March 14, 2018 REPORT #E18-304

Secondary Glazing System (SGS) Moisture Analysis and Validation

Prepared For NEEA: Rob Curry, Sr. Project Manager

Prepared by: Robert Hart

Ernest Orlando Lawrence Berkeley National Laboratory 1 Cyclotron Rd. Berkeley, CA 94720 510-486-4000

Northwest Energy Efficiency Alliance PHONE 503-688-5400EMAIL info@neea.org

Disclaimer

ThisdocumentwaspreparedasanaccountofworksponsoredbytheUnitedStatesGovernment.Whilethisdocumentisbelievedtocontaincorrectinformation,neithertheUnitedStatesGovernmentnoranyagencythereof,norTheRegentsoftheUniversityofCalifornia,noranyoftheiremployees,makesanywarranty,expressorimplied,orassumesanylegalresponsibilityfortheaccuracy,completeness,orusefulnessofanyinformation,apparatus,product,orprocessdisclosed,orrepresentsthatitsusewouldnotinfringeprivatelyownedrights.Referencehereintoanyspecificcommercialproduct,process,orservicebyitstradename,trademark,manufacturer,orotherwise,doesnotnecessarilyconstituteorimplyitsendorsement,recommendation,orfavoringbytheUnitedStatesGovernmentoranyagencythereof,orTheRegentsoftheUniversityofCalifornia.TheviewsandopinionsofauthorsexpressedhereindonotnecessarilystateorreflectthoseoftheUnitedStatesGovernmentoranyagencythereoforTheRegentsoftheUniversityofCalifornia.

1. EXECUTIVE SUMMARY ArefinedmethodologyforsimulatingthehygrothermalconditionsadjacenttoandonglasssurfacesisdevelopedandperformedfornineproductsasanextensiontotheworkpresentedinSecondaryGlazingSystem(SGS)Thermal,Solar,andEnergyPerformanceAnalysisandValidation(Hart2005).ExtensionstoBerkeleyLabTHERMandWINDOWsoftwaretoolsareimplementedandweintroducetheconceptofcondensationresistanceofunsealedgaps(CRU)indicesasacompaniontotheexistingNFRCCRratings.Thesemodelsarevalidatedthroughexperimentsbylocaltemperatureandmoisturepropagationmeasurements,andthereforeprovideaccuratedeterminationofCRUatpredeterminedhumidityratios.ThereportedCRUnumbersseemtobemostlyontheverylowend(i.e.,verypoorperformance)forallunsealedunitsduetotheuseofhumidityratiosthatarerepresentativeofindoorroomair.Thisindicatesthatfurtherresearchmightbeneededtoestablishexpectedmoisturecontentinunsealedgapsfordifferentproducttypesandtorelatethemtoindoorroomair,sothatmorerepresentativeCRUprocedurecanbedeveloped.FourSGSsystemsaremeasuredforairleakageandmoisturepropagationperformance.Theresultsvarygreatlybetweenproducts;frompreventingallairleakageandmostmoisturetransfertonoresistancetoairormoisturetransfer.ThemeasuredperformancedataiscombinedwiththeresultsofEnergyPlusannualenergysimulationstodeterminetrendsandrelativecondensationperformanceofnineSGSproducts.Wemaketheassumptionthattherearenomoisturesourcesorsinks,andthereisnoliquidtransportflux.Bothoftheseassumptionsaresignificantinthatcondensedmoistureisconsideredoutofthesystem,potentiallymisjudgingthecondensationtime.Withtheseassumptionsandknowingthatallbuildingsarecontrolledandperformdifferently,theresultspresentedhereshouldbeviewedonlyasindicatorsofrelativeperformancebetweenSGSproductsandnotabsolutecondensationpotential.TheresultsshowthatallSGSsystemscontainingunsealedglazingcavitiesincreasecondensationriskoversinglepanebasewindows.Condensationriskishighestonnorthfacingsurfaces,andlowestoneastfacing,butthetimedifferenceisrelativelysmall.Condensationalsooccursmostoftenduringunoccupiedhours.Finally,lowwatervapordiffusionresistancefactorstotheoutsidecoupledwithhighroom-sideresistancetypicallyresultsinthefewestcondensationhours,whiletheoppositecase(highresistancetotheoutsideandlowresistanceroom-side)resultsinthegreatestnumberofcondensationhours.FutureworkshouldincludeinstallationandmonitoringofSGSinrealbuildingstovalidatethesimulationresults.TheCRUmetricisintroducedasapreliminarystepwiththelong-termgoalofastandardizedmetricforcondensationpotentialofSGSandotherattachmentproducts.FurtherdevelopmentoftheCRUmetricshouldbedonetoensureallsignificantaspectsofSGSdesign,suchasresistancetoairleakage

andmoisturetransfer,areconsideredandpresentedfairlywithrespecttotheexistingCRstandards.2. INTRODUCTION BackgroundTheNorthwestEnergyEfficiencyAlliance(NEEA)isinterestedinacceleratingtheadoptionofenergy-savingbuildingenvelopeproducts.ThemarketNEEAismostinterestedinrelativetosecondaryglazingsystems(SGS)consistsofexistingmulti-storyofficebuildingswithsingleglazed,non-thermallybrokenaluminumwindowframesconstructedbetweenthemid-1950sandthemid-1980s.Forthisproject,SGSproductsaredefinedasoneormorepaneglazingunitsdesignedforinsertionintoexistingcommercialstorefrontorcurtainwallsystemswithmonolithicglazing.TheSGSisinstalledfromtheinteriorwiththeintentofimprovingthethermalperformanceoftheexistingglazingsystem.Condensationhasbeenapersistentandoftenmisunderstoodproblemassociatedwithwindows.Itoccurswhenthesurfacetemperatureofawindowcomponentdropsbeloweitherthedewpointorfrostpointoftheairadjacenttothesurface.Incoldclimates,single-glazedwindowscharacteristicallysufferfromwatercondensationandtheformationoffrostontheinsidesurfaceoftheglassinwinter.Condensationcanalsobeaproblemontheinteriorsurfacesofwindowframes.Metalframes,inparticular,conductheatveryquickly,andwill“sweat”orfrostupincoolweather.Solvingthiscondensationproblemwasamajormotivationforthedevelopmentofthermalbreaksforaluminumwindows.Infiltrationeffectscanalsocombinewithcondensationtocreateproblems.Ifapathexistsforwarm,moisture-ladenairtomovethroughoraroundthewindowframes,themoisturewillcondensewhereverithitsitsdewpointtemperature,ofteninsidethebuildingwall.Framesmustbeproperlysealedwithinthewallopeningtopreventthispotentialproblem.Insomeinstances,theinfiltrationairwillbedry,suchasoncoldwinterdays,anditwillthushelpeliminatecondensationonthewindowsurfaces.CondensationriskhasbeenidentifiedbyNEEAasapotentialbarriertobroadSGSmarketpenetration.Somebuildinganalysissoftware,suchasWUFI(Fraunhofer2001),attempttopredictmoisturetransferandcondensationinbuildings.ThesetoolsthougharenotdirectlyapplicabletoSGSproducts.ThecondensationpotentialofSGSsystemsinrealbuildingsisunknown.AreporttitledSecondaryGlazingSystem(SGS)Thermal,Solar,andEnergyPerformanceAnalysisandvalidation,byR.Hartet.al.wasproducedin2015asafirststepintheanalysisofSGS.ThereportestablishedaninitialdatabaseofSGSproductperformance.ThisreportexpandsthatresearchintomoisturetransferandcondensationresistanceofSGS.Therearemultipleobjectivestothisreport,themostsubstantialbeingarefinedmethodologyforsimulatingthehygrothermalconditionsadjacenttoandonglasssurfaces.ExtensionstoBerkeleyLabTHERMand

