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Energy and Buildings 48 (2012) 18–28

Contents lists available at SciVerse ScienceDirect

Energy and Buildings

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valuation of various turbulence models for the prediction of the airflow andemperature distributions in atria

hafqat Hussain, Patrick H. Oosthuizen ∗, Abdulrahim Kalendarepartment of Mechanical and Materials Engineering, Queen’s University, Kingston, ON, Canada K7L 3N6

r t i c l e i n f o

rticle history:eceived 9 July 2011eceived in revised form0 December 2011ccepted 2 January 2012

eywords:FD modelingtrium

a b s t r a c t

In this paper the performance of various turbulence models potentially suitable for the prediction ofindoor air flow and temperature distributions in an atrium space was evaluated in a systematic way. Theinvestigation tested these models for various thermal conditions in atria of different geometrical configu-ration in two existing buildings using the Reynolds Averaged Navier–Stokes (RANS) modeling approach.The RANS turbulence models that were tested include the one-equation model (the Spallart–Allamaras)and two-equation models (the standard k-�, RNG k-�, realizable k-�, standard k-� and SST k-� mod-els). The radiation exchange between the surfaces of the atrium space was considered using the DiscreteTransfer Radiation Model (DTRM). The resultant steady state governing equations were solved using a

urbulence modelsalidationxperimental measurements

commercial CFD solver FLUENT. The numerical results obtained for a particular time of the day werecompared with the experimental data available. Relatively good agreement between the experimentaland CFD predictions was obtained for each model. However, from the results obtained, it was found thatthe performance of two-equation turbulence models is better than one-equation model and among thetwo-equation models, the SST k-� model showed relatively better prediction capability of the indoor

spac

environment in an atrium

. Introduction

An atrium is generally defined as a large and tall glazed space in auilding. Some of the reasons why atria are now so widely used are:1) they add very significantly to the beauty of the building; (2) theyllow sunlight to penetrate deep into the building and as a resultromote the health and psychological well-being of the building’sccupants leading to an improvement in morale; (3) they have theotential to reduce energy usage in the building. Energy usage cane decreased by using an atrium space in the building as a resultf daylighting (use of solar illumination in place of artificial light-ng), by the use of natural ventilation in summer and solar heatingn winter depending on outdoor environmental conditions. While

large number of buildings involving atria have been constructednd while some have proved to be very successful a number othersave been unsuccessful for a variety of reasons. These failures alloint to the need for improved design procedures for atria. Some ofhe problems that can arise with the use of atria are thermal discom-

ort associated with high temperature regions and with thermaltratification resulting from solar heating and with strong buoyantows, glare, and, potentially, the rapid spread of a fire and smoke.

∗ Corresponding author. Tel.: +1 613 533 2573; fax: +1 613 533 6489.E-mail addresses: shafqat55@yahoo.com (S. Hussain), oosthuiz@me.queensu.ca

P.H. Oosthuizen), kalendar@hotmail.com (A. Kalendar).

378-7788/$ – see front matter © 2012 Elsevier B.V. All rights reserved.oi:10.1016/j.enbuild.2012.01.004

e than k-�-models.© 2012 Elsevier B.V. All rights reserved.

Designing an atrium should involve minimizing these problems andmaximizing the desirable features associated with the use of anatrium. To do this normally requires the calculation of the flow,temperature distribution, and radiation distribution in a proposedatrium during its preliminary design stage.

Because the flow in an atrium space can involve many complexfeatures such as mixed forced and natural convection and com-plex radiation–convection interactions, it is often a difficult taskto analyze the flow and thermal phenomena in an atrium space.Computational fluid dynamic (CFD) methods are now being widelyused for this purpose. However, the analysis is made difficult by thefact that the atrium is usually large and the numerical analysis canrequire significant computer power. Direct numerical simulation(DNS) of the flow, which is normally mainly turbulent, is in practiceat this time not feasible because of the cost and the long computerrun times required because of the size of most atria. Therefore a tur-bulence model together with the Reynolds averaged equations isnormally used for the study of atrium buildings. However, becauseof the complex characteristics of the flow in an atrium space, it isoften not clear which turbulence model to use. Further, the lackof extensive experimental measurements in atria makes the selec-tion of a turbulence model and the estimation of the accuracy of

numerical results rather more difficult.

