3-D Studies of Heat Transfer and Airflow in an Unconditioned Thai Buddhist Temple
By
A. Sreshthaputra, J. Haberl Department of Architecture
M.J. Andrews
Department of Mechanical Engineering
Texas A&M University College Station Texas 77843-3123
ABSTRACT
In this paper, we report 3-D Computational Fluid Dynamics (CFD) simulations, DOE-2 simulations, and measurements associated with the heat transfer performance of an unconditioned 100-year-old Buddhist temple located in Bangkok, Thailand. The heat transfer characteristics of this traditionally designed temple are reviewed and compared with modern designs using measurements. By comparison with DOE-2 and local measurements the overall performance of the CFD simulation has been validated. Large-scale, 3-D CFD simulations indicated poor thermal comfort conditions in this temple. The CFD/DOE-2 simulation suggested several remedial changes that could be implemented to improve the indoor comfort.
NOMENCLATURE
AS Surface area (m2)
Cp Specific Heat of Air (1.05 kJ/kg.K) D Building Length (m) = 20 m
fv Volumetric Porosity
fs Surface Permeability
H Enthalpy (J/kg)
h Heat transfer coefficient (W/m2K)
k Turbulence kinetic energy (m2/s2) kroof Roof wall thermal conductivity (W/m.K)
Nu Nusselt number
P Pressure (N/m2)
p
Modified pressure (N/m2)Pr Prandtl number
S Source term
Uo Overall heat transfer coefficient (W/m2K) u x-direction velocity (m/s)
v y-direction velocity (m/s)
Vinlet Inlet Air Velocity (m/s)
w z-direction velocity (m/s)
z z direction
Greek
∆rroof Roof thickness (m)
ε Turbulence kinetic energy dissipation rate (m2/s3) Γ Diffusion coefficient
µ Laminar viscosity (Pa s)
µeff Effective viscosity (Laminar + Turbulent) (Pa s) ρ Density (kg/m3)
INTRODUCTION
In hot-humid climates, particularly in developing countries, the use of air-conditioners is becoming common in residential and commercial buildings. However, there are buildings that do not use air-conditioning systems for various reasons, for example economic hardship and
religious constraints. Therefore, these buildings use only passive cooling by means of natural ventilation to obtain comfort conditions. Passive cooling design strategies in the hot-humid regions are difficult to accomplish because of excessive amounts of moisture in the air, which causes occupants to be uncomfortable. For this reason, passive cooling designs in the hot-humid climates need careful attention in terms of building design, orientation, planning, material selection, window treatment, and proper operation. Unfortunately, the traditional education in architecture today orients students toward designs with air-conditioning systems. Practical advice for buildings without air-conditioning system in hot-humid climates is not always given since
most passive cooling techniques were developed for either hot-arid or temperate climates where outdoor air has lower humidity, and buildings can take advantage of large diurnal temperature swings (Cook, 1989).
The introduction of modern architectural design into buildings that serve traditional and long standing purposes such as temples, has brought with it a host of heat transfer problems. In this paper, we study a newly built Buddhist temple located in an urban area of Bangkok, Thailand (Sreshthaputra, 2002). We have found from measurements that during the day the inside of the building heats up, with the result that it becomes uncomfortably hot. In contrast, more traditional Buddhist temple designs provide a cooler internal temperature during the heat of the day. Our results indicate that even with new construction techniques and materials, a new design of Buddhist temples has failed to keep the indoor cool, compared with the performance of the old temple constructed over one hundred years ago. Therefore, our purpose is to explore the cooling and heating effect of the temple in the traditional design.
To perform our study, we have adopted the DOE-2 simulation tool (LBNL, 1994; 2001), and also performed 3-D Computational Fluid Dynamic (CFD) simulations. DOE-2 was used because of its ability to simulate the overall thermal performance of the building using the hourly outdoor weather data. In addition, DOE-2 can handle many variables of interest such as hourly indoor temperature, surface temperature, and solar gain, which can be reported from the program.
However, DOE-2 needs the air infiltration rate calculated by CFD to provide accurate simulations of unconditioned buildings in which major heat gain components occur due to the incoming outside air. But CFD needs information regarding the building envelop such as solar heat gain, and surface temperatures to form accurate boundary conditions. Thus, in this application the simulation tools support each other. The fidelity of these two analysis procedures is quite different, with DOE-2 looking at the overall performance of the building, and CFD with the capability of looking at the detailed flows and physical processes occurring in the building.
