Optimization of Architectural Form for Thermal Comfort in Naturally Ventilated Gymnasium at Hot and Humid Climate by Orthogonal Experiment

Abstract

As the gymnasiums in subtropical region with hot and humid climate are naturally ventilated during non-competition periods, occupants exercising indoors often feel uncomfortable, especially in summer. In order to provide thermally comfortable and healthy environment for the occupants, the design on architectural form is found to be an effective solution on improving indoor thermal comfort of naturally ventilated gymnasiums. Therefore, a new perspective regarding optimization of naturally ventilated gymnasiums is proposed in the aspect of the architectural form. This paper presents the optimization of architectural form in naturally ventilated gymnasiums in which simulation and orthogonal experiment methods are combined. Through numerical simulation with FlowDesigner software, the significance of architectural form affecting indoor thermal comfort has been given, and the optimal architectural forms of naturally ventilated gymnasium are determined. The results show that the roof insulation type is the most significant factor influencing indoor thermal comfort; thus, it should be considered primarily in optimization. Moreover, the range analysis and variance analysis reveal the rankings of the factors for the gymnasium thermal comfort. In addition, it is demonstrated that the optimal gymnasium model, when compared with the initial gymnasium model, has a satisfactory effect on improving the indoor thermal comfort, as the average value of Predicted Thermal Sensation (PTS) in August decreased from 1.11 (Slightly hot) to 0.86 (Comfortable). This study provides a new insight for the designers in optimizing the architectural form of gymnasiums for achieving the indoor thermal comfort at hot and humid climate.

Full text

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Energies2021,14,3228.https://doi.org/10.3390/en14113228www.mdpi.com/journal/energies
Article
OptimizationofArchitecturalFormforThermalComfort
inNaturallyVentilatedGymnasiumatHotandHumid
ClimatebyOrthogonalExperiment
XiaodanHuang
1,2,
*,QingyuanZhang
2
andInekoTanaka
2

1
SchoolofArtandDesign,GuangdongUniversityofTechnology,Guangzhou510090,China
2
InstituteofUrbanInnovation,YokohamaNationalUniversity,Kanagawa240‐8501,Japan;
cho‐seigen‐jc@ynu.ac.jp(Q.Z.);itanaka@ynu.ac.jp(I.T.)
*Correspondence:dandyhuang@163.com
Abstract:Asthegymnasiumsinsubtropicalregionwithhotandhumidclimatearenaturallyven‐
tilatedduringnon‐competitionperiods,occupantsexercisingindoorsoftenfeeluncomfortable,es‐
peciallyinsummer.Inordertoprovidethermallycomfortableandhealthyenvironmentforthe
occupants,thedesignonarchitecturalformisfoundtobeaneffectivesolutiononimprovingindoor
thermalcomfortofnaturallyventilatedgymnasiums.Therefore,anewperspectiveregardingopti‐
mizationofnaturallyventilatedgymnasiumsisproposedintheaspectofthearchitecturalform.
Thispaperpresentstheoptimizationofarchitecturalforminnaturallyventilatedgymnasiumsin
whichsimulationandorthogonalexperimentmethodsarecombined.Throughnumericalsimula‐
tionwithFlowDesignersoftware,thesignificanceofarchitecturalformaffectingindoorthermal
comforthasbeengiven,andtheoptimalarchitecturalformsofnaturallyventilatedgymnasiumarede‐
termined.Theresultsshowthattheroofinsulationtypeisthemostsignificantfactorinfluencingindoor
thermalcomfort;thus,itshouldbeconsideredprimarilyinoptimization.Moreover,therangeanalysis
andvarianceanalysisrevealtherankingsofthefactorsforthegymnasiumthermalcomfort.Inaddition,
itisdemonstratedthattheoptimalgymnasiummodel,whencomparedwiththeinitialgymnasium
model,hasasatisfactoryeffectonimprovingtheindoorthermalcomfort,astheaveragevalueofPre‐
dictedThermalSensation(PTS)inAugustdecreasedfrom1.11(Slightlyhot)to0.86(Comfortable).This
studyprovidesanewinsightforthedesignersinoptimizingthearchitecturalformofgymnasiumsfor
achievingtheindoorthermalcomfortathotandhumidclimate.
Keywords:thermalcomfort;architecturalform;gymnasium;hotandhumidclimate;
orthogonalexperiment

1.Introduction
Asapublicspaceforsports,exercises,andentertainments,gymnasiumsplayanim‐
portantroleinpeople’sdailylife.Inthesubtropicalareas,thethermalcomfortofoccupants
exercisingingymnasiumsisrelatedtotheutilizationrateofgymnasiums,energyconsump‐
tion,andhumanhealth.Inhotandhumidclimate,occupantspreferpursuingthermalcomfort
byairconditionerswhendoingsports.However,althoughtheairconditionersprovideacom‐
fortableenvironmentforoccupantsdirectly,thiswouldincreaseenergyconsumptionandcar‐
bondioxideemissions.Moreover,humanadaptiveabilitytothenaturalenvironmentwould
beweakened,aswellastheirhealth,whileexercisinginsuchplacesforalongtime[1].There‐
fore,thestudyonthethermalcomfortinnaturallyventilatedgymnasiumathotandhumid
climatehasbeensignificantlyregardedtoday[2].
Peoplecouldachievethermalcomfortmainlyfromtwoaspectsbytwomethods:One
isindividualadjustment,suchastheactivitylevel,clothing,andpsychologicalexpecta‐
Citation:Huang,X.;Zhang,Q.;
Tanaka,I.Optimization
ofArchitecturalFormforThermal
ComfortinNaturallyVentilated
GymnasiumatHotandHumid
ClimatebyOrthogonalExperiment.
Energies2021,14,3228.
https://doi.org/10.3390/en14113228
AcademicEditors:PatrickPhelan
andBorisIgorPalella
Received:1April2021
Accepted:29May2021
Published:31May2021
Publisher’sNote:MDPIstays
neutralwithregardtojurisdictional
claimsinpublishedmapsand
institutionalaffiliations.

Copyright:©2021bytheauthors.
LicenseeMDPI,Basel,Switzerland.
Thisarticleisanopenaccessarticle
distributedunderthetermsand
conditionsoftheCreativeCommons
Attribution(CCBY)license
(http://creativecommons.org/
licenses/by/4.0/).

