Advanced Building Physics - Psychrometry
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L.D.D Advanced Building Physics - Psychrometry The word 'Psychrometer' is originally from the Greek meaning of 'cold' + 'meter', i.e. literally meaning a measurer of cold. The gaseous phase of the moist air mixture can be treated as a mixture of two ideal gases: dry air and water vapour. It is a good approximation to treat water vapour as an ideal gas? p v <p vsat is always valid, and p vsat (5 °C) = 0.87 kPa p vsat (45 °C) = 9.59 kPa while the critical pressure of water is equal to p cr = 22 MPa ---> p R =p v /p cr < 10 -4 << 1 At 100 kPa, if the water vapour would be at atmospheric pressure (and in moist air this never happens) the maximum error that could be done approximating it as an ideal gas would be of 1.6%. 1 - Mixtures of gases and vapours In a mixture of gases, the components that are condensed alone are called condensable components, while the others (incondensable components) are called gases and are completely mixed. Consider a mixtures in which the following assumptions are valid: - The gaseous phase obeys the ideal gas law - The condensed phase are incompressible and do not dissolve non-condensable gases in these conditions: The vapour behaves as if it were present alone in the same volume and at the same temperature of the mixture. For a homogeneous state (gaseous) in whic there are two components (a, non condensable, and v, consensable) it is valid the second equation of state of ideal gases, where p is the total pressure, T the temperature in Kelvin and N the total number of moles (N = N a +N v ): pV = NRT = (N a +N v )RT = N a RT + N v RT and defining the partial pressures p a and p v as: p a V=N a RT and p v V=N v RT, we obtain: pV = p a V+p v V Dalton's law: p = p a +p v
Transcript of Advanced Building Physics - Psychrometry
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AdvancedBuildingPhysics-Psychrometry
Theword'Psychrometer'isoriginallyfromtheGreekmeaningof'cold'+'meter',i.e.literallymeaningameasurerofcold.Thegaseousphaseofthemoistairmixturecanbetreatedasamixtureoftwoidealgases:dryairandwatervapour.Itisagoodapproximationtotreatwatervapourasanidealgas?pv<pvsatisalwaysvalid,andpvsat(5°C)=0.87kPapvsat(45°C)=9.59kPawhilethecriticalpressureofwaterisequaltopcr=22MPa--->pR=pv/pcr<10
-4<<1At100kPa,ifthewatervapourwouldbeatatmosphericpressure(andinmoistairthisneverhappens)themaximumerrorthatcouldbedoneapproximatingitasanidealgaswouldbeof1.6%.1-MixturesofgasesandvapoursInamixtureofgases,thecomponentsthatarecondensedalonearecalledcondensablecomponents,whiletheothers(incondensablecomponents)arecalledgasesandarecompletelymixed.Consideramixturesinwhichthefollowingassumptionsarevalid:-Thegaseousphaseobeystheidealgaslaw-Thecondensedphaseareincompressibleanddonotdissolvenon-condensablegasesintheseconditions:Thevapourbehavesasifitwerepresentaloneinthesamevolumeandatthesametemperatureofthemixture.Forahomogeneousstate(gaseous)inwhictherearetwocomponents(a,noncondensable,andv,consensable)itisvalidthesecondequationofstateofidealgases,wherepisthetotalpressure,TthetemperatureinKelvinandNthetotalnumberofmoles(N=Na+Nv):pV=NRT=(Na+Nv)RT=NaRT+NvRTanddefiningthepartialpressurespaandpvas:paV=NaRTandpvV=NvRT,weobtain:pV=paV+pvVDalton'slaw:p=pa+pv
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2-HomogeneousequilibriumstatesofmoistairInthehomogeneousstatesofequilibriumofmoistair,thereisnocondensate,neitherliquid(L)norsolid(S).
ML=MS=0Humidityratiox(moisturecontentofair)forhomogeneousgaseousstates:
Mv/Mda[Kgvap/Kgda]
TakingintoaccountthatwecanusetheidealgasmodelfordryairandvapourpaV=NaRTpvV=NvRTitfollows:
Thereforethemaxuminpossiblevalueforhumidityratioisdeterminedbythemaximumpossiblevalueforthepartialpressureofthewatervapour.