In recent years, CFD has become quite widely used in the designand operation of buildings and building systems and is proving to bean extremely valuable tool in the design of buildings and building

and Bu

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ystems. Discussions of the application of CFD in the building sys-ems field are given, for example, in [1–8]. The application of CFD totrium type buildings has received some attention, e.g., see [9–13].

review of the use of CFD methods in studies of the flow andemperature distributions in buildings incorporating atria is giveny Oosthuizen and Lightstone [14], but because of the complex-

ty of the flows involved and of the interaction between the variousodes of heat transfer there remain some concerns about the accu-

acy of the results obtained. More comparison between CFD resultsnd experimental results would answer some of these concerns.

In the past some researchers have given attention to the evalu-tion of various turbulence models used in the CFD analysis of thendoor airflows in simple geometries. Zhai et al. [15] reviewed therimary turbulence models that have been used for indoor environ-ent modeling. This study identified a few turbulence models that

howed great potential for modeling airflows in enclosed environ-ents. From this study, it was concluded that different turbulenceodels can be applied for diverse indoor simulations. Each turbu-

ence model has its own pros and cons and there are no universalurbulence models for indoor airflow simulation. Zhang et al. [16]valuated the performance of eight turbulence models for fourndoor airflows in simple geometries and compared the numericalredictions with available experimental data from literature. It wasoncluded that LES provides the most detailed flow features whilehe computing time is much higher than RANS models. Amonghe RANS models, the RNG k-� and a modified V2-f model showedetter performance over four cases studied. It was highlighted byhe authors that each model has good accuracy in certain flowategories, each flow type favors different turbulence model andhe selection of a suitable model depends mainly on the accuracyeeded and computing time afforded.

Gebremedhin and Wu [17] used five RANS models to simulate ventilated animal facility and concluded that the RNG k-� models the most suitable for modeling the flow field. Coussirat et al.18] evaluated the performance of six turbulence models for theFD simulations of free and forced convection in double-glazedentilated facades. Fluid and solid phase temperatures were com-ared with experimental results available in the literature. It wasoncluded that the RNG k-� turbulence model seems to performetter than the other turbulence models tested for predicting ther-al phenomena when there are zones of low velocities within the

acade configuration. Walsh and Leong [19] carried out numericalodeling of thermal environment due to natural convection inside

n air-filled cubic cavity using several commonly used turbulenceodels. It was found that the standard k-ε model was the most

ffective model to use. Rohidin and Moshfegh [20] investigated these of CFD as a tool for the prediction of the flow pattern and tem-erature distributions in large and complex packaging facility andresented a comparison between three eddy viscosity turbulenceodels, i.e., the standard k-�, the RNG k-�, and the realizable k-

, and compared the predictions with field measurements. It wasound that the RNG k-� model was the one most concurrent withhe measured values.

Stamou and Katsiris [21] used four turbulence models to pre-ict air velocity and temperature distributions in a model officeoom with ventilation and compared the predictions with thexperimental measurements. It was found that all the models pre-ict satisfactorily the main qualitative flow features with slightlyest performance from the SST k-� model. Chen [22] simulatedarious convective airflows and an impinging flow using five tur-ulence models. From the results it was shown that RNG k-� modelad the best overall performance in terms of accuracy, numer-

cal stability and computing time. Stavrakakis and Koukou [23]tudied natural cross-ventilation in a test chamber with open-ngs at non-symmetrical locations experimentally and numerically.he computational part of the study consisted of the steady-state

ildings 48 (2012) 18–28 19

application of three Reynolds-Averaged Navier–Stokes (RANS) tur-bulence models: the standard k-ε, the RNG k-� and the realizablek-ε models. It was concluded that the numerical predictionsobtained by turbulence models were generally in acceptable agree-ment with the experimental measurements. The RNG-k-� modelperformed relatively better, especially for temperature predictions.Arun and Tulapurkara [24] simulated the turbulent flow inside anenclosure with central partition with three turbulence models: theRNG k-�, a Reynolds stress model and the SST k-� model. It wasshown that SST k-� model’s capability is better to capture flowfeatures like exit of flow with swirl, flow in reverse direction andthe movement of vortices.

Cable and Oosthuizen [25] investigated the use of severalturbulence models for predicting the velocity and temperaturedistributions for three flow situations in simple geometries. Thenumerical predictions were compared with the experimental mea-surements. It was concluded by the authors that all the turbulencemodels gave satisfactory results and the choice of model useddepends on time and computational power restraints. Kuznik et al.[26] predicted velocity and air temperatures in a mechanically ven-tilated room with a strong jet inflow using four RANS turbulencemodels and compared the results with experimental measure-ments. It was noted that all the models can accurately predict thevelocity and temperatures for the isothermal and hot cases but thek-� model appears most reliable. Other similar studies have beencarried out e.g., see studies [27–32].