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tion[3–6];theotheristhermalenvironmentregulating,suchastheindoorairtemperature,
relativehumidity,meanradianttemperature,andairvelocity[3,4].Althoughoccupants
couldadjustthemselvesonachievingthermalcomfort,theregulatingonthermalenviron‐
mentcouldbemoreeffectiveandcomprehensive[7,8].Furthermore,intheaspectofar‐
chitecturaldesign,improvingthethermalenvironmentbyadjustingthearchitectural
formsisoneofthemosteffectivemethodstoachievethermalcomfort.
Intheresearchofthecorrelationbetweenthearchitecturalformandthethermalcom‐
fort,Wei[9]focusedonthemainenergy‐savingmeasuresofgymnasiumbuildingsand
analyzedthesignificantsequenceoftheimpactofpassiveenergy‐savingtechnologieson
theenergyconsumptionandthecoolingload.AccordingtoWei,theexternalshadingand
naturallightingwerethemostsignificantfactors;however,theirordersweredifferent
duetotheirrespectiveinfluencecharacteristics.Yangetal.[10]investigatedtheadaptive
thermalcomfortandclimateresponsivestrategiesindry‐hotanddry‐coldareasinChina
andfoundthatthearchitecturewithasemi‐basementcouldsatisfythethermalcomfort
efficiently,followedbynightventilationinsummer.Li[11]simulatedthewindpressure
inagymnasiuminhotandhumidareainChinatoanalyzetheinfluencesofinterfaceform
onnaturalventilationandfoundthattheformofasymmetricinterfacecouldimprovethe
ventilationcapacity.Huangetal.[12]analyzedthetopandsideinterfaceformsofgym‐
nasiumsinGuangzhou,Chinaandfoundthatthedoubleskinroofandopenableside
interfacecouldenhancethehumanthermalcomfort.Althoughthestudiescorrelatedbe‐
tweenthearchitecturalformandthethermalcomfortcanbefound,mostofthemarefo‐
cusedondwelling,school,andofficebuildings[13–18].Thesestudiesrarelyfocusedon
thegymnasiumbuilding,whichplayedadistinctiveroleonthermalcomfortforthefea‐
turesoflargespace,specificfunction,andcertaingroupofpeople.Inaddition,fewre‐
searchstudiesmulti‐factorbyorthogonalexperimentmethod[19–21].Mostofthem,how‐
ever,focusonsingleinfluentialfactorofbuildingform,rarelyconductcomprehensive
andintegratedanalysisonmulti‐factor,whichhasamorepracticalandmeaningfulfor
theresearchofthermalcomfort.
Thisstudyaimstoimprovetheindoorthermalcomfortofnaturallyventilatedgym‐
nasiumsathotandhumidclimatethroughcomprehensivearchitecturalformoptimiza‐
tion.Basingonthefieldinvestigationin15gymnasiumsinGuangzhouChina,whichisa
typicalcityinsubtropicalregionwithhotandhumidclimate[22],aninitialmodelofgym‐
nasiumwasestablishedtoanalyzetheindoorthermalcomfortandexploretheoptimizing
orientation.Anorthogonalexperimentwithvarietyoffactorsandlevelschosenbyana‐
lyzingthefieldinvestigationwasthenconductedandsimulatedwiththeFlowDesigner
software.Basedonthesimulationresults,thesignificantfactorsofarchitecturalformon
thermalcomfortwereidentified.Furthermore,theoptimalcombinationofarchitectural
formsofgymnasiumwassuggestedtoprovidereferenceforthegymnasiumsdesignat
hotandhumidclimate.
2.MaterialsandMethods
Inordertoanalyzethethermalcomfortwithmultiplefactorsandtheoptimization
ofarchitecturalformingymnasiums,ahybridmethodthatcombinestheorthogonalex‐
perimentandcomputersimulationisconductedinthisstudy,showninFigure1.

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Figure1.Flowchartofthehybridmethodforsimulationandoptimization.
2.1.SimulationToolandItsValidation
Thefirststepaimstoconsiderasuitabletoolforthermalenvironmentsimulation.In
ordertoachieveaccuratecalculation,simulationtoolshavebeendevelopedbyresearch‐
ersandengineers,suchasEcotect,TRNSYS,PHOENICS,Fluent,andFlowDesigner.Con‐
sideringthattheairtemperature,relativehumidity,airvelocity,andthethermalcomfort
inthedynamicthermalenvironmentarethemainfactorsinvolvedinthisstudy,
FlowDesigner,atypeofcomputationalfluiddynamics(CFD)simulationsoftwarewas
usedinthisstudyforthethermalandfluidsimulationsofgymnasiums.Thissoftwarecan
enablewindandthermalanalysisbyeasilyimporting3Dmodelsofbuildingsorurban
blocksdevelopedbymodelingtools,whichcouldprovideearlyanalysisandreducethe
designtime.Therefore,itisfriendlytousedandverifiedinmanystudies[23–25].
InordertoverifytheaccuracyoftheresultsfromtheFlowDesigner,thethermalen‐
vironmentbetweensimulationandthatfromfieldmeasurementsarecompared.Thefield
measurementwasconductedinagymnasiumlocatedatthedowntownareaofGuang‐
zhou,China,between28Julyand10August2016.Thegymnasiumwascompletedin1996
withthestructureofsteel.Itisopenonthesouth,east,andnorthsides,withasizeof57.6
m×31.2m×10.8minlength,width,andheight.Thereare3basketballcourtsinthe
gymnasiumsandaremainlyusedforathletes’dailytrainingandexercises.Thegymna‐
siumisindoorgymnasiumsandnaturalventilatedduringthemeasurement.Thevalues
oftheindoorairtemperature,indoorrelativehumidityandindoorairvelocityweremeas‐
uredinthecompetitionfieldofgymnasiumat30‐mininterval,from9:00to18:00.The
physicalmeasuringinstrumentswerearrangedinfivepoints,asshowninFigure2,
aroundthecompetitionfieldataheightof1.1minlinewiththerelevantstandards[26].
Inturnsofsimulation,thegymnasiumwassimulatedusingtheFlowDesignerwiththe
weatherdataforthesimulationisobtainedfromTheUnitedStatesNationalClimaticData
Center[27],whichprovidesglobalhistoricalweatherandclimatedatafromobservations.
Preliminary analysis
Determining optimization target and method
Suggesting the initial model
Simulations and orthogonal experiment
Selecting orthogonal table, factors and levels
Establishing numerical simulation models on FlowDesigner
Conducting orthogonal experiments (numerical simulations)
Optimization analysis
Range analysis
Variance analysis
Proposing optimal architectural form of gymnasium

