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Building and Environment 52 (2012) 152e161

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Building and Environment

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Validation of numerical modeling of conditions in an atrium space with a hybridventilation system

Shafqat Hussain, Patrick H. Oosthuizen*

Department of Mechanical and Material Engineering, Queen’s University, 130 Stuart, Kingston, ON, Canada K7L 3N6

a r t i c l e i n f o

Article history:Received 29 September 2011Received in revised form4 December 2011Accepted 21 December 2011

Keywords:CFD simulationsAtrium buildingSolar-assisted hybrid ventilationValidation

* Corresponding author. Tel.: þ1 613 533 2573.E-mail address: oosthuiz@me.queensu.ca (P.H. Oo

0360-1323/$ e see front matter � 2012 Elsevier Ltd.doi:10.1016/j.buildenv.2011.12.016

a b s t r a c t

Quite extensive measurements undertaken in a three-story atrium space (floors 14the16th) witha hybrid solar-assisted natural ventilation system in the Engineering building of the Concordia University,Montreal, Canada have recently become available. The thermal conditions of the atrium space have beenstudied numerically using the Reynolds Averaged Navier-Stokes (RANS) modeling approach. The RANSturbulence models that were tested include the standard k-ε, RNG k-ε, ‘realizable’ k-ε, and SST k-uturbulence models. The radiation exchange between the surfaces of the atrium space was consideredusing the Discrete Transfer Radiation Model (DTRM). The resultant steady state governing equationswere solved using a commercial CFD solver FLUENT. Numerical results were obtained for the conditionsexisting when measurements were taken in the Concordia atrium on typical clear days with the blindsfully open or fully closed and with the natural ventilation system (NV) ON or OFF. The CFD modelpredictions were validated by the comparison against the experimental measurements available and itwas found that the numerical predictions implying CFD model agree well with the measurements.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

A hybrid ventilation system in an atrium building can be utilizedas an effective cooling system to significantly reduce energy usedby the air conditioning system. It can be described as a two-modesystem using buoyancy-driven and mechanical cooling systems ora combination of both at different times of the day or season. Theopen space concept of atria, with high ceilings, lends well topromoting natural temperature stratification, and hence enhancesthe stack effect. Advanced stack-ventilated atria buildings have thepotential to consume much less energy for space conditioning thantypical mechanically ventilated buildings. The proper design ofnatural ventilation must be based on detailed understanding ofairflow within enclosed spaces governed by pressure differencesdue to wind and buoyancy forces.

In recent years, CFD has become quite widely used in the designand operation of buildings and building systems and is proving tobe an extremely valuable tool in the design of buildings andbuilding systems. Discussions of the application of CFD in thebuilding systems field are given, for example, in [1e8]. The

sthuizen).

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application of CFD to atrium type buildings has received someattention, e.g., see [9e13], but because of the complexity of theflows involved and of the interaction between the various modes ofheat transfer there remain some concerns about the accuracy of theresults obtained. More comparison between CFD results andexperimental results would answer some of these concerns. Thereare some experimental results for atrium type buildings, e.g., see[14e19], but the need exists for more comprehensive, long-timemeasurements in atria buildings in various parts of the world.Guohui Gan [20] studied solar heated open cavities including solarchimneys for enhancing natural ventilation of buildings usinga commercial CFD package to predict buoyant airflow rates in thecavities. The CFD model was validated by comparing the numericalresults against the measured data and a good agreement betweenthe predictions and measurements was reported. Stavrakakis et al.[21] examined natural cross ventilation with openings at non-symmetrical locations in a test chamber both experimentally andnumerically using advanced computational fluid dynamics tech-niques to determine the airflow pattern and indoor thermal envi-ronment. The temperatures and velocities were measured atcertain locations in the chamber, during noon and afternoon hoursof typical summer days. Authors used three Reynolds AveragedNavier-Stokes (RANS) turbulence models: the standard k-epsilon,the RNG k-epsilon and the so called “realizable” k-epsilonmodels toobtain numerical results. It was noted that all turbulence models

