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{{#Wiki_filter:COTTAP-2,REV.1THEORYANDINPUTDESCRIPTIONMANUALPreparedby.N.A.ChaikoandH.J.Murphy'5(<NOVEMBER5,19909103260165910319PDRADOCK05000337PPDR PALForm2454i10/83)Cat,s973401$E-B-NA-046R-.01'ept.DateIt-I>19~~DesignedbyApprovedbyPENNSYLVANIAPOWER&LIGHTCOMPANY
{{#Wiki_filter:COTTAP-2, REV.1THEORYANDINPUTDESCRIPTION MANUALPreparedby.N.A.ChaikoandH.J.Murphy'5(<NOVEMBER5,19909103260165 910319PDRADOCK05000337PPDR PALForm2454i10/83)Cat,s973401$E-B-NA-046R-.01'ept.DateIt-I>19~~DesignedbyApprovedbyPENNSYLVANIA POWER&LIGHTCOMPANY-ERNo.CALCULATION SHEETPROJECTCONTENTS1~INTRODUCTION 2.METHODOLOGY 2.1ModelDescription 2.1.1MassandEnergyBalanceEquations 2.1.1.12.1.1.2BalanceEquations withoutMassTransferBetweenCompartments BalanceEquations withMassTransferBetweenCompartments 2.1.2SlabHeatTransferEquations 122.1.2.1Conduction EquationandBoundaryConditions 2.1.2.2FilmCoefficients 2.1.2.3InitialTemperature Profiles1317232.1.3SpdcialPurposeModels2.1.3.12.1.3.22.1.3.32.1.3.42.1.3.52.1.3.62.1.3.72.1.3.82.1.3.92.1.3.10PipeBreakModelCompartment LeakageModelCondensation ModelRainoutModelRoomCoolerModelHotPipingModelComponent Cool-Down ModelNaturalCirculation ModelTime-Dependent Compartment ModelThinSlabModel242528333435394143432.2Numerical SolutionMethods3.DESCRIPTION OFCODEINPUTS533.1ProblemDescription Data(Card1of3)3.2ProblemDescription Data(Card2of3)3.3ProblemDescription Data(Card3of3)3.4ProblemRun-TimeandTrip-Tolerance Data54555960 rrPE1.Form2lSl(rar831Ckr,l973401$E-B-NA-046Rev.0l''Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~LofPENNSYLVANIA POWER&LIGHTCOMPANY.ERNo.CALCULATION SHEET3.53.63.73.83.93.103.113.123.133.143.153.163.173.183.193.203.213.223.233.243.253.263.27ErrorTolerance forCompartment Ventilation
-10.00100.00.5014.7050.00100.00.5014.70100.00100.00.5014.70~~~~~~~~~Ij44~I1~0~~~0440I~~0~~0~0~~14I0~0~~~~~10~00~I~0~I444440~00i44~i00~41J44~40~~~0~04044~0~0t4~100~~~4l~~i1~0~~~0~0~~~~00~~l~4044~444~~0~~~0~
-10.00100.00.5014.7050.00100.00.5014.70100.00100.00.5014.70~~~~~~~~~Ij44~I1~0~~~0440I~~0~~0~0~~14I0~0~~~~~10~00~I~0~I444440~00i44~i00~41J44~40~~~0~04044~0~0t4~100~~~4l~~i1~0~~~0~0~~~~00~~l~4044~444~~0~~~0~
FIGURE4.6COMPARISONOFCOTTAPCALCULATEOCOMPARTMENTTEMPERATUREWITHANALYTICALSOLUTIONFORSAMPLEPROBLEM2135130OOOLLILJJ,0125120115110105LegendANALYTICAL~COTTAP10001020TIME(hr)3040 PP8,LForm24'10/N
FIGURE4.6COMPARISON OFCOTTAPCALCULATEO COMPARTMENT TEMPERATURE WITHANALYTICAL SOLUTIONFORSAMPLEPROBLEM2135130OOOLLILJJ,0125120115110105LegendANALYTICAL
~COTTAP10001020TIME(hr)3040 PP8,LForm24'10/N)Ca).t973401SE-9-.NA=046Rev.0gDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER8cLIGHTCOMPANYERNo.CALCULATION SHEETThewallsofthecompartment consistof3slabs:averticalwall(slabl),aceiling(slab2),andafloor(slab3)whichisincontactwiththeoutsideground.Thetemperature, relativehumidity, andpressurewithinthetime-dependent compartment areheldconstantthroughout thetransient.
 

Revision as of 19:45, 29 June 2018

COTTAP-2,Rev 1,Theory & Input Description Manual.
ML17157A804
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Issue date: 11/05/1990
From: CHAIKO M A, MURPHY M J
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{{#Wiki_filter:COTTAP-2, REV.1THEORYANDINPUTDESCRIPTION MANUALPreparedby.N.A.ChaikoandH.J.Murphy'5(<NOVEMBER5,19909103260165 910319PDRADOCK05000337PPDR PALForm2454i10/83)Cat,s973401$E-B-NA-046R-.01'ept.DateIt-I>19~~DesignedbyApprovedbyPENNSYLVANIA POWER&LIGHTCOMPANY-ERNo.CALCULATION SHEETPROJECTCONTENTS1~INTRODUCTION 2.METHODOLOGY 2.1ModelDescription 2.1.1MassandEnergyBalanceEquations 2.1.1.12.1.1.2BalanceEquations withoutMassTransferBetweenCompartments BalanceEquations withMassTransferBetweenCompartments 2.1.2SlabHeatTransferEquations 122.1.2.1Conduction EquationandBoundaryConditions 2.1.2.2FilmCoefficients 2.1.2.3InitialTemperature Profiles1317232.1.3SpdcialPurposeModels2.1.3.12.1.3.22.1.3.32.1.3.42.1.3.52.1.3.62.1.3.72.1.3.82.1.3.92.1.3.10PipeBreakModelCompartment LeakageModelCondensation ModelRainoutModelRoomCoolerModelHotPipingModelComponent Cool-Down ModelNaturalCirculation ModelTime-Dependent Compartment ModelThinSlabModel242528333435394143432.2Numerical SolutionMethods3.DESCRIPTION OFCODEINPUTS533.1ProblemDescription Data(Card1of3)3.2ProblemDescription Data(Card2of3)3.3ProblemDescription Data(Card3of3)3.4ProblemRun-TimeandTrip-Tolerance Data54555960 rrPE1.Form2lSl(rar831Ckr,l973401$E-B-NA-046Rev.0lDept.Date19DesignedbyApprovedbyPROJECTSht.No.~LofPENNSYLVANIA POWER&LIGHTCOMPANY.ERNo.CALCULATION SHEET3.53.63.73.83.93.103.113.123.133.143.153.163.173.183.193.203.213.223.233.243.253.263.27ErrorTolerance forCompartment Ventilation-FlowMassBalanceEditControlDataEditDimension DataSelection ofRoomEditsSelection ofThick-Slab EditsSelection ofThin-Slab EditsReference Temperature andPressureforVentilation FlowsStandardRoomDataVentilation FlowDataLeakageFlowDataCirculation FlowDataAir-FlowTripDataHeat.LoadDataHotPipingDataHeat-Load TripDataPipeBreakDataThickSlabData(Card1of3)ThickSlabData(Card2of3)ThickSlabData(Card3of3)ThinSlabData(Card1of2)ThinSlabData(Card2of2)Time-Dependent RoomData(Card1of2)Time-Dependent RoomData(Card2of2)61616263636464656667686970717374757879808182844.SAMPLEPROBLEMS854.14.24.3444.54.6Comparison ofCOTTAPResultswithAnalytical SolutionforConduction throughaThickSlab(SampleProblem1)Comparison ofCOTTAPResultswithAnalytical SolutionforCompartment Heat-UpduetoTrippedHeatLoads(SampleProblem2)COTTAPResultsforCompartment CoolingbyNaturalCirculation (SampleProblem3)COTTAPResultsforCompartment Heat-UpResulting fromaHigh-Energy PipeBreak(SampleProblem4)COTTAPResultsforCompartment Heat-UpfromaHot-PipeHeatLoad(SampleProblem5)Comparison ofCOTTAPResultswithAnalytical SolutionforCompartment Depressurization duetoLeakage(SampleProblem6)859698103112117:~ PPLLForm2l54l1$S3)C4t.e9Q401F-B-NA.-046Rev.01'ept.Date19DesignedbyApprovedbyPROJECT~~~Sht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET5.REFERENCES APPENDZXATHERMODYNAMZC ANDTRANSPORT PROPERTZES OFAZRANDWATER122126 l PPKLForm2I54(1083)Cat.t9%401$F-B-NA=046Rev.apDept.Date19DesIgnedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET1.INTRODUCTION COTTAP(Compartment Transient Temperature AnalysisProgram)isacomputercodedesignedtopredictindividual compartment environmental conditions inbuildings wherecompartments areseparated bywallsofuniformmaterialcomposition. Userinputdataincludesinitialtemperature,

pressure, andrelativehumidityofeachcompartment.

