Journal Identification = ENB Article Identification = 3230 Date: July 19, 2011 Time: 7:44 pm

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Energy and Buildings 43 (2011) 2404–2413

Contents lists available at ScienceDirect

Energy and Buildings

j our na l ho me p age: www.elsev ier .com/ locate /enbui ld

educed-scale building model and numerical investigations to buoyancy-drivenatural ventilation

hristine Walkera, Gang Tana,b,∗, Leon Glicksmana

Massachusetts Institute of Technology, Building Technology Program, 77 Massachusetts Avenue, Cambridge, MA 02139, United StatesUniversity of Wyoming, Department of Civil and Architectural Engineering, 1000 E. University Avenue, Dept. 3295, Laramie, WY 82071, United States

r t i c l e i n f o

rticle history:eceived 18 November 2010eceived in revised form 9 April 2011

a b s t r a c t

Similarities of a reduced-scale building model using air as the working fluid for buoyancy-driven naturalventilation have been analyzed and experiments were carried out using the scaled model for a commonnatural ventilation building, which has open office floor plans connected to a central atrium. Both open

ccepted 30 May 2011

eywords:atural ventilationcaled modelFD

and closed cases have been investigated for the stack vents, located at the top of the atrium. Inputs forthe scaled building model were taken from results measured in the prototype building by the authors.The parameters of the scaled building model’s experiments thus were used as inputs into a compu-tational fluid dynamics (CFD) simulation model to compare predicted and measured airflow patterns,temperatures and velocity distributions in the scaled building model.

rototype building

. Introduction

Natural ventilation is driven by two forces, buoyancy effect andind pressure. Often design characteristics, such as ventilation

tacks, are used to assist buoyancy driven ventilation [1]. Under-tanding how natural ventilation affects the indoor environmentf a building, particularly the ventilation rates and indoor air tem-erature, is important in evaluating the design of these low energyuildings. The most popular methods for predicting or evaluat-

ng ventilation performance include analytical models, empiricalodels, small-scale experimental models, full-scale experimen-

al models, multizone models, zonal models, and computationaluid dynamics (CFD) models [2], as well as field monitoring stud-

es. In general, field monitoring studies (e.g., visualization and floweasurement) of buoyancy ventilation in full-scale buildings are

hallenging due to the existence of ambient wind. Scaled mod-ls setting up in a controlled chamber will not only overcome thisroblem but also thoroughly investigate buoyancy-driven ventila-ion under different geometric and/or heat load scenarios. Scaled

odels are used to simulate ventilation trends and the resultingata may be extrapolated to the full scale prototype. In order for

he results of the scaled models to be applicable to the full-scaleuilding, there are several specific areas of similarity that shoulde achieved: similarity of velocity distribution, airflow pattern,

∗ Corresponding author at: University of Wyoming, Department of Civil and Archi-ectural Engineering, 1000 E. University Avenue, Dept. 3295, Laramie, WY 82071,nited States. Tel.: +1 307 766 2017; fax: +1 307 766 2221.

E-mail address: gtan@uwyo.edu (G. Tan).

378-7788/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.enbuild.2011.05.022

© 2011 Elsevier B.V. All rights reserved.

and temperature distribution. These criteria can be approximatelysatisfied when geometric similarity is met, and kinematic and ther-mal similarities are within reasonable ranges [3]. For scaled modelexperiments, a significant amount of previous research [4,5] usedwater as the working fluid in which buoyancy forces are producedby salinity differences within the fluid. Alternatively, using air asthe working fluid may make the understanding to the flow pat-tern and flow rates more straightforward since the buoyancy forcescan be directly triggered with internal heat loads the same as inthe real world. Therefore, this paper presents results from a scaledbuilding model using air as the working fluid for buoyancy-drivennatural ventilation. Necessary dimensional and similarity analysispresented in this paper shows that the dimensionless character-istic parameters of a scaled model using air as the working fluidare comparable to a scaled model using water as the workingfluid.

Besides predicting ventilation performance in buildings, scaledmodels in this paper were also used to generate data to validatenumerical models, especially CFD models. In cases with relativelysimple buildings, such as a single zone with one lower and oneupper level opening, analytical models can be developed to deter-mine the neutral plane based on density differences, temperaturedifferences, or surplus heat [6,7]. On the other hand, for morecomplex geometries, often CFD is used to model the detailed per-formance of natural ventilation [8]. This paper uses a CFD model toinvestigate the buoyancy-driven ventilation of the scaled model

and the results have been compared against the scaled model’smeasurement. Thus, the scaled model serves to validate the useof CFD model to simulate buoyancy driven natural ventilation. Sev-eral aspects of the models have been compared, including internal

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C. Walker et al. / Energy and Buildings 43 (2011) 2404–2413 2405

Nomenclature

g gravitational force per unit mass, m/s2

� density, kg/m3

u velocity, m/sp pressure, N/m2

x coordinate, m� dynamic viscosity, N s/m2

coefficient of thermal expansion, 1/Kcp specific heat, kJ/(kg K)� temperature, K� thermal conductivity, W/(m K)T temperature, KH characteristic height, mRe Reynolds numberPe Peclet numberAr Archimedes numberGr Grashof numberPr Prandtl numberQ heat flux, kW/m2

A opening area, m2

B buoyancy flux, m4/s2

� difference

Subscript/superscriptref reference pointB buoyancy

tt

2

iiaitce(ttbt

* dimensionless operator∞ infinite

emperatures, velocities, and airflow patterns, for two configura-ions: atrium stack vents open and closed.