S. Hussain, P.H. Oosthuizen / Building and Environment 52 (2012) 152e161 153

applied agreed relatively well with the experimental measure-ments. P. Rohdin and B.Moshfegh [22] presented a comparison ofbetween three eddy-viscosity turbulence models, i.e. the standardk-ε, the RNG k-ε and the realizable k-ε, used for the predictions ofthe flow pattern and temperature distribution in the large indus-trial facility. The predictions were compared with field measure-ments and the RNG k-εmodel was found to be the most concurrentwith the measured values. Rundle et al. [23] carried out a system-atic validation of a commercial CFD code against experimentalmeasurements and concluded that CFD can be used successfully tosimulate the heat transfer and fluid flow in atria geometries andprovides recommendations regarding turbulence and relative heattransfer modeling. Some comparison of CFD results and experi-mental measurements in atria type buildings has been undertaken,e.g., see [24e26], but the need for more such studies is evident.Some attention has also been given to the evaluation of the use ofvarious turbulence models in the CFD analysis of buildings, e.g., see[27e34]. A review of the use of CFD methods in studies of the flowand temperature distributions in buildings incorporating atria isgiven in [35].

The objective of the present work is to use different turbulencemodels for the analysis of hybrid ventilation systems integratedwith atria with blinds open or closed and validate the numericalresults obtained by comparing with the experimental dataavailable. The numerical results were compared with the avail-able experimental measurements allowing an assessment to bemade of the accuracy of the numerical results obtained with thevarious turbulence models. The experimental results used in thepresent study for the validation of numerical predictions aregiven in [18].

2. Building description

The basic hybrid ventilation design concept of the Engi-neering Building of Concordia University consists of five 3-storyatria (separated with a floor slab) connected with floor grilleshaving motorized dampers to achieve buoyancy driven flow andinlet corridor grilles with motorized dampers (opening areaabout 1.4 m2) located at the end of the corridors in the South and

Fig. 1. Exterior view of the atrium in the Engineering building of Concordia University.

North façade of each floor. Fig. 1 shows an exterior view of theatrium.

The natural ventilation system operates when the outdoortemperature is between 15 �C and 25 �C and the relative humidity isless than 60%. The inlet corridor grilles and the floor grilles con-necting the atria are controlled by the building automation system,the control being based on weather monitoring data. The controlsystem either opens or closes the valves simultaneously. The atriaare located on the southwest façade of the building e 35� west ofsouth and they are equipped with motorized blinds. More infor-mation on the design approach that was followed can be found in[17]. Important areas and dimensions of the atrium are given inTable 1. In the atrium there is a mechanical air supply and returnsystem shown in Fig. 2. When the building is in the natural venti-lation mode: (i) the corridor inlet grilles located on the South andNorth façade and the floor grilles connecting the atria opensimultaneously, (ii) the mechanical supply flow rate in the atrium isreduced to a minimumvalue, (iii) the atrium exhaust located on thehighest point in the atrium (see Fig. 2) opens, and (iv) the supplyunits located at the corridors close.

3. Experimental data

The experimental data recorded by E. Mouriki (2009) [18] usedto validate the numerical results obtained using CFD simulationsare described here briefly. Mouriki [18] measured glass and blindssurface and air temperatures at various locations in the top atrium(14the16th floor), for different positions of the blinds (open/closed) focusing mostly on clear days. Thermocouples with anaccuracy of better than 0.5 �C were mounted at different locations(see Table 2) around the atrium to measure glass, blind and airtemperatures. A schematic of the atrium indicating the location ofthe thermocouples is shown in Fig. 2. Four velocity sensors wereinstalled at the atrium air supply and exhaust, as well at thecorridor grilles (North and South façades) to monitor the airvelocity in the range 0.05e10 m/s with an accuracy of 0.03 � 1% m/s. Air velocity at floor grilles in the atrium was measured fordifferent conditions with an accuracy of 0.1 � 3% m/s. Tempera-tures, air supply and exhaust velocities were recorded every 1 minwhile air velocity and pressure drop at the corridor grilles wererecorded every 5 s. Transmitted solar radiation in the atrium wasalso measured and representative weather conditions (tempera-ture and humidity) were obtained through the weather datastation located on the roof of the building. Wind speed anddirection data were taken from the Dorval airport weather station.Details on the experimental measurements for different cases canbe found in [18].

4. Numerical modeling

A CFD model of an atrium space shown in Fig. 2 was used tosimulate the indoor thermal environment of the atrium usinga commercial CFD software, FLUENT 6.3.26. The airflow pattern andtemperature distributions in the atrium are governed by theconservation laws of mass, momentum and energy. Because thenatural ventilation is a phenomenon of random nature due to theconstant changes of external weather conditions, anymathematicalmodel applied for the prediction of natural ventilation shouldinclude the dynamic nature of the external conditions. In applyinga CFD method one should ideally use a time-dependent approach,which, however, would require knowledge of the time-dependentvariations of the boundary conditions used. This technique wouldprovide very detailed and useful information about natural venti-lation but it requires excessive computational resources for prac-tical applications. A simplified approach to overcome such

Fig. 2. Atrium sketch and locations thermocouples [18].