From the literature survey, it was observed that the RANS tur-bulence models have been widely used for modeling convectiveindoor airflows in simple geometries due to the less computationalcost involved. Most of these comparative studies conclude that k-� models are capable to simulate indoor airflows but the RNG k-�model is slightly better than the other models in terms of the overallsimulation performance. The k-� models have been recently usedfor a few indoor airflow simulations. These studies indicate thatthe k-� models present a new potential modeling indoor environ-ment with good accuracy, numerical stability and claim that theSST k-� model has a better overall performance than the k-� mod-els due to its multiple advantages, such as simple, accurate, goodwall treatment, high quality for temperature predictions and easycombination with other models for modeling indoor environmentairflows.

However, from the literature survey it was found that mostof the studies performed for the evaluation of turbulence modelsdeal with the prediction of indoor airflows in simple geometries.Some studies deal with the complex situations but did not con-sider the interactions of solar radiation with convective airflows.Present work was undertaken in order to evaluate the differentturbulence models in combination with a radiation model for theprediction of air flow and temperature distributions in atria of dif-ferent geometrical configuration in two existing buildings underforced ventilation conditions for which experimental data are avail-able. The numerical results have been compared with the availableexperimental measurements allowing an assessment to be madeof the accuracy of the numerical results obtained with the vari-ous turbulence models. The experimental data used in the presentstudy for the validation of numerical predictions were recorded byMouriki [33] and Laouadi and Atif [34].

2. Atria buildings considered

2.1. Concordia university atrium building

Quite extensive measurements undertaken in part of an atriumspace (14–16th floors) of the Engineering building at the Concor-dia University located in Montreal, Canada shown in Fig. 1, have

20 S. Hussain et al. / Energy and Buildings 48 (2012) 18–28

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Fig. 1. Outside view of the Concordia atrium fac ade.

ecently become available. The experimental data was recorded byouriki [33] and the details on the experimental measurements

an be found in [35]. The atrium is a part of a larger system of fiveertically connected atria shown in Fig. 1. Each atrium is three floorsigh and can be connected to adjacent atria by vents. The volumef the atrium considered is 1345 m3 shown in Fig. 2. The recordedata includes the air temperature measurements inside the atriumpace at different locations along the strings of the thermocouplesrranged in vertical lines when the atrium was disconnected fromhe lower atria in the system shown in Fig. 3. The numerical resultsor the atrium were obtained using the various turbulence modelsnd were compared with the experimental measurements allowingn assessment to be made of the accuracy of the results obtained.

.2. Ottawa atrium building

The second atrium space that was considered for which exper-mental data is available is in a three-storey building located in

he region of Ottawa, Canada. The atrium has an octagonal shapeith a pyramidal skylight and is surrounded by walkways that

ead to adjacent meeting or interview rooms and office spaces. Thetrium was monitored experimentally and numerically in June and

Fig. 2. Geometric representation of the atrium.

Fig. 3. Atrium sketch and locations of thermocouples [33].

December 1995 by Abdelaziz [34]. The plan and cross-sectionalview of the atrium and thermocouples position for temperaturemeasurements are shown in Figs. 4 and 5 respectively.

3. CFD modeling

In the present CFD modeling work, it was assumed that (i) theairflow is steady, turbulent and three-dimensional, (ii) the time-averaged governing equations can be used in conjunction with aturbulence model to adequately predict the airflow, (iii) the air-flow is single phase, i.e., the effects of dust particles and watervapors are neglected, (iv) the airflow at any inlet vent is uni-form, (v) the air properties are constant, except for the densitychange with temperature that gives rise to the buoyancy forces,this being treated using the Boussinesq Approximation, and (vi)external ambient conditions are steady. Six RANS turbulence mod-els were tested in this study: (1) Spallart–Allamaras, (2) standardk-epsilon (STD k-�), (3) renormalization group k-epsilon (RNG k-�), (4) realizable k-epsilon, (5) standard k-omega (STD k-�), and(6) shear stress transport k-omega (SST k-�) models for the assess-ment of indoor thermal environment. The theoretical details of theturbulence models used can be seen in literature. In obtaining thenumerical solution, the computational mesh was generated usingthe program GAMBIT and governing equations were numericallysolved using the commercial computational fluid dynamics (CFD)solver FLUENT. For the discretization of the governing equations,the second order upwind scheme was used for all the variablesexcept pressure. The discretization of pressure is based on the bodyforce weighted discretization scheme. The SIMPLE algorithm wasadopted to couple the pressure and momentum equations. Whenthe sum of the absolute normalized residuals for all the cells in flowdomain became less than 10−6 for energy and 10−4 for all other vari-ables, the solution was considered converged. Grid dependence ofeach case was tested using three grids to ensure that grid resolutionwould not have a notable impact on the results. For validation, thenumerical results were compared with the available experimentalresults.