. Prototype building

The prototype building is a naturally ventilated building locatedn a temperate climate. The building is a commercial office build-ng, three stories in height, with an open floor plan connected ton atrium configuration. The floor plan, area included in the models shown by dashed lines in the floor plan and the cross-section ofhe prototype building in Figs. 1 and 2. As outlined in Fig. 1, theentral section of the building, shown in dashed lines for the mod-led area, is naturally ventilated and measures 33 m × 30 m × 15 mlength × width × height), which includes three occupied floors and

he stack portion of the atrium. The atrium roof has 5 evenly dis-ributed stack vents in parallel, to assist with ventilation of theuilding. Three of these stack vents are within the central section,he modeled area. The two areas seen in Fig. 2 (ground floor north

Fig. 1. Prototype sample floor plan (dashed lines indicate modeled area).

Fig. 2. Prototype cross section (arrows show operable window heights).

and the second floor south) that are not included in the model arenot conditioned by natural ventilation. They are separated from themodeled area by walls or fully closed-off by doors. The prototypebuilding has upper and lower windows across the fac ade on eachfloor for the purpose of ventilation. Both the lower and upper win-dows are awning-type windows, which leads to a certain degree ofdifficulty when modeling an effective opening area. The awning-type windows protrude from the building at an angle, allowing airto enter not only in the horizontal plane, but also through triangularshaped vertical pieces. Through field measurements using a specialwindow airflow device, the ratio of ventilation effective area to theoverall window area was determined to be approximately 30% [9].

Field monitoring studies obtained pertinent data through mon-itoring and observations in the building over a 16-month periodof time. These data include internal temperatures, air flow pat-terns, air velocities, energy usage and internal loads, and numberof occupants. These data were then used to define the scaled andCFD model parameters if needed. A combination of electrical mon-itoring and personnel count provided the needed data for the totalheat input into each floor of the building. This paper adopts theaverage of a weekday during peak hours as the internal heat load,approximately 20 W/m2. Since the summer conditions are of mostimportance when the windows are open and the natural ventila-tion in use to cool the building, the models are focused on naturalventilation in summer.

3. Scaled building model

Considerable research have been carried out on buoyancy drivennatural ventilation [10], though not for this particular geometryscaled down using air as the working fluid. Additionally, an under-standing of the pure buoyancy-driven ventilation, rarely occurringin the real-world without any wind, will provide a basis on which tobuild the understanding of airflow and temperature patterns whenwind-assisted flow is also present.

3.1. Similarity analysis

We start with dimensional analysis, where a simplified formof the Navier–Stokes equation and energy equation for air willbe re-written into dimensionless style. The one-dimensionalNavier–Stokes equation for steady, incompressible and turbulentflow is given by:

∂u

∂x(�u) = −∂p

∂x+ �

∂

∂x

(∂u

∂x

)− �g �T (2)

where � is the air density at some reference temperature, �T is thetemperature difference from air temperature at infinite far away(T∞), and � is the dynamic viscosity.

Journal Identification = ENB Article Identification = 3230 Date: July 19, 2011 Time: 7:44 pm

2 Build

�

wtd

vol

u

w

vvb

pa

u

u

w

pan

b

�

ibmbmiti

406 C. Walker et al. / Energy and

The energy equation is given by:

cpu∂�

∂x= �

∂

∂x

(∂�

∂x

)(3)

here cp is the specific heat of air and � is the thermal conduc-ivity of air and � = (T − T∞)/�Tref while �Tref is the temperatureifference between the inlet and outlet.

Here we introduce another parameter, the reference buoyancyelocity, which is dependent on the height between the inlet andutlet as well as the temperature difference between inlet and out-et. The reference buoyancy velocity is given by:

B =√

gˇH �Tref (4)

here H is the height between the inlet and the outlet.This reference buoyancy velocity is the ideal upper limit for the

elocity without any viscous forces and can be substituted for theelocity term in a buoyant Reynolds number, which, when squared,ecomes the Grashof number.