However, as Figure 1a, 1b show, the architectural design of a temple involves a complex
arrangement of windows, columns, open areas, and roof, that is a leading edge challenge for a full 3-D, CFD simulation that we describe in this paper.
To our knowledge there is no previous work that studies the heat transfer performance of an old Buddhist temple, indeed, there are very few 3-D, CFD studies of real 3-D structures of any type. Our literature reviews found several papers from Awolesi et al., (1991), Yau and Whittle (1991), Vazquez (1991), Alamdari et al., (1991), and Awbi (1991a, 1991b), where CFD studies have been performed for flows over buildings, or through rooms. These simulations, like our own, use a control volume based CFD procedure that solves the fundamental equations that
govern the transport of mass, momentum, and heat. However, we have not found any study that uses CFD to study the solar-driven, heat transfer of such a complicated structure as the temple shown in Figure 1.
Before describing the DOE-2 and CFD simulations in detail it is worthwhile covering some of the basic information that will guide the analysis. First the temple was divided into 5 major components, namely; roof, attic, interior living spaces, windows, walls, and floor. The significance of the division is the ability to thermally analyze the building with DOE-2, and also to present a preliminary discussion of the most important aspects of the design on the heat transfer performance. Perhaps the most important observation is that the building temperature is dampened by the floor/ground temperature. The implications of this are that it would be hard to cool the building below the floor/ground temperature, and that this also presents a goal for the design. Secondly, thermal variations of the building are largely driven by the solar flux that varies during the day, and over the year. Thus, any simulation of the heat transfer characteristics of the temple must accurately account for the direct and diffuse solar flux on the roof, and sidewalls of the building, including the effects of shading. The attic, without ventilation, effectively provides an oven that sits atop the living space causing a ceiling-level heat source.
The walls and floor provide thermal inertia, and the walls and roof may also provide thermal insulation for exterior temperature and solar heat flux. The windows provide a means to insulate the interior spaces from hot air during the day, and ventilation by cooler air at night, thus damping out some of the thermal fluctuations in the living spaces.
With this initial qualitative perspective on how the temple operates, we next describe details of the data collection instruments, the DOE-2 calculations and the CFD simulations, with a discussion of what can realistically be expected. This is followed by results from the simulations and discussion. The paper closes with conclusions and acknowledgements.
INSTRUMENTATION
The indoor air temperature, relative humidity, and floor surface temperature of the case study temples were measured using micro data-loggers installed in secured boxes (Onset, 2002).
Six data-loggers were used to measure the room temperature and floor surface temperature (using a surface-mounted external sensor). For each temple, five measurements were taken: 1) indoor air temperature and relative humidity at the floor level, 2) indoor air temperature and relative
humidity at the ceiling level, and 3) the indoor floor surface temperature. Hourly data were retrieved once a month beginning in February 1999. In addition, wall surface temperature measurements were collected using a handheld infrared thermometer during the period from
October 1999 through January 2000. All data-loggers were calibrated at the Energy Systems Laboratory, Texas A&M University using a sling psychrometer, a glass thermometer, and a calibrated digital temperature/relative humidity sensor (Sreshthaputra, 2002).
DETAILS OF THE CFD SIMULATIONS Governing Equations
The 3-D CFD simulations presented in this paper have been performed with the HEATX code written by Andrews and reported in Prithiviraj and Andrews (1998a, 1998b). The HEATX code was originally written for the simulation of large shell-and-tube heat exchangers. However, since these devices have complex geometries, including many twisting flow passages, the code was well suited to the complex geometries of architectural design.
A statistical representation of turbulence was adopted to overcome the problem of
representing a wide range of time and length scales in turbulent flows. The Reynolds stresses that originate from the statistical averaging are modeled using the Boussinesq (1877) eddy viscosity approximation. A modified two equation k-ε turbulence model with source terms for turbulence generation and dissipation due buoyancy has been used (Snider and Andrews, 1994). Our reason to adopt the k-ε model is due to a lack of detailed experimental knowledge of the turbulence field within the temple. Hence, we feel it is better to use a turbulence model whose attributes, good and bad, are well known rather than a more sophisticated RNG or Reynolds stress model, for which the need in modeling a temple is not known in the present context. We also use the
“porosity” formulation embedded in the HEATX program.