3.1. Radiation model

Heat transfer by thermal radiation is extremely important toconsider in many modeling cases such as the case being investi-

gated here. To account for radiation, radiation intensity transportequations (RTEs) are solved. FLUENT offers five radiation models;Discrete Transfer Radiation Model (DTRM); P-1 Radiation Model;Rosseland Radiation Model; Surface to Surface (S2S) Radiation

S. Hussain et al. / Energy and Buildings 48 (2012) 18–28 21

f the a

MaasmriaFtt

Figs. 4 and 5. (Fig. 4) Plan and cross-section view o

odel; and Discrete Ordinates (DO) Radiation Model. DTRM radi-tion model was found suitable for the present study. The mainssumption followed in the DTRM model is that radiation leavingurface element in a specific range of solid angles can be approxi-ated by a single ray. It uses a ray-tracing algorithm to integrate

adiant intensity along each ray. It is relatively simple model andncrease accuracy by increasing number of rays while applies to

wide range of optical thicknesses. A solar calculator available inLUENT was used to calculate the beam direction and irradiation ofhe sun. The solar calculator can be used to find the sun location inhe sky with given inputs of time date and global position.

trium [34]. (Fig. 5) Positions of thermocouples [34].

3.2. Concordia atrium modeling

3.2.1. Geometrical modelFor simulations, the geometrical model was prepared using

a simplified model of the atrium interior space. The generaldimensions were followed but for convenience the staircase,furniture and openings to the corridor adjacent to the atrium

were ignored, as were small nooks in the design. The generaldimensions of the model constructed using the GAMBIT soft-ware can be seen in Fig. 2. The atrium has an overall size of12.050 m × 9.390 m × 13.015 m.

2 and Buildings 48 (2012) 18–28

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.2.2. Numerical model

.2.2.1. Near-wall turbulence modeling. The turbulence modelssed have the potential to accurately solve the turbulent flowsway from the walls. However there is need to adapt these mod-ls to solve for flows near walls. The layer that is adjacent to theall is termed the “viscous sub-layer”. At the wall the velocity is

ero and therefore the velocities in this region are very low, theow is effectively laminar with the effect of the viscosity beingominant. The outer region termed the “fully-turbulent layer” ishere turbulence has a dominant effect on the flow. Between the

iscous sub-layer and the fully turbulent layer there is a transi-ion region termed buffer layer. To resolve the flow near the wallsstandard wall functions” were used for k-epsilon and “advancedall functions” for k-omega turbulence models, which consist of

emi-empirical formulas that link the viscosity-affected region andhe fully turbulent region. The standard wall functions require aange of 30 ≤ y+ ≤ 300 for accurate prediction of the turbulent flowounded by walls while advanced wall functions require a range of+ ∼10 found in the literature for building simulations. The variable+, termed as the dimensionless wall distance, was used to find auitable correct grid size near the walls.

.2.2.2. Mesh design. An appropriate modeling of the turbulencehenomena involved in the atrium space implies that the meshhould be designed to properly define a minimum cell size toompute the turbulent mixing appropriately with the proposedeometry. Mesh density depends on the near-wall modeling strat-gy adopted for resolving the problem under turbulent flowonditions, and is determined by the y+ characteristic parame-er. The overall dimensions of the solution domain as mentionedbove were used and a three-dimensional model was built in ordero perform suitable turbulence modeling. It also took advantagef specific features of the CFD solver used (Fluent16.3.2 such asolar load radiation models, which are only available for three-imensional geometries). Nielsen [36] provides a correlation forhoosing the initial cell count for the mesh. The correlation useds N = 44,400 × V0.38 where N is the number of cells and V is theolume in m3. It is important to emphasize that there cannot be

truly universal correlation of volume and cell count, due to theact that complexities of the flows in buildings can greatly differnd therefore influence the number of cells required. The volumef the atrium considered is 1345 m3 which according to Nielsen’sorrelation, corresponds to roughly 686,000 cells. Keeping in viewhis correlation, y+ requirements near the walls and computationalapability of the available computers, the cell count in the range00,000–900,000 was used in present simulations. As explainedbove, the required y+ values for k-� models using standard wallunctions in the range 30–300 and for k-� models using advancedall functions y+ ∼10 were used. To obtain the required y+ values,

he wall adjacent cells had to be a very small. To avoid excessiveomputational effort fine mesh near the walls and coarser meshway from wall was used as shown in Fig. 6.