We define dimensionless factors x* = x/H, u* = u/uB, and p∗ =/�u2

B. Then substitute them into Eq. (2) along with the Boussinesqpproximation:

∂u∗

∂x∗ (u∗) = −∂p∗

∂x∗ + �

�ouBH

∂

∂x∗

(∂u∗

∂x∗

)− gH �Tref

u2B

� (5)

∂u∗

∂x∗ (u∗) = −∂p∗

∂x∗ + 1ReB

∂

∂x∗

(∂u∗

∂x∗

)− Ar� (6)

Also substitute into Eq. (3)

∗ ∂�

∂x∗ = �

�cpuBH

∂

∂x∗

(∂�

∂x∗

)(7)

∗ ∂�

∂x∗ = 1ReBPr

∂

∂x∗

(∂�

∂x∗

)(8)

here,

�

�uBH= 1

RegH �Tref

u2B

= Ar

�

�cpuBH= 1

RePr

(9)

Here note that the Archimedes number equals to one for theure buoyancy-driven condition. �Tref can be obtained throughn energy balance: heat input equals heat loss through advection,eglecting heat loss through the envelope:

Q = �AcpuB �Tref

Q = �Acp

√gˇH�Tref �Tref

(10)

Solving for the reference temperature, �Tref, this equationecomes:

Tref =[

Q/A

�cp

√gˇH

]2/3

(11)

Three similarities, geometric, kinematic, and thermal similar-ties, should be achieved for the scaled model to the full scaleuilding. Geometric similarity is the easiest of these criteria toeet; simply scale down the linear dimensions of the full-scale

uilding equally for three dimensions. In this paper, the scaled

odel is one-twelfth of the size of the prototype building, both

n overall geometry and in effective opening sizes. For example,he aspect ratio of occupied zone length to atrium height was setn the reduced scale model to equal that ratio in the prototype, 3.6.

ings 43 (2011) 2404–2413

For kinematic similarity, the ratios of the fluid velocities and accel-erations must be equal. From similarity theory, a scale model forbuoyancy-driven natural ventilation will replicate the kinematicboundary conditions, of the prototype if the Prandtl, Reynolds, andArchimedes numbers (Archimedes number combines the Grashofand Reynolds numbers) are identical for both cases [11]. However,it is impossible to achieve this goal [12] when using air as theworking fluid, although it does match the Prandtl number. Sincefor pure buoyancy ventilation the Archimedes number is equal toone, the Reynolds and Grashof numbers are not independent whereReynolds number is equal to the square root of Grashof number.Literature has stated that under this situation it is impossible tomatch Grashof number while the most important is to ensure thatflow falls in the fully turbulent region [13], i.e. Re > 2.3 × 103.

When evaluating the dimensionless parameters, the charac-teristic length selected will have an impact on the Reynolds andGrashof numbers, and therefore the flow regime and heat transferwithin the model. For the scaled air model, the primary characteris-tic length used in evaluating the occupied zones was the hydraulicdiameter of the cross section of a single floor. The hydraulic diam-eter is one of the determinant factors describing the main flowthrough the model, which gives a characteristic length of 0.53 m.However, the height of the atrium is used in evaluating the buoy-ancy velocity, since it is the height difference between the inletand the outlet, at the top of the stack, which drives the air flow.The Reynolds number for the model is approximately 8.03 × 104,which indicates fully-developed turbulent flow. To compare theair model with water model, Table 1 shows the values of dimen-sionless parameters for the full-scale building, scaled air and scaledwater models. The prototype building’s air flow is also in theturbulent regime (Re = 1.42 × 106). Both prototype building andscaled-models using air or water as working fluids have Re andPe values in excess of 103. Therefore, in some cases, the flow inthe scaled-models may be independent of viscous and diffusiveeffects. Research work discussed in [12] has compared the lab-oratory models and full-scale measurements and confirmed thatlarge-scale flows are represented at scaled-models.

3.2. Scaled building model descriptions

A scaled model of the naturally ventilated prototype buildingwas created at one-twelfth scale, and evaluated using air as theworking fluid. The central section of the building was modeled,encompassing two floors of open floor office plan and the centralatrium. The buoyancy forces were created by simulating the inter-nal loads of the building using heaters. In order to scale the internalloads, data from the prototype building were used to appropriatelysize the heaters. The prototype building’s total internal load wasmeasured to be 30 kW, which resulted in a distributed heat load ofapproximately 20 W/m2. Therefore the scaled model heaters weresized to twelve times the heat input of the prototype building, or235 W/m2, to provide the buoyancy flux ratio same as the geometricratio (i.e. 1/12), and in [12] the buoyancy flux B is defined as:

B = gˇQ

�cp(12)

Inside the model there are a total of eight, 6 in. by 10 in. heaters,rated at 5 W/in2. This represents all of the interior loads for the pro-totype or typical commercial office building, including plug loads(computers, printers, etc.), lighting loads, and occupant loads.

The size of the model is 2.9 m × 1.8 m × 1.2 m(length × width × height). It has two occupied zones on each

side of the atrium; at the ground and first floors on the southernhalf of the model, and at the first and second floors of the northernhalf of the model. The opening between the occupied spaces andthe atrium is not quite restricted except a 0.9 m high clear glass

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C. Walker et al. / Energy and Buildings 43 (2011) 2404–2413 2407

Table 1Summary of values and dimensionless parameters for full-scale building, scaled air and scaled water models.

