CFD modeling for natural ventilation in a lightwell connected to outdoor through horizontal voids

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CFD modeling for natural ventilation in a lightwell connected to outdoor through horizontal voids
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  EnergyandBuildings86(2015)502–513 ContentslistsavailableatScienceDirect Energy   and   Buildings  journalhome   page:www.elsevier.com/locate/enbuild CFD   modeling   for   natural   ventilation   in   a   lightwell   connected   tooutdoor   through   horizontal   voids Tareq   Gaber   Farea a , ∗ ,   Dilshan   Remaz   Ossen a ,   Saqaff    Alkaff  b ,   Hisashi   Kotani c a DepartmentofArchitecture,FacultyofBuiltEnvironment,UniversitiTeknologiMalaysia,81310UTM,Johor,Malaysia b DepartmentofMechanical,FacultyofEngineering&Technology,MultimediaUniversity,Malaysia c DepartmentofArchitecturalEngineering,GraduateSchoolofEngineering,OsakaUniversity,Japan a   r   t   i   c   le   i   n   f   o  Articlehistory: Received23October2013Receivedinrevisedform8October2014Accepted14October2014Availableonline23October2014 Keywords: NaturalventilationLightwellHorizontalvoidHigh-risebuildingsCFD a   b   s   t   r   a   c   t Lightwell   or   deep   courtyard   iscommonly   used   in   high-rise   deep   layout   plan   buildings   and   are   usuallyimplemented   to   admit   daylight   and   to   induce   natural   ventilation   into   targeted   spaces.   Upward   flow   inthe   lightwell   is   dominant   due   to   buoyancy   effect;   however,   direct   connection   to   the   outdoor   throughhorizontal   void   may   assist   or   oppose   the   upward   airflow   in   the   lightwell.   Thisarticle   mainly   investi-gates   the   effect   of    different   vertical   and   horizontal   positions   ofthe   void   connected   to   the   lightwell   onthe   upward   flow   with   different   wind   directions.   Computational   Fluid   Dynamics   (CFD)   was   employed   tosimulatethe   airflow   inside   the   lightwell.   The   simulation   results   were   validated   and   confirmed   a   goodagreement   with   the   experimental   data.   The   configuration   of    the   lightwell   connection   clearly   indicate   thestrong   influence   on   upward   flow   in   the   internal   lightwell;   however,   the   double-level   void   in   cross-flowconfiguration   wasfound   more   effective   thanother   configurations   in   terms   of    airflow   velocity   and   tem-perature.   Wind   direction   is   an   important   parameter   which   influences   air   flow   patterns   and   velocity   inthe   lightwell.   This   study   provides   proper   guidelines   to   predict   ventilation   performance   andto   improvethe   design   of    naturally   ventilated   high-rise   buildings.©2014   Elsevier   B.V.   All   rights   reserved. 1.Introduction Naturalventilationisconsideredoneofthemostfundamentallowcostpassivecoolingstrategies[1,2],contributingtoreductions inenergyconsumptionwithoutcompromisingthermalcomfortandtheairqualityinsidethebuilding[3].Naturalventilationcan beprovidedinsideandaroundbuildingsbywind-alone,buoyancy-aloneoracombinationofboth,whichisdefinedasnaturalconvectionflow[4–6].Naturalconvectionflowisaneffective meansofprovidingindoorventilationinbuildingswhenwindandbuoyancyhavethesamedirection[6,7].Inordertosimplifythe predictionofsteadynaturalconvectionflowcharacteristicsinthebuildings,Etheridgeclassifiedtwomaintypesofopeningswithrespecttoaspectratio L / d h ,where L isthelengthparalleltostream-linesand d h  isthecrosssizethatflowsperpendicular[5].Incases