.2.2.3. Boundary conditions. Boundary conditions were set aslose as possible to the experimental data available. The wall sur-aces interior to the building were assumed to be adiabatic. The mixhermal boundary conditions were used for the fac ade glass sur-ace. The fac ade glass used in the Concordia atrium was known toe argon filled double glazing (6 mm glass/12 mm air space/6 mmlass) with a 0.1 low e-coating on the outer surface of the inte-ior pane. The optical properties of the glazing (semi transparent)sed in the previous studies with solar transmittance of 36% and

bsorptivity of 17.5% were used. The modeling of the glazing wasimplified as a single glazing and effective thermal conductivityf 0.0626 W/m2 K for the glazing with a total overall thickness4 mm was used. The heat transfer on the outside of the glazing

Fig. 6. Schematic of the grid chosen for the initial simulations.

due to the convection from the wind was accounted for. The out-side air temperature, wind direction and the magnitude given inthe experimental data were used. The surface of the facade is atangle of 35◦ west of south. The external heat transfer coefficientwas calculated to be 31.84 using the Palyvos [37] correlation forwindward surfaces that is: hw = 7.4 + 4Vw. The corresponding windspeed velocity (Vw) of 6.1 m/s was used in this equation. The radi-ation exchange between the facade and the sky was also takeninto account. The sky temperature was calculated to be 14.1 ◦C

using the Mills [38] correlation, Tsky = [εskyT4out]

1/4here the emis-

sivity of the sky (εsky) for the daytime was calculated to be 0.82using the relation, εsky = 0.727 + 0.0060Tout with an ambient tem-perature Tout of 28.6 ◦C. The net area of the air supply from theair-conditioning system was chosen to account for the presenceof the vanes across the vent. Experimental data was available forthe velocity and temperature values of the air entering the atriumfrom this vent. The velocity was set equal to 4.5 m/s while the tem-perature was 15 ◦C. The calculated Reynolds number was 146633based on the conditions at the supply, indicating the flow to be tur-bulent. The turbulence parameters such as the hydraulic diameterand the turbulence intensity were specified at the inlet using therelations, hydraulic diameter = 2 × LW/L + W and turbulent inten-sity = 0.16 × Re−1/8 respectively. The return vent near the top of theeast wall was modeled outflow, satisfying the condition that massflow rate out of this vent equals the mass flow rate into the atriumfrom the inlet vent.

3.2.2.4. Mesh sensitivity of the numerical results. A mesh sensitiv-ity test was carried out to examine the mesh independence of thenumerical results. Three mesh densities were investigated: Mesh1(433k elements), Mesh 2(858k elements, see Fig. 6) and Mesh3(1235k elements). The numerical results shown in this sectionwere obtained using the SST k-� turbulence model with the DTRMradiation model applied to the conditions existing at the Concordiaatrium at 16:00 h on the 1st August 2007. The velocity and meanair temperature profiles along the height of the atrium at x = 3 mand z = 4.5 for three mesh densities are shown in Fig. 7a and b.Table 1 shows the typical effect of grid density on predicted aver-age temperatures along different heights in the atrium. There is a

difference of less than 1% among the results using three Mesheswhich indicates the mesh independency of the numerical resultsobtained.

S. Hussain et al. / Energy and Buildings 48 (2012) 18–28 23

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Fig. 7. Velocity (a) and average temperature profiles (b) along th

. Results and discussion

In all the simulations run, the numerical results were obtainedhen the convergence criteria were met after approximately 7000

terations using a mesh in the range of 800k–900k cells. The

ig. 8. Comparison of the air temperatures profiles along the height of the atrium at x =007.

ht of the atrium at x = 3 m and z = 4.5 m for three mesh densities.

results are presented here in two sections. Section 4.1 presentsthe numerical results for the Concordia atrium. In Section 4.1.1

the performance of six turbulence models (one-equation andtwo-equations) is evaluated based on the comparison of the numer-ical predictions with the measurements of temperatures in the

0.24 m and z = 4.22 m using different turbulence models at 16:00 h on 1st August

24 S. Hussain et al. / Energy and Buildings 48 (2012) 18–28

Table 1Typical effect of grid density on predicted temperatures (◦C) (SST k-� turbulencemodel).