Air-building Air-model Water model Water model

Scale factor 1 12 12 20ˇ (1/◦K) 0.0033 0.0033 0.0002 0.0002�T (◦K) 5 30 6 6g′ = gˇ�T 0.163 0.970 0.012 0.012H = height of atrium (m) 15 1.25 1.25 0.75Lcs (m) 6.32 0.53 0.53 0.32Pr 0.7 0.7 7.0 7.0

6 8.0 4 5 4

5.66.4

gtbobowibatwtmsTb

(cbsi(t‘tF

isalhcs

Re 1.42 × 10Pe 9.98 × 105

Gr 2.03 × 1012

rille in the prototype building between the occupied space andhe atrium. There are seven sets of windows per floor level onoth the north and south fac ades. Each window set is comprisedf an upper and lower window opening. For the north side of theuilding, these openings are 2 cm × 17 cm (height × width), whilen the south fac ade they are 2 cm × 12 cm (height × width), sizes ofhich represent windows’ effective areas in the prototype build-

ng. In addition, this accurately follows the design in the prototypeuilding, where the southern openings are smaller overall in lengths compared to those on the north side of the building. Due tohe complex geometry of the awning-type windows, the openingsere simplified to a vertical cut-out in the fac ade. There are also

hree openings along the center of the roof of the atrium, whicheasure 7.5 cm × 7.5 cm. These openings are representative of the

tack vents used to assist ventilation in the prototype building.hese openings can either be open or closed depending on the caseeing modeled.

The model was constructed of medium density fiberboardMDF), plywood and insulation board. The walls of the model wereomprised of a single layer of 1/2 in. MDF and 1(1/2) in. insulationoard. The floors within the model, including the roofs, were con-tructed of 1/8th inch plywood and a layer of insulation board. Thensulation was required to reduce the heat loss to the test chamberexternal environment) and the heat transfer between floors. Inchhick dowel rods were used as support columns along the atrium. Aview window’ made of Plexiglas was incorporated into the modelo aide in airflow visualization of the interior portions of the model.ig. 3 shows the picture of the scaled air model.

The scaled model is situated in an insulated test chamber thats 5.16 m × 3.65 m × 2.43 m (length × width × height). The dimen-ions of the test chamber along with the overall model dimensionsre presented in Fig. 4. All of the surrounding walls have an insu-

2

ating value of R-30, or 5.3 m K/W. The test chamber has its owneating, ventilating, and air-conditioning unit and controls. Theontrol interface allows the operator to control set-points of theystem, including supply air temperature and airflow rate. Dur-

Fig. 3. Picture of the scaled air model in the test chamber.

3 × 10 1.54 × 10 7.14 × 102 × 104 1.08 × 106 4.99 × 105

5 × 109 2.36 × 1010 5.10 × 109

ing experiments, the scaled building model’s openings did not facenor were they close to any test chamber’s supply air diffusers inorder to eliminate any stray air currents and simulate the purebuoyancy-driven natural ventilation passing through the scaledmodel. This paper investigates steady-state buoyancy-driven nat-ural ventilation under different scenarios. For each scenario, whenthe experiment reaches steady state, the test chamber air wouldstay at a nearly constant temperature distribution because (1) theheat flux from heaters is constant; and (2) the air-conditioning sys-tem serving the test chamber is maintained at a constant air volumeand supply air temperature.

3.3. Model experiments

The scaled building model was outfitted with 50 thermocouplesand 6 globe anemometers, both connected to separate data loggingdevices. The thermocouple tips were painted silver in order to mini-mize the impacts from radiation. Accurately measuring the ambientconditions (in the test chamber) is important to understand ver-tical temperature stratifications and determine the inputs for theCFD model. For the buoyancy-driven experiments, the temperatureof air-conditioning supply air to the test chamber was controlledbetween 13 and 22 ◦C for various ventilation scenarios. Air temper-ature entering the model was slightly higher than the supply airtemperature due to heat gains occurring in the test chamber. Thesurrounding wall temperatures of the test chamber were measuredin the range of 20–23 ◦C.

Two cases were evaluated in this paper: with the atrium stackvents open and with them closed, under supply air temperatureof 20 and 13 ◦C, respectively. The model was allowed to run whilebeing monitored to ensure it reaches a steady state when the tem-perature variation falls within ±0.5 ◦C for more than 10 min. When asteady state occurred, air velocity and temperature measurements

were taken at the entry and exit points of airflow, and through-out the internal space. Besides the globe anemometers inside themodel, a hand-held hot-wire anemometer was also used to conductair velocity measurements at the window face in order to calculate

Fig. 4. Reduced-scale model and test chamber dimensions.