Table 1Dimensions and areas in the Atrium [18].

Dimensions

Atrium height 13.02 m Façade Glass Area 97.00 m2 Floor Grills(net) Area 1.97 m2

Atrium Width 9.39 m Façade Blind Area 82.00 m2 Corridor grills(net) Area 1.40 m2

Atrium Depth 12.05 m Air Supply (net) Area 0.40 m2 Air Exhaust(net) Area 5.40 m2

Air Return(net) Area 7.44 m2 Floor Grills(net) Area 1.97 m2

S. Hussain, P.H. Oosthuizen / Building and Environment 52 (2012) 152e161154

restrictions is the steady-state assumption, as most phenomenatake place at almost steady-state conditions over long periods oftime. Furthermore, during day-time cycles in real buildings,temperature changes occur but the steady-state assumption isconsidered to be valid over long periods of time. Thus, in order torecognize the potential time-averaged value of temperatures andvelocities, the solution was obtained using the Reynolds averagedgoverning equations for steady, incompressible, three-dimensionaland turbulent flow. The CFD model was assumed to be steady-state

Table 2Air and surface temperatures e thermocouples mounted on the atrium façade and space

Left façade Middle façade

Height (m) Number of t/c Height (m) Numbe

10.25 3 (glass, blind, room air) 10.9 4 (glass9.35 4 (glass

6.165 3 (glass, blind, room air) 6.9 4 (glass5.2 4 (glass

2.1 3 (glass, blind, room air) 3.05 4 (glass1.35 4 (glass

Total 9 24

Height (m) East wallnumber of t/c

West wallnumber of t/c

East corridorsnumber of t/c

Wn

10.25 1 1 1 16.165 1 1 1 12.1 1 1 1 1Total 3 3 3 3

and the simulation time was chosen to 16:00 h when the experi-mental measurements were recorded. In dealing with the buoy-ancy forces in the momentum equations the Boussinesq approachwas adopted, i.e., it was assumed that the fluid properties areconstant except for the density change with temperature whichgives rise to the buoyancy forces, these being dealt with a linearrelation between the density change and the temperature change.In addition, the dissipation term in the energy equation wasneglected due to the low velocities involved.

Four turbulence models: (1) k-epsilon-standard (k-ε STD), (2)k-epsilon-renormalization group (k-ε-RNG) (3) k-epsilon- realiz-able and (4) k-omega-shear stress transport (k-u-SST) models wereused in this study for the assessment of indoor thermal environ-ment. Moreover, body average weighted and SIMPLE algorithmwere used for space discretization and coupling between pressureand velocity, while second order upwind scheme was used to dis-cretize the momentum and other equations in the numericalsimulations. Convergence was considered to have been reachedwhen the energy residual was less than 0.001% and the flow vari-ables residuals reached less than 0.1% over the last 100 iterations.Initial numerical results were obtained with three different meshesto determine that the mesh used was fine enough to allow thedetails of the flow to be predicted with adequate accuracy (seelater) but that was not so fine as to require excessive computationaltimes.

4.1. Radiation model

Heat transfer by thermal radiation is extremely important to beconsidered to model an atrium space. To account for radiation,radiation intensity transport equations (RTEs) are solved. Localabsorption by fluid and at boundaries links RTEs with energyequation. FLUENT offers five radiation models; Discrete TransferRadiation Model (DTRM); P-1 Radiation Model; Rosseland Radia-tion Model; Surface to Surface (S2S) Radiation Model; and DiscreteOrdinates (DO) Radiation Model. DTRM radiation model was found

[18].