Grid Cell count Average airtemperature atheight 2.1 m

Average airtemperature atheight 6.16 m

Average airtemperature atheight 10.25 m

Grid 1 433,224 22.18 23.25 25.79Grid 2 858,800 22.31 23.36 25.85

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Fig. 9. Comparison of the predicted and measured mean air temperatures at high,

Grid 3 1,235,055 22.37 23.39 25.99

oncordia University atrium at 16:00 h on 1st August, 2007. In Sec-ion 4.1.2 the numerical results obtained at 13:00, 14:00, 15:00 and6:00 h at three levels of the Concordia atrium using four turbu-

ence models (two-equations) are presented and compared withhe experimental data. Section 4.2 shows the numerical resultsbtained for the atrium space in the Ottawa atrium building.n Section 4.2.1 the performance of three turbulence models isresented and the results are validated by comparing with thexperimental measurements available. In Section 4.2.2 the numer-cal results obtained for the Ottawa atrium using only SST-k-�urbulence model and DTRM radiation model are compared withhe measured and computed results obtained by Laouadi and Atif34].

.1. Results for Concordia atrium

.1.1. Performance of the six turbulence modelsThe performance of six turbulence models in predicting the flow

nd temperature distributions in the Concordia atrium is presentedere. A series of simulations were run using the Spallart–Allamaras,he standard k-�, RNG k-�, realizable k-�, the standard k-� and SST-� models. In these simulations, the average air and fac ade tem-erature distribution along the height of the atrium were calculatedt 16:00 h on 1st August 2007 and compared with experimentalata available given in [33]. The comparison of air temperaturesredicted by various turbulence models and measured values atifferent locations in atrium space are given in Table 2(a)–(c).rom the results it can be seen that the percentage error betweenredictions and measurements is relatively higher (4–10%) forhe Spallart–Allamaras model and lower (0.1–5%) for the SST k-

model. The predicted and measured air temperatures profiles at = 0.24 m and z = 4.22 m along the height of the atrium are shownn Fig. 8. The two-equation k-� and k-� turbulence models gaveesults relatively better than one-equation turbulence model (thepallart–Allamaras) and agreed with the experimental results to anccuracy that indicates that these can be used in, at least, the pre-iminary design of atria. The possible reason for the discrepancyetween the predictions and measurements can be contributedo the experimental error, the error caused by the assumptionsdopted in the numerical model i.e., the thermal mass of the wallshich were assumed insulated during simulations. It was noted

hat temperature gradients exist in the atrium space, increasingrom the lower level to the top level of the atrium space. The over-ll temperature stratification from the floor to the mid-height ofhe atrium the temperatures vary from 22 to 26 ◦C. At the veryop of the atrium hotter air at 30–32 ◦C exists. The temperaturesoted in the occupied area of the atrium are in the comfortableone (22–24 ◦C).

.1.2. Performance of the four turbulence modelsAfter the initial comparison of the predicted and measured

esults, four turbulence models: the standard k-�, RNG k-�, realiz-ble k-�, and SST k-� models were selected to run the simulationsf the Concordia atrium at different times of the day at 13:00, 14:00,5:00 and 16:00 on 1st August 2007. Fig. 9 shows the comparison

middle, and low levels in the atrium at 13:00 h 14:00, 15:00 and 16:00 h on 1stAugust, 2007.

of predicted and measured mean air temperatures at high, mid-dle, and low levels of the atrium. From the results obtained,it can be seen that numerical results are in good agreementwith the experimental results. However, the SST k-� turbulencemodel’s performance is slightly better than the k-� turbulencemodels.

4.2. Results for Ottawa atrium

4.2.1. Performance of the three turbulence modelsAfter the case study of the Concordia atrium and evaluation

of turbulence models, three turbulence models: the standard k-�,

RNG k-�, and SST k-� models were earmarked to run the sim-ulations for the Ottawa atrium. The numerical results obtainedwere compared with the experimental measurements available.The adjoining spaces were considered as adjacent spaces with

S. Hussain et al. / Energy and Buildings 48 (2012) 18–28 25

Table 2(a)–(c) The comparison of experimental and numerical predictions of air temperatures using different turbulence models.