Inaddition, ventilation flow,leakageandcirculation pathdata,steambreakandtimedependent heatloaddataaswellasphysicalandgeometric datatodefineeachcompartment mustbesuppliedasnecessary. Thecodesolvestransient heatandmassbalanceequations todetermine temperature,

pressure, andrelativehumidityineachcompartment.

Afinitedifference solutionoftheone-dimensional heatconduction equationiscarriedoutforeachthickslabtocomputeheatflowsbetweencompartments andslabs.Thecoupled,equations governing thecompartment andslabtemperatures aresolvedusingavariable-time-step O.D.E.(Ordinary Differential Equation) solverwithautomatic errorcontrol.COTTAPwasprimarily developed tosimulatethetransient temperature responseofcompartments withintheSSESUnit1andUnit2secondary containments duringpost-accident conditions. Compartment temperatures areneededtoverifyequipment qualification (EQ)andtodetermine whetheraneedexistsforsupplemental cooling. PPdLForm2i54(10/83)Cat.S9D401(FBfqA-Q45Rev.QDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER8LIGHTCOMPANYERNo.CALCULATION SHEETThescaleofthisproblemisratherlargeinthatamodeloftheUnit1IandUnit2secondary containments consistsofapproximately 120Scompartments and800slabs.Inadditiontothelargesizeoftheproblem,thetemperature behavioristobesimulated overalongperiodoftime,typically onehundreddays.Ztistherefore necessary todevelopacodethatcannotonlyhandlealargevolumeofdata,butcanalsoperformtherequiredcalculations withareasonable amountofcomputertime.ZnadditiontolargescaleproblemsCOTTAPiscapableofmodelingroomheatupduetobreaksinhotpipingandcooldownduetocondensation andrainout.Italsocontainsanaturalcirculation modeltosimulateinter-compartment flow.Thepurposeofthiscalculation istodemonstrate thevalidityofthiscomputercodewithregardtothetypesofanalysesdescribed above.Thisvalidation processiscarriedoutinsupportofthecomputercodedocumentation packagePCC-SE-006. pphLForm2454lror83rCar,e97&orS<-B-NA-046geeO~.Dept.Date19DesignedbyApprovedbyPROJECTSht.No.of8PENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET2.METHODOLOGY 2.1ModelDescritionThecompartment massandenergybalanceequations, slabheatcondition equations, andtheCOTTAPspecialpurposemodelsarediscussed inthissection.Anoutlineofthenumerical solutionprocedure usedtosolvethemodelingequations isthengiven.2.1.1MassandEnerBalanceEationsTwomethodsareavailable inCOTTAPforcalculating transient compartment conditions. Thedesiredmethodisselectedthroughspecification ofthe1mass-tracking parameter MASSTR(seeproblemdescription datacardsinsection3.2).2.1.1.1BalanceEationswithoutMassTransferbetweenComartmentsIfMASSTR0,thecompartment massbalanceequations areneglected andthetotalmassineachcompartment isheldconstant'throughout thecalculation. Thisoptioncanbeusedifthereisnoairflowbetweencompartments orifairflowisduetoventilation flowonly'(i.e.,therearenoleakageorcirculation flowpaths).InCOTTAP,ventilation flow PPhl.Fofrft24541fof83)Cat.ff973lolSE-B-NA-046Rev.0];Dept.Date19DesignedbyApprovedbyPROJECTSht.No.fffofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETratesareheldconstantattheirinitialvalues>thus,ifthenetflowoutofeachcompartment iszeroinitially, thenthereisnoneedforacompartment massbalancebecausethemassofairineachcompartment remainsconstant. Znthismodeofcalculation, themoisturecontentoftheair(asspecified bythevalueofcompartment relativehumidityontheroomdatacards,seesection3.12)isonlyusedtocalculate thefilmheattransfercoefficients forthickslabs;theeffectofmoisturecontentontheheatcapacityanddensityofairisneglected. Thecompartment energybalanceusedinCOTTAPforthecaseofMASSTR=OisPCVdT=Q+0+0+Qava-rlightQpanelmotorcoolerQwallmiscpipingdtN+PW.(T.+a)C(T.)j=1vjvjopavjwhereT~compartment (room)temperature (F),0Zt~time(hr),pdensityofairwithincompartment (ibm/ft),3aCconstant-volume specificheatofair(Btu/ibmF),0va3V~compartment volume(ft),(2-1)Qlihcompartentlightingheatlead(Btu/hr). lightpanelQotor=compartment electrical panelheatload(Btu/hr), =compartment. motorheatload(Btu/hr), PP9t.Form2454t>583)Cat,e913%1SE-B-NA-046Rev0g:Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANY.ERNo.CALCULATION SHEETcoolerpipingwallcompartment coolerload(Btu/hr), heatloadduetohotpiping(Btu/hr), rateofheattransferfromwallstocompartment air(Btu/hr), miscNvmiscellaneous compartment heatloads(Btu/hr), numberofventilation flowpathsconnected tothecompartment, WVjTVjC(T.)pavjventilation flowrateforpathj(ibm/hr), ~airtemperature forventilation pathj(F),0specificheatofairevaluated atT.(Btu/ibmF),0v3a=459.67F.0Ventilation flowratesarepositiveforflowintothecompartment andnegativeforflowoutofthecompartment. Compartment

lighting, panel,motorandmiscellaneous loads,whichareinputtothecode,remainatinitialvaluesthroughout thetransient unlessactedonbyatrip.Heatloadsmaybetrippedon,off,orexponentially decayedatanytimeduringthetransient.