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Figure2.Theinteriorviewandplanofthemeasuredgymnasiums(Points○1to○5representthe
locationsofthemeasuringinstruments).
Figure3showsthevariationsofindoorairtemperature,relativehumidity,andair
velocitybetweenmeasurementandsimulation,eachvaluerepresentsasinglepointat
each30min.Thevariationtendenciesofairtemperatureinmeasurementandsimulation,
asshowninFigure3a,areconsistentwitheachother,aswellasthetendencyofrelative
humidity,asshowninFigure3b.Thebiggestdifferencebetweenmeasureddataandsim‐
ulateddataofairtemperatureis2.92°Cappearingat14:30on10August,andtheleast
differenceis0.01°Cat10:30on4August.Asfarasrelativehumidity,thebiggestdiffer‐
enceis24.78%at14:30on28Julyandtheleastdifferenceis0.02%at16:30on29July.While
thevariationofairvelocitybetweenmeasurementandsimulationarelessconsistent,as
showninFigure3c,theaveragevaluesofmeasurementandsimulationare0.31m/sand
0.43m/s,respectively,whichshowslittledifference.

(a)Variationofindoorairtemperature

(b)Variationofindoorrelativehumidity
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Air temperature (
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Relative humidity (%)
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(c)Variationofindoorairvelocity
Figure3.Comparisonofthethermalenvironmentvariationsbetweenmeasurementandsimulation.
Thereasonforthediscrepancybetweenthesimulateddataandthemeasureddatais
thatthebuildingenvironmentisidealinsimulation,whilethebuildingenvironmentis
complexandchangeableinpractice.Forexample,theperformanceofthematerialiscon‐
stantinthesimulatedenvironmentbutischangeableintheactualenvironmentwiththe
changeofthethermalenvironment;theparametersofinsolationaresimpleinthesimu‐
lation,buttheconditionsofinsolationintheactualenvironmentarecomplex,which,toa
certainextent,affectstheairtemperatureandradiation.Ontheotherhand,thesimulation
accuracyislimited;forinstance,theaccuracyofthegridsettinginthesimulationsoftwareis
limited,andtheparameterconditionsofthespecialmodelarelimited,whichleadstothedif‐
ferencebetweenthesimulationdataandthemeasureddata.Althoughtherearesomeerrors
betweenthem,thetrendsandaveragevaluesshowninFigure3arestillrelativelyconsistent.
Therefore,webelievethattheFlowDesignersoftwarecanbeusedinthisstudy.
2.2.SelectionofThermalComfortModel
Sincethethermalcomfortisthemainissuediscussedinthisstudy,athermalcomfort
modelwouldbeselected.Thethermalcomfortmodels,suchasPMVandSET,arewidely
usedaroundtheworld;however,noneofthemispropertoevaluatethethermalcomfort
formovingsubjects,suchasathletes[3,4,28].Forexample,PMVislimitedtothesteady
stateenvironment,andSETcouldbeappliedinthenaturallyventilatedenvironment;
however,itcouldonlybeusedforthepeopleinlowmetabolicrate.Becausetheresearch
objectinthisstudyisthethermalcomfortinthestateofexerciseinnaturallyventilated
gymnasiums,athermalcomfortmodelthatisapplicablefortheoccupantsinhighmeta‐
bolicratesingymnasiumsisrequired.Throughthefieldsurveyonthethermalsensation
ofexercisingoccupantsingymnasiumsinhot‐humidareaofChina,amodelcalledthe
PredictedThermalSensation(PTS)wasproposedinapreviousstudy[29].Thismodelis
availableforaccuratelyestimatingthethermalsensationofoccupantswithexercisesin
gymnasiumsathotandhumidclimateinChina.ThePTSmodelisformulatedinEquation
(1),andthescaleisshowninTable1.
PTS=−5.127+0.201Top+0.001Wa−0.045v+0.002M−1.184Icl(R2=0.814),(1)
wherePTSisthePredictedThermalSensation,whosevaluesrangesfrom−3to3asthe
TSVdoes;Topistheoperativetemperaturein°Crangesfrom10°Cto40°C;Waisthe
humidityratioing/kg’variesfrom8g/kg’to25g/kg’;vistheairvelocityinm/s;Misthe
metabolicrateinW/m2,whosevaluesrangesfrom250W/m2to350W/m2;Iclistheclothing
insulationinclovariesfrom0.22cloto0.29clo.
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Air velocity (m/s)
Measured data Simulated data

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Table1.ScaleofPTSmodel.
−3−2−10+1+2+3
ExtremelycoldColdSlightlycoldComfortableSlightlyhotHotExtremelyhot
2.3.PrincipleofOrthogonalExperiment
Orthogonalexperimentisasystematicandstatisticalmethodforachievingtheopti‐
mizationofmultiplefactorswithdifferentlevelsofvalues[20].Thesestandardarrays
providethewayofconductingtheminimalnumberofexperimentswhichcouldgivethe
fullinformationofallthefactorsthataffecttheperformanceparameter.Theorthogonal
tableisthefoundationoftheorthogonalexperiment,asshowninEquation(2).
Ln(mk),(2)
whereListhesymboloftheorthogonaltable;nisthenumberoftrialsarrangedinthe
orthogonalexperiment;misthenumberoflevels;kisthenumberoffactors.
2.3.1.RangeAnalysis
Astheappropriateanalysismethodsfortheorthogonalexperiment,twomethodsare
introduced,rangeanalysisandvarianceanalysis[21].Rangeanalysisaimstodetectthe
levelsofdifferentinfluentialfactorsonindices,asshowninEquation(3).Inthisanalysis,
thelargervalueofRj,thegreaterimportanceofthefactor.
Rj=max(kji)−min(kji),(3)
whereRjistherangeofvaluesbetweenthemaximumandminimumvaluesofKji.Kjiis
theaveragevalueofthesumoftheexperimentalresultsatalllevels(i,i=1,2,3)ofeach
factor(j,j=A,B,C,D,E,F).
2.3.2.VarianceAnalysis
Forfurtheranalysis,thevarianceanalysiscanbeusedtodeterminetheinfluences
fromexperimentalconditions,errorsandthesignificantoffactors.Inthevarianceanaly‐
sis,thesumofthesquareddeviation(SS),thedegreeoffreedom(df),andthevarianceof
thefactororerror(V)areexpressedasEquations(4)and(5).TheFvalueiscomparedto
acriticalvalueofasignificantlevel,whichisnormallysetat0.05.Theimpactofthese‐
lectedfactoronthetestresultsisconsideredtobesignificantifitisgreaterthanthecritical
value,andviceversa.
SS ∑