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3-MoistairEnthalpyWeneedtodefineaquantityinordertodescribetheexchangesofenergy.Letsintroduceenthalpy.
Todeterminetheenthalpyofanystate,itisnecessarytodefineareferencestatetowhichassignarbitrarilythevalueofzeroenthalpy.Theenthalpyofanyotherstatewillthenbecalculatedasadifference.T=0-->ha(Ref.)=0--->ha(F)=ha(F)-ha(Ref.)Weneednowtodefineareferencestatefordryairandoneforwater.1)SpecificenthalpyofdryairhaSincewehavesupposedthatdryaircanbetreatedasanidealgas,theenthalpydoesnotdependonpressure:itisnotnecessarytospecifypressureofreferencestate-Tref=273,15K=0°CRememberingthatforanidealhasdh=cpforeverytransformation
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2)SpecificenthalpyofwatervapourhvForwater,wecannotchooseastateclosetocriticalpointasreferencestate.Letsassumeasreferencestatetheliquidphaseattriplepoint,forwhichenthalpyissetequaltozero.Tref,w=273,15K=0°CWeneedtovaporizewaterfromliquidtovapourat0°C
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1+2)Enthalpyofthemoistairmixturespecifictothemassofdryair
4-MollierpsychrometricchartThemoistairinthehomogeneousstatesisatwo-componentandonephasesystem,thereforeithasthreedegreesoffreedom.Ifwewanttorepresentthehomogeneousstatesonatwo-dimensionaldiagram,itisnecessarytosetaparameter:theMollierdiagramrepresentsthedifferentpossiblestatesofamoistairmixtureatagiventotalpressure.y-axis:specificenthalpiesarerepresentedhx-axis:humidiyratiosarerepresentesXTheinclinationoftheaxisischosensothattheisothermT=0°Cresultshorizontal.4-ASHRAEPsychrometricdiagramThefundamentalvariablesarealsotheenthalpyspecifictodryairmassandhumidityratio.Theisothermshavevariableinclinations.TheAshraediagrammightbeobtainedfromtheMollieronebyflippingandrotatingit.
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4-MAINTRANSFORMATIONSOFMOISTAIRATCONSTANTPRESSURE4.1HeatingConsidertheprocessifdeliveringheattoamassofdryairMda.Weoperateatconstanttotalepressurewhileprovidingheat.ThehumidityratioXdoesnotvaryandthetemperatureTincreases.A---->B
Atconstantpressure,theheatexchangedbyoursystemisequaltotheenthalpychangeofthesystemitself,therefore:
Massconservation1)Mda1=Mda2=Mda2)Mv1=X1Mda=X2Mda=Mv2-->X1=X2EnergyconservationH1+Qin=H2
---->Mdah1+Qin=Mdah2--->h1+(Qin/Mda)=h2
Relativehumidityisdecreased.
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4.2CoolinganddehumidificationConsideramassofdryairMda.Operateatconstanttotalpressurewhilesubtractingheat.ThehumidityratioXdoesnotvaryandtemperatureTdecreases.Ifwecontinuesubtracting,theairmassreachesthesaturationconditionsR(dewpoint).
IfthecoolingcontinuestillTE<TR,somecondensateisformed.Thefinalmixtureofmoistairandcondensatewillhavethesamefractionofwater'smassoftheinitialmoistair(butcontentofvapourwaterisdecreased).