wheretheaspectratioisverylow(e.g.conventionalwindows)theflowpatternisseparatedattheedgesoftheopening.Therefore,incasewithlower L / d h  value,moststudiesutilizedthestill-airdis-chargecoefficient( C  d )whileinlongopenings(large L / d h  value) ∗ Correspondingauthor.Tel.:+60142382465;fax:+6075557411. E-mailaddress: tareqgfarea@outlook.com(T.G.Farea). theReynoldsnumberdependencyisimportant[8].Mostprevi- ousstudieswereconductedinisolatedspaces,e.g.simpleroomshavesmallopenings,withverylowvalueof  L / d h  [4,9].Researchtodaypaysmoreattentionthanbeforetothestudyofspecialbio-climaticdesignstrategieswithverylarge L / d h  values,forexamplewindtower[10]andcourtyard[11]. Internallightwellshaveverylarge L / d h  valueandusuallyimple-mentedinbuildingswithadeeplayoutplaninordertoprovidenaturalventilationanddaylighttoinnerspaceswhicharefarfromtheperimeterofthebuilding.Thelightwellwithinhigh-risebuild-ingsmay   actonlyasventilationshaft[12,13].Inordertoguarantee aneffectiveventilationperformance,mostbuildingcodesprescribetheminimumlightwellsizeinrelationtothebuildingheight[13].However,thereareotherimportantfactorsindeterminingtheair-flowperformanceinthelightwellsuchasheattransferfromwallsurfacesofthelightwellandadjoiningspacesthroughwindows(openingswithlower L / d h  value)andconnectionstotheoutdoorthroughhorizontalvoids(openingswithlarger L / d h  value).Infact,theideaofconnectinglightwellstotheoutdoorthroughhorizontalvoidsisnotnew,andhasbeenthefocusofmanypreviousstud-ies[13–17].Horizontalvoidsareusuallyfoundinthefirstfloor inhigh-risebuildingsandservemulti-purposeusessuchascarparks[18].Moreover,horizontalvoidsarefoundinthemiddle http://dx.doi.org/10.1016/j.enbuild.2014.10.0300378-7788/©2014ElsevierB.V.Allrightsreserved.  T.G.Fareaetal./EnergyandBuildings86(2015)502–513 503 floorsofhigh-risebuildings,andareusedasrefugefloors[19],servicefloors[18],windfloors(e.g.inLibertyTower,Japan)and skygardensinluxuryresidentialbuildings(e.g.TheMet,Thailand).Therefore,iflightwellsareappropriatelyanddirectlyconnectedtotheoutdoorthroughhorizontalvoids(e.g.appropriatepositionandsize),theoutdoorwindflowwillprovidethebuoyancy-inducedflowinthelightwell[20,21].However,theconnectionconfigura- tionbetweenthelightwellandhorizontalvoidcouldopposethebuoyancy-inducedflowandthusdecreasethevelocityofupwardflow[6,9].Thesepossibilitiesarerequiredmoreinvestigationsto optimizetheappropriateconfigurationforprovidingairflowinthebuilding,particularlywhenbothspacescomewithverylarge L / d h value.TheCFDapplicationshavebecomethemostpopularinbuild-ingventilationstudies[1,22],particularlythevalidationmodels [23,24].ManystudiesarebasedonvalidatedCFDformodelingnaturalconvectionflowinconnectedspaces(largespaceslinkedbetweenseveralroomsorfloors)inhighrisebuildings.Itwasfoundthatmostofthesestudieswereconductedinatriumspace(e.g.[7,23,25,26])andsolarchimneys[27,28]butnotinlightwells. Theairflowmechanisminthesespaces(inparticular,lightwellsandatriums),isalmostthesame,withthemostimportantdiffer-encebeingthatthelightwellopenstotheoutdoorthroughtheskyopening,makingtheflowinsidethelightwellmorecomplexanduncontrolled.However,theliteratureindicatesthatonlysemi-enclosed(re-entrant)andattachedlightwellswereinvestigatedinmanypreviousstudies[15,24,29].Internallightwells,however, havetheworstpositionintermsofconnectiontotheoutdoor,butveryfewstudieshavebeenconductedtoinvestigatetheirinfluenceonairflow.Kotanietal.