WINDOWsoftwaretoolsareimplementedandweintroducetheconceptofcondensationresistanceofunsealedgaps(CRU)indicesasacompaniontotheexistingNFRCCRratings.Thesemodelsarevalidatedthroughexperimentsbylocaltemperatureandmoisturepropagationmeasurements.AmethodologyforpredictingcondensationthroughannualenergymodelingsoftwareisdevelopedandusedtopredictcondensationinDOEprototypecommercialbuildingsfornineSGSproducts.ProductdefinitionsThenineproductsanalyzedinthisreportarethesameproductsdefinedinthepreviouslymentionedLBNLreportanditsappendices(Hart2015).Asingleclearglazednon-thermallybrokenaluminumcommercialstorefrontwindowframeisusedasthebaselineglazingsystem.Itisdesignatedasrepresentativeofcommercialwindowsconstructedbetweenthemid-1950sandthemid-1980s.ThegroupofSGSproductssimulatedrepresentsthediversityofcurrentcommerciallyavailableproducts.AlltestedSGSuseglassastheprimaryglazingmaterial.Glazingsvaryfromsinglepaneglasstotriplepanewithasuspendedcenterlayerfilm.Aminimumofonelow-ecoatingispresentinallsystems;withthemostinsulatingproductsutilizinginsulatedglazingunits(IGU)andmultiplelow-ecoatings.Mostsystemssupporttheglazingwithaluminumframingthatattachesdirectlytotheinsidedimensionsofthebasewindow,whileoneproductattachesdirectlytothebasewindowglassandanothermountsexternaltothebaseframe.AlphabeticdesignationsareusedthroughoutthisreportinordertomaintainanonymityoftestedSGS.AlltestedSGSproductscreateaninsulatingairspacebetweenthebasewindowglassandtheSGSglass.Forthepurposesofcondensationresistance,onlyhermeticallysealedanddesiccatedcavitiesareconsideredsealed.Allcavitiesthatarenothermeticallysealednordesiccatedareconsideredunsealed,meaningtheyallowmoisturetotransferfromeithertheroom-sideorexteriorenvironment.GoverningequationsMoisturetransferthroughwindowsprimarilyoccursbymoistairmovementanddiffusion.Moistairmovementoccursthroughleaksandcracksintheframe-wall,frame-glazing,andframe-sashinterfaces.Thedrivingmechanismformoistairmovementthroughwindowsistheairpressuredifferencefrominteriortoexteriorsurfaces.Pressureacrossthebuildingenvelopeoccursfromairdensitygradientsdrivenbyindoor-outdoortemperaturedifferences,bouncy(stackeffect)intallbuildings,wind,andunbalancedmechanicalsystems.Flowthroughbuildingcomponentscantypicallybedescribedbythepowerlawequation(Eq.1).Equations2and3relateairvolumeinthepowerlawequationtomoisture[ASHRAE2009].𝑉 = 𝑐 ∆𝑃 ! [1]

𝑉 = !!!!!

! [2]

𝑊 = !!

!! [3]

whereV [m3] air volume 𝑉 [m3/s] airflowratec [m3/s-Pan] flowcoefficientn [-] pressureexponentP [Pa] ambientairpressureρ [kg/m3] airdensitymw [kg] masswatervaporma [kg] massairW [kgw/kga] HumidityratioMoisturediffusionisdrivenbythegradientofwatervaporpartialpressureintheair.Diffusionofmoisturefromareasofhighconcentrationtolowconcentrationonlybecomessignificantwhenlittletonoairmovementoccurs.Fick’sLaw,orthemoisturediffusionequation,isusedtopredictmoisturevapordiffusion.Thisequation(eq.4)isanalogoustotheheatequationorFourier’sLaw.Equations5and6relatevapordiffusiontowatervaporpartialpressure,airpressure,andtemperature[Kunzel1995].!"!"= −∇ ∙ 𝑔! + 𝑔! + 𝑆! [4]

where𝑔! = − !

!∇𝑃! [5]

𝛿 = 2.0 ∙ 10!! 𝑇!.!" 𝑃 [6]t [s] timegw [kg/m2s] liquidtransportfluxdensitygv [kg/m2s] vapordiffusionfluxdensitySw [kg/m2s] moisturesourceorsinkδ [kg/msPa] watervapordiffusioncoefficientinairµ [-] watervapordiffusionresistancefactorPw [Pa] watervaporpartialpressureT [K] ambientairtemperatureCondensationformsatthecoldestlocations,typicallythelowercornersoredgesofaninsulatedproductevenwhenthecenterofglazingisabovethelimitforcondensation.Generally,astheinsulatingvalueoftheglazingisimproved,theareawherecondensationcanoccurisdiminished.WithSGSproductsthough,condensationpotentialmayincreasewiththeinsulatingvalueoftheproduct.Thisisbecausethetemperatureoftheglassclosesttotheexteriorbecomescolderandis