 W
w,(4)
V=SS/df,(5)
whereSSisthesumofthesquareddeviation;Wkistheresultsofeachtrial(k,k=1,2,3,
……,n);wisthearithmeticaverageofWk;dfisthedegreeoffreedom;Visthevariance
ofthefactor.
2.4.StatisticalAnalysis
Inthisstudy,theresearchprocessbeginswiththeorthogonalexperimentaldesign,
thenconductsthesimulationofthetrialsinorthogonalexperiments,and,finally,analyzes
theoptimizationresultintheaspectofthermalcomfort.Asthesimulationin
FlowDesigneronlyoutputsthevaluesofairtemperature(Ta),surfacetemperature(Tk),
relativehumidity(RH),andairvelocity(v),afurthercalculationshouldbeconductedto
obtainthePTSvalue.
ThePTSequation,asshowninEquation(1),containsfiveparameters:operativetem‐
perature(Top),humidityratio(x),airvelocity(v),metabolicrate(M),andclothinginsula‐
tion(Icl).Theoperativetemperature(Top)canbecalculatedwithEquation(6)[3],andthe
meanradianttemperature(Tr)iscalculatedwithEquation(7)[4,30].Thehumidityratio

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

(Wa)iscalculatedbytherelativehumidity(RH),asshowninEquation(8).Themetabolic
rateiscalculatedbasinguponthemeasurementofheartrateproposedintheISO8996[31].
Sincetheexercisingstateingymnasiumisthepremiseofthestudy,theaveragevalueof
300W/m2collectedfromthepreviousfieldsurveyisappliedinthispaper.Theclothing
insulation,calculatedfromASHRAEStandard55‐2017[3],is0.22clofortheoccupants
exercisingingymnasiumathotandhumidclimate.
Top=ATa+(1−A)Tr,(6)
T
∑

 T
F ,(7)
𝑊
0.622  
,(8)
whereTopistheoperativetemperaturein°C;Aisacoefficientasafunctionoftheaverage
airvelocity[3];Taistheairtemperaturein°C;Tristhemeanradianttemperaturein°C;
TNisthesurfacetemperatureofsurface(N)in°C;Fp‐Nistheanglefactorbetweenaperson
(p)andsurface(N);Waisthehumidityratioing/kg’;RHistherelativehumidityin%;pas
isthesaturatedwatervaporpressureinPa;pistheatmosphericpressureinPa.
3.TheInitialModelofGymnasiuminHotandHumidArea
3.1.TheSituationofGymnasiumsinGuangzhouCity
Thebasicforoptimizingthearchitecturalformofgymnasiumisfirsttorealizethe
situationofgymnasiumsexhaustively.Toobtainthearchitecturalparametersofgymna‐
siums,investigationwascarriedoutaround15naturallyventilatedgymnasiumsin
Guangzhou.Theinvestigationincludesthebuildingsize,audiencecapacity,auditorium
layout,buildingmaterial,andthecharacteristicsofthearchitecturalforms.Table2gives
thebuildinginformationofinvestigatedgymnasiums,presentingthatthegymnasium
sizesaremediuminmajorwitharound3000~6000seatsandtwo‐sidedauditorium.Most
ofthegymnasiumsarebuiltbythematerialofreinforcedconcrete.Intermsofthewindow
position,mostofthewindowsininvestigatedgymnasiumsareattheheightofthewalls.
Asthewindow‐to‐wallratio(WWR)stipulatinglessthan0.7inpublicbuildingsaccording
totherelevantregulationsofChina[32],theWWRinmostinvestigatedgymnasiums
achievethisstandard,and10ofthemevenlessthan0.3.Intheaspectofroofslope,8
gymnasiumsarehorizontalroofs,and7aresloperoofs.Sincetheshadingisimportantin
southernChina,overhangingeavesarebuiltinmostofthegymnasiumswithdifferent
depths.
Table2.InformationofnaturallyventilatedgymnasiumsinGuangzhouCity.
ParameterSituationPercentage
SizeMedium8/15
Small7/15
Audiencecapacity(seat)3000~60008/15
≤30007/15
Auditoriumlayout(side)
≤29/15
>26/15
BuildingmaterialReinforcedconcrete14/15
steel1/15
Buildingheight(meter)
≤1510/15
>155/15
Mainwindowposition
Heightofthewalls8/15
Bottomofthewalls2/15
Bothheightandbottomofthewalls2/15
Ontheroo
f
3/15

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window‐to‐wallratio(WWR)
≤0.310/15
0.3~0.75/15
Roofslope
Horizontalroof8/15
Singleslope3/15
Multi‐slope4/15
OverhangingeaveWithoutoverhangingeave2/15
Withoverhangingeave13/15
3.2.PlanLayoutoftheInitialModelofGymnasium
AbstractingthemainparametersfromtheinvestigatedgymnasiumsinGuangzhou,
aninitialmodelofgymnasiumisbuiltupasabasisforsimulationandoptimizationin
thenextstep,theplanlayoutandperspectiveoftheinitialgymnasiummodelareshown
inFigure4.Thegymnasiummodelissettledinmediumsizewithatotalareaof3150m
2
.
Therearetwosidesauditoriuminit,with3688seats.Thebuildingmaterialisreinforced
concrete,andtheexternalwallsare0.3minthickness.Windowsarebuiltonthehigh
positionofthesouthwallandnorthwall.AlthoughtheWWRoftheinvestigatedgymna‐
siumsarearound0.3,theopenableandtransparentwindowsarefew.Thus,theWWRof
initialmodelissetin0.1asthewindowsareallopenableandtransparent.Inaddition,the
roofofinitialmodelishorizontal,whilethedepthofoverhangingeaveis1m.