[16,30,31]conductedmanyexperimentalhigh-rise buildingsmodelsinawindtunnel,andempiricalmodelswereusedtoinvestigatetheairflowcharacteristicsinsideaninternallightwellconnectedtotheoutdoorthroughahorizontalvoid.Theabovestudiesinvestigatedtheeffectoftheheatmagnitudeanditssourceposition,airvelocityandvoidsizeontheairflowrate,airtemper-atureandairflowpatterninlightwells.Ontheotherhand,studiesconductedbyGan[32,33]inverticalenclosuresinvestigatedthe effectofenclosuresizeandthelimitednumberofinletpositionswithdifferentheatvaluesandpositions.AlthoughtheresultsarebasedonCFDsimulations,theexperimentswerelimitedtotwodimensionalmodelsandconsideredonlyasinglewinddirection.ArecentstudybyChiangandAnhexaminedtheeffectofsev-eralvoidpositionsonair-velocityandtemperaturegradientinaninternallightwellofahigh-risebuildingusingCFDsimulations[15].Thenumberofhorizontalandverticalvoidpositionswerelimitedtobottom,top,cross-flowandwindwardpositions,andconsideredonlyasinglewinddirection.Anotherrecentstudy,alsobasedonCFD,evaluatedthenaturalconvectionflowinlightwellinahigh-riseofficebuildingandcompareditwithsegmentedlightwells(byhorizontalvoid)andisolatedspaceconfigurations[20].The studyindicatedthatpotentiallightwells(eithersegmentedornon-segmented)aremoreeffectivethanisolatedspaceintermsof providingincreaseairflowrate.However,segmentedlightwellsarepreferredastheyreducerecirculationflowwhichiscommoninnon-segmented,particularlythosefoundinthebottomandtoppartsofthelightwell.TheabovestudiesindicatethatthereisalackofextensiveanddetailedsensitivitystudiesinvolvingCFDsimulationofnaturalcon-vectionflowinlightwells.ThesimulationresultsareverysensitivetoawiderangeofcomputationalparametersandsettingsthathavetobesetbytheuserofCFD.Therefore,detailedandgenericsensitiv-itystudiesoftheinfluenceoftheseparameters,e.g.computationaldomainsize,gridresolutionandturbulencemodelsonthesimu-lationresultsarerequiredtoprovidebestpracticeguidelinesforusingCFDwithmoreaccuracyandreliability[34,35].Thecurrentstudyusedasmall-scalemodelthatwastestedexperimentallybyKotanietal.[16],andreproducedinaCFDsim- ulationwithtwoobjectives.ThefirstistoperformavalidationandsensitivityanalysistoverifythereliabilityandaccuracyofCFDinpredictingthenaturalconvectionflowinsidethelightwellsinhigh-risebuildingsbycomparingtheresultswithexperimentaldata.Thesecondobjectiveistoexaminetheeffectofthevoidpositionsandwinddirectionontheupwardflowinsidethelightwell.Theresultsofthisstudywillcontributetowardidentifyingappropriatevoidpositionsinordertoprovideupward-crossflowinlightwells.Thiswillbepreferredtoremovingheatfromthecoreofthebuilding,thusprovidingforbetterairqualityandthermalcomforteitherinthelightwellspaceasunoccupiedspaceorinadjoiningindoorroomsasoccupiedspace. 2.Windtunnelexperiment(WTE) Kotanietal.conductedawindtunnelexperiment(WTE)usingasmall-scalemodelforahigh-risebuildinglightwellconnectedwithbottomvoid[16].Theexperimentpredictedtheairtemper- atureandairflowrateaswellasairflowpatterninthelightwell.Thebuildingmodel(1:250)representsarealforty-storeyhigh-risebuildingwithsquareplandimensionof36m × 36m × 120m(width × depth × height).Thelightwellinthecoreofthebuildingpassverticallythroughallthefloorswithoutanyopeningsexceptthebottomlateralhorizontalvoid(onesideopeninwindwarddirection)andthetopverticaloutlet(skyopening).ThebuildingmodelusedintheWTE   was   scaledto1:250.Theoutlineofthemodelthereforehasdimensionsof144mm × 144mm   × 480mm.Thevolumeofthelightwellandtheareaofthehorizontalvoidare72mm   × 72mm × 468mmand72mm   × 12mm(width × height)respectivelyasillustratedin(Fig.1).Theexperimentalconditions werespecifiedintermsofrateofheatgenerationinthelightwell,rangingfrom10to40W,   andwindvelocityinthewindtunnelwhichrangedfrom0to1.5m/s.Thewinddirectioninallcaseswasperpendiculartothewindwardfac¸    adewherethehorizontalvoidwaslocated.Tomeasuretheairtemperature,fivethermocouplesweresetverticallyinthelightwell.MoredetailedinformationabouttheexperimentalsettingscanbefoundinKotanietal.