adjacenttoanun-desiccatedairspace.Condensationpotentialincreasesastheoutdoortemperatureisloweredandtheindoorrelativehumidityincreases.NFRChasdevelopedacondensationresistance(CR)valueforratinghowwellafenestrationproductcanresisttheformationofcondensationontheroomsidesurfaceoftheproductataspecificsetofenvironmentalconditions.TheCRcalculationmethodisdefinedintheNFRC500:ProcedureforDeterminingFenestrationProductCondensationResistanceValues(NationalFenestrationRatingCouncil,2013).ThecondensationresistancemodeloutlinedinNFRC500isdevelopedaroundcondensationonroom-sideexposedsurfacesbecausefactory-sealedinsulatedglazingutilizesapermanentsealtopreventtheintroductionofmoisturebetweenglass.Thevoidmaybefilledwithairordrygases,suchasargon.Adesiccantmaterialintheedgespacerbetweenthepanesisusedtoabsorbanyresidualmoistureintheunitwhenitisfabricatedoranysmallamountthatmightmigrateintotheunitovermanyyears.NFRC500anditsaccompanyinguserguideNFRC501(NationalFenestrationRatingCouncil,2013)containmoreinformationaboutcondensationresistance.TheNFRCCRratingisdesignedforcomparisonofroomsidecondensationpotential.Thecondensationresistanceofunsealedgaps(CRU)proceduredevelopedinthisreportisintendedtodothesameforproductswithunsealedglazingcavities,suchasSGS.TheimportantassumptionmadeinthedevelopmentofCRUisthatsamehumiditycontentofairwasassumedasinCRdetermination(30%,50%,and70%RHat70F),sothatnumbersarebettercomparabletoCR.3. ANALYSIS PROCEDURE Airmovement,localtemperatures,andmoisturediffusionintoandthroughSGSmustbecharacterizedinordertodescribemoisturepropagationandcondensationresistance.Themeasurementandsimulationanalysisproceduresdescribedinthefollowingsectiondetailthemethodsusedinthisreport.MeasurementsAirmovement,localtemperatures,andmoisturediffusionaremeasuredindependentlyusingthreedifferentmeasurementsproceduresdescribedinthefollowingsections.AirmovementAAMA/WDMA/CSA101/I.S.2/A440[AAMA2008]definesairleakageresistancecriterianewfenestrationproductsmustmeetforqualificationintheUS.ThisstandardthoughisnotnecessarilyrepresentativeoftheSGStargetmarketofinstalledsingle-panealuminumwindows.Todeterminetypicalairleakage,wemeasureabaselinesystemaswellasseveralassembledSGSutilizingthestandardtestmethodformeasuringairleakageforwindowsdefinedinASTME283[ASTM2012].Airflowmeasurementsaretakenforarangeofpressuresbetween50Paand

230Pa.Thepressureusedforratingresidential(R)windowsat75Paisincluded.Thehigher300Papressureforratingarchitectural(AW)windowswasnotachievableinallcaseswithourtestequipmentandisthereforeomitted.MeasurementsareperformedwiththeWindMakerPLUStestkitmanufacturedbytheRMGroup.Figure1illustratesthelaboratoryset-up.CalibrationisperformedwiththeWindMakerCalibrationBoxmanufacturedtotheAAMA204-98[AAMA1998]specifications.Theresultsfromthistestarepresentedintheformofvolumetricflowrateperunitwindowarea,q[L/s-m2],asafunctionofdifferentialpressure,P[Pa].

Figure1.Schematicoflaboratorywindowairleakagemeasurements[ASTM2012]LocalTemperaturesThesimulatedCRandCRUvaluesarehighlydependentonaccuratepredictionofsurfacetemperatures.Toverifysimulatedsurfacetemperatures,thebasewindowandaselectionoffourSGSsystemsweretestedintheLBNLlaboratoryoverarangeofoutdoortemperaturesfrom15Cto-15Cwiththeroomtemperatureheldataconstant21C.ThermocoupleswereplacedattheCOGandEOGofsurface#2,ontheframeintheunsealedcavityspace,andtheCOGandEOGoftheroomsidesurface.AtypicalexampleofthethermocoupleplacementisgiveninFigure2.

Figure2.Typicalthermocouple(TC)placementforvalidationtesting

MoisturetransferThereisnowindowindustrystandardformeasuringmoisturediffusionandexistingstandardprocedurestructures,suchasISO12572[ISO2001],areimpracticalforwindowsystems.Anewprocedureisthereforeusedinthisreport.Aspreviouslydiscussed,Fick’slawgovernsmoisturediffusion,wherethemoisturefluxisproportionaltotheconcentrationdifference.ThislawisanalogoustoFourier’sLawforheatconduction,wheretheheatfluxisproportionaltothetemperaturedifference.Forheattransfertheproportionalityconstantisdefinedasthethermalconductivity,whileinmoisturetransferitisdefinedasthepermeability.OurgoalistodeterminethewatervaporpermeabilityoftheSGSsystemsasafunctionoftheaveragewatervaporpartialpressure,Pw,betweentheindoorandoutdoorenvironment.Forthepurposesofouranalysis,wewillrepresentthepermeabilityasµ,orthewatervapordiffusionresistancefactorasdefinedinEquation5.µisaconvenienttermforanalysisanddescribestheratioofdiffusionthroughamaterialtothediffusionofmoistureinairatagiventemperatureandpressure.Themeasurementmethodweuseisanalogoustotypicalproceduresforthermaltesting.Tobegintesting,thesystemisallowedtocomeintoequilibrium.Themoisturecontentinonespaceisthenadjustedsuddenlybytheintroductionorremovalofwatervaportodisruptthebalance.Humidityandtemperaturesensors

TCCOG-U

TCEOG-U

TCFRAME-U

TCCOG-R

TCEOG-R

areinstalledonbothsidesofthewindowandwithintheunsealedglazingcavitytomonitorthestateofeachairspace.WerecordthesevaluesinordertocalculatethepartialpressuresonallsidesoftheSGSasfunctionsoftime.Therateofchangeofmoistureinthegapiscorrelatedtothepartialpressuredifferencetodeterminethepermeability.Animportantaspectofdiffusiontestingistominimizeairmasstransfer.Aspreviouslystated,thetransferofmoistairmasstypicallydominatesmoisturetransferwhenitoccurs.Controllingthepressuredifferentialacrosstheunitremovesthedriverforairmasstransfer.Thisisaccomplishedbymaintainingthermalandairpressureequilibriumonbothsidesofthewindow.Thewatervapordiffusionresistancefactor,µ,isdeterminedfromthetestresultsutilizingtheproceduredescribedschematicallyinFigure3,whereφistherelativehumidity.CalculationsforspacepropertiesareperASHRAE2009,andµissolvedforwithequation7wherediffusionoccursbetweenonlytwospaces:

Figure3.Schematicofwatervapordiffusionresistancefactorcalculationfrom

measurementsSimulationSimulationisperformedtodeterminewhencondensationwithSGSmightoccurasastandardizedproductcomparisonviatheCRUmetricandinrealbuildingswithannualenergysimulations.

Name: Calculate water vapor diffusion resistance factor, mu, from IR lab measurements Date: 3/3/16

Tree Diagram

t?1 T1 P1

W1 Pw_1 W2 Pw_2

?1-2

Measurements

Water vapor diffusion resistance factor

Calculated Space 2 propertiesCalculated Space 1 properties

?2 T2 P2

? 1 ? 2

moving mean over 5 minutes to smooth readings

2nd order polynomial fit to W, P, ? as a functions of time

?1 ?2

Condensation Resistance for Unsealed Glazing Gaps (CRU) TheNFRCCRvalueisanindicatorofcondensationperformanceontheinterior,orroomside,surfaceofaproductonly.Anewmodel,calledthecondensationresistanceforunsealedglazinggaps(CRU),isdevelopedaspartofthisreport.TheprimarydifferentiatorsbetweenthemodelsareshowninFigure4.TheNFRCCRsurfacesareadaptedtoincludetheleftandrightsidesofeachunsealedgapandtheframesurfacebetweenthem.