Figure4.Planlayoutandperspectiveoftheinitialgymnasiummodel.
3.3.SimulationoftheInitialModelofGymnasium
TheFlowDesignerisusedtosimulatethethermalparametersoftheinitialmodel
overaperiodofonemonth(August)onanhourlybasis.Theweatherdataforsimulation
isobtainedfromtheEnergyPlus[33].Asthegymnasiumisaplaceforsport,thesimula‐
tionzoneofinitialmodelisthecompetitionfield,asshownintheredarea(48.6m×32.4
m×1.1m)ofFigure3.Thenaturalventilationmodeisadoptedinthissimulation,with
theinfluenceofsolarradiationconsideredinthesimulation.Inthecalculationprocess,
theHypothesisofBoussinesqisused,whichmeansthechangeoffluiddensityonlywould
affectthebuoyancy.Moreover,thedetaileddesignparameterinformationaboutthe
buildingenvelopeisdescribedinTable3.Thesimulatedresultsofoperativetemperature,
relativehumidity,airvelocity,andthePTSvaluesoverAugustonanhourlybasisare

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showninFigure5.Thesettingsininitialmodelsimulationareusedforfurthersimulations
ofoptimization.
Table3.Designparameterinformationofthebuildingenvelope.
ComponentMaterialsU‐Value(W/(m
2
·K))
Exteriorwall13mmdecorativebrick+20mmlimemortar+10mmExpandedPolystyrene(EPS)
insulation+240mmaeratedconcrete+20mmlimemortar0.5
Roof
40mmC20fineaggregateconcrete+20mmcementmortar+5mmwaterproof
membrane+30mmcementmortar+60mmExtrudedPolystyrene(XPS)insulation
+20mmcementmortar+120mmreinforcedconcrete+20mmcementmortar
0.35
WindowAluminiumframe+6mmclearsingleglazing6.073
Floor20mmcementmortar+100mmreinforcedconcrete+20mmcementmortar2.813
Foundation20mmcementmortar+80mmfineaggregateconcrete+500mmrammedclay0.887
Figure5presentsthattheindooroperativetemperatureofinitialmodelrangesfrom
27.02°Cto32.27°CinAugust,withanaveragevalueof29.29°Candtherelativehumidity
changesfrom73.64%to89.87%,withanaveragevalueof82.41%,whichisconsistentwith
thefeaturesofthehot‐humidclimate.Inaddition,theaverageairvelocityis0.21m/s,
meetingtherequirementofwindspeedforsports[34].IntheaspectofPTSvalue,the
averagePTSis1.11,whichrepresents“slightlyhot”inthermalsensation.Furthermore,
themaximumvaluereaches1.71,whichiscloseto“hot”inthermalsensation,indicating
thattheindoorthermalcomfortofinitialmodelisnoteffective,andthemeasuresshould
betakentoimprovethethermalcomfortinsummerdays.

(a)(b)(c)(d)
Figure5.Simulatedresultsofinitialmodelofgymnasium.(a)TherangeofoperativetemperatureofinitialmodelinAu‐
gust;(b)TherangeofrelativehumidityofinitialmodelinAugust;(c)TherangeofairvelocityofinitialmodelinAugust;
(d)TherangeofPredictedThermalSensationofinitialmodelinAugust.
4.SimulationResultsandOptimizationAnalysis
Inordertoproposeanoptimalstrategyofarchitecturalformforindoorthermalcom‐
fortofgymnasiums,thefactorsandcorrespondinglevelsofarchitecturalformthataffect‐
ingthermalcomfortofgymnasiumareselectedbasedontheinitialmodelinthissection.
Later,thesimulationsareconductedinFlowDesignerfollowedbythetrialsgenerated
fromtheorthogonalexperimentaldesign.Afterobtainingthethermalenvironmentdata
fromsimulations,thePTSvaluescanbecalculated.Throughtherangeanalysisandvari‐
anceanalysisofPTSvalues,theoptimizedarchitecturalformofgymnasiumissuggested.


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4.1.SimulationFactorsandLevelsofOrthogonalExperiment
Therearemanyfactorsofarchitecturalformthatinfluenceindoorthermalcomfort
ofgymnasium.Accordingtotheinitialmodelandthepreviousresearch,sixparameters
ofarchitecturalformareaddressedinthisstudy,namelythemainwindowposition(A),
southWWR(B),northWWR(C),roofinsulationtype(D),roofslope(E),anddepthofover‐
hangingeave(F).Thesesixparametersaretakenasthefactorsoforthogonalexperiment,and
threelevelsarechosenforeachfactor.TheorthogonalexperimentisshowninTable4.
Table4.Factorsandcorrespondinglevelsoforthogonalexperiment.
FactorLevel1Level2Level3
(A)MainwindowpositionHighatthesouthand
northwall
Lowatthesouthwallandhighatthe
northwall
Highatthesouthwallandlowat
thenorthwall
(B)SouthWWR10%20%30%
(C)NorthWWR10%20%30%
(D)RoofinsulationtypeSingleskinroofDoubleskinroofInsulatedroof
(E)RoofslopeHorizontalroofRisefromsouthtonorthRisefromnorthtosouth
(F)Depthofoverhangingeave1m5m9m
 FactorA:Thewindowpositionaffectsthenaturalventilationandthermalcomfort,
aswellasevenenergyconsumption.Inpreviousresearch,Prakash[35]identifieda
newsetofstrategiestolocatethewindowopeningswhichcouldreducethePMVby
0.12%.Kimetal.[36]demonstratedthatthebuildingsachievethelowestenergycon‐
sumptionwhenthewindowswerelocatedinthemiddleheightinallorientations.
AsthewinddirectioninGuangzhouismainlyfromsoutheasttonorthwest,thewin‐
dowpositiononsouthandnorthismorevaluabletostudythanthatoneastand
west.ThethreelevelsinfactorAinthisstudyaredifferentpositionsofmainwin‐
dowsthatwereselectedfromtheresultofinvestigationandtherelevantresearch.
 FactorBandC:Asasignificantfactoraffectingonindoorthermalenvironment,the
WWRplaysanimportantroleinarchitecturaldesign.Thereareextensiveresearch
andeffortsfocusedontheWWRuptonow.Kahsayetal.[37]triedtoanalyzethe
optimizationofwindowconfigurationforahigh‐risebuildingtominimizeitsenergy
consumption,andheobtainedtheoptimumWWRof30%,48%,and30%foraroom
locatedonthe2nd,15th,and29thfloor,respectively.Wenetal.[38]tooktheindoor
airtemperatureastheparametertoevaluatetheoptimalWWRandproposedaWWR
mapsforthearchitecturaldesignintheearlystages.Accordingtotherelevantre‐
searchandregulationsofChina,aswellastheinvestigationinGuangzhou,theWWR
inthestudyarechoseninthreelevels,10%,20%,and30%.
 FactorD:Theheatgainfromthesolarradiationisakeyprobleminthebuildingsin
southofChina.Sincetheroofsurfacesarethemainpositionsabsorbingradiantheat,
theinsulationmeasuresofroofsarecritical.Zingreetal.[39]comparedthethermal
performancesbetweenthedoubleskinroofandtheinsulatedroofinSingapore,
foundthatthedoubleroofperformsbetterinreducingheatgainintothebuilding
duringdaytimes.Yangetal.[15]analyzedthecorrelationsbetweenindoorthermal
comfortandDouble‐SkinFaçadesindifferentclimaticconditionsandfoundthatthe
solarheatgaincoefficientoftheexternalwindowoftheDouble‐SkinFaçadespos‐
sessedthehighestimportanceaffectingindoorthermalcomfort.Inthisstudy,three
typesofroofareselectedtodiscusstheoptimumforthegymnasiumsinhotand
humidclimate.Thesingleskinroofistheordinaryreinforcedconcreteroofwithout
anypassivecooling;thedoubleskinroofiswithanaircavityof500mmthickness
inside;theinsulatedroofcomposesofreinforcedconcreteandaninsulationboardof
20mmthickness.
 FactorE:Roofslopecanregulatethenaturalventilationandcoolingeffect.Maoand
Yang[40]investigatedtheheattransferperformanceofdouble‐slopehollowglazed