[16]. 3.CFDvalidationandsensitivityanalysis AcommercialCFDcodeANSYSFluentwasusedtosimulateairflowandtemperatureinthelightwell.Steady-stateairflowandheattransferthroughathree-dimensionalmodelwas   car-riedout.ThissectiondiscussestheexecutionofthemethodutilizedtovalidateandcomparetheCFDsimulationmodelswithWTEmodeldevelopedbyKotanietal.[16]Computationalset-tingsandparametersforreferencecaseandsensitivityanalysisareperformed.Thereferencecasesettingsarebasedoncom-mon   andbestpracticeguidelinesofcomputationalparameters.Asystematicsensitivityanalysiswasconductedontherefer-encecasetostudytheimpactofawiderrangeofcomputationalparametersonthereferencecase.Allcomputationalparame-tersforreferencecaseandsensitivityanalysisareshowninTable1.  3.1.Flowdomainandgeometry AbuildingmodelwithdimensionssimilartothemodelusedintheWTE   studyhasbeenusedintheCFDvalidation.Thecompu-tationaldomainofthereferencecase,however,wassetaccordingtobestpracticeguidelines(e.g.[7,36,37]).Thewindwarddistance (frombuildingsurfacetoinlet)andleewarddistance(frombuild-ingsurfacetooutlet)weresetas5Hand10H,respectively,where  504 T.G.Fareaetal./EnergyandBuildings86(2015)502–513 Fig.1. PerspectiveviewofthecomputationaldomainsizeusedinnumericalstudyshowsthebuildingmodellocationandpossiblewinddirectioninletandbuildingmodeldimensionsusedbyKotanietal.[12].  Table1 Conditionsofcomputationalflowparametersforsensitivityanalysiswithindicationofthereferencecaseconditions.GriddiscretizationDomainsizeWallHeatsourceResidualsTurbulenceM.  A(3.89 × 10 5 ) RecommendStandardWF Surfaceflux10 − 5 RNG k – ε B   (5.51 × 10 5 )WindtunnelEnhancedWTSpacevolume10 − 8 R  k – ε C   (9.32 × 10 5 )SST k – ω SSTNote:Exceptfirstrow,itisnotnecessarilyeachrowusedtogetherinonesimulation.WF,   wallfunctions;WT,   walltreatment;M,   model. Histheheightofthebuilding.Thelateralandthedistancefromthetopofthebuildingtothetopofthedomainweresetas5H.Theresultingcomputationaldomainsizeis7.344m × 7.344m × 2.88m(width × depth × height).Sincetherecommendedsizedoesnothavethesamedimensionsasthewindtunnel,anothercomputa-tionaldomainwithsimilarcrosssectiondimensionstothewindtunnel,1.4m × 1.6m(depth × height)wasmodeledforthesensi-tivityanalysis.However,thesizeofthecrosssectionoftheinflowdomainshouldbecommensuratewithrecommendedblockageratio[36,38].Theblockageratioofthecrosssectionofthewind tunnelandsurfacebuildingareawasabout3.1%whichindicatesanacceptablemaximumvalue.Takingintoaccountthecomputa-tionaltime,thewindwardandleewarddistancesweresetat2Hand4H,respectively,andthecrosssectionofthewindtunnelwasmaintained.AirflowrateandtemperatureresultsinthelightwellofeachofthetwodomainsizeswerecomparedwiththeWTE   data.Fig.2showsthattherecommendedsizedomainproducedresultsthatareclosesttotheexperimentaldata.Inordertoexamineallcomputationaldomaincandidatesunderthesameconditions,theywerediscretizedwiththesamemeshsizeandcellsgrowthrate.  3.2.Griddiscretization Thecomputationaldomainwasdiscretizedusinganunstruc-turedgridwithhighresolutioninthelightwellandthehorizontalvoid,wherehigh-gradientflowzonesexists(Fig.3).Agrowthrate of1.1%inalldirectionsfromthesezoneswasimplementedforthemeshesinwholedomain.Thespatialdomainwasdividedintotetrahedralelements.Gridsensitivitytestwascarriedoutwithadifferentnumbersofcells.Therefore,threemeshtypesaremadeupof3.89 × 10 5 (GridA),5.51 × 10 5 (GridB),9.32 × 10 5 (GridC)cells.SimulationresultsoftheabovemeshtypeswerecomparedwiththeWTE   data.Fig.4showsthatGridAisappropriatetoobtain reasonableairtemperatureandairflowrateresultsinthelightwellascomparedtotheWTE   resultswithlesscomputationaltime.Itshouldbenotedherethattheupwindschemeofsecond-orderaccuracyandSIMPLEsolutionalgorithmwereusedforthecon-vectiontermswhiletheleastsquarecell-basedgradientforspatialdiscretizationwasusedbythesimulationforthediffusiontermsof thegoverningequations. 