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2 Buildings 43 (2011) 2404–2413

awtstvt

4

sgcbcsabtttsa–cattdibsiaDnCt2tawh

atvfwppsitqTa

5

tpv

the scaled building model were recorded once the model reachedsteady-state. It is found that the internal temperatures are cooleston the ground floor, and warmest on the second floor. There wassome amount of temperature variation in both the scaled model

408 C. Walker et al. / Energy and

n airflow balance. Air velocities at multiple locations along theindow face were monitored and the volume flow rate through

he window was thus calculated using the average air movementpeed, which was adjusted using empirical discharge coefficientshat were obtained by flow hood measurements at sample stackents and windows. Smoke pencils were used to view airflow pat-erns of air throughout the internal space.

. CFD model

A CFD model with the same geometry and dimensions as thecaled building model was created using the PHOENICS [14] pro-ram that is a general-purpose software package. The boundaryonditions of the CFD model were made to simulate the test cham-er’s actual conditions, including the model’s location within thehamber, dimensions, and measured wall temperatures. In a briefummary, the CFD model uses following boundary conditions: (a)n conditioned room with the same dimensions as the test cham-er; (b) the surrounding walls of the room having the same constantemperature distribution as the test chamber’s internal surfaceemperature; (c) a same size of inlet locating at the same place ashe air-conditioning system’s air diffuser in the test chamber whichupplies the same amount of airflow at the same temperature; (d)

same size of outlet locating at the same place – ceiling mounted as the return air grille in the test chamber. The CFD model hasutouts for the window and stack vent openings, at the same sizes the scaled air model. Due to the good insulation, adiabatic condi-ions were used to approximate all external walls and the floors ofhe scaled model in CFD simulation. This simplification is made toetermine the idealized case that has no heat loss to the surround-

ng environment, though this is not quite the same case in the scaleduilding model. The CFD model also uses prescribed heat sources toimulate the heaters in the physical scaled model, and therefore thenternal loads for the prototype building. The heaters are located inpproximately the same location as in the scaled building model.ue to the elevated temperature, radiation in the scaled model doesot accurately simulate radiation in the prototype building. In theFD model, radiation in the heated, or occupied, zone was assessedhrough an iterative process. It was determined that approximately0% of the heater power was radiated to the ceiling from the highemperature heater surfaces, thereby increasing the temperaturest that level of the zone. To account for this, a second heat sourceas prescribed in the CFD model, converting 20% of the originaleat input from the ceiling back into the space.

The CFD model uses k–ε model as the turbulence model. Chennd Glicksman [15] concluded that the RNG k–ε model provideshe best results building ventilation simulations. Previous work hasalidated the method of using CFD for full building simulations andor single full sized rooms [16,17]. Data from the prototype buildingere once used to study a full scale CFD simulation of the building’sarticular zone for an interesting flow pattern [18]. However, thisaper is more focused on validating CFD model using data from thecaled building model’s experimental work. The use of air veloc-ties, internal temperature distribution and airflow patterns fromhe scaled building model ensures that the CFD simulation is ade-uately modeling the phenomena occurring in the scaled model.he CFD model uses a fine grid mesh (approximately 63 × 59 × 72)nd enough iteration to ensure that the results converged.

. Results

A comparison was made between the data obtained from thewo models (reduced-scale building model and CFD model): tem-erature and airflow, including internal and external temperatureariations, air velocities and internal air flow patterns. Two cases

Fig. 5. Ground floor plan and thermocouple locations in the prototype building.

were compared, with all three stack vents open and with themclosed.

5.1. Internal temperatures

The surrounding conditions of the scaled building model withinthe experimental test chamber were recorded and used as input forthe CFD model. Then the resulting internal temperature measure-ments were recorded and are compared to the CFD simulation. Datafrom the thermocouples in the scaled building model are comparedto similar location points in the CFD model in order to comparethe temperature variation across each floor and between floors(Figs. 5–7).

5.1.1. Stacks openWith the stack vents open, the internal temperatures within

Fig. 6. First floor plan and thermocouple locations in the prototype building.

Journal Identification = ENB Article Identification = 3230 Date: July 19, 2011 Time: 7:44 pm

C. Walker et al. / Energy and Buildings 43 (2011) 2404–2413 2409

F

aitotwrifll

mFeacft

0

10

20

30

40

50

60

70

1 2 3 4 5 6 7

Physical ModelCFD Model

Location

Tem

pera

ture

(oC

)

ig. 7. Second floor plan and thermocouple locations in the prototype building.

nd the CFD model from the window, where ambient air enterednto the heated space, and the atrium, where the air exhausted uphrough the stack vents. The temperature varied between 35 ◦Cn the ground floor, in a jet from a window, to almost 59 ◦C onhe second floor. Note that the temperature in the scaled modelas increased to ensure that the flow was in the fully turbulent

egime. The temperature comparison between the scaled build-ng model and the CFD simulation are presented in Figs. 8–10, byoor level while Figs. 5–7 show the corresponding measurement

ocations.There are some small disparities between the scaled building

odel and the CFD model results (e.g., see location point #1 inigs. 8 and 9), which is in part due to slight differences between thexact location of the thermocouple in the scaled building model

nd the point investigated in the CFD model. The temperaturean vary if the measurement for either model is in a jet flowrom the window, or in a lower velocity area outside of, or onhe edge of, a jet. Other possible reasons that may introduce the

0

10

20

30

40

50

60

70

1 2 3 4 5 6 7 Locat

Tem

pera

ture

(oC

)

Fig. 9. First floor temperature comparisons (st

Fig. 8. Ground floor temperature comparisons (stacks open, ambient temperature20 ◦C).

disparities are radiative effects of the heaters within the heatedzone and the heat transfer between floors in the scaled model.In contrast, the CFD model assumes adiabatic walls and floors,and therefore a space is not influenced by heated zones above orbelow.