Useoftheheatloadtripisdiscussed inSection3.19,andtheexponential decayapproximation isdiscussed inSection2.1.3.7.Thecompartment roomcoolerloadisaheatsinkandisinputasanegativevalue.Thecodeautomatically adjuststhisloadforchangesinroom ppd,LForm2454n0/831Cat.<<97340ISE-~-NA-046Rev.QPDept.Date19DesignedbyApprovedbyPROJECTSht.No.4ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETItemperature. Coolanttemperature isinputforeachcoolerandremainsconstantthroughout thetransient. Seesection2.1.3.5foradetaileddescription ofthiscalculation. Theinitialcompartment pipingheatloadsandoverallheattransfercoefficients arecalculated byCOTTAPbasedonpipingandcompartment inputdata.Overallheattransfercoefficients forhotpipingareheldconstantthroughout thetransient andheatloadsarecalculated basedontemperature differences betweenpipesandsurrounding air.Nocreditistakenforcompartment heatrejection toapipewhencompartment temperature exceedspipetemperature. Whenthissituation occurs,thepipingheatloadissettozeroandremainsthereunlesscompartment temperature decreases belowpipetemperature. Ifthisshouldoccurapositivepipingheatloadwouldbecomputedintheusual'anner. Pipingheatloadsaswellasroomcoolerloadsmaybetrippedon,off,orexponentially decayed.SeeSection2.1.3.6foradetaileddescription ofthepipingheatloadcalculation. Therateofheattransferfromwallstocompartment airiscalculated fromNEh.A.(T.-T),wwall.jjsurfjr'~1(2-2)whereN~thenumberof'walls(slabs)surrounding theroom,wh.=filmheattransfercoefficient (Btu/hrftF),20j PP5LForm2L54(la(83)Cat.%7340lSE-8-NA-046Rev.Qy'ept.Date19DesignedbyApprovedby'ROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETA.=surfaceareaofwall(ft),2andT.=wallsurfacetemperature (F).0surfjUseofMASSTR=Oisonlyvalidforthecasewherecompartment temperatures undergosmallormoderatevariations. Forthesesituations, maintaining constantmassinventory ineachcompartment isafairlygoodapproximation sincedensitychangesaresmall.Iflargetemperature changesoccur,compartment massinventories willundergosignificant fluctuations inordertomaintainconstantpressure. Inthissituation amodelwhichaccountsformassexchangebetweencompartments isrecpxired. UseofMASSTR=.O, whereapplicable, ishighlydesirable especially forproblemswithmanycompartments andslabsbecauselargesavingsincomputation timecanberealized. ThemoregeneralcaseofMASSTR=1isdescribed below.2.1.1.2BalanceEationswithMassTransferBetweenComartmentsWhenthemass-tracking optionofCOTTAPisselected(MASSTR~1), specialpurposemodelsareavailable fordescribing airandwater-vapor leakagebetweencompartments, circulation flowsbetweencompartments, andtheeffectofpipebreaksuponcompartment temperature andrelativehumidity. ppat.FormP<<5<<<1$83tC<<t.<<973<<01S~-B"NA-G46Rev.Q]Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETandA.~surfaceareaofwall(ft),2jT.~wallsurfacetemperature (F).0surfjUseofMASSTR~Oisonlyvalidforthecasewherecompartment temperatures undergosmallormoderatevariations. Forthesesituations, maintaining constantmassinventory ineachcompartment i.safairlygoodapproximation sincedensitychangesaresmall.Iflargetemperature changesoccur,compartment massinventories willundergosignificant fluctuations inordertomaintainconstantpressure. Inthissituation amodelwhichaccountsformassexchangebetweencompartments isrequired. UseofMASSTR=O, whereapplicable, is.highlydesirable especially forproblemswithmanycompartments andslabsbecauselargesavings,incomputation timecanberealised. ThemoregeneralcaseofMASSTR~1isdescribed below.2.1.1.2BalanceEationswithMassTransferBetweenComartmentsWhenthemass-tracking optionofCOTTAPisselected(MASSTR~1), specialpurposemodelsareavailable fordescribing ai.randwater-vapor leakagebetweencompartments, circulation flowsbetweencompartments, andtheeffectofpipebreaksuponcompartment, temperature andrelativehumidity. pplLLForm2<<sin0183)C<<t.<<913401SE-B-NA-046RevQpDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETTheairandvapormassbalanceerpxations thataresolvedbyCOTTAPforthecaseofMASSTR~1areNVdP~PW.Y-a.vjvjdtj~lNl+EW.Y3<<<<133N+Z(W~Y~~-W~Y~l<<cj,incj,incj,outcj,outjul(2-3)NVdP~PW.(1Y.)dtj~lNl+gW.(1-Y.)1313N+Z[W..(1-Y..)-W.(1-Yccj,incj,incj,outcj,out+W-W-Wbscondro'2-4)wherep~compartment airdensity(ibm/ft),3a3pcompartment watervapordensity(ibm/ft),vNnumberofventillation flowpathsconnected tothevcompartment, ppct.Form2454nOI83iCol,I873401Ix-SE-B-NA-046Rev,pg>Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~OofPENNSYLVANIA POWER8LIGHTCOMPANYERNo.CALCULATION SHEETN~numberofleakagepathsconnected tothe1compartment, N~numberofcirculation pathsconnected tocthecompartment, W.~totalmassflowthroughleakagepathj(ibm/hr), ljW..=totalinletmassflowthroughcirculation cj,inpathj(ibm/hr), W.=totaloutletmassflowthroughcirculation cj,outpathj(ibm/hr), lY.~airmassfractionforventilation pathj,vjY.~airmassfractionforleakagepathj,ljY..~airmassfractionofinletflowforcj,incirculation pathj,Y.=airmassfractionofoutletflowforcj,outcirculation pathj,Wbsteamflowratefrompipebreak(ibm/hr), bsW=watervaporcondensation rate(ibm/hr), condW~watervaporrainoutrate(ibm/hr). roThecompartment energybalanceforMASSTR1isVf(T+a)pdC(T)+pC(T)+pdh(T)roa~araparv~rrr <<PP<<LForm2<<54nOr83)C<<r.<<9'<<OiSE-B-NA-046Rev.01'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET-pR-pR]dT~-V(T+a)C(T)dpvvaa-rropar-adtdt-Vh(T)dp+(T+a)(RdP+RdP)VvdvoZpaddt+Q.+Q+0+Q +QlightpanelQmotorcoolerpiping+0+0.+Q+Whmallmiscbreakbsv,break-Wh(T)-Wh(T)N+EW.[Y.(T.+a)C(T.)+(1-Y.)h(T.)]j=lvjvjrjopavjvjvvjN+QW1[Y1(T1+a)C(T1)+(1Y1)h(T1) Ij=lljljljopa1jljvljN+ZW..[Y..(T..+a)C(T..)j1cj,incj,incj,inopacj,in+(1-Y..)h(T.)]cj,invcj,inNcW.[Y.(T+a)C(T)cj,outcj,outroparj<<<<1+(1Y.)h(T)],cj,outvr(2-5)wherehsaturated watervaporenthalpy(Btu/ibm), h=enthalpyofsteamexitingbreak(Btu/ibm) v,breakh(P)ifpipecontainsliquid,vrh(P)ifpipecontainssteam,vpP~compartment pressure(psia),rP=pressureoffluidwithinpipe(psia),P ppB,LFoim2i54n(v83)Cat.e973401SE-B-NA-046Rev.Py'ept.Date19DesignedbyApprovedbyPROJECTSht.No.I~ofPENNSYLVANIA POWER&LIGHTCOMPANY-ERNo.CALCULATION SHEETR~idealgasconstantforsteam(0.1104Btu/ibmR)vR~idealgasconstantforair(0.0690Btu/ibmR),0Qheattransferred toairandwatervaporfrombreakliquidexitingbreakasitcoolstocompartment temperature (Btu/hr), CWsteamflowrateexitingpipebreak(ibm/hr), bsh~saturation enthalpyofliquidwater(Btu/ibm). fAllothervariables in(2-5)areaspreviously defined.Thebasicassumption usedinderiving(2-5)isthattheairandwatervaporbehaveasidealgases.Thisisareasonable assumption aslongascompartment pressures areclosetoatmospheric pressurewhichshouldnearlyalwaysbethecase.2.1.2SlabHeatTransferBationsTheslabmodelinCOTTAPdescribes thetransient behaviorofrelatively thickslabswhichhaveasignificant thermalcapacitance. Eoreachthickslab,theone-dimensional unsteadyheatconduction equationissolvedto,~ PP41,Form2454(10/831Col.4973401SE-B-NA-046Rey0>Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANY.ERNo.CALCULATION SHEETobtaintheslabtemperature profilefromwhichtherateofheattransferbetweentheslabandadjacentroomsiscomputed. Allthickslabsmustbecomposedofasinglematerial: composite wallscannotbemodeledwithCOTTAP.AspecialmodelisalsoincludedinCOTTAPfordescribing heatflowthroughthinwallswhichhavelittlethermalcapacitance. Thethinslabmodelisdiscussed insection2.1.3.10. 2.1.2.1Conduction EationandBoundaConditions Thetemperature distribution withintheslabisdetermined bysolutionoftheone-dimensional unsteadyheatconduction