00.050.10.150.20.250.30.350.40.455      H     (    m     ) 10   15   20   25 T SmRecoExp. 30 (Q=2.76) (Q=2.61)(Q=2.80) C allmmend Fig.2. Temperaturedistribution( T  )andairflowrate( Q  )alongtheheight( H  )ofthelightwellinsmall(windtunnelsize)andrecommendedsimulationdomainsizescomparedwithexperimentaldata.  T.G.Fareaetal./EnergyandBuildings86(2015)502–513 505 Fig.3. Griddiscretizationofthewholedomain(a)withmoreelaborationinthebuilding(b)andthelightwellwithvoid(c).  3.3.Boundaryconditions 3.3.1.Inletwindprofile InletwindprofilewasgeneratedincomputationaldomaincorrespondingtotheprofilegeneratedintheWTE.Therefore,one-fourthpowerlawprofilewasgeneratedforareferencevelocityof1.0m/s   andtheresultsshowthatthenumericalprofileisingoodagreementwiththewindprofilegeneratedintheWTE   model(Fig.5).Basedonturbulentintensity( I  u )profilewhichwas   generatedintheWTE, k and ε profileswereverticallygeneratedinthecompu-tationaldomaininletbyintroducingthefollowingequations[36]: k (  y ) = ( I  u (  y ) U  (  y )) 2 (1) ε (  y ) = C  1 / 2   k (  y ) U  ref   y ref  ˛   y y ref   ( ˛ − 1) (2) 00.050.10.150.20.250.30.350.40.455   10      H     (    m     ) Grid B 15 GridGri 20   25 T CExpd A 30 (Q=2.76)A (Q=2.76)B (Q=2.65)C (Q=3.00) o C . Fig.4. Airtemperaturedistribution( T  )andairflowrate( Q  )alongtheheight( H  )of thelightwellforthreetypesofmeshes,coarse3.89 × 10 5 (GridA),fine5.51 × 10 5 (GridB)andfinest9.32 × 10 5 (GridC)comparedwithexperimentaldata(Exp.). where C    isanempiricalconstantequalto0.09.Thesetwoequa-tionscanbeusedtoderivethespecificdissipationrate ω asshowninthefollowingequation: ω (  y ) = ε (  y ) C   k (  y ) (3)Inadditiontothesesolversettings,theintermittencywasfixedat1fortheSSTmodelasthestudyconsideredafullyturbulentflow.  3.3.2.Near-walltreatment  Toapplytheappropriatenear-walltreatmentmethod,simula-tionswerecarriedoutusingastandardwallfunctionandenhancedwalltreatmentmethodsandtheresultswerecomparedwiththeWTE   data.Standardwallfunctiondependsondimensionlessparameter  y +asverticalwalldistancevector.Insmoothwallsthefirstgridcellshouldbewithinthevalidity30<  y +<300[39]or30<  y +<500[40].Therefore,toachieve  y +withintheserec-ommendedranges,coarsemeshwithaminimumsizeof0.005mwasused.Inaddition,simulationwas   carriedoutwiththesameminimumsizebutwithinflationmeshtechnique,providedinANSYS-Meshingsoftware,whichisusedtooptimizethewalllayersofthefloorboundary.Inaddition,enhancedwalltreatmentmethodwasemployedbutwithhighmeshresolution,whereasmallermin-imumsizewasused(0.004m),   asnomeshsizelimitationsare 00.20.40.60.811.20   0.2   0.4   0.6   0.8   1Measured wind velocityOne-fourth Power low profile      H     (    m     ) u   (m/s) Fig.5. Generatinginletprofilenumericallybyone-fourthpowerlowandcomparingwithexperimentalinlet.  506 T.G.Fareaetal./EnergyandBuildings86(2015)502–513 00.050.10.150.20.250.30.350.40.455   10   15   20   25   30 (Q=2.76)(Q=2.76)(Q=2.68)(Q=2.61) T o C      H     (    m     ) Standard WFStandardWF+ifla.Enhanced WTExp. Fig.6. Temperaturedistribution( T  )andairflowrate( Q  )alongtheheight( H  )of thelightwellfornear-walltreatmentadoptingthestandardwallfunction(WF),theenhancedwalltreatment(WT)andstandardwallfunctionwithinflationmesh(WF   +infla). requiredinthismethod.CFDsimulationswereconductedunderthethreetypesofnear-walltreatmentsettingsandcomparedwithWTE   data.TheairflowrateandtemperatureresultsinthelightwellforthethreetypesagreewithWTE   data(Fig.6).Althoughthere isaverysmalldiscrepancyintemperatureprofileswithandwith-outusinginflationmesh,thismethodhasastrongeffectontheairflowrateresultsasshowninFig.6.Therefore,thestandard wallfunctionwithinflationwasusedinfurthersimulationsinthisstudy.  