The average internal temperatures for each zone are calculatedto investigate the temperature variation between floors. It wasfound that the temperature varied about 8 ◦C from the ground floorto the second floor, as shown in Table 2, where the floor aver-age includes atrium area while the heated zone average does notinclude atrium area. On average, the internal air temperatures in the

scaled model for the stacks open case vary from 43 to 51 ◦C fromthe ground floor to the second floor, with a temperature differenceof approximate 8 ◦C.

8 9 10 11 12 13 14 15

Physical ModelCFD Model

io n

acks open, ambient temperature 20 ◦C).

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2410 C. Walker et al. / Energy and Buildings 43 (2011) 2404–2413

Table 2Stacks open case: average temperature variation by floor and orientation.

Floor avg (◦C) Heated zoneavg (◦C)

South halfavg (◦C)

North halfavg (◦C)

Ground floorScaled air model 43.34 42.28 42.28 –CFD model 44.05 43.39 43.39 –

First floorScaled air model 45.16 43.36 43.89 43.03CFD model 42.72 41.00 40.51 41.49

9.15

8.66

5

pslwwtgtm

sspialssto

5

a

F2

the CFD and scaled building models for air velocity and air flowrates.

Overall, the measured air velocities for both the lower windows

Second floorScaled air model 51.26 4CFD model 51.04 4

.1.2. Stacks closedIn the case where the atrium stack vents were closed, the tem-

eratures within the space shifted, and the temperatures in theecond floor were warmer. This was due to the heated air from theower floors exhausting through the second floor lower and upper

indows. As with the stacks open case, the cooler temperaturesere on the ground floor, and the warmest temperatures were on

he second floor. The temperatures varied between 39 ◦C on theround floor and almost 62 ◦C on the second floor. The tempera-ure comparisons between the scaled building model and the CFD

odel for the stacks closed case are presented in Figs. 11–13.Overall the temperatures compared relatively well between the

caled model and the CFD simulation. The first floor data are con-istently higher in the measured experimental data than for theredicted CFD simulation. This is again due to the heat transfer

ssues that the CFD software does not model. When comparing theverage floor temperatures to determine the variation due to floorevel, there is some increase in temperature due to floor level, ashown in Table 3. On average, the internal air temperatures in thecaled model for the stacks closed case vary from 39 to 54 ◦C fromhe ground floor to the second floor, with a temperature differencef 15 ◦C.

.2. Air velocities and patterns

The amount of air flowing through the models impacts themount of heat that is able to be removed from the space. How-

0

10

20

30

40

50

60

70

1 2 3 4 5 6 7 8

Physical ModelCFD Model

Locatio n

Tem

pera

ture

(oC

)

ig. 10. Second floor temperature comparisons (stacks open, ambient temperature0 ◦C).

– 49.15– 48.66

ever, this is limited by the inlet and outlet areas, whichever isthe more restrictive. In addition to the temperature distributionsin the scaled air and CFD models, air velocities at the inlets andoutlets were also obtained, and air flow and mass flow balanceswere calculated. Since the inlets and outlets in the CFD simula-tion are ideally controlled, with no unplanned infiltration, thismay help in determining the tightness of the scaled buildingmodel.

5.2.1. Stacks openIn the case where the atrium stack vents are open, the air enters

in both the lower and upper windows for the ground and first floorlevels, although the south side’s vents for the first floor have asmall net ventilation rate, leaving the model. At the second floorlevel, the air exhausts through both windows. The air velocitymeasurements taken at the window, supplemented with airflowvisualization using smoke pencils, were used to determine an over-all airflow balance on the scaled model. The relative velocities werethen compared, and the amount of error, or discrepancy betweenthe amount of air entering versus leaving the building, determined.Table 4 presents the data obtained for the stacks open case for both

and the upper vents are similar in the CFD model and scaled model.

0

10

20

30

40

50

60

70

1 2 3 4 5 6 7

Physical ModelCFD Model

Location

Tem

pera

ture

(oC

)

Fig. 11. Ground floor temperature comparison (stacks closed, ambient temperature13 ◦C).

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C. Walker et al. / Energy and Buildings 43 (2011) 2404–2413 2411

Table 3Stacks closed case: average temperature variation by floor and orientation.