Derivation of the equations governing fluid flow and heat transfer presented have been given in Prithiviraj and Andrews (1998a), the steady governing equation may be written:
( f ρφ V - f
Γφ∇φ ) = fS
φ⋅
∇ r
(1) where Γφ is the diffusion coefficient, f the porosity, and S a source for variable φ. The source
terms for the various φ‘s and the diffusion coefficients Γφ are given in Table 1.
For example, the continuity equation is expressed in the Cartesian (x-y-z) coordinates adopted for the simulation.
( ) ( ) ( )
0 z =
w + f
v + f
x u
fs s s
∂ ρ
∂
∂ ρ
∂ ρ
∂
∂ y (2)
The effective viscosity µeff is given by
µ µ ρ
ε
µ eff
2
= + C k
(3) where µ is the laminar viscosity, k is the turbulence kinetic energy, and ε is the turbulence
dissipation rate,
p
is the modified pressure given as:p = p + 2
(4)3 k
ρPr is the laminar Prandtl number. G is the production of turbulence kinetic energy from shear and buoyancy and C1, C2, Cµ, σk, and σε are turbulence model constants from Launder and Spalding (1974), and C3 was assigned by Snider and Andrews (1994).
Roof Heat Exchange Formulation
The variation of Ht across the roof appears through a cell heat source q, which is given as:
volume C /
H C A H U
= q
p in p out s
o
− (5)
where Hout and Hin are enthalpies of air outside and inside the roof respectively.
The HEATX code solves these governing equations using finite volumes (Patankar, 1980), in which the temple and surrounding space is subdivided into finite-sized control volume.
The control volumes are chosen so that the surfaces of the temple correspond to the surfaces of the control volumes. The control volumes are then used to form balances of mass, momentum and heat balances around a control volume and thus form an algebraic equation that corresponds to the fundamental governing partial differential equations. The very complex geometry of a temple precludes the use of body-fitted co-ordinates; instead we use a porosity formulation in which solid walls are assigned a porosity of 0, while open volumes are assigned a value of 1. This formulation restricts the accuracy of the simulation to the size of the cell, but this is also the limit of the numerical representation of gradients. Thus, the angled roof is represented by a set of steps. With sufficient number of volumes the geometries can be represented quite well and is aptly shown in Figure 2. One concern is the resolution offered to the small-scale details
associated with such items as flows through windows, or small vents. Ideally, the grid should be locally refined around the detailed items, however, the complexity of the temple geometry, and in particular the number of windows, columns and vents, prevents such high-resolution calculations.
Instead, we have chosen to perform a grid refinement and show that for the parameters we are
interested in our grids adequately resolve the flows and heat transfer. However, we recognize that the detailed flows around and through small-scale features such as windows may not be accurately represented. None-the-less we did check to see that the overall performance of the temple is well simulated.
Boundary Conditions and Computational Details
For the inflow boundary conditions, the outdoor weather data on a typical summer day at noon were used for input to the CFD simulation. In particular, the outdoor air was at 32 °C (90
°F) coming from the northeast direction at 1 m/s (2.24 mph). The turbulence kinetic energy and its dissipation rate were set according to the formulas; k = (0.05Vinlet)2 and å = (0.090.75 k 1.5)/D, giving values of at 2.5 x 10-3 m2/s2 and 2.5 x 10-5 m2/s3 respectively. The solar radiation received on the roof surface was assigned a value at 960 W/m2 obtained from DOE-2. The measured floor surface temperature was 28 °C (82.4 °F). The interior wall surface temperature was assigned as 30 °C (86 °F) obtained from DOE-2.
Computational grids used for the work presented herein are shown in Figure 2. The total number of computational cells is 313,000, which is considered a moderately high number of computational cells by current CFD standards. Our formulation involves solving equations for pressure, 3 components of velocity, temperature, turbulence kinetic energy, and its dissipation rate, both for steady and transient problems. For the calculation presented in this paper, we ran a typical steady state computation, which takes 2 days of CPU time on a non-networked Pentium III PC computer. For a grid refinement, we performed another calculation using a coarse grid size with a total of 87,690 cells (79 x 37 x 30), and the results were found to be consistent with those obtained from fine-grid calculations with 2.07 % difference for the indoor temperature at the center of the building, and 5.8 % difference for the temperature at the center of the attic.