Y(m) Temperature, T (◦C)

Experimental Turbulence models

SST k-� STD k-� STD k-� RNG k-� Realizable k-� Spalart–Allmaras

(a) At x = 5.96 m and z = 7 m2.1 24 22.87 21.87 22.94 22.38 22.67 21.766.16 24.5 24.55 23.17 23.83 23.54 24.23 23.12

10.25 26.2 26.52 25.81 25.27 25.91 25.34 24.74

Y(m) Experimental % error

2.1 24 4.7 8.8 4.4 6.7 5.5 9.36.16 24.5 0.2 5.4 2.7 3.9 1.1 5.6

10.25 26.2 1.1 1.4 3.5 1.1 3.2 5.5

Y(m) Temperature, T (◦C)

Experimental Turbulence models

SST k-� STD k-� STD k-� RNG k-� Realizable k-� Spalart–Allmaras

(b) At x = 5.78 m and z = 1.05 m2.1 22.3 22.37 22.77 22.03 21.91 23.43 23.456.16 25.1 24.47 22.4 23.93 23.34 23.43 22.9

10.25 26.1 26.20 25.88 25.96 25.84 25.5 25.07

Y(m) Experimental % error

2.1 22.3 0.3 2.1 1.2 1.7 5.0 5.36.16 25.1 2.5 10.7 4.6 7.0 6.6 8.7

10.25 26.1 0.4 0.8 0.5 0.9 2.2 3.9

Y(m) Temperature, T (◦C)

Experimental Turbulence models

SST k-� STD k-� STD k-� RNG k-� Realizable k-� Spalart–Allmaras

(c) At x = 8.81 m and z = 4.44 m2.1 23 22.71 22.12 23.27 22.42 23.04 22.126.16 24.6 24.72 23.1 24.45 23.36 23.66 23.07

10.25 26.3 26.55 25.8 26.08 25.17 25.64 25.08

Y(m) Experimental % error

2.1 23 0.5 3.8 1.1 2.5 0.1 3.86.16 24.6 0.4 6.0 0.6 5.0 3.8 6.2

10.25 26.2 0.3 1.9 0.4 4.2 2.5 4.6

Fig. 10. Simulated atrium space (a) and schematic of the grid chosen for the simulations (b).

2 and Buildings 48 (2012) 18–28

clAistcpCwTmuibsise

4

m

Fig. 11. Comparison of the measured and predicted indoor mean temperatures of

6 S. Hussain et al. / Energy

onstant uniform temperatures. Fig. 10(a) and (b) shows a simu-ated atrium space and schematic of the grid chosen respectively.

mesh independence test was carried out to examine the meshndependence of the numerical results. To ensure a convergedolution of CFD simulation, grid independence was tested by fur-her refining the grid for the atrium space, which showed a littlehange in the predicted flow pattern and averaged temperaturerofiles. The numerical procedures used for the simulations ofoncordia atrium were followed using the boundary conditionshen the experimental data was recorded by Abdelaziz [34].

he numerical results obtained were compared with the experi-ental measurements for the validation of the numerical model

sed. Fig. 11 shows the comparison of measured and predictedndoor temperatures of the atrium at three floors using three tur-ulence models at 12:00 h on June 11, 1995. This comparisonhows a good agreement between the measured and predictedndoor temperatures. The SST k-� turbulence model gave resultslightly better than the RNG k-� and STD k-� turbulence mod-ls.

.2.2. Performance of the SST-k-� turbulence modelMore simulation were run using only the SST-� turbulence

odel to further confirm its reliability of the prediction under the

Fig. 12. Velocity contours (a) and vectors (b) in the atrium space u

Fig. 13. Temperature contours in the atrium space using k-�-SST turbulence

the atrium at three floors using three turbulence models: the k-�-STD, k-�-RNG andk-�-SST models at 12:00 h on June 11, 1995.

experimental conditions when measurements were made by Abde-

laziz [34]. The qualitative numerical results indicating the velocitycontours and vectors in the atrium space are shown in Fig. 12.The temperature contours obtained for the conditions at 12:00 h

sing k-�-SST turbulence model at 12:00 h on June 11, 1995.

model at 12:00 h on June 11, 1995 (a) and on December 10, 1995 (b).