Figure4.A)NFRC500CRareas.B)ProposedCRUareas

WhenimplementingtheCRUmodeltherearetwosimulationlimitationsthatmustbeconsidered.First,themodelisbasedontheassumptionthattheunsealedairspacecanberepresentedasasealedcavitywithaconvectionairloop.Ourvalidationtestingconfirmsthatthesealedmodelassumptionissuitableforallproductsexaminedinthisreport.Second,themodelassumesnon-glazingsurfaceswithintheunsealedgapareadiabatic(noheattransferthroughthesurface).Figure5illustratesthisarea.Inpractice,thisassumptionresultsinsimulatedframetemperatureshigherthanrealwindowsbecausethecoldwashofairresultingfromtheconvectionloopontheouterglasspanetotheframesurfaceisnotaccountedfor.TheEOGsurfaceistypicallyofgreatestconcern,butincertainconfigurationstheframesurfacemaybethecondensationdriverandcondensationpotentialwillbeunderpredicted.Forthevalidationcasesexaminedinthisproject,thepredictedframetemperaturewas1.5Cwarmeronaveragethanmeasuredtemperature.

CRe [2.5” from sightline]

CRc

CRf

CRUe Left

CRUc Left

CRUf

CRUe Right

CRUc Right CRe

[2.5” from sightline]

CRc

CRf

Figure5.SurfacesmarkedwithblackdashedlineareadiabaticintheCRUmodel.WholebuildingOurprocedureisbrokenintotwosteps;firstwholebuildingenergyanalysisisperformedin15-minutetimestepsforonerepresentativeyear,thenthesimulatedenvironmentalconditionsateachtimestepareusedtosimulatetheexpectedmoisturecontentandifcondensationriskinSGSforthesametimestepsoftherepresentativeyear.Allbuildingsareunique,thereforetheresultspresentedherearemeantforcomparativeanalysisbetweensimilarproductsandshouldnotbeconsideredasindicatorsofactualperformanceinanyoneparticularbuilding.EnergyPlusisanenergyanalysisandthermalloadsimulationprogram.Basedonthedescriptionofabuilding,EnergyPluscalculatesheatingandcoolingloadsnecessarytomaintainthermalcontrolsetpoints.Simultaneousintegrationofthese—andmanyother—detailsverifythattheEnergyPlussimulationperformsasarealbuildingwould(U.S.DepartmentofEnergy,2013).TheDOE,inconjunctionwiththreeofitsnationallaboratories,hasdevelopedcommercialreferencebuildings.ThesereferencebuildingsprovidecompletedescriptionsforwholebuildingenergyanalysisusingEnergyPlussimulationsoftware.Thereare16buildingtypesthatrepresentapproximately70%ofthecommercialbuildingsintheU.S.Thesemodulesprovideaconsistentbaselineof

CRU surface model

adiabatic

comparison.Referencebuildingsareprovidedfornewconstruction,existingbuildingsconstructedafter1980,andexistingbuildingsconstructedbefore1980(USDepartmentofEnergy).Inadditiontothe16buildingtypes,16climatezones,whichrepresentallU.S.climates,wereusedtocreatethereferencebuildings.Theclimatesaresimulatedusingtypicalmeteorologicalyear(TMY)datasetsderivedfromthe1961-1990and1991-2005NationalSolarRadiationDataBasearchives.TheTMY3saredatasetsofhourlyvaluesofsolarradiationandmeteorologicalelementsfora1-yearperiod.Becausetheyrepresenttypicalratherthanextremeconditions,theyarenotsuitedfordesigningsystemstomeettheworst-caseconditionsoccurringatalocation(TheNationalRenewableEnergyLaboratory,2015).TheEnergyPlusprototypebuildingsandclimatesinvestigatedinthisstudywereselectedtomatchNEEAsrequirementsbasedontheirtargetmarketfortheSGSproducts.Table1summarizestheselectedbuildingandclimatesimulationparameters.

Table1.EnergyPlusprototypebuildingparametersParameter DescriptionConstructiontype Existingbuildingsconstructedbefore1980("pre-1980")

Buildingtype LargeOfficeMediumOfficeSmallOffice

Climatezone

Zone3:Oakland,CAZone4:Portland,ORZone5:Spokane,WAZone6:Missoula,MT

Thethreebuildingtypesandfourclimatezonescombinewithninewindowoptionsforatotalof108annualenergysimulations.AllbuildingHVACsystemsaresizedforthebasewindowsystemthenthesimulationsarererunwitheachSGSproduct.Surfacecondensationoccurswhenasurfacetemperatureisatorbelowthedewpointtemperatureofmoistairadjacenttothatsurface.TopredictcondensationofanSGSproductasafunctionoftimeinEnergyPlus,wethereforedeterminethesurfacetemperatureofeachsurfaceandthedewpointtemperatureoftheairadjacenttothatsurfaceateverytimestepweareinterestedin.Ifthedewpointtemperatureoftheadjacentairisbelowthatofthesurfaceweassumecondensationoccurredfortheentirelyofthattimestep.Agranularityof15-minutesisusedintheEnergyPlussimulations.SurfacetemperatureisdeterminedinEnergyPlususingtheComplexFenestrationCalculationModulewithwindowinputBSDFidffilesgeneratedinBerkeleyLabWINDOWandTHERM(Mitchell2013).Useofthismoduleallowsfor15-minutetime

stepcenter-of-glass(COG)temperatureoutputforeachglazingsurfaceintheSGS.AnimportantassumptionmadeinthisanalysisisthattheCOGisthelowesttemperatureoneachsurface.Analysispresentedinthisreportshowsthattheedge-of-glass(EOG)inSGSproductsistypicallycolderthanCOGandbyasmuchas1.5°Cinextremeindoor-outdoortemperaturegradients.TheCOGsurfacetemperatureassumptionthereforereducesthetotaloverallpredictedcondensationtimefornearlyallSGSproducts.ExteriordewpointtemperatureisaninputfromtheTMYweatherdata.InteriorzonedewpointsarecalculatedbyEnergyPlusbasedontheinputweather,HVAC,buildingproperties,etc.DewpointsintheunsealedglazingcavitiescommonwithSGSproductsisperformedafterthecompletionoftheEnergyPlussimulationusingtheprocessdescribedschematicallyinFigure6.Adetailedstep-by-stepdescriptionofthealgorithmandtheequationsusedisprovidedinAppendix1.

Figure6.Schematicofalgorithmtodeterminesurfacecondensationfrom

EnergyPlusoutputs

Name: NEEA EnergyPlus Moisture model Date: 2/29/16

Tree Diagram

tTout? in Tin Pout Tdp_outwin TS2 TS3

Pws_in

Pw_in

Tdp_in

Pin

PBG

Pw_out

wout

TBG

? BG

?

w? BG

?in

?out

ENERGYPlus Outputs

Material Properties

Calculated Outdoor properties

Calculated Indoor properties

Calculated Between Glass properties

Condensation determination

TheprocessistocomputetherequiredindoorandoutdoormoistairpropertiesforeachtimestepbasedontheEnergyPlusoutputs.Then,startingfromthefirstdatapointintheset,(January1at00:15inthiswork)calculatetheexpectedbetweenglassmoistairpropertiesofthenexttimestepiteratively.Equations7–9arethefundamentalequationsusedintheiterativeprocess.Equation7isbasedonEquation4withtheassumptionsthattherearenomoisturesourcesorsinks,andthereisnoliquidtransportflux.Bothoftheseassumptionsarepotentiallysignificantinthatcondensedmoistureisconsideredoutofthesystem,potentiallyunderestimatingthecondensationtime.Equation8isidenticaltoEquation6,andEquation9isusedtodeterminethebetweenglasspartialwaterpressureusedasaninputinthenexttimestepoftheiteration.𝑊 ∙ 𝜌! !! = 𝑊 ∙ 𝜌! !! + 𝛿 𝑡! − 𝑡!