Right façade

r of t/c Height (m) Number of t/c

, blind, cavity, room air) 10.25 3 (glass, blind, room air), blind, cavity, room air), blind, cavity, room air) 6.165 3 (glass, blind, room air), blind, cavity, room air), blind, cavity, room air) 2.1 3 (glass, blind, room air), blind, cavity, room air)

9

est corridorsumber of t/c

Staircasenumber of t/c

Air supplynumber of t/c

Exhaust numberof t/c

1 1 1113 1 1

S. Hussain, P.H. Oosthuizen / Building and Environment 52 (2012) 152e161 155

suitable for the present studies. The main assumption followed inthe DTRM model is that radiation leaving a surface element ina specific range of solid angles can be approximated by a single ray.It uses a ray-tracing algorithm to integrate radiant intensity alongeach ray and is relatively a simple model and increase accuracy byincreasing number of rays while applies to a wide range of opticalthicknesses. A solar calculator is also available in FLUENT tocalculate the beam direction and irradiation. The solar calculatorwas used to find the sun’s location in the sky with the given inputsof time, date and the global location.

4.2. Numerical methodology

4.2.1. Geometrical modelThe simulations were run using a somewhat simplified

geometrical model of the atrium interior space. The generaldimensions were used but for convenience the staircase, furnitureand openings to the corridor adjacent to the atrium were ignored,as were small nooks in the atrium. The general dimensions of thegeometrical model used can be seen in Fig. 3. The atrium has anoverall size of 12.05 m � 9.39 m � 13.02 m and volume of theatrium considered is 1345 m3.

4.2.2. Boundary conditionsThe boundary conditions were set close to the experimental

conditions mentioned in Table 3. Appropriate boundary conditionswere determined using the experimental data available and theweather information obtained from Environment Canada (2008).The wall surfaces interior to the building were assumed to beadiabatic. The mix thermal boundary conditions were used for thefaçade glass surface. The façade glass used in the Concordia atriumwas known to be argon filled double glazing (6mm glass/12mm airspace/6 mm glass) with a 0.1 low e-coating on the outer surface ofthe interior pane. The optical properties of the glazing (semitransparent) used in the previous studies with solar transmittanceof 36% and absorptivity of 17.5% were used. The modeling of theglazing was simplified as a single glazing and effective thermalconductivity of 0.0626 W/m2 K for the glazing with a total overallthickness 24 mmwas used. The heat transfer on the outside of theglazing due to the convection from thewindwas accounted for. Theoutside air temperature, wind direction and themagnitude 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 (2008) [37] correlation

Fig. 3. Geometry of the Concordia atrium (a) and si

for windward surfaces that is: hw ¼ 7.4 þ 4Vw. The correspondingwind speed velocity (Vw) of 6.1 m/s was used in this equation. Theradiation exchange between the facade and the sky was also takeninto account. The sky temperature was calculated to be 14.1 �Cusing the Mills (1999) [38] correlation, Tsky ¼ ½εsky T4

out�1=4 here theemissivity of the sky (εsky) for the daytimewas calculated to be 0.82using the relation, εsky ¼ 0.727 þ 0.0060Tout with an ambienttemperature Tout of 28.6 �C. The net area of the supply vent waschosen to account for the presence of the vanes across the vent. Theatrium side wall containing the supply and return vent and theconcrete position of the equivalent vent is shown in Fig. 3. Exper-imental data was available for the velocity and temperature valuesof the air entering the atrium from supply vent. The turbulenceparameters such as the turbulence intensity were specified at theinlet. The flow was assumed to be uniformly distributed on allsupply openings with constant vertical velocity. Furthermore, atthe exhaust openings, it was assumed zero gradients normal to theopenings for all of the solved variables, and the flow rates wereequal to their actual values. Indoor and outdoor conditions used inthe experimental measurements [18] and in present simulations ontypical clear days are shown in Table 3.

4.2.3. Mesh designA modeling of the turbulence phenomena involved in the

atrium space implies that the mesh should be used to properlydefine a minimum cell size to compute the turbulent mixingappropriately with the proposed geometry. Mesh density useddepends on the near-wall modeling strategy determined by the yþcharacteristic parameter. The overall dimensions of the solutiondomain as mentioned above were used and a three-dimensionalmodel was used in order to perform suitable turbulencemodeling. Nielsen (2007) [36] provides a correlation for choosingthe initial cell count for the mesh. The correlation used isN ¼ 44400 � V0.38 where N is the number of cells and V is thevolume in m3. It is important to emphasize that there can’t bea truly universal correlation of volume and cell count, complexitiesof the flows in buildings can greatly differ and therefore influencethe number of cells required. The volume of the atrium consideredis 1345 m3 which according to Nielsen’s correlation, corresponds toroughly 808,000 cells. Keeping in view the required yþ values nearthe walls and computational capability of the available computers,cell count in the range 800,000e1200,000 was used in the presentsimulations. As explained above, the required yþ values for k-εmodels using standard wall functions in the range 30e300 and for

de wall containing supply and return vent (b).