S. Hussain et al. / Energy and Buildings 48 (2012) 18–28 27

16

18

20

22

24

26

28

Te

mp

era

ture

(C

)

16

18

20

22

24

26

28

Te

mp

era

ture

(C

)

16

18

20

22

24

26

28

Te

mp

era

ture

(C

)

16:00 AM 2

16:00 AM

12:00PM6:00 AM

2 6:00:00PM P

Firs

6:002:00PM P

Seco

6:00PM

Th

P 6:00 AMM

Time

st FloorAb

Ab

Pre

P 6:00 AMM

Time

ond FloorAb

Ab

Pr

6:00 AM

Time

hird FloorAbd

Abd

pre

6:012:00PM 0

bdelaziz(1999), m

bdelaziz(1999),c o

resent predicted

612:00PM

bdelaziz(1999), m

bdelaziz(1999),c o

resent predicted

6:12:00PM 0

delaziz(1999),me

delaziz(1999),co

esent predicted

0PM

measured

omputed

:00PM

measured

omputed

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easured

omputed

Fig. 14. Comparison of the measure and computed results by Abdelaziz [34] andpresent CFD predictions of the average temperature values in the atrium space atthree floors using the k-�-SST model on June 10–11, 1995.

otompsrmnnw(taScm

Fig. 15. Comparison of the measure and computed results by Abdelaziz [34] andpresent CFD predictions of the average temperature values in the atrium space at

tested.

n June 11, December 10, 1995 are shown in Fig. 13. Tempera-ure stratification can be observed from the bottom to top levelf the atrium space. Figs. 14 and 15 show the comparison of theeasured and computed results by Abdelaziz [34] and SST-k-�

redicted results of the average temperature values in the atriumpace at three floors on June 10–11 and 9–10 December 1995espectively. A good agreement was found among the measure-ents and the SST-k-� turbulence models’s predictions. It was

oted that the temperature stratification in the summer was pro-ounced. The maximum predicted temperature of the atrium spaceas roughly the same as the maximum measured temperature

29 ◦C) reported by Abdelaziz [34]. The predicted and measuredemperatures of the atrium floors showed the same trend andre in good agreement. From the results it was noted that theST-k-� model predicted the temperature values better than the

omputed values obtained by Abdelaziz [34] using ESP-r (zonalethod).

three floors using the k-�-SST model on December 9–10, 1995.

5. Conclusions

This study evaluated the overall performance of various com-monly used turbulence models in combination with a radiationmodel DTRM for modeling complex airflows and temperature dis-tributions under forced ventilation conditions in atria of differentgeometrical configurations in two existing buildings. The modelaccuracy has been analyzed in terms of the average temperaturesat various heights in atria by comparing their predicted values withthe experimental data. Due to the complexity involved in the flowfeatures in atria, a strictly quantified and objective description ofthe evaluation of the turbulence models is difficult. In the presentstudy the relative error between prediction and measurement atmeasured points shown in Table 2 has been used as a major crite-rion for the evaluation of the performance of the turbulence models

From the results, it was noted that the relative percentage errorbetween predictions and measurements was less than 10% for allthe models used. The present research indicates that that all the

2 and Bu

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[37] J.A. Palyvos, A survey of wind convection coefficient correlations for building

8 S. Hussain et al. / Energy

urbulent models tested predict satisfactorily the main qualitativeeatures of the flow and temperature distributions in the atria withlightly better performance with the SST k-� model. The findingsf the present study are in agreement with the literature researchather in the present study more complex flow situations in atriaf the two existing buildings have been simulated with solar radia-ions interactions under forced ventilation conditions. The researchrovides another example to prove that the CFD method usingANS modeling approach is reliable to simulate the thermal envi-onment in atrium space. The achievements can contribute to someeference value in engineering applications.

Finally it is recommended from the present study and literatureurvey that the use of the SST k-� turbulence in combination withTRM radiation model is the best option to simulate the thermalnvironment in an atrium space due to its accuracy, its computingfficiency and its potential to combine the good features of a k-�odel near wall boundaries and a transformed k-� model in regions

ar from walls. The switch between the k-� and k-� formulations isontrolled by blending functions in the SST k-� turbulence model.owever it should be highlighted that generality cannot be claimed

rom these results, since the performance of the turbulence modelsested is problem dependant.

cknowledgment

This work was funded by the Canadian Solar Buildings Researchetwork, a strategic NSERC (Natural Sciences and Engineeringoundation of Canada) Network.

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