!!_!"!!!_!"!!"∙!!! !!

+ !!_!"#!!!_!"!!"#∙!!! !!

[7]

𝛿 = 2.0 ∙ 10!! 𝑇!"!.!" !! 𝑃!" !! [8]𝑃!_!" =

!∙!!"!.!"#$%&! !!"

[9]Figure7showsboxplotsoftheoutdoor-indoorairpressuredifferentialforeach15-minutetimestepoftheTMYgroupedbyeachlocationandbuildingtype.Themeanandquartilesofthepressuredifferentialrangefrom0to5PaandwouldresultininsignificantpressuredrivenairflowthroughSGSsystems.Therefore,moistairmovementthroughtheSGSsystemsisassumednegligibleandisnotconsideredinthecondensationanalysis.

Figure7.Boxplotsofoutdoor-indoorpressuredifferenceforeach15-minute

timestepOurtechniqueofdeterminingbetween-glassmoistairpropertiesaftertheEnergyPlussimulationiscompletedrequiresthatindoorspacesaresolargethatthesimulatedmoisturemassintoandoutofthebetweenglassSGSspaceforallSGSinaninteriorzonehasinsignificantimpactontheoverallinteriorzonemoisturecontent.ComparingthetotalmoisturemassintoandoutoftheSGStothetotalmoisturecontentinthezoneschecksthisassumption.Figure8showsboxplotsofthisratioforalltimestepsconsideredinthestudy.Onaverage,thechangeinSGSbetween-glassmoisturemassisapproximately3e-6percentofthetotalroommoisturemass.Thegivenassumptionthereforehasinsignificantimpactonthesimulationaccuracy.

−15

−10

−5

0

5

10

15

Spokane MT_Missoula Oakland Portland

Out

door−I

ndoo

r Pre

ssur

e [P

a]

Small Office

−15

−10

−5

0

5

10

15

Spokane MT_Missoula Oakland Portland

Out

door−I

ndoo

r Pre

ssur

e [P

a]

Medium Office

−15

−10

−5

0

5

10

15

Spokane MT_Missoula Oakland PortlandBuilding Location

Out

door−I

ndoo

r Pre

ssur

e [P

a]

Large Office

Student Version of MATLAB

Figure8.RatioofmoisturecontentinZonetomoisturechangeinSGS.

4. RESULTS Thefollowingsectionoutlinestheresultsfromourmeasurementsandsimulations.MeasurementsAirmovementInitialairflowmeasurementswithbaseframeonlyresultedinnegligibleflowthroughthewindow.Thisresultisexpectedandtypicalfornewfixedtypeframessuchasthebaselinewindowusedforthisstudy.InordertoquantifytheimpactofSGSonairleakage,leakagepathsareartificiallyintroducedintothebaseframeby

−4

−3

−2

−1

0

1x 10−5

Spokane MT_Missoula Oakland PortlandWin

dow

moi

stur

e/Zo

ne m

oist

ure

[Kg/

Kg] Small Office

−8

−6

−4

−2

0

2x 10−5

Spokane MT_Missoula Oakland PortlandWin

dow

moi

stur

e/Zo

ne m

oist

ure

[Kg/

Kg] Medium Office

−8

−6

−4

−2

0

2

x 10−5

Spokane MT_Missoula Oakland PortlandBuilding Location

Win

dow

moi

stur

e/Zo

ne m

oist

ure

[Kg/

Kg] Large Office

Student Version of MATLAB

removingmultiplesectionsofglazingsealattheheadandsillonbothsidesoftheglazing.Themodifiedbaseframeconstructionremaineduntouchedfortheremainderofairleakagetesting.Windowairleakageistypicallyreportedasanabsolutevolumeofflowperareaofwindow.Asadd-onproductsthough,SGSperformancecannotbeaccuratelymeasuredwithoutadefinedbaseline.SincenobaselinewindoworairleakageiscurrentlydefinedforSGS,ouranalysispresentsresultsasapercentreductioninairleakagevolumeperareaofwindow.Thisallowsforeasycomparisonbetweenproducts.Figure9showsthepercentairleakageimprovementforalltestedproductsoverarangeofpressures.Attheextremesofperformance,ProductGeliminatedallairleakagefortheentirerangeofpressuresmeasured,whileProductAhadnomeasureableimpacttoleakage.ProductEshowedflowreductionrangingbetween50–70percent,andProductIwaslesseffectivewith0–30percentreductioninairleakage.TheflowresolutionofourtestequipmentistheprimaryreasonforthelargejumpsinperformanceseeninProductI.

Figure9.ReductioninairleakageofSGSproductscomparedtobaseframe

LocaltemperaturesColdsideconditionswereheldforaminimumofonehourin5Cincrementsbetween15Cand-15C.Figures10-14showthesimulationpredictedsurfacetemperaturescomparedtothemeasuredsurfacetemperaturesforfourcases:Base,H,G,A,andIrespectively.TheBaseframeissingleglazingandthereforeonlyroomsidesurfacetemperaturesarerecordedandaNFRCCRispossibletogeneratewhile

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aCRUnumberisnot.Theresultsshowagreementbetweensimulatedandmeasuredperformancewithin1Cthroughout.

Figure10.MeasuredsurfacetemperaturesonbasewindowProductHinFigure11createsatriplepaneIGUbysealinganddesiccatingtheairspacebetweenthebasewindowandSGSglazing.Thus,theNFRCCRcalculationmethodologyusedforthebasewindowappliestothisproductaswell.ThecreatedtriplepaneIGUishighlyinsulatingsothetimetoreachsteadystatetemperaturesonmostsurfacesisgreaterthantheallottedthreehoursateachcoldsidecondition.Theextendeddurationatthefinalcoldsidestatethoughshowsthatthesimulatedandmeasuredsurfacetemperaturesagainmatchwithin1Cforallsurfaces.

Figure11.MeasuredsurfacetemperaturesonproductHProductsG,A,andIinFigures12-14introducetheuseofthenewlydevelopedCRUmodel.TheCOG-UandEOG-Utemperaturesmatchwithin1C,similartotheNFRCCRmodelsabove.TheFRAMEtemperaturesthougharenotwithinthistolerance,anddifferencesofupto2Cshown.Thisdiscrepancyistheresultofusinganequivalentconductivityforthegasspacebelowthetopmostbaseframesightline.Theexplanationforthissimulationmethodisgivenintheprevioussection.Theequivalentconductivityassumptionalwaysresultsinunderpredictionofthesillframetemperature(incaseswhereTcoldislessthanTroom).