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roofwithdifferentslopeanglesinhotsummerandcoldwinterregions,andthere‐
sultsindicatethattheinnersurfacetemperatureoftheroofreducedobviouslywith
theroofslopedecreases.SincethewinddirectioninGuangzhouissoutheast‐to‐
northwest,thethreelevelsofroofslopeinthisstudyaremainlyconsiderthesouth‐
northdirection.
 FactorF:Theoverhangingeaveinfluencesnaturalventilationandshading,aswell
asheatinsulation.Li[11]simulatedthesymmetricalandasymmetricalmodelsofa
gymnasiuminGuangzhouandrecommendedadjustingthewidthandangleofthe
overhangingeavesofthegymnasiumstoimprovethethermalperformance.Dueto
mostoftheinvestigatedgymnasiumsinGuangzhouownoverhangingeavesonthe
roofs,thethreelevelsoffactorFaredifferentinthedepthofoverhangingeave.
4.2.RangeAnalysis
Sincethesixfactors(A~F)andthreelevels(1~3)foreachfactorareselectedforthe
orthogonalexperiment,theorthogonaltableL18(37)isadoptedaccordingtotheprinciple
oforthogonalexperiment.Then,the18testsaregeneratedandsimulatedinFlowDesigner
toobtainthethermalenvironmentdataandthePTSdata.Table5illustratestherange
analysisresultsfortheinfluenceofdifferentfactorsonthethermalcomfort(PTS).Bycom‐
paringtheRjvaluesofeachfactor,theinfluenceofthesixfactorsonPTSarerankedas
follows:D>A=E>F>C>B.Themostinfluentialfactoronthermalcomfortingymnasium
istheroofinsulationtype.Then,itisfollowedbythemainwindowposition,roofslope,
depthofoverhangingeave,northWWR,andsouthWWR.
Theroofinsulationtypebecomesthemostimportantfactorbecausetheclimatecon‐
ditionsofhightemperatureandhighradiationinGuangzhoumakethebuildingroofre‐
ceivemoreheatthanotherinterfaces.Therefore,differentroofinsulationtypeswouldob‐
viouslyanddirectlyaffecttheheatgainoftheroof,furtherinfluencingtheindoorairtem‐
peratureandmeanradianttemperaturewhichdirectlyaffecttheindoorthermalcomfort.
Inaddition,themainwindowpositionandroofsloperanksecond,probablybecausethey
couldinfluencethewindenvironmenttoacertainextent,whichfurtheraffecttheindoor
thermalcomfort.
Table5.Resultsandrangeanalysisoftheorthogonalexperiments.
TestNumberFactorResultofPTS
ABCDEF
11111111.110
21222220.924
31333330.984
42131221.119
52212330.892
62323110.965
73122130.913
83233211.065
93311321.299
101123321.182
111231131.022
121312210.961
132132310.907
142213121.03
152321231.053
163113231.087
173221311.227
183332120.912

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

K
1
6.1836.3186.3796.8305.9526.235
K
2
5.9666.1606.2645.5096.2096.466
K
3
6.5036.1746.0096.3136.4915.951
k
1
1.0311.0531.0631.1380.9921.039
k
2
0.9941.0271.0440.9181.0351.078
k
3
1.0841.0291.0021.0521.0820.992
R0.0900.0260.0620.2200.0900.086
FactorrankingD>A=E>F>C>B
4.3.CorrelationsbetweenFactorsandIndicator
Thecorrelationsbetweentheindexofinterest(PTS)andthesixcorrespondingfactors
(A~F)arepresentedinFigure6.Itillustratestheinfluencerulesoffactorslevelsonthe
PTSintheprocessofoptimizationofarchitecturalform.TakingFactorAasanexample,
thePTSvalueinLevel1,2,and3is1.031,0.994,and1.084,respectively.Asthevaluein
Level2achievesthelowest,Level2istheoptimumforFactorA.Inthesameway,Factor
B,C,D,E,andFachievethelowestPTSvaluesinLevel3,Level3,Level2,Level1,and
Level3,respectively.Thus,combiningtheoptimallevelofeachfactors,theoptimumcom‐
binationofarchitecturalformisA
2
B
2
C
3
D
2
E
1
F
3
,whichrepresentsthewindowsareatthe
lowpositiononthesouthwallandatthehighpositiononthenorthwall;thesouthWWR
is20%,andnorthWWRis30%;theroofishorizontalanddoubleskin,andthedepthof
overhangingeaveis9m.

Figure6.CorrelationsbetweenthefactorsandthePTS.
BecauseoftheprevailingsoutheastwindinsummerinGuangzhou,thelowwindow
onthesouthwallintroducesthesoutherlywindtothegreatestextent.Meanwhile,thanks
tothethermalpressuredifferenceandthewindpressuredifferencebetweenthewind‐
wardsideandtheleewardside,theindoorhotairflowsoutthroughthehighwindowon
thenorthwall,formingagoodnaturallyventilatedenvironment.Furthermore,alarge
WWRalsoimprovesthenaturalventilation.Asfarasthegymnasiumroofisconcerned,
thedoubleskinroofwouldbenefitfromtheairgap,whichactsasaninsulationlayerto
allowtheairflowtoeffectivelytakeawaytheheattooutdoorenvironment,reducingheat
gainfromtheindoorenvironmentthroughtheprimaryroof.Inaddition,the9‐mover‐
hangingeavecanobtainabettershadingeffect,whichplaysanimportantroleinreducing
solarradiationandindoortemperature.