Massconservation1)Mda1=Mda2=Mda2)X1Mda=X2Mda+Mc-->X2=X1-MC/MdaEnergyconservationMdah1+Qin=Mdah2+Mchc(hc=CpLT2°C)CpL=4.186butMchc<<Mdah1---->Mdah1+Qin=Mdah2
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4.3AdiabaticmixingThesystem1(moistair)ismaintainedatconstantpressure,whileasystem2(moistair,vapourorliquidwater)isinjectedthroughavalve.IfQABistheheatsuppliedtothesystem,andweindicatethewiththeletter'm'theconditionsoftheobtainedmixture,wecanwritetheenergybalance
Massconservation1)Mda1+Mda2=Mda32)X1Mda1+X2Mda2=Mda3X3-->X3=(Mda1X1+Mda2X2)/(Mda1+Mda2)
EnergyconservationMda1h1+Mda2h2=Mda3h3--->h3=(Mda1h1+Mda2h2)/(Mda1+Mda2)
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4.4Waterinjection1)Liquidform
Massconservation1)Mda1=Mda2=Mda2)MdaX1+Mh2o=MdaX2-->X2=X1+(Mh2o/Mda)EnergyconservationMdah1+Mh2ohh2o=Mdah2--->h2=h1+(Mh2o/Mda)hh20Buthh20=CpLTh2o<<h1,2-->transformationalmostisoenthalpic-->T2<T1
2)Vapourform
Massconservation1)Mda1=Mda2=Mda2)MdaX1+Mh2o=MdaX2-->X2=X1+(Mh2o/Mda)EnergyconservationMdah1+Mh2ohh2o=Mdah2--->h2=h1+(Mh2o/Mda)hh20Withthh20=λv+CpvTh20-->h2>h1--->T2>T1
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5-INSTRUMENTSTOMEASURETHEMOISTURECONTENT1)Slingpsychrometer
Consistsintwoglassthermometerscontainingaliquid,usuallymercury.Onethermometermeasurestheairtemperaturewhiletheotheronemeasuresthewet-bulbtemperature.Afterthewickisdippedindistilledwater,aweatherobserverwhirlstheslingpsychrometeraround,usingthehandle.
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Astheinstrumentsiswhirled,waterevaporatesfromthewhickonthewet-bulbthermometerandcoolsthetermometer.Thewet-bulbthermometercoolstothelowestvaluepossibleinafewminutes.Thisvalueisknownasthewet-bulbtemperature.Thedriertheairthemorethethermometercoolsandhence,thelowerthewet-bulbtemperature.Theobserverusesatable(oracomputerprogram)todeterminerelativehumidityandhumidityratiobasedonthereadingsofdryandwet-bulbtemperatures.2)ChilledmirrordewpointhygrometerAhygrometerisaninstrumentusedformeasuringthemoisturecontentintheenvironmentalair,orhumidity.Thechilledmirrordewpointhygrometerisoneofthemostpreciseinstrumentsavailable.Accuracyof0.2°Cwitharelativehumidityaccuracyof+/-0.5%.Needsfrequentcleaningandperiodiccalibration.3)Humiditysensors3.1-Capacitivehumiditysensors:theeffectofhumidityonthedielectricconstantofapolymerismeasured.Ifcalibrated,accuracyof+/-2%RHintherangeof5-95%RH.Robustagainsteffectssuchascondensationaandtemporaryhightemperatures.3.2-Resistivehumiditysensors:thechangeinelectricalresistanceofamaterialduetohumidityismeasured.Typicalmaterialsaresaltsandconductivepolymers.Lesssensitivethancapacitivesensors.Accuracyupto+/-3%RH.3.3-Thermalconductivityhumiditysensors:thechangeinthermalconductivityofairduetohumidityismeasured.Thesesensorsmeasureabsolutehumidityratherthanrelativehumidity.6-THEBUILDINGAIRCONDITIONINGPROCESSConsideraroomthatwedesiretokeepatcertainconditionsoftemperatureandhumidity.Comfortsetpoints:-Summer:operativetemperature26degrees,maxrelativehumidity60%-Winter:operativetemperature20degrees,minrelativehumidity25% Considerasoursystemunderstudythemoistaircontainedintheroom,andsuppose:-FixedTandRH-Airwellmixed(parametershavesamevaluesineachpoint)-Constantmassairflowexchangedwithothersystems-->Sothesystemisuniformandisstationaryconditions.Theaircontainedintotheroomwillreceive:1)Energy(heat)frominternalsurfaceofthewalls(ΔTint-ext)2)Energyduetoelectromagneticradiations(solar,sky..)3)Energyduetoinfiltrations4)Energyduetointernalgains5)Watervapourgeneratedbyoccupants
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6)Watervapourgeneratedbyinternalsources(showers,kitchen,vegetation..)7)WatervapourduetoΔTint-extbetweenincomingandoutgoingflowofairTheair-conditioningdeviceshouldbeabletokeepthesystemconstantlyinthefixedchosenconditions;theexchangesdescribedas'heatandhumiditygains'(or'zoneloads')havetobecounterbalancedbytheair-conditioningsysteminordertokeepthesysteminthedesiredstationaryconditions.-ControlandreduceheatgainsthroughtheenvelopeHeatentersthroughtheexternalsurfacebecauseofsolarradiationsandΔTint-ext.Ahighreductionoftheamountofheatpassingthroughtheexternalsurfacecanbeachievedbymeansofsolarprotectionsandsurfacefinishingswithadequatevaluesofreflectivityandemissivity.Andalsolimitingairexchangeswhenoutsideairiswarmerthaninsideair.