DETAILS OF DOE-2 SIMULATIONS
DOE-2 (LBNL, 1994; 2001), developed by the Lawrence Berkeley National Laboratory, is an hourly-based thermal simulation program. This public-domain simulation program allows users to perform hourly building energy simulations for the whole year using ASHRAE’s algorithms. Heat transfer by conduction and radiation through walls, roofs, floors, windows, and doors are calculated separately using response factors, in which the thermal mass effects are carefully considered. Interior surface convection is computed based on user-specified convection coefficients, while the exterior convection is calculated by the program itself, based on the surface roughness and outdoor wind speeds.
DOE-2 was primarily designed to help building designers perform annual calculations of the energy consumed by heating and cooling systems. However, this study dealt with a building with no heating, ventilating, and air-conditioning (HVAC) system, and operated with natural ventilation at all times. So, to simulate the effect of natural ventilation with DOE-2, the temple was divided into two zones (i.e., indoor space and attic space), where heat gains from the outside and inside caused the indoor temperatures to float freely. In terms of heat gains by natural ventilation, both spaces were treated like closed boxes with outdoor air supplied to the spaces by means of air leakages from the outside. The amount of outside air infiltrations in ft3/min was obtained from the CFD calculation, where it was computed using the average velocity of air passing through all window areas and openings.
In our study, we used DOE-2 to accurately calculate the solar radiation flux on the roof and wall surfaces, which was later used in the CFD calculations. In turn, CFD was used to calculate the airflow rate and convection coefficients for DOE-2. Finally, to calibrate the DOE- 2/CFD simulation model, we compared the hourly indoor zone temperatures reported by DOE-2 with our measured indoor air temperatures from the Buddhist temple. Actual weather data was also used to drive the DOE-2 simulation (Royal Thai Meteorological Department, 2000).The comparison results in Figure 3 show a good agreement between the simulation and the measurements taken during a two-week summer period in 1999.
RESULTS AND DISCUSSION 1. Measurement Results
Figure 4 shows time-series plots of the indoor and outdoor conditions in the old temple as measured during the summer of 1999. During the mid-summer days, the outdoor air temperature swings were between 80-95 °F, while the floor of the temple remained constant at about 82 °F.
The indoor air temperatures followed the outdoor, however with less fluctuations. Clearly, both indoor and outdoor conditions were beyond the limit of thermal comfort, which is established generally at about 78-80 °F. It is also found that during the night the indoor temperatures were higher than the outdoor especially on the cloudy days. These results indicated that high-mass walls played a major role in keeping the indoor cooler than the outdoor during the day, but warmer during the night. In addition, on rainy days, with less solar radiation and cooler outdoor temperatures, the indoor was still hotter all day and night. This is clearly a result of high-thermal mass associated with lower rates of thermal radiation from building’s surfaces to the cloudy night sky. The building stored heat during the day, but it had a difficulty in releasing the heat back to the surroundings at night by convection and radiation because the temple shutters were closed
during the evening, and the night sky was usually cloudy, which helped prevent nighttime radiation. Therefore we felt that ventilating the building with cooler outdoor air at night and together with reduced daytime ventilation may produce more comfortable indoor conditions.
2. Calibrated DOE-2 Simulation Results
By supplying an average airflow rate and convection coefficient simulated by CFD to the DOE-2 program, DOE-2 calculated the indoor air temperatures, which were then compared with local measurements. The overall thermal performance of the case-study temple is presented in Figure 5. The figure indicates that the effort to combine DOE-2 and CFD to simulate the case- study temple was successful since the simulated hourly indoor temperatures have a good agreement with measured data throughout the year. However, there is a systematic difference between the amplitude of the diurnal temperature swings of the measured and DOE-2 simulated indoor temperatures. This results from a number of factors. First, an average maximum air infiltration rate calculated by a steady state CFD simulation using the average maximum outdoor wind speed may be slightly too high for a one-year hourly DOE-2 simulation. This caused DOE-2 simulated indoor temperatures to follow the outdoor temperatures that had more fluctuation than what really occurred inside the temple. A transient CFD calculation using an average 24-hour wind speed profile would be more accurate, and it would be interesting to pursue this in future work.
Second, although the infiltration rate assigned in DOE-2 might be appropriate, variations of daily ventilation schedules of the temple may cause this error. The ventilation schedule assigned in DOE-2 was obtained from a discussion with maintenance personnel. However, from our several site visits to collect the data, it was found that sometimes the temple was closed without reason during the afternoon. This caused the indoor temperatures to have less fluctuation when compared with the DOE-2 results.