Figure12.MeasuredsurfacetemperaturesonproductG

Figure13.MeasuredsurfacetemperaturesonproductA

Figure14.MeasuredsurfacetemperaturesonproductIMoisturetransferDetailedmeasurementsforproductGarepresentedinFigure15toillustratetheprocessusedtodeterminethewatervapordiffusionresistancefactor,µ.Figure15ashowstheadjacentroomairhumidityisbroughtquicklyto100%andthenheldatthatpointwhilemoistureisallowedtodiffuseintothebetween-glassspace.Figure15bshowsthecalculatedpartialwatervaporpressuresofeachspace.Figure15cshowsthecalculatedmoisturecontentofthebetweenglassspaceandapolynomialfittothemeasurements.Thepolynomialfitisthenusedtodetermineµ,asisshowninFigure15d.Theaverageµisdeterminedfromalldatapriortoanyinflectionpointofmoisturecontent,orwhenthebetween-glassspacebecomessaturated.Thisinflectionpointcanbeseenatapproximately2600minutesinFigure15c.

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Figure15a-d.VapordiffusionmeasurementandcalculationdetailsforproductG.

TheprocessdescribedaboveisrepeatedforallproductslistedinTable2.Ventdirectiontotheoutsidedescribesvapordiffusionthroughthebaseframe.Thecalculateddiffusioncoefficientfortwotestsislessthan1,meaningcalculatedmoisturediffusionisfasterthandiffusionthroughair.Thisresultisnotpossiblewithoutsomeunaccountedforpressuredifferenceorairmovement.Avalueofoneisthereforeusedtorepresentas-measuredperformanceofthesetestsinthesubsequentbuildingsimulations.Basedonthepreviousairflowmeasurements,theproductsperformasexpected.ProductAdidnotreduceairflowandalsoshowednoresistancetomoistureflow.ProductGprovidedthegreatestresistancetoairflowandthegreatestresistancetomoistureflow.

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Table2.Vapordiffusionmeasurementsummary

ProductVentDirection

Outside InsideBase 0.3 -A 10.6 0.6G - 2.3I - 1.8

SimulationCondensationresistanceThesimulatedCRandCRUvaluesforeachwindowareshowninTable5.WheretheCRUcalculationisnotapplicablebecausethesystemdoesnotcontainanunsealedgap,thefieldisleftblank.ItisclearfromtheCRU–Ventedtotheinteriorboundarycondition(BC)thatthecondensationresistanceissignificantlydecreasedwhenanSGSproductventssolelytoroomair.TheprimarydriverforlowCRUvaluesisthetemperaturereductiononthebasewindowglasscoupledwiththehighdewpointofroomair.ThesignificantsurfacetemperaturereductionscanbeseeninthetestresultswhencomparingFigures10(basewindow)toFigures12-14.ManyrealbuildingbasewindowsarenotcompletelysealedtooutsideairinfiltrationsotheCRUfortheunsealedgapventedtoamixtureofexteriorandinteriorairisalsoofinterest.

Table5.SimulatedCRandCRUProduct CR CRU

VentedtointeriorBCBase 12.2 -A 21.6 1.96B 27.0 -C 26.8 -D 26.8 -E 22.1 1.38F 22.0 4.23G 26.0 4.24I 23.9 3.64J 24.5 3.57

Figure16showsthesimulatedCRUforproductFoverarangeofunsealedgapairhumidityratios.Thehumidityratioofthesimulatedexteriorboundaryconditionisaround0.001Kg(H2O)/Kg(dryair)asshownbythesolidblackverticalline,soaCRUof100isexpectedforallhumidityratiosbelowthatlevelsincenocondensationcanoccur.SincetheSGSproductshowninsulatesthebasewindowglassandreducesitstemperature,thereisahighlynon-lineardropinCRUoncethehumidity

ratioisincreasedabovetheexteriorhumidityratio.ThisdropexplainstherelativelylowCRUnumbersreportedinTable5.

Figure16.CRUforProductFasafunctionofunsealedgaphumidityratioWholebuildingTheannualwholebuildingcondensationsimulationresultscanbeparsedinmanyways.Threedifferentmethodsarepresentedhere.ThelargeofficeinMissoulaMtwithproductAisusedtorepresentatypicalresultoftheanalysisinthefollowingfigures.Figure7showstheaccumulated15-minutetimestepswhencondensationoccurstoprovideanideaoftotalcondensationriskovertime.Forthecaseshown,andtypicallyforallunitsexamined,weobservethatcondensationriskisgreatestwithinthefirstandlast100daysofthecalendaryear.Eastfacingwindowshavethelowestcondensationrisk,whilenorthfacinghasthegreatestrisk.Northfacingwindowsarerarelyexposedtodirectsunandtheassociatedsurfaceheating,sothisresultalignswithourintuition.South,east,andwestwindowsperformsimilarlyinwinterandfall(first50daysandlast100daysofyear).Eastwindowsthoughshowfewersummercondensationhours.

Figure17.Accumulatedcondensationtime.Largeoffice,MissoulaM,productA.

Thereducedcondensationhoursoneastwindowsinsummercanbeattributedtosolarheatingofthosewindowsfrommorningsun.Figure18showsthisbysplittingthecumulativecondensationhoursbyhourofdayanddirection.Forthemajorityofhoursallfoursurfacesaresimilar.From7am–10amthough,boththesouthandeastfacingwindowshavesignificantlyfewercondensedhoursthannorthandwestfacing.Theeastfacingwindowsalsoshowfewercondensedhoursrelativetosouthfacing,primarilyinthe7amand8amhours.AnadditionalsignificantobservationmadefromFigure18isthedaytonightcondensationdeviationforallorientations.Fromlatemorningtolateafternoonlittletonocondensationoccurs.Startinginlateafternoon,thelikelihoodofcondensationincreaseseachhouruntilitreachesapeakinhours4and5.Athour6condensationriskquicklydiminishesuntilhour11wheretheriskreturnstominimal.Thestrongestcorrelationtothecondensationpatternseenistheoutdoor

BuildingType:LgOffice, Location:MT_Missoula, WindowType:A

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airtemperature.ThiscorrelationisshowninFigure18withalinegraphoftheinversetomeantemperatureateachhour.Eachbuildingisrunona7am–10pmHVACscheduleandthereisnovisiblecorrelationseenintheHVACscheduletocondensationrisk.

Figure18.Cumulativecondensationhoursbyhourofdayanddirection.Largeoffice,

midfloor,MissoulaM,productA.Thedetailedanalysisshownaboveisusefulforunderstandingcondensationtrendsinallproducts.Tounderstandhowproductscomparerelativetoeachothersummarizedresultsareused.Oneofthelargestissueswithcondensationisviewduringoccupiedperiods.Summarizedcondensationhoursbasedonatypicalbuildingschedulewithopenhoursof7am–7pmandthemeasuredmoisturediffusionpropertiesareprovidedinFigures19-21.Themeasuredwatervapordiffusionresistancefactorsareusedintheanalysis.Wheremeasuredfactorsarenotavailablearepresentativevalueofµin=2isusedforroomsidediffusionandµout=10.6foroutsidediffusion.ThefiguresshowthatlittletonocondensationoccursonthebasewindoworproductsB,C,andD.Eachoftheseproductshasasealedcavity,oraroom-sidecondensationsurface.Forallotherproducts,condensationhoursaredominantlyduringnon-businesshours.TheSGSproductU-factorcorrelatesmostcloselywithcondensationhours,whereloweru-factorshavehighercondensationpotential.ThisobservationappliesonlytotheSGSproductswithunsealedcavities.

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Figure19.Smallofficetotalcondensationhoursbasedontypicalbuildingschedule.

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Figure20.Mediumofficetotalcondensationhoursbasedontypicalbuilding

schedule.

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Figure21.Largeofficetotalcondensationhoursbasedontypicalbuildingschedule.Thepreviousresultswereformeasuredwatervapordiffusionresistancefactors.Inordertoillustratetheimpactofµoncondensationhours,Figure22showsacomparisonofnon-businesshourtotalcondensationbasedonfivedifferentµinandµoutcombinationsinlargeofficebuildings.Theplotsshowthatlowresistancetotheoutsidecoupledwithhighroom-sideresistancetypicallyresultsinthefewestcondensationhours,whiletheoppositecase(highresistancetotheoutsideandlowresistanceroom-side)resultsinthegreatestnumberofcondensationhours.Inthecasewhereresistanceisquitehighinbothdirections,theinitialmoisturecontentofthespaceisveryimportant.Intheextreme,noinitialmoisturecontentispresent(similartoasealedcavity)andcondensationneveroccurs.Lowinitialmoistureis

Large Office

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usedinthisanalysisat1/10oftheroommoistureonthefirst15-minutetimestepofJanuary1.

Figure22.Condensationtimefordifferentinsideandoutsidewatervapordiffusion

resistancefactorcombinations.LargeOffice,non-businesshours.5. SUMMARY & CONCLUSIONS ArefinedmethodologyforsimulatingthehygrothermalconditionsadjacenttoandonglasssurfacesisdevelopedandperformedfornineproductsasanextensiontotheworkpresentedinHart,2005.ExtensionstoBerkeleyLabTHERMandWINDOWsoftwaretoolsareimplementedandweintroducetheconceptofcondensationresistanceofunsealedgaps(CRU)indicesasacompaniontotheexistingNFRCCRratings.Thesemodelsarevalidatedthroughexperimentsbylocaltemperatureandmoisturepropagationmeasurements,andthereforeprovideaccuratedetermination

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Measuredµin=1 µout=1

µin=1000 µout=1

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ofCRUatpredeterminedhumidityratios.ThereportedCRUnumbersseemtobemostlyontheverylowend(i.e.,verypoorperformance)forallunsealedunitsduetotheuseofhumidityratiosthatarerepresentativeofindoorroomair.Thisindicatesthatfurtherresearchmightbeneededtoestablishexpectedmoisturecontentinunsealedgapsfordifferentproducttypesandtorelatethemtoindoorroomair,sothatmorerepresentativeCRUprocedurecanbedeveloped.FourSGSsystemsaremeasuredforairleakageandmoisturepropagationperformance.Theresultsvarygreatlybetweenproducts;frompreventingallairleakageandmostmoisturetransfertonoresistancetoairormoisturetransfer.ThemeasuredperformancedataiscombinedwiththeresultsofEnergyPlusannualenergysimulationstodeterminetrendsandrelativecondensationperformanceofnineSGSproducts.Wemaketheassumptionthattherearenomoisturesourcesorsinks,andthereisnoliquidtransportflux.Bothoftheseassumptionsaresignificantinthatcondensedmoistureisconsideredoutofthesystem,potentiallymisjudgingthecondensationtime.Withtheseassumptionsandknowingthatallbuildingsarecontrolledandperformdifferently,theresultspresentedhereshouldbeviewedonlyasindicatorsofrelativeperformancebetweenSGSproductsandnotabsolutecondensationpotential.TheresultsshowthatallSGSsystemscontainingunsealedglazingcavitiesincreasecondensationriskoversinglepanebasewindows.Condensationriskishighestonnorthfacingsurfaces,andlowestoneastfacing,butthetimedifferenceisrelativelysmall.Condensationalsooccursmostoftenduringunoccupiedhours.Finally,lowwatervapordiffusionresistancefactorstotheoutsidecoupledwithhighroom-sideresistancetypicallyresultsinthefewestcondensationhours,whiletheoppositecase(highresistancetotheoutsideandlowresistanceroom-side)resultsinthegreatestnumberofcondensationhours.FutureworkshouldincludeinstallationandmonitoringofSGSinrealbuildingstovalidatethesimulationresults.TheCRUmetricisintroducedasapreliminarystepwiththelong-termgoalofastandardizedmetricforcondensationpotentialofSGSandotherattachmentproducts.FurtherdevelopmentoftheCRUmetricshouldbedonetoensureallsignificantaspectsofSGSdesign,suchasresistancetoairleakageandmoisturetransfer,areconsideredandpresentedfairlywithrespecttotheexistingCRstandards.6. ACKNOWLEDGEMENT ThisworkwassupportedbytheNorthwestEnergyEfficiencyAlliance(NEEA)andtheAssistantSecretaryforEnergyEfficiencyandRenewableEnergy,BuildingTechnologiesProgram,oftheU.S.DepartmentofEnergyunderContractNo.DE-AC02-05CH11231.