Onceloadshavebeenreducedbytheuseofpassivemeans,inordertoramaininacomfortrangeinsomecasesitmightstillbenecessarytointroduceanactiveairhandlingsystem.Weanalizeasystemthatusesairasawaytotransferenergyandwatervapourtotheairoftheroom.AHU:airhandlingunit:
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-SummerairconditioningWesearchtheinputconditions(i)knowingtheindoordesiredconditions(a)andtheexternalconditions(e).Forsemplicity,treatthesystemwithoutrecirculation.
Wegetanequationwithtwounknowns(hi,Xi).There'sagraphicalmethodtosolvethisproblem.Onthepsychrometricdiagramtheequationwrittenaboveisrepresentedbyastraightlinepassingthrougha.Thepointiissituatednecessarilyonthisstraightline,whichisalsocalledintroductionlineorroomline.Notethatinsummer
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Inordertofindtheexactintroductionpoint,weneedtoconsiderseveralissuesandboundariesgiventothesummerconditions:1-ComfortinT:|Ti-Ta|=10/12°C2-Comfortinairvelocity:noise3-COP(limitedbyTi-Ta)4-Energy-->fansconsumption5-Installations(limitincosts)or(limitinMda)
-WinterairconditioningInthiscase,theexternalconditionsarecolderandatlowerXthanthedesiredones.Theequationsofbalanceareequaltothoseofthesummercase,buttheterm(Q/V+h)isnegativeandthestraightlinehasgotanegativeslope.Startingfromeweheatuptob,pointwhichcorrespondstotheintersectionbetweenthestraightlineatconstantXpassingthrougheandtheisoenthalpicpassingthroughthedewpointofi,whichweindicateasRi.BetweenbandRiweoperateahumidificationwithliquidwater,thereforewemovealongtheisoenthalpicutilsaturation.Atthispointweoperateasecondheating,uptothedesiredconditions.
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Note:Dewtemperature:temperatureofthemixtureatwhich,inatrasformationwithpandXconstant,thevaporstartstocondense.8-SENSIBLEANDLATENTHEATEXCHANGERememberthatforamixtureofidealgasessuchasthegaseousphaseofmoistair,withconstantCpaandCpvwehave:H=Ha+Hv.
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Ifwewanttofindthe'thermalfactor'R(orSensibleheatingratioSHR),itisdefinedas:
9-THERMODYNAMICTEMPERATUREOFWETBULBANDITSAPPROXIMATIONConsideramoistairattemperaturetandhumidityratioX.-->atemperaturet*existsatwichaliquidorsolidH2Oevaporatesintotheairadiabaticallyanditbringstheairatsaturationexactlyatthesametemperaturet*andtotalpressure.Duringthisadiabaticprocess,atconstantt=t*:-HumidityratioincreasesfromXtoXS*correspondingtosaturationattemperaturet*-DryairmassspecifichentalpyincreasesfromhtohS*correspondingtot*-H2Omassaddedperunitmassofdryairis(XS*-X)=ΔX-Energy/enthalpyaddedperunitmassofdryairis(XS*-X)hw*
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10-PSYCHROMETRICPROCESSESANDAPPLICATIONSTheanalysisofpsychrometricprocessesisperformedbyconsideringacontrolvolumeandthenapplyingtheprinciplesoftheconservationofmassandenergytothecontrolvolume.Changesinpotentialandkineticenergyarenegligible,thustheenergyequationreducesto:
1)AdiabaticmixingofTwostreamsofmoistair
Thelastequationtellsusthattheprocessfromstate2to3hasthesameslopeoftheprocessfromstate1to3,sothestate3mustlieonastraightlineconnecting1and2.Thelenghtsofthelinesegmentsareproportionaltothemassflowratesofdryairmixed.
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IntheUS,sometimesitisusedanapproximateequationinvolvingdrybulbtemperaturesofairstreamsinordertofindthemixed-aircondition.ma3cp3t3=ma1cp1t1+ma2cp2t2ifwemaketheapproximationthatthespecificheatsofthemixturesareapproximatelyequal:t3=(ma1/ma3)t1+(ma2/ma3)t2-->theaccuracyiswellwithintheaccuracywithwhichonecanreadthepsychrometricchart2)DehumidificationofMoistairbycooling
Ifmoistairiscooledbelowitsdewpoint,condensationofmoisturewilloccur.Theidealprocesscorrespondstooneinwhichtheairisuniformlyandperfectlycontactedbythecoolingcoil.Inthiscasenocondensationoccursuntiltheaverageorbulktemperatureoftheairreachesthedewpointtemperature.Inarealprocesstheairdoesnotcomeintoperfectoruniformcontactwiththeheat-exchangersurfaces,sothetemperaturenearthesurfaceswilldropbelowthedewpointtemperature,whiletheatnearthecenterramainsabove.Analternativeapproachtoanalyzethecooling/dehumidifyingprocessusesasocalledbypassfactor.Considerarealprocess(b).Drawastraightlinethatconnectsstates1and2andwhichisextendedtothesaturationcurveatstated.Thispointrepresentstheapparatusdewpoint(orcoolingcoil)temperaturetd,whiletheremainingairbypassedthecoolingcoil.Thefinalstate(state2)isthenthoughtastheadiabaticmixtureofthebypassedair(1)andthesaturatedair(d).
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Notethatthesensible-heatratio(SHR)canbereaddirectlyoffthepsychrometricchartforthestraightlineconnectingstates1andd.3)EvaporativecoolingofmoistairInhotanddryclimatesevaporativecoolingcanbeaneffectivemeansofreducingairtemperature.Ratherthanpassingtheairthroughacoolingcoil,wecantakeadvantageofthelowhumiditytoachievecooling.Thisisaccomplishedbypassingtheairstreamthroughaspraydevice(evaporativecooler)usingdirectlyrecirculatedwater.ThankstothelowRH,partoftheliquidwaterstreamevaporates.Theenergyfortheevaporationprocesscomesfromtheairstream:theoveralleffectistocoolandhumidifytheair.
Detailedanalysisoftheevaporative-coolingprocess,incaseof:a)Theevaporationrateismuchsmallerthanthewater-recirculationrate(-->energyintroducedbythemakeupwaterisnegligible)b)Thewallsofthedeviceareadiabaticc)ThepoweroftherecirculationpumpisnegligibleResults:1-Theairpassingthroughtheevaporativecoolerundergoesaconstantwet-bulbtemperatureprocess2-Alltheliquidintheapparatusisatwet-bulbtemperatureoftheairstream
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Theminimuntemperaturetowhichtheaircanbecooledisthewet-bulbtemperaturet*.Theextenttowhichtheleavingairtemperatureapproachesthisminimumtemperatureisreferredtoasthesaturationeffectiveness,ec.