Floor avg (◦C) Heated zoneavg (◦C)

South halfavg (◦C)

North halfavg (◦C)

Ground floorScaled air model 39.01 39.59 39.59 –CFD model 35.98 36.32 36.32 –

First floorScaled air model 47.06 45.24 45.11 45.36CFD model 45.80 43.72 43.65 43.78

Second floorScaled air model 54.10 51.95 – 51.95CFD model 54.14 51.60 – 51.60

Table 4Stacks open case: air velocity and flow-rate measurement comparison.

Orientation CFD model (m/s) Scaled air model (m/s) CFD model (m3/s) Scaled air model (m3/s)

Window Vent Window Vent Window Vent Window Vent

Ground 0.72 0.62 0.74 0.64 0.0122 0.0105 0.0124 0.0107First south 0.42 0.15 0.40 −0.33 0.0071 0.0025 0.0067 −0.0055

0.19−0.31

HwTtschhew

5

slv

First north 0.43 0.19 0.42

Second −0.33 −0.60 −0.23

Stacks −0.82 −0.71

owever, there is some air exhausting from the first floor south ventindow in the scaled model, which is not the case in the CFD model.

he exhausting of air at this location impacts the exiting air veloci-ies at the other three locations, second floor window and vent andtacks, causing further mismatch with the CFD model. This coin-ides with the internal temperatures for the physical model beingigher than in the CFD model, due to the heat transfer betweeneated zones and to the ambient. The airflow balances or differ-nce between amounts of air entering versus leaving the modelere within 10%.

.2.2. Stacks closed

When the stacks were closed off, the air entered through both

ets of windows on the ground floor, window and vent, and theower windows on the first floor. Air exhausted through the upperent windows on the first floor, as well as both sets of windows on

0

10

20

30

40

50

60

70

1 2 3 4 5 6 7 Locatio

Tem

pera

ture

(oC

)

Fig. 12. First floor temperature comparison (st

0.0103 0.0045 0.0100 0.0045 −0.0080 −0.0143 −0.0054 −0.0073

−0.0245 −0.0212

the second floor. The impact of heat transfer differences betweenthe scaled building model and the CFD model were more restricted,since there were fewer air flow paths in the models. Again the aver-age measured velocities for each window for both the physical andCFD models are presented along with the air flow rates in Table 5.

Unlike the stacks open case, the airflows in and out of the samewindows for both models. However, it is the magnitude of air-flow out of the vent window on the second floor that has themost significant difference. This is in part due to some heat lossthrough the ceiling or roof of the second floor heated zone. Ifthere is heat loss through the envelope of the model, then thetemperature difference between internal and ambient is reduced,

thereby reducing the pressure difference and velocity flow of theair. The overall airflow balance for the stacks closed case is justover 19% for the scaled building model, and about 2% for the CFDmodel.

8 9 10 11 12 13 14 15

Physical ModelCFD Model

n

acks closed, ambient temperature 13 ◦C).

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2412 C. Walker et al. / Energy and Buildings 43 (2011) 2404–2413

Table 5Stacks closed case: air velocity and flow-rate measurement comparison.

Orientation CFD model (m/s) Scaled air model (m/s) CFD model (m3/s) Scaled air model (m3/s)

Window Vent Window Vent Window Vent Window Vent

Ground 0.64 0.57 0.67 0.54 0.0108 0.0096 0.0112 0.0091First south 0.36 −0.22 0.32 −0.16First north 0.37 −0.21 0.42 −0.19Second −0.43 −0.66 −0.40 −0.49

0

10

20

30

40

50

60

70

1 2 3 4 5 6 7 8

Physical ModelCFD Model

Location

Tem

pera

ture

(oC

)

F1

5b

rrelasfl

Fb

ig. 13. Second floor temperature comparison (stacks closed, ambient temperature3 ◦C).

.3. Reduced-scale model’s results scale back to prototypeuilding

Using the similarity analysis, we can scale the experimentalesults from the reduced-scale model back to corresponding envi-onmental parameters for the prototype building. In the modelxperiments, thermocouples were located at the columns for each

evel to measure the vertical temperature distribution. The columnsre located between the heated zones and the atrium. Fig. 14hows the temperature distribution along a column of each ‘half’oor for the prototype building from scale model experimental

ig. 14. Temperature stratification from reduced-scale model’s results to prototypeuilding: scale back.

0.0061 −0.0037 0.0053 −0.0027 0.0088 −0.0049 0.0101 −0.0046 −0.0102 −0.0158 −0.0096 −0.0119

results, using similarity to scale back. More field measurementsshould be taken to compare the scaling back data from the scaledmodel’s measurements. However, this work will be challenging asthe outdoor environmental conditions are not controllable in fieldmeasurement. It is quite difficult to find pure buoyancy-driven nat-ural ventilation on field, especially with fluctuating wind.