equation, aTpat-<aTtax22ss(2-6)subjecttothefollowing boundaryandinitialconditions:

3TBxX~BT3xX~L-h[T(t)-T(o,t)],-1rlks-h[T(Lt)-T(t)J,-2skz2(2-7)(2-8)whereT(x,o)ax+b,sT(x,t)=slabtemperature (F),0sIt~time(hr),(2-9) PP&LForm245'0r&3) Col,0970401SE-B-NA-046R~v01'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETx~spatialcoordinate (ft),~thermaldiffusivity ofslabmk/(pC)(ft/hr),2sps~thermalconductivity (Btu/hrftF),p~slabdensity(ibm/ft),3Cmspecificheatofslabmaterial(Btu/ibmF)ps1h~filmcoefficient forheattransferbetweenthyslab1andtheroomonside1oftheslab(Btu/hrftF),h=filmcoefficient forheattransferbetweenthyslab2andtheroomonside2oftheslab(Btu/hrftF),T1(t)Temperature ofroomonside1ofslab(F),rlT2(t)=Temperature ofroomonside2ofslab(F).r2Theslabandroomarrangement described bytheseequations isshowninFigure2.1.Notethatthespatialcoordinate iszeroonside1oftheslabandisequaltoLonside2,whereListhethickness oftheslab.Valuesofthermalconductivity, density,andspecificheataresuppliedforeachslabandheldconstantthroughout thecalculation. Therateofheatflowfromtheslabtotheroomonside1oftheslabisgivenbyq(t)hA[T(o,t)<<T(t)],(2-10) PP&LForm2<<&d(l0(83)Cat.<<913<<OfSE-B-NA-046Rev()yDept.Date19DesignedbyApprovedbyPROJECTSht.No.~8ofPENNSYLVANIA POWER8LIGHTCOMPANYERNo.CALCULATION SHEETal(t)~SS(t)Roomonside1ofslabattemperature T.l(t)r'1SlabTemp<<T(x,t)sRoomonside2ofslabattemperature T(t)r2SidelofslabFilmcoefficient hlHeatTransferArea,A~Side2ofslabFilcoefficient. h2HeatTransferArea,AX=OX=LFigure2.1Thickslabandadjacentrooms PPtLLForrtt2454(10I83)C91,991340tNA-046Rev.0g:Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~&ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETandtherateofheattransferfromtheslabtotheroomonside2isobtainedfromq(t)~hA[T(L,t)-T(t)J,(2-11)whereAisthesurfaceareaofonesideoftheslab.Aslabcanalsobeincontactwithoutsideground.Calculation oftheheatlossfromaslabtooutsidegroundwouldinvolvemodelingofmulti<<dimensional unsteadyconduction whichwouldgreatlycomplicate theanalysis. Asasimplifying approximation, heattransferfrombelowgradeslabstotheoutsidegroundisneglected bysettingthefilmcoefficient equaltozeroattheoutersurfaceofeveryslabincontactwiththeoutsideground.Thisisaconservative approximation inthesensethattheheatlossfromthebuildingwillbeunderpredicted givingrisetoslightlyhigherthanactualroomtemperatures. Thegoverning equations forabelowgradeslabwithside2incontactwithgroundare(2-6)through(2-9)butwithhsetequaltozero.Ifside1oftheslabisin2contactwithgroundthenhlissettozero. ppALForm245'$83)C4t.l873i01NA046ReyQ)Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~7ofPENNSYLVANIA POWER5LIGHTCOMPANY-ERNo.CALCULATION SHEET2.1~2.2FilmCoefficients Filmcoefficients forslabscanbesuppliedasinputdataorvaluescanbecalculated bythecode(seesection3.21foradiscussion ofhowtoselectthedesiredoption).Zfthefilmcoefficients aresuppliedasinputdata,twosetsofcoefficients arerequiredforslabswhicharefloorsandceilings(aslabisdefinedasafloororaceilingdepending uponitsorientation withrespecttotheroomonside1oftheslab).Avaluefromthefirstsetisusedifheatflowbetweentheslabandtheadjacentroomisintheupwarddirection; avaluefromthesecondsetisusedifthedirection ofheatflowisdownward. Onlyonesetoffilmcoefficients isrequiredforverticalslabsbecauseinthiscasethecoefficients donotdependuponthedirection ofheatflow.User-supplied coefficients areheldconstantthroughout theentirecalculation. Natural-convection filmcoefficients are,however,temperature dependent, andvaluesrepresentative oftheaverageconditions duringthetransient shouldbeused.Suggested valuesofnaturalconvection filmcoefficients forinteriorwallsandforcedconvection coefficients forwallsincontactwithoutsideairaregiveninref.11,p.23.3;notethattheradiative heattransferIlcomponent isalreadyincludedinthesecoefficients. l PPELForm2454noI83)CSt.4973S01SE-B-NA-046Rev.ay'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~of.PENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETCorrelations arealsoavailable inCOTTAPforcalculation ofnaturalconvection filmcoefficients. Coefficients forverticalslabsarecalculated from(ref.8p.442)h=kclC0.825+0.387Ra[1+(0492/P)9/16)8/27 (2-12)whereh1=naturalconvection film.coefficient forverticalclslab(Btu/hrftF),20k~thermalconductivity ofair(Btu/hrftF),C~characteristic lengthofslab(slabheightinft).TheRayleighandPrantlnumbersaregivenbyRa~g8(3600)(T-T)C/@(x)P23surfrL(2-13)Pr~AC/k,P(2-14)whereg~acceleration duetogravity(32.2ft/sec),20-1gcoefficient ofthermalexpansion forair(R),g~kinematic viscosity ofair(ft/hr),2 PPiLLFOrm2i54tttt183tCat.tt913401SE-8-NA-046RevQPDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER8LIGHTCOMPANYERNo.CALCULATION SHEETa=thermaldiffusivity ofair(ft/hr),2"viscosity ofair(ibm/hr-ft). Airproperties areevaluated atthethermalboundarylayertemperature whichistakenastheaverageoftheslabsurfacetemperature andthebulkairtemperature ofthecompartment. Themoisturecontentofthe,airisalsoaccounted forincalculating theproperties (seeAppendixAforcalculation ofairproperties). Forhorizontal slabs,thenaturalconvection coefficient forthecaseofdownwardheat,flowiscalculated from(ref.17)h~0.58kRa1/5c2L(2-15)andforthecaseofupwardheat,flowthecorrelations are(ref.8,p.445)h~0.54kRa1/4c3L(Ra<10)7(2-16)h0.15kRa1/3c3C(Ra>10)7(2-17)Thecharacteristic lengthforhorizontal slabsistheslabheattransferareadividedbytheperimeter oftheslab(ref.18). PPdLForm2l54nOI831CaLl973401J.SE-B-NA-046R".0y'ept.Date19DesignedbyApprovedbyPROJECTSht.No.40ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETTheeffectofradiative heattransferbetweenslabsandcompartment airisalsoincludedintheCOTTAP-calculated filmcoefficients. Fortheapplications ofinterest, temperature differences betweenaslabsurfaceandthesurrounding gasmixturearerelatively small(typically <10F).Therefore thefollowing approximate relationproposedbyHottel(ref.19pp.209-301)forsmalltemperature differences 'isusedtocomputetheradiation coefficient: h~(6+1)(4+a+b-c) eQTn<a3w,avav2(2-18)whereoTavTZStetan-Boltzman constant(0.1712x10 Btu/hrftR),-8[[(T+a)+(T+a)]/2)(R)441/4orosurfo~compartment airtemperature (F),T~slabsurfacetemperature (F),0surfsCw,av~slabemissivity ~watervaporemissivity evaluated atTava~459.67F.0Onlythewatervaporcontribution totheairemissivity isincludedinequation(2-18)becausegasessuchasNand0.aretransparent tothermal22'III PP&LForm2454n0r&3)Col.