3.3.3.Heatgeneration HeatinthelightwellwasgeneratedbytwocoiledwirefixedsymmetricallyalongitsverticalaxisinWTE.Numerically,itisdif-ficulttosimulatetheheatreleasedfromacoiledwire.Therefore,twodifferentmethodsasprovidedinthesolver(ANSYS-Fluent)havebeenusedtorepresentheatgenerationinthelightwellthatcorrespondstothoseprovidedintheWTE.TheCFDisabletopre-scribesurfaceheatfluxontheinsidesurfacesofthelightwell,andbyspecifyingthevolumetricrateofheatgenerationofthelightwellvolume[41].Anequivalentheatfluxof290W/m 2 wassettorepresentthe40WinWTE,tomeettheheatgenerationinsidethelightwellemittedbythelightwellsurfaces.Forgeneratingheatbyspecify-ingvolumetricrate,allcellsinthelightwellspacewereseparatedwithintheflowdomaininordertogenerateheatthatmeetheatgeneratedintheWTE.Thisseparatedheatwasdividedintotenvirtualregionsandthetotalrequiredenergywasdistributedver-ticallyandequallyforthesevirtualregionstototal16,000W/m 3 whichisalsoequivalent40W.   Inaddition,heatlossfromthelightwellwascalculatedinthecaseofheatgenerationviathelightwellvolume(asnotedin[16])andtheresultsalsowere comparedwithpreviouscases.Fig.7illustratesthattheheatgen- erationthroughprescribingsurfaceheatfluxmethodisclosertoWTE   dataascomparedwithtemperatureandairflowrateinthelightwell.Theprescribedambientairtemperatureof12 ◦ CforthecomputationaldomaincorrespondswiththatusedfortheWTE. 00.050.10.150.20.250.30.350.40.455   10   15   20   25   30   35 (Q=2.76) (Q=2.76)(Q=2.36) (Q=2.10)  T o C      H     (    m     ) Exp.FluxSpace volume (no loss)Space volum (loss 40%) Fig.7. Temperature( T  )andairflowrate( Q  )usingdifferentmethodsforheatgen-eratingby;wallfluxfromtheinternalsurfacesofthelightwell,lightwellvolumewithandwithoutcalculatingheatlosssuggestedbytheauthorsoftheexperimentalstudy,comparedwithexperimentaldata(Exp.).  3.4.Turbulencemodeling  SincetheflowintheWTE   isturbulent( R e >4000),theReynoldsAveragedNavier–Stokes(RANS)modelswereemployedtomodelthemeanairflowinthelightwell.UsingRANSapproachfora3-Dsteady-stateflow,thetime-averagecontinuity(masscon-servation),Navier–Stokes(momentumconservation)andenergy(energyconservation)equationscanbewritten,respectively,as: ∂∂  x i ( u i ) = 0 , (4) ∂∂  x  j ( u  j u i ) =− ∂  p ∂  x i + ∂∂  x  j   ∂ u i ∂  x  j  + ∂   t ij ∂  x  j + g  i , (5) ∂∂  x  j ( u  j T  ) = ∂∂  x  j  kc   p ∂ T  ∂  x  j  + ∂ q t  j ∂  x  j + S t   (6)where   t ij  =−   ¯ u  i u   j  isturbulentstresstensor, q t  j  =−   ¯ u   j t  isturbu-lentheatflux,and S  t   isthesourcetermforenergy. T  and u ,aretheaveragecomponentsofvelocityandtemperature,while u  and t  arethefluctuatingcomponents.SinceselectinganappropriateCFDapproachandaturbulencemodelarethemostcriticalfactorsinfluidflowstudies[42],the currentstudyemployedfouroftheRANS-basedturbulencemod-elstoexaminetheirperformance.Performancewas   measuredintermsoftheabilitytopredicttemperature,airflowrate,andair-flowpatterninthelightwellconnectedtoabottomvoid.ThesearetheRe-normalize k – ε (R  k – ε ),RNG k – ε ,andSST k – ω ,andSST.Thesemodelshavebeenselectedastheyarecommonlyfoundinthelit-erature.ThecomparisonsbetweenallmodelswerepresentedinSection5.  3.5.Convergencecriteria Previousstudies[37,43]recommendedthatconvergenceofthe scaledresidualsdownto10 − 5 isacceptable.However,forvalidationstudiestheuseofmuchlowerresidualstoreachtheconvergedsolutionhasbeenrecommended[37].Inthecurrentstudytwo
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