To develop and calibrate the DOE-2 simulation model with the CFD infiltration rate, a statistical analysis of error between the simulated and measured values was performed. The calculated root mean squared error (RMSE) was 1.52 (we use this rather than the CV-RMSE since the CV-RMSE would reflect the use of Farenheit and might be misleading). The normalized mean-biased error (NMBE) was –1.12 %. They were considered excellent compared to the ASHRAE-sponsored Predictor Shootouts I and II (Kreider, J. and Haberl, J., 1994; Haberl, J. and Thamilseran, S., 1996). Once the calibrated simulation model was developed, it was then used to obtain a better understanding of how the building performed thermally, including new design strategies and changes to operational modes.
3. CFD Simulation Results
Figure 6 shows the airflow across the building. The outside air comes in at a 45° angle to the front entrance, passing through the colonnade and then through the interior space. It is found from the velocity plot that airspeeds increase significantly at the outside corners and at the side openings. This agrees with our observation taken at the site, where we noticed increasing airspeeds at the windows, producing slightly more comfortable conditions.
However, inside the temple space, where major indoor religious activities take place, it is found that the air velocities decrease greatly. Air stagnation that occurs in the interior space causes the indoor conditions to be stuffy and less comfortable due to poor ventilation. This agrees with the observation at the site, where smoke produced by candles and incenses is often trapped inside the space, which further deteriorates the indoor environment. This insight gained from the CFD simulation points to the need to redesign the proper sizes and locations of windows that would produce more airflow across the building in the evening.
Figure 7 shows an effect of incoming air flowing through the building. In this velocity plot the airspeeds seem to increase significantly across the openings with vortices occurring right above and below the window levels. It is also found that stagnation causes the indoor air to be trapped at the level just below the ceiling. Based on observations made at the site, this condition leads to two undesirable outcomes to the case-study building. First, smoke produced by incenses rises and is trapped at the ceiling level. This causes the ceiling and interior decorations (e.g. wall paintings, chandeliers) to become stained over time.
Second, since the ceiling is hot during the day, air stagnation tends to decrease thermal convection causing the ceiling surface not to cool down. The hot ceiling radiates heat to occupants, which contributes to already uncomfortable conditions. It is anticipated that
ventilating the air at the ceiling level could solve these problems. However, designers must keep in mind that stirring hot air from the ceiling down to occupancy level may not produce a desirable effect; so ceiling fans may not be a good option unless the building is properly designed.
Figure 8 shows pressure profiles along the flow domain with zero pressure reference. In this figure it is clear that the building becomes as an obstacle to the flow field. Positive pressure occurs at the location where the air first reaches the building, and negative pressure occurs where the air leaves the building. The negative pressure is also clearly seen at the openings where air is passing through with high velocities as seen in Figure 7. These pressure differentials play a major role in ventilating the building because they provide suction that drive airflows across the
openings at higher speeds.
However, the high positive pressure at the inflow also indicates that the building is not designed properly for the outdoor air to pass through at the maximum ventilation rate. If the new design needs more ventilation, redesigning the building with proper orientation to the direction of the prevailing wind could provide more desirable effects. This problem may be solved by adding building components (e.g., fins, overhangs) that help direct the incoming air to the inside of the building.
Figure 9 shows plots of the temperature of the air passing through the building with buoyancy effects considered. Solar radiation heats up the outside roof surfaces, and heat is transferred to the attic, causing the attic to be hotter especially in the area right beneath the roof.
Inside the attic, buoyancy causes the attic air to circulate and it stirs and mixes hot air from the roof with the cooler air at the ceiling. It is found that the back roof (leeward) is hotter than the front (windward). This is because the incoming air takes away an amount of heat from the windward roof surface through convection, while at the back roof; a re-circulation of air occurs and it reduces the local heat transfer by convection. This hot air vortex also acts as an insulation layer that prevents convective removal of heat, thus heating up the back roof.
