NUMERICAL STUDY OF THE AIRFLOW AND TEMPERATURE DISTRIBUTIONS IN AN ATRIUM. Murat Nihat Basarir. in conformity with the requirements for

NUMERICAL STUDY OF THE AIRFLOW AND TEMPERATURE DISTRIBUTIONS IN AN ATRIUM by Murat Nihat Basarir A thesis submitted to the Department of Mechanical and Materials Engineering in conformity with the requirements for the degree of Master of Science (Engineering) Queen s University Kingston, Ontario, Canada September, 2009 Copyright Murat Nihat Basarir, 2009

Abstract Computational fluid dynamics (CFD) has been extensively used in the study of building energy usage and thermal comfort in buildings, however there remains the need to thoroughly evaluate the accuracy of the results given by such CFD methods. The present study involves a numerical investigation of the flow and temperature distribution in the atrium situated in the Concordia University Engineering Building. The study involved a steady-state simulation of the conditions in the atria on August 1, 2007, a date for which experimental data was available for validation of the numerical results. The commercial CFD solver FLUENT was used to solve the equations that govern the flow in the atrium. The realizable k- turbulence model incorporating buoyancy force effects was used. During the period studied a forced airflow through the atrium existed due to a mechanical air supply vent near the floor level. The natural convection in the atrium, induced by the temperature differences resulting mainly from the incoming solar radiation, was modeled using the bousinessq approximation. In general, good agreement was obtained between the numerical and experimental results. The numerical results also predicted the thermal stratification in the atrium relatively accurately. A parametric study was performed to assess the sensitivity of the numerical results to the assumed boundary conditions used in the study. An evaluation of the thermal comfort levels in the atrium was also undertaken using the numerical results. This indicated that while regions of thermal discomfort did exist in the atrium, these regions constituted only a small part of the atrium. i

Acknowledgements Foremost, I would like to express my sincere gratitude to my supervisor, Prof. Dr. Patrick Oosthuizen. He has guided and supported me throughout my work and provided me with opportunities to broaden my knowledge. I am proud to have been a Masters student of a professor who has such extensive experience and kind personality. I would like to thank Dr. M. Lightstone and Charles Rundle of McMaster University, and Eleni Mouriki, Dr. A. Athienitis and Patagiota Karava from Concordia University for their assistance and involvement in this project. My colleagues in the Heat Transfer Laboratory have always provided a friendly and engaging atmosphere to work in. I would like to thank all my friends and especially Abdul Kalendar, Adam Rysanek, Enis Hasim for the many insightful conversations. I would like to thank Jane Paul and McLaughlin Hall staff for their smiles and administrative assistance. I am grateful for the financial support from Natural Sciences and Engineering Research Council of Canada (NSERC) through the Solar Buildings Research Network and the Department of Mechanical Engineering at Queen's University. I would like to thank my family for the love and support they have provided throughout my Masters Degree program. The values they have taught me enabled me to finish this thesis and for this I cherish both of you. ii

I dedicate this thesis to my Mother and Father, Education has always been the talk of our family and will be for the years to come iii

Table of Contents Abstract... i Acknowledgements... ii Table of Contents... iv List of Figures... vi List of Tables... x Nomenclature... xii Chapter 1 Introduction... 1 1.1 Buildings, Energy and the Environment... 1 1.2 Problem Definition... 2 1.3 Objectives and Methodology... 2 1.4 Literature Review... 3 1.4.1 CFD based Building Simulation... 3 1.4.2 Atrium Buildings... 5 1.4.3 CFD Studies of Atria... 8 1.4.4 Thermal Comfort... 9 1.4.5 Discomfort due to Draft... 11 1.4.6 Vertical Air Temperature Difference... 13 Chapter 2 Background Theory and Numerical Model... 15 2.1 Introduction... 15 2.2 Fundamentals of CFD... 16 2.3 Assumptions... 16 2.4 Governing Equations... 16 2.5 Turbulence Modeling... 17 2.5.1 k- Turbulence Model... 19 2.5.2 Near-Wall Turbulence Modeling... 20 2.6 Radiation Modeling... 21 2.7 Numerical Solution Method... 22 2.8 Solver Settings... 23 iv

Chapter 3 CFD Modeling of the Concordia Atrium... 25 3.1 Geometry... 25 3.2 Mesh Generation... 29 3.3 Mesh Independence Testing... 32 3.4 Boundary Conditions... 38 3.5 Solar Load Model... 41 Chapter 4 Results and Discussion... 42 4.1 Introduction... 42 4.2 Validation Case... 42 4.3 Effect of Internal Radiation Exchange... 46 4.4 Effect of Outside Temperature... 51 4.5 Effect of Outside Wind Speed... 61 4.6 Effect of Absorptivity of the Glass... 69 4.7 Cases for Different Time of Day... 78 4.8 Cases for Different Location... 89 4.9 Thermal Comfort... 97 4.9.1 Discomfort Due to Draft... 98 4.9.2 Vertical Air Temperature Difference... 102 Chapter 5 Conclusions and Recommendations for Future Work... 104 5.1 Conclusions... 104 5.2 Recommendations... 106 References... 108 Appendix A... 112 Input values for FLUENT modeling of the Concordia Atrium... 112 Appendix B... 120 Additional Thermal Comfort Study Results... 120 v

List of Figures Figure 1-1 Components of average energy use during a 50-year life cycle of typical office buildings in Vancouver and Toronto... 1 Figure 1-2 The interaction between design factors and thermal effect... 4 Figure 1-3 Telus William Farrell Atrium located in British Columbia... 6 Figure 1-4 Layout of an Atrium... 7 Figure 1-5 Outside view of the Concordia Atrium facade... 7 Figure 1-6 Relative performance versus deviation from optimal comfort temperature... 10 Figure 1-7 Operative temperature tolerances for winter conditions... 10 Figure 1-8 age of people dissatisfied as a function of mean air velocity... 12 Figure 1-9 Draft conditions dissatisfying 15% of population... 13 Figure 1-10 age of seated people dissatisfied as function of air temperature difference between head and ankles... 14 Figure 2-1 Subdivisions of the near-wall region... 20 Figure 2-2 Segregated pressure based solver... 23 Figure 3-1 Geometric representation of the Concordia Atrium... 25 Figure 3-2 The dimensions of the supply and return on east wall... 26 Figure 3-3 Floor layout of the atrium... 26 Figure 3-4 Schematic of the thermocouple locations on the facade... 27 Figure 3-5 Schematic outlining the thermocouple locations for air temperature readings... 28 Figure 3-6 Top view of the thermocouple locations for air temperature readings... 28 Figure 3-7 Guideline for cell count in building simulations... 30 Figure 3-8 Boundary layers at the corner of the west wall and the facade... 31 Figure 3-9 Contour plot of y + for the facade... 32 Figure 3-10 Location of lines used to investigate temperature and velocity variation... 33 Figure 3-11 Vertical air temperature along the center of atrium... 34 Figure 3-12 Glass temperature along center of facade... 35 Figure 3-13 Velocity magnitude along horizontal line at the center of atrium... 36 Figure 3-14 Schematic of the grid chosen for the present study... 37 Figure 3-15 The orientation of the Concordia building... 39 Figure 4-1 Glass temperature contours on the facade for validation case... 43 vi

Figure 4-2 Air temperature contours at various heights for validation case... 43 Figure 4-3 Glass temperature contours on the facade without internal radiation exchange... 46 Figure 4-4 Glass temperatures along the middle of the facade for cases investigating internal radiation... 47 Figure 4-5 Air temperature contours at various heights... 48 without internal radiation exchange... 48 Figure 4-6 Air temperatures along center vertical line 0.24 m away from the facade for cases investigating radiation model... 48 Figure 4-7 Glass temperature contours on the facade when T out = 23.6 o C... 51 Figure 4-8 Glass temperature contours on the facade when T out = 28.6 o C... 52 Figure 4-9 Glass temperature contours on the facade when T out = 33.6 o C... 52 Figure 4-10 Glass temperatures along the middle of the facade for cases with different outside temperatures... 53 Figure 4-11 Air temperature contours at various heights when T out = 23.6 o C... 55 Figure 4-12 Air temperature contours at various heights when T out = 28.6 o C... 56 Figure 4-13 Air temperature contours at various heights when T out = 33.6 o C... 56 Figure 4-14 Air temperatures along center vertical line 0.24m away from the facade for cases with different outside temperature... 57 Figure 4-15 Glass temperature contours on the facade when V w = 3 m/s... 61 Figure 4-16 Glass temperature contours on the facade when V w = 6 m/s... 62 Figure 4-17 Glass temperature contours on the facade when V w = 9 m/s... 62 Figure 4-18 Glass temperatures along the middle of the facade for cases with different wind speeds... 63 Figure 4-19 Air temperature contours at various heights when V w = 3 m/s... 65 Figure 4-20 Air temperature contours at various heights when V w = 6 m/s... 65 Figure 4-21 Air temperature contours at various heights when V w = 9m/s... 66 Figure 4-22 Air temperatures along center vertical line 0.24m away from the facade for cases with different wind speed... 66 Figure 4-23 Glass temperature contours on the facade when α=16 %... 70 Figure 4-24 Glass temperature contours on the facade when α=17.5 %... 70 Figure 4-25 Glass temperature contours on the facade when α=19 %... 71 Figure 4-26 Glass temperatures along the middle of the facade for cases with different glass absorptivity... 72 vii

Figure 4-27 Air temperature contours at various heights when α = 16 %... 74 Figure 4-28 Air temperature contours at various heights when α = 17.5%... 74 Figure 4-29 Air temperature contours at various heights when α = 19 %... 75 Figure 4-30 Air temperatures along center vertical line 0.24m away from the facade for cases with different glass absorptivity... 75 Figure 4-31 Contours of solar heat flux on the facade and walls of the atrium at 14:30... 80 Figure 4-32 Glass temperature contours on the facade at 14:30... 80 Figure 4-33 Air temperature contours in the atrium at various heights for 14:30... 82 Figure 4-34 Contours of solar heat flux on the facade and walls of the atrium at 17:30... 85 Figure 4-35 Glass temperature contours on the facade at 17:30... 86 Figure 4-36 Air temperature contours in the atrium at various heights for 17:30... 87 Figure 4-37 Contours of solar heat flux on the facade and walls of the atrium at 16:00 in Calgary (Longitude: -114, Latitude: 51)... 89 Figure 4-38 Contours of solar heat flux on the facade and walls of the atrium at 16:00 in Halifax (Longitude: -63, Latitude: 45)... 90 Figure 4-39 Contours of solar heat flux on the facade and walls of the atrium at 16:00 in Vancouver (Longitude: -123, Latitude: 49)... 90 Figure 4-40 Glass temperature contours on the facade at 16:00 in Calgary... 91 Figure 4-41 Glass temperature contours on the facade at 16:00 in Halifax... 91 Figure 4-42 Glass temperature contours on the facade at 16:00 in Vancouver... 92 Figure 4-43 Glass temperatures along the middle of the facade for 16:00... 93 Figure 4-44 Air temperature contours in the atrium at various heights... 94 for 16:00 in Calgary... 94 Figure 4-45 Air temperature contours in the atrium at various heights... 94 for 16:00 in Halifax... 94 Figure 4-46 Air temperature contours in the atrium at various heights... 95 for 16:00 in Vancouver... 95 Figure 4-47 Air temperatures along center vertical line 0.24m away from the facade for 16:00.. 96 Figure 4-48 Air temperature contours for three vertical planes in the atrium... 97 Figure 4-49 Region of occupied workspace for investigation of thermal comfort... 98 Figure 4-50 Air temperature contours at a height of 1.1 m... 99 Figure 4-51 Velocity magnitude contours at a height of 1.1 m... 99 Figure 4-52 Turbulence intensity contours at a height of 1.1 m... 100 viii

Figure 4-53 Velocity vectors on a vertical plane normal to supply vent... 101 Figure 4-54 Prediction of percentage dissatisfied due to draft in the occupied area of the atrium... 101 Figure 4-55 Prediction of percent dissatisfied due to vertical temperature difference in the occupied area of the atrium... 102 ix

List of Tables Table 3-1 Positions of the glass thermocouples... 27 Table 3-2 Positions of air thermocouples... 29 Table 3-3 Specifications of the boundary layers for different surfaces... 31 Table 3-4 Mesh densities for the different grids... 33 Table 3-5 age difference of air temperature between grids... 34 Table 3-6 age difference of glass temperature between grids... 35 Table 3-7 age difference of velocity magnitude between grids... 36 Table 3-8 Average temperature and velocities in certain regions... 37 Table 3-9 Solar load parameters used in the study... 41 Table 4-1 Glass temperature comparison of numerical and experimental data for validation case 44 Table 4-2 Air temperature comparison of numerical and experimental data for validation case.. 45 Table 4-3 Overall percent differences in air and glass temperatures between numerical and experimental data for validation case... 45 Table 4-4 Glass temperature comparison of numerical and experimental data for the case without internal radiation exchange... 49 Table 4-5 Air temperature comparison of numerical and experimental data for the case without radiation... 50 Table 4-6 Glass temperature comparison of numerical data between Main Case - T out = 28.6 o C and Lower Case - T out = 23.6 o C... 54 Table 4-7 Glass temperature comparison of numerical data between Main Case - T out = 28.6 o C and Higher Case - T out = 33.6 o C... 54 Table 4-8 Air temperature comparison of numerical data between Main Case - T out = 28.6 o C and Lower Case - T out = 23.6 o C... 58 Table 4-9 Air temperature comparison of numerical data between Main Case - T out = 28.6 o C and Higher Case - T out = 33.6 o C... 59 Table 4-10 Overall percent differences in numerical air and glass temperatures when T out is lowered by 5 o C... 59 Table 4-11 Overall percent differences in numerical air and glass temperatures when T out is raised by 5 o C... 60 Table 4-12 Glass temperature comparison of numerical data between Main Case - V w = 6 m/s and Lower Case - V w = 3 m/s... 63 x

Table 4-13 Glass temperature comparison of numerical data between Main Case - V w = 6 m/s and Higher Case - V w = 9 m/s... 64 Table 4-14 Air temperature comparison of numerical data between Main Case - V w = 6 m/s and Lower Case - V w = 3 m/s... 67 Table 4-15 Air temperature comparison of numerical data between Main Case - V w = 6 m/s and Upper Case - V w = 9 m/s... 68 Table 4-16 Overall percent differences in numerical air and glass temperatures when the outside wind speed is decreased by 50%... 69 Table 4-17 - Overall percent differences in numerical air and glass temperatures when the outside wind speed is increased by 50%... 69 Table 4-18 Glass temperature comparison of numerical data between Main Case - α = 17.5 % and Lower Case - α = 16 %... 72 Table 4-19 Glass temperature comparison of numerical data between Main Case - α = 17.5 % and Higher Case - α = 19 %... 73 Table 4-20 Air temperature comparison of numerical data between Main Case - α = 17.5 % and Lower Case - α = 16 %... 76 Table 4-21 Air temperature comparison of numerical data between Main Case - α = 17.5 % and Higher Case - α = 19 %... 77 Table 4-22 Overall percent difference in numerical air and glass temperatures when absorptivity is lowered to 16 %... 78 Table 4-23 Overall percent difference in numerical air and glass temperatures when absorptivity is raised to 19 %... 78 Table 4-24 Solar irradiation and outside conditions for at time of 14:30... 79 Table 4-25 Glass temperature comparisons of numerical and experimental data for 14:30... 81 Table 4-26 Air Temperature comparison of numerical and experimental data for 14:30... 82 Table 4-27 Overall percent difference in air and glass temperatures for 14:30... 83 Table 4-28 Solar irradiation and outside conditions for a time of 17:30... 84 Table 4-29 Glass temperature comparison of numerical and experimental data for 17:30... 86 Table 4-30 Air temperature comparison of numerical and experimental data for 17:30... 88 Table 4-31 - Overall percent difference in air and glass temperatures for 17:30... 89 Table 4-32 Glass temperature comparison of numerical data at 16:00 for all simulated cities... 92 Table 4-33 Air temperature comparison of numerical data for 16:00 for all simulated cities... 95 xi

Nomenclature c p Specific heat J/kgK C 1 C 2 C 3 C Constant used in k- turbulence model Constant used in k- turbulence model Constant used in k- turbulence model Constant used in k- turbulence mode g Gravitational acceleration m/s 2 h heat transfer coefficient W/(m 2 K) k turbulence kinetic energy m 2 /s 2 L Mean beam length m P Pressure Pa q Heat flux W/m 2 q Heat source W/m 3 Re Reynolds Number t time s T temperature C/K Tu turbulence intensity u velocity component in the x direction m/s u friction velocity v velocity component in the y direction m/s V velocity m/s W Width m w velocity component in the z direction m/s x horizontal coordinate m y vertical coordinate m y Dimensionless wall distance z vertical coordinate m xii

Greek Symbols thermal expansion coefficient K -1 fluid density kg/m 3 dynamic fluid viscosity Pa. s t eddy viscosity Pa. s absorption coefficient or absoprtivity Stefan-Boltzmann Constant (5.672 x10-8 W/m 2 K 4 ) s k Scattering coefficient Constant used in k- turbulence model Constant used in k- turbulence model t Turbulent Prandtl number rate of dissipation of kinetic energy or emissivity m 2 /s 3 t kinematic fluid viscosity m 2 /s Subscripts a c w sky dp out sd air temperature optimal comfort wind sky dew point outside standard deviation of the velocity xiii

Chapter 1 Introduction 1.1 Buildings, Energy and the Environment The built environment accounts for roughly 30 percent of Canada s energy usage and approximately 28 percent of greenhouse gas emissions (Ayoub et al., 2000). Figure 1-1 displays the breakdown of the average total energy that an office building consumes throughout its lifetime (Cole and Kernan, 1996). Figure 1-1 Components of average energy use during a 50-year life cycle of typical office buildings in Vancouver and Toronto (Cole and Kernan, 1996) 1

As seen in the figure, the operating energy constitutes a major part of the total energy consumed throughout the lifetime of a building. The building design analysis tools utilized today aim to significantly reduce this operating energy. It is important to remember that while trying to reduce energy consumption, the building must still serve its core purpose, which is to provide shelter from the outside environment and offer a comfortable indoor environment. Studies have shown that occupants will quickly respond to any discomfort by taking actions to regain their comfort. However these actions may adversely affect energy consumption, such as turning on lights or opening windows when outdoor conditions are unsuitable. Therefore accurate prediction of thermal comfort during the design of the building is vital to maintaining low energy consumption (Nicol, 2003). 1.2 Problem Definition The present work was motivated by the lack of CFD validation studies for large air spaces such as atrium buildings. The availability of experimental air and glass temperature measurements in the atrium situated inside the Concordia University Engineering Building has made it possible to compare extensive experimental data with numerical CFD results. This comparison was undertaken in the present study and the results give insight into the ability to accurately model the conditions that occur in an atrium building using a CFD model. 1.3 Objectives and Methodology The main objective of this study was to create and evaluate a CFD model of the Concordia University Atrium to predict the air and glass temperatures in the atrium on a 2

specific day and at a specific time of day, thus examining the accuracy of such studies to predict the air flow and temperature distributions existing in atria. The findings of this study can also serve as a reference when developing guidelines for CFD modeling of large glazed buildings. To achieve these goals, the work was conducted in the following separate stages: Stage 1 Literature Review: Investigate published work on the CFD modeling of buildings and review methods of predicting thermal comfort in buildings Stage 2 CFD Model: Construct a CFD Model of the Concordia Atrium for the analysis of the flow and temperature distribution on the facade and inside the atrium Stage 3 Model Validation: Compare the numerical results with the available experimental data Stage 4 Model Assessment: Conduct a parametric study to further understand the effect of the assumed boundary conditions Stage 5 Thermal Comfort Analysis: Investigate the possibility of thermal discomfort due to draught and temperature stratification in the atrium 1.4 Literature Review 1.4.1 CFD based Building Simulation The modeling of the thermal characteristics of buildings using CFD has been largely influenced by the availability of increased computing power over roughly the past twenty years (Nielsen et al., 2007). The evolution of computer technology allowed software to realistically predict both heat transfer and air flow in reasonably short computing run 3

times. Chow (1996) and Gan et al. (1994) described how architects and engineers could use such simulations to improve their intuitive designs and evaluate methods to reduce energy consumption. To fully integrate CFD simulation into the design process, the timeline of the simulation must be in line with the design timeline. Figure 1-2 (Negrao, 1995) displays how the basic features of the building, such as orientation and shape make a large contribution to the thermal dynamics of a building. Due to the limited information available during the early design stages, guidelines are required on the simplifications that can be made in a CFD model to allow users to model buildings early in the design stage when significant changes can still be made. Figure 1-2 The interaction between design factors and thermal effect (Negrao, 1995) Zhai (2006) describes the many ways that CFD programs can be utilized such as in; site planning, natural ventilation (Mak, 2002), smoke and contamination control (Colquhoun et al., 2003) but one of its primary uses is the evaluation of indoor air quality and the assessment of a proposed HVAC system. 4

There has been many CFD building simulations conducted for smaller spaces. Studies conducted by Abanto (2004) and Posner (2003) examined conditions in offices, using modeled occupants to study the thermal conditions around seated persons. A similar study was undertaken by Sakai (2007) looking at the effect of ventilation rates on a seated person in a lavatory. As computational cost decreased, CFD methods have been more commonly used to model larger spaces. Operation of HVAC systems used in stadiums has been studied in detail by Stamou et al. (2008 and 2007). Mechanically ventilated theatres were investigated by Kavgic et al. (2008) and Cheong et al. (2003), where the numerical thermal comfort results were compared with field measurements and surveys. It was found that adjustments in the ventilation system could improve the thermal comfort conditions and energy efficiency. CFD models that have high computational cost and long run times can occur if full account is taken of the entire building thermal loads. Such lengthy CFD simulations can limit the number of different concepts analyzed and hinder the speed at which the designconstruction process can move forward. It is for this reason that guidelines for the simplification of CFD models are required. Validation of these CFD simulations using experimental data acquired from real life buildings is also necessary to ensure the accuracy of such guidelines (Laouadi et al., 1999). 1.4.2 Atrium Buildings A modern atrium can be defined as a large open space spanning several floors and having large glazed areas (Channell, 2009). Apart from their unique aesthetics they are appealing to many people due to the connection they provide with the outdoors for occupants. They are desirable working environments due to the enhanced natural daylighting through the 5

large glazing. The Telus William Farrell Atrium in British Columbia shown in Figure 1-3, displays the mentioned characteristics of atriums. Figure 1-3 Telus William Farrell Atrium located in British Columbia Due to their large geometries, they also have the capacity to make use of natural ventilation due to buoyancy forces caused by the solar radiation (Cook et al., 2005). In cooler climates, they allow for passive heating techniques from the direct heat gain in the sunspace with heat stored in thermal mass. Atria vary in shape and size, mainly determined by the geometry of the building in which they will be incorporated. The Concordia Atrium is of the general type shown in Figure 1-4 (Saxon, 1983). 6

Figure 1-4 Layout of an Atrium (Saxon, 1983) The outside view of Concordia Engineering building can be seen in Figure 1-5. Figure 1-5 Outside view of the Concordia Atrium facade 7

1.4.3 CFD Studies of Atria Although there has been significant amount of research on CFD simulation of various building types, limited work has been done on investigating atrium buildings (IEA, 1996). One of the first major studies involving CFD modeling of atria was conducted by Schild et al. (1995). This comprehensive study aimed to investigate the important factors to consider when undertaking CFD simulations of atria. It investigates a 10 m by 10 m twodimensional atrium with a forced air supply. The findings of the study indicated the importance of near-wall modeling due to its effect on the heat transfer rate from the wall to the air. The importance of the net solar gain and its distribution on the surfaces of the atrium was also shown. Lau et al. (2003) investigated the vertical temperature stratification and the possible cooling load reduction during the operation of a displacement ventilation system in a 25m high atrium. The measured surface temperatures were used as boundary conditions to the model and the different heating loads were investigated. They suggested that the boundary conditions of the wall temperatures had the greatest effect on the model. Ji et al. (2007) investigated natural ventilation in an enclosure that was attached to an atrium. The predictions were compared with small-scale experiments. The findings indicated that the mesh used had an effect on where vertical temperature gradients occurred. A recent study conducted by Liu et al. (2009) described an attempt to develop a methodology for predicting the performance of buoyancy-driven ventilation in atrium buildings at an early design stage. The study revealed that the external ambient 8

temperature has a great influence on the temperature stratification when the flow is solely driven by buoyancy forces. The different thermal loads inside the atrium were found to have a small effect on the indoor temperature. 1.4.4 Thermal Comfort One of the major applications of building simulation tools is in the prediction of thermal comfort in occupied spaces. There have been many efforts to define thermal comfort but the most widely used definition is found in the ASHRAE Handbook of Fundamentals 2009, which describes it as that state of mind which expresses satisfaction with the thermal environment. From this definition it is important to note that not only the physical environment is important but the psychological and physiological conditions also have an effect. Studies have also shown that there is a link between thermal comfort and productivity. Seppanen and Fisk (2006) investigated performance of workers in a call center, using the average time per call as a measure of performance. Figure 1-6 shows the percentage change in performance when workers were exposed to hotter and colder temperatures relative to an optimal comfort temperature T c. 9

Figure 1-6 Relative performance versus deviation from optimal comfort temperature, T c (Seppanen and Fisk, 2006) The accuracy demanded of a CFD simulation is linked to the desired thermal comfort. A stringent temperature range for thermal comfort will require the simulation to be correspondingly very accurate. Figure 1-7 (Schild et al., 1995) illustrates the varying design tolerances for the corresponding predicted percentage dissatisfied (PPD) values. For example, a desired PPD of 20 % would result in a design tolerance of +/- 3.9 o C. Figure 1-7 Operative temperature tolerances for winter conditions (Schild et al., 1995) 10

Thermal comfort in a building space will, in general, depend on age and gender of the person involved, clothing, temperature, air velocity turbulence level, temperature gradients, relative humidity, mean radiant temperature and time of exposure. Some of these factors contributing to discomfort are discussed below. 1.4.5 Discomfort due to Draft Draft is one of the major reasons for discomfort; draft can be caused by improper design of the HVAC system or ineffective natural ventilation methods. This undesired increase in air velocity around the body could lead to a demand for higher air temperatures or for the ventilation to be halted, which in turn can alter the operating conditions in the building. It has been found that people are more sensitive to cold drafts then warm drafts; the same velocity of air may result in discomfort during cooling in summer than in heating during winter. To quantify the effect of air velocity on discomfort, Fanger and Christensen (1986) established the percentage of the population feeling discomfort due to a draft when subjected to airflows at different velocities. Figure 1-8 shows the percentage of people that felt discomfort on the head region as a function of air velocity for various air temperatures. 11

Figure 1-8 age of people dissatisfied as a function of mean air velocity (Fanger and Christensen, 1986) A study considering the air velocity over the whole body performed by Berglund and Fobelets (1987) found that for speeds up to 0.25 m/s people did not feel uncomfortable. An investigation of turbulence intensity effects along with velocity was conducted by Fanger et al. (1989). They derived an equation for age Dissatisfied (PD), this being a function of air temperature, velocity and turbulence intensity. Their equation is as follows: 0.62 34 T V 0.05 0.37V Tu 3.14 PD a (1.1) The turbulence intensity (Tu) in the equation is given by: Tu V V sd 100 (1.2) where V is the mean velocity and V sd is the standard deviation of the velocity. 12

Figure 1-9 demonstrates the effect of taking into consideration the turbulent intensity, displaying the conditions at which 15 % of occupants will feel discomfort. Figure 1-9 Draft conditions dissatisfying 15% of population (Fanger et al., 1989) It can be seen in Fig. 1-9, for an air temperature of 24 o C, the acceptable mean air speed varies between 0.35 m/s to 0.13 m/s for the range of turbulent intensities shown. 1.4.6 Vertical Air Temperature Difference In buildings and in atriums in particular, there can be a difference in air temperature at various heights, which may cause discomfort at the occupant level. Experimental work conducted by Olesen et al. (1979) exposed a group of subjects to various temperature gradients between the head and the feet. Although the participants could change the average temperature in the test room, the vertical temperature difference was kept constant. Figure 1-10 depicts the results obtained in the study, the figure indicating the 13

increase in the percent dissatisfied as a function of temperature. The rise in discomfort level as temperature difference increases will be clearly noted. Figure 1-10 age of seated people dissatisfied as function of air temperature difference between head and ankles (Olesen et al., 1979) 14

Chapter 2 Background Theory and Numerical Model 2.1 Introduction Computational Fluid Dynamics involves numerically modeling fluid flows. The results provide information about the flow, temperature and heat transfer. There are three stages in a CFD analysis. Pre-Processor: The pre-processor allows the user to define the geometry of the model, which establishes the computational domain for the situation considered. This computational domain is further divided into smaller cells by creating a mesh. The conditions on the boundaries of the solution domain are also defined in the pre-processor. Solver: FLUENT, a CFD software based on the finite volume method, calculates and solves for the physical quantities such as mass, momentum, energy within the nodes inside each cell. Post-Processor: The post-processor tools assist in the interpretation of the results. Lines and surfaces can be defined and the distribution of variables on these lines and surfaces can be displayed. Velocity plots can help visualize characteristics of the flow and to identify points of interest. The exporting tool for data can be used with third-party programs such as Excel for additional analysis of the solution. 15

2.2 Fundamentals of CFD The core of CFD relies on the solution of the equations that govern fluid flow. These nonlinear partial differential equations are discretized allowing them to be converted to algebraic equations, which are solved in the case of FLUENT using the finite volume method (Beausoleil-Morrison, 2000). The following sections will review the equations that govern fluid flow and the turbulence models. 2.3 Assumptions The following assumptions have been used for the simulation of the flow inside the atrium: Steady-State Three-dimensional Bousinessq Approximation for the buoyancy forces which implies that only the density change with respect to temperature are considered and all other properties are considered constant 2.4 Governing Equations Since air inside the atrium is a Newtonian fluid, the equations for conservation of mass, momentum and energy that govern the fluid flow are as follows (Incropera et al., 2002): Conservation of Mass: t ( u) ( v) ( w) 0 (2.1) x y z 16

Conservation of Momentum The y-coordinate is chosen to be in the vertical direction, i.e., in the direction the buoyancy forces act. The conservation of momentum equations in the three coordinate directions are: Momentum for the x direction t ( u) x ( uu) y ( vu) P ( wu) z x 2 u x 2 u 2 y 2 u 2 z 2 (2.2) Momentum for the z direction t ( w) x ( uw) y ( vw) P ( ww) z z 2 w x 2 w 2 y 2 w 2 z 2 (2.3) Momentum for the y direction t ( v) x ( uv) y ( vv) z ( wv) P y 2 v x 2 v 2 y 2 v g T 2 z 2 T (2.4) Conservation of Energy t ( c pt) x ( uc pt) y ( vc pt) z ( wc pt) k 2 T x 2 T 2 y 2 T q 2 z 2 (2.5) 2.5 Turbulence Modeling The above equations apply in turbulent flow but to solve them requires very high computational resources, however these equations can be modified to account for 17

turbulence. These modified equations are called the Reynolds averaged equations, which for any instant in time the value of any flow variable is the sum of the time-mean value of the variable and an instantaneous deviation of the variable from this mean value. For example, u = u u', u representing the time-mean quantity and u the instantaneous fluctuating quantity. Furthermore with the use of eddy viscosity in the momentum equations and the turbulent Prandtl number in the energy equation, simplification of these fluctuating quantities can be achieved, resulting in the governing equations in the following forms: Continuity: x ( u) y ( v) ( w) 0 (2.6) z Momentum in the x-direction 2 2 2 P u u u ( u) ( uu ) ( vu ) ( wu ) (2.7) t x y z x t 2 2 2 x y z Momentum in the y-direction ( v) ( uv) ( vv) ( wv) t x y z P y t 2 v x 2 v 2 y 2 v g T 2 z 2 T (2.8) Momentum in the z-direction P ( w) ( uw) ( vw) ( ww) t x y z z 2 w 2 w t 2 2 2 x y z 2 w (2.9) 18

Energy Equation: ( c pt ) ( uc pt ) ( vc pt ) ( wc pt ) t x y z k 2 T x 2 T 2 y 2 T T c p t q (2.10) 2 z 2 x i x i t 2.5.1 k- Turbulence Model The k- turbulence model has been adopted in the present study due to its generality and robustness in most flow situations as found through case studies conducted in literature by Zhang (2007) and Murakami et al. (1998). The k- turbulence model is based on the use of semi-empirical equations for the quantities, k, the turbulent kinetic energy and, the rate of dissipation of turbulent kinetic energy. The t in the above governing equations are solved using t t and where t is found k 2 from t C. The term C is a constant which leaves k and to be determined from the equations shown below. t k t ( k) ( kui ) Gk Gb YM S K xi x (2.11) j k x j 2 t ( ) ( ui ) C Gk C Gb C S t xi x j 1 3 2 (2.12) x j k k G k is the generation of turbulent kinetic energy due to mean velocity gradients; G b is the generation of turbulent kinetic energy due to buoyancy, and Y M a term that contributes to the overall dissipation rate. S and S k are source terms that can be input specified by the user. 19

The standard k - model uses the following constants: C =0.09 C 1 =1.44 C 2 =1.92 k =1 =1.3 The turbulence model used in this study is the Realizable k - turbulence model with full buoyancy effects, which is a variant of the Standard k - model. The Realizable k- has increased accuracy of predicting complex secondary flows and also accounts for recirculation. It also has a new formulation of turbulent viscosity and transport equation for (FLUENT, 2006). 2.5.2 Near-Wall Turbulence Modeling The standard k- turbulence model has the potential to accurately solve for turbulent flows away from walls. However there is a need to adapt this model to solve for flows near walls. Figure 2-1 (FLUENT, 2006) outlines the three main regions near walls. Figure 2-1 Subdivisions of the near-wall region, u being the friction velocity (FLUENT, 2006) 20

The layer that is adjacent to the wall is termed the viscous sublayer. At the wall the velocity is zero and therefore the velocities in this region are very low, the flow is effectively laminar with the effect of the viscosity being dominant. The outer region termed the fully-turbulent layer is where turbulence has a dominant effect on the flow. Between the viscous sublayer and the fully turbulent layer there is a transition region termed the buffer layer. To resolve the flow in this region standard wall functions are used, which consist of semi-empirical formulas that link the viscosity-affected region and the fully turbulent region. The standard wall functions, require a range of 30 < y + < 300 for accurate prediction of turbulent flow bounded by walls. The variable y +, which is termed the dimensionless wall distance, is used to find a suitable correct grid size near the walls. It is given by y u y /, where y represents the distance of the cell center to the wall. 2.6 Radiation Modeling To account for the effects of solar radiation entering the atrium, the solar load model in FLUENT was activated. This model constructs the sun's location in the sky from the specified year, month, date, time of day, location and orientation of the building. Using this information, the diffuse and direct solar loading is calculated. In the present model, the glass absorbs part of the solar radiation and the transmitted portion is absorbed by the interior surfaces. It is important to mention that solar loading does not take into consideration the radiative exchange between the internal walls of the atrium. This is done through activating a radiation model. 21

There are five radiation models available in FLUENT, each having its own strengths and weaknesses. The optical thickness of the problem dictates the choice of the model. The optical thickness is given by the following equation: Optical Thickness = ( α + σ s ) L (2.13) where α is the absorption coefficient of the gas through which the radiation is passing, σ s is the scattering coefficient of the gas and L is the mean beam length. The medium in an atrium is air, which is considered a non-participating medium due its very low absorption and scattering coefficients. Out of the models available for low optical thicknesses, the Discrete Transfer Radiation Model (DTRM) was chosen as it can predict the temperature distribution in simple geometries, such as an atrium, with modest computational effort (Braun et al., 2004, FLUENT, 2006). 2.7 Numerical Solution Method The governing equations together with the equations for turbulent kinetic energy and rate of dissipation of turbulent kinetic energy form a set of seven differential equations that describe the flow in the control volume. As it would be impossible to analytically solve these equations, a numerical solution is obtained using the finite volume method. This allows the differential equations to be converted into a set of algebraic equations. Figure 2-2 demonstrates the segregated solution method for solving these algebraic equations sequentially. 22

Figure 2-2 Segregated pressure based solver A solution is considered converged when the changes of a property from iteration to iteration are below a specified level. The amount that each property changes per iteration is controlled by an under-relaxation factor, thus controlling the fluctuations in each cell giving more stability to the solution. The iteration process will stop once the convergence criterion is reached in all of the cells. 2.8 Solver Settings The choice of solver settings used has been based on various studies conducted in literature involving modeling of large air spaces (Nielsen, 2007). The FLUENT documentation also includes guidelines for setting up problems that involve natural convection caused by solar loading. 23

The following solver settings were used in all the simulations in this study: Double Precision, Segregated Steady Solver Body Force Weighted Discretization for Pressure Second Order Upwind Discretization for momentum, turbulence and energy Under-relaxation factors for pressure, density, body forces, momentum, turbulent kinetic energy, turbulent dissipation rate, turbulent viscosity and energy equal to 0.3, 1, 1, 0.2, 0.8, 0.8, 1, and 0.9 respectively. SIMPLE Pressure-Velocity coupling Convergence criteria of 0.0001 24

Chapter 3 CFD Modeling of the Concordia Atrium 3.1 Geometry The modeling of one of the atriums existing in the Concordia University Engineering Building is the focus of this study. The atrium spans three stories, the general dimensions of the model constructed using the software GAMBIT is seen in Figure 3-1. The atrium has an overall size of 12.05 m x 9.39 m x 13.02 m. The area of the supply and return are shown in Figures 3-2 and the floor plan in Figure 3-3. The staircase and furniture have not been considered and the opening to the corridors adjacent to the atrium has been ignored. Figure 3-1 Geometric representation of the Concordia Atrium 25

Figure 3-2 The dimensions of the supply and return on east wall Figure 3-3 Floor layout of the atrium 26

Figures 3-4, 3-5, 3-6 and Tables 3-1, 3-2 outline the locations and coordinates where the experimental data were available (Mouriki, 2009). Figure 3-4 Schematic of the thermocouple locations on the facade Table 3-1 Positions of the glass thermocouples 27

Figure 3-5 Schematic outlining the thermocouple locations for air temperature readings Figure 3-6 Top view of the thermocouple locations for air temperature readings 28

Table 3-2 Positions of air thermocouples 3.2 Mesh Generation After the geometry was created in GAMBIT, the next step was to generate a suitable mesh. The grid quality is vital to obtaining accurate simulations; a coarse grid will lead to large numerical errors, however it is computationally expensive to have a very fine grid throughout the domain when dealing with large buildings (Stamou et al., 2006). The rectangular geometry allowed a structured hexahedral grid to be employed, allowing the cells to be in line with the boundary layers and air supply. 29

Figure 3-7 (Nielsen, 2007) provides a rough guideline for choosing the initial cell count for the mesh. The equation of the line is N = 44400 x V 0.38, where N is the number of cells and V is the volume in m 3. It is important to emphasize that there can t be a truly universal correlation of volume and cell count, due to the fact that complexities of the flows in buildings can greatly differ and therefore influence the number of cells required. Figure 3-7 Guideline for cell count in building simulations (Nielsen, 2007) The volume of the atrium considered is 1345 m 3, which according to Figure 3-7, corresponds to roughly 686,000 cells. This cell count was used to run an initial simulation to investigate shear stress at walls. As explained in section 2.5.2, the required y+ values for standard wall functions are between 30-300. To obtain the required y+ values, the wall adjacent cells had to be a very small. To avoid excessive computational effort a mesh boundary layer was adopted to blend the fine mesh near the walls to the coarser mesh found in the core region. 30

Figure 3-8 demonstrates the use of mesh boundary layers for a corner and details of all the mesh boundary layers attached to each wall are given in Table 3-3. Figure 3-8 Boundary layers at the corner of the west wall and the facade While developing the mesh boundary layers, the grid size change and aspect ratio values were checked to ensure that they fell within the guidelines set in the GAMBIT documentation (GAMBIT, 2006). Table 3-3 Specifications of the boundary layers for different surfaces Back West Glass East First Row 2 cm 2 cm 7 cm 2 cm Growth Factor 1.2 1.2 1.4 1.2 Rows 12 12 2 12 31

The use of these mesh boundary layers allowed accurate prediction of flow near the walls. To correctly capture the convective heat transfer from the glass, special care was given to obtain values closer to y + =30 for the facade as seen in Figure 3-9. Figure 3-9 Contour plot of y + for the facade 3.3 Mesh Independence Testing Mesh independence testing was undertaken to ensure that the results derived were independent of the number of mesh points used. Three different grids were adopted for the present mesh independence study. Table 3-4 lists the cell count for each of the three grids used. 32

Table 3-4 Mesh densities for the different grids Cell Count Grid 1 680,616 Grid 2 773,318 Grid 3 1,008,504 The temperature along a vertical line at the middle of the facade and along a vertical centerline in the atrium were analyzed to evaluate the effect of the grid used, these locations are shown in Figure 3-10. The variation of air velocity along a horizontal line at a height of 1.1 m in the atrium was also analyzed. Figure 3-10 Location of lines used to investigate temperature and velocity variation 33

It can be seen in Figure 3-11 that all grids give very similar results for air temperatures. Table 3-5 shows the percentage differences between the grids for regions of greatest difference in temperature. Figure 3-11 Vertical air temperature along the center of atrium Table 3-5 age difference of air temperature between grids 4 < y < 8 (m) Grid 1-2 0.877 % Grid 2-3 0.119 % Figure 3-12 shows the variation of temperature along the vertical middle line along the facade. The coarsest grid, Grid 1, with 680616 cells, at heights between 6 to 9 m, gives 34

results that differ from those given by Grids 2 and 3. The other grids however give results that are in relatively close agreement. The 3 main regions of difference and their corresponding percentage difference is given in Table 3-6. Figure 3-12 Glass temperature along center of facade Table 3-6 age difference of glass temperature between grids 6 < y < 9 (m) 9 < y <11 (m) 6 < y < 11 (m) Grid 1-2 3.09 % 1.83 % 0.9 % Grid 2-3 0.23 % 0.52 % 0.28 % The velocity profiles along the horizontal line at a height of 1.1 m are shown in Figure 3-13. The difference between results given using the coarsest grid 1 and the results given using the other two grids is evident in the region 1 m to 7 m as can be seen from the results given in Table 3-7. 35

Figure 3-13 Velocity magnitude along horizontal line at the center of atrium Table 3-7 age difference of velocity magnitude between grids 1 < x < 7 (m) Grid 1-2 10.87 % Grid 2-3 2.93 % Considering both the temperature and velocity, the percentage change from grid to grid of temperatures and velocities decreased as more dense grids were used. Table 3-8 shows the average temperatures and velocities in the specified regions. 36

Table 3-8 Average temperature and velocities in certain regions Average Air Temperature in region 4m - 8m ( o C) Average Glass Temperature in region 6m - 11m ( o C) Average Air Velocity in region 6m - 11m (m/s) Grid 1 24.35 39.80 0.13 Grid 2 24.13 40.16 0.14 Grid 3 24.16 40.27 0.15 It was determined after investigation of temperature and velocity variations that Grid 2 with 773,318 cells was a good balance between the required computational resources and the ability to resolve the details of the flow to the required degree. Figure 3-14 shows the grid that was used to generate the results in this study. Figure 3-14 Schematic of the grid chosen for the present study 37

3.4 Boundary Conditions The appropriate boundary conditions were determined using the data from the Concordia experiments and the weather information obtained from Environment Canada (2008). The wall surfaces interior to the building was assumed to be adiabatic. Facade The main feature of the atrium, the facade, was known to be argon filled double glazing (6mm glass/12mm air space/6mm glass) with a 0.1 low-e coating on the outer surface of the interior pane. The exact values of the optical properties of the glazing was not available however from the information provided the optical properties were set to a solar transmittance of 36% and an absorptivity of 17.5%. The modeling of the glazing was simplified as a single glazing. To capture the thermal effects of the air space between the double glazing, the corresponding h value for the air space between the glazing was assumed to be 2.7 W/m 2 K (ASHRAE, 2009). The thermal conductivity of the 2 panes were also included using a value of 0.917 W/mK. This resulted in an effective thermal conductivity of 0.0626 W/mK for the glazing with a total overall thickness 24 mm. The heat transfer on the outside of the glazing due to the convection from the wind was accounted. The outside air temperature, wind direction and the magnitude were determined from Environment Canada (2008). The Figure 3-15 is a representation of the direction of the wind at 16:00 on August 1, 2007. 38

Figure 3-15 The orientation of the Concordia building The surface of the facade shown in red is at angle of 35 o west of south. It can be seen that the wind is coming at an angle of 5 o to the glazing, making the facade a windward surface. There are many different correlations in the literature to determine the external heat transfer coefficient for buildings, some examples being the works of Sharples (1984) and Emmel (2007). The paper by Palyvos (2008) summarizes and outlines the different correlations found in literature. On the basis of thirty available linear correlations, he comes up with the following average correlation for windward surfaces: h 7.4 4 (3.1) w V w The corresponding wind speed velocity of 6.1m/s was used with this equation to determine the external heat transfer coefficient, this being 31.84 W/m 2 K. The radiation exchange between the facade and the sky was also taken into account. The emissivity of the sky for the daytime was calculated to be 0.82 using equation 39

0.727 0.0060 sky T DP. The calculated sky emissivity along with an ambient temperature of 28.6 o C was used in equation T sky 4 4 [ ] 1/ skytout which resulted in an effective sky temperature of 14.21 o C (Mills, 1999). Supply and Return Particular attention was given to the boundary conditions at the inlet vent as these can have a significant effect on the accuracy of the predicted temperature and flow patterns within the atrium. After investigation of the supply vent flow, it was found that the flow was exiting parallel to the floor. The inlet was therefore modeled using an opening with a constant velocity. The net area of the supply was chosen to account for the presence of the vanes across the vent. Experimental data was available for the velocity and temperature values of the air entering the atrium from this vent. The velocity was set to 4.5 m/s while the temperature was 15 o C. The calculated Reynolds number was 146633 based on the conditions at the supply, indicating the flow to be turbulent. The turbulence parameters such as the hydraulic diameter and the turbulence intensity were specified at the inlet. Equations 3.2 and 3.3 were used to calculate the hydraulic diameter and the turbulence intensity. Hydraulic Diameter = 2 LW L W (3.2) Turbulence Intensity = 0.16 Re -1/8 (3.3) The return vent near the top of the east wall was modeled as an outflow, the mass flow rate out of this vent equaled the mass flow rate into the atrium from the inlet vent. 40

3.5 Solar Load Model Table 3-9 outlines the information regarding the solar loading at 16:00 on August 1, 2007. The sunshine factor relates to the cloudiness of the day, it was mostly clear therefore a factor of 1 was used indicating a day with little or no cloud cover. The direct, diffuse irradiation values were also incorporated into the model. Table 3-9 Solar load parameters used in the study Sun Direction Vector x y z -0.60 0.69-0.40 Sunshine Fraction 1 Direct Normal Solar Irradiation (at Earth's surface) [W/m 2 ] 820 Diffuse Solar Irradiation - vertical surface [W/m 2 ] 104 Diffuse Solar Irradiation - horizontal surface [W/m 2 ] 104 41

Chapter 4 Results and Discussion 4.1 Introduction This chapter will present a comparison of the numerical results obtained and the experimental data gathered by Mouriki (2009). The main focus will be to compare air and glass temperatures at various locations. Contour plots based on the numerical results will also be presented. In addition to the comparison of numerical and experimental results, the effects of changes in the model parameters were studied. A thermal comfort study of draught and vertical temperature difference will also be presented in this section. 4.2 Validation Case The validation case, also referred as the Main Case, involved using all the boundary conditions that were discussed in section 3.2. The numerical glass temperatures are shown in Figure 4-1. 42

Figure 4-1 Glass temperature contours on the facade for validation case The presence of the hotter glass region on the left hand side is mainly due to the geometry of the atrium. This region is in close proximity to a wall that partially traps the hot air. Figure 4-2 Air temperature contours at various heights for validation case 43

Figure 4-2 shows contour plots of the numerically predicted temperatures at heights of 2, 6.165 and 10.25 meters above the floor. Visual examination of these results indicates that there are small temperature variations over individual planes particularly at the back of the atrium, away from the supply. It will be seen that there is an accumulation of cold air near the west wall resulting from the impingement of the cool supply air on this wall. Tables 4-1 and 4-2 give a comparison between the numerical and experimental results at each location where experimental data was available. The corresponding difference in temperature and the percentage differences are also presented. Table 4-1 Glass temperature comparison of numerical and experimental data for Comparison between validation experimental case values and Case 4 Comparison between experimental values and Case 4 GLASS HIGH Coordinates Experimental Temperature, Numerical T, (ºC) ΔT, (ºC) Difference GLASS HIGH Coordinates ΔT, (ºC) FL_G_T 0,10.25,7.26 Experimental 34.20 Numerical 37.55 3.35 Difference 9.8 % FM_G_TH FL_G_T 0,10.25,7.26 0,10.9,4.22 34.90 34.20 36.99 37.55 2.09 3.35 6.0 9.8 % FM_G_TH FM_G_TL 0,9.35,4.22 0,10.9,4.22 33.60 34.90 36.81 36.99 3.21 2.09 9.6 6.0 % FM_G_TL FR_G_T 0,10.25,1.24 0,9.35,4.22 32.80 33.60 37.48 36.81 4.68 3.21 14.3 9.6 % FR_G_T 0,10.25,1.24 33.88 32.80 37.21 37.48 3.34 4.68 14.3 9.8 % 33.88 37.21 3.34 9.8 % GLASS MID Coordinates Experimental Temperature, Numerical T, (ºC) ΔT, (ºC) Difference GLASS MID Coordinates ΔT, (ºC) FL_G_M 0,6.165,7.26 Experimental 31.70 Numerical 37.47 5.77 Difference 18.2 % FM_G_MH FL_G_M 0,6.165,7.26 0,6.9,4.22 34.10 31.70 35.73 37.47 1.63 5.77 18.2 4.8 % FM_G_MH FM_G_ML 0,5.2,4.22 0,6.9,4.22 31.70 34.10 35.06 35.73 3.36 1.63 10.6 4.8 % FM_G_ML FR_G_M 0,6.165,1.24 0,5.2,4.22 32.50 31.70 32.52 35.06 0.02 3.36 10.6 0.1 % FR_G_M 0,6.165,1.24 32.50 35.20 32.52 2.70 0.02 8.3 0.1 % 32.50 35.20 2.70 8.3 % GLASS LOW Coordinates ΔT, (ºC) Experimental Temperature, Numerical T, (ºC) Difference GLASS LOW Coordinates ΔT, (ºC) FL_G_B 0,2.1,7.26 Experimental 30.90 Numerical 36.58 5.68 Difference 18.4 % FM_G_BH FL_G_B 0,3.05,4.22 0,2.1,7.26 30.10 30.90 35.20 36.58 5.10 5.68 17.0 18.4 % FM_G_BH FM_G_BL 0,1.35,4.22 0,3.05,4.22 29.50 30.10 34.73 35.20 5.23 5.10 17.7 17.0 % FM_G_BL FR_G_B 0,1.35,4.22 0,2.1,1.24 29.80 29.50 30.38 34.73 0.58 5.23 17.7 1.9 % FR_G_B 0,2.1,1.24 30.08 29.80 34.22 30.38 4.15 0.58 13.8 1.9 % 30.08 34.22 4.15 13.8 % 44

Table 4-2 Air temperature comparison of numerical and experimental data for Comparison between validation experimental case values and Case 4 AIR HIGH Coordinates ΔT, (ºC) Experimental Numerical Difference FL_R_T 0.24,10.25,7.26 26.80 26.49-0.31-1.1 % FM_R_TH 0.24,10.9,4.22 28.20 26.56-1.64-5.8 % FM_R_TL 0.24,9.35,4.22 27.20 25.70-1.50-5.5 % FR_R_T 0.24,10.25,1.24 26.60 25.91-0.69-2.6 % EW_16 5.96,10.25,7 26.20 25.43-0.77-3.0 % WW_16 5.78,10.25,1.05 26.10 25.90-0.20-0.8 % AA_16 8.81,10.25,4.44 26.30 26.11-0.19-0.7 % 26.77 26.01-0.76-2.8 % AIR MID Coordinates ΔT, (ºC) Experimental Numerical Difference FL_R_M 0.24,6.165,7.26 25.90 25.40-0.50-1.9 % FM_R_MH 0.24,6.9,4.22 25.60 24.86-0.74-2.9 % FM_R_ML 0.24,5.2,4.22 24.40 23.93-0.47-1.9 % FR_R_M 0.24,6.165,1.24 26.30 22.38-3.92-14.9 % EW_15 5.96,6.165,7 24.50 24.14-0.36-1.5 % WW_15 5.78,6.165,1.05 25.10 24.02-1.08-4.3 % AA_15 8.81,6.165,4.44 24.60 24.05-0.55-2.2 % 25.20 24.11-1.09-4.3 % AIR LOW Coordinates ΔT, (ºC) Experimental Numerical Difference FL_R_B 0.24,2.1,7.26 23.90 24.00 0.10 0.4 % FM_R_BH 0.24,3.05,4.22 23.90 23.42-0.48-2.0 % FM_R_BL 0.24,1.35,4.22 23.40 22.57-0.83-3.6 % FR_R_B 0.24,2.1,1.24 23.00 21.77-1.23-5.4 % EW_14 5.96,2.1,7 24.00 23.10-0.90-3.8 % WW_14 5.78,2.1,1.05 22.30 23.67 1.37 6.2 % AA_14 8.81,2.1,4.44 23.00 23.49 0.49 2.1 % 23.36 23.14-0.21-0.9 % Table 4-3 presents a summary of the numerical and experimental temperature differences averaged over the various points. Table 4-3 Overall percent differences in air and glass temperatures between numerical and experimental data for validation case 45

In comparing the experimental and numerical results it should be stressed that the thermal properties, in particular the optical properties of the glass were not accurately known which may account for some of the differences between the sets of results. 4.3 Effect of Internal Radiation Exchange It is important to evaluate the significance of modeling internal longwave radiation since due to the complexity of the radiation model there is a substantial increase in required simulation runtime. This case examines the results obtained when the internal longwave radiation model has been turned off. Contours of facade temperature when internal radiation is ignored are shown in Figure 4-3. Figure 4-3 Glass temperature contours on the facade without internal radiation exchange It is apparent that the predicted glass is hotter when internal radiation is not accounted, this being particularly true in the upper region of the facade. Certain hot spots appear in the upper right region where low flow velocities exist. Due to the movement of air that 46

Temperature (ºC) cools the left side of the facade, there exists a region where temperatures range from 34 o C and 38 o C. In Figure 4-4, the temperatures at different heights along the center-line of the facade are shown. It will be noted that there are significant differences between the two sets of numerical data for heights above 5 m. 41 39 37 35 33 31 29 27 25 0 2 4 6 8 10 12 Height (m) Experimental Radiation Model OFF Radiation Model ON Figure 4-4 Glass temperatures along the middle of the facade for cases investigating internal radiation Figure 4-5 displays the contours of air temperature. Figure 4-6 shows only slight variations in the air temperature between the cases investigating the effect of internal radiation exchange. 47

Temperature (ºC) Figure 4-5 Air temperature contours at various heights without internal radiation exchange 30 29 28 27 26 25 24 23 22 21 20 0 2 4 6 8 10 12 Height (m) Experimental Radiation Model OFF Radiation Model ON Figure 4-6 Air temperatures along center vertical line 0.24 m away from the facade for cases investigating radiation model A comparison of numerical and experimental glass and air temperatures for the case when radiative exchange between the internal surfaces has been ignored are shown in Table 4-4 48

and 4-5. It will be seen from these results that the percentage difference compared to experimental, ranges between 9.8% to 17 % for glass temperatures, while for air temperatures all fall below 5.7 %. Table 4-4 Glass temperature comparison of numerical and experimental data for the Comparison case between without internal experimental radiation values exchange and and Case Comparison between experimental values and and Case 3 GLASS HIGH Coordinates ΔT, (ºC) GLASS HIGH Coordinates Experimental Numerical ΔT, (ºC) Difference FL_G_T 0,10.25,7.26 Experimental 34.20 Numerical Difference 38.56 4.36 12.7 FL_G_T 0,10.25,7.26 34.20 38.56 4.36 12.7 % FM_G_TH 0,10.9,4.22 34.90 39.34 4.44 12.7 FM_G_TH 0,10.9,4.22 34.90 39.34 4.44 12.7 % FM_G_TL 0,9.35,4.22 33.60 39.45 5.85 17.4 FM_G_TL 0,9.35,4.22 33.60 39.45 5.85 17.4 % FR_G_T 0,10.25,1.24 32.80 41.24 8.44 25.7 FR_G_T 0,10.25,1.24 32.80 41.24 8.44 25.7 % 33.88 39.65 5.77 17.0 33.88 39.65 5.77 17.0 % GLASS MID Coordinates ΔT, (ºC) GLASS MID Coordinates Experimental Numerical ΔT, (ºC) Difference Experimental Numerical Difference FL_G_M 0,6.165,7.26 31.70 40.82 9.12 28.8 FL_G_M 0,6.165,7.26 31.70 40.82 9.12 28.8 % FM_G_MH 0,6.9,4.22 34.10 41.10 7.00 20.5 FM_G_MH 0,6.9,4.22 34.10 41.10 7.00 20.5 % FM_G_ML 0,5.2,4.22 31.70 35.68 3.98 12.6 FM_G_ML 0,5.2,4.22 31.70 35.68 3.98 12.6 % FR_G_M 0,6.165,1.24 32.50 32.15-0.35-1.1 FR_G_M 0,6.165,1.24 32.50 32.15-0.35-1.1 % 32.50 37.44 4.94 15.2 32.50 37.44 4.94 15.2 % GLASS LOW Coordinates ΔT, (ºC) GLASS LOW Coordinates Experimental Numerical ΔT, (ºC) Difference Experimental Numerical Difference FL_G_B 0,2.1,7.26 30.90 35.31 4.41 14.3 FL_G_B 0,2.1,7.26 30.90 35.31 4.41 14.3 % FM_G_BH 0,3.05,4.22 30.10 33.93 3.83 12.7 FM_G_BH 0,3.05,4.22 30.10 33.93 3.83 12.7 % FM_G_BL 0,1.35,4.22 29.50 33.72 4.22 14.3 FM_G_BL 0,1.35,4.22 29.50 33.72 4.22 14.3 % FR_G_B 0,2.1,1.24 29.80 29.18-0.62-2.1 FR_G_B 0,2.1,1.24 29.80 29.18-0.62-2.1 % 30.08 33.04 2.96 9.8 30.08 33.04 2.96 9.8 % 49

Table 4-5 Air temperature comparison of numerical and experimental data for the case without radiation Comparison between experimental values and and Case 3 Comparison between experimental values and and Case 3 AIR HIGH Coordinates ΔT, (ºC) Experimental Numerical Difference AIR FL_R_T HIGH 0.24,10.25,7.26 Coordinates 26.80 26.25 ΔT, -0.55 (ºC) -2.0 % Experimental Numerical Difference FM_R_TH 0.24,10.9,4.22 28.20 26.75-1.45-5.1 FL_R_T 0.24,10.25,7.26 26.80 26.25-0.55-2.0 % FM_R_TL 0.24,9.35,4.22 27.20 25.97-1.23-4.5 % FM_R_TH 0.24,10.9,4.22 28.20 26.75-1.45-5.1 % FR_R_T 0.24,10.25,1.24 26.60 26.31-0.29-1.1 FM_R_TL 0.24,9.35,4.22 27.20 25.97-1.23-4.5 % EW_16 5.96,10.25,7 26.20 25.90-0.30-1.1 FR_R_T 0.24,10.25,1.24 26.60 26.31-0.29-1.1 % WW_16 5.78,10.25,1.05 26.10 26.23 0.13 0.5 EW_16 5.96,10.25,7 26.20 25.90-0.30-1.1 % AA_16 8.81,10.25,4.44 26.30 26.18-0.12-0.5 WW_16 5.78,10.25,1.05 26.10 26.23 0.13 0.5 % 26.77 26.23-0.54-2.0 AA_16 8.81,10.25,4.44 26.30 26.18-0.12-0.5 % 26.77 26.23-0.54-2.0 % AIR MID Coordinates ΔT, (ºC) Experimental Temperature, Numerical T, (ºC) Difference AIR FL_R_M FL_R_M MID 0.24,6.165,7.26 0.24,6.165,7.26 Coordinates 25.90 25.90 25.25 ΔT, 25.25-0.65 (ºC) Experimental Numerical -0.65 Difference -2.5-2.5 % FM_R_MH FM_R_MH FL_R_M 0.24,6.165,7.26 0.24,6.9,4.22 0.24,6.9,4.22 25.90 25.60 25.60 25.25 24.89 24.89-0.65-0.71-0.71-2.5-2.8-2.8% FM_R_ML 0.24,5.2,4.22 24.40 23.58-0.82-3.4 FM_R_ML FM_R_MH 0.24,5.2,4.22 0.24,6.9,4.22 25.60 24.40 24.89 23.58-0.71-0.82-2.8-3.4% FM_R_ML FR_R_M 0.24,6.165,1.24 26.30 21.84-4.46-16.9 FR_R_M 0.24,6.165,1.24 0.24,5.2,4.22 24.40 26.30 23.58 21.84-0.82-4.46-16.9-3.4 % FR_R_M EW_15 5.96,6.165,7 24.50 24.10-0.40-1.6 EW_15 0.24,6.165,1.24 5.96,6.165,7 26.30 24.50 21.84 24.10-4.46-0.40-16.9-1.6% WW_15 5.78,6.165,1.05 25.10 23.01-2.10-8.3 WW_15 EW_15 5.78,6.165,1.05 5.96,6.165,7 24.50 25.10 24.10 23.01-0.40-2.10-1.6-8.3 % WW_15 AA_15 5.78,6.165,1.05 8.81,6.165,4.44 25.10 24.60 23.01 23.76-2.10-0.84-8.3-3.4% AA_15 8.81,6.165,4.44 24.60 23.76-0.84-3.4 AA_15 8.81,6.165,4.44 24.60 25.20 23.76 23.78-0.84-1.42-3.4-5.7% 25.20 23.78-1.42-5.7 % 25.20 23.78-1.42-5.7 % AIR LOW Coordinates ΔT, (ºC) AIR LOW Coordinates Experimental Temperature, Numerical T, (ºC) ΔT, (ºC) Difference AIR LOW Coordinates FL_R_B 0.24,2.1,7.26 Experimental 23.90 Numerical ΔT, (ºC) Experimental Numerical 23.37-0.53 Difference Difference -2.2 % FM_R_BH FL_R_B 0.24,3.05,4.22 0.24,2.1,7.26 23.90 23.37 22.75-0.53-1.15-0.53-2.2-4.8-2.2% FM_R_BH FM_R_BL 0.24,3.05,4.22 0.24,1.35,4.22 23.90 23.40 22.75 22.35-1.15-1.05-4.8-4.5-4.8% FM_R_BL FR_R_B 0.24,1.35,4.22 0.24,2.1,1.24 23.40 23.00 22.35 21.59-1.05-1.41-4.5-6.1-4.5% FR_R_B EW_14 0.24,2.1,1.24 5.96,2.1,7 23.00 24.00 21.59 22.65-1.41-1.35-6.1-5.6 % WW_14 EW_14 5.78,2.1,1.05 5.96,2.1,7 24.00 22.30 22.65 23.19-1.35 0.89-5.6 4.0 % WW_14 AA_14 5.78,2.1,1.05 8.81,2.1,4.44 22.30 23.00 23.19 22.67 0.89-0.33-1.5 4.0 % AA_14 8.81,2.1,4.44 23.00 23.36 22.67 22.65-0.33-0.71-1.5-3.0 % 23.36 22.65-0.71-3.0 % These results can be compared with the case where internal radiation effects were considered which were given in Tables 4-1 and 4-2. Considering this mode of heat transfer between the internal walls is therefore important, increasing the accuracy of the numerical simulation. 50

4.4 Effect of Outside Temperature This comparison aims to establish the importance of the outside air temperature (T out ) on the numerical results. The values obtained from weather data are for a specific location, and may not be the actual values existing during the testing. It is therefore important to evaluate different outside air temperatures to determine if this could account for some of the differences between the numerical and the experimental results. Figures 4-7, 4-8 and 4-9 show the temperatures on the facade with different outside temperatures. Figure 4-7 Glass temperature contours on the facade when T out = 23.6 o C 51

Figure 4-8 Glass temperature contours on the facade when T out = 28.6 o C Figure 4-9 Glass temperature contours on the facade when T out = 33.6 o C 52

Temperature (ºC) 40 39 38 37 36 35 34 33 32 31 30 0 2 4 6 8 10 12 Height (m) To = 23.6ºC To = 28.6ºC To = 33.6ºC Figure 4-10 Glass temperatures along the middle of the facade for cases with different outside temperatures It will be observed that when the outside temperature is increased, the glass temperatures increase and decrease when the temperature is lowered as expected. Figure 4-10 shows the variation of glass temperatures for the two numerical models. It will be seen that the relationship between outside temperature and glass temperature is not linear; the temperature of the glass at each point along the middle center line increased roughly by 1 o C for the higher outside temperature case (T o = 33.6 o C) whereas the temperatures dropped by roughly 1.7 o C in the lower outside temperature case (T o = 23.6 o C ). Table 4-6 and Table 4-7 give the individual temperature differences and their respective percent difference. 53

Table 4-6 Glass temperature comparison of numerical data between Comparison between Main Case Main Case - T out = 28.6 o (T o =28.6ºC) and Lower Case (T C and Lower Case - T out = 23.6 o =23.6ºC) C Comparison between Main Case (T o =28.6ºC) and Lower Case (T o =23.6ºC) GLASS Comparison HIGH between Coordinates Main Case (T o =28.6ºC) and Lower ΔT, Case (ºC) (T o =23.6ºC) Main Temperature, Case Lower T, (ºC) Case Difference GLASS FL_G_T HIGH Coordinates 0,10.25,7.26 37.55 35.91 ΔT, -1.64 (ºC) -4.4 % Main Case Lower Case Difference FM_G_TH 0,10.9,4.22 36.99 Temperature, T, 35.22 (ºC) -1.77-4.8 GLASS FL_G_T HIGH Coordinates 0,10.25,7.26 37.55 35.91 ΔT, -1.64 (ºC) -4.4 % FM_G_TL 0,9.35,4.22 Main 36.81 Case Lower 34.96 Case -1.86 Difference -5.0 FM_G_TH 0,10.9,4.22 36.99 35.22-1.77-4.8 FR_G_T FL_G_T 0,10.25,1.24 0,10.25,7.26 37.48 37.55 35.53 35.91-1.96-1.64-5.2-4.4 % FM_G_TL 0,9.35,4.22 36.81 34.96-1.86-5.0 FM_G_TH 0,10.9,4.22 37.21 36.99 35.40 35.22-1.81-1.77-4.9-4.8 % FR_G_T 0,10.25,1.24 37.48 35.53-1.96-5.2 FM_G_TL 0,9.35,4.22 36.81 34.96-1.86-5.0 % 37.21 35.40-1.81-4.9 FR_G_T 0,10.25,1.24 37.48 Temperature, T, 35.53 (ºC) -1.96-5.2 % GLASS MID Coordinates ΔT, (ºC) Main 37.21 Case Lower 35.40 Case -1.81 Difference -4.9 % GLASS FL_G_M MID Coordinates 0,6.165,7.26 Main 37.47 Case Lower 35.72 ΔT, Case -1.75 (ºC) Difference -4.7 % FM_G_MH 0,6.9,4.22 35.73 Temperature, T, 33.74 (ºC) -1.99 GLASS -5.6 FL_G_M MID Coordinates 0,6.165,7.26 37.47 35.72 ΔT, -1.75 (ºC) -4.7 % FM_G_ML 0,5.2,4.22 Main 35.06 Case Lower 33.15 Case -1.91 Difference -5.5 FM_G_MH 0,6.9,4.22 35.73 33.74-1.99-5.6 FR_G_M FL_G_M 0,6.165,1.24 0,6.165,7.26 32.52 37.47 31.10 35.72-1.42-1.75-4.4-4.7 % FM_G_ML 0,5.2,4.22 35.06 33.15-1.91-5.5 FM_G_MH 0,6.9,4.22 FR_G_M 0,6.165,1.24 35.20 35.73 32.52 33.43 33.74 31.10-1.77-1.99-1.42-5.0-5.6-4.4 % FM_G_ML 0,5.2,4.22 35.06 33.15-1.91-5.5 % 35.20 33.43-1.77-5.0 FR_G_M 0,6.165,1.24 32.52 Temperature, T, 31.10 (ºC) -1.42-4.4 % GLASS LOW Coordinates ΔT, (ºC) Main 35.20 Temperature, Case Lower 33.43 T, (ºC) Case -1.77 Difference -5.0 % GLASS FL_G_B LOW Coordinates 0,2.1,7.26 Main 36.58 Case Lower 35.20 ΔT, Case -1.38 (ºC) Difference -3.8 % FM_G_BH FL_G_B 0,3.05,4.22 0,2.1,7.26 35.20 Temperature, T, 36.58 33.63 (ºC) 35.20-1.57 GLASS LOW Coordinates ΔT, -1.38 (ºC) -4.5-3.8 % FM_G_BH FM_G_BL 0,1.35,4.22 Main 0,3.05,4.22 34.73 Case Lower 35.20 33.13 Case 33.63-1.60 Difference -1.57-4.6-4.5 FM_G_BL FR_G_B FL_G_B 0,1.35,4.22 0,2.1,1.24 0,2.1,7.26 30.38 36.58 34.73 29.26 35.20 33.13-1.12-1.38-1.60-3.7-3.8-4.6 % FM_G_BH FR_G_B 0,3.05,4.22 0,2.1,1.24 34.22 35.20 30.38 32.81 33.63 29.26-1.42-1.57-1.12-4.1-4.5-3.7 % FM_G_BL 0,1.35,4.22 34.73 33.13-1.60-4.6 % 34.22 32.81-1.42-4.1 FR_G_B 0,2.1,1.24 30.38 29.26-1.12-3.7 % 34.22 32.81-1.42-4.1 % Table 4-7 Glass temperature comparison of numerical data Comparison between Main Case (T between Main Case - T out = 28.6 o =28.6ºC) and Higher Case (T C and Higher Case - T out = 33.6 o =33.6ºC) o C Comparison between Main Case (T o =28.6ºC) and Higher Case (T o =33.6ºC) GLASS HIGH Coordinates ΔT, (ºC) Main Temperature, Case Higher T, (ºC) Case Difference GLASS FL_G_T HIGH Coordinates 0,10.25,7.26 37.55 38.59 ΔT, 1.03 (ºC) Main Case Higher Case Difference 2.7 % FM_G_TH FL_G_T 0,10.25,7.26 0,10.9,4.22 36.99 37.55 38.12 38.59 1.12 1.03 3.0 2.7 % FM_G_TH FM_G_TL 0,9.35,4.22 0,10.9,4.22 36.81 36.99 37.85 38.12 1.03 1.12 2.8 3.0 % FM_G_TL FR_G_T 0,10.25,1.24 0,9.35,4.22 37.48 36.81 38.43 37.85 0.95 1.03 2.5 2.8 % FR_G_T 0,10.25,1.24 37.21 37.48 38.24 38.43 1.03 0.95 2.8 2.5 % 37.21 38.24 1.03 2.8 % GLASS MID Coordinates ΔT, (ºC) Main Temperature, Case Higher T, (ºC) Case Difference GLASS FL_G_M MID Coordinates 0,6.165,7.26 37.47 38.39 ΔT, 0.92 (ºC) Main Case Higher Case Difference 2.4 % FM_G_MH FL_G_M 0,6.165,7.26 0,6.9,4.22 35.73 37.47 36.84 38.39 1.12 0.92 3.1 2.4 % FM_G_MH FM_G_ML 0,5.2,4.22 0,6.9,4.22 35.06 35.73 36.12 36.84 1.06 1.12 3.0 3.1 % FM_G_ML FR_G_M 0,6.165,1.24 0,5.2,4.22 32.52 35.06 33.30 36.12 0.77 1.06 2.4 3.0 % FR_G_M 0,6.165,1.24 35.20 32.52 36.16 33.30 0.97 0.77 2.7 2.4 % 35.20 36.16 0.97 2.7 % GLASS LOW Coordinates ΔT, (ºC) Main Temperature, Case Higher T, (ºC) Case Difference GLASS FL_G_B LOW Coordinates 0,2.1,7.26 36.58 37.70 ΔT, Main Case Higher Case 1.12 (ºC) Difference 3.1 % FM_G_BH FL_G_B 0,3.05,4.22 0,2.1,7.26 35.20 36.58 36.19 37.70 0.98 1.12 2.8 3.1 % FM_G_BH FM_G_BL 0,1.35,4.22 0,3.05,4.22 34.73 35.20 35.68 36.19 0.95 0.98 2.7 2.8 % FM_G_BL FR_G_B 0,1.35,4.22 0,2.1,1.24 30.38 34.73 31.19 35.68 0.81 0.95 2.7 Table 4-7 (Continued) % FR_G_B 0,2.1,1.24 34.22 30.38 35.19 31.19 0.96 0.81 2.8 2.7 % 34.22 35.19 0.96 2.8 % 54

Main Case Higher Case Difference FL_G_M 0,6.165,7.26 37.47 38.39 0.92 2.4 % FM_G_MH 0,6.9,4.22 35.73 36.84 1.12 3.1 % FM_G_ML 0,5.2,4.22 35.06 36.12 1.06 3.0 % FR_G_M 0,6.165,1.24 32.52 33.30 0.77 2.4 % 35.20 36.16 0.97 2.7 % GLASS LOW Coordinates ΔT, (ºC) Main Case Higher Case Difference FL_G_B 0,2.1,7.26 36.58 37.70 1.12 3.1 % FM_G_BH 0,3.05,4.22 35.20 36.19 0.98 2.8 % FM_G_BL 0,1.35,4.22 34.73 35.68 0.95 2.7 % FR_G_B 0,2.1,1.24 30.38 31.19 0.81 2.7 % 34.22 35.19 0.96 2.8 % The air temperature contours for different outside temperatures are shown in Figure 4-11, 4-12 and 4-13. Figure 4-11 Air temperature contours at various heights when T out = 23.6 o C 55

Figure 4-12 Air temperature contours at various heights when T out = 28.6 o C Figure 4-13 Air temperature contours at various heights when T out = 33.6 o C 56

Temperature (ºC) Figure 4-14 shows the variation of the air temperature along a vertical line located 0.24 m away from the facade for the three outside air temperatures considered. 28 27 26 25 24 23 22 0 2 4 6 8 10 12 Height (m) To = 23.6ºC To = 28.6ºC To = 33.6ºC Figure 4-14 Air temperatures along center vertical line 0.24m away from the facade for cases with different outside temperature A similar trend can be seen for air temperatures, i.e., a higher outside temperature leads to higher atrium air temperatures. The air temperatures vary to a lesser degree then the facade temperatures as shown in Tables 4-8 and 4-9. 57

Table 4-8 Air temperature comparison of numerical data Comparison between Main between Case Main - T out Case = 28.6 (T C and Lower Case - T out = 23.6 o o =28.6ºC) and Lower Case (T o =23.6ºC) C Temperature, T, T, (ºC) (ºC) AIR HIGH Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_R_T 0.24,10.25,7.26 26.49 25.95-0.55-2.1 % FM_R_TH 0.24,10.9,4.22 26.56 26.16-0.40-1.5 % FM_R_TL 0.24,9.35,4.22 25.70 25.40-0.30-1.1 % FR_R_T 0.24,10.25,1.24 25.91 25.45-0.46-1.8 % EW_16 5.96,10.25,7 25.43 24.98-0.44-1.7 % WW_16 5.78,10.25,1.05 25.90 25.51-0.40-1.5 % AA_16 8.81,10.25,4.44 26.11 25.50-0.61-2.3 % 26.01 25.56-0.45-1.7 % AIR MID Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_R_M 0.24,6.165,7.26 25.40 24.89-0.51-2.0 % FM_R_MH 0.24,6.9,4.22 24.86 24.29-0.57-2.3 % FM_R_ML 0.24,5.2,4.22 23.93 23.50-0.43-1.8 % FR_R_M 0.24,6.165,1.24 22.38 22.26-0.12-0.5 % EW_15 5.96,6.165,7 24.14 23.99-0.15-0.6 % WW_15 5.78,6.165,1.05 24.02 23.71-0.31-1.3 % AA_15 8.81,6.165,4.44 24.05 23.67-0.38-1.6 % 24.11 23.76-0.35-1.5 % AIR LOW Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_R_B 0.24,2.1,7.26 24.00 23.70-0.30-1.3 % FM_R_BH 0.24,3.05,4.22 23.42 23.28-0.14-0.6 % FM_R_BL 0.24,1.35,4.22 22.57 22.50-0.07-0.3 % FR_R_B 0.24,2.1,1.24 21.77 21.82 0.05 0.2 % EW_14 5.96,2.1,7 23.10 22.95-0.15-0.6 % WW_14 5.78,2.1,1.05 23.67 23.36-0.31-1.3 % AA_14 8.81,2.1,4.44 23.49 23.01-0.48-2.0 % 23.14 22.95-0.20-0.9 % 58

Table 4-9 Air temperature comparison of numerical data Comparison between Main Case (T o between Main Case - T out = 28.6 =28.6ºC) and Higher Case (T o =33.6ºC) Comparison between Main Case (T C and Higher Case - T out = 33.6 o C o =28.6ºC) and Higher Case (T o =33.6ºC) AIR HIGH Coordinates ΔT, (ºC) Main Temperature, Case Higher T, (ºC) Case Difference AIR FL_R_T HIGH 0.24,10.25,7.26 Coordinates 26.49 26.72 ΔT, 0.23 (ºC) Main Case Higher Case Difference 0.9 % FM_R_TH FL_R_T 0.24,10.25,7.26 0.24,10.9,4.22 26.56 26.49 26.80 26.72 0.24 0.23 0.9 % FM_R_TH FM_R_TL 0.24,9.35,4.22 0.24,10.9,4.22 25.70 26.56 25.88 26.80 0.18 0.24 0.7 0.9 % FM_R_TL FR_R_T 0.24,10.25,1.24 0.24,9.35,4.22 25.91 25.70 26.23 25.88 0.32 0.18 1.2 0.7 % FR_R_T EW_16 0.24,10.25,1.24 5.96,10.25,7 25.43 25.91 25.66 26.23 0.24 0.32 0.9 1.2 % WW_16 EW_16 5.78,10.25,1.05 5.96,10.25,7 25.90 25.43 26.25 25.66 0.35 0.24 1.3 0.9 % WW_16 AA_16 8.81,10.25,4.44 5.78,10.25,1.05 26.11 25.90 26.33 26.25 0.23 0.35 0.9 1.3 % AA_16 8.81,10.25,4.44 26.01 26.11 26.27 26.33 0.25 0.23 1.0 0.9 % 26.01 26.27 0.25 1.0 % AIR MID Coordinates ΔT, (ºC) Main Temperature, Case Higher T, (ºC) Case Difference AIR FL_R_M MID 0.24,6.165,7.26 Coordinates 25.40 25.69 ΔT, 0.28 (ºC) Main Case Higher Case Difference 1.1 % FM_R_MH FL_R_M 0.24,6.165,7.26 0.24,6.9,4.22 24.86 25.40 25.09 25.69 0.23 0.28 0.9 1.1 % FM_R_MH FM_R_ML 0.24,5.2,4.22 0.24,6.9,4.22 23.93 24.86 24.16 25.09 0.23 0.9 % FM_R_ML FR_R_M 0.24,6.165,1.24 0.24,5.2,4.22 22.38 23.93 22.44 24.16 0.06 0.23 0.3 0.9 % FR_R_M EW_15 0.24,6.165,1.24 5.96,6.165,7 24.14 22.38 24.13 22.44-0.01 0.06 0.0 0.3 % WW_15 EW_15 5.78,6.165,1.05 5.96,6.165,7 24.02 24.14 24.14 24.13-0.01 0.12 0.5 0.0 % WW_15 AA_15 8.81,6.165,4.44 5.78,6.165,1.05 24.05 24.02 24.21 24.14 0.16 0.12 0.7 0.5 % AA_15 8.81,6.165,4.44 24.11 24.05 24.26 24.21 0.15 0.16 0.6 0.7 % 24.11 24.26 0.15 0.6 % AIR LOW Coordinates ΔT, (ºC) Main Temperature, Case Higher T, (ºC) Case Difference AIR FL_R_B LOW Coordinates 0.24,2.1,7.26 24.00 24.17 ΔT, 0.18 (ºC) Main Case Higher Case Difference 0.7 % FM_R_BH FL_R_B 0.24,3.05,4.22 0.24,2.1,7.26 23.42 24.00 23.54 24.17 0.12 0.18 0.5 0.7 % FM_R_BH FM_R_BL 0.24,1.35,4.22 0.24,3.05,4.22 22.57 23.42 22.71 23.54 0.14 0.12 0.6 0.5 % FM_R_BL FR_R_B 0.24,1.35,4.22 0.24,2.1,1.24 21.77 22.57 21.87 22.71 0.10 0.14 0.5 0.6 % FR_R_B EW_14 0.24,2.1,1.24 5.96,2.1,7 23.10 21.77 23.29 21.87 0.19 0.10 0.8 0.5 % WW_14 EW_14 5.78,2.1,1.05 5.96,2.1,7 23.67 23.10 23.78 23.29 0.11 0.19 0.5 0.8 % WW_14 AA_14 8.81,2.1,4.44 5.78,2.1,1.05 23.49 23.67 23.57 23.78 0.09 0.11 0.4 0.5 % AA_14 8.81,2.1,4.44 23.14 23.49 23.28 23.57 0.13 0.09 0.6 0.4 % 23.14 23.28 0.13 0.6 % Table 4-10 Overall percent differences in numerical air and glass temperatures when T out is lowered by 5 o C 59

Table 4-11 Overall percent differences in numerical air and glass temperatures when T out is raised by 5 o C As seen in Tables 4-10 and 4-11, the outside ambient temperature has more of an effect on the glass temperatures then the inside air temperature because of a higher external heat transfer coefficient on the outer surface. Also it is important to notice the nonlinearity of the relationship between the outside temperature and the temperatures measured in the model. 60

4.5 Effect of Outside Wind Speed The outside wind speed also varies with geographical location, similar to outside temperature, the wind speed may vary in different locations within a city, it is also dependent on the orientation of the building and the buildings in its vicinity. Its value affects the solution through the h value for the outside of the facade. A study was conducted to establish the importance of the outside wind speed (V w ) on the model. The facade temperatures shown in Figures 4-15, 4-16 and 4-17 are for different wind speeds. It will be noted that there are no visually distinguishable differences between the three results. Figure 4-15 Glass temperature contours on the facade when V w = 3 m/s 61

Figure 4-16 Glass temperature contours on the facade when V w = 6 m/s Figure 4-17 Glass temperature contours on the facade when V w = 9 m/s The results given in Figure 4-18 further illustrate this point showing results that are almost identical for various wind speeds. 62

Temperature (ºC) 40 39 38 37 36 35 34 33 32 31 30 0 2 4 6 8 10 12 Height (m) Vw = 3 m/s Vw = 6 m/s Vw = 9 m/s Figure 4-18 Glass temperatures along the middle of the facade for cases with different wind speeds Table 4-12 and 4-13 give further proof that the results are almost indistinguishable as the percentage differences found in the results are all below 0.5 %. Table 4-12 Glass temperature comparison of numerical data between Main Case - V w = 6 m/s and Lower Case - V w = 3 m/s GLASS HIGH Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_G_T 0,10.25,7.26 37.55 37.61 0.06 0.2 % FM_G_TH 0,10.9,4.22 36.99 37.02 0.03 0.1 % FM_G_TL 0,9.35,4.22 36.81 36.89 0.07 0.2 % FR_G_T 0,10.25,1.24 37.48 37.48 0.00 0.0 % 37.21 37.25 0.04 0.1 % GLASS MID Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_G_M 0,6.165,7.26 37.47 37.74 0.27 0.7 % FM_G_MH 0,6.9,4.22 35.73 35.48-0.25-0.7 % FM_G_ML 0,5.2,4.22 35.06 34.83-0.24-0.7 % FR_G_M 0,6.165,1.24 32.52 32.28-0.24-0.7 % 35.20 35.08-0.12-0.3 % GLASS LOW Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_G_B 0,2.1,7.26 36.58 37.18 0.60 1.6 % FM_G_BH 0,3.05,4.22 35.20 35.03-0.17-0.5 % FM_G_BL 0,1.35,4.22 34.73 34.35-0.39-1.1 % 63 FR_G_B 0,2.1,1.24 30.38 30.18-0.20-0.7 % 34.22 34.18-0.04-0.1 %

GLASS HIGH Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_G_T 0,10.25,7.26 37.55 37.61 0.06 0.2 % FM_G_TH 0,10.9,4.22 36.99 37.02 0.03 0.1 % FM_G_TL 0,9.35,4.22 36.81 36.89 0.07 0.2 % FR_G_T 0,10.25,1.24 37.48 37.48 0.00 0.0 % 37.21 37.25 0.04 0.1 % Table 4-12 (Continued) GLASS MID Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_G_M 0,6.165,7.26 37.47 37.74 0.27 0.7 % FM_G_MH 0,6.9,4.22 35.73 35.48-0.25-0.7 % FM_G_ML 0,5.2,4.22 35.06 34.83-0.24-0.7 % FR_G_M 0,6.165,1.24 32.52 32.28-0.24-0.7 % 35.20 35.08-0.12-0.3 % GLASS LOW Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_G_B 0,2.1,7.26 36.58 37.18 0.60 1.6 % FM_G_BH 0,3.05,4.22 35.20 35.03-0.17-0.5 % FM_G_BL 0,1.35,4.22 34.73 34.35-0.39-1.1 % FR_G_B 0,2.1,1.24 30.38 30.18-0.20-0.7 % 34.22 34.18-0.04-0.1 % Table 4-13 Glass temperature comparison of numerical data between Main Case - V w = 6 m/s and Higher Case - V w = 9 m/s GLASS HIGH Coordinates ΔT, (ºC) Main Case Higher Case Difference FL_G_T 0,10.25,7.26 37.55 37.53-0.02-0.1 % FM_G_TH 0,10.9,4.22 36.99 36.91-0.09-0.2 % FM_G_TL 0,9.35,4.22 36.81 36.72-0.09-0.3 % FR_G_T 0,10.25,1.24 37.48 37.38-0.11-0.3 % 37.21 37.13-0.08-0.2 % GLASS MID Coordinates ΔT, (ºC) Main Case Higher Case Difference FL_G_M 0,6.165,7.26 37.47 37.63 0.16 0.4 % FM_G_MH 0,6.9,4.22 35.73 35.47-0.26-0.7 % FM_G_ML 0,5.2,4.22 35.06 34.81-0.25-0.7 % FR_G_M 0,6.165,1.24 32.52 32.38-0.14-0.4 % 35.20 35.07-0.12-0.3 % GLASS LOW Coordinates ΔT, (ºC) Main Case Higher Case Difference FL_G_B 0,2.1,7.26 36.58 37.11 0.53 1.5 % FM_G_BH 0,3.05,4.22 35.20 35.02-0.19-0.5 % FM_G_BL 0,1.35,4.22 34.73 34.42-0.31-0.9 % FR_G_B 0,2.1,1.24 30.38 30.36-0.02-0.1 % 34.22 34.23 0.00 0.0 % The air temperature contours shown in Figures 4-19, 4-20 and 4-21 are all very similar at each plane. 64

Figure 4-19 Air temperature contours at various heights when V w = 3 m/s Figure 4-20 Air temperature contours at various heights when V w = 6 m/s 65

Temperature (ºC) Figure 4-21 Air temperature contours at various heights when V w = 9m/s Figure 4-22 and Table 4-14 and 4-15 give further evidence that wind effects are small. 28 27 26 25 24 23 22 0 2 4 6 8 10 12 Height (m) Vw = 3 m/s Vw = 6 m/s Vw = 9 m/s Figure 4-22 Air temperatures along center vertical line 0.24m away from the facade for cases with different wind speed 66

Table 4-14 Air temperature comparison of numerical data between Main Case - V w = 6 m/s and Lower Case - V w = 3 m/s AIR HIGH Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_R_T 0.24,10.25,7.26 26.49 26.31-0.19-0.7 % FM_R_TH 0.24,10.9,4.22 26.56 26.54-0.02-0.1 % FM_R_TL 0.24,9.35,4.22 25.70 25.59-0.11-0.4 % FR_R_T 0.24,10.25,1.24 25.91 25.73-0.17-0.7 % EW_16 5.96,10.25,7 25.43 25.63 0.20 0.8 % WW_16 5.78,10.25,1.05 25.90 25.84-0.06-0.3 % AA_16 8.81,10.25,4.44 26.11 26.02-0.08-0.3 % 26.01 25.95-0.06-0.2 % AIR MID Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_R_M 0.24,6.165,7.26 25.40 25.21-0.19-0.8 % FM_R_MH 0.24,6.9,4.22 24.86 24.62-0.24-1.0 % FM_R_ML 0.24,5.2,4.22 23.93 23.88-0.06-0.2 % FR_R_M 0.24,6.165,1.24 22.38 22.47 0.09 0.4 % EW_15 5.96,6.165,7 24.14 23.89-0.24-1.0 % WW_15 5.78,6.165,1.05 24.02 23.94-0.07-0.3 % AA_15 8.81,6.165,4.44 24.05 24.06 0.01 0.0 % 24.11 24.01-0.10-0.4 % AIR LOW Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_R_B 0.24,2.1,7.26 24.00 24.15 0.16 0.6 % FM_R_BH 0.24,3.05,4.22 23.42 23.54 0.12 0.5 % FM_R_BL 0.24,1.35,4.22 22.57 22.68 0.12 0.5 % FR_R_B 0.24,2.1,1.24 21.77 21.87 0.10 0.5 % EW_14 5.96,2.1,7 23.10 22.90-0.20-0.9 % WW_14 5.78,2.1,1.05 23.67 23.62-0.05-0.2 % AA_14 8.81,2.1,4.44 23.49 23.46-0.03-0.1 % 23.14 23.17 0.03 0.1 % 67

Table 4-15 Air temperature comparison of numerical data between Main Case - V w = 6 m/s and Upper Case - V w = 9 m/s AIR HIGH Coordinates ΔT, (ºC) Main Case Upper Case Difference FL_R_T 0.24,10.25,7.26 26.49 26.36-0.14-0.5 % FM_R_TH 0.24,10.9,4.22 26.56 26.55-0.01 0.0 % FM_R_TL 0.24,9.35,4.22 25.70 25.64-0.06-0.2 % FR_R_T 0.24,10.25,1.24 25.91 25.74-0.16-0.6 % EW_16 5.96,10.25,7 25.43 25.51 0.08 0.3 % WW_16 5.78,10.25,1.05 25.90 25.85-0.06-0.2 % AA_16 8.81,10.25,4.44 26.11 26.07-0.03-0.1 % 26.01 25.96-0.05-0.2 % AIR MID Coordinates ΔT, (ºC) Main Case Upper Case Difference FL_R_M 0.24,6.165,7.26 25.40 25.26-0.15-0.6 % FM_R_MH 0.24,6.9,4.22 24.86 24.68-0.17-0.7 % FM_R_ML 0.24,5.2,4.22 23.93 23.85-0.08-0.4 % FR_R_M 0.24,6.165,1.24 22.38 22.40 0.02 0.1 % EW_15 5.96,6.165,7 24.14 24.02-0.12-0.5 % WW_15 5.78,6.165,1.05 24.02 23.95-0.07-0.3 % AA_15 8.81,6.165,4.44 24.05 24.03-0.02-0.1 % 24.11 24.03-0.09-0.4 % AIR LOW Coordinates ΔT, (ºC) Main Case Upper Case Difference FL_R_B 0.24,2.1,7.26 24.00 24.06 0.06 0.3 % FM_R_BH 0.24,3.05,4.22 23.42 23.46 0.04 0.2 % FM_R_BL 0.24,1.35,4.22 22.57 22.71 0.15 0.6 % FR_R_B 0.24,2.1,1.24 21.77 21.97 0.20 0.9 % EW_14 5.96,2.1,7 23.10 23.01-0.09-0.4 % WW_14 5.78,2.1,1.05 23.67 23.49-0.19-0.8 % AA_14 8.81,2.1,4.44 23.49 23.26-0.22-0.9 % 23.14 23.14-0.01 0.0 % The average differences are seen in Tables 4-16 and 4-17, which for the current study all fall below a percentage difference of 0.2 %. 68

Table 4-16 Overall percent differences in numerical air and glass temperatures when the outside wind speed is decreased by 50% Table 4-17 - Overall percent differences in numerical air and glass temperatures when the outside wind speed is increased by 50% Overall, it can be concluded that the wind speed variations resulted in no major changes in the temperature predictions. 4.6 Effect of Absorptivity of the Glass The optical properties of the facade controls the fraction of the incident radiation that is absorbed, transmitted and reflected. The absorptivity (α) of the glass was approximated from available literature (ASHRAE, 2009), because this value of absorptivity was approximate, it is important to examine the effect of changing the absorptivity while keeping the transmissivity constant. The results given in the earlier cases were for an assumed absorptivity of 17.5%. The glass temperature contours for the range of absorptivities of 16%, 17.5% and 19% are shown in Figures 4-23, 4-24 and 4-25. 69

Figure 4-23 Glass temperature contours on the facade when α=16 % Figure 4-24 Glass temperature contours on the facade when α=17.5 % 70

Figure 4-25 Glass temperature contours on the facade when α=19 % The variations of glass temperatures along the vertical center line of the facade which are given in Fig 4-26 show that over the range of absorptivities considered, the absorptivity value has a relatively small effect on the facade temperature. Between the highest absorptivity of 19 % and the lowest absorptivity of 16 %, the average variation was about 1 o C. 71

Temperature (ºC) 38 37 36 35 34 33 32 0 2 4 6 8 10 12 Height (m) α = 16.0 α = 17.5 α = 19.0 Figure 4-26 Glass temperatures along the middle of the facade for cases with different glass absorptivity Tables 4-18 and 4-19 display the differences between the glass temperatures when the absorptivities are changed. The highest percent difference being 2 % which corresponds to a T of 0.7 o C Table 4-18 Glass temperature comparison of numerical data Comparison between Main Case (α=17.5) and Lower Case (α=16) between Main Case - α = 17.5 % and Lower Case - α = 16 % GLASS HIGH Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_G_T 0,10.25,7.26 37.55 37.01-0.54-1.4 % FM_G_TH 0,10.9,4.22 36.99 36.35-0.64-1.7 % FM_G_TL 0,9.35,4.22 36.81 36.30-0.52-1.4 % FR_G_T 0,10.25,1.24 37.48 37.03-0.45-1.2 % 37.21 36.67-0.54-1.4 % GLASS MID Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_G_M 0,6.165,7.26 37.47 37.11-0.36-1.0 % FM_G_MH 0,6.9,4.22 35.73 35.22-0.51-1.4 % FM_G_ML 0,5.2,4.22 35.06 34.16-0.91-2.6 % FR_G_M 0,6.165,1.24 32.52 31.49-1.03-3.2 % 35.20 34.49-0.70-2.0 % GLASS LOW Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_G_B 0,2.1,7.26 36.58 72 36.41-0.17-0.5 % FM_G_BH 0,3.05,4.22 35.20 34.15-1.05-3.0 % FM_G_BL 0,1.35,4.22 34.73 33.91-0.83-2.4 % FR_G_B 0,2.1,1.24 30.38 29.74-0.64-2.1 % 34.22 33.55-0.67-2.0 %

Comparison between Main Case (α=17.5) and Lower Case (α=16) GLASS HIGH Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_G_T 0,10.25,7.26 37.55 37.01-0.54-1.4 % FM_G_TH 0,10.9,4.22 36.99 36.35-0.64-1.7 % FM_G_TL 0,9.35,4.22 36.81 36.30-0.52-1.4 % Table 4-18 (Continued) FR_G_T 0,10.25,1.24 37.48 37.03-0.45-1.2 % 37.21 36.67-0.54-1.4 % GLASS MID Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_G_M 0,6.165,7.26 37.47 37.11-0.36-1.0 % FM_G_MH 0,6.9,4.22 35.73 35.22-0.51-1.4 % FM_G_ML 0,5.2,4.22 35.06 34.16-0.91-2.6 % FR_G_M 0,6.165,1.24 32.52 31.49-1.03-3.2 % 35.20 34.49-0.70-2.0 % GLASS LOW Coordinates ΔT, (ºC) Main Case Lower Case Difference FL_G_B 0,2.1,7.26 36.58 36.41-0.17-0.5 % FM_G_BH 0,3.05,4.22 35.20 34.15-1.05-3.0 % FM_G_BL 0,1.35,4.22 34.73 33.91-0.83-2.4 % FR_G_B 0,2.1,1.24 30.38 29.74-0.64-2.1 % 34.22 33.55-0.67-2.0 % Table 4-19 Glass temperature comparison of numerical data Comparison between Main Case (α=17.5) and Higher Case (α=19) between Main Case - α = 17.5 % and Higher Case - α = 19 % Comparison between Main Case (α=17.5) and Higher Case (α=19) GLASS HIGH Coordinates ΔT, (ºC) Main Case Higher Case Difference GLASS FL_G_T HIGH Coordinates 0,10.25,7.26 37.55 37.98 ΔT, 0.43 (ºC) 1.1 % Main Case Higher Case Difference FM_G_TH 0,10.9,4.22 36.99 37.26 0.26 0.7 FL_G_T 0,10.25,7.26 37.55 37.98 0.43 1.1 % FM_G_TL 0,9.35,4.22 36.81 37.25 0.44 1.2 FM_G_TH 0,10.9,4.22 36.99 37.26 0.26 0.7 % FR_G_T 0,10.25,1.24 37.48 38.01 0.53 1.4 FM_G_TL 0,9.35,4.22 36.81 37.25 0.44 1.2 % 37.21 37.63 0.41 1.1 FR_G_T 0,10.25,1.24 37.48 38.01 0.53 1.4 % 37.21 37.63 0.41 1.1 % GLASS MID Coordinates ΔT, (ºC) Main Case Higher Case Difference GLASS FL_G_M MID Coordinates 0,6.165,7.26 37.47 37.95 ΔT, 0.48 (ºC) 1.3 % Main Case Higher Case Difference FM_G_MH 0,6.9,4.22 35.73 35.84 0.11 0.3 FL_G_M 0,6.165,7.26 37.47 37.95 0.48 1.3 % FM_G_ML 0,5.2,4.22 35.06 35.15 0.09 0.3 FM_G_MH 0,6.9,4.22 35.73 35.84 0.11 0.3 % FR_G_M 0,6.165,1.24 32.52 32.71 0.19 0.6 FM_G_ML 0,5.2,4.22 35.06 35.15 0.09 0.3 % 35.20 35.41 0.22 0.6 FR_G_M 0,6.165,1.24 32.52 32.71 0.19 0.6 % 35.20 35.41 0.22 0.6 % GLASS LOW Coordinates ΔT, (ºC) Main Case Higher Case Difference GLASS FL_G_B LOW Coordinates 0,2.1,7.26 36.58 37.53 ΔT, 0.95 (ºC) 2.6 % Main Case Higher Case Difference FM_G_BH 0,3.05,4.22 35.20 35.65 0.44 1.3 FL_G_B 0,2.1,7.26 36.58 37.53 0.95 2.6 % FM_G_BL 0,1.35,4.22 34.73 34.67-0.06-0.2 FM_G_BH 0,3.05,4.22 35.20 35.65 0.44 1.3 % FR_G_B 0,2.1,1.24 30.38 30.53 0.15 0.5 FM_G_BL 0,1.35,4.22 34.73 34.67-0.06-0.2 % 34.22 34.60 0.37 1.1 FR_G_B 0,2.1,1.24 30.38 30.53 0.15 0.5 % 34.22 34.60 0.37 1.1 % The air temperature contours shown in Figures 4-27, 4-28 and 4-29 display no major changes to the air temperature. 73

Figure 4-27 Air temperature contours at various heights when α = 16 % Figure 4-28 Air temperature contours at various heights when α = 17.5% 74

Temperature (ºC) Figure 4-29 Air temperature contours at various heights when α = 19 % 27 26 25 24 23 22 21 0 2 4 6 8 10 12 Height (m) α = 16.0 α = 17.5 α = 19.0 Figure 4-30 Air temperatures along center vertical line 0.24m away from the facade for cases with different glass absorptivity 75

The air temperature values shown in Figure 4-30 differ on average by less than 0.5 o C. Overall the results shown in Tables 4-20 and 4-21, indicate the use of an absorptivity value of 17.5% is acceptable for the present study. Table 4-20 Air temperature comparison of numerical data Comparison between Main Case (α=17.5) and Lower Case (α=16) between Main Case - α = 17.5 % and Lower Case - α = 16 % Comparison between Main Case (α=17.5) and Lower Case (α=16) AIR HIGH Coordinates ΔT, (ºC) Main Case Lower Case Difference AIR FL_R_T HIGH 0.24,10.25,7.26 Coordinates 26.49 26.08 ΔT, -0.42 (ºC) -1.6 % Main Case Lower Case Difference FM_R_TH 0.24,10.9,4.22 26.56 26.40-0.16-0.6 FL_R_T 0.24,10.25,7.26 26.49 26.08-0.42-1.6 % FM_R_TL 0.24,9.35,4.22 25.70 25.35-0.35-1.4 FM_R_TH 0.24,10.9,4.22 26.56 26.40-0.16-0.6 % FR_R_T 0.24,10.25,1.24 25.91 25.90 0.00 0.0 FM_R_TL 0.24,9.35,4.22 25.70 25.35-0.35-1.4 % EW_16 5.96,10.25,7 25.43 25.30-0.12-0.5 FR_R_T 0.24,10.25,1.24 25.91 25.90 0.00 0.0 % WW_16 5.78,10.25,1.05 25.90 25.77-0.14-0.5 EW_16 5.96,10.25,7 25.43 25.30-0.12-0.5 % AA_16 8.81,10.25,4.44 26.11 25.85-0.26-1.0 WW_16 5.78,10.25,1.05 25.90 25.77-0.14-0.5 % 26.01 25.81-0.21-0.8 AA_16 8.81,10.25,4.44 26.11 25.85-0.26-1.0 % 26.01 25.81-0.21-0.8 % AIR MID Coordinates ΔT, (ºC) Main Case Lower Case Difference AIR FL_R_M MID 0.24,6.165,7.26 Coordinates 25.40 25.04 ΔT, -0.36 (ºC) -1.4 % Main Case Lower Case Difference FM_R_MH 0.24,6.9,4.22 24.86 24.62-0.23-0.9 FL_R_M 0.24,6.165,7.26 25.40 25.04-0.36-1.4 % FM_R_ML 0.24,5.2,4.22 23.93 23.58-0.35-1.5 FM_R_MH 0.24,6.9,4.22 24.86 24.62-0.23-0.9 % FR_R_M 0.24,6.165,1.24 22.38 22.13-0.25-1.1 FM_R_ML 0.24,5.2,4.22 23.93 23.58-0.35-1.5 % EW_15 5.96,6.165,7 24.14 23.73-0.41-1.7 FR_R_M 0.24,6.165,1.24 22.38 22.13-0.25-1.1 % WW_15 5.78,6.165,1.05 24.02 23.33-0.68-2.8 EW_15 5.96,6.165,7 24.14 23.73-0.41-1.7 % AA_15 8.81,6.165,4.44 24.05 24.10 0.05 0.2 WW_15 5.78,6.165,1.05 24.02 23.33-0.68-2.8 % 24.11 23.79-0.32-1.3 AA_15 8.81,6.165,4.44 24.05 24.10 0.05 0.2 % 24.11 23.79-0.32-1.3 % AIR LOW Coordinates ΔT, (ºC) Main Case Lower Case Difference AIR FL_R_B LOW Coordinates 0.24,2.1,7.26 24.00 23.96 ΔT, -0.04 (ºC) -0.2 % Main Case Lower Case Difference FM_R_BH 0.24,3.05,4.22 23.42 23.10-0.32-1.4 FL_R_B 0.24,2.1,7.26 24.00 23.96-0.04-0.2 % FM_R_BL 0.24,1.35,4.22 22.57 22.48-0.09-0.4 FM_R_BH 0.24,3.05,4.22 23.42 23.10-0.32-1.4 % FR_R_B 0.24,2.1,1.24 21.77 21.67-0.09-0.4 FM_R_BL 0.24,1.35,4.22 22.57 22.48-0.09-0.4 % EW_14 5.96,2.1,7 23.10 22.76-0.34-1.5 FR_R_B 0.24,2.1,1.24 21.77 21.67-0.09-0.4 % WW_14 5.78,2.1,1.05 23.67 23.51-0.17-0.7 EW_14 5.96,2.1,7 23.10 22.76-0.34-1.5 % AA_14 8.81,2.1,4.44 23.49 23.37-0.11-0.5 WW_14 5.78,2.1,1.05 23.67 23.51-0.17-0.7 % 23.14 22.98-0.17-0.7 AA_14 8.81,2.1,4.44 23.49 23.37-0.11-0.5 % 23.14 22.98-0.17-0.7 % 76

Table 4-21 Air temperature comparison of numerical data Comparison between Main Case (α=17.5) and Higher Case (α=19) between Main Case - α = 17.5 % and Higher Case - α = 19 % Comparison between Main Case (α=17.5) and Higher Case (α=19) AIR HIGH Coordinates ΔT, (ºC) Main Case Higher Case Difference FL_R_T 0.24,10.25,7.26 Temperature, 26.49 T, 26.32 (ºC) -0.17 AIR HIGH Coordinates ΔT, (ºC) -0.6 % FM_R_TH 0.24,10.9,4.22 Main 26.56 Case Higher 26.53 Case -0.03 Difference -0.1 % FM_R_TL FL_R_T 0.24,10.25,7.26 0.24,9.35,4.22 26.49 25.70 26.32 25.74-0.17 0.04-0.6 0.2 % FM_R_TH FR_R_T 0.24,10.25,1.24 0.24,10.9,4.22 26.56 25.91 26.53 25.79-0.03-0.12-0.1-0.4 % FM_R_TL EW_16 0.24,9.35,4.22 5.96,10.25,7 25.70 25.43 25.74 25.71 0.04 0.28 0.2 1.1 % FR_R_T WW_16 0.24,10.25,1.24 5.78,10.25,1.05 25.91 25.90 25.79 25.77-0.12-0.13-0.4-0.5 % EW_16 AA_16 8.81,10.25,4.44 5.96,10.25,7 25.43 26.11 25.71 25.64-0.47 0.28-1.8 1.1 % WW_16 5.78,10.25,1.05 25.90 26.01 25.77 25.93-0.13-0.08-0.5-0.3 % AA_16 8.81,10.25,4.44 26.11 25.64-0.47-1.8 % 26.01 Temperature, T, 25.93 (ºC) -0.08-0.3 % AIR MID Coordinates ΔT, (ºC) Main Case Higher Case Difference FL_R_M 0.24,6.165,7.26 Temperature, 25.40 T, 25.61 (ºC) 0.20 AIR MID Coordinates ΔT, (ºC) 0.8 % FM_R_MH 0.24,6.9,4.22 Main 24.86 Case Higher 24.68 Case -0.18 Difference -0.7 % FM_R_ML FL_R_M 0.24,6.165,7.26 0.24,5.2,4.22 25.40 23.93 25.61 23.95 0.20 0.01 0.8 0.1 % FM_R_MH FR_R_M 0.24,6.165,1.24 0.24,6.9,4.22 24.86 22.38 24.68 22.68-0.18 0.29-0.7 1.3 % FM_R_ML EW_15 0.24,5.2,4.22 5.96,6.165,7 23.93 24.14 23.95 23.75-0.38 0.01-1.6 0.1 % FR_R_M WW_15 0.24,6.165,1.24 5.78,6.165,1.05 22.38 24.02 22.68 24.05 0.29 0.03 1.3 0.1 % EW_15 AA_15 8.81,6.165,4.44 5.96,6.165,7 24.14 24.05 23.75 24.20-0.38 0.15-1.6 0.6 % WW_15 5.78,6.165,1.05 24.02 24.11 24.05 24.13 0.03 0.02 0.1 0.1 % AA_15 8.81,6.165,4.44 24.05 24.20 0.15 0.6 % 24.11 Temperature, T, 24.13 (ºC) 0.02 0.1 % AIR LOW Coordinates ΔT, (ºC) Main Case Higher Case Difference FL_R_B 0.24,2.1,7.26 Temperature, 24.00 T, 24.26 (ºC) 0.26 AIR LOW Coordinates ΔT, (ºC) 1.1 % FM_R_BH 0.24,3.05,4.22 Main 23.42 Case Higher 23.85 Case 0.43 Difference 1.8 % FM_R_BL FL_R_B 0.24,1.35,4.22 0.24,2.1,7.26 24.00 22.57 24.26 22.76 0.26 0.19 1.1 0.9 % FM_R_BH FR_R_B 0.24,3.05,4.22 0.24,2.1,1.24 23.42 21.77 23.85 21.96 0.43 0.19 1.8 0.9 % FM_R_BL EW_14 0.24,1.35,4.22 5.96,2.1,7 22.57 23.10 22.76 23.16 0.19 0.06 0.9 0.3 % FR_R_B WW_14 0.24,2.1,1.24 5.78,2.1,1.05 21.77 23.67 21.96 23.74 0.19 0.07 0.9 0.3 % EW_14 AA_14 8.81,2.1,4.44 5.96,2.1,7 23.10 23.49 23.16 23.45-0.04 0.06-0.2 0.3 % WW_14 5.78,2.1,1.05 23.67 23.14 23.74 23.31 0.07 0.17 0.3 0.7 % AA_14 8.81,2.1,4.44 23.49 23.45-0.04-0.2 % 23.14 23.31 0.17 0.7 % Summaries of the effect of absorptivity values on the glass and air temperatures shown in Table 4-22 and 4-23 indicate that for both the glass and the air temperature readings all fall below a difference of 0.7 C. 77

Table 4-22 Overall percent difference in numerical air and glass temperatures when absorptivity is lowered to 16 % Table 4-23 Overall percent difference in numerical air and glass temperatures when absorptivity is raised to 19 % 4.7 Cases for Different Time of Day Due to the large glazing area in the Concordia Atrium, the dominant thermal loading is due to the sun s rays entering the atrium. The results presented above were for a time of 16:00. To determine the ability of the model to predict conditions at different times during the day, simulations were run for two additional times; 14:30 and 17:30. The outside boundary conditions such as the wind speed, outside air temperature and the positioning of the sun were adjusted for the particular time. The results were compared with experimental measurements. 78

The solar irradiation and outside conditions for 14:30 are given in the Table 4-24. Table 4-24 Solar irradiation and outside conditions for at time of 14:30 Sun Direction Vector x y z -0.54 0.84-0.06 Sunshine Fraction 1 Direct Normal Solar Irradiation (at Earth's surface) [W/m 2 ] 863 Diffuse Solar Irradiation - vertical surface [W/m 2 ] 123 Diffuse Solar Irradiation - horizontal surface [W/m 2 ] 109 Outside Heat Transfer Coefficient [W/m 2 -C] 27.96 Outside Air Temperature [ o C] 28.2 At 14:30 the sun s ray only strike the floor of the atrium as seen in Figure 4-31, contours of glass temperatures are shown in Figure 4-32. 79

Figure 4-31 Contours of solar heat flux on the facade and walls of the atrium at 14:30 Figure 4-32 Glass temperature contours on the facade at 14:30 80

The percentage differences between the experimental and numerical results are shown in Table 4-25. The differences are very similar to those in the main case which was run for 16:00. Table 4-25 Glass temperature comparisons of numerical and experimental data for 14:30 14:30 GLASS HIGH Coordinates ΔT, (ºC) Experimental Temperature, Numerical T, (ºC) Difference GLASS HIGH Coordinates FL_G_T 0,10.25,7.26 33.70 36.03 ΔT, 2.33 (ºC) Experimental Numerical Difference 6.9 % FM_G_TH FL_G_T 0,10.25,7.26 0,10.9,4.22 34.30 33.70 35.94 36.03 2.33 1.64 6.9 4.8 % FM_G_TH FM_G_TL 0,9.35,4.22 0,10.9,4.22 33.20 34.30 35.89 35.94 1.64 2.69 4.8 8.1 % FM_G_TL FR_G_T 0,10.25,1.24 0,9.35,4.22 32.70 33.20 36.31 35.89 2.69 3.61 11.0 8.1 % FR_G_T 0,10.25,1.24 33.48 32.70 36.04 36.31 3.61 2.57 11.0 7.7 % 33.48 36.04 2.57 7.7 % GLASS MID Coordinates ΔT, (ºC) Experimental Temperature, Numerical T, (ºC) Difference GLASS MID Coordinates FL_G_M 0,6.165,7.26 31.60 36.96 ΔT, 5.36 (ºC) Experimental Numerical Difference 17.0 % FM_G_MH FL_G_M 0,6.165,7.26 0,6.9,4.22 33.60 31.60 34.52 36.96 5.36 0.92 17.0 2.7 % FM_G_MH FM_G_ML 0,5.2,4.22 0,6.9,4.22 31.40 33.60 33.29 34.52 0.92 1.89 2.7 6.0 % FM_G_ML FR_G_M 0,6.165,1.24 0,5.2,4.22 32.00 31.40 31.53 33.29-0.47 1.89-1.5 6.0 % FR_G_M 0,6.165,1.24 32.15 32.00 34.07 31.53-0.47 1.92-1.5 6.0 % 32.15 34.07 1.92 6.0 % GLASS LOW Coordinates ΔT, (ºC) Experimental Temperature, Numerical T, (ºC) Difference GLASS FL_G_B LOW Coordinates 0,2.1,7.26 30.30 35.66 ΔT, Experimental Numerical 5.36 (ºC) Difference 17.7 % FM_G_BH FL_G_B 0,3.05,4.22 0,2.1,7.26 29.50 30.30 35.32 35.66 5.36 5.82 17.7 19.7 % FM_G_BH FM_G_BL 0,1.35,4.22 0,3.05,4.22 28.90 29.50 34.11 35.32 5.82 5.21 19.7 18.0 % FM_G_BL FR_G_B 0,1.35,4.22 0,2.1,1.24 29.70 28.90 30.11 34.11 5.21 0.41 18.0 1.4 % FR_G_B 0,2.1,1.24 29.60 29.70 33.80 30.11 0.41 4.20 14.2 1.4 % 29.60 33.80 4.20 14.2 % Air temperature contours can be seen in Figure 4-33. A comparison of the numerically predicted and experimental air temperatures is shown in Table 4-26. 81

Figure 4-33 Air temperature contours in the atrium at various heights for 14:30 Table 4-26 Air Temperature comparison of numerical and experimental data for 14:30 AIR HIGH Coordinates ΔT, (ºC) Experimental Numerical Difference FL_R_T 0.24,10.25,7.26 26.60 25.80-0.80-3.0 % FM_R_TH 0.24,10.9,4.22 27.20 25.75-1.45-5.3 % FM_R_TL 0.24,9.35,4.22 27.30 25.09-2.21-8.1 % FR_R_T 0.24,10.25,1.24 27.00 25.32-1.68-6.2 % EW_16 5.96,10.25,7 26.10 25.03-1.07-4.1 % WW_16 5.78,10.25,1.05 25.80 25.32-0.48-1.8 % AA_16 8.81,10.25,4.44 25.90 24.91-0.99-3.8 % 26.56 25.32-1.24-4.7 % AIR MID Coordinates ΔT, (ºC) Experimental Numerical Difference FL_R_M 0.24,6.165,7.26 26.80 24.83-1.97-7.4 % FM_R_MH 0.24,6.9,4.22 25.60 24.24-1.36-5.3 % FM_R_ML 0.24,5.2,4.22 24.70 23.59-1.12-4.5 % FR_R_M 0.24,6.165,1.24 26.40 22.28-4.12-15.6 % EW_15 5.96,6.165,7 24.80 23.27-1.53-6.2 % WW_15 5.78,6.165,1.05 25.10 23.98-1.12-4.5 % AA_15 8.81,6.165,4.44 24.60 23.94-0.66-2.7 % 25.43 23.73-1.70-6.7 % AIR LOW Coordinates ΔT, (ºC) Experimental Numerical Difference FL_R_B 0.24,2.1,7.26 23.80 24.23 0.43 1.8 % FM_R_BH 0.24,3.05,4.22 23.40 23.45 0.05 0.2 % FM_R_BL 0.24,1.35,4.22 23.00 22.60-0.40-1.8 % FR_R_B 0.24,2.1,1.24 22.90 82 21.79-1.11-4.8 % EW_14 5.96,2.1,7 23.20 23.09-0.11-0.5 % WW_14 5.78,2.1,1.05 22.30 23.39 1.09 4.9 % AA_14 8.81,2.1,4.44 22.80 23.48 0.68 3.0 % 23.06 23.15 0.09 0.4 %

AIR MID Coordinates ΔT, (ºC) Experimental Numerical Difference FL_R_M 0.24,6.165,7.26 26.80 24.83-1.97-7.4 % FM_R_MH 0.24,6.9,4.22 25.60 24.24-1.36-5.3 % FM_R_ML 0.24,5.2,4.22 24.70 23.59-1.12-4.5 % FR_R_M 0.24,6.165,1.24 26.40 22.28-4.12-15.6 % EW_15 5.96,6.165,7 24.80 23.27-1.53-6.2 % WW_15 5.78,6.165,1.05 25.10 23.98-1.12-4.5 % AA_15 8.81,6.165,4.44 Table 4-26 24.60 (Continued) 23.94-0.66-2.7 % 25.43 23.73-1.70-6.7 % AIR LOW Coordinates ΔT, (ºC) Experimental Numerical Difference FL_R_B 0.24,2.1,7.26 23.80 24.23 0.43 1.8 % FM_R_BH 0.24,3.05,4.22 23.40 23.45 0.05 0.2 % FM_R_BL 0.24,1.35,4.22 23.00 22.60-0.40-1.8 % FR_R_B 0.24,2.1,1.24 22.90 21.79-1.11-4.8 % EW_14 5.96,2.1,7 23.20 23.09-0.11-0.5 % WW_14 5.78,2.1,1.05 22.30 23.39 1.09 4.9 % AA_14 8.81,2.1,4.44 22.80 23.48 0.68 3.0 % 23.06 23.15 0.09 0.4 % The air temperatures shown in Table 4-26 display similar range of differences as seen in case for a time of 16:00. Table 4-27 below outlines the accuracy achieved for the numerical model to predict an earlier time of day. From these results it can be concluded that the model is equally well suited to predict an earlier time during the day. Table 4-27 Overall percent difference in air and glass temperatures for 14:30 The models ability to also predict conditions at a time later during the day was also investigated by running the simulation at a time of 17:30. Table 4-28 gives the solar irradiation and outside conditions for this time of 17:30. 83

Table 4-28 Solar irradiation and outside conditions for a time of 17:30 Sun Direction Vector x y z -0.54 0.47-0.70 Sunshine Fraction 1 Direct Normal Solar Irradiation (at Earth's surface) [W/m 2 ] 717 Diffuse Solar Irradiation - vertical surface [W/m 2 ] 75 Diffuse Solar Irradiation - horizontal surface [W/m 2 ] 90 Outside Heat Transfer Coefficient [W/m 2 -C] 29 Outside Air Temperature [ o C] 28.3 The solar loading for the case run at a time of 17:30 is distributed mainly between the floor and the east wall as shown in Figure 4-34. 84

Figure 4-34 Contours of solar heat flux on the facade and walls of the atrium at 17:30 The glass temperature contours for a time of 17:30 are shown in Figure 4-35. These results exhibit a different trend than those observed in the results from the earlier times of 14:30 and 16:00. The colder region on the right hand region of the facade is larger than at the earlier times due to the decreased solar loading. 85

Figure 4-35 Glass temperature contours on the facade at 17:30 Table 4-29 shows the percentage differences between the numerical and experimental glass temperatures at a time of 17:30. The agreement of glass temperature predictions at a time of 17:30 is more accurate compared to 16:00, the difference in average temperatures are shown to be all less than 1.63 o C compared to experimental. Table 4-29 Glass temperature comparison of numerical and experimental data 17:30 for 17:30 GLASS HIGH Coordinates ΔT, (ºC) Experimental Numerical Difference FL_G_T 0,10.25,7.26 33.10 34.76 1.65 0.5 % FM_G_TH 0,10.9,4.22 33.80 33.76-0.04 0.0 % FM_G_TL 0,9.35,4.22 32.70 33.45 0.75 0.2 % FR_G_T 0,10.25,1.24 31.40 34.28 2.88 0.9 % 32.75 34.06 1.31 4.0 % GLASS MID Coordinates ΔT, (ºC) Experimental Numerical Difference FL_G_M 0,6.165,7.26 30.90 33.74 2.84 9.2 % FM_G_MH 0,6.9,4.22 32.90 31.41-1.49-4.5 % FM_G_ML 0,5.2,4.22 30.50 30.79 0.29 0.9 % FR_G_M 0,6.165,1.24 31.00 27.55-3.45-11.1 % 31.33 30.87-0.45-1.5 % GLASS LOW Coordinates ΔT, (ºC) Experimental Numerical Difference FL_G_B 0,2.1,7.26 29.70 33.14 3.44 11.6 % FM_G_BH 0,3.05,4.22 28.80 86 31.02 2.22 7.7 % FM_G_BL 0,1.35,4.22 28.30 30.54 2.24 7.9 % FR_G_B 0,2.1,1.24 28.50 27.12-1.38-4.8 % 28.83 30.46 1.63 5.7 %

GLASS HIGH Coordinates ΔT, (ºC) Experimental Numerical Difference FL_G_T 0,10.25,7.26 33.10 34.76 1.65 0.5 % FM_G_TH 0,10.9,4.22 33.80 33.76-0.04 0.0 % FM_G_TL 0,9.35,4.22 32.70 33.45 0.75 0.2 % FR_G_T 0,10.25,1.24 31.40 34.28 2.88 0.9 % 32.75 34.06 1.31 4.0 % GLASS MID Coordinates ΔT, (ºC) Experimental Numerical Difference FL_G_M 0,6.165,7.26 30.90 33.74 2.84 9.2 % FM_G_MH 0,6.9,4.22 32.90 31.41-1.49-4.5 % FM_G_ML 0,5.2,4.22 30.50 30.79 0.29 0.9 % FR_G_M 0,6.165,1.24 31.00 27.55-3.45-11.1 % 31.33 30.87-0.45-1.5 % GLASS LOW Coordinates ΔT, (ºC) Experimental Numerical Difference FL_G_B 0,2.1,7.26 29.70 33.14 3.44 11.6 % FM_G_BH 0,3.05,4.22 28.80 31.02 2.22 7.7 % FM_G_BL 0,1.35,4.22 28.30 30.54 2.24 7.9 % FR_G_B 0,2.1,1.24 28.50 27.12-1.38-4.8 % 28.83 30.46 1.63 5.7 % The air temperature contours on three levels are shown in Figure 4-36. These results indicate that there is less stratification between the planes at 2.1 m and 6.165 m. The temperatures on these planes vary between 20 o C and 22 o C. Figure 4-36 Air temperature contours in the atrium at various heights for 17:30 Table 4-30 shows that the air temperature differences between the numerical and experimental are higher than those obtained at 16:00. 87

Table 4-30 Air temperature comparison of numerical and experimental data for 17:30 17:30 AIR HIGH Coordinates ΔT, (ºC) AIR HIGH Coordinates Experimental Numerical ΔT, (ºC) Difference Experimental Numerical Difference FL_R_T 0.24,10.25,7.26 26.20 24.08-2.12-8.1 FL_R_T 0.24,10.25,7.26 26.20 24.08-2.12-8.1 % FM_R_TH 0.24,10.9,4.22 27.90 24.41-3.49-12.5 FM_R_TH 0.24,10.9,4.22 27.90 24.41-3.49-12.5 % FM_R_TL 0.24,9.35,4.22 26.80 23.15-3.65-13.6 FM_R_TL 0.24,9.35,4.22 26.80 23.15-3.65-13.6 % FR_R_T 0.24,10.25,1.24 26.00 23.51-2.49-9.6 FR_R_T 0.24,10.25,1.24 26.00 23.51-2.49-9.6 % EW_16 5.96,10.25,7 26.10 23.28-2.82-10.8 EW_16 5.96,10.25,7 26.10 23.28-2.82-10.8 % WW_16 5.78,10.25,1.05 26.20 23.52-2.68-10.2 WW_16 5.78,10.25,1.05 26.20 23.52-2.68-10.2 % AA_16 8.81,10.25,4.44 26.10 23.69-2.41-9.2 AA_16 8.81,10.25,4.44 26.10 23.69-2.41-9.2 % 26.47 23.66-2.81-10.6 26.47 23.66-2.81-10.6 % AIR MID Coordinates ΔT, (ºC) AIR MID Coordinates Experimental Numerical ΔT, (ºC) Difference Experimental Numerical Difference FL_R_M 0.24,6.165,7.26 26.50 22.69-3.81-14.4 FL_R_M 0.24,6.165,7.26 26.50 22.69-3.81-14.4 % FM_R_MH 0.24,6.9,4.22 25.70 21.38-4.32-16.8 FM_R_MH 0.24,6.9,4.22 25.70 21.38-4.32-16.8 % FM_R_ML 0.24,5.2,4.22 24.30 21.22-3.08-12.7 FM_R_ML 0.24,5.2,4.22 24.30 21.22-3.08-12.7 % FR_R_M 0.24,6.165,1.24 25.50 20.41-5.09-20.0 FR_R_M 0.24,6.165,1.24 25.50 20.41-5.09-20.0 % EW_15 5.96,6.165,7 24.50 21.55-2.95-12.0 EW_15 5.96,6.165,7 24.50 21.55-2.95-12.0 % WW_15 5.78,6.165,1.05 25.10 21.06-4.04-16.1 WW_15 5.78,6.165,1.05 25.10 21.06-4.04-16.1 % AA_15 8.81,6.165,4.44 24.60 21.58-3.02-12.3 AA_15 8.81,6.165,4.44 24.60 21.58-3.02-12.3 % 25.17 21.41-3.76-14.9 25.17 21.41-3.76-14.9 % AIR LOW Coordinates ΔT, (ºC) AIR LOW Coordinates Experimental Numerical ΔT, (ºC) Difference Experimental Numerical Difference FL_R_B 0.24,2.1,7.26 23.40 21.91-1.49-6.4 FL_R_B 0.24,2.1,7.26 23.40 21.91-1.49-6.4 % FM_R_BH 0.24,3.05,4.22 22.80 21.32-1.48-6.5 FM_R_BH 0.24,3.05,4.22 22.80 21.32-1.48-6.5 % FM_R_BL 0.24,1.35,4.22 22.80 20.70-2.10-9.2 FM_R_BL 0.24,1.35,4.22 22.80 20.70-2.10-9.2 % FR_R_B 0.24,2.1,1.24 22.30 19.89-2.41-10.8 FR_R_B 0.24,2.1,1.24 22.30 19.89-2.41-10.8 % EW_14 5.96,2.1,7 23.10 20.63-2.47-10.7 EW_14 5.96,2.1,7 23.10 20.63-2.47-10.7 % WW_14 5.78,2.1,1.05 22.20 21.41-0.79-3.5 WW_14 5.78,2.1,1.05 22.20 21.41-0.79-3.5 % AA_14 8.81,2.1,4.44 22.80 21.25-1.55-6.8 AA_14 8.81,2.1,4.44 22.80 21.25-1.55-6.8 % 22.77 21.02-1.75-7.7 22.77 21.02-1.75-7.7 % In the main case considered the glass temperatures were over-predicted on average by 10.64 %, because of the lower solar intensity at 17:30 the average error is reduced to 2.74%. However, as can be seen from Table 4-31 the average percentage error for the air predictions have gone up to 11 %. This could be the result of ignoring the thermal mass in the numerical study. At the later time the air temperature is dropping more rapidly, increasing the importance of accounting for the thermal mass. 88

Table 4-31 - Overall percent difference in air and glass temperatures for 17:30 4.8 Cases for Different Location The performance of the atrium at three cities across Canada was investigated for this study, primarily looking at the effect of the different orientation of the sun to the atrium. The atrium orientation was kept constant, however due to the locations of Calgary, Halifax and Vancouver a different distribution and intensity of the solar loading was present in each case. The outside boundary conditions (i.e air temperature, wind speed) were the same as the main validation case. Below are the three figures 4-37, 4-38 and 4-39 showing the variation of the incoming sun at 16:00. Figure 4-37 Contours of solar heat flux on the facade and walls of the atrium at 16:00 in Calgary (Longitude: -114, Latitude: 51) 89

Figure 4-38 Contours of solar heat flux on the facade and walls of the atrium at 16:00 in Halifax (Longitude: -63, Latitude: 45) Figure 4-39 Contours of solar heat flux on the facade and walls of the atrium at 16:00 in Vancouver (Longitude: -123, Latitude: 49) These variations in solar heat flux directly effect the predicted numerical glass temperature as seen by the results shown in Figures 4-40, 4-41 and 4-42. 90

Figure 4-40 Glass temperature contours on the facade at 16:00 in Calgary Figure 4-41 Glass temperature contours on the facade at 16:00 in Halifax 91

Figure 4-42 Glass temperature contours on the facade at 16:00 in Vancouver Figure 4-43 shows the glass temperatures along the vertical center line of the facade for each different location. Considering the average temperatures in Table 4-32, the results indicate the glass temperatures are highest in Calgary followed by Vancouver, Montreal and Halifax. Table 4-32 Glass temperature comparison of numerical data at 16:00 for all simulated cities 92

Table 4-32 (Continued) Figure 4-43 Glass temperatures along the middle of the facade for 16:00 Air temperatures contours on horizontal planes in the atrium for each location are shown in Figures 4-44, 4-45 and 4-46. 93

Figure 4-44 Air temperature contours in the atrium at various heights for 16:00 in Calgary Figure 4-45 Air temperature contours in the atrium at various heights for 16:00 in Halifax 94

Figure 4-46 Air temperature contours in the atrium at various heights for 16:00 in Vancouver The air temperature results are summarized in Table 4-33 and Figure 4-47. Table 4-33 Air temperature comparison of numerical data for 16:00 for all simulated cities AIR HIGH Coordinates AIR HIGH Coordinates Montreal Calgary Halifax Vancouver Montreal Calgary Halifax Vancouver FL_R_T 0.24,10.25,7.26 26.49 27.59 25.99 27.16 FL_R_T 0.24,10.25,7.26 26.49 27.59 25.99 27.16 FM_R_TH 0.24,10.9,4.22 26.56 27.77 26.04 27.34 FM_R_TH 0.24,10.9,4.22 26.56 27.77 26.04 27.34 FM_R_TL 0.24,9.35,4.22 25.70 27.28 25.36 26.61 FM_R_TL 0.24,9.35,4.22 25.70 27.28 25.36 26.61 FR_R_T 0.24,10.25,1.24 25.91 27.43 25.47 26.94 FR_R_T 0.24,10.25,1.24 25.91 27.43 25.47 26.94 EW_16 5.96,10.25,7 25.43 27.08 25.55 26.60 EW_16 5.96,10.25,7 25.43 27.08 25.55 26.60 WW_16 5.78,10.25,1.05 25.90 27.34 25.37 26.87 WW_16 5.78,10.25,1.05 25.90 27.34 25.37 26.87 AA_16 8.81,10.25,4.44 26.11 27.35 25.18 26.83 AA_16 8.81,10.25,4.44 26.11 27.35 25.18 26.83 26.01 27.40 25.57 26.91 26.01 27.40 25.57 26.91 AIR MID Coordinates AIR MID Coordinates Montreal Calgary Halifax Vancouver Montreal Calgary Halifax Vancouver FL_R_M 0.24,6.165,7.26 25.40 26.91 25.00 26.36 FL_R_M 0.24,6.165,7.26 25.40 26.91 25.00 26.36 FM_R_MH 0.24,6.9,4.22 24.86 26.50 24.28 25.95 FM_R_MH 0.24,6.9,4.22 24.86 26.50 24.28 25.95 FM_R_ML 0.24,5.2,4.22 23.93 25.55 23.69 25.12 FM_R_ML 0.24,5.2,4.22 23.93 25.55 23.69 25.12 FR_R_M 0.24,6.165,1.24 22.38 23.22 22.46 22.75 FR_R_M 0.24,6.165,1.24 22.38 23.22 22.46 22.75 EW_15 5.96,6.165,7 24.14 25.12 23.73 24.51 EW_15 5.96,6.165,7 24.14 25.12 23.73 24.51 WW_15 5.78,6.165,1.05 24.02 25.66 24.00 24.94 WW_15 5.78,6.165,1.05 24.02 25.66 24.00 24.94 AA_15 8.81,6.165,4.44 24.05 25.51 24.02 25.00 AA_15 8.81,6.165,4.44 24.05 25.51 24.02 25.00 24.11 25.50 23.88 24.95 24.11 25.50 23.88 24.95 AIR LOW Coordinates AIR LOW Coordinates Montreal Calgary Halifax Vancouver Montreal Calgary Halifax Vancouver FL_R_B 0.24,2.1,7.26 24.00 25.11 24.31 24.83 FL_R_B 0.24,2.1,7.26 24.00 25.11 24.31 24.83 FM_R_BH 0.24,3.05,4.22 23.42 24.22 23.66 23.70 FM_R_BH 0.24,3.05,4.22 23.42 24.22 23.66 23.70 FM_R_BL 0.24,1.35,4.22 22.57 23.57 22.64 23.23 FM_R_BL 0.24,1.35,4.22 22.57 23.57 22.64 23.23 FR_R_B 0.24,2.1,1.24 21.77 95 22.73 21.73 22.32 FR_R_B 0.24,2.1,1.24 21.77 22.73 21.73 22.32 EW_14 5.96,2.1,7 23.10 24.37 22.82 23.86 EW_14 5.96,2.1,7 23.10 24.37 22.82 23.86 WW_14 5.78,2.1,1.05 23.67 24.65 23.56 24.30 WW_14 5.78,2.1,1.05 23.67 24.65 23.56 24.30 AA_14 8.81,2.1,4.44 23.49 24.73 23.41 24.44 AA_14 8.81,2.1,4.44 23.49 24.73 23.41 24.44 23.14 24.20 23.16 23.81 23.14 24.20 23.16 23.81

FL_R_M 0.24,6.165,7.26 25.40 26.91 25.00 26.36 FM_R_MH 0.24,6.9,4.22 24.86 26.50 24.28 25.95 FM_R_ML 0.24,5.2,4.22 23.93 25.55 23.69 25.12 FR_R_M 0.24,6.165,1.24 22.38 23.22 22.46 22.75 EW_15 5.96,6.165,7 24.14 25.12 23.73 24.51 WW_15 5.78,6.165,1.05 24.02 25.66 24.00 24.94 AA_15 8.81,6.165,4.44 24.05 25.51 24.02 25.00 Table 4-33 (Continued) 24.11 25.50 23.88 24.95 AIR LOW Coordinates Montreal Calgary Halifax Vancouver FL_R_B 0.24,2.1,7.26 24.00 25.11 24.31 24.83 FM_R_BH 0.24,3.05,4.22 23.42 24.22 23.66 23.70 FM_R_BL 0.24,1.35,4.22 22.57 23.57 22.64 23.23 FR_R_B 0.24,2.1,1.24 21.77 22.73 21.73 22.32 EW_14 5.96,2.1,7 23.10 24.37 22.82 23.86 WW_14 5.78,2.1,1.05 23.67 24.65 23.56 24.30 AA_14 8.81,2.1,4.44 23.49 24.73 23.41 24.44 23.14 24.20 23.16 23.81 Figure 4-47 Air temperatures along center vertical line 0.24m away from the facade for 16:00 96

4.9 Thermal Comfort In this section a study of thermal comfort, considering draught and vertical air temperatures differences in the Concordia University Atrium in Montreal at time of 16:00 on Aug. 1, 2007 will be presented. The purpose of this study is to determine the parts of the atrium where thermal comfort problems may arise. Figure 4-48 shows the temperature contours on three vertical planes in the atrium. The first plane shows the incoming cool air. The overall temperature stratification over the three vertical planes can be clearly seen; from the floor to the mid-height of the atrium the temperatures vary from 20 o C to 25 o C. At the very top of the atrium hotter air temperatures ranging from 28 o C and 30 o C exists. Figure 4-48 Air temperature contours for three vertical planes in the atrium 97

Figure 4-49 shows the region that was used to investigate thermal comfort since only this part of the atrium is frequently occupied, serving as a workspace for students. Figure 4-49 Region of occupied workspace for investigation of thermal comfort 4.9.1 Discomfort Due to Draft To calculate risk of thermal discomfort due to draft, the following equation discussed in 0.62 section 1.4.5 is used. 34 t V 0.05 0.37V Tu 3.14 PD a. This equation requires the values of three parameters; velocity, air temperature and turbulence intensity to be known. These parameters were evaluated at a height of 1.1 m, which covers the head, neck, shoulder region of a seated person. Figures 4-50, 4-51 and 4-52 show contours of the three required parameters over a horizontal plane at a height of 1.1m. The rectangular region outlined in these figures illustrates the occupied area. 98

Figure 4-50 Air temperature contours at a height of 1.1 m Figure 4-50 shows the presence of cool air near the west wall due to the position of the supply. However in most regions of the atrium the air temperature is approximately 23 o C. Figure 4-51 Velocity magnitude contours at a height of 1.1 m 99

Figure 4-51 shows that the air velocities away from the walls in the atrium fall below 0.1 m/s. Near the walls higher velocities of up to 0.6 m/s can be observed. The turbulence intensity shown in Figure 4-52 indicates that, as with the velocity, the highest values occur near the walls. This results from the impingement of the air from the supply on the west wall. This is illustrated by the velocity vector plot shown in Figure 4-53. Figure 4-52 Turbulence intensity contours at a height of 1.1 m 100

Figure 4-53 Velocity vectors on a vertical plane normal to supply vent Using the values of the thermal comfort parameters given in Figures 4-50, 4-51 and 4-52 the values of PPD over the region considered is displayed in Figure 4-54. Figure 4-54 Prediction of percentage dissatisfied due to draft in the occupied area of the atrium 101

Due to both low temperatures and high velocities the PPD near the facade and west wall are above 50 %. However, in the region away from the wall towards the middle of the atrium, values of 0 to 20 % are obtained. The thermal comfort requirements can be less stringent for places that are not occupied throughout the whole day (Schild et al., 1995). This is the case for the atrium as well, since it tends to be used mostly by students for short periods of time between classes. 4.9.2 Vertical Air Temperature Difference Another cause of thermal discomfort discussed in section 1.4.4, is the vertical air temperature differences that occupants are experiencing. Figure 4-55 shows the temperature difference between the temperatures at the ankles and the head, ankles taken at a height of 0.1 m and head at 1.1 m. Figure 4-55 Prediction of percent dissatisfied due to vertical temperature difference in the occupied area of the atrium 102

Close to the west wall the PD values range between 5 % to 13 %, however the majority of the space falls below a ΔT of 3 o C, which corresponds to a PD of less than 5%. This demonstrates that vertical air temperature differences are moderate and shouldn t cause major comfort issues for the occupants. 103

Chapter 5 Conclusions and Recommendations for Future Work The present work was undertaken due to the few available studies where numerical results for flow and temperature in an atrium are compared with measured results. The availability of experimental air and glass temperature measurements in the Concordia University Engineering Building Atrium in Montreal presented an opportunity to compare experimental data and numerical results for an atrium of relatively large size. Validation of CFD simulations using experimental data acquired from real life atriums is necessary to give a clearer indication of the ability of CFD to accurately model the conditions that occur in such a building. 5.1 Conclusions The main conclusions that can be drawn from the results obtained in the present study are: i) The results for the main case considered, which were for a time of 16:00 on August 1, 2007, showed that satisfactory agreement between the experimental and numerical results was obtained. The glass temperatures on average were over predicted by 10 % whereas the air temperatures on average were under predicted by 2.7 %. The differences between the experimental and numerical values of the air temperatures was less then +/- 1.1 C. This accuracy can be considered sufficient for preliminary design studies. ii) The importance of incorporating internal radiation heat exchange in the atrium has 104

been established. The results showed that it is important to take into account radiant heat exchange between the internal surfaces of the atrium to further increase accuracy of air and facade temperature predictions. iii) The simulations conducted in this study were mainly for one specific time of day. To evaluate the ability of the numerical model to predict air and glass temperatures at various times of day; simulations at earlier and later times than the main case was run. The results for a time of 14:30 were found to be similar to those obtained for the main case (16:00). However the results for the later time, 17:30 showed that the air temperatures were under predicted. This may be due to the exclusion of the thermal mass in the numerical model. iv) In order to study how the location of an atrium effects the temperature distribution inside, simulations were run for the cities; Calgary, Halifax and Vancouver. The different solar loads in these cities at the chosen time were accounted but the same external atmospheric conditions were assumed. The results indicated that both the glass and air temperatures are highest in Calgary followed by Vancouver, Montreal and Halifax. This can be related to the different orientation of the sun relative to the atrium leading to differences in the solar heat flux. v) The exact atmospheric conditions at the location of the atrium were unavailable. The information at a relatively distant point from the atrium was used in the study. To gain further understanding of the sensitivity of the results to the atmospheric conditions such as; outside temperature, wind speed and location; calculations with various atmospheric parameters were undertaken. The wind speed was found to have a negligible effect on both the air and glass temperatures with a percentage 105

difference of +/- 0.5 %. The outside air temperature was found to have a more significant effect; lower and higher ambient temperatures resulting in a +/- 5 % difference. vi) Due to the limited information on the optical properties of the facade, a study of the effect of varying the absorptivity of the glass was conducted. The findings indicated that a change in absorptivity from 16 % to 19 % resulted in a +/- 2 % difference on average for both glass and air temperatures. Thus the effect of changing the absorptivity was found to be relatively small. vii) The possibility of thermal discomfort due to draft was evaluated for the area of the atrium where occupants would be present in the atrium. The findings indicated low thermal comfort levels near the walls. However regions toward the middle of the atrium, where the student workspace is placed, the PPD was found to be between 0-20 %. viii) The vertical air temperature differences in the atrium were also evaluated and it was found that in 90 % of the workspace the vertical air temperature difference was 3 o C or less, which corresponds to a PD of less than 5 %. 5.2 Recommendations i) A transient analysis should be conducted for the duration of one entire day. If such a study is to be performed, it is important to incorporate thermal mass into the simulation, since it can dampen temperature fluctuations through out the day. This would require a thorough analysis of the walls enclosing the atrium. ii) The effect of varying the forced flow rate into the atrium should be studied. Also 106

the effect of the vent position on the results should be studied and its consequences on thermal comfort examined. iii) Calculations should be carried out for various days throughout the year including winter days to study the year round performance of the atrium iv) Due to the importance of internal radiation it is important to evaluate different surface-to-surface radiation models. If the geometry of the building is complex or the inclusion of furniture and equipment is required in order to avoid excessive computing times, it would be advantageous to choose a relatively simple radiation model. 107

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Appendix A Input values for FLUENT modeling of the Concordia Atrium 112

Numerical Model FLUENT Version: 3d, dp, pbns, rke (3d, double precision, pressure-based, realizable k-epsilon) Release: 6.3.26 Model Settings ----------------------------------------------------------------- Space 3D Time Steady Viscous Realizable k-epsilon turbulence model with full buoyancy effects Wall Treatment Standard Wall Functions Heat Transfer Enabled Solidification and Melting Disabled Radiation Discrete Transfer Model Species Transport Disabled Coupled Dispersed Phase Disabled Pollutants Disabled Boundary Conditions name id type -------------------------------------- volume_air 2 fluid inside 3 interior ceiling 4 wall back 5 wall right_wall 6 wall return 7 outflow supply 8 velocity-inlet left_wall 9 wall glass 10 wall floor 11 wall default-interior 13 interior 113

Volume_air Condition Value ----------------------------------------------------------- Material Name air Ceiling Condition Value ----------------------------------------------------------- Wall Thickness (m) 0 Heat Generation Rate (w/m3) 0 Material Name insulated_wall Heat Flux (w/m2) 0 Convective Heat Transfer Coefficient (w/m2-k) 0 Enable shell conduction? no Internal Emissivity 0.8 External Emissivity 1 Participates in Solar Ray Tracing? yes Back Condition Value ----------------------------------------------------------- Wall Thickness (m) 0 Heat Generation Rate (w/m3) 0 Material Name insulated_wall Heat Flux (w/m2) 0 Convective Heat Transfer Coefficient (w/m2-k) 0 Enable shell conduction? no Internal Emissivity 0 External Emissivity 1 Participates in Solar Ray Tracing? yes 114

Right Wall Condition Value ----------------------------------------------------------- Wall Thickness (m) 0 Heat Generation Rate (w/m3) 0 Material Name insulated_wall Heat Flux (w/m2) 0 Convective Heat Transfer Coefficient (w/m2-k) 0 Enable shell conduction? no Internal Emissivity 0.84 External Emissivity 1 Participates in Solar Ray Tracing? yes Supply Condition Value ---------------------------------------------------- Velocity Magnitude (m/s) 4.5 X-Component of Flow Direction 1 Y-Component of Flow Direction 0 Z-Component of Flow Direction 0 X-Component of Axis Direction 1 Y-Component of Axis Direction 0 Z-Component of Axis Direction 0 X-Coordinate of Axis Origin (m) 0 Y-Coordinate of Axis Origin (m) 0 Z-Coordinate of Axis Origin (m) 0 Angular velocity (rad/s) 0 Temperature (K) 288 Turbulent Kinetic Energy (m2/s2) 1 Turbulent Dissipation Rate (m2/s3) 1 Turbulent Intensity (%) 0.036 115

Turbulent Length Scale (m) 1 Hydraulic Diameter (m) 0.53 Turbulent Viscosity Ratio 10 Participates in Solar Ray Tracing no Left Wall Condition Value ----------------------------------------------------------- Wall Thickness (m) 0 Heat Generation Rate (w/m3) 0 Material Name insulated_wall Heat Flux (w/m2) 0 Convective Heat Transfer Coefficient (w/m2-k) 0 Enable shell conduction? no Internal Emissivity 0.6 External Emissivity 1 Participates in Solar Ray Tracing? yes Glass Condition Value ----------------------------------------------------------- Wall Thickness (m) 0.024 Heat Generation Rate (w/m3) 0 Material Name glass Heat Flux (w/m2) 0 Convective Heat Transfer Coefficient (w/m2-k) 31.84 Free Stream Temperature (K) 301.75 Enable shell conduction? yes Internal Emissivity 0.84 External Emissivity 0.84 External Radiation Temperature (K) 287.36 Participates in Solar Ray Tracing? yes Transmissivity 0.36 116

Absorptivity 0.175 Floor Condition Value ----------------------------------------------------------- Wall Thickness (m) 0 Heat Generation Rate (w/m3) 0 Material Name insulated_wall Heat Flux (w/m2) 0 Convective Heat Transfer Coefficient (w/m2-k) 0 Enable shell conduction? no Velocity Magnitude (m/s) 0 Internal Emissivity 0.8 External Emissivity 1 Participates in Solar Ray Tracing? yes Solver Controls Equation Solved ------------------- Flow yes Turbulence yes Energy yes Relaxation Variable Relaxation Factor ---------------------------------------------- Pressure 0.3 Density 1 Body Forces 1 Momentum 0.2 Turbulent Kinetic Energy 0.8 117

Turbulent Dissipation Rate 0.8 Turbulent Viscosity 1 Energy 0.9 Pressure-Velocity Coupling ------------------ Type SIMPLE Discretization Scheme Variable Scheme ------------------------------------------------ Pressure Body Force Weighted Momentum Second Order Upwind Turbulent Kinetic Energy Second Order Upwind Turbulent Dissipation Rate Second Order Upwind Energy Second Order Upwind Material Properties Material: insulated_wall (solid) Property Units Method Value(s) --------------------------------------------------- Density kg/m3 constant 10 Cp j/kg-k constant 830 Thermal Conductivity w/m-k constant 0.1 Material: glass (solid) Property Units Method Value(s) ------------------------------------------------------ Density kg/m3 constant 2225 Cp j/kg-k constant 835 Thermal Conductivity w/m-k constant 0.062579997 118

Material: air (fluid) Property Units Method Value(s) --------------------------------------------------------------------- Density kg/m3 boussinesq 1.1799999 Cp (Specific Heat) j/kg-k constant 1006.43 Thermal Conductivity w/m-k constant 0.0242 Thermal Expansion Coefficient 1/k constant 0.00334 119

Appendix B Additional Thermal Comfort Study Results 120

Prediction of percentage dissatisfied due to draft at a height of 0.1 m in the occupied area of the atrium 0.1 meters above the ground Inlet / Outlet 121

Prediction of percentage dissatisfied due to draft at a height of 1.1 m & 1.2 m in the occupied area of the atrium 1.1 meters above the ground 1.2 meters above the ground Inlet / Outlet Inlet / Outlet 122

Prediction of percentage dissatisfied due to draft at a height of 1.3 m & 1.4 m in the occupied area of the atrium 1.3 meters above the ground 1.4 meters above the ground Inlet / Outlet Inlet / Outlet 123

Prediction of percentage dissatisfied due to draft at a height of 1.5 m & 1.6 m in the occupied area of the atrium 1.5 meters above the ground 1.6 meters above the ground Inlet / Outlet Inlet / Outlet 124

Prediction of percentage dissatisfied due to draft at a height of 1.7 m & 1.8 m in the occupied area of the atrium 1.7 meters above the ground 1.8 meters above the ground Inlet / Outlet Inlet / Outlet 125

Prediction of percentage dissatisfied due to draft at a height of 1.9 m & 2.0 m in the occupied area of the atrium 1.9 meters above the ground 2.0 meters above the ground Inlet / Outlet Inlet / Outlet 126