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
4.4.VarianceAnalysis
Table6presentstheresultsofthevarianceanalysis.Thesumofthesquareddeviation
(SS),thedegreeoffreedom(df),thevarianceofthefactor(V)andFvalue(F)havebeen
calculatedaccordingtotheregulationofvarianceanalysisinorthogonalexperiment.By
comparingtheFvaluesofeachfactortothecriticalvalueF(0.05),Roofinsulationtypeisthe
mostsignificantfactorinfluencingthethermalcomfort.Thefactorsofmainwindowpo‐
sition,roofslope,depthofoverhangingeave,northWWR,andsouthWWRarelesssig‐
nificantthanthefactorofroofinsulationtype.
Table6.VarianceanalysisofthePTS.
FactorSSdfVFF(0.05)Significance
A0.02420.0120.7213.74*
B0.00320.0020.0903.74
C0.01220.0060.3613.74
D0.14820.0744.4463.74**
E0.02420.0120.7213.74*
F0.02220.0110.6613.74
Deviation0.231140.016 
Note1:*representsthesignificanceofthedifferentfactor.Themorethe**areshown,thehigherthe
significanceofthecorrespondingfactoris.
5.DiscussionontheOptimizationEffects
5.1.OptimizedModelvs.InitialModel
Comparingwiththeinitialmodelofgymnasium,theoptimizedmodelofgymna‐
siumimprovesalot,aslistedinTable7.Thechangeofwindowposition,aswellasWWR,
improvesthenaturalventilationastheindooraverageairvelocityincreasesfrom0.21m/s
to0.77m/sonsummerdays.Asasignificantfactor,thedoubleskinroofinoptimalmodel
improvesthethermalperformances,theindooraverageoperativetemperaturedecreases
from29.3°Cto28.21°C,andthePTSdropsfrom1.11(slightlyhot)to0.86(comfortable).
Table7.Comparisonofarchitecturalformsandthermalperformancesbetweentheinitialmodelandtheoptimizedmodel.
ParametersInitialModelOptimizedModel
WindowpositionHightothesouthandnorthLowtothesouthandhightothenorth
WWRSouthandnorthfor10%Southfor20%andnorthfor30%
RoofinsulationtypeSingleskinreinforcedconcreteDoubleskinreinforcedconcrete
RoofslopeHorizontalroo
f
Horizontalroo
f

Depthofoverhangingeave(m)19
Indooravg.operativetemperature(°C)29.3028.21
Indooravg.humidityratio(g/kg’)20.1620.15
Indooravg.airvelocity(m/s)0.210.77
Indooravg.PTS1.110.86
Figure7showsthevariationofhourlyaveragePTSoftheinitialmodelandtheopti‐
mizedmodelinAugust.TheaveragePTSvaluesintheoptimizedmodelareslightlylower
thanthoseintheinitialmodelbefore11am.Then,thegapbetweenthemgrowstoaround
0.7untilmidnight.ThegapofPTSismainlyreflectedintheafternoonbecausethewall
andthegroundhadacertainheatstoragecapacity,whiletheheataccumulatesinthe
daytimestartstodissipateintheafternoonduetothetimegap.Therefore,theindoor
temperatureandradiationofthegymnasiumwithoutoptimizationincreasesrapidly,
whichresultsinanincreaseofthePTSvalue.Onthecontrary,theoptimizedgymnasium
formimprovestheindoorthermalenvironmentandwindenvironment,thusslowing

Energies2021,14,322814of18


downtheincreaseoftheindoortemperatureandradiation,increasingtheindoorairflow
rate,butreducingthePTSvalue.Thisphenomenonindicatesthattheoptimizedgymna‐
siumformcouldimprovetheindoorthermalcomforttosomeextent,andsuchoptimized
gymnasiumswouldbebeneficialtopeopleandthecities.

Figure7.VariationofhourlyaveragePTSbetweentheinitialmodelandtheoptimizedmodelin
August.
5.2.ComparingwithOtherStudies
Thisstudyprovesthattheroofinsulationtypeisthemostsignificantarchitectural
formaffectingindoorthermalcomfortofgymnasiumsathot‐humidclimates.Meanwhile,
thedoubleskinroof,benefitingfromtheeffectofthermalinsulationofairgap,obtainsa
betterthermalcomfortthanthesingleskinroofandinsulatedroof.Similarresultshave
beenfoundinotherrelevantstudies.Gaglianoetal.[41]foundthatthedoubleskinroof
couldconstituteaninterestingsysteminordertoreduceheattransferfromtheroofinto
thebuilding,allowingsignificantheatfluxreduction(upto50%)duringsummer.Omar
etal.[42]investigatedthebenefitsofusingdoubleskin‐ventilatedroofsforreducingcool‐
ingloadsanddiscoveredthatusingthedoubleskinroofcouldenhancealmost50%ofthe
energysavingrateratherthanusingthesingleskinroof.Moreover,theenergysaving
efficiencycouldbeevenbetter,upto85%,incasetheroofhasaninsulatedlayer.Zingre
etal.[39]foundthatperformanceofthedoubleskinroofwas28–34%betterthanthatof
theinsulatedroofinreducingheatgainintothebuildingduringdaytimeandallowed3–
5timesmoreheatlossfromthebuildingduringnight‐time.Theseresultsreflectthatthe
doubleskinroof,astheoptimumtypeofroofinsulation,playsanimportantroleinim‐
provingthethermalenvironmentandthermalcomfort.Meanwhile,theresultsalsoillus‐
tratethattheoptimizationofarchitecturalformshasagreatimpactontheindoorthermal
environmentandthermalcomfort.Inthepreviousresearch,Huangetal.[12]foundthat
thegymnasiumwithlargeopeningonthesideinterfaceandmulti‐storyroofachieved
lowerindoortemperatureandbetterventilationefficiency.Besides,Li[11]studiedthe
influenceoftheoverhangingeaveofgymnasiumonthermalcomfortinhot‐humidre‐
gionsandfoundthatadeepoverhangingeaveandsloperoofwereinstrumentalinin‐
creasingthedifferenceofwindpressurebetweenthewindwardsideandtheleewardside,
whichenhancedtheairvelocityby57%comparedtotheformofflatroofandwithout
overhangingeaves.TheresultoftheroofslopeinLi’sstudyisdifferentfromthatinthis
study,whichfoundthatthehorizontalroofwastheoptimumform,probablybecauseof
thedifferencesintheselectionoffactors,optimizationmethods,andmicro‐environment
conditions.However,theresearchideasandtheresultsofoverhangingeavesaresimilar
tothoseinthisstudy.Inaddition,althoughtheWWRforpublicbuildingsshouldnot