Table 3Indoor and outdoor conditions on typical clear days [18].

Cases Date/Time (16:00 h) Outdoor airtemperature (�C)

Solar radiation(w/m3)

Naturalventilation

Mechanical air Blinds

Temp. (�C) Flow rate (m3/s)

Case A Sep 23rd, 2007 20 250 ON 17 0.20 ClosedCase B Sep 1st, 2007 20 205 ON 17 0.12 OpenCase C July 25th, 2007 26 130e180 OFF 14 1.60 ClosedCase D Nov 2nd, 2007 6 280 OFF 14 1.20 Open

S. Hussain, P.H. Oosthuizen / Building and Environment 52 (2012) 152e161156

k-u models using advanced wall functions yþ w10 were used. Toobtain the required yþ values, the wall adjacent cells had to bea very small. To avoid excessive computational effort finemesh nearthe walls and coarser mesh away from walls was used shown inFig. 4.

4.2.4. Mesh sensitivity testA mesh sensitivity test was carried out to examine the mesh

independence of the numerical results. Three mesh densities wereinvestigated: Mesh 1(402k elements), Mesh 2(808k elements, seeFig. 4) and Mesh 3 (120k elements). The simulation results shownin this section were obtained using the k-u-SST turbulence modelalong with the DTRM radiation model applied to the conditionsexisting for the experimental measurements. The average airtemperatures over a horizontal plane for three mesh densities atdifferent heights are given in Table 4 and predicted verticaltemperature values at various heights along of the vertical line atthe center the atrium using three mesh densities are shown inFig. 5. It was determined from the predicted temperature distri-butions that the meshes used resulted in solutions with very smalldifference and provided a good balance between the requiredcomputational resources and the accuracy of the results.

5. Results and discussions

The results obtained are presented here in two sections: Section5.1 presents the qualitative results and in Section 5.2 the quanti-tative numerical results for the different cases are displayed. Thecomparison of the experimental measurements and numericalpredictions is also described in this section.

Fig. 4. Mesh structure for CF

5.1. Cases considered for simulations

Four different cases of indoor and outdoor conditions of theatrium space shown in Table 3 were simulated to study the effect ofhybrid ventilation with blinds fully open or closed using fourturbulence models: the standard k-ε, RNG k-ε, ‘realizable’ k-ε, andSST k-u turbulence model along with the radiation model and aredescribed below briefly:

� Case-A: with natural ventilation ON, blinds closed and reducedsupply airflow (0.2 m3/s).

� Case-B: with natural ventilation ON, blinds open and reducedsupply airflow (0.12 m3/s).

� Case-C: with natural ventilation OFF, blinds closed and supplyairflow (1.6 m3/s).

� Case-D: with natural ventilation OFF, blinds open and supplyairflow (1.2 m3/s).

The qualitative numerical results obtained for the case-A at16:00 h on 23/09/2007 with blind open and natural ventilationON are shown in Figs. 6e8. Figs. 6 and 7 show the velocity andtemperature contours along the planes parallel to the façade nearthe inlets (x ¼ 0.5, 3 and 11.5 m) of the atrium space respectivelywhile Fig. 8 shows the velocity and temperature contours alongthe middle vertical plane perpendicular to the facade of theatrium. It can be seen that temperature stratification layers existin the atrium space and the temperature increases from bottomto the top level of the atrium. The temperatures found in theoccupied area of the atrium space are in the range 26e27 �Cwhich are within the comfortable zone. In the fluid phase, dueto the presence of differentiated flow zones within the compu-tational domain (high-speed flow zones near the inlets and

D simulations (Mesh2).

20

22

24

26

28

30

32

1m 3m 6m 9m

Tem

pera

ture

(C)

Height of the atrium

402191 cells

808500 cells

1202960 cells

Fig. 5. Predicted vertical temperatures at various heights along the vertical line at thecenter of the atrium for three mesh densities.

Table 4Typical effect of mesh density on predicted temperatures (�C).

Mesh Cell count Average airtemperature atheight 2.1 m

Average airtemperature atheight 6.165 m

Average airtemperature atheight 10.25 m

Mesh-1 402,191 26.93 28.63 31.06Mesh-2 808,500 26.76 28.61 30.81Mesh-3 1,202,960 26.69 28.59 30.76

S. Hussain, P.H. Oosthuizen / Building and Environment 52 (2012) 152e161 157

a quasi-stagnated flow zone near the outlets), free and forcedconvection effects in the flow pattern and heat transfer can beobserved. It can be seen that in the presence of solar radiation,free convection effects are shown by the formation of air streamsmoving upward in the atrium space. From these figures it is seen

Fig. 6. Velocity contours near the inlets of the atrium with blinds closed an

Fig. 7. Temperature contours near the inlets of the atrium along the

that the air temperature stratification typically ranges from 2 to7 �C from lower to top level of the atrium with the naturalventilation system ON and blinds closed depending on weatherconditions and cooling levels. The velocity varies from 0.01 to0.40 m/s and turbulence intensity lies in the range 2e12% fromlower to top level in the center of the atrium space. Maximumtemperatures are typically found at the upper part of the atriumwhile lowest temperatures are at the lower levels near the floorin the occupied area of the atrium.

5.2. Comparison between experimental measurements andnumerical predictions

This sub-section presents a comparison between the measuredand predicted temperature values for all the cases considered usingfour turbulence models: the k-ε-STD, the k-ε eRNG, the k-ε-‘real-izable’, the k-u-SST. The aimwas not only to validate the CFDmodelbut also to compare the performance of the different turbulencemodels to capture the airflow pattern and temperature distributionwithin the atrium space. Average values of temperatures at top,middle and low levels of the atrium were used for the comparisonof measurements and predictions are shown in Tables 5e8 alongwith the percentage error between predicted values and themeasured ones. Fig. 9 shows the predicted and measured averagedair temperature profiles along the height of the atrium at 16:00 hon typical clear days for four cases considered with the blindsfully open or fully closed and with the natural ventilation systemON or OFF. The corresponding indoor and outdoor conditions are

d natural ventilation ON (velocities in m/s) at 16:00 h on 23/09/2007.

vertical planes parallel to the façade glass (temperature in �C).

Fig. 8. Velocity and temperature contours along the middle vertical plane perpendicular to the facade of the atrium.

Table 5Comparison of measured and predicted average values of temperatures for Case-A.

Height (m) Measured T(�C) k-u-SST T(�C) % error k-ε-STD T(�C) % error k-ε-RNG T(�C) % error k-ε-Relizable (�C) % error

10.90 31.00 29.99 0.03 31.39 0.01 31.63 0.02 31.45 0.0110.25 30.50 31.02 0.01 30.97 0.01 30.86 0.01 30.92 0.019.35 29.50 28.43 0.03 30.36 0.03 30.74 0.04 29.98 0.016.90 28.00 27.32 0.02 27.89 0.003 27.5 0.01 27.76 0.0086.16 28.50 28.01 0.01 28.61 0.004 28.07 0.01 28.52 0.00075.20 28.80 27.03 0.06 27.14 0.05 28.18 0.02 26.98 0.063.05 27.90 26.98 0.03 26.89 0.03 28.05 0.005 26.87 0.032.10 27.80 26.55 0.04 26.93 0.03 26.68 0.04 26.79 0.031.35 28.20 27.22 0.03 27.01 0.04 26.28 0.07 26.87 0.04

Table 6Comparison of measured and predicted average values of temperatures for case-B.

Height (m) Measured T(�C) k-u-SST T(�C) % error k-ε-STD T(�C) % error k-ε-RNG T(�C) % error k-ε-Relizable (�C) % error

10.90 30.00 28.74 0.04 28.34 0.05 27.92 0.07 28.07 0.0610.25 29.20 28.44 0.02 28.18 0.03 27.98 0.04 28.22 0.039.35 29.10 27.64 0.05 27.88 0.04 27.56 0.05 28.05 0.036.90 28.10 27.24 0.03 27.76 0.01 27.30 0.03 27.84 0.016.16 28.00 27.24 0.02 27.40 0.02 27.20 0.03 27.35 0.025.20 27.90 27.5 0.01 27.46 0.01 26.92 0.03 27.17 0.023.05 27.70 27.39 0.01 26.93 0.02 27.01 0.02 26.83 0.032.10 27.40 26.69 0.02 26.63 0.03 26.78 0.02 26.50 0.031.35 27.00 27.73 0.02 27.02 0.0007 27.04 0.001 27.17 0.006

Table 7Comparison of measured and predicted values of temperatures for case-C.