7. REFERENCES AmericanArchitecturalManufacturersAssociation(AAMA),2008.AAMA/WDMA/CSA101/I.S.2/A440NAFS–NorthAmericanFenestrationStandard/SpecificationforWindows,Doors,andSkylights.Schaumburg,Il.AAMA,1998.GuidelinesForAAMAAccreditationOfIndependentLaboratoriesPerformingOn-SiteTestingOfFenestrationProducts.Schaumburg,Il.AmericanSocietyofHeating,Refrigerating,andAir-ConditioningEngineers,Inc.(ASHRAE),2009.HandbookofFundamentals,Atlanta,GA.ASTMStandardE283,2012.StandardTestMethodforDeterminingtheRateofAirLeakageThroughExteriorWindows,CurtainWalls,andDoorsUnderSpecifiedPressureDifferencesAcrosstheSpecimen,ASTMInternational,WestConshohocken,PA.Fraunhofer-Gesellschaft,2001.WUFIBIO.TheFraunhoferInstituteforBuildingPhysics.München,Germany.Hart,Robert,H.Goudey,R.Mitchell,M.Yazdanian,D.C.Curcija.2015.SecondaryGlazingSystem(SGS)Thermal,Moisture,andSolarPerformanceAnalysisandvalidation.NorthwestEnergyEfficiencyAlliance.Report#E15-293.ISO12572,2001.Hygrothermalperformanceofbuildingmaterialsandproducts--Determinationofwatervapourtransmissionproperties.Kunzel,HartwigM.,1995.SimultaneousHeatandMoistureTransportinBuildingComponents.TheFraunhoferInstituteofBuildingPhysics.München,Germany.Mitchell,R.,Kohler,C.,Curcija,D.,Zhu,L.,Vidanovic,S.,Czarnecki,S.,etal.(2013).THERM6.3/WINDOW6.3NFRCSimulationManual.LawrenceBerkeleyNationalLaboratory.Berkeley,CA:UniversityofCalifornia.U.S.DepartmentofEnergy.(2013,October30).EnergyPlusEnergySimulationSoftware.RetrievedJanuary12,2015,fromUSDOEEnergyEfficiency&RenewableEnergywebsite:http://apps1.eere.energy.gov/buildings/energyplus/energyplus_about.cfmTheNationalRenewableEnergyLaboratory.(2015,January19).NationalSolarRadiationDataBase.RetrievedJanuary21,2015,fromRenewableResourceDataCenter:http://rredc.nrel.gov/solar/old_data/nsrdb/1991-2005/tmy3/

8. APPENDIX 1 Thenumericalprocesstodetermineifcondensationoccursbetween-glassisdescribedinthissection.Thisprocessisusedtodeveloptheresultspresentedinthesimulationsectionoftheresults.Unlessotherwisenoted,allreferencedequationsaretakenfromASHRAE2009andpresentedintheformF#.#for(F)undamentals,chapter.equation.1. WindowmodelsaredefinedusingBSDFidfinputsforEnergyPlus.Thisis

requiredtoobtainglasssurfacetemperatures.ThesefileswereproducedinBerkeleyLabWINDOW7.3forthiswork.

2. 15-minutetimestepEnergyPlussimulationisperformed.Thefollowingoutputsarerequiredforallsimulations.Zonedataisrequiredforeachperimeterzone.

t Date/TimeTout Environment:SiteOutdoorAirDrybulbTemperature[C]Tout_dp Environment:SiteOutdoorAirDewpointTemperature[C]Pout Environment:SiteOutdoorAirBarometricPressure[Pa]Tin ZoneAirTemperature[C]ϕin ZoneAirRelativeHumidity[%]win ZoneMeanAirHumidityRatio[kgWater/kgDryAir]TS2 SurfaceWindowBackFaceTemperatureLayer1[C]TS3 SurfaceWindowFrontFaceTemperatureLayer2[C]

3. Foreach15minutetimestep:3.1. CalculatePws_in by using the following equations F1.5-6, given the input of

Tin [K] from Energy Plus: For−100<T>0°C

ln𝑃!" = 𝐶! 𝑇 + 𝐶! + 𝐶!𝑇 + 𝐶!𝑇! + 𝐶!𝑇! + 𝐶!𝑇! + 𝐶! ln𝑇 For0<T>200°C

ln𝑃!" = 𝐶! 𝑇 + 𝐶! + 𝐶!"𝑇 + 𝐶!!𝑇! + 𝐶!"𝑇! + 𝐶!" ln𝑇

where

C1=−5.6745359E+03C2=6.3925247E+00C3=−9.6778430E–03C4=6.2215701E−07C5=2.0747825E−09C6=−9.4840240E−13C7=4.1635019E+00C8=−5.8002206E+03C9=1.3914993E+00C10=−4.8640239E−02C11=4.1764768E−05C12=−1.4452093E−08

C13=6.5459673E+00Pws [Pa] saturationpressure

3.2. CalculatePw_inbyusingequationF1.24,giventheinputofϕin[-]fromEnergy

Plus:

𝜙 =𝑃!𝑃!" !,!

3.3. CalculateTin_dpbyusingequationF1.39-40,giventheinputofPw_infrom3.2:

ForTdp≤0°C

𝑇!" = 6.09+ 12.608𝛼 + 0.4959𝛼! For0<Tdp>93°C

𝑇!" = 𝐶!" + 𝐶!"𝛼 + 𝐶!"𝛼! + 𝐶!"𝛼! + 𝐶!"𝑃!!.!"#$whereα=ln(Pw);C14=6.54C15=14.526C16=0.7389C17=0.09486C18=0.4569

3.4. CalculatePinbyusingequationF1.22,giventheinputofPw_infrom3.2andwinfromEnergyPlus:

𝑃 = 𝑃! 1+

𝑤0.621945

3.5. CalculatePBGbytakingtheaverageofPinfrom3.4andPoutfromEnergyPlus:

𝑃!" =𝑃!" + 𝑃!"#

2

3.6. CalculatePw_outbyusingtheinputofTout_dpfromEnergyPlusandequationfrom3.1,wherePw=Pws(Tdp).

3.7. CalculateWoutbyusingtheinputsofPoutfromE+andPw_outfrom3.6,and

equationfrom3.4rearrangedtosolveforW.

𝑊 = 0.621945𝑃!

𝑃 − 𝑃!

3.8. CalculateTBGbytakingtheaveragetemperaturebetweenTS2andTS3fromEnergyPlus.

𝑇!" =𝑇!! + 𝑇!!

2

3.9. CalculationofTBG_dewisaniterativeprocessbyloopingthrough3.9.1–3.9.3foreachtimestep.

3.9.1. WρBGateachtimestepissolvedforbyutilizingthefollowing

equations:

𝑊 ∙ 𝜌! !! = 𝑊 ∙ 𝜌! !! + 𝛿 𝑡! − 𝑡!𝑃!_!" − 𝑃!_!"𝜇!" ∙ Δ𝑥! !!

+𝑃!_!"# − 𝑃!_!"𝜇!"# ∙ Δ𝑥! !!

𝛿 = 2.0 ∙ 10!! 𝑇!"!.!" !! 𝑃!" !!

att=1

𝑊!" =𝑊!" +𝑊!"#

2

𝑊 ∙ 𝜌! =𝑊!" ∙ 𝜌!

𝑃! =𝑃 ∙𝑊!"

0.621945+ 𝑊!"

3.9.2. CalculateWBGateachtimestepbydividingWρBGbytheairdensity.

𝑊 =𝑊 ∙ 𝜌!𝜌!

3.9.3. CalculatePw_BGateachtimestepbyequationfrom3.4rearrangedto

solveforpartialwaterpressure.

𝑃!_!" =𝑃 ∙𝑊!"

0.621945+ 𝑊!"

3.10. AfterPw_BGisdeterminedforeachtimestep,TBG_dewissolvedforusing

equationfrom3.3.

3.11. SurfacecondensationisthendeterminedbycomparingTBG_dewtotheglasssurfacetemperatureateachtimestep.Ifsurfacetemperatureisbelowthespacedewpointtemperaturethesurfacecontainscondensationatthattimestep.