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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 [email protected]
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
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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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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.