Height (m) Measured T(�C) k-u-SST T(�C) % error k-ε-STD T(�C) % error k-ε-RNG T(�C) % error k-ε-relizable (�C) % error

10.90 28.00 26.48 0.05 26.03 0.07 25.97 0.07 27.58 0.0110.25 27.80 26.26 0.05 25.91 0.06 25.56 0.08 27.37 0.019.35 27.20 25.44 0.06 25.12 0.07 25.05 0.08 26.61 0.026.90 25.80 23.97 0.07 23.73 0.08 23.85 0.07 25.14 0.026.16 25.50 23.47 0.08 22.72 0.10 22.17 0.13 24.49 0.045.20 25.30 22.94 0.09 23.21 0.08 22.68 0.10 24.40 0.033.05 23.00 21.50 0.06 21.58 0.06 21.34 0.07 23.27 0.012.10 22.00 20.88 0.05 22.72 0.03 20.84 0.05 22.50 0.021.35 21.70 20.68 0.04 21.04 0.03 20.39 0.06 23.32 0.07

Table 8Comparison of measured and predicted values of temperatures for case-D.

Height (m) Measured T(�C) k-u-SST T(�C) % error k-ε-STD T(�C) % error k-ε-RNG T(�C) % error k-ε-relizable (�C) % error

10.90 29.60 30.34 0.02 30.66 0.03 32.28 0.09 32.07 0.0810.25 29.00 29.73 0.02 30.45 0.05 31.84 0.09 31.40 0.089.35 27.60 29.00 0.05 29.60 0.07 31.00 0.12 30.64 0.116.90 26.50 27.08 0.02 26.71 0.008 28.67 0.08 28.40 0.076.16 26.00 26.30 0.01 26.15 0.005 27.89 0.07 27.6 0.065.20 25.50 25.74 0.01 25.18 0.01 27.07 0.06 27.07 0.063.05 25.00 23.30 0.06 23.12 0.07 25.91 0.03 25.01 0.00042.10 24.50 23.18 0.05 22.55 0.08 24.36 0.005 24.16 0.011.35 24.00 21.69 0.01 22.72 0.05 23.38 0.02 23.22 0.03

S. Hussain, P.H. Oosthuizen / Building and Environment 52 (2012) 152e161158

Average Air Temperature Profiles-Blinds Closed-Natural Ventilation

ON (23/9/2007)

Case-A

Case-B

Case-C

Case-D

18

20

22

24

26

28

30

32

34

36

0 2 4 6 8 10 12

Height (m)

Te

mp

era

tu

re

(o

C)

Measured

k-w-SST

k-e-STD

k-e-RNG

k-e-Relizable

Average Air Temperature Profiles-Blinds Open-Natural Ventilation ON

(01/09/2007)

18

20

22

24

26

28

30

32

34

36

0 2 4 6 8 10 12

Height (m)

Te

mp

era

tu

re

(o

C)

Measured

k-w-SST

k-e-STD

k-e.RNG

k-e-Realiz

Average Air Temperature Profiles-Blinds Closed-Natural Ventilation OFF

(25/07/2007)

18

20

22

24

26

28

30

32

34

36

0 2 4 6 8 10 12

Height (m)

Te

mp

era

tu

re

(o

C)

Measured

k-w-STD

k-e-STD

k-e-RNG

k-e-Relizable

Average Air Temperature Profiles-Blinds Open-Natural Ventilation OFF

(01/09/2007)

18

20

22

24

26

28

30

32

34

36

0 2 4 6 8 10 12

Height (m)

Te

mp

era

tu

re

(o

C)

Measured

k-w-SST

k-e-STD

k-e.RNG

k-e-Realiz

Fig. 9. Air temperature profiles in the atrium on typical days with the blinds open orfully closed and with the natural ventilation system ON or OFF.

S. Hussain, P.H. Oosthuizen / Building and Environment 52 (2012) 152e161 159

summarized in Table 3. For the case-D the comparisons of predic-tions of the turbulence intensity (%) profiles with different turbu-lence models at various locations in the atrium (a) x ¼ 0.24 m,z ¼ 4.22 m (b) x ¼ 5.96 m, z ¼ 7 m (c) x ¼ 8.8 m, z ¼ 4.44 m areshown in Fig. 10.