CONCLUSION
An accurate assessment of naturally ventilated buildings in a hot-humid climate was accomplished with an in-depth DOE-2 and CFD analysis, a combination of advanced simulation tools. Detailed investigations of the space planning, building material, configuration of the openings, and operational schedules are essential for developing and testing of practical passive cooling techniques for unconditioned buildings in the tropics. This investigation is useful for building designers in terms of how to redesign and renovate this kind of building to improve indoor comfort conditions without using mechanical A/C system. Our preliminary analyses indicate that the traditional Buddhist temple design can be improved with several design and operation strategies, including: building orientation, a low-absorptivity roof surface, ceiling insulation, solar shading, attic ventilation, and night ventilation of the temple space. Ceiling fans may not be a good option unless the building is properly designed. Detailed design guidelines and additional details concerning the work can be found in Sreshthaputra (2002).
ACKNOWLEDGMENTS
This work was supported by the Department of Architecture and the Department of Mechanical Engineering, Texas A&M University. The instrumentation used for the
measurements were supported by the Royal Thai Government and the American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE) through a student grant.
REFERENCES
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2 (June)
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Royal Thai Meteorological Department. (2000). Bangkok Hourly Weather Data. Bangkok, Thailand Snider, D.M. and Andrews, M.J. (1996). "The Simulation of Mixing Layers Driven by Compound
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Sreshthaputra, A. (2002). Building Design and Operation for Improving Thermal Comfort in Naturally Ventilated Buildings in a Hot-Humid Climate. Ph.D. Dissertation, Department of Architecture, Texas A&M University, in preparation.
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The Institute of Mechanical Engineers.
φ
S
φ Γφu
x u
∂ µ ∂
∂
∂ x
eff- p
+ µeffv
y - p
effy v +
µ
∂∂
∂
∂
µeffw
g
zz +
- p µ
eff∂ ρ
∂
∂
z w
+ ∂ µeff
H
roof
−
Cp H Cp
H Volume
A
U
o roof outsidecell insidecell µ µPr + Pr
t t
k G -ρε
µσ
t k
ε
C k k - G C
2 2 1
ρ ε
ε
µσε
t
Table 1. Coordinate Source Terms and Diffusion Coefficients.
Figure 1a. Exterior View of the Old Temple Showing the Front Entrance
Altar Main Ent'
Figure 1b. Ground Floor Plan of the Old Temple
Figure 2 Computational Grids Showing the Case-study Temple and its Surroundings
Summer: Indoor Temperature (F)- DOE-2 Calculation VS Measurement
60 65 70 75 80 85 90 95 100
3/29/99 3/30/99 3/31/99 4/1/99 4/2/99 4/3/99 4/4/99 4/5/99 4/6/99 4/7/99 4/8/99 4/9/99 4/10/99 4/11/99
DOE-2 Measured
Figure 3 Indoor Temperature: DOE-2 Simulation Results as Compared With the Measurement from 3/29/99 to 4/11/99
Summer Days:
0 20 40 60 80 100 120 140
3/29/99 3/30/99 3/31/99 4/1/99 4/2/99 4/3/99 4/4/99 4/5/99 4/6/99 4/7/99 4/8/99 4/9/99 4/10/99 4/11/99 degree F
0 300 600 900 1200 1500 1800 2100 W /m2
Indoor Outdoor Ground Attic (sim) Solar
Figure 4 Time-series Plot of Indoor and Outdoor Conditions of the Case-study Temple as Measured During Summer 1999 (3/29/99 - 4/11/99).
Indoor Temperature (F): DOE-2 Calculation VS Measurement (5th Calibration)
40 50 60 70 80 90 100
1/1/99 1/16/99 1/31/99 2/15/99 3/2/99 3/17/99 4/1/99 4/16/99 5/1/99 5/16/99 5/31/99 6/15/99 6/30/99 7/15/99 7/30/99 8/14/99 8/29/99 9/13/99 9/28/99 10/13/99 10/28/99 11/12/99 11/27/99 12/12/99 12/27/99
DOE 2 Measured
Figure 5 DOE-2 Indoor Temperature Simulation Results as Compared With On-site Measurements for a One-year Period (1/1/99 – 12/31/99).
Figure 6 Vector Plot Showing Airflow Through the Building at Noon on 3/30/99.
Figure 7 Vector Plot Showing Airflow Across the Openings of the Building at Noon on 3/30/99.
Figure 8 Contour Plots Showing Air Pressure Across the Building at Noon on 3/30/99.
Figure 9 Contour Plots Showing the Temperature of the Air Passing Through the Space With Buoyancy Considered on a Sunny Day at Noon (3/30/99)