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exceed70%,asshownintheDesignStandardforEnergyEfficiencyofPublicBuildings
[32],thisstudyobtainsamoredetailedandtargetedoptimalWWRforgymnasiums(20%
forsouthWWRand30%fornorthWWR)throughinvestigationandoptimization.
5.3.PracticalImplication
Theanalysesinthisstudyindicatethattheroofinsulationisthemostinfluentialfac‐
toronthermalcomfortingymnasiumsathotandhumidclimate.Furthermore,theopti‐
mizedarchitecturalformofgymnasiumhasbeenachievedbytheorthogonalexperiment.
Thisstudyexpandstheapplicationoforthogonalexperimenttomulti‐factorresearchon
gymnasiumdesign.Byconductingalimitednumberofexperimentsintheorthogonal
array,fullinformationoffactorsiseffectivelyobtained.Thismethod,asminimizingthe
effortandtimeduringanalyzes,canbeanalternativeapproachforintegratedarchitec‐
turaldesign.Theresultsinthisstudycanprovideatechnicalreferenceforthegymnasium
design,aswellasaguidelinefortheresearchofsimilartypeofarchitecturelocatedin
regionswithotherclimates.
5.4.Limitations
Althoughthisstudyconductedanorthogonaldesigntoprovideanoptimizationanal‐
ysisoftheinfluencingfactorsofthegymnasiumthermalcomfort,therearesomelimitations.
First,thesmallnumberoffactorsandlevelsofgymnasiumformsinthestudymayaffect
thereliabilityandcomprehensivenessoftheresults.Second,thestudyconsidersonlythe
superpositionoffactors,whiletheinteractionsamongthefactorsarenotinvestigated.Fi‐
nally,theorthogonalexperimentinthisstudyshowsaprocessofaparametricsearchwith‐
outanyiteration.Therefore,weconductin‐depthandprecisestudiesonoptimizationof
gymnasiumformforthermalcomfort,focusingonvariousinfluentialfactorsandlevelsand
thediscussionontheinteractionsamongfactorsandtherigorousofexperiment,soasto
improvethefeasibilityoftheoptimizationdevelopedinthisstudy.
6.Conclusions
Thisstudyhasconductedanorthogonaldesigntoprovideanoptimizationanalysisof
theinfluencingfactors(gymnasiumarchitecturalform)ofthegymnasiumthermalcomfort
inGuangzhouathotandhumidclimate.Theorthogonalexperimentsareappliedassisted
byfieldinvestigationandsimulationswiththeFlowDesigner.Theresultsareanalyzedus‐
ingrangeanalysisandvarianceanalysis,andthemainconclusionsaresummarized.
(1) Sevenhundredandtwenty‐nineexperimentshavebeendramaticallydecreasedto
18testsbythemethodoforthogonalexperiment.
(2) Therangeanalysisandvarianceanalysisdemonstratethattheinfluenceofthesix
factorsonPTS(PredictedThermalSensation)arerankedas:Roofinsulationtype>
Mainwindowposition=Roofslope>Depthofoverhangingeave>Northwindow‐
to‐wallratio>Southwindow‐to‐wallratio.
(3) Intermsofthermalcomfortofgymnasiums,theoptimizedarchitecturalformturns
outtobethecombinationofthewindowsatthelowpositionandhighpositionon
thesouthandnorthwall,respectively;thesouthandnorthwindow‐to‐wallratioof
20%and30%,respectively;ahorizontalroofwithdoubleskinandtheoverhanging
eavewiththedepthof9m.
(4) ThePTS(PredictedThermalSensation)valuedecreasesfrom1.11(slightlyhot)to0.86
(comfortable)viaoptimizationonthegymnasiumforms,andthegapofPTSvaluebe‐
tweeninitialmodelandoptimizedmodelismainlyreflectedintheafternoon.
(5) Thefindingsbenefitdesignersandresearcherstodeterminethekeyparametersin
thegymnasiumarchitecturaldesignandtooptimizethethermalcomfort,aswellas
energyefficiency.

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AuthorContributions:Conceptualization,X.H.,Q.Z.,andI.T.;Methodology,X.H.andQ.Z.;Inves‐
tigation,X.H.;Resources,Q.Z.andI.T.;Software,X.H.andI.T.;Writing‐originaldraft,X.H.;Writ‐
ing‐reviewandediting,Q.Z.andI.T.Allauthorshavereadandagreedtothepublishedversionof
themanuscript.
Funding:ThisresearchwasfundedbytheYouthFoundationofGuangdongUniversityofTechnol‐
ogy,China(GrantNo.17ZK0008).ThisresearchwasalsosupportedbytheresearchfundofYoko‐
hamaNationalUniversityin2020.
InstitutionalReviewBoardStatement:Notapplicable.
InformedConsentStatement:Notapplicable.
DataAvailabilityStatement:Thedatapresentedinthisstudyareavailableonrequestfromthe
correspondingauthor.
ConflictsofInterest:Theauthorsdeclarenoconflictofinterest.
Nomenclature
SymbolTitleUnitofMeasure
AAcoefficientasafunctionoftheairvelocity/
dfDegreeoffreedom/
FStatisticfortest/
Fp‐NAnglefactorbetweenaperson(p)andsurface(N)/
fsSaturatedwatervaporpressurePa
IclStaticclothinginsulationclo
kNumberoffactorsinorthogonalexperiment/
KjiSumoftheexperimentalresults/
kjiAveragevalueofKji/
LSymboloftheorthogonaltable/
MMetabolicrateW/m2
mNumberoflevelsinorthogonalexperiment/
nNumberoftrialsinorthogonalexperiment/
pAtmosphericpressurePa
PTSPredictedThermalSensation/
RjRangeofvaluesbetweenthemaximumandminimumvaluesofkji/
RHRelativehumidity%
SSSum