All the turbulence models predicted the results in a goodagreement with the temperature measurements for all the casesconsidered. However, k-u SST model gave results more close to themeasurements and better prediction of turbulence intensity (seeFig. 10) also noted in the previous study [32]. The resulting averagetemperatures for the Case-B, with natural ventilation ON and blindsopen, vary from 27.5 �C at the floor to about 28.5 �C in the proximityof the ceiling. At the low and middle levels the predicted values oftemperatures are very close to the measured values but at the toplevel there is a discrepancy of almost 0.2e2 �C which may beattributed to the thermal mass of the ceiling which was assumedadiabatic in simulations. In the Case-C with natural ventilationOFF and blinds closed during summer, the resulting temperaturevaries from 20.5 �C at floor level to about 26 �C near the ceiling. Thedifference betweenpredicted andmeasured values of temperaturesat the middle and high levels as compared to the low level can becontributed to the thermal mass of the building. Case-D withnatural ventilation OFF and blinds open during the winter season,the resulting temperature varies from 22 �C at the floor level toabout 28 �C near the ceiling. In this case the calculated values areunder-predicted at the low level and over-predicted at the top levelby about 2 �C which can also be contributed to the thermal mass offloor and ceiling which were assumed to be adiabatic insimulations.

It is seen that the numerical predictions obtainedwere generallyin acceptable agreementwith the experimental measurements. Theaverage difference between the predicted and measured airtemperatures was in the range 1e8%. The possible reason for thediscrepancy can be contributed to experimental error, the errorcaused by the assumptions adopted in the numerical model i.e.,the thermal mass of the walls which were assumed insulatedduring simulations and other heat sources in the atrium thatwere not considered in simulations.

6. Conclusion

This research work focused on the validation of CFD modelfor the airflow pattern and temperature distribution in a three-story atrium space. The numerical results are compared withthe experimental results. The numerical results obtained indicatethat the RANS turbulence models include the standard k-epsilon,RNG k-epsilon, ‘realizable’ k-epsilon, and SST k-omega turbu-lence models give results that agreed relatively well with theexperimental results to an accuracy that they can be used in, atleast, the preliminary design of the atria. However, k-u SSTmodel gave results more close to the measurements and showedbetter prediction of turbulence intensity as compared to k-εmodels. The shear stress transport (SST) model of Menter [39],which was created for complex flows, blends the k-ε modelequations with the Wilcox k-u model equations [40], based onproximity to no-slip surfaces has better capability of turbulencepredictions. The SST model uses a limiter for the eddy-viscositythat has been seen to yield better agreement with experimentsfor complex flows.

The influence of gravitational body forces on the velocityfields within the atrium space was observed. It was seen that inthe presence of solar radiation, free convection effects areshown by the formation of air stream moving upward aroundthe hot surfaces. Higher air temperature stratification in thethree-story atrium was observed in the case where the natural

0

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6

8

10

12

0 2 4 6 8 10 12

Height (m)

Turb

ulen

ce in

tens

ity (%

)

k-omega SSTk-epsilon STDk-epsilon RNGk-epsilon Realizable

a

0

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4

6

8

0 2 4 6 8 10 12

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b

Turb

ulen

ce in

tens

ity (%

)

k-omega SSTk-epsilon STDk-epsilon RNGk-epsilon Realizable

c

0

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8

10

0 2 4 6 8 10 12

Height (m)

Turb

ulen

ce in

tens

ity (%

)

k-omega SSTk-epsilon STD

k-epsilon RNGk-epsilon Realizable

Fig. 10. Comparisons of predictions of the turbulence intensity (%) profiles withdifferent turbulence models at various locations in the atrium (a) x ¼ 0.24 m,z ¼ 4.22 m (b) x ¼ 5.96 m, z ¼ 7 m (c) x ¼ 8.8 m, z ¼ 4.44 m.

S. Hussain, P.H. Oosthuizen / Building and Environment 52 (2012) 152e161160

ventilation system was OFF and the blinds were closed. Lowertemperature stratification with the natural ventilation systemON is due to the strong convection. Strong stack effect createsinflow on lower floors and results in high air flows at floorgrilles and exhaust.

From this work and also as observed by others in literature, itis concluded that CFD proves to be a reliable tool for modelingflow and heat transfer in an atrium space integrated with hybridventilation system including conduction, convection andradiation heat transfer phenomena. It is possible to analyze theflow rate and temperature distributions within the atriumnumerically.

Acknowledgment

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

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