6. Discussion

Further analyses of the data helped to determine the variationsbetween the scaled building model and the CFD model. To assessthe difference in predicted and measured temperature, the differ-ence between the experimentally measured temperature and thetemperature for the same location in the CFD model, divided bythe CFD temperature in degree C was used as the percent error.The maximum error between the internal temperatures for scaledbuilding model and the CFD model for the stacks open case is 12%,which occurs at the ground level at location 10. This was thought tobe due to the exact location difference of the thermocouple mea-surement and CFD model reported result. The average percent erroris less than 2.5% for all of the thermocouple locations. For the stacksclosed case, the maximum error between the two models occurredat the ground level, and is 15% at location 3. This was thought tobe due to the exact location difference of the thermocouple in themodel as compared to the reporting location in CFD. The averagepercent error for the entire model is 3.3%. Overall, the correlationcoefficient between the two data sets is 0.946, with unity being aperfect correlation. From this point of view, CFD simulation resultshave been validated by the scaled model experiments, althoughCFD simulation should be further validated by field measurementsto the prototype building.

The scaled model experiments not only validated CFD sim-ulation, but also found useful structural components in naturalventilation buildings. For example, the stack vents along the atriumas design characteristics were found to influence not only the inter-nal temperatures in both models, but also the amount of air flowingthrough the models. Having the stack vents open allowed for almosttwice as much air to flow through the model. This was due to theincreased overall height and the decreased flow resistance for theexhaust, further driving the buoyancy ventilation. The internal tem-perature variation from ground floor to the second floor increasedby almost 7 ◦C with the stacks closed case. Instead of having justover 50% of the hot air exhausting through the stack vents in theatrium, with the stacks closed case the neutral plane in the buildingwas lowered, and air exhausted through both sets of openings onthe second floor in addition to the upper vents on both sides of thefirst floor. Thus, incorporating stack vents to assist with buoyancydriven natural ventilation can have a significant impact on not onlythe internal temperatures, but also the airflow through the building.

The comparison between the CFD model results against the tem-perature and velocity measurements recorded in the reduced-scalemodel were quite informative.. However, there are limitations in

both the CFD simulations and the scaled model that need to beunderstood before using either technique for evaluating a building.The CFD model in this paper uses adiabatic surfaces for walls, floors,and ceilings, and does not account for heat loss through a build-

Journal Identification = ENB Article Identification = 3230 Date: July 19, 2011 Time: 7:44 pm

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[17] Q. Chen, Prediction of room air motion by Reynolds-stress models, Building andEnvironment 31 (1996) 233–244.

C. Walker et al. / Energy and

ng or model envelope, nor heat transfer occurring between floors.ith models that use air as the fluid, there is a small amount of

adiation between surfaces when there are internal loads present,hich the current CFD runs do not account for. The heat source

hat was defined in the CFD program is the amount of heat outputrom a particular surface (e.g., heater surfaces), but surface proper-ies are not accounted for. As with the scaled model’s experimental

easurements, there is a certain degree of variation and error ineasurements and environmental conditions in the test chamber

annot be absolutely controlled. For example the air handling unithat moderates the internal environment of the test chamber has aet-point temperature that keeps the temperature within 1–2 ◦C ofhe set-point. In CFD modeling, the ambient conditions are definednd do not vary at all. In both the CFD and scaled building mod-ls, the locations of the velocity measurement points can impacthe resulting average air velocity at an inlet or outlet, because ofelocity variation across the opening.

The scaled experimental model proved useful in understand-ng the impact of model material properties on the heat loss andnternal temperatures within the model. Our experimental stud-es required us insulating the MDF additionally in order to reduceeat crossing transfer from one zone to another zone through MDFalls/floors. In general, better thermal resistance of the modelaterial would reduce this heat loss’ effect to indoor air temper-

ture distribution within the scaled model. In the CFD model, theetermination of heat loss through the model building’s envelope,nd the magnitude of that heat loss to the overall heat flow throughhe model are important. If the heat loss through the envelope was

ore significant, an additional heat loss would have to be applied tohe relevant surfaces. In this paper, we found from aforementionednvestigations there is good agreement between the CFD simula-ion and the scaled building model for the both stack vent open andlosed cases, the heat loss through the envelope can be neglected forhe most part. Further analysis into the impact of adjusting designharacteristics on the buoyancy ventilation performance may beecessary. More comparisons between the scaled-model resultsnd prototype building’s measurement have been addressed in [9],hich scaled model temperature up to prototype building in order

o evaluate its scalability.

This paper presents the methodology of using scaled model

ombined with CFD simulation to help understand buoyancy nat-ral ventilation. However, limitations of this methodology shoulde noticed, once again, such as: (1) using air as working fluid gen-

[

ings 43 (2011) 2404–2413 2413

erates relatively higher indoor air temperature distribution, whichwould increase heat loss through model walls, floors, or envelope;(2) radiation heat transfer from heaters is difficult to control inscaled model experiment while it is not significantly present in thereal full-size building; (3) it is difficult to incorporate some detailsof the physical scale model into the CFD model, such as heat transferthough envelope and floors.

References

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