@910401SE-8-NA-046Rev0>'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETradiation (ref.11,p.3.11),andtheeffectduetoCOisnegligible 2becauseofitssmallconcentration (0.03%byvolume,ref.12,p.F-206).Theemissivity ofwatervaporisafunctionofthepartialpressureofwatervapor,themeanbeamlength,thegastemperature, andthetotalpressure(ref.13,pp.10-57, 10-58).TheCess-Lian equations (ref.21),whichgiveananalytical approximation totheemissivity chartsofHottelandEgbert(ref.22),areusedtocomputethewatervaporemissivity. Theseeuqations aregivenby6(TP,P,PL)=A[1exp(AX)]1/2waw'wmo1(2-19)X(T,PiP,PL)~PLI300tamwmLT3P+[5(300/T) +0.5]Paw(101325)(2-20)whereT~gastemperature (K),P~airpartialpressure(Pa),P~watervaporpartialpressure(Pa),andL~averagemeanbeamlength(m).mThecoefficients AandAarefunctions ofthegastemperature, andforpurposesofthiswork,theyarerepresented bythefollowing polynomial expressions: pp&LForm245<<(lorLr'rCar.<<sncorDept.Date19DesignedbyApprovedbyPROJECTSht.No.22ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETandA(T)~0.6918-2.898x10T-1.133x10T-5-920(2-21)A(T)=1.0914+1.432x10T+3.964x10T(2-22)where273K<T<600K.TabularvaluesofAandAoverthewidero1temperature range300K<T<1500Kareavailable (ref.21).Znequation(2-18),8hasthevalue0.45,andaandCaredefinedbyI)in[a(TP<<P<<PL)]awmBln(PL)wm(2-23)and3ln[e(T,P,P,PL)]wmr)ln(T)(2-24)n,Valuesofaandbareobtainedthroughdifferentiation oftheCess-Lian equations. TheaveragemeanbeamlengthLforacompartment ismcalculated fromLR3.5V/Am(2-25)Whichissuggested forgasvolumesofarbitrary shape(ref.19).Zn(2-25)Visthecompartment volumeandAistheboundingsurfacearea. PP&1.Form245ln0r831Cat.e973401SE.-B-NA-046Rev.0yDept.Date19DesignedbyApprovedbyPROJECTSht.No.~~of.PENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET2.1.2.3InitialTemeratureProfilesTheinitialtemperature distribution withinathickslabisobtainedbysolvingthecorresponding steady-state problem,dT(x,O)/dx=0,22=s(2-26)dT(x,O)dx-h[T(0)-T'0,0)]g0klrls(2-27)dT(x,o)dx-2s'2-h[T(LrO)-T(0)].x=L(2-28)ThesolutionisT(xO)=ax+b,swhere(2-29)h[T(0)T(0)]k+hL+kh/h (2-30)b~T(0)+kh[T(0)-T(0)l~h[k+hL+kh/h]1221(2-31)Equation(2-29)isanimplicitrelationforthetemperature profilebecauseofthetemperature dependence ofthefilmcoefficients. Aniterative solutionofeq.(2-29)iscarriedoutinCOTTAP. ppBLForm2454n$83)Ca<.s9rm>SE-B-NA-046Rev.0y'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~+ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET2.1.3SecialPuoseModels2.1.3.1PieBreakModelPipebreakscanbemodeledinanyCOTTAPstandardcompartment. Linesmaycontainsteamorsaturated waterasindicated bytheFluidStateflag,ZBFLG,onthePipeBreakinputdatacards(seeSection3.20).Zfthepipecontainswater,thefollowing energybalanceissolvedsimultaneously withthecontinuity equationtodetermine theflowrateofsteamexitingthebreak:Wh(P)~Wh(P)+[W-W]h(P),btfpbsvrbsfr(2-32)whereWtotalmassflowexistingthebreak(ibm/sec.), Wbsteamflowexitingbreak(ibm/sec.), bsh~enthalpyofsaturated liquid(Btu/ibm), fh~enthalpyofsaturated vapor(Btu/ibm), vP~fluidpressurewithinpipe(psia),PP~compartment pressure(psia).rIAsaconservative approximation, theliquidexitingthebreakiscooledtoroomtemperature andthesensibleheatgivenoffisdeposited inthe ppd1.Form2l54nord3lCat,t973l01SF-B-NA-046Rev.01'ept.Date19DesIgnedbyApprovedbyPROJECTSht.No.4~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETcompartment airspace.Thisheatsourceisrepresented bytheterm,Q-,ineq.(2-5)andiscalculated frombreakQ=lW-Wb][h(P)-h(T)](2-33)whereTisthecompartment temperature. rThetotalmassflowoutthebreakandthepipefluidpressurearespecified asinputtothecode.Znthecasewherethepipecontainshigh-pressure steam,allofthemassandenergyexitingthebreakisdeposited directlyintotheairspaceofthecompartment. Thisisareasonable approximation forsteamlinepressures ofinterestinboilingwaterreactors. 2.1.3.2ComartmentLeakageModelZnter-compartment leakagepathssuchasdoorwaysandventilation ductscanbemodeledusingtheleakagepathmodelinCOTTAP.Leakagepathsarespecified onleakagepathdatacards(Section3.14)byinputting theleakagepathZDnumber,flowarea,pressurelosscoefficient, ZDnumbersofroomsconnected bytheleakagepath,andthealloweddirections for PP&t.Form2c54ttor&3)Cat,rr97340tSE-B"NA-046Rev.0>Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETleakageflow.Zfaleakagepathlosscoefficient issettoanegativevalue,thenleakageflowiscalculated fromthesimpleproportional controlmodel:WmC(A/A)'Plpllmax(2-34)whereW=leakageflowrate(ibm/hr), plAlproportionality constant(ibm-in/hr-lbf), 2leakagepathflowarea(ft),2A=maxflowareaforallleakagepaths(ft),2rIIPpressuredifferential betweencompartments (psia).TheconstantCisspecified ontheinputdatacards(Section3.2).Themodelgivenby(2-34)isusedprimarily tomaintainconstantpressureincompartments byallowingmassto"leak"fromonecompartment toanother.Forexample,acompartment containing heatloadscanbeconnected, bywayofaleakagepath,toalargecompartment whichrepresents atmospheric conditions. Thecompartment willthenbemaintained atatmospheric pressureeventhoughsignificant airdensitychangesoccurduetocompartment heatup. PP&LForm2c54nor83iCol.@973401SE-B-NA-046Rev.Qg'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~4ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETAleakagemodelsuitableforcalculation ofcompartment pressuretransients canbeselectedbysettingtheassociated losscoefficient equaltoapositivequantity. Znthiscasetheleakagerateiscomputedbybalancing theintercompartment pressuredifferential withanirreversible pressureloss:1lili(3600)~hP2gP1A1(144)2(2-35)whereK=losscoefficient forleakagepath(basedonAl),2A=leakagearea(ft),1W=leakageflowrate(ibm/hr), 1p=densitywithincompartment whichisthesourceoftheleakage1flow(ibm/ft),3BP=pressuredifference betweencompartments associated withleakagepath(psia).Amaximumleakageflowrateforeachpathiscalculated fromWlpmin(ViV)C1tmax1'p2'2-36) PP4lForm2454(10/83)C4t.rr973401SE-B-NA-Q46Rev.Qg'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~4of.PENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETwhereVlandVarethevo1umes(ft)ofthecompartments connected by33theleakagepath,p(ibm/ft)istheaverageofthegasdensity-1forthetwocompartments, andC2(hr)isauserspecified p2constant. 2.1.3.3Condensation ModelCOTTAPis-capableofmodelingwatervaporcondensation withincompartments andalsoallowsmoisturerainoutincompartments wheretherelativehumidityreaches100%.Condensation isinitiated onanyslabifthesurfacetemperature isatorbelowthedewpointtemperature oftheair/vapor mixtureinthecompartment. Thiscondition issatisfied whenT(T(P)surf-satv(2-37)whereT(P)isthesaturation temperature ofwaterevaluated atthesat,vpartialpressureofvaporwithinthecompartment. Tfistheslabsurfsurfacetemperature. pp&LForm2l54n0/83)Cat.e973401SE-B-NA-046Rev,0fDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETZnordertoavoidnumerical instabilities causedbyrapidfluctuation betweennaturalconvection andcondensation heattransfermodes,thecondensation coefficient islinearlyincreased toitsfullvalueovera2minuteperiod.Similarly, thecondensation coefficient isdecreased overa2minuteperiodifcondensation isswitchedoff.Modulating thetransitions betweenthetwoheattransfermodesallowsuseofmuchlargertimestepsthanwouldotherwise bepossible. Thecondensation heattransfercoefficient iscalculated fromtheexperimentally determined Uchidacorrelation whichincludesthediffusional resistance effectofnon-condensible gasesonthesteamcondensation rate(ref.16p.65,ref.20).ValuesoftheUchidaheattransfercoefficient, asafunctionofthecompartment air/steam massratio,aregiveninTable2.3.COTTAPuseslinearinterpolation toobtainthecondensation coefficient atthedesiredconditions. PPa1.Formtfa5l(10/831Cat.ffgrm1'1SE-B-NA-046Rev,01Dept.Date19DesignedbyApprovedbyPROJECTSht,No.aloofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETTable2.3UchidaHeatTranferCoefficient* MassRatio(Air/Steam) ,HeatTransferCoefficient (Btu/hr-ft -P)(0.100.500.801.301.802.303.004.005.007.0010.0014.0018.0020.00>50.00280.25140.1398.1863;1046.0037.0129.0823.9720.9717.0114.0110.019.018.002.01*Valuesfromref.16,p.65 PP&LForm2I54(>0183)Cat.%13401SE-B-NA-046Rev.0>'ept.Date19DesIgnedbyApprovedbyPROJECTSht.No.~IofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETThecompartment gasmixturecontainsalargepercentage ofairevenunderconditions wherecondesnation occurs.Undertheseconditions, naturalconvection heattransferbetweenairandwallsisstillsignificant. Znaddition, radiation heattransferbetweenthevaporandwallsalsooccursduringcondensation. Underconditions wherecondensation occurs,therateofheattransfertoawalliscalculated froma=-hA(T-Tuwrsurf(2-38)whereq=rateofheattransfertothewall(Btu/hr), h=Uchidaheattransfercoefficient (Btu/hr>>ft -F),20uA=wallsurfacearea(ft),2woT~compartment airtemperature (F),rT~wallsurfacetemperature (F).0surf PPALForm2454I>0/80)Cat.40%401~)SE-8-NA-046Rev.QglDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETThecorresponding condensation rateatthewallsurfaceiscalculated fromW=(h-h)A(T-Tconduwrsurfh(2-39)whereandh=naturalconvection/radiation heattransfercoefficient, h+h,cr(Btu/hr-ft -F),20h=naturalconvection coefficient (Btu/hr-ft -F),20c-20h=thermalradiation coefficient (Btu/hr-ft -F).rEquation(2-39)accountsforthefactthatduringcondensation asignificant fractionofthetotalheattransferratetotheslabsurfaceisintheformofsensibleheat.Incomputing thesensibleheatfraction, itisassumedthatthecondensate temperature isapproximately equaltotheslabsurfacetemperature, i.e.,themajorresistance tocondensation 'Iheattransferisassociated withthediffusion layerratherthanthecondensate film. PP6LForm2l54nOI83lCol.@913403SE-B-NA-046Rev.0>'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~~of.PENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET2.1.3.4RainOutModelRainoutphenomena isimportant incompartments containing pipebreaks.ThemodelusedinCOTTAPisasimpleproportional controlmodelthatmaintains compartment relativehumidityatorbelow100%.Ztisactivated whentherelativehumidityreaches99%.Therainoutofvaporiscalculated fromandW=(200.0RH-198.0)max(W.,C)(RH>0.99),rovap,in'l(2-40)W~0.0ro(RH<0.99),(2-41)whereW~rateofvaporrainout(ibm/hr), roCuserspecified constant(seesection3.2),rlW.netvapormassflowintothecompartment (ibm/hr), vap,inRH=relativehumidity. PPAL.Form2454n0/83lCjt,097340l'SE-B-NA-046R-v.oy:Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~~ofPENNSYLVANIA POWER&LIGHTCOMPANY'ERNo.CALCULATION SHEET2.1.3.5RoomCoolerModelTheroomcoolerloadisassumedtobeproportional tothedifference betweencompartment ambienttemperature andtheaveragecoolanttemperature. Ztiscalculated asfollows:=C(T-T),coolc,avgr(2-42)whereQcoolCTc,avgand~coolerload(Btu/hr), 0-T),Btu/hrF,Qcoolinitialc,avginitialrinitial0=averagecoolanttemperature (F),(T.+T)/2c,inc,outoT=compartment temperature (F).rTheinletcoolingwatertemperature, Ti,issuppliedasinput,andthec,in'utlet coolingwatertemperature, T,iscalculated fromthecoolingcgoutwaterenergybalance,Q=C(T-T)~WC(T-T),coolc,avgrcoolpwc,inc,outwhere(2-43)W~coolingwaterflowrate(ibm/hr), cool pphLForm2454nar83)car.rr973401S~-8-NA-046Rev.0>Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETC=specificheatofwater(1Btu/ibmF).0pwThecodecheckstoensurethatthefollowing condition ismaintained throughout thecalculation: !WC(T-T.)cool-coolpwrc,in(2-44)2.1.3.6HotPiingModelInCOTTAP,theentirepipingheatloadisdeposited directlyintothesurrounding air.Thisisaconservative modelingapproachbecauseinrealityasubstantial amountoftheheatgivenoffbythepipingistransferred directlytothewallsofthecompartment byradiative means.Iffilmcoefficients accounting forradiative heattransferbetweencompartment airandwallsareusedincompartments containing largepipingheatloadssomeofthisconservatism mayberemoved.ThepipingheatloadterminEquations (2-1)and(2-5)iscalculated fromQ..=VIED(TT)ipipingfr'2-45) PPlkLForm2c54tlor83>CaLtr013401SF-"B-NA"046Rev.OltDept.Date19DesignedbyApprovedbyPROJECTSht.No.~4ofPENNSYLVANIA POWER&LIGHTCOMPANY-ERNo.CALCULATION SHEETwhereU=Overallheattransfercoefficient (Btu/hr-ft -F),20D~outsidediameterofpipeorinsulation (ft),L~pipelength(ft),T~Pipefluidtemperature (F),0T~Compartment temperature (F).0rCOTTAPcalculates Ubasedoninitialconditions andholdsthevalueconstantthroughout thetransient. Calculation ofUforinsulated anduninsulated pipesisconsidered separately. Inbothcases,however,thethermalresistance ofthefluidandthemetalisneglected. Forinsulate'd pipes,theoverallheattransfercoefficient iscalculated fromU~D.ln(D/D)+12kH+Hcr(2-46)whereD~Insulation outsidediameter(ft),iD~Pipeoutsidediameter(ft),P0k~Insulation thermalconductivity (Btu/hrftF),20H~Convective heattransfercoefficient (Btu/hrftF),cH~Radiation heattransfercoefficient (Btu/hrftF).20r pp2LForm2454n0/821Cht.rr973401SE"B-NA-046Rev.Qy'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~3ofPENNSYLVANIA POWER&LIGHTCOMPANYER,No.CALCULATION SHEETForuninsulated pipes,U~H+Hcr(2-47)Theconvective heattransfercoefficient, H,iscalculated fromthec~'ollowing correlation forahorizontal cylinder(ref.8,p.447):H=(k./D)cairo0.60+0.387Ra9/168/27[1+(0.559/Pr) )(2-48)wherek.=thermalconductivity ofair(Btu/hr-ft-F),0airD=pipeoutsidediameterforuninsulated pipes(ft),0~Insulation outsidediameterforinsulated pipes(ft),Ra~Rayleighnumber,andPr~Prandtlnumber.In(2>>48),theairthermalconductivity, Rayleighmember,andPrandtlnumberareallevaluated atthefilmtemperature whichistheaverageofthesurfacetemperature andthebulkairtemperature (ref.8,p.441).Hiscalculated from(ref.10,pp.77-78)rH~CG(T-T)/(T-T)I44rrsurfrs(2-49)wheree~pipesurfaceemissivity, PP41.Form2454110I831Ca1.rr973401SE-8-NA-046Rcv.QyDept.Date19DesignedbyApprovedbyPROJECTSht.No.~Sof.PENNSYLVANIA POWER&LIGHTCOMPANfERNo.CALCULATION SHEET-82o4amStephanBoltzmanconstant(0.1712xl0 Btu/hr-ft -R),0T~compartment ambienttemperature (R),r0T=pipesurfacetemperature (R)foruninsulated pipessurf0insulation surfacetemperature (R)forinsulated pipes.TheRayleighnumberisgivenby:R~(3600)g(T-T)D23asurfro(2-50)whereg~32.2ft/sec2g~volumetric thermalexpansion coefficient (1/R),02v~kinematic viscosity (ft/hr),a~thermaldiffusivity (ft/hr),20T~pipesurfacetemperature (F)foruninsulated pipe,surf0~insulation surfacetemperature (F)forinsulated pipe,0T~compartment ambienttemperature (F),rD~pipeoutsidediameter(ft)foruninsulated pipe,0~insulation outsidediameter(ft)forinsulated pipe.ThePrandtlnumberiscalculated fromPr~CI1/k,P(2-51) PPALForm2954(10/83)Cat,rt923401SE-B-NA-046Re..0>Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~9ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETwhereC=specificheat(Btu/ibmF),0PI2=viscosity (ibm/fthr),k=thermalconductivity (Btu/hrftF).02.1.3a7ComonentCool-Down ModelZnCOTTAP,thecoolingdownprocessofacomponent suchasapipefilledwithhotstagnantfluidorapieceofmetalequipment thatisnolongeroperating issimulated throughuseofalumped-parameter heattransfermodel.Theequationgoverning thecool-down processispCVdT=-UA[T(t)-T(t)],pdtr(2-52)withT(t)mT00(2-53)whereTisthecomponent temperature, p,C,andVarethedensity,Pspecificheatandvolumeofthecomponent. Uistheoverallheattransfercoefficient, Aistheheattransferarea,Tistheambientroomrtemperature, andtisthetimeatwhichthecomponent startstocool0down. PPdLForm2<<5<<(10)83)ca~.<<9yuoiSE-8-NA-046Rev.01'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~>ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETSincemostoftheroomsinthesecondary containment areratherlarge,itisreasonable toassumethatthecomponent temperature changesmuchfasterthantheroomtemperature> thatis,T(t)isfairlyconstantduringthercooldownprocessofthecomponent. Withthisassumption, T(t)canberreplacedwithT(t)inequation(2-52)toobtainroVPCdUA[T-T(t)I=-UA[T(t)-T (t)I.UAdtr0r0,(2-54)Rewriting (2-45)intermsoftheheatlossfromthecomponent, Q,gives+d=-Q(t),Ydt(2-55)Y~pCV/UA.PwhereYisthethermaltimeconstantofthecomponent andisgivenby(2-56)Thesolutionto(2-46)isQ(t)~Q(t)exp[-(t-t )/Y].00(2-57)Theapproximation givenby(2-48)isusedinCOTTAPwhenaheatloadistrippedoffwithanexponential decayattime,t.0Thetimeconstant, Y,foracomponent canbespecified ontheheatloadtripcards(seesection3.19),orinthecaseofhotpiping,thetimeconstantmayhecalculated hythecode.Potpipesfilledwithliquid,the~~ PPI,(.Form2454(l0/83IC4(.4973401SE-B-NA"046Rev.QPDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANY.ERNo.CALCULATION SHEETvolumeaveragedensityandthemassaveragespecificheatofthelicgxidandmetalareusedinthecalculation ofY.Forpipesinitially filledwithsteam,thevolumeaveragedensityisused,andtheaveragespecificheatiscalculated fromC=([U(T)-U(T)]/(T-T)+MC)/(M+M),pffofroforompmfm'2-58)whereU=totalinternalenergyofthefluid(Btu),fTtheinitialfluidtemperature "(F),foT=theinitialroomtemperature (F),0zoM=massofmetal(ibm),mMmassoffluid(ibm),fC=specificheatofthemetal(Btu/ibmF).0pm2.1.3.8NaturalCirculation ModelThenaturalcirculation modelinCOTTAPcanbeusedtodescribed mixingofairbetweentwocompartments whichareconnected byflowpathsatdifferent elevations. Therateofaircirculation betweencompartments iscalculated bybalancing thepressuredifferential, duetothedifference inairdensitybetweencompartments, againstlocalpressurelosseswithinthecirculation path; pphLForm2a5arr0'83tCat,rr9734mNA"046Rev.Qy'.Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER8LIGHTCOMPANYERNo.CALCULATION SHEETW=36002g(P-P)(E-E)ca2alu1(2-59)whereW=circulation flowrate(ibm/hr), cp,p=airdensities incompartments connected bycirculation ala2path(p>p),ibm/ft,3E,EuK,Ku~elevations oflowerandupperflowpathsrespectively (ft),ampressure-loss coefficients forlowerandupperflowpathsrespectively, A,A~flowareasoflowerandupperflowpathsrespectively 1'(ft)agmacceleration duetogravity(32.2ft/sec).Aleakagepath(seeSection2.1.3.2)isincludedinthecirculation pathmodelinordertomaintainthesamepressureinbothcompartments. Thus,theflowratecalculated fromeq.(2-59)isadjustedtoaccountforthisleakage. rrrr6r.Form2r54l10r86)Carrr97>0> SE-B-NA-046Rev.0y'ept.Date19DesignedbyApprovedbyPROJECTShr.No.~80f.PENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET2.1.3.9Time-DeendentComartmentModelAsmanyasfiftytime-dependent compartments canbemodeledwithCOTTAP.Znthismodel,transient environmental conditions aresuppliedasinputdata.Thedataissuppliedintabularformbyenteringupto500datapointsforeachtime-dependent room,witheachdatapointconsisting ofavalueoftime,roomtemperature, relativehumidity, andpressure. Amethodisalsoavailable inCOTTAPtodescribeperiodictsinusoidal) temperature variations withinaroom.Inusingthisoption,theamplitude andfrequency ofthetemperature oscillation andtheinitialroomtemperature aresuppliedinplaceofadatatable.2.1.3.10ThinSlabModelZtisnotnecessary tousethedetailedslabmodeldiscussed insection2.1.2todescribeheatflowthroughthinslabswithlittlethermalIcapacitance. Slabsofthistypehavenearlylineartemperature

profiles, Iandthus,theheatflowthroughtheslabcanbecalculated byusinganIoverallheattransfercoefficient.

Therateofheattransferthroughathinslabisobtainedfrom PP8,1.Form2a541101821 C91.rr913401SE-B-NA-046Rev.Pg:Dept.Date19DesignedbyApprovedbyPROJECTSht.No.9+ofPENNSYLVANIA POWER&LIGHTCOMPANY.ERNo.CALCULATION SHEETq=UA[T(t)-T(t)J,(2<<60)whereq=rateofheattransferfromtheroomonside1oftheslabtotheroomonside2(Btu/hr), U=overallheattransfercoefficient'for thethinslab(Btu/hrftF),20A=heattransferareaofonesideofthethinslab(ft).2Overallheattransfercoefficient dataisinputtoCOTTAPforeachofthe1thinslabsandthevaluesare.heldconstantthroughout thecalculation. Forthinslabsthatmodelfloorsorceilings, twovaluesofUmustbesupplied; oneforupwardheatflowandtheotherfordownwardheatflow.ForthinslabsthatareverticalwallsonlyonevalueofUcanbesupplied. Upto1200thinslabscanbemodeledwithCOTTAP.2.2Numerical SolutionMethodsThegoverning equations tobesolvedconsistof3N+Nordinarysrtdrdifferential equations andNpartialdifferential equations, whereNisssrIthenumberofstandardrooms,Nisthenumberoftime-dependent rooms,tdr ppht.aorn2a5attor83tCat.e973401S~-8-INA-046Rev.0gIDept.Date19DesignedbyeApprovedbyPROJECTSht.No.~~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETandNisthenumberofthickslabs.Anenergybalanceandtwomasssbalancesaresolvedforeachofthestandardroomstodetermine airtemperature, airmass,andvapormass.Inaddition, theone-dimensional heatconduction equationissolvedforeachofthethickslabs.Ordinarydifferential equations arealsogenerated forthetime-dependent rooms;theseequations areusedonlyfortimestepcontrolandwillbediscussed laterinthissection.Theinitialvalueordinarydifferential equationsolver,LSODES(Livermore SolverforOrdinaryDifferential Equations withGeneralSparseJacobianMatrices), developed byA.C.Hindmarsh andA.H.ShermanisusedwithinCOTTAPtosolvethedifferential equations whichdescribetheproblem.LSODESisavariable-time-step solverwithautomatic errorcontrol.Thissolveriscontained withintheDSS/2softwarepackagewhichwaspurchased fromLehighUniversity (refe2).BeforeLSODEScanbeappliedtothesolutionofthegoverning equations inCOTTAP,theNpartialdifferential equations describing heatflowthroughsIIthickslabsmustbereplacedwithasetofordinarydifferential IIIequations. Thisisaccomplished throughapplication oftheNumerical MethodofLines(NMOL)(ref.3).IntheNMOL,afinitedifference approximation isappliedonlytothespatialderivative inequation(2-6), PP8t.Form2454rror83>Car,rr97340ISE-B-AtA-046";.01Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETthusapproximating thepartialdifferential equationwithNcoupledordinarydifferential equations oftheformdT.=T.,i~1,2,...rN, ~3.sxxi(2-61)whereNisthenumberofequallyspacedgridpointswithintheslab,TS3.isthetemperature atgridpointi,andT.isthefinite-difference SXX1approximation tothesecond-order spatialderivative atgridpointi.Fourth-order finitedifference formulasareusedwithinCOTTAPtocalculate theT..Theseformulasarecontained withinsubroutine SXX3.DSS044whichwaswrittenbyW.E.Schiesser. Thissubroutine isalsocontained withintheDSS/2softwarepackage.Fortheinteriorgridpointsafourth-order centraldifference formulaisusedtocomputeTSXXiT.~1[-T.+16T.-30T.+16T.-T.]SXX3.-2Si-2126Si1S3.si+1si+2+O(~)i(2-62)wherei=3,4,...,N-2, andf5isthespacingbetweengridpoints.Asix-point sloppingdifference formulaisusedtoapproximate T.atiSXX1equalto2andN-lr PPSt,Form2954l10/831Cat.9973aotSE-B-NA-046Rev.o]Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETT~1[10T-15T-4T+14T-6T+T]sxx2-2s1s2s3s4s5s6and+0(~)a(2-63)T1[10T-15T-4T+14T-6T+T]sxxN-1-2126sNsN-1sN-2sN-3sN-4sN-5+O(6).(2-64)Thefinitedifference approximations attheendpointsareformulated intermsofthespatialderivative oftheslabtemperature attheboundaries ratherthanthetemperature, inordertoincorporate theconvective boundaryconditions (2-7)and(2-8).TheformulasareT=1[-415T+96T-36T+32Tsxxl-2~sl1266s2s3-s434-3T-506T]+0(h),2(2-65)andT~1[-415T+96T-36T+32TsxxN-2-sN1266sN-1sN-2-sN-33.-3T+506T]+O(b),2(2-66)whereTandTaregivenbysxlsxNT1h[T(t)T(t)]k(2-67) PP3,rForm2<<54(19r83)Cat.<<973401'SE-B-NA-046Rev.pi'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER8LIGHTCOMPANY.ERNo.CALCULATION SHEETandT=-h2tT(t)-T(t)].k(2-68)Thetotalnumberofordinarydifferential equations, N,tobesolvedis<<q<<nowgivenbyNN=3N+N+Neqsrtdr.~gj'~1(2<<69)whereN,isthenumberofgridpointsforslabj.Notethatatleastsixgridpointsmustbespecified foreachslab.Ztwaspreviously mentioned thatequations aregenerated foreachtime-dependent roomandareusedforpurposesofinfluencing theautomatic timestepcontrolofLSODES.Theequationgenerated foreachtimedependent roomisdT~g(t),(2-70)whereTisthetime-dependent roomtemperature andg(t)isthetimetdrderivative oftheroomtemperature attimet.Forroomswheretemperature versustimetablesaresupplied, g(t)isestimated byusingathree-point LaGrangeinterpolation polynomial. Forroomswithsinusoidal temperature pp&LForm2a&a(10r&31Cat,e913401SE-B-NA-046novo1Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETvariations, calculation ofg(t)isstraightforward. Theseequations areinputtoLSODESsothatthetimestepsizecanbereducedifveryrapidtemperature variations occurwithinatime-dependent room.Asufficient numberofcallswillthenbemadetothetemperature-versus-time tablesandtheroomtemperatures willbeaccurately represented. COTTAPcanaccessfivedifferent solutionoptionsofLSODES.Thedesiredoptionisselectedthroughspecification ofthesolutionmethodflag,MF(seesection3.2).TheallowedvaluesofMFare10,13,20,23,and222.Thefinite-difference formulasusedinLSODESarelinearmulti-step methodsoftheformk2Y=Ea.y.-hEB.F33~033(2-71)wherehisthestepsize,andtheconstants a.,and8.aregiveninj'ref.1,pp.113and217.Thesystemofdifferential equations beingsolvedareoftheformdy=F(y,t),dt(2-72)withy(0)-y~o(2-73) pp6LForm9<<5<<n0'83)Cat,<<973<<0iSE-8-NA-046Rev,QDept.Date19DesignedbyApprovedbyPROJECTSht.No.$0ofPENNSYLVANIA POWER&LIGHTCOMPANY.ERNo.CALCULATION SHEETEquation(2-71)describes twobasicsolutiontechniques, Adam'smethodandGearsmethod(ref.5and6),depending uponthevaluesofkandk.If12k~1,eq.(2-62)corresponds toAdam'smethod,andifk=0itreducesto12Gear'smethod.Inbothcases,theconstant8isnon-zero. 0Since8go,thefinite-difference equations compriseanimplicitalgebraic 0systemforthesolution.y .InLSODES,thedifference equations arensolvedbyeitherfunctional iteration orbyavariation ofNewton'smethod.Ifthefunctional iteration procedure ischosen,anexplicitmethodisusedtoestimateavalueofy;thepredicted valueisthenn'ubstituted intotheright-hand-side ofeq.(2-71)andanewvalueofynisobtained. Successive valuesofyarecalculated fromeq.(2-71),byniteration, untilconvergence isattained. MP~10corresponds toAdam'methodwithfunctional iteration, andMP=20corresponds toGear'smethodwithfunctional iteration. Unfortunately, thefunctional iteration schemegenerally requiressmalltimestepsinordertoconverge. Themethodcan,however,beusefulforrapidtransients ofshortduration. Thetimesteplimitations associated withthefunctional iteration procedure canbeovercome, atleasttosomedegree,byusingNewton's PPALForm2954ttarot)Cat.9913lolSE-8-NA-046Rev.P~Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~SofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETmethodtosolvetheimplicitdifference equations. Foreaseofdiscussion, solutionofeq.(2-71)withNewton'smethodwillbedescribed forGear'sequations (k=0)only;theprocedure issimilarwhenappliedto2theAdam'smethodequations. Theconventional formofNewton'siteration schemeappliedtoGear'sdifference equations isdescribed by7[s+1]~[s]'[s]-1~[s]37k-Za.y"~"hBF(ty))1[s]in-ion'ni=1(2-74)whereIistheidentitymatrix,[BF/By]istheJacobianmatrix,andthesuperscript sistheiteration step.In(2-74)theJacobianisevaluated ateveryiteration stepalongwiththeinversