9.4% 0.46 10.9 7.8% -0.36 External Wall Insulation Thickness Doubled -5.7 9.8% 0.48 10.4 7.7% -0.36 Summer Infiltration Maximum (1.3ACH) 0.0 6.1% 0.22 - - - EN V EL O PE Winter Infiltration Maximum (0.3ACH) - - - 12.9 7.2% -0.33 South Orientation With No Fins -6.2 9.5% 0.46 8.0 7.4% -0.33 West Orientation With No Fins -7.5 9.5% 0.46 10.3 7.7% -0.36 O R IE N TA TI O N North Orientation With No Fins -0.2 8.2% 0.38 10.8 7.9% -0.37 Adaptive Clothing -5.8 6.1% 0.23 10.8 6.0% -0.22 Summer Occupancy Period Changed To 7AM-4PM -5.7 9.6% 0.47 - - - A D A PT A TI O N Winter Occupancy Period Changed To 9AM-6PM - - - 11.0 7.9% -0.37 Table 3.4. The results of the screening analyses for the typical summer and winter days. 26 3.2.1. Increasing the Range of Setpoints Regarding Vancouver’s mild weather condition, a broader range of setpoint, eliminated the slab energy consumption over the typical summer day. However, because no cooling was provided from the ceiling slab, the zone air and mean radiant temperatures were both increased in comparison to the baseline. This increased the average occupants’ thermal dissatisfaction by 2.5%. Figure 3.4 shows the impacts of increasing the range setpoints on the zone air temperature and PPD values over the typical summer day of Vancouver. Figure 3.4. Increasing the range of setpoints over the typical summer day. Although increasing the range of setpoints over the typical winter day reduced the zone required heating load by 22%, the preheating was still required to avoid exceeding the desired range of setpoints over the early hours of the occupancy period. This was mainly due to the large heating load, which was required to treat the minimum fresh air for the occupants. As shown in Figure 3.5, with lower zone air temperature the occupants’ thermal dissatisfaction was significantly increased. The initial modeling with a broader range of setpoint over the typical winter day showed that when the minimum required fresh air was warmed up with a separate air handling unit and introduced into the thermal zone at the zone air temperature, there was no need for heating from the ceiling slab. This suggests the importance of the fresh air heating load over the typical winter day on the zone thermal performance. 0 4 8 12 16 20 24 23 23.5 24 24.5 25 Hour C Baseline Setpoint Range: 18C-26C 0 4 8 12 16 20 245% 8% 11% 14% 17% Hour PP D Baseline Setpoint Range: 18C-26C ZONE AIR TEMPERATURE PREDICTED PERCENTAGE OF DISSATISFIED 27 Figure 3.5. Increasing the range of setpoints over the typical winter day. 3.2.2. Floor Slab Cooling/Heating Having the radiant cooling slab in the floor reduced the convection heat transfer between the slab and the zone air. Therefore, to maintain the zone air temperature within the desired range of setpoints, the slab temperature was significantly reduced. With respect to the thermal mass of the slab, this increased the zone required cooling load by 67%. Because the thermal comfort was calculated for a seated person (i.e. 60 cm above the floor) at the centre of the zone with the large view angle to the floor, the reduction in the floor temperature significantly reduced the mean radiant temperature and improved thermal comfort over the typical summer day. Figure 3.6 shows the impacts of floor slab cooling on the thermal performance of baseline zone. For the typical winter day, the floor slab heating enhanced the convection heat transfer from the slab to the zone air and reduced the slab temperature in compare to the baseline. This resulted in 30% reduction in the slab energy consumption from 6AM to 9AM. However, because of the small difference between the zone air and slab temperatures, shown in Figure 3.7, additional heating was required later in the afternoon to maintain the zone air temperature above the heating setpoint. As a result, the floor slab heating reduced the total slab energy consumption over the typical winter day by 8%. 0 4 8 12 16 20 245% 10% 15% 20% 25% Hour PP D Baseline Setpoint Range: 18C-26C ZONE AIR TEMPERATURE PREDICTED PERCENTAGE OF DISSATISFIED 0 4 8 12 16 20 2418 19 20 21 22 Hour C Baseline Setpoint Range: 18C-26C 28 0 4 8 12 16 20 2422 22.5 23 23.5 24 24.5 Hour C Baseline Floor Slab 0 4 8 12 16 20 2420 21 22 23 24 25 Hour C Baseline Floor Slab 0 4 8 12 16 20 244% 6% 8% 10% 12% Hour PP D Baseline Floor Slab 0 4 8 12 16 20 2422.5 23 23.5 24 24.5 Hour C Baseline Floor Slab ZONE AIR TEMPERATURE PREDICTED PERCENTAGE OF DISSATISFIED MEAN RADIANT TEMPERATURE SLAB TEMPERATURE Figure 3.6. Floor slab cooling over the typical summer day. The lower slab temperature reduced the mean radiant temperature and increased dissatisfaction with the thermal environment. As shown in Figure 3.7, the slightly lower zone air temperature also contributed to the increase in the PPD values. 3.2.3. Increasing the Zone Air Speed The baseline zone air diffusers were used to split the minimum required fresh air flow emerging from the air duct into individual jets and guide them into the desired directions. They reduced the air speed at the centre of the zone, where occupants’ thermal sensations were investigated, to 10% of its value inside the air duct. By doubling the zone air speed, the occupants’ thermal comfort was improved in summer. This was caused by the higher air movement around their body while they were feeling warm. 29 Figure 3.7. Floor slab heating over the typical winter day. In winter, however, higher zone air speed increased local discomfort caused by draft (i.e. the unwanted local cooling of the body caused by air movement). This increased the averaged occupants’ thermal dissatisfaction over the typical winter day by 2%. Since the mass flow rate of the fresh air was not changed in comparison to the baseline, this parameter did not affect the zone required cooling/heating load. Figure 3.8 shows the impacts of increasing the air speed on the occupants’ thermal comfort. 3.2.4. Changing the Glazing System The alternative glazing system for the CIRS offices at the design phase was HI-P GRN W/LE CLR. The thermal and optical properties of this glazing system are summarized in Table 3.5. 0 4 8 12 16 20 245% 8% 11% 14% 17% Hour PP D Baseline Floor Slab ZONE AIR TEMPERATURE PREDICTED PERCENTAGE OF DISSATISFIED MEAN RADIANT TEMPERATURE SLAB TEMPERATURE 0 4 8 12 16 20 2419 21 23 25 27 29 Hour C Baseline Floor Slab 0 4 8 12 16 20 2420.5 21 21.5 22 22.5 23 Hour C Baseline Floor Slab 0 4 8 12 16 20 2419.5 20 20.5 21 21.5 Hour C Baseline Floor Slab 30 Figure 3.8. Increasing the zone air speed. Incidence Angles [Deg] Alternative Glazing System R = 1.46 [m2.K/W] HI-P GRN W/LE CLR N or m al 0 40 50 60 70 80 H em is ., D iff us e Solar Transmittance 0.22 0.21 0.19 0.17 0.12 0.06 0.18 Front Reflectance 0.07 0.07 0.09 0.13 0.22 0.46 0.12 Back Reflectance 0.23 0.23 0.24 0.28 0.37 0.57 0.27 Outer Layer Absorptance 0.67 0.68 0.67 0.66 0.62 0.46 0.65 Inner Layer Absorptance 0.04 0.05 0.05 0.05 0.04 0.03 0.04 Table 3.5. Specifications of the alternative glazing system for the CIRS offices. With its higher thermal resistance, the alternative glazing system notably improved the building envelope. However, comparing its optical properties with those of the baseline glazing system, the alternative glazing did not significantly changed the amount of transmitted solar radiation in compare to the baseline. Therefore, the impacts of changing the glazing system on the zone thermal performance over the typical summer day were trivial. However, as shown in Figure 3.9, due to the large temperature gradient between the indoor and outdoor air in winter, the alternative glazing system reduced the zone required heating load by 26%. PREDICTED PERCENTAGE OF DISSATISFIED (WINTER) 0 4 8 12 16 20 247% 8% 9% 10% 11% 12% Hour PP D Baseline Increased Air Speed PREDICTED PERCENTAGE OF DISSATISFIED (SUMMER) 0 4 8 12 16 20 246% 7% 8% 9% 10% 11% Hour PP D Baseline Increased Air Speed 31 Figure 3.9. Using the alternative glazing system over the typical winter day. 3.2.5. Removing the Vertical Fins The vertical fins on the east façade of the baseline zone reduced the amount transmitted direct solar radiation from sunrise to noon. As previously shown in Figure 3.2, for the typical summer day, the sunrise is early in the morning and the amount of direct solar radiation is relatively high. Therefore, by removing the vertical fins from the baseline zone, the required cooling load over the typical summer day was increased by 22%. The larger amount of transmitted direct solar radiation increased the zone mean radiant temperature. Consequently, the higher mean radiant and zone air temperatures increased the thermal dissatisfaction over the typical summer day. The impacts of the vertical fins on the zone thermal performance and the occupants’ thermal sensations over the typical summer day are shown in Figure 3.10. ZONE AIR TEMPERATURE PREDICTED PERCENTAGE OF DISSATISFIED ZONE REQUIRED HEATING LOAD SLAB TEMPERATURE 0 4 8 12 16 20 240 1000 2000 3000 4000 5000 6000 Hour W Baseline HI-P GRN W/LE CLR 0 4 8 12 16 20 247% 8% 9% 10% 11% Hour PP D Baseline HI-P GRN W/LE CLR 0 4 8 12 16 20 2419.5 20 20.5 21 21.5 Hour C Baseline HI-P GRN W/LE CLR 0 4 8 12 16 20 2422 23 24 25 26 27 28 Hour C Baseline HI-P GRN W/LE CLR 32 Figure 3.10. Removing the vertical fins over the typical summer day. Figure 3.11 shows the importance of having the vertical fins on the east façade over the typical summer day. According to this Figure, removing the fins has effectively increased the amount of transmitted direct solar radiation and interior surface temperature of the lower glazing system. Figure 3.11. The lower glazing system thermal performance, without the vertical fins, over the typical summer day. ZONE AIR TEMPERATURE PREDICTED PERCENTAGE OF DISSATISFIED SLAB TEMPERATURE 0 4 8 12 16 20 2423.4 23.6 23.8 24 24.2 24.4 Hour C Baseline No Fin 0 4 8 12 16 20 246% 7% 8% 9% 10% 11% Hour PP D Baseline No Fins 0 4 8 12 16 20 2423.2 23.4 23.6 23.8 24 24.2 Hour C Baseline No Fin MEAN RADIANT TEMPERATURE 0 4 8 12 16 20 2421.5 22 22.5 23 23.5 24 Hour C Baseline No Fin 0 4 8 12 16 20 240 100 200 300 400 Hour W Baseline No Fin TRANSMITTED DIRECT SOLAR RADIATION INTERIOR PANE TEMPERATURE 0 4 8 12 16 20 2422 23 24 25 26 Hour C Baseline No Fin 33 For the typical winter day, the amount of direct solar radiation that affected the external surface of the baseline zone was considerably small. Therefore, removing the vertical fins had a negligible impact on the zone thermal performance and occupants’ thermal sensations. 3.2.6. Removing the Horizontal Overhang Similar to the vertical fins, the horizontal overhang was used on the east façade to reduce the transmitted direct solar radiation in the morning. The screening analyses showed that regarding the small solar altitude angles in the morning and the design of the vertical fins, the horizontal overhang on the east façade had a negligible effect in reducing the transmitted direct solar radiation. Because of the larger amount of incident direct solar radiation and the higher solar altitude angle, removing the horizontal overhang was slightly more effective in reducing the slab energy consumption over the summer in comparison to winter. 3.2.7. Increasing the Zone Thermal Mass Thermal mass, which is characterized by heat capacity, describes the ability of an opaque envelope to dampen and delay the transfer of heat. To investigate the effects of increasing the zone thermal mass, the heat capacities of the zone opaque surfaces were increased by 20%, while their thermal resistances were kept constant. Regarding the diurnal variation in outdoor air temperature over the typical summer day, the increase in the zone thermal mass, improved the pre-cooling effect of the outdoor air at night. With higher heat capacity, the opaque surfaces stored cooling at night and reduced the zone required cooling load over the typical summer day by 35%. The peak cooling load was also reduced by 13% and shifted to one hour later. The reduction in the zone air and mean radiant temperatures, caused by the pre-cooling of the zone surfaces at night, improved thermal comfort over the early hours of occupancy period. Figure 3.12 summarizes the impacts of increasing the zone thermal mass on the baseline zone over the typical summer day of Vancouver. 34 Figure 3.12. Increasing the zone thermal mass over the typical summer day. Because of the small amount of solar radiation and low outdoor air temperature over the typical winter day, the effect of increasing the zone thermal mass on the required heating load and occupants’ thermal comfort were insignificant. 3.2.8. Increasing the Insulation Thickness The 6 cm insulation layer inside the baseline external wall was doubled to reduce the heat flow between the zone air and outdoor air. Regarding the fact that the baseline zone has only one external surface with 70% glazing area, the additional insulation layer had a small impact on the slab energy consumption and the occupants’ thermal sensations over the typical summer day. However, due to the large temperature gradient between the indoor and outdoor air in winter, the higher thermal resistance of the external wall, reduced the required heating load by 3%. Despite 0 4 8 12 16 20 24-1400 -1200 -1000 -800 -600 -400 -200 0 Hour W Baseline Increased Thermal Mass 0 4 8 12 16 20 245% 6% 7% 8% 9% 10% 11% Hour PP D Baseline Increased Thermal Mass ZONE AIR TEMPERATURE PREDICTED PERCENTAGE OF DISSATISFIED ZONE REQUIRED COOLING LOAD 0 4 8 12 16 20 2423 23.2 23.4 23.6 23.8 24 24.2 Hour C Baseline Increased Thermal Mass 0 4 8 12 16 20 2423 23.5 24 24.5 Hour C Baseline Increased Thermal Mass MEAN RADIANT TEMPERATURE 35 the increase in the interior surface temperature of the external wall, the change in the mean radiant temperature and occupants’ thermal comfort was still insignificant. This was due to the small area of the external wall as well as the reduction in the slab temperature. 3.2.9. Increasing the Infiltration Rate For the typical summer day, the infiltration rate was increased by opening the operable windows. As the detailed modeling of air infiltration rates with open windows was not the purpose of this research, the infiltration flow rate was approximated at 1.3 ACH (Wallace et al. 2002). Comparing the outdoor air temperature, shown in Figure 3.2, with the desired range of setpoints, the higher air exchange rate significantly reduced the zone air temperature and eliminated the need for the cooling system. With the reduction in the difference between the indoor and outdoor air temperatures around noon, the cooling effect of the outdoor air was slightly reduced. The variation in the zone air temperature with higher air exchange rate is shown in Figure 3.13. Figure 3.13. Increasing the air exchange rate over the typical summer day (zone air temperature). The lower zone air temperature reduced the interior temperature of different zone surfaces and consequently resulted in a reduction in the mean radiant temperature. As shown in Figure 3.14, the lower zone air and mean radiant temperatures considerably improved the thermal comfort level over the occupancy period in summer. 0 4 8 12 16 20 2422 22.5 23 23.5 24 24.5 25 Hour C Baseline 1.3 ACH ZONE AIR TEMPERATURE 36 Figure 3.14. Increasing the air exchange rate over the typical summer day (occupants’ thermal sensations). For the typical winter day, the air infiltration rate for a building in moderate weather condition was approximated at 0.3 ACH (Sherman 1980) and selected as an alternative for the baseline zone. Because of the large temperature difference between the indoor and outdoor climates in winter, the higher air infiltration rate increased the zone required heating load by 20%. With higher air infiltration rate, more heating was required in order to maintain the zone air temperature above the heating setpoint. This resulted in having a higher slab temperature in compare to the baseline. The higher slab temperature increased the mean radiant temperature and consequently improved the occupants’ thermal sensations over the typical winter day. The impacts of increasing the air infiltration rate in winter are shown in Figure 3.15. 3.2.10. Relocating the Baseline Zone to the South Façade To investigate the impacts of orientation on the zone thermal performance and occupants’ thermal comfort, the baseline zone was placed on the east, south, west, and north façades. The vertical tilted fins were removed from the baseline zone in all the previous four cases to provide symmetry in the comparisons. For the typical summer day, relocating the zone to the south façade resulted in having the direct solar radiation, which is the main portion of the total solar radiation, on the external surface later in the morning. This reduced the zone air temperature and eliminated a need for cooling over the 0 4 8 12 16 20 245% 6% 7% 8% 9% 10% 11% Hour PP D Baseline 1.3 ACH 0 4 8 12 16 20 2421 22 23 24 25 Hour C Baseline 1.3 ACH PREDICTED PERCENTAGE OF DISSATISFIED MEAN RADIANT TEMPERATURE 37 Figure 3.15. Increasing the air infiltration rate over the typical winter day. early hours of the occupancy period. Also, because the solar altitude angles are near their maximum values around noon, the horizontal overhang on top of the south façade glazing system was much more effective in reducing the transmitted direct solar radiation in compare to the baseline. These reduced the required cooling load over the typical summer day by 11%. The lower zone air temperature in the morning slightly reduced the temperature of the zone interior surfaces and improved the occupants’ thermal comfort in the morning. Figure 3.16 summarizes the zone thermal performance and occupants’ thermal sensations for the typical summer day of Vancouver. It is important to note that the transmitted solar radiation in the following Figures shows the amount of direct solar radiation that was transmitted from the lower glazing system with the overhang on the top. For the typical winter day, the south façade received direct solar radiation from sunrise to sunset. However, the east façade was only affected by the direct solar radiation from sunrise to noon 0 4 8 12 16 20 2420 22 24 26 28 30 Hour C Baseline 0.3 ACH 0 4 8 12 16 20 246% 7% 8% 9% 10% 11% Hour PP D Baseline 0.3 ACH 0 4 8 12 16 20 2421 21.5 22 22.5 23 23.5 Hour C Baseline 0.3 ACH 0 4 8 12 16 20 2419.5 20 20.5 21 21.5 22 Hour C Baseline 0.3 ACH ZONE AIR TEMPERATURE PREDICTED PERCENTAGE OF DISSATISFIED SLAB TEMPERATUREMEAN RADIANT TEMPERATURE 38 0 4 8 12 16 20 24 23.5 23.7 23.9 24.1 24.3 Hour C East South 0 4 8 12 16 20 246% 7% 8% 9% 10% 11% Hour PP D East South ZONE AIR TEMPERATURE PREDICTED PERCENTAGE OF DISSATISFIED TRANSMITTED DIRECT SOLAR RADIATIONMEAN RADIANT TEMPERATURE 0 4 8 12 16 20 2423.2 23.4 23.6 23.8 24 24.2 Hour C East South 0 4 8 12 16 20 240 100 200 300 400 Hour W East South Figure 3.16. Having the zone on the south facade over the typical summer day. solar time. Also, the smaller solar altitude angles in winter in compare to summer reduced the shading effect of the horizontal overhang. Therefore, the large amount of direct solar radiation that affected the south façade at the small solar incident angles around noon considerably increased the amount of transmitted direct solar radiation in compare to the baseline. The additional solar heat gain reduced the required heating load by 25%. It also increased the zone air temperature from noon to the end of the occupancy period and improved the occupants’ thermal sensations over this time. Figure 3.17 shows the zone thermal performance and the occupants’ thermal sensations over the typical winter day. 3.2.11. Relocating the Baseline Zone to the West Façade Because there was no direct solar radiation on the west façade until the noon solar time, the zone air temperature and the required cooling load were both less than the baseline’s in the morning. However, the direct solar radiation affected the west façade in the afternoon when the outdoor air 39 Figure 3.17. Having the zone on the south facade over the typical winter day. temperature was near its maximum value. Therefore, the cooling system operated at a higher capacity in the afternoon to maintain the zone air temperature below the cooling setpoint over the occupied hours. Consequently, the total slab energy consumption over the typical summer day was increased by 8%. With lower zone air and mean radiant temperatures, shown in Figure 3.18, occupants’ thermal comfort was improved over the early hours of the occupancy period. As shown in Figure 3.18, because the amount of normal direct solar radiation and solar incident angle values are symmetry around noon solar time, there was no noteworthy difference between the total amount of transmitted direct solar radiation from the east and west glazing systems over the typical summer day. For the typical winter day, the amount of solar radiation that affected the east and west façades, shown in Figure 3.19, was considerably smaller in compare to its value in summer. Also, the solar azimuth angles varied in a smaller range, which resulted in having the sunrise later in the 0 4 8 12 16 20 2419.5 20 20.5 21 21.5 22 Hour C East South ZONE AIR TEMPERATURE PREDICTED PERCENTAGE OF DISSATISFIED TRANSMITTED DIRECT SOLAR RADIATIONMEAN RADIANT TEMPERATURE 0 4 8 12 16 20 2421 21.5 22 22.5 23 Hour C East South 0 4 8 12 16 20 240 60 120 180 240 Hour W East South 0 4 8 12 16 20 246% 7% 8% 9% 10% 11% Hour PP D East South 40 morning and the sunset earlier in the afternoon. Therefore, the thermal performance of the baseline zone was not significantly altered when the zone was relocated to the west façade. Figure 3.18. Having the zone on the west facade over the typical summer day. Figure 3.19. Having the zone on the west facade over the typical winter day. 0 4 8 12 16 20 240 30 60 90 120 Hour W East West 0 4 8 12 16 20 2419.5 20 20.5 21 21.5 Hour C East West ZONE AIR TEMPERATURE TRANSMITTED DIRECT SOLAR RADIATION 0 4 8 12 16 20 246% 8% 10% 12% Hour PP D East West 0 4 8 12 16 20 2423.4 23.6 23.8 24 24.2 24.4 Hour C East West 0 4 8 12 16 20 240 100 200 300 400 500 Hour W East West 0 4 8 12 16 20 2423 23.5 24 24.5 Hour C East West ZONE AIR TEMPERATURE PREDICTED PERCENTAGE OF DISSATISFIED TRANSMITTED DIRECT SOLAR RADIATIONMEAN RADIANT TEMPERATURE 41 3.2.12. Relocating the Baseline Zone to the North Façade For the typical summer day, a small amount of direct solar radiation affected the north façade over short period of time near sunrise and sunset. The significant reduction in the solar heat gain maintained the zone air temperature less than the cooling setpoint until the last hours of the occupancy period. This reduced the slab energy consumption by 97%. The reduction in the zone air temperature and the amount of transmitted direct solar radiation reduced the interior temperature of different zone surfaces. Therefore, with lower zone air and mean radiant temperatures, the averaged occupants’ thermal dissatisfaction was reduced by 2%. Figure 3.20 shows the zone thermal performance on the north façade for the typical summer day. Figure 3.20. Having the zone on the north facade over the typical summer day. It should be noted that, in real projects, more lighting is required for the north façade office spaces to compensate the reduction in the daylight. Therefore, depending on the incremental lighting, the savings might be reduced. 0 4 8 12 16 20 240 100 200 300 400 Hour W East North 0 4 8 12 16 20 2422.5 23 23.5 24 24.5 Hour C East North 0 4 8 12 16 20 2422 23 24 25 Hour C East North 0 4 8 12 16 20 245% 7% 9% 11% Hour PP D East North ZONE AIR TEMPERATURE PREDICTED PERCENTAGE OF DISSATISFIED TRANSMITTED DIRECT SOLAR RADIATIONMEAN RADIANT TEMPERATURE 42 Because of the smaller range of solar azimuth angles, there was no direct solar radiation on the north façade over the typical winter day. However, the amount of incident direct solar radiation on the east façade was so small that its impact on the zone thermal performance and occupants’ thermal comfort was negligible. 3.2.13. Adaptive Clothing The effect of adaptive clothing on the occupants’ thermal sensations was investigated by varying the clothing level as a linear function of the outdoor air temperature. Therefore, the maximum and minimum clothing were respectively assigned to the coldest and hottest hours of the year. For other outdoor air temperatures the clothing level was calculated by: - 0.017 5.88 outclo T= + (3-1) outT : Outdoor air temperature [ ]K clo : Clothing level To develop the previous equation the maximum clothing (i.e. 1.25 clo) was assumed to be trousers, t-shirt, long-sleeve shirt, long-sleeve sweater, and suit jacket and the minimum (i.e. 0.67 clo) was trousers and short-sleeve shirt. As shown in Figure 3.21, adaptive clothing significantly improved occupants’ thermal comfort for both typical summer and winter days. Figure 3.21. Adaptive clothing over the typical summer and winter days. 0 4 8 12 16 20 245% 7% 9% 11% Hour PP D Baseline Adaptive Clothing 0 4 8 12 16 20 245% 7% 9% 11% Hour PP D Baseline Adaptive Clothing PREDICTED PERCENTAGE OF DISSATISFIED (WINTER)PREDICTED PERCENTAGE OF DISSATISFIED (SUMMER) 43 3.2.14. Adjusting the Occupancy Period The general purpose of adjusting the occupancy period over the summer is to avoid having a direct solar radiation on the zone external surface when the outdoor air temperature is near its maximum value. However, because the baseline zone did not have any external surface on the west façade, changing the occupancy period did not significantly affect the zone thermal performance. Over the typical winter day, the occupancy period was shifted one hour forward to increase the amount of solar heat gain. However, because of the small amount of solar radiation in winter, this also had a negligible impact on the zone thermal performance. 3.3. Whole Year Analyses According to the results of the screening analyses, the operational parameters that most significantly affected the HVAC energy consumption and/or occupants’ thermal sensations over the typical summer and winter days are: • Increasing the range of setpoints • Adaptive clothing • Increasing the air exchange rate over the cooling season The impacts of these parameters and their combination on the thermal performance of the baseline zone were investigated over the whole year, using the hourly Canadian Weather for Energy Calculations (CWEC) weather file of Vancouver, shown in Figure 3.22. The CWEC file contains hourly weather observations representing an artificial one-year period specifically designed for building energy calculations. These observations were derived from the Canadian Energy and Engineering Data Sets (CWEEDS) of hourly weather information from 1953 to1995. Further details on the CWEC file are given in Appendix A1.4.1. These files are available from Environment Canada, and are normally included in the standard building energy models. 44 Figure 3.22. The monthly averaged CWEC climate data of Vancouver. By implementing this climate data, the numerical model was initially applied on the baseline zone, explained in section 3.1, to investigate its thermal performance over the whole year. Figure 3.23 shows the histogram of the hours that the radiant ceiling slab provided heating/cooling into Figure 3.23. Baseline slab energy consumption over the whole year (Histogram). J F M A M J J A S O N D J2 4 6 8 10 Month H um id ity R at io [g w at er /k g d ry ai r] J F M A M J J A S O N D J2.5 3 3.5 4 4.5 Month W in d Sp ee d [m /s ] J F M A M J J A S O N D J0 80 160 240 320 Month N or m al D ir ec t S ol ar R ad ia tio n [W /m 2 ] J F M A M J J A S O N D J0 5 10 15 20 Month D ry -b ul b Te m pe ra tu re [C ] -3 -2 -1 0 1 2 3 4 5 6 70 100 200 300 400 500 Required Heating Load [kW] H ou r The HVAC system is off for 7704 hours (88% of the year) 45 the zone air at different capacities to maintain the zone air temperature at the desired range of setpoints. The positive and negative values on the horizontal axis are respectively heating and cooling capacities. According to the baseline zone control strategy the HVAC system was off over 7704 hours of the year. The daily mean and maximum required heating loads for the baseline zone are shown in Figure 3.24. It should be noted that the negative values on the vertical axis are cooling capacities. Figure 3.24. Baseline slab energy consumption over the whole year (Daily). The previous graph shows that it is possible to maintain the zone air temperature at the desired range of setpoints over about ten days in May and September without any energy consumption. The histogram of the baseline thermal comfort indicators, weighted averaged by the number of occupants, is shown in Figure 3.25. The two peaks in the PMV values correspond to the occupants’ thermal sensations over the heating and cooling seasons. Once the thermal performance of the baseline zone was determined, the impacts of the previous three operational parameters and their combination on the slab energy consumption and J F M A M J J A S O N D J-3 -2 -1 0 1 2 3 4 5 6 7 Month R eq ui re d H ea tin g Lo ad [k W ] Daily Max.Daily Mean 46 Figure 3.25. Baseline thermal comfort indicators over the whole year (Histogram). occupants’ occupants’ thermal comfort were investigated over the whole year. The final results of these analyses are summarized in Table 3.6. As previously mentioned the slab energy consumption in Table 3.6 refers to the heating/cooling that should be supplied to the slab to maintain the zone air temperature between the heating and cooling setpoints over the occupancy period. A detailed explanation on each of the previous analyses is provided in the following subsections. Slab Energy Consumption [kW.hr/m2.a] Results Analyses Cooling Heating Total Averaged PPD over the Occupied Hours Baseline 28 59 87 7.4% Increasing the range of setpoints 18 45 63 16.7% Adaptive clothing 28 59 87 5.8% Increasing the air exchange rate over the cooling season 15 59 75 7.2% Combination 5 45 50 11.7% Table3.6. The results of the whole year analyses. -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10 400 800 1200 PMV H ou r 0% 2% 4% 6% 8% 10% 12% 14%0 400 800 1200 PPD H ou r 47 3.3.1. Increasing the Range of Setpoints According the baseline zone control strategy, explained in section 3.1, over the time that the zone air temperature was within the desired range of setpoints, no cooling/heating was provided from the radiant ceiling slab into the zone air. Therefore, as shown in Figure 3.26, increasing this range to 18˚C-26˚C resulted in approximately 300 hours reduction in the operation of the HVAC system over the whole year. This reduced the annual slab energy consumption by 28%. Figure 3.26. Energy consumption with a broader range of setpoints over the whole year (Histogram). According to Figure 3.27, with a broader range of setpoints the number of days that there was no need for heating/cooling has notably increased. Increasing the range of setpoints also slightly dampened the peak loads both in heating and cooling seasons. This may reduce the capital cost for new projects by sizing the HVAC system at smaller capacity. By letting the zone air temperature more closely track patterns in the outdoor climate, the averaged occupants’ thermal dissatisfaction was increased by 9.3% in compare to the baseline. As shown in Figure 3.28, the PMV values were almost equally shifted from the neutral thermal sensation for both heating and cooling seasons. -3 -2 -1 0 1 2 3 4 5 6 70 100 200 300 400 500 Required Heating Load [kW] H ou r Baseline Setpoint Range: 18C-26C The HVAC system is off for 7704 hours (88% of the year) The HVAC system is off for 8007 hours (91% of the year) 48 Figure 3.27. Energy consumption with a broader range of setpoints over the whole year (Daily). -1.5 -1 -0.5 0 0.5 1 1.50 500 1000 1500 PMV H ou r 0% 5% 10% 15% 20% 25% 30%0 500 1000 1500 PPD H ou r Baseline Setpoint Range: 18C-26C Baseline Setpoint Range: 18C-26C Figure 3.28. Thermal comfort indicators with a broader range of setpoints over the whole year (Histogram). 3.3.2. Adaptive Clothing According to the screening analyses, the occupants’ thermal sensations were significantly improved over the typical summer and winter days by having them adapt their clothing based on the outdoor air temperature. Therefore, the same variation profile for the clothing level (i.e. J F M A M J J A S O N D J-3 -2 -1 0 1 2 3 4 5 6 7 Month R eq ui re d H ea tin g Lo ad [k W ] Daily Max.Daily Mean 49 equation 3-1), was applied to investigate the impacts of the adaptive clothing on the occupants’ thermal comfort over the whole year. The PMV histogram in Figure 3.29 shows that with adaptive clothing the occupants’ thermal comfort was improved over both heating and cooling seasons. As a result, the occupants’ thermal dissatisfactions were also effectively shifted toward its minimum value (i.e. 5%). -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10 500 1000 1500 2000 PMV H ou r 0% 2% 4% 6% 8% 10% 12% 14%0 1000 2000 3000 4000 PPD H ou r Baseline Adaptive Clothing Baseline Adaptive Clothing Figure 3.29. Thermal comfort indicators with adaptive clothing over the whole year (Histogram). 3.3.3. Increasing the Air Exchange Rate over the Cooling Season A controlling system was defined in the numerical model that opened the operable windows when the outdoor air was colder than the zone air over the cooling season. As the zone air temperature became closer to the heating setpoint, the windows were closed to prevent the heating system from turning on. Because the detailed modeling of air exchange rates with open windows was not the purpose of this research, the air exchange rate with open window was approximated at 1.3 ACH (Wallace et al. 2002). As shown in Figure 3.30, increasing the air exchange rate over the cooling season reduced the operation of the cooling system by approximately 300 hours. This resulted in 14% reduction in total slab energy consumption over the whole year. 50 -3 -2 -1 0 1 2 3 4 5 6 70 100 200 300 400 500 Required Heating Load [kW] H ou r Baseline Increased Air Exchange The HVAC system is off for 7704 hours (88% of the year) The HVAC system is off for 7984 hours (91% of the year) Figure 3.30. Energy consumption with higher air exchange rate (Histogram). Figure 3.31 shows that the higher air exchange rate over the cooling season has increased the number of days that there was no need for cooling. J F M A M J J A S O N D J-3 -2 -1 0 1 2 3 4 5 6 7 Month R eq ui re d H ea tin g Lo ad [k W ] Daily Max.Daily Mean Figure 3.31. Energy consumption with higher air exchange rate (Daily). Comparing the Vancouver climate data (i.e. Figure 3.22) with the zone desired range of setpoints; the higher air exchange rate reduced the zone air temperature when the occupants were 51 feeling warm. As shown in Figure 3.32, this improved the occupants’ thermal comfort and slightly shifted the positive PMV values toward the neutral thermal sensations. -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10 400 800 1200 PMV H ou r 0% 2% 4% 6% 8% 10% 12% 14%0 400 800 1200 PPD H ou r Baseline Increased ACH Baseline Increased ACH Figure 3.32. Thermal comfort indicators with higher air exchange rate (Histogram). 3.3.4. Combination Scenario According to the previous analyses, a broader range of setpoints reduced the annual slab energy consumption at the cost of higher thermal dissatisfaction. The adaptive clothing, however, improved occupants’ thermal comfort without any effect on the energy. Finally, increasing the air exchange rate improved both energy and thermal comfort; but only over the cooling season. Therefore, all the previous operational parameters were simultaneously applied to the baseline zone to investigate their interactions on the zone thermal performance and occupants’ thermal sensations over the whole year. As shown in Figure 3.33, the combination scenario reduced the operation of the HVAC system by approximately 600 hours. This resulted in 42% reduction in total annual slab energy consumption in compare to the baseline. It should be noted that the reduction in the required heating load was only caused by increasing the range of setpoints. However, the required cooling load was reduced by both higher air exchange rate and a broader range of setpoints. 52 -3 -2 -1 0 1 2 3 4 5 6 70 100 200 300 400 500 Required Heating Load [kW] H ou r Baseline Combination The HVAC system is off for 7704 hours (88% of the year) The HVAC system is off for 8291 hours (95% of the year) Figure 3.33. Energy consumption with the combination scenario over the whole year (Histogram). Figure 3.34 shows that the number of days for which there was no need for heating/cooling was also significantly increased, especially over the cooling season. As previously mentioned a broader range of setpoints has also slightly dampened the peak loads both over the heating and cooling seasons. This may reduce the size the HVAC system and consequently the capital cost of new projects. J F M A M J J A S O N D J-3 -2 -1 0 1 2 3 4 5 6 7 Month R eq ui re d H ea tin g Lo ad [k W ] Daily Max.Daily Mean Figure 3.34. Energy consumption with the combination scenario over the whole year (Daily). 53 The increase in the occupants’ thermal dissatisfaction due to a broader range of setpoints was considerably reduced by having the occupants adapt their clothing based on the outdoor air temperature. The higher air exchange rate over the cooling season also contributed to the occupants’ thermal comfort when they were feeling warm. Figure 3.35 compares the occupants’ thermal comfort indicators for the combination scenario against those of the baseline. It should be noted that although the average occupants’ thermal dissatisfaction for the combination scenario exceed the limit of the thermal comfort standard (i.e. 10% PPD), in practice the average thermal dissatisfaction over the whole year exceed 30% - 40% PPD in many buildings. -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10 700 1400 2100 PMV H ou r 0% 5% 10% 15% 20% 25% 0 400 800 1200 PPD H ou r Baseline Combination Baseline Combination Figure 3.35. Thermal comfort indicators with the combination scenario over the whole year (Histogram). 3.4. Climate Change Increase in the global average air and ocean temperatures, widespread melting of snow and ice, and rising global average sea level prove that warming of the climate system is unquestionable. Therefore, the effects of the global warming on the thermal performance of the baseline zone were investigated, by implementing the latest version of the Canadian Regional Climate Model (CRCM 3.6) for climate change simulations. CRCM 3.6 follows the IPCC IS92a forcing scenario and produces the monthly climate data with a 45 km horizontal grid size mesh. 54 The widely-used IPCC IS92a scenario was released by the Intergovernmental Panel on Climate Change in 1992. It was then implemented by a large number of climate modeling groups who have contributed to the IPCC Third Assessment Report. This scenario includes the direct effect of sulphate aerosols and has effective CO2 concentration increasing at 1% per year after 1990, shown in Figure 3.36. Figure 3.36. Increase in the effective CO2 concentration, based on the IPCC IS92a scenario. Figure 3.37 compares the current monthly averaged solar radiation and dry-bulb temperature of Vancouver against their values, predicted by CRCM 3.6 for the year 2050. This comparison shows that unlike the dry-bulb temperature, solar radiation is not significantly affected by the climate change. Therefore, to produce the hourly global warming climate data, the Vancouver CWEC weather file was modified, based on the discrepancies between the monthly averaged values of the dry-bulb temperature for the current time and the year 2050. By implementing the hourly global warming climate data, the numerical model was applied on the baseline zone, explained in section 3.1, to investigate its thermal performance for 2050. Figure 3.38 shows the effect of global warming on the histogram of the hours that the ceiling slab provided heating/cooling to the baseline zone at different capacities. According to this Figure, the total operating hours of the HVAC system was not significantly affected by the climate change. However, the higher outdoor air temperature, shown in Figure 3.37, notably increased the number of hours that the slab was operating in the cooling mode. 1850 1900 1950 2000 2050 21000 500 1000 1500 Year Ef fe ct iv e C O 2 C on ce nt ra tio n [p pm ] 55 Figure 3.37. The effects of climate change on the amount of solar radiation and dry-bulb temperature. -3 -2 -1 0 1 2 3 4 5 6 70 100 200 300 400 500 600 Required Heating Load [kW] H ou r Current 2050 The HVAC system is off for 7704 hours (88% of the year) The HVAC system is off for 7634 hours (87% of the year) Figure 3.38. Energy consumption with climate change over the whole year (Histogram). 0 3 6 9 120 70 140 210 280 350 Month In ci de nt S ol ar R ad ia tio n [W /m 2 ] Current 2050 0 3 6 9 120 5 10 15 20 25 Month D ry -b ul b Te m pe ra tu re [C ] Current 2050 0 3 6 9 120 5 10 15 20 25 Month M ea n D ai ly M ax . T em pe ra tu re [C ] Current 2050 0 3 6 9 120 5 10 15 20 25 Month M ea n D ai ly M in . T em pe ra tu re [C ] Current 2050 56 As shown in Figure 3.39, with global warming, the cooling season was extended by approximately one month. Also, the number of days that there was no need for heating/cooling were increased and shifted toward the heating season. Finally, with higher outdoor air temperature, the peak heating loads that determine the size of the heating system were reduced. Figure 3.39. Energy consumption with climate change over the whole year (Daily). Figure 3.40 shows that although the averaged thermal dissatisfaction was not significantly affected by the climate change, the number of hours that the occupants’ were feeling warm was notably increased. Once the baseline zone thermal performance for the year 2050 was determined, the effects of the combination scenario on its annual slab energy consumption and occupants’ thermal sensations were studied. Table 3.7 summarizes the final results of these analyses. 3.4.1. Combination Scenario As shown in Figure 3.41, with higher air exchange rate over the cooling season and a broader range of setpoints, the combination scenario reduced the operation of the HVAC system by J F M A M J J A S O N D J-3 -2 -1 0 1 2 3 4 5 6 7 Month R eq ui re d H ea tin g Lo ad [k W ] Daily Max. Daily Mean 57 approximately 600 hours. This resulted in 50.4% reduction in total annual slab energy consumption in comparison to that of the baseline zone in 2050. Figure 3.40. Thermal comfort indicators with climate change over the whole year (Histogram). Slab Energy Consumption [kW.hr/m2.a] Results Analyses Cooling Heating Total Averaged PPD over the Occupied Hours Current Baseline 28 59 87 7.4% Combination 5 45 50 11.7% 2050 Baseline 39 42 81 7.4% Combination 9 31 40 11.8% Table 3.7. The results of the whole year analyses for the current time and 2050. According to Figures 3.33 and 3.41, the total operating hours of the HVAC system with the combination scenario was almost the same for the current time and the year 2050. However, since the heating system was operating at lower capacities in 2050, shown in Figure 3.42, the total annual slab energy consumption was 10.4 kW.hr/m2.a less than its value for the current time. Figure 3.42 shows that the combination scenario has also effectively increased the number of days that there was no need for heating/cooling. -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10 400 800 1200 PMV H ou r 0% 2% 4% 6% 8% 10% 12% 14%0 400 800 1200 PPD H ou r Current 2050 Current 2050 58 Figure 3.41. Energy consumption with climate change and combination scenario over the whole year (Histogram). Figure 3.42. Energy consumption with climate change and combination scenario over the whole year (Daily). The combination scenario resulted in a modest increase in the occupants’ thermal dissatisfaction, which was caused by having a broader range of setpoints. However, the higher air exchange rate over the cooling season and the adaptive clothing for the occupants both contributed to the occupants’ thermal comfort. Figure 3.43 compares the occupants’ thermal comfort indicators for the combination scenario against those of the baseline in 2050. -3 -2 -1 0 1 2 3 4 5 6 70 100 200 300 400 500 600 Required Heating Load [kW] H ou r Baseline (2050) Combination (2050) The HVAC system is off for 7634 hours (87% of the year) The HVAC system is off for 8314 hours (95% of the year) J F M A M J J A S O N D J-3 -2 -1 0 1 2 3 4 5 6 7 Month R eq ui re d H ea tin g Lo ad [k W ] Daily Max. Daily Mean 59 Figure 3.43. Thermal comfort indicators with climate change and combination scenario (Histogram). -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10 500 1000 1500 PMV H ou r 0% 4% 8% 12% 16% 20%0 500 1000 1500 PPD H ou r Baseline (2050) Combination (2050) Baseline (2050) Combination (2050) 60 Chapter Four: Conclusions and Future Work 4.1. Conclusions The principal objective of this thesis work was to use a numerical model to investigate the interactions between the energy consumption in Heating, Ventilating, and Air Conditioning (HVAC) systems and occupants’ thermal comfort in commercial buildings. According to the previous studies (ANSI/ASHRAE STANDARD 55-2004) the thermal comfort in indoor environments responds to the interactions of the thermal environmental (i.e. temperature, thermal radiation, humidity, and air speed) and personal factors (i.e. activity and clothing). However, these interactions can hardly be captured by the existing building energy simulation programs. Therefore, a numerical model was developed to perform a thermal analysis of a single zone, which might represent a room or an entire building, and simultaneously investigate its occupants’ thermal comfort as a non-linear function of the thermal environmental and personal factors. The heat balance method, as the most accurate approach with the least number of assumptions, was applied in the model for the zone thermal analysis. This required that the First Law of Thermodynamics be enforced at each building element/air interface and on a control volume around the zone air mass. The thermal comfort calculations were carried out by implementing the current thermal comfort standard. The model was then validated and applied to a single generic zone, to investigate the impacts of variation in occupants’ behaviors, building’s envelope, HVAC system, and climate on both energy consumption and thermal comfort. This zone represents the perimeter office spaces of the Centre for Interactive Research on Sustainability (CIRS). The current design of these office spaces was selected as the baseline for the analyses. CIRS, which will be built in the Lower Mainland of British Colombia, is designed to be among the most innovative and high performance buildings in North America. The initial screening analyses were carried out over the typical summer and winter days of Vancouver to determine the parameters for which the impacts on the energy and/or thermal 61 comfort of the baseline zone were most significant. Among the large number of parameters involved, the most important ones are summarized in Table 4.1. Reduction in the energy and improvement in thermal comfort were resulted in having a positive percentage of variation in this table. Measures No. Summer Winter 1 Increasing the Air Exchange Rate (100%) Improving the Glazing System (26%) 2 Increasing the Range of Setpoints (100%) South Orientation (25%) H V A C E ne rg y C on su m pt io n1 3 North Orientation (97%) Increasing the Range of Setpoints (22%) 1 Increasing the Air Exchange Rate (4%) Increasing the Range of Setpoints (-12%) 2 Adaptive Clothing (4%) Adaptive Clothing (2%) Th er m al C om fo rt 2 3 Increasing the Range of Setpoints (-2%) Floor Slab Cooling/Heating (-2%) Table 4.1. Measures with the highest impact on energy and thermal comfort. Table 4.1 shows that, without any incremental cost, the energy consumption in both new and existing buildings may significantly be reduced by the following operational parameters: • Increasing the range of setpoints • Adaptive clothing • Increasing the air exchange rate over the cooling season Therefore, the impacts of these parameters on the thermal performance of the baseline zone were investigated over the whole year. A broader range of setpoints reduced the total annual energy consumption of the baseline zone by 28% at the cost of 9% increase in the averaged occupants’ thermal dissatisfaction. Varying the occupants’ clothing as a linear function of the outdoor air temperature notably shifted the averaged thermal dissatisfaction toward its minimum value but it ______________________________________________________________________________ 1. (Alternative Energy Consumption - Baseline Energy Consumption)/ Baseline Energy Consumption 2. (Alternative Averaged PPD - Baseline Averaged PPD) 62 did not have any effect on energy. Finally, increasing the air exchange rate reduced the total annual energy consumption of the baseline zone by 14% and also slightly improved the occupants’ thermal sensations. However, it was only effective over the cooling season. Regarding the results of the whole year analyses, the previous three operational parameters were simultaneously applied to the baseline zone. The primary purpose of defining the combination scenario was to dampen the increase in the occupants’ thermal dissatisfaction, caused by the broader range of setpoints, with higher air exchange rate over the cooling season and adaptive clothing for the occupants. The combination scenario reduced the total annual energy consumption of the baseline zone by 42% at the cost of only 4% increase in the averaged occupants’ thermal dissatisfaction. Considering the life of a building and warming of the global climate, the thermal performance of the baseline zone as well as the impacts of the combination scenario on its annual energy consumption and thermal comfort were also investigated for the year 2050. According to these analyses, global warming reduced both the size and operation of the heating system. However, it extended the cooling season by approximately one month. Overall, global warming reduced the total annual energy consumption of the baseline zone by 7% with a negligible change in the occupants’ thermal sensations. Global warming enhanced the effect of the combination scenario in reducing the baseline annual energy consumption. First, because the heating system was operating at a smaller capacity and over a shorter period of time; and second, with a longer cooling season, the higher air exchange rate became more effective in reducing the annual energy consumption. Consequently, the combination scenario reduced the total annual energy consumption of the baseline zone by 50% at the cost of only 4% increase in the averaged occupants’ thermal dissatisfaction in 2050. The final results of the whole year analyses are summarized in Table 4.2. It should be noted that the CIRS office spaces are not unique in benefiting from the careful treatment of comfort. These energy savings are achievable in almost any type of building, by understanding the interactions between the occupants’ thermal comfort and building thermal performance. 63 In general, the knowledge gained by performing a thermal analysis of a single zone with the numerical model will provide guidelines for the design and operation of more complex buildings. The model allows a more systematic approach to investigate the impacts of different measures related to the occupants’ behaviors, building’s envelope, HVAC system, and climate on both energy and thermal comfort. This approach eliminates the intricacy and imprecision, associated with the commercial software in evaluating these measures. Slab Energy Consumption [kW.hr/m2.a] Analyses Results Measures Cooling Heating Total Averaged Percentage of Thermal Dissatisfaction Baseline 28 59 87 7.4% Increasing the range of setpoints 18 45 63 16.7% Adaptive clothing 28 59 87 5.8% Increasing the air exchange rate over the cooling season 15 59 75 7.2% Current Combination 5 45 50 11.7% Baseline 39 42 81 7.4% Global Warming Combination 9 31 40 11.8% Table 4.2. The final results of the whole year analyses. 4.2. Future Work The single zone numerical model, developed in MATLAB for investigating the interactions between thermal comfort and HVAC energy consumption in indoor environments, has laid the foundation for future thermal comfort and building energy simulation studies. The main areas for further exploration are: • Validating the results of the numerical model with an experimental study. This could provide insight into how effectively the model could predict the actual thermal sensations of the zone occupants. 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Introduction To capture the temperature distributions inside the external opaque surfaces one dimensional transient conduction formulation was applied and solved with an explicit finite difference method. This requires that the thickness of these surfaces be divided into a known number of grids. Depending on the location of the grid points four different cases may occur: • Case One: Grid points inside slabs. • Case Two: Grid points on the boundary of two adjacent slabs. • Case Three: Grid point on the exterior surface. • Case Four: Grid point on the interior surface. This appendix presents a comprehensive explanation on the application of the heat balance method in each of these cases. In addition to the main assumptions of the heat balance method, the following assumptions were made for the external opaque surfaces: • Thermal properties of the slabs (e.g. thermal conductivity, specific heat capacity, Thermal diffusivity, etc.) are always constant. • The first law of thermodynamics was simplified to: net to sys net by sys Eq W τ− − − − ∂− = ∂ (A1-1) :net to sysq − − Rate of adding heat to the system. 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ :net by sysW − − Rate of work done by the system. 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ :Eτ ∂ ∂ Rate of change in internal energy of the system. 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ 0net by sys net to sys EW q τ− − − − ∂= → = ∂ (A1-2) 72 A1.2. Case One: Grid Points inside Slabs The schematic of the case one scenario is shown in Figure A1.1. The conduction heat transfers from/to adjacent grid points are the only heat fluxes that affect the control volume. The direction of these heat fluxes may change depending on the temperatures of the interior and exterior surfaces. Specific direction (i.e. from inside to outside) was assumed to derive the governing equation for this case. Figure A1.1. Case One: Grid points inside slabs. Applying the first law of thermodynamics on the control volume: net to sys Eq τ− − ∂= ∂ (A1-3) g g+1g-1 qx x+Δqx 2 xΔ k Control Volume 2 xΔxΔ Tg+1Tg-1 Tg 73 In which: E Tc dxρτ τ ∂ ∂=∂ ∂ (A1-4) : Density of the slabρ 3 kg m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . : Specific heat capacity of the slabc . J kg K ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . : Rate of change of temperature . T K Sτ ∂ ∂ ⎡ ⎤⎢ ⎥⎣ ⎦ Considering the heat fluxes on the control volume, shown in Figure A1.1: net to sys x x xq q q qdx− − +Δ= − + (A1-5) : Heat generation inside the slabq 3 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . Replacing (A1-4) and (A1-5) in (A1-3) and applying the Fourier’s law: T T T Tk k k dx qdx c dx x x x x ρ τ ⎛ ⎞∂ ∂ ∂ ∂ ∂⎛ ⎞ ⎛ ⎞− − − − + =⎜ ⎟ ⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠⎝ ⎠ (A1-6) : Thermal conductivity of the slabk . W m K ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . Regarding that the thermal properties of the slabs were assumed to be constant: 2 2 T Tk q c x ρ τ ∂ ∂+ =∂ ∂ (A1-7) Considering the explicit finite difference approach: 1 1 2 p p g g g T TT x x − − −∂ ⎤ ≈⎥∂ Δ⎦ (A1-8) 74 1 1 2 p p g g g T TT x x + + −∂ ⎤ ≈⎥∂ Δ⎦ (A1-9) 1 12 1 12 2 2 2 2 ( ) p p pg g g g g g T T x x T T TT x x x + − − + ∂ ∂⎤ ⎤−⎥ ⎥∂ ∂⎦ ⎦ + −⎤∂ ≈ =⎥∂ Δ Δ⎦ (A1-10) p and g in the previous equations, respectively represent the time and the grid point position (i.e. counted from inside to outside). Implementing these equations in (A1-7): 1 1 1 2 2 1 ( ) p p p p p g g g g gT T T T Tq x k α τ + − ++ − −+ =Δ Δ (A1-11) α : Thermal diffusivity 2ms ⎡ ⎤⎢ ⎥⎣ ⎦ . Rearranging Equation (A1-11), 1pgT + (i.e. temperature of the grid g at the next time step) may be calculated by: 2 1 1 12 2 ( ) 1 2 ( ) ( ) p p p p g g g g q xT T T T x k x α τ α τ+ − + ⎛ ⎞ ⎛ ⎞Δ Δ Δ= + + + −⎜ ⎟ ⎜ ⎟Δ Δ⎝ ⎠⎝ ⎠ (A1-12) A1.3. Case Two: Grid Points on the Boundary of Two Adjacent Slabs Typically, the external opaque surfaces comprise different slabs. Unlike the previous case, the grid points that are located on the boundary of two adjacent slabs do not have identical thermal properties on both sides. Therefore, a novel formulation is required to calculate their temperatures for the next time step. Figure A1.2 shows the control volume and the transient heat fluxes involved in this case. The direction of these heat fluxes may change depending on the temperatures of the interior and exterior surfaces. To derive the governing equation for the temperature at the next time step, it was assumed that the direction of the heat flow is from inside to outside. 75 Figure A1.2. Case Two: Grid points on the boundary of two adjacent slabs. Applying the first law of thermodynamics on the control volume: x x x Tq q qdx c dxρ τ+Δ ∂− + = ∂ (A1-13) Considering the Fourier’s law: 1 2 1 2 1 1 2 2 1 1 1 2 2 2 2 2 2 2g g T T dx dx T dx T dxk k q q c c x x ρ ρτ τ− + ⎛ ⎞ ⎛ ⎞∂ ∂ ∂ ∂⎤ ⎤ ⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟− − − + + = +⎜ ⎟ ⎜ ⎟⎥ ⎥⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎦ ⎦ ⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠ (A1-14) Using the finite difference approach: g g+1g-1 qx x+Δqx 2 xΔ k1 k2 Control Volume 2 xΔ 2 xΔ 2 xΔ Tg+1Tg-1 Tg 76 ( ) 11 11 2 p p g g g g g g avg avg T T T T T T k k q x c x x x ρ τ + − +− − −+ + Δ = ΔΔ Δ Δ (A1-15) In which, ( )avgcρ and avgq are: ( ) 1 1 2 2 2avg c cc ρ ρρ +⎛ ⎞= ⎜ ⎟⎝ ⎠ (A1-16) 1 2 2avg q qq += (A1-17) Therefore, 1pgT + may be determined by: ( ) ( )1 2 1 21 1 2 12 2 ( )( ) 1 ( ) ( ) p p p p g g g avg g avg avg k kT k T k T q x T c x c x ττ ρ ρ + − + ⎡ ⎤+ ΔΔ ⎡ ⎤ ⎢ ⎥= + + Δ + −⎣ ⎦Δ Δ⎢ ⎥⎣ ⎦ (A1-18) A1.4. Case Three: Grid Point on the Exterior Surface The main transient heat fluxes that affect the exterior of the external opaque surfaces are illustrated in Figure A1.3. Before considering the application of the heat balance method for this case, these heat fluxes should be described. A1.4.1. External Shortwave Solar Radiation That part of the solar irradiation that is not scattered or absorbed with in the earth’s atmosphere is called direct irradiation. This is accompanied by irradiation that has been scattered or reemitted, called diffuse irradiation. Solar irradiation may also be reflected onto a surface from the nearby surfaces, which in this case is a reflected irradiation. Thus, the total irradiation ( )tG on 77 the surface normal to the sun’s rays is made up of direct irradiation ( )DG , diffuse irradiation ( )dG , and reflected irradiation ( )RG : t D d RG G G G= + + (A1-19) Figure A1.3. Transient heat fluxes on the exterior surfaces of a building. Depending on the absorptivity of the exterior surfaces, the absorbed shortwave solar radiation may be calculated by: , ,SW solar ext sol tq Gα= (A1-20) solα : Solar absorptivity of the surface, dimensionless. However, the external opaque surfaces are hardly normal to the sun’s rays; Therefore, the effects of solar angles should also be considered in the previous equations. The main solar angles are OUT Tout Sun Tsky GD Gd GR Exterior Convection Longwave Radiation To/From the Ground and Surroundings Longwave Radiation To/From the Sky Direct Irradiation Diffuse Irradiation Direct and Diffuse Irradiation Tgr OUT Tout ZONE TinF en es tra tio n Control Volume 78 shown in Figure A1.4. To calculate these solar angles, the following three fundamental quantities should first be identified: • Location on the earth’s surface (latitude [deg]) • Time of day (hour angle [deg]) • Day of year (sun’s declination [deg]) Figure A1.4. Different solar angles between the sun and a surface in an arbitrary direction (ASHRAE 2005). The hour angle is the angle between the meridian passing the surface and sun’s rays direction. This can be calculated by: ( )15 12H LST= − (A1-21) In which, LST is the local solar time and equal to: 79 ( )(4min/ deg)L SLST LCT L L EOT= − − + (A1-22) : Local civil timeLCT . : Longitude [deg]LL . : Standard meridians [deg]SL . : Equation of time [min]EOT . Spencer (1971) determined EOT by: [ ]229.2 0.002cos( ) 0.032sin( ) 0.015cos(2 ) 0.041sin(2 )EOT N N N N= − − − (A1-23) where N is: 0.9863( 1)N n= − (A1-24) n : Number of days 1 n≤ ≤ 365. Spencer (1971) also developed an equation for calculating the sun’s declination for different days of the year: 0.396 - 22.913cos( ) 4.025sin( ) - 0.387cos(2 ) 0520sin(2 ) - 0.155cos(3 ) 0.0848sin(3 ) N N N N N N δ = + + + (A1-25) Once the latitude, the hour angle, and the sun’s declination are determined, the other solar angles may be calculated using the analytical geometry: • Solar altitude angle[deg] is the angle between the sun’s ray and the projection of that ray on the horizontal surface and may be computed by: sin cos( )cos( )cos( ) sin( )sin( )L H Lβ δ δ= + (A1-26) : Latitude[deg]L 80 • Solar azimuth angle[deg] , measured from the south is: sin( )sin( ) sin( )cos( ) cos( )cos( ) L L β δφ β −= (A1-27) • Solar incident angle[deg] is the angle between the sun’s rays direction and normal to the surface. This can be estimated by: cos( ) cos( )cos( )cos( ) sin( )cos( )θ β γ β= Σ + Σ (A1-28) Σ : Surface tilt angle [deg] is the angle between the normal of the surface and the normal of the horizontal surface. γ in the previous equation, is the surface-solar azimuth angle, given by: γ φ= − Ψ (A1-29) Ψ : Surface azimuth angle, measured from the south[deg] Applying these solar angles, the total solar irradiation, incident on different zone surfaces can be calculated by adding the following three terms: • Direct solar irradiation: On a surface of arbitrary orientation, the direct solar irradiation, may be computed by: D N NDG =C G max(cos ,0)θ (A1-30) Direct solar irradiation:DG 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . NC : Atmospheric clearness number, dimensionless. : Normal direct solar irradiationNDG 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . Note that the solar incident angles of higher than 90˚, results in having no direct solar irradiation on the surface (i.e. the surface is completely shaded). 81 • Diffuse solar irradiation: To calculate the diffuse solar irradiation, the sky was assumed to be isotropic (i.e. uniformly bright, excepting the sun). therefore, on a clear day the diffuse solar irradiation that strikes a given surface is: NDCGsky se d eos A F G A = (A1-31) Diffuse solar irradiation:dG 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . C : The ratio of diffuse irradiation to direct normal irradiation, dimensionless. seF : The fraction of the diffuse radiation in the sky that strikes a given surface, dimensionless. eosA : Area of an external opaque surface 2m⎡ ⎤⎣ ⎦ . skyA : Sky area 2m⎡ ⎤⎣ ⎦ . Although it is difficult to directly determine seF , the fraction of the energy that leaves the surface and strikes the sky directly (i.e. esF ) can easily be determined from the geometry: 1 cos( ) 2es F + Σ= (A1-32) Considering the reciprocity relationship between view factors: sky se eos esA F A F= (A1-33) Therefore, Equation (A1-31) can be simplified to: d NDG =CG esF (A1-34) Where, esF is estimated by (A1-32). 82 • Reflected solar irradiation: Assuming that the ground reflects diffusely, and considering the reciprocity relationship between view factors, the solar irradiation reflected from the ground onto a surface with arbitrary orientation is: R tH g egG G Fρ= (A1-35) RG : Reflected solar irradiation 2 w m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . tHG : Rate at which the sum of the direct and diffuse solar irradiation strikes the ground 2 w m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . gρ : Reflectance of the ground, dimensionless. egF : View factor of the external opaque surface to the ground, dimensionless. Using the analytical geometry, egF in the previous equation is: 1 cos( ) 2eg F − Σ= (A1-36) Identifying the direct, diffuse and reflected solar irradiation, the total solar irradiation incident on a given surface may be calculated by: N ND NDC G max(cos ,0) CGt es tH g egG F G Fθ ρ= + + (A1-37) tG : Total solar irradiation on a surface of arbitrary orientation 2 w m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ The underlined terms in the previous equation are available on an hourly basis for different cities of Canada from CWEC (Canadian Weather for Energy Calculations) weather files. These files are produced by Numerical Logics in collaboration with Environment Canada and the National Research Council of Canada. They contain hourly weather observations representing an artificial one-year period specifically designed for building energy calculations. Figure A1.5 is an example of these weather files for January 1st in Vancouver. 83 Figure A1.5. Vancouver CWEC climate data for January 1st. A1.4.2. External Longwave Radiation The next heat flux that affects the exterior surfaces is the longwave radiation. The external opaque surfaces radiate to/from the surrounding ground, vegetations, other buildings, and the sky. To make the problem tractable, the following assumptions were made: • Each surface emits and reflects diffusely and is gray. • Radiation to the sky, where the atmosphere is actually a participating medium, was modeled as heat transfer to/from a surface with an effective sky temperature. • The zone sits on a flat featureless plane with a temperature equal to that of the outdoor air. With these assumptions, the long wave radiation heat flux is: , ,LW rad ext ground skyq q q= + (A1-38) , ,LW rad extq : The net longwave radiation heat flux from the exterior surface 2 w m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . groundq : The net longwave radiation heat flux from the surface to the ground 2 w m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . skyq : The net longwave radiation heat flux from the surface to the sky 2 w m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . 84 Depending on the temperatures of the sky, the ground and the external opaque surface, the direction of the longwave radiation heat flux may change. Assuming specific direction for this heat flux (i.e. from inside to outside) and applying the Stefan-Boltzmann Law, Equation (A1-38) may be written as: ( ) ( ) ( ) ( ) 4 4 4 4 , , 4 4 4 4 LW rad ext eg es g es es sky eg es out es es sky q F T T F T T F T T F T T εσ εσ ⎡ ⎤= − + −⎣ ⎦ ⎡ ⎤= − + −⎣ ⎦ (A1-39) ε : Long-wave emittance of the surface, dimensionless. σ : Stefan-Boltzmann constant 2 4 W m K ⎡ ⎤⎢ ⎥⎣ ⎦ . esT : Exterior surface temperature[ ]K . outT : Dry bulb air temperature[ ]K . gT : Ground surface temperature[ ]K . skyT : Effective sky temperature[ ]K . egF : View factor of the external opaque surface to the ground, dimensionless. esF : View factor of the external opaque surface to the sky, dimensionless. esF and egF in the previous equation may respectively be found from (A1-32) and (A1-36). McClellan & Pedersen (1997) estimated the effective sky temperature, seen by horizontal surface under clear sky condition by: , 6sky Horz outT T= − (A1-40) ,sky HorzT : Effective sky temperature for a horizontal surface[ ]K . The effective sky temperature on non-horizontal surfaces was approximated by Walton’s heuristic model (1983): 85 , ,cos 1 cos2 2sky sky Horz out T T TΣ ⎡ ⎤ ⎡ ⎤Σ Σ⎛ ⎞ ⎛ ⎞= + −⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦ (A1-41) ,skyT Σ : Effective sky temperature for a tilt surface[ ]K . In order to linearize equation (A1-39), the radiation heat transfer coefficients were defined as follow: ( ) ( ) 4 4 , 1 cos( ) 2 es out rad gr es out T T h T T εσ ⎡ ⎤− Σ⎛ ⎞ −⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥= −⎢ ⎥⎢ ⎥⎣ ⎦ (A1-42) ( ) ( ) 4 4 , 1 cos( ) 2 es sky rad sky es sky T T h T T εσ ⎡ ⎤+ Σ⎛ ⎞ −⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥= −⎢ ⎥⎢ ⎥⎣ ⎦ (A1-43) As a result, the net longwave radiations from the exterior surfaces may be determined by: ( ) ( ), , , ,LW rad ext rad gr es out rad sky es skyq h T T h T T= − + − (A1-44) A1.4.3. External Convection According to the temperatures of the external opaque surfaces and that of the outdoor air, the direction of the convection heat flux may change. Applying the classical formulation, the convection heat flux from these surfaces to the outdoor air is: ( ), ,conv ext conv ext es outq h T T= − (A1-45) ,conv extq : Convection heat flux from the exterior surface to the outdoor air 2 w m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . ,conv exth : Convection heat transfer coefficient on the exterior of the external opaque surface 2. w m K ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . 86 Since the 1930's, substantial research has gone into the formulation of models for estimating the exterior convection coefficient. Among all these, the DOE-2 convection model seems to strike a reasonable balance for accuracy and ease of use. This model reflects the effects of natural and forced components by introducing the following correlation: , ( )conv ext n f f nh h R h h= + − (A1-46) nh : Natural convection component 2. w m K ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . fh : Forced convection component 2. w m K ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . fR : Surface roughness multiplier, dimensionless. ASHRAE (1993) computed the natural convection component for the upward heat flow by: ( )1/ 3 9.482 7.238 cos es out n T T h −= − Σ (A1-47) For downward heat flow, the natural convection component is: ( )1/ 3 1.81 1.382 cos es out n T T h −= + Σ (A1-48) Note that Equations (A1-47) and (A1-48) are equivalent for vertical surfaces. The DOE-2 convection model defines the forced convection component by: ( ) ( )22 bf n windh h aV= + (A1-49) ,a b : Constants given in Table A1.1. windV : Wind speed at standard condition m s ⎡ ⎤⎢ ⎥⎣ ⎦ 87 Direction 3. Ja m K ⎡ ⎤⎢ ⎥⎣ ⎦ b Windward 2.38 0.89 Leeward 2.86 0.617 Table A1.1. Convection correlation coefficients (Yazdanian and Klems 1994). Leeward in the previous Table is defined as greater than 100 degrees from normal incidence (Walton 1981). fR in Equation (A1-46) is based on the ASHRAE graph of surface conductance (ASHRAE 1981) and can be obtained from the following Table : Roughness Index Rf Example Material 1 (Very Rough) 2.17 Stucco 2 (Rough) 1.67 Brick 3 (Medium Rough) 1.52 Concrete 4 (Medium Smooth) 1.13 Clear pine 5 (Smooth) 1.11 Smooth Plaster 6 (Very Smooth) 1.00 Glass Table A1.2. Surface roughness multipliers (Walton 1981). After identifying all the heat fluxes that affect the exterior of the external opaque surfaces, the first law of thermodynamics was applied to balance them with the conduction heat transfer from/to the adjacent grid point. The control volume and the heat fluxes involved are shown in Figure A1.6. Assuming that the heat flow direction is from inside to outside: , , , , , 2 2cond SW sloar ext LW rad ext conv ext dx cdx Tq q q q q ρ τ ∂+ − − + = ∂ (A1-50) 88 Figure A1.6. Case Three: Grid point on the exterior surface of a building. where, longwave radiation and convection heat fluxes were respectively determined from (A1- 44) and (A1-45): 1 , , , , , ( ) ( ) ( ) 2 2 es es SW solar ext rad gr es out rad sky es sky conv ext es out T Tk q h T T h T T x x c x Th T T q ρ τ − − + − − − −Δ Δ Δ ∂− − + = ∂ (A1-51) Rearranging the previous equation based on the exterior surface temperature: ( ) 1 , , , , , , 1 , , , , 2 2 es SW sloar ext rad gr air out rad sky sky conv ext out p p p rad gr air rad sky conv ext es es es T xk q h T h T h T q x k c xh h h T T T x ρ τ − + Δ⎛ ⎞+ + + + +⎜ ⎟Δ⎝ ⎠ Δ⎛ ⎞− + + + = −⎜ ⎟Δ Δ⎝ ⎠ (A1-52) gg-1 2 xΔ k Control Volume 2 xΔ Tg-1 Tg OUT Tout condq , ,SW solar ext q ,conv ext q , ,LW rad ext q 89 Finally, the temperature of the grid point on the exterior of the external opaque surfaces at the next time step may be calculated by: ( ) 21 , , , , ,2 2 1 , , , 2 2 2 ( ) 2 p es SW sloar ext rad gr out rad sky sky conv ext out p es es rad gr rad sky conv ext t x xT q h T h T h T q x k k x xT T h h h t k α α + − ⎧Δ Δ Δ= + + + +⎨Δ ⎩ ⎫⎛ ⎞Δ Δ ⎪+ + − + + − ⎬⎜ ⎟Δ ⎪⎝ ⎠⎭ (A1-53) A1.5. Case Four: Grid Point on the Interior Surface Figure A1.7 shows the main heat fluxes that affect the interior of the external opaque surfaces. Before deriving the governing equation for this case, these heat fluxes should be identified. Figure A1.7. Transient heat fluxes on the interior surfaces of a building. Sun GD Gd GR External Opaque Surfaces (Walls/Roof) Fe ne st ra tio n Interior Convection Transmitted Diffuse Solar Radiation Radiation between internal surfaces OUT Tout OUT Tout Fe ne st ra tio n Direct Irradiation Diffuse Irradiation Direct and Diffuse Irradiation Diffuse Reflected Solar Radiation from the Floor Transmitted Direct Solar Radiation Radiation from Internal Heat Gains ZONE Tin Control Volume 90 A1.5.1. Longwave Radiation between Surfaces To model the radiation heat exchange between interior surfaces, the zone air was assumed to be completely transparent to the Longwave radiation (Pedersen et al.1997). Also, the radiation to/from the furnishings is ignored, because in most situations describing the furnishings in detail is likely to be burdensome and has little point as the arrangement of the furnishings rarely remains constant over the life of the building. Among different models that have investigated the long wave radiation between interior surfaces (Carrol 1980, Walton 1980, Davies 1988, and Liesen 1997), Walton’s mean radiant temperature method was found to be a reasonably simple model with an acceptable accuracy. For each surface in the zone, the model represents all of the other surfaces as a single fictitious surface with a representative area, emissivity, and temperature. The area of the fictitious surface is the sum of the other areas of the other surfaces: 1 (1 ) N fs i si i A A ς = = −∑ (A1-54) fsA : The area of the fictitious surface 2m⎡ ⎤⎣ ⎦ . iA : The area of the i th surface 2m⎡ ⎤⎣ ⎦ . siς : Kronecker delta: 1 if s=i 0 if s i ⎧⎪⎨⎪⎩ ≠ N : Number of zone interior surfaces. The emissivity of the fictitious surface is an area-weighted average of the individual surface emissivities: 1 1 (1 ) (1 ) N i i si i fs N i si i A A ε ς ε ς = = − = − ∑ ∑ (A1-55) 91 fsε : Emissivity of the fictitious surface, dimensionless. iε : Emissivity of the ith surface, dimensionless. The temperature of the fictitious surface is an area-emissivity-weighted temperature: 1 1 (1 ) (1 ) N i i i si i fs N i i si i A T T A ε ς ε ς = = − = − ∑ ∑ (A1-56) fsT : Temperature of the fictitious surface[ ]K . iT : Interior temperature of the i th surface[ ]K . Walton (1980) approximated the view factor of the fictitious surface by: 1 11 1 fs fss s s f fs F A A εε ε ε = ⎛ ⎞ −− + + ⎜ ⎟⎜ ⎟⎝ ⎠ (A1-57) Applying the Stefan-Boltzmann Law, the longwave radiation coefficient is: ( ) 4 4 , , is fs LWrad in s fs is fs T T h F T T σ −= − (A1-58) ,LWrad inh : The longwave radiation coefficient on the interior of surface “s” 2. w m K ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . The direction of the longwave radiation may change depending on the temperatures of the zone interior surfaces. Assuming that the direction of the heat flow is from inside to outside, the net longwave radiation absorbed by each specific surface may be calculated by: ( ), , , ,LWrad in s LWrad in s fs isq h T T= − (A1-59) ,LWrad inq : The net longwave radiation to the interior of surface “s” 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . 92 A1.5.2. Radiation from Internal Heat Gains The radiative portion of the sensible heat gain from people, lighting, and equipment is assumed to be uniformly distributed on all the interior surfaces. Therefore, the radiation heat flux on each of the interior surfaces from internal heat gains may be calculated by: , , , , , , 1 rad people S people rad light lighting rad equip S equipment rad Sihg N i i F Q F Q F Q q A = + += ∑ (A1-60) ,rad Sihgq : Total radiation heat flux from internal heat gains 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . ,S peopleQ : Total sensible heat gain from people[ ]W . lightingQ : Total heat gain from lighting[ ]W . ,S equipmentQ : Total sensible heat gain from equipment[ ]W . radF : Radiative fraction, dimensionless. 1 N i i A = ∑ : Sum of the all interior surfaces 2m⎡ ⎤⎣ ⎦ . According to the design and specifications of a building, ASHRAE (2005) provides appropriate values for the terms in the previous equation. A1.5.3. Transmitted Solar Radiation The transmitted direct and diffuse solar radiations from the glazing systems affect the heat balance on the zone interior surfaces. These two terms were calculated, using the following equations: ( ), , 1 m TSHG D IAC D sl g D i i q T T A Gθ = = ∑ (A1-61) ,TSHG Dq : Total transmitted direct solar radiation[ ]W . 93 IACT : Interior solar attenuation coefficient (i.e. Internal shading) of window i, dimensionless. DT θ : Direct transmissivity of window i at incident angle ofθ , dimensionless. ,sl gA : Sunlit area of window i at incident angle ofθ 2m⎡ ⎤⎣ ⎦ . m : Number of windows. ( ), 1 ( ) m TSHG d IAC d g d R i i q T T A G Gθ = = +∑ (A1-62) ,TSHG dq : Total transmitted diffuse solar radiation[ ]W . dT θ : Diffuse transmissivity of window i, dimensionless. gA : Glazing area of window i 2m⎡ ⎤⎣ ⎦ . The optical properties of the standard glazing systems at a range of incident angles, required in the previous equations, have been tabulated in ASHRAE (2005). To determine the transmitted direct solar radiation from a glazing system with external shadings (i.e. overhangs or side fins), the sunlit area was calculated by applying the analytical geometry. Figure A1.8 illustrates a window with a horizontal overhang on the top and vertical fins on both sides. The shadow height ( HS ) and shadow width ( WS ), respectively produced by the horizontal ( HP ) and vertical ( vP ) projections, are equal to: ( )cos sin tanW VS P λ λ γ= + (A1-63) tan cosH H S P βγ ⎛ ⎞= ⎜ ⎟⎝ ⎠ (A1-64) λ : Angle between the normal of the fin and the normal of the glazing surface[deg] . Having these two, the sunlit area, required in equation (A1-61), is: , ( * ( ) * )sl g g H H WA A W S H S S= − + − (A1-65) 94 Figure A1.8. Glazing system with external shadings. To calculate the portion of the total transmitted solar radiation absorbed by each of the zone surfaces, the following two assumptions were made: • All transmitted direct solar radiation incident on the floor and absorbed in proportion to the floor solar absorptance. • The reflected portion from the floor is added to the calculated total transmitted diffuse radiation and the sum is uniformly absorbed by all the interior surfaces. Considering these assumptions, the solar radiation absorbed by all the interior surfaces, except the floor, are identical and equal to: , , , 1 (1 )TSHG d floor TSHG D solar in N i i q q q A α = + −= ∑ (A1-66) ,solar inq : Solar radiation absorbed by the zone interior surfaces (except the floor) 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . PH Sw SH PV Left Vertical Projection Right Vertical Projection Horizontal Projection λ 95 However, the solar radiation absorbed by the floor may be calculated by: , , , , 1 (1 )TSHG d floor TSHG D floor TSHG D solar floor N floor i i q q q q AA α α = + −= + ∑ (A1-67) ,solar floorq : Solar radiation absorbed by the floor 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . A1.5.4. Internal Convection The convection heat flux from/to interior surfaces was modeled, using the classical formulation. Assuming the direction of the heat flow is from inside to outside, the convection heat flux from the zone air to the interior surfaces is: ( ), , , ,conv in s conv in s in isq h T T= − (A1-68) , ,conv in sq : Convection heat flux to the interior of surface “s” 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . , ,conv in sh : Convection heat transfer coefficient on the interior of surface “s” 2 .K W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . inT : Zone air temperature[ ]K . isT : Interior surface temperature[ ]K . Depending on the orientation of the surface and the direction of the heat flow, the convection heat transfer coefficient on interior surfaces may be obtained from Table A1.3: Orientation of surface Direction of heat flow , 2 .conv in W m K h ⎡ ⎤⎢ ⎥⎣ ⎦ Horizontal Upward 4.15 Horizontal Downward 1.02 Vertical Horizontal 3.18 Table A1.3. Convection heat transfer coefficients on interior surfaces (McQuiston et al. 2005). 96 Once the heat fluxes on the interior surfaces of a building have been determined, the first law of thermodynamics can be applied on the control volume shown in Figure A1.9 to balance them with the conduction heat transfer to the adjacent grid point. Figure A1.9. Case Four: Grid point on the interior surface of a building. , , , , 2 2cond LWrad in rad Sihg solar in conv in q q dx cdx Tq q q q ρ τ ∂− + + + + + = ∂ (A1-69) Substituting from (A1-59) and (A1-68): ( ) ( )2 , , , , 2 2is iLWrad in fs is rad Sihg solar in conv in n isT T x c x Tk h T T q q h T T qx ρ τ− Δ Δ ∂− + − − =Δ ∂+ + + + (A1-70) g g+1 2 xΔ k Control Volume 2 xΔ Tg-1Tg In Tin condq ,rad Sihg q ,conv in q , ,LW rad in q ,solar in q 97 Rearranging based on the interior surface temperature: ( ) 2 , , , , 1 , , 2 2 LWrad in fs rad Sihg solar in conv in in p p p LWrad in conv in is is is T x h q q h q x k h h x k T T c xT T Tρ τ + Δ+Δ Δ ⎛ ⎞+ + + +⎜ ⎟⎝ ⎠ Δ⎛ ⎞− + + = −⎜ ⎟ Δ⎝ ⎠ (A1-71) As a result, the temperature of the grid point on the interior of the external opaque surfaces at the next time step may be calculated by: ( ) 21 , , , ,2 2 2 , , 2 2 2 ( ) 2 p is LWrad in fs rad Sihg solar in conv in in p is LWrad in conv in h q q h h h t x xT T T q x k k x xT T t k α α + ⎧Δ Δ Δ= + + + +⎨Δ ⎩ ⎫⎛ ⎞Δ Δ ⎪+ + − + − ⎬⎜ ⎟Δ ⎪⎝ ⎠⎭ (A1-72) It is important to note that in order to avoid violating the second law of thermodynamics the coefficient of the temperature at the current time ( pT ) in all the previous four cases (i.e. Equations A1-12, A1-18, A1-53, A1-72) should be positive. This limiting condition was used to determine the maximum time step for the model. 98 Appendix Two: Heat Balance Method on the Transparent Surfaces Considering the thermal network for a double-pane window shown earlier in Figure 2.2, the only heat flux that has not been investigated in Appendix One is the absorbed solar radiation. The solar radiations incident from outside and inside are absorbed throughout a glazing system rather than just at the exterior and interior surfaces. Therefore, a novel formulation is required for calculating the absorbed solar radiation by each pane. The outside-to-inside solar radiation absorbed by each pane may be computed by summing the contributions of the direct radiation (i.e. only incident on the sunlit area of the glazing) as well as the diffuse and reflected radiations (i.e. incident over the entire area of the glazing). Therefore, the outside-to-inside solar radiation absorbed by the exterior pane of a glazing system is equal to: ( ),, , ,sl gWsolarf e D f e D df e d R g A q G G G Aθ α α⎛ ⎞= + +⎜ ⎟⎜ ⎟⎝ ⎠ (A2-1) ,Wsolarf eq : Outside-to-inside solar radiation absorbed by the exterior pane 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ ,D f eθα : Direct absorptivity of an exterior pane at the incident angle ofθ , dimensionless. ,df eα : Diffuse absorptivity of an exterior pane, dimensionless. The direct, diffuse, and reflected solar irradiation may respectively be calculated by (A1-30), (A1-34), and (A1-35). The sunlit area is determined in Appendix One by (A1-65). Also, the subscript f in the previous equation specifies that the absorptivities apply for solar radiation coming from the front or exterior of a glazing system. The outside-to-inside solar radiation incident on the interior pane is the portion of the total shortwave solar radiation that has been transmitted from the exterior pane: ( ),, , , , ,sl gWsolarf i D f i D f e D df i df e d R g A q G G G Aθ θ α τ α τ⎛ ⎞= + +⎜ ⎟⎜ ⎟⎝ ⎠ (A2-2) 99 ,Wsolarf iq : Outside-to-inside solar radiation absorbed by the interior pane 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . ,D f iθα : Direct absorptivity of an interior pane at the incident angle ofθ , dimensionless. ,df iα : Diffuse absorptivity of an interior pane, dimensionless. ,D f eθτ : Direct transmissivity of an exterior pane at the incident angle ofθ , dimensionless. ,df eτ : Diffuse transmissivity of an exterior pane, dimensionless. As previously mentioned in Appendix One, the diffuse solar radiation incident from inside on the zone interior surfaces, is the sum of the reflected solar radiation from the floor and the total transmitted diffuse radiation. This is calculated in Appendix One by (A1-66). Therefore, the inside-to-outside solar radiation absorbed by the interior pane may be determined by: , , ,Wsolarf i db i solar inq qα= (A2-3) ,Wsolarf iq : Inside-to-outside solar radiation absorbed by the interior pane 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . Because only the transmitted inside-to-outside solar radiation from the interior pane incidents on the exterior pane: , , , ,Wsolarb e db e db i solar inq qα τ= (A2-4) ,Wsolarb eq : Inside-to-outside solar radiation absorbed by the exterior pane 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . The subscript b specifies that the absorptivities apply for solar radiation coming from the back or interior of a glazing system. As a result, the total solar radiation absorbed by the exterior pane can be computed by: ( ),, , , , , ,sl gWsolar e D f e D df e d R db e db i solar in g A q G G G q Aθ α α α τ⎛ ⎞= + + +⎜ ⎟⎜ ⎟⎝ ⎠ (A2-5) ,Wsolar eq : Total solar radiation absorbed by the exterior pane 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . 100 Similarly, the total solar radiation absorbed by the interior pane is: ( ),, , , , , , ,sl gWsolar i D f i D f e D df i df e d R db i solar in g A q G G G q Aθ θ α τ α τ α⎛ ⎞= + + +⎜ ⎟⎜ ⎟⎝ ⎠ (A2-6) ,Wsolar iq : Total solar radiation absorbed by the interior pane 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . Also, for a single pane glazing system, the total absorbed solar radiation is: ( ),, ,sl gWsolar p D f D df d R db solar in g A q G G G q Aθ α α α⎛ ⎞= + + +⎜ ⎟⎜ ⎟⎝ ⎠ (A2-7) ,Wsolar pq : Total solar radiation absorbed by a single pane glazing system 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . The optical properties of the standard glazing systems at a range of incident angles, required in the previous equations, have been tabulated in ASHRAE (2005). Figure A2.1 illustrates the heat fluxes that affect the control volume around the exterior pane. Applying the first law of thermodynamics on this control volume: net to sys net by sys Eq w t− − − − ∂+ = ∂ (A2-8) Because there is no work inside the control volume: 0net by sysw − − = (A2-9) Regarding the first assumption of the transparent surfaces (i.e. windows behave in a quasi- steady-state mode): 0E t ∂ =∂ (A2-10) 101 Figure A2.1. Heat fluxes on the exterior pane of a glazing system. Therefore, the application of the first law of thermodynamics on each pane can be simplified to: 0net to sysq − − = (A2-11) According to the directions of the heat flows shown in Figure A2.1: , , , , , , 0Wsolar e LW rad ext conv ext rad airspace conv airspaceq q q q q+ + + + = (A2-12) Considering the forth assumption of the transparent surfaces (i.e. combining the convection and radiation heat fluxes for the air space) and implementing (A2-5), (A1-44), and (A1-45) in the previous equation: Convection Net Longwave Radiation from the Sky and Surroundings Combined Radiation and Convection Outside-To-Inside Shortwave Solar Radiation Air Space Exterior Pane OUT Tout peT Inside-To-Outside Transmitted Solar Radiation Control Volume 102 ( ) ( ) ( ), , , , ( ) 0pe pe peWsolar e rad gr out rad sky sky conv ext out airspace pi peh T T h T T h T Tq U T T+ − + − + − + − = (A2-13) airspaceU : Thermal conductance of the air spaces 2. W m K ⎡ ⎤⎢ ⎥⎣ ⎦ . Finally, the temperature of the exterior pane is: , , , , , , , Wsolar e rad gr out rad sky sky conv ext out airspace pi pe rad gr rad sky conv ext airspace h h h h h h q T T T U T T U + + + += + + + (A2-14) Similarly, the temperature of the interior pane can be calculated by balancing the heat fluxes that affect the control volume shown in Figure A2.2. Figure A2.2. Heat fluxes on the interior pane of a glazing system. Outside-To-Inside Shortwave Solar Radiation Inside-To-Outside Transmitted Solar Radiation Control Volume piT Radiation from Internal Heat Gains Convection Net Longwave Radiation from the Other Interior Surfaces Inside-To-Outside Transmitted Solar Radiation Interior Pane Air Space IN Tin 103 , , , , , , 0Wsolar i LWrad in rad Sihg conv in rad airspace conv airspaceqq q q q q+ + + + + = (A2-15) Replacing from (A2-6), (A1-59), (A1-60), and (A1-68): ( ) ( ), , , , ( ) 0iWsolar i LWrad in fp pi rad Sihg conv in n pi airspace pe piT T q h T Tq h U T T− −+ + + + − = (A2-16) Thus, the temperature of the interior pane is: , , , , 2 , , Wsolar i rad in fp rad Sihg conv in in airspace pi rad in conv in airspace h q h h h q T T U T T U+ + + + += + (A2-17) peT and piT at each time step are calculated by iterations through (A2-14) and (A2-17). In case of having a single pane glazing system, the heat balance equation may be written as: , , , , , , , 0Wsolar p LW rad ext conv ext LWrad in rad Sihg conv inqq q q q q+ + + + + = (A2-18) Implementing (A2-7), (A1-44), (A1-45), (A1-59), (A1-60), and (A1-68) in the previous equation: ( ) ( ) ( ) ( ) ( ) , , , , , , , 0 p p p i Wsolar p rad gr out rad sky sky conv ext out LWrad in fp p rad Sihg conv in n p h T T h T T h T T T T q h T T q h − − + − + − + − + + + = (A2-19) Finally, the temperature of a single pane glazing system may be computed by: , , , , , , , , , , , , Wsolar p rad gr out rad sky sky conv ext out rad in fp rad Sihg conv in in p rad gr rad sky conv ext rad in conv in h h h h q h h h h h h q T T T T T T + + + + + + += + + + (A2-20) It is important to note that a window with more than two panes would be analyzed in the same manner, but there would be an additional heat balance equation for each additional pane. 104 Appendix Three: Heat Balance Method on the Internal Opaque Surfaces As previously mentioned, the numerical model developed in this study is only capable of performing the thermal analysis for a single zone. Therefore, to avoid violating the first law of thermodynamics, it was assumed that there is an adiabatic boundary condition on the exterior surfaces of partitions, floor and ceiling. With this assumption and considering the thermal mass of these surfaces, the first law of thermodynamics was applied on the thermal network for the internal opaque surfaces, shown in Figure 2.3, as follow: net to sys net by sys Eq w t− − − − ∂+ = ∂ (A3-1) Because no work is done inside the control volume, the previous equation may be written as: net to sys Eq t− − ∂= ∂ (A3-2) Regarding that the internal opaque surfaces are not exposed to the outside heat fluxes, their temperature fluctuations are considerably smaller in compare to the external surfaces’. A reasonably simple model with an acceptable accuracy for capturing these fluctuations is the lumped heat capacity method. Implementing this method and considering the directions of the heat fluxes shown in Figure 2.3: , , , , is LWrad in rad Sihg solar in conv in ios Tq q q q qL cLρ τ ∂+ + + + = ∂ (A3-3) : Thickness of the internal opaque surface [ ].iosL m Substituting from (A1-59), (A1-60), and (A1-68) the previous equation for each of the zone internal surfaces may be written as: 105 ( ) ( ), , , , i isLWrad in fs is rad Sihg solar in conv in n is ios Th T T q q h T T qL cL τρ ∂− − = ∂+ + + + (A3-4) Where ,solar inq is estimated by (A1-67) for the floor and (A1-66) for all the other interior surfaces. At each time-step and for each specific surface the following term is constant: , , , , ,LWrad in f s rad Sihg solar in conv in in ioshh T q q T qL ξ+ + + + = (A3-5) This simplifies (A3-4) into: ( ), , isLWrad in conv in is iosh Th T cLξ ρ τ∂− + = ∂ (A3-6) Rearranging the previous equation based on isT : , , 0LWrad in conv inis is ios ios hhT T cL cL ξ τ ρ ρ +⎛ ⎞ ⎛ ⎞∂ + − =⎜ ⎟ ⎜ ⎟∂ ⎝ ⎠ ⎝ ⎠ (A3-7) Defining a and b as follow: , ,c LWrad in s ios ios h h a cL b cL ρ ξ ρ ⎧ +⎛ ⎞=⎪ ⎜ ⎟⎪ ⎝ ⎠⎨ ⎛ ⎞⎪ = ⎜ ⎟⎪ ⎝ ⎠⎩ (A3-8) Results in: 0is is T aT bτ ∂ + − =∂ (A3-9) 106 By defining χ as: is is b TT a χχ τ τ ∂ ∂= − → =∂ ∂ (A3-10) (A3-9) can be written as: 0aχ χτ ∂ + =∂ (A3-11) 1 exp( ) p p a t χ χ + = − Δ (A3-12) : Indicator of time.p As a result, the temperature of each of the internal opaque surfaces at the next time step may be calculated by: 1 /(exp( ) (1 exp( ))p pis is p is b aT T at at T + = − + − − (A3-13) In which a and b are given in (A3-8). 107 Appendix Four: Heat Balance Method on the Zone Air This appendix investigates the application of the heat balance method on the zone air for both sensible and latent heat fluxes. As previously mentioned, In addition to the main assumptions of the heat balance method, it was assumed that in the both of the previous cases, the zone air has a negligible thermal mass and it behaves in a quasi-steady-state mode. This simplifies the first law of thermodynamics into: 0net to sysQ − − = (A4-1) :net to sysQ − − Rate of adding heat to the system[ ]W . A4.1. Sensible Heat Balance on the Zone Air The sensible heat fluxes that affect the zone air control volume are shown in Figure 2.4. Regarding the directions of these heat fluxes, the sensible heat balance on the zone air may be written as: , , , , 0conv in Sihg conv S infiltration S systemQ Q Q Q+ + + = (A4-2) ,conv inQ : Sum of the convection heat fluxes from all the interior surfaces to the zone air[ ]W . ,Sihg convQ : Total sensible convection heat flux from internal heat gains[ ]W . ,S infiltrationQ : Total sensible infiltration load[ ]W . ,S systemQ : Heat insertion from the HVAC system to the zone air[ ]W . To solve the previous equation for the required sensible HVAC energy consumption and/or zone air temperature, the heat fluxes involved should first be identified. A4.1.1. Convection from the Zone Interior Surfaces The application of the heat balance method on different zone surfaces resulted in calculating their interior surface temperatures. Having these temperatures the classical formulation was used to determine the convection heat fluxes from these surfaces to the zone air. 108 , , , , , 1 1 ( ) N N conv in s conv zoneair s s conv in s is in s s Q A q A h T T = = = = −∑ ∑ (A4-3) , ,conv zoneair sq : Convection heat flux from the interior of surface “s” to the zone air 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . N : Number of zone surfaces with different temperature, dimensionless. A4.1.2. Convection from the Internal Heat Gains The convective portion of the sensible heat gain from people, lighting, and equipment, instantaneously affect the zone air control volume. This may be calculated by: , , , , , ,Sihg conv conv people S people conv light lighting conv equip S equipmentQ F Q F Q F Q= + + (A4-4) ,Sihg convQ : Total convection heat flux from internal heat gains[ ]W . convF : Convective fraction, dimensionless. According to the design and specifications of a building, ASHRAE (2005) provides appropriate values for the terms in the previous equation. It is important to note that the sum of the radiative (i.e. previously discussed in Appendix One) and convective fractions for each of the internal heat gains is always equal to unity. 1rad convF F+ = (A4-5) A4.1.3. Sensible Infiltration Infiltration is the unintended flow of air from the outdoor environment directly into the thermal zone. Infiltration is generally caused by the opening and closing of exterior doors, cracks around windows, and even in very small amounts through building elements. The equation used to calculate the sensible infiltration load is: , , ( )S infiltration a p out out inQ m C T T= − (A4-6) am : Mass flow rate of the infiltrating air kg s ⎡ ⎤⎢ ⎥⎣ ⎦ . ,p outC : Specific heat capacity of the outdoor air . J kg K ⎡ ⎤⎢ ⎥⎣ ⎦ . 109 Because in most cases the detail information on air leakage characteristics is not available; the mass flow rate of the infiltrating air is calculated by implementing the air-change method. ( ) 3600 zone a air ACH V m ρ ⎛ ⎞= ⎜ ⎟⎝ ⎠ (A4-7) airρ : Density of the outdoor air 3 kg m ⎡ ⎤⎢ ⎥⎣ ⎦ . zoneV : Zone volume 3m⎡ ⎤⎣ ⎦ . ACH : Number of air-change per hour, dimensionless. As the detailed modeling of the air infiltration rates was not the purpose of this study, ACH in the previous equation was estimated by appraising the building type, construction, and use. The density and the heat capacity of the outdoor air, required for calculating the infiltration load, are not directly given in the CWEC weather files (i.e. shown in Figure A1.5). The following procedure was implemented to calculate them based on the outdoor air temperature, dew point temperature, and atmospheric pressure. These are all provided on an hourly basis by the CWEC weather files. The dew point temperature is the temperature of the saturated moist air at the same pressure and humidity ratio as the given mixture. Therefore, the humidity ratios at both the dew point and outdoor air temperatures are identical and equal to the ratio of the mass of water vapor to the mass of dry air in the mixture at the dew point temperature. , , , 0.622v v out v outvout a a a v out M P Pmw m M P P P = = = − (A4-8) outw : Outdoor air humidity ratio at the dew point temperature water Dryair kg kg ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . vM : Molecular weight of water vapor, equal to 18.02 kg kmol ⎡ ⎤⎢ ⎥⎣ ⎦ . aM : Molecular weight of dry air, equal to 28.97 kg kmol ⎡ ⎤⎢ ⎥⎣ ⎦ . 110 vm : Mass of water vapor[ ]kg . am : Mass of dry air [ ]kg . ,v outP : Partial pressure of water vapor in the outdoor air at the dew point temperature[ ]Pa . aP : Partial pressure of dry air at the dew point temperature[ ]Pa . P : Atmospheric pressure from the CWEC weather files [ ]Pa . At dew point temperature the partial pressure of water vapor is equal to its saturation pressure. The saturation pressures for the water vapor at a range of temperatures are tabulated in ASHRAE (2005). Calculating the outdoor air humidity ratio, its specific heat capacity may be determined by: 3 , , , , , 10 (1 1.86 )p out p out air out p out water outC C w C w= + = + (A4-9) , ,p out airC : Specific heat capacity of dry air at constant pressure, 1000 . J kg K ⎡ ⎤⎢ ⎥⎣ ⎦ . , ,p out waterC : Specific heat capacity of water vapor at constant pressure, 1860 . J kg K ⎡ ⎤⎢ ⎥⎣ ⎦ . Finally, the density of the outdoor air can be calculated by applying the ideal gas law. air a out P R T ρ = (A4-10) aR : Dry air gas constant, 287 . J kg K ⎡ ⎤⎢ ⎥⎣ ⎦ . A4.1.4. Sensible Heat Insertion Rate from the HVAC System The rate at which HVAC systems heat the zone air is considered as the system sensible heat insertion rate. This rate is positive when the HVAC system is heating the zone and negative when the HVAC system is cooling the zone. Depending on the control strategy used for the zone 111 air temperature, the heat insertion rate from the HVAC system may be defined in three distinct forms. A4.1.4.1. Maintaining a Fixed Zone Air Temperature The first control strategy, typically used in the design load calculations, is to keep the zone air temperature constant. Thus, the HVAC system sensible heat insertion rate may be estimated by rearranging (A4-2) as follow: , , , ,( )S system Surfaces conv Sihg conv S infiltrationQ Q Q Q= − + + (A4-11) Applying (A4-3), (A4-4), and (A4-6) in the previous equation, the total heat insertion rate from the HVAC system is: , , , , 1 ( ) ( ) N S system s conv in s is in Sihg conv a p out in s Q A h T T Q m C T T = ⎛ ⎞= − − + + −⎜ ⎟⎝ ⎠∑ (A4-12) A4.1.4.2. No Control on the Zone Air Temperature The second control strategy that may represent the naturally ventilated buildings is setting the HVAC system heat insertion rate equal to zero. , 0S systemQ = (A4-13) A4.1.4.3. Maintaining the Zone Air Temperature between the Heating and Cooling Setpoints The third control strategy (i.e. the most general formulation) is to maintain the zone air temperature between the specific heating and cooling setpoints. In this strategy, the HVAC system heat insertion rate is zero, unless the zone air temperature goes beyond the range of temperatures, specified by the heating and cooling setpoints. The HVAC system heat insertion rate in this case is calculated using the generic proportional control loop feedback mechanism. 112 For the zone air temperature less than the heating setpoint and higher than the cooling setpoint, this mechanism respectively produces heating and cooling. As a result, the heat insertion rate for the third control strategy may be defined as: , 0 ( ) ( ) setH in setC S system S setH in in setH S setC in setC in T T T Q T T T T T T T T < <⎧⎪= Λ − ≤⎨⎪Λ − ≤⎩ (A4-14) SΛ : Sensible proportional constant W K ⎡ ⎤⎢ ⎥⎣ ⎦ . setCT : Cooling setpoint temperature[ ]K . setHT : Heating setpoint temperature[ ]K . The sensible proportional constant in the previous equation is tuned according to the HVAC system. Choosing a too large or too small proportional constant respectively results in having an unstable or less sensitive controlling mechanism. Once the heat fluxes on the zone air control volume have been identified, the zone air temperature may be calculated using (A4-2). Depending on the control strategy used for the zone air temperature, three different scenarios may occur: • For the first control strategy (i.e. maintaining a fixed zone air temperature) the zone air temperature is defined as an input. Thus, the application of the sensible heat balance method on the zone air in this case, only results in calculating the HVAC system heat insertion rate from (A4-12). • For the second control strategy the HVAC system does not participate in heating and/or cooling the zone air. Applying (A4-3), (A4-4), (A4-6), and (A4-13) in (A4-2): , , , 1 ( ) ( ) 0 N s conv in s is in Sihg conv a p out in s A h T T Q m C T T = − + + − =∑ (A4-15) Rearranging the previous equation based on the zone air temperature: 113 , , , 1 , , 1 N s conv in s is Sihg conv a p out s in N s conv in s a p s A h T Q m C T T A h m C = = + + = + ∑ ∑ (A4-16) • For the third control strategy, the HVAC system attempts to maintain the zone air temperature between the heating and cooling setpoints. With the initial assumption that the zone air temperature is inside this range, the HVAC system heat insertion rate, from (A4-14), will be zero. Therefore, the zone air temperature may be calculated using (A4- 16). However, if the calculated zone air temperature goes beyond the range of temperatures, specified by the heating and cooling setpoints, the initial assumption that the HVAC system does not participate in heating/cooling the zone air is invalid. Thus, by implementing (A4-3), (A4-4), and (A4-6) in (A4-2), the sensible heat balance on the zone air can be written as: , , , , 1 ( ) ( ) 0 N s conv in s is in Sihg conv a p out in S system s A h T T Q m C T T Q = − + + − + =∑ (A4-17) Depending on the calculated zone air temperature, the HVAC system heat insertion in the previous equation may be implemented from (A4-14). , , , 1 , , 1 , , , 1 , , 1 N s conv in s is Sihg conv a p out S setH s in setHN s conv in s a p S s in N s conv in s is Sihg conv a p out S setC s setC inN s conv in s a p S s A h T Q m C T T T T A h m C T A h T Q m C T T T T A h m C = = = = ⎧ + + + Λ⎪⎪ ≤⎪ + + Λ = ⎨ + + + Λ ≤ + + Λ ∑ ∑ ∑ ∑ ⎪⎪ ⎪⎪⎪⎪⎪⎩ (A4-18) A4.2. Latent heat balance on the zone air Assuming that the moisture diffusion through the building envelope is negligible, the main latent heat fluxes that affect the zone air control volume are caused by internal heat gains and 114 infiltration. Regarding the directions of these heat fluxes, shown in Figure 2.5, the latent heat balance on the zone air may be written as: , , , 0L ihg L infiltration L systemQ Q Q+ + = (A4-19) ,L ihgQ : Total humidification from internal heat gains[ ]W . ,L infiltrationQ : Total humidification due to infiltration[ ]W . ,L systemQ : Total humidification rate from the HVAC system to the zone air[ ]W . A4.2.1. Latent Internal Heat Gain People and some equipment (e.g. coffee brewer, dish washer, food warmer) increase the zone air humidity ratio. According to the people’s activity levels and the zone’s appliances, appropriate values for the latent internal heat gains may be extracted from ASHRAE (2005). , , ,L ihg L people L equipmentQ Q Q= + (A4-20) ,L peopleQ : Total latent heat gain from people[ ]W . ,L equipmentQ : Total latent heat gain from equipment[ ]W . A4.2.2. Latent infiltration As previously mentioned, Infiltration is the unintended flow of air from the outdoor environment directly into the thermal zone. The infiltrated air affects the zone air humidity ratio by: 2, , ( )L infiltration a fg H O out inQ m h w w= − (A4-21) 2,fg H O h : Enthalpy of the evaporation of water at 0˚ C (i.e. 2.5e6 J kg ⎡ ⎤⎢ ⎥⎣ ⎦ ). outw : Outdoor air humidity ratio water Dryair kg kg ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . inw : Zone air humidity ratio water Dryair kg kg ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . 115 am and outw in the previous equation are respectively calculated using (A4-7) and (A4-8). A4.2.3. Humidification Rate from the HVAC System Depending on the control strategy used for the zone air humidity ratio, the HVAC system humidification may be defined in three different forms: A4.2.3.1. Maintaining a fixed zone air Humidity Ratio In this control strategy the zone air humidity ratio is constant. Therefore, the latent heat balance on the zone air control volume is only solved for the HVAC system humidification load. This may be calculated by implementing (A4-20) and (A4-21) in (A4-19) as follows: 2, , , ( ( ))L system L ihg a fg H O out inQ Q m h w w= − + − (A4-22) A4.2.3.2. No Control on the Zone Air Humidity Ratio In this strategy the HVAC system does not participate in humidification or dehumidification of the zone air. , 0L systemQ = (A4-23) A4.2.3.3. Maintaining the Zone Air Humidity Ratio in the Specific Range In this control strategy the zone air humidity ratio is not affected by the HVAC system unless it goes beyond its specific range, defined as an input. Similar to the third control strategy used for the sensible heat balance on the zone air, the generic proportional control loop feedback mechanism was implemented to maintain the zone air humidity ratio inside the desired range of condition. If the zone air humidity ratio becomes less than its minimum, the HVAC system humidifies the air (i.e. positive latent heat flux). Similarly, the HVAC system dehumidifies the 116 air (i.e. negative latent heat flux) when the zone air humidity ratio is higher than its maximum. This control strategy can be summarized as follow: min max , min min max max 0 ( ) ( ) in L system L in in L in in w w w Q w w w w w w w w < <⎧⎪= Λ − ≤⎨⎪Λ − ≤⎩ (A4-24) LΛ : Latent proportional constant, tuned according to the HVAC system W K ⎡ ⎤⎢ ⎥⎣ ⎦ . maxw : Maximum zone air humidity ratio water Dryair kg kg ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . minw : Minimum zone air humidity ratio water Dryair kg kg ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . Once all the latent heat fluxes that affect the zone air control volume are identified, the zone air humidity ratio is calculated by solving the latent heat balance formulation. Depending on the control strategy used for the zone air humidity ratio, this may be viewed in three distinct scenarios: • In the first control strategy the zone air humidity ratio is defined as an input. Therefore, the latent heat balance formulation on the zone air is only solved for calculating the HVAC system humidification load from (A4-22). • In the second control strategy the HVAC system does not participate in humidification and/or dehumidification of the zone air. Applying (A4-20), (A4-21), and (A4-23) in (A4- 19): 2, , ( ) 0L ihg a fg H O out inQ m h w w+ − = (A4-25) Rearranging the previous equation based on the zone air humidity ratio: 117 2 2 , , , L ihg a fg H O out in a fg H O Q m h w w m h += (A4-26) • For the third control strategy, the HVAC system attempts to maintain the zone air humidity ratio in the specific range, defined as an input. With the initial assumption that the zone air humidity ratio is inside this range, the HVAC system humidification rate, from (A4-24), will be zero. Therefore, the zone air humidity ratio may be calculated using (A4-26). However, if the calculated zone air humidity ratio goes beyond its range, the initial assumption that the HVAC system does not participate in the zone air latent heat balance is invalid. Thus, by implementing (A4-20) and (A4-21) in (A4-19), the zone air latent heat balance may be written as: 2, , , ( ) 0L ihg a fg H O out in L systemQ m h w w Q+ − + = (A4-27) Depending on the calculated zone air humidity ratio, the HVAC system humidification rate in the previous equation can be implemented from (A4-24). 2 2 2 2 , , min min , , , max max , L ihg a fg H O out L in a fg H O L in L ihg a fg H O out L in a fg H O L Q m h w w w w m h w Q m h w w w w m h + + Λ⎧ ≤⎪ + Λ⎪= ⎨ + + Λ⎪ ≤⎪ + Λ⎩ (A4-28) 118 Appendix Five: Thermal Comfort Model A5.1. Heat Balance Method on a Body The thermal comfort model is developed by applying the heat balance method on the control volume around a body. Assuming that the body behaves in a quasi-steady-state condition, the total heat production within the body (i.e. caused by metabolic activities) is balanced with the total dissipated heat from the body to the surrounding environment through the skin surface and respiratory tract. Therefore, at neutral thermal sensation, the application of the heat balance method results in: Sskin Lskin resM W Q Q Q− = + + (A5-1) M : Rate of metabolic heat production 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . W : Rate of mechanical work accomplished 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . SskinQ : Sensible heat loss from skin 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . LskinQ : Latent heat loss from skin 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . resQ : Total heat loss through respiration 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . All the proceeding terms have units of power per surface area of the nude body. DuBois (1916) estimated the nude body surface area by the following empirical equation: 0.425 0.7250.202DA m l= (A5-2) DA : Nude body surface area 2m⎡ ⎤⎣ ⎦ . m : Weight [ ]kg . l : Height [ ]m . Depending on the activity levels, the metabolic heat generations are tabulated in ASHRAE (2005). It is important to note that, for typical office activities, the mechanical work is so small that it 119 can be neglected in compare to the metabolic heat generation. The other heat fluxes on the right hand side of (A5-1) are defined as follows: A5.1.1 Sensible Heat Loss from Skin The sensible heat loss from the skin to the surrounding environment can be divided into: • Heat flux from the skin surface to the outer clothing surface by conduction heat transfer through the clothing insulation. -sk cl Sskin cl T TQ R = (A5-3) SskinQ : Heat flux from the skin surface to the outer clothing surface 2 W m ⎡ ⎤⎢ ⎥⎣ ⎦ . skT : Skin surface temperature[ ]C . clT : Clothing surface temperature[ ]C . clR : Thermal resistance of clothing, tabulated in ASHRAE (2005) 2.m C W ⎡ ⎤⎢ ⎥⎣ ⎦ . • Heat flux from the outer clothing surface to the environment by convection and radiation heat transfers. ( - ) ( - ) Sskin cl rcl cl r cl ccl cl inQ f h T T f h T T= + (A5-4) SskinQ : Heat flux from the outer clothing surface to the environment 2 W m ⎡ ⎤⎢ ⎥⎣ ⎦ . clf : Clothing area factor, tabulated in ASHRAE (2005), dimensionless. rclh : Radiative heat transfer coefficient on the outer clothing surface 2. W m C ⎡ ⎤⎢ ⎥⎣ ⎦ . cclh : Convective heat transfer coefficient on the outer clothing surface 2. W m C ⎡ ⎤⎢ ⎥⎣ ⎦ . rT : Mean radiant temperature[ ]C . 120 The previous equation may be written as: ( - )Sskin cl cl cl oQ f h T T= (A5-5) Where clh and oT are respectively combined heat transfer coefficient on the clothing outer surface and operative temperature of the surrounding environment. These two terms are calculated by: rcl r ccl ino rcl ccl h T h TT h h += + (A5-6) cl rcl cclh h h= + (A5-7) Because the sensible heat losses from the skin, calculated by (A5-3) and (A5-5), are always in series and equal, the total sensible heat loss from the skin can be determined by combining the previous equations to eliminate clT as follow: - 1 sk o Sskin cl cl cl T TQ R f h = + (A5-8) The skin surface temperature is estimated by the following linear regression equation (Rohles and Nevins 1971): 35.7 0.0275( )skT M W= − − (A5-9) The zone air operative temperature is a function of the mean radiant temperature. This temperature is determined by calculating the plane radiant temperature in six directions (up, down, right, left, front, and back). For each direction: 121 44plane 1 T n i p i i T F − = = ∑ (A5-10) The view factors in the previous equation are determined from Figure A5.1. Figure A5.1. Analytical formulas for calculating angle factor for small plane element (ASHRAE 2005). A2 a b c dA1 A2 a b c dA1 ax c by c ⎧ =⎪⎪⎨⎪ =⎪⎩ ax b cy b ⎧ =⎪⎪⎨⎪ =⎪⎩ 1 1 1 2 2 2 2 2 1 tan tan 2 1 1 1 1 d x y y xF x x y yπ − − − ⎛ ⎞⎜ ⎟= +⎜ ⎟+ + + +⎝ ⎠ 1 1 1 2 2 2 2 2 1 1 1tan tan 2d yF y x y x yπ − − − ⎛ ⎞⎜ ⎟= −⎜ ⎟+ +⎝ ⎠ 122 Once the plane radiant temperatures in all directions are computed, the mean radiant temperature for a seated person may be calculated using the following empirical equation developed by Korsgaard (1949): ( ) ( ) ( ) ( ){ ( ) ( ) } ( ) 0.18 0.22 0.3 2 0.18 0.22 0.3 r plane plane plane plane plane plane T T up T down T right T left T front T back ⎡ ⎤ ⎡ ⎤= + + +⎣ ⎦ ⎣ ⎦ ⎡ ⎤ ⎡ ⎤+ + ÷ + +⎣ ⎦⎣ ⎦ (A5-11) The values of clR and clf may both be determined from ASHRAE (2005) according to the clothing level. For clothing insulation values that are expressed in clo units (i.e. clI ), clR can be calculated using the following equation (ASHRAE 2005): 0.155cl clR I= (A5-12) Table A5.1 gives values for typical office clothing ensembles. Ensemble Description clR clI clf cli Trousers, short-sleeved shirt 0.09 0.57 1.15 0.36 Trousers, long-sleeved shirt 0.09 0.61 1.20 0.41 Same as above, plus vest and T-shirt 0.18 1.14 1.32 0.32 Knee-length skirt, short-sleeved shirt, panty hose, sandals 0.08 0.54 1.26 - Knee-length skirt, long-sleeved shirt, full slip, panty hose 0.1 0.67 1.29 - Table A5.1. Specification of the typical office clothing ensembles (ASHRAE 2005). Finally, the combined heat transfer coefficient on the outer surface of clothing is calculated by adding the radiative and convective heat transfer coefficients. The radiative heat transfer coefficient is nearly constant for typical indoor temperature. Based on ASHRAE (2005), this is 4.7 2 . W m C ⎡ ⎤⎢ ⎥⎣ ⎦ . The convective heat transfer is caused by zone air movement and/or occupants’ movements. For office spaces with moving air where occupants are seated, the convective heat transfer coefficient on the outer clothing surface may be estimated by the following empirical equation developed by Mitchell (1974): 123 0.6 3.1 0 0.2 8.3 0.2 4ccl V h V V ≤ ≤⎧= ⎨ ≤ ≤⎩ (A5-13) V : Air velocity inside the zone m s ⎡ ⎤⎢ ⎥⎣ ⎦ . For other conditions ASHRAE (2005) provides appropriate values for cclh . A5.1.2. Latent Heat Loss from Skin The total latent heat loss from the skin is caused by both sweat evaporation and natural diffusion of water through the skin. Similar to Equation (A5-8), the maximum latent heat loss from the skin may be determined by: , , max , ( ) 1/( ) sk s v a Lskin e cl cl e P P Q R f h −= + (A5-14) maxLskinQ : Maximum latent heat loss from the skin 2 W m ⎡ ⎤⎢ ⎥⎣ ⎦ . ,v aP : Water vapor pressure in ambient air[ ]kPa . ,sk sP : Water vapor pressure at skin (i.e. assumed to be the same as the saturated water vapor pressure at skT [ ]kPa . ,e clR : Evaporative heat transfer resistance of clothing layer 2.m kPa W ⎡ ⎤⎢ ⎥⎣ ⎦ . eh : Evaporative heat transfer coefficient 2. W m kPa ⎡ ⎤⎢ ⎥⎣ ⎦ . Woodcock (1962) and Oohori et al. (1985) estimated ,e clR in the previous equation by: e,R clcl cl R i LR = (A5-15) cli : Clothing vapor permeation efficiency, ASHRAE (2005), dimensionless. LR : Lewis ratio constant, for typical indoor conditions is 16.5. 124 Clothing vapor permeation efficiencies for typical office clothing are provided in Table 5.1. Where cli is not available, McCullough et al. (1989) suggests an average value of 0.34. The evaporative heat transfer coefficient in (A5-14) is calculated by applying the Lewis relation (ASHRAE 2005): e c h LR h = (A5-16) Rohles and Nevins (1971) introduced the following empirical linear regression equation to estimate the latent heat loss from the skin by sweat evaporation: 0.42( 58.15)LsweatQ M W= − − (A5-17) LsweatQ : Evaporative heat loss by regulatory sweating 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . Once the maximum latent heat loss and sweat evaporation heat loss are respectively determined from (A5-14) and (A5-17), the wet skin fraction may be defined as (ASHRAE 2005): max 0.06 0.94 Lsweat Lskin Qwet Q = + (A5-18) This fraction is the ratio of the actual latent heat loss from the skin to its maximum possible with the same conditions and a completely wet skin. Therefore the actual latent heat loss from the skin may be estimated by: max( )Lskinact LskinQ wet Q= (A5-19) A5.1.3. Total Heat Loss through Respiration The total heat loss through respiration is a combination of the sensible and latent heat losses and is defined by: 125 ( )res ex in res D m i iQ A −= (A5-20) resm : Pulmonary ventilation rate kg s ⎡ ⎤⎢ ⎥⎣ ⎦ . ini : Zone air enthalpy J kg ⎡ ⎤⎢ ⎥⎣ ⎦ . exi : Exhaust air enthalpy J kg ⎡ ⎤⎢ ⎥⎣ ⎦ . Studies by McCutchan and Taylor (1951), Fanger (1970), Holmer (1984) simplified the previous equation into: , 0.0014 (34 ) 0.0173 (5.87 )res Sres Lres in v inQ Q Q M T M P= + = − + − (A5-21) SresQ : Sensible respiration heat loss 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . LresQ : Latent respiration heat loss 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . ,v inP : Partial pressure of water vapor at the dew point temperature in the zone air [ ]kPa . A5.2. PMV-PPD Model Once all the heat fluxes that affect the control volume around a body are identified, the main heat balance equation, given by (A5-1), may be applied to evaluate a neutral thermal sensation in a quasi-steady-state condition as a combination of the indoor thermal environmental and personal factors. The environmental factors are temperature, thermal radiation, humidity, and air speed. These factors are determined from the previous applications of the heat balance method on different zone surfaces and on the zone air. The personal factors are those of activity and clothing. For typical office activities, Fanger (1982) assumed all the sweat generated is evaporated. This eliminated the clothing vapor permeation efficiency from the main heat balance equation. Fanger 126 (1982) also applied the Stefan-Boltzmann law for calculating the radiant heat exchange and evaluated the saturated vapor pressure at skT with a linear approximation. These simplified the main heat balance equation on the control volume around the body into: ( ) ( ) ( ) ( ) 448 , , 3.96*10 273 273 3.05 5.73 0.007( ) 0.42 58.15 0.0173 (5.87 ) 0.0014 (34 ) cl cl r cl ccl cl in v in v in in M W f T T f h T T M W P M W M P M T − ⎡ ⎤− = + − + + −⎣ ⎦ ⎡ ⎤ ⎡ ⎤+ − − − + − −⎣ ⎦⎣ ⎦ + − + − (A5-22) Where: ( ) ( ){ ( ) ( ) ( ) ( )} , , 35.7 0.0275 3.05 5.73 0.007 0.42 58.15 0.0173 5.87 0.0014 34 cl cl v in v in in T M W R M W M W P M W M P M T ⎡ ⎤= − − − − − − − −⎣ ⎦ ⎡ ⎤− − − − − − −⎣ ⎦ (A5-23) Fanger (1982) used the following relationships to estimate the clothing area factor and convective heat transfer coefficient on the outer clothing surface: cl cl 1 0.2 I 0.5 clo 1.05 0.1 I 0.5 clo cl cl cl I f I + <⎧= ⎨ + >⎩ (A5-24) 0.25(2.38( ) ,12.1 )ccl cl inh max T T V= − (A5-25) Implementing the predicted mean vote (PMV) index, (A5-22) was expanded for situations where subjects were not at a neutral thermal sensation. The PMV index was developed based on the imbalance between the actual heat flow from the body in a given environment and the heat flow required for optimum comfort at the specified activity. This index predicts the mean response of a large group of occupants on their thermal sensations according to the ASHRAE thermal sensation scale. ( )0.303exp 0.036 0.028PMV M⎡ ⎤= − + Γ⎣ ⎦ (A5-26) Γ : Thermal load on a body 2Wm ⎡ ⎤⎢ ⎥⎣ ⎦ . 127 Where, thermal load on a body is the difference between the left and right sides of (A5-22). Determining the PMV from the previous equation, the predicted percent dissatisfied (PPD) with the zone thermal environment may be calculated by: ( )4 2100 95exp 0.03353 0.2179PPD PMV PMV⎡ ⎤= − − +⎣ ⎦ (A5-27) According to the current comfort standard (ANSI/ASHRAE STANDARD 55-2004), to have a thermally comfortable environment, the PPD values should not exceed 20%. A5.3. Local Thermal Discomfort In addition to the evaluation of thermal comfort for the body as a whole, the effects of the local thermal discomfort are also considered in the thermal comfort model. The local thermal discomfort may be caused by an asymmetric radiant field, draft, zone air temperature stratification, or contact with a hot or cold floor. These factors are described in the following sections. A5.3.1. Radiant Temperature Asymmetry Radiant asymmetry is the difference in the plane radiant temperatures seen by a small flat element looking in opposite directions. The plane radiant temperature in each direction may be calculated from (A5-10). Table A5.2 specifies the limits for radiant temperature asymmetry. Having radiant asymmetry more than the limits shown in this table causes local discomfort and reduces the thermal acceptability of the surrounding environment. Cold windows and over-sized ceiling heating panels are the most common causes of radiant asymmetry in office spaces. Warm Ceiling Cool Wall Cool Ceiling Warm Wall < 5 < 10 < 14 < 23 Table A5.2. Allowable Radiant Temperature Asymmetry [˚C] (ANSI/ASHRAE STANDARD 55-2004). 128 A5.3.2. Draft Draft is unwanted local cooling of the body caused by air movement. In office spaces draft sensation increases the demand for higher zone air temperature or that the HVAC system to be stopped. Fanger et al. (1989) estimated the percentage of people dissatisfied due to annoyance by draft with: ( )( )( )0.6234 0.37 3.14 0.05draft inPD T VTu V= − + − (A5-28) draftPD : Percent dissatisfied due to draft, percentage. Tu : Turbulence intensity, percentage. In general, the turbulence intensity in zones with displacement ventilation or without mechanical ventilation is 20%. This increases to 35% for zones with mixing ventilation. It is important to note that in order to avoid draft sensation inside the zone, the values of draftPD should not exceed 20% (ANSI/ASHRAE STANDARD 55-2004). A5.3.3. Vertical Air Temperature Difference The zone air temperature stratification with warm and cold air respectively at the head (1.1 m above the floor) and feet (0.1 m above the floor) levels may cause local thermal discomfort for the occupants. The maximum allowable temperature difference between head and feet is 3˚C (ANSI/ASHRAE STANDARD 55-2004). A5.3.4. Floor Surface Temperature Having a too warm or too cool floor may lead to local discomfort of the feet. For feet thermal comfort of people wearing shoes, the temperature of the floor is even more important than the material of the floor covering. ANSI/ASHRAE STANDARD 55-2004 specifies the following criteria for the floor temperature when the occupants are wearing lightweight indoor shoes: 19˚C flT≤ ≤29˚C (A5-29) 129 For heavier shoes this criteria would be more conservative. 130 Appendix Six: Validations of the Main Individual Modules A6.1. Conduction Process through the External Opaque Surfaces The transient conduction formulation for the heat transfer through the external opaque surfaces was compared with the fundamental heat transfer problems. This comparison led to determining the accuracy of the formulation. It also investigated the conservation of energy based on the following equation: max 2 1 2 1 2 1 max max ( 1) 1 1 1 2 ( ) ( ) ( ) ( ) 2 2 gn t t t t t tt net g g g g i g c x c xq HG T T T T c x T Tρ ρ ρ − = = Δ Δ+ = − + − + Δ −∑ ∑ (A6-1) t netq : Net heat flux to the external opaque surface at each time step 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . HG : Heat generation inside the external opaque surface at each time step 2 W m ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦ . Where the superscripts are indicators of time and the subscripts are indicators of the grid point position. n in the previous equation is calculated by: 2 1t tn t −= Δ (A6-2) In which 1t and 2t are respectively the time at the start and end of the period of study. A6.1.1. Transient Conduction with Heat Generation inside the Control Volume The plane wall with a grid resolution of 1 mm has a thickness of 5 mm. The wall is initially at the uniform temperature of 100˚C until it is suddenly subjected to an internal heat generation of 50 MW/m3 and the convection boundary conditions A and B, respectively on its left and right hand sides. The schematic of the problem is shown in Figure A6.1. 131 460197800 c [J/kg.C]k [W/m.C]ρ [kg/m3] The Wall’s Thermal Properties T [C]h [W/m2.C] 20500B 120400A Convection Boundary Conditions 1 2 3 4 5 6 Figure A6.1. The thermal properties and the convection boundary conditions of the plane wall. By using the analytical solutions, Holman (2001) calculated the grid points’ temperatures for several time increments of 0.45 s. Using the same grid resolution and time step, these temperatures were also computed by the numerical model. Table A6.1 compared the results. Analyses Second Grid Points 0.45 9 45 270 1 106.8826 190.0725 320.5766 347.2085 2 106.478 190.9618 323.6071 350.676 3 106.1888 190.7033 324.2577 351.512 4 105.3772 189.3072 322.5298 349.7165 5 104.4622 186.7698 318.4229 345.2893 Grid Point Temperatures [C] (Holman 2001) 6 102.4416 183.0735 311.9341 338.2306 1 106.8826 190.0721 320.5764 347.2095 2 106.4779 190.9614 323.6069 350.6771 3 106.1887 190.7029 324.2574 351.5131 4 105.3771 189.3069 322.5296 349.7175 5 104.4622 186.7694 318.4227 345.2904 Grid Point Temperatures [C] (Numerical Model) 6 102.4416 183.0731 311.9339 338.2316 1 0.0000% -0.0002% -0.0001% 0.0003% 2 -0.0001% -0.0002% -0.0001% 0.0003% 3 -0.0001% -0.0002% -0.0001% 0.0003% 4 -0.0001% -0.0002% -0.0001% 0.0003% 5 0.0000% -0.0002% -0.0001% 0.0003% Differences in Grid Point Temperatures 6 0.0000% -0.0002% -0.0001% 0.0003% Table A6.1. Computed grid points’ temperatures by different analyses. 132 The conservation of energy was also investigated at each time interval by implementing (A6-1). The results are shown in Table A6.2. Second Grid Points 0.45 9 45 270 Net Energy to the Control Volume [J/m2] 9.7E+04 1.6E+06 4.0E+06 4.4E+06 Increase in the Internal Energy of the Control Volume [J/m2] 9.7E+04 1.6E+06 4.0E+06 4.4E+06 Difference 0.0000% -0.0004% -0.0010% 0.0045% Table A6.2. Energy conservation analyses of the numerical model. This analysis shows that the numerical model conserves energy and is able to predict the temperature distribution inside the external opaque surfaces with 0.001% accuracy. A6.1.2. Transient Conduction in Semi-Infinite Solid A large slab of aluminum at a uniform temperature of 200˚C suddenly has its surface temperature lowered to 70˚C. Assuming the slab as a semi-infinite surface, the error functions was applied to calculate the total heat removed from the slab per unit surface area and the temperature at a depth of 4 cm after 40 s: 0 0 ( , ) xerf 0.3847 (4,40) 120 2 ti T x t T T C T T α − = = ⇒ =− Δ (A6-3) 60 0 20 ( )Total Heat Removed 2 ( ) 21.13*10 t i i k T T t Jdt k T T mt παπα − ⎡ ⎤= = − = − ⎢ ⎥⎣ ⎦∫ (A6-4) Estimating the semi-infinite surface as a 20 cm slab, the numerical model was applied to model the thermal performance of the slab. Table A6.3 summarizes the effect of different time-steps on the results. This shows that the results are not significantly affected by the change in the size of the time-step The similar study, summarized in Table A6.4, was conducted to investigate the effect of refining the mesh on the results. This study showed that although refining the mesh improves accuracy of 133 predicting temperature distribution inside the surface, it significantly increases the computational cost. This trade off is illustrated in Figure A6.2. Based on these comparisons and regarding the required accuracy for building thermal analyses, the numerical model uses a grid resolution of 5mm. the time-step is then determined to avoid violating the second law of thermodynamics with the grid resolution of the model. Numerical Model Method Parameters Analytical Solution Small Medium Large Δt [sec] - 0.0185 0.0094 0.0047 Temperature after 40sec at Depth of 4cm[C] 120 120.0095 120.0109 120.008 Total Heat Removed after 40sec [J/m2] -21130000 -21132000 -21133000 -21135000 Difference in Temperature - 0.0079% 0.0091% 0.0067% Difference in Energy - 0.0095% 0.0142% 0.0237% Table A6.3. The effect of improving the size of the time-step on the results. Numerical Model Method Parameters Analytical Solution Coarse Fine Refine Δx [mm] - 4 2 1 Temperature after 40sec at Depth of 4cm[C] 120 120.0272 120.0095 120.0073 Total Heat Removed after 40sec [J/m2] -21130000 -21124000 -21132000 -21134000 Temperature Difference with Analytical Solution - 0.0227% 0.0079% 0.0061% Energy Difference with Analytical Solution - -0.0284% 0.0095% 0.0189% Computational Cost - 3 sec 42 Sec 19 min Table A6.4. The Effect of refining the mesh on the results. A6.2. Calculations of the View Factors and the Mean Radiant Temperature For the generic zone, shown in Figure A6.3, the view factors, plane radiant temperatures in different directions, and the mean radiant temperature were calculated by the numerical model for a seated person at the centre of the zone. The results were then compared with those predicted by the analytical solutions. It is important to note that the seated person is considered as a point located 60 cm above the floor (ASHRAE 2005). 134 Figure A6.2. Grid study on the explicit finite difference method. Figure A6.3. A generic zone with a square floor area Figure A6.3. The schematic of the generic zone. This generic zone has windows on south and east facades. The method that was implemented to calculate the view factors of these windows is illustrated in Figure A6.4. 3 m 6 m 6 m 1.2 m 1 m 3 m 2 m 3 m 1.2 m North Wall 1 Wall 2 Partition 1 Partition 2 0.0000% 0.0050% 0.0100% 0.0150% 0.0200% 0.0250% 0.0300% Coarse Fine Refine Grid Resolution Accuracy 0 200 400 600 800 1000 1200 Computational Cost [sec] Accuracy Computational Cost 135 Table A6.5 shows the view factors of different zone surfaces, computed by both the numerical model and the analytical solutions. The last column summarizes the imaginary interior temperature of different zone surfaces. Implementing these temperatures, the plane radiant temperatures in different directions and the zone mean radiant temperature were calculated by the numerical model as well as the analytical solutions. This is shown in Table A6.6. These comparisons prove that the numerical model is capable of computing the plane radiant temperatures in different direction and the zone mean radiant temperature with an acceptable accuracy. These temperatures are used to predict the thermal sensations of the zone occupants. Figure A6.4. View factors of the south and east windows. Method Zone Surfaces Numerical Model Analytical Solutions Imaginary Interior Surface Temperatures Roof 0.6591 0.6591 47.0000 Floor 0.9683 0.9683 27.0000 Partition One UP 0.0852 0.0852 27.0000 Partition One DN 0.0079 0.0079 27.0000 Partition Two UP 0.0852 0.0852 27.0000 Partition Two DN 0.0079 0.0079 27.0000 Wall One UP 0.0163 0.0690 47.0000 Wall One DN 0.0000 0.0079 47.0000 Window One UP 0.0690 0.0163 67.0000 Window One DN 0.0079 0.0000 67.0000 Wall Two UP 0.0309 0.0543 37.0000 Wall Two DN 0.0024 0.0055 37.0000 Window Two UP 0.0543 0.0309 57.0000 Window Two DN 0.0055 0.0024 57.0000 SUM 2 2 - Table A6.5. View factor and imaginary interior temperature of different zone surfaces. 1.2 m 0.6 m 0.5 m 1.5 m 3 m UP DOWN Wall 1 0.5 m F1 F2 FWIN =FUP= F1-F2 1.2 m 0.6 m 1.9 m FUP FDOWN FWIN =FUP+ FDOWN 1.5 m 3 m UP DOWN Wall 2 136 Method Temperatures Numerical Model Analytical Solutions UP 44.0189 44.0189 Down 27.3159 27.3159 Left 35.1846 35.1846 Right 36.8206 36.8206 Back 37.1392 37.1392 Plane Radiant Temperatures Front 34.8599 34.8599 Zone Mean Radiant Temperature 35.9151 35.9151 Table A6.6. The plane and mean radiant temperatures. A6.3. Thermal Comfort Model The current thermal comfort standard (ANSI/ASHRAE STANDARD 55-2004) defines a comfort zone on the psychometric chart for 80% occupant acceptability. The values of the indoor thermal environmental and personal factors that are used to generate this zone are summarized in Table A6.7. Indoor Thermal Environmental Factors Personal Factors Run Air Temperature [C] Relative Humidity [%] Mean Radiant Temperature [C] Air Speed [m/s] Metabolic Rate [Met] Clothing [clo] 1 19.6 86 19.6 0.1 1.1 1 2 23.9 66 23.9 0.1 1.1 1 3 25.7 15 25.7 0.1 1.1 1 4 21.2 20 21.2 0.1 1.1 1 5 23.6 67 23.6 0.1 1.1 0.5 6 26.8 56 26.8 0.1 1.1 0.5 7 27.9 13 27.9 0.1 1.1 0.5 8 24.7 16 24.7 0.1 1.1 0.5 Table A6.7. Values used to generate the comfort envelope on the psychometric chart These values were implemented by the numerical model to predict the PMV and PPD values. The results were then compared against those provided by the thermal comfort standard. This comparison, shown in Figure A6.5, proves that the numerical model is able to predict the occupants’ thermal sensations with an acceptable accuracy. 137 Figure A6.5. The numerical model vs. the current thermal comfort standard. Numerical Model Thermal Comfort Standard -1.0 -0.5 0.0 0.5 1.0 1 2 3 4 5 6 7 8 Run PMV 9.0% 9.5% 10.0% 10.5% 11.0% 1 2 3 4 5 6 7 8 Run PPD 138 Appendix Seven: Whole Model Validation with IES<VE> As previously mentioned in Chapter One, IES<VE> is an integrated building thermal analysis software system that has been developed based on the heat balance method. It also has an inherent thermal comfort model that could predict occupants’ thermal sensations as a non-linear function of the thermal environmental and personal factors. It is important to note that IES<VE> has been validated against ANSI/ASHRAE Standard 140-2001, which is the standard method of test for the evaluation of building energy analysis computer programs. The numerical model and IES<VE> were both applied on the baseline single generic zone, explained in Chapter Three, to investigate its thermal performance and occupants’ thermal sensations. Regarding the difference in the accuracy of the controlling system used in the numerical model from that of IES<VE>, the zone air temperature was fixed at 22˚C rather than changing in the range of setpoints. Also, it was assumed that the minimum fresh air for the occupants was separately treated and introduced into the zone at the zone air temperature. Based on ASHRAE design weather data for Vancouver international Airport, the hottest and the coldest months of the year are respectively August and January. Therefore, the summer and winter analyses were carried out over the middle day of these months. The climate data of these two days are shown in Figure A7.1. Implementing these climate data, the sensible heat (or if negative, cooling) required to maintain the zone air temperature at 22˚C was calculated using both models. Also, for the clothing level of 0.71clo (i.e. trousers, long-sleeve shirt, sitting on standard office chair), the thermal comfort indicators were computed by the numerical model and compared against those predicted by IES<VE>. Figure A7.2 shows a comparison of the results. The whole model validation showed that the numerical model is computing solutions that are reasonable compared to IES<VE>. The main sources of discrepancies between the results are: • Interactions between the Adjacent Zones: Regarding that the numerical model is only able to perform the thermal analysis for a single zone; the thicknesses of the interior 139 Figure A7.1. The hourly climate data for the 15th of August and January. surfaces in the IES<VE> model were increased to reduce the heat transfer from/to the adjacent zones. The optimum thicknesses of these surfaces were determined by trial and error to eliminate the heat transfer through these surfaces with the minimum increase in the zone thermal mass. • Optical Properties of the Glazing Systems: It is not possible to define all the optical properties of a glazing system at different incident angles in IES<VE>. Considering the 70% glazing area on the external wall, this may cause discrepancies in the transmitted solar radiation. • Implementing Different Standards: Unlike the numerical model that has been developed based on the ASHRAE standard (i.e. American Society of Heating, Refrigerating and Air-Conditioning Engineers), IES<VE> uses the CIBSE standard (i.e. Chartered Institution of Building Services Engineers) to calculate the heat fluxes from/to the building envelope. • Infiltration Load: The numerical model calculates the infiltration load based on the specific heat capacity and density of the outdoor air, which are updated on an hourly 0 4 8 12 16 20 240 250 500 750 Hour N or m al D ir ec t S ol ar R ad ia tio n [W /m 2 ] Aug 15 Jan 15 0 4 8 12 16 20 24-4 4 12 20 Hour D ry -b ul b Te m pe ra tu re [C ] Aug 15 Jan 15 0 4 8 12 16 20 240 1.5 3 4.5 Hour W in d Sp ee d [m /s ] Aug 15 Jan 15 0 4 8 12 16 20 242 5 8 11 Hour H um id ity R at io [g w at er /k g d ry ai r] Aug 15 Jan 15 140 Figure A7.2. The numerical model vs. IES<VE>. basis depending on the climate data. However, IES<VE> computes the infiltration load according to the zone air specific heat capacity and the constant air density of 1.2 kg/m3. Considering the infiltration load calculated by the numerical model a variation profile was assigned to the mass flow rate of infiltrated air in the IES<VE> model to eliminate the discrepancies between the results. • Radiation Heat Transfer Coefficients: The numerical model updates the radiation heat transfer coefficients on the zone surfaces according to their temperatures. However, these coefficients are always constant in the IES<VE> model. 0 4 8 12 16 20 24-0.52 -0.5 -0.48 -0.46 -0.44 Hour PMV Numerical Model IES<VE> 0 4 8 12 16 20 2410% 11% 12% 13% 14% Hour PPD Numerical Model IES<VE> 0 4 8 12 16 20 249% 9.5% 10% 10.5% 11% Hour PPD Numerical Model IES<VE> 0 4 8 12 16 20 24-100 0 100 200 300 400 500 Hour W Numerical Model IES<VE> 0 4 8 12 16 20 24 -0.64 -0.61 -0.58 -0.55 -0.52 Hour PMV Numerical Model IES<VE> 0 4 8 12 16 20 24-500 -400 -300 -200 -100 0 100 Hour W Numerical Model IES<VE> SUMMER DAY WINTER DAY
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Interaction between thermal comfort and HVAC energy consumption in commercial buildings Taghi Nazari, Alireza 2008
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Title | Interaction between thermal comfort and HVAC energy consumption in commercial buildings |
Creator |
Taghi Nazari, Alireza |
Publisher | University of British Columbia |
Date Issued | 2008 |
Description | The primary purpose of the current research was to implement a numerical model to investigate the interactions between the energy consumption in Heating, Ventilating, and Air Conditioning (HVAC) systems and occupants’ thermal comfort in commercial buildings. A numerical model was developed to perform a thermal analysis of a single zone and simultaneously investigate its occupants’ thermal sensations as a non-linear function of the thermal environmental (i.e. temperature, thermal radiation, humidity, and air speed) and personal factors (i.e. activity and clothing). The zone thermal analyses and thermal comfort calculations were carried out by applying the heat balance method and current thermal comfort standard (ASHRAE STANDARD 55-2004) respectively. The model was then validated and applied on a single generic zone, representing the perimeter office spaces of the Centre for Interactive Research on Sustainability (CIRS), to investigate the impacts of variation in occupants’ behaviors, building’s envelope, HVAC system, and climate on both energy consumption and thermal comfort. Regarding the large number of parameters involved, the initial summer and winter screening analyses were carried out to determine the measures that their impacts on the energy and/or thermal comfort were most significant. These analyses showed that, without any incremental cost, the energy consumption in both new and existing buildings may significantly be reduced with a broader range of setpoints, adaptive clothing for the occupants, and higher air exchange rate over the cooling season. The effects of these measures as well as their combination on the zone thermal performance were then studied in more detail with the whole year analyses. These analyses suggest that with the modest increase in the averaged occupants’ thermal dissatisfaction, the combination scenario can notably reduce the total annual energy consumption of the baseline zone. Considering the global warming and the life of a building, the impacts of climate change on the whole year modeling results were also investigated for the year 2050. According to these analyses, global warming reduced the energy consumption for both the baseline and combination scenario, thanks to the moderate and cold climate of Vancouver. |
Extent | 1556382 bytes |
Subject |
HVAC Thermal comfort Energy Heating Cooling Ventilation Numerical modeling |
Genre |
Thesis/Dissertation |
Type |
Text |
File Format | application/pdf |
Language | eng |
Date Available | 2008-03-19 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivatives 4.0 International |
DOI | 10.14288/1.0066315 |
URI | http://hdl.handle.net/2429/597 |
Degree |
Master of Applied Science - MASc |
Program |
Mechanical Engineering |
Affiliation |
Applied Science, Faculty of Mechanical Engineering, Department of |
Degree Grantor | University of British Columbia |
Graduation Date | 2008-05 |
Campus |
UBCV |
Scholarly Level | Graduate |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
Aggregated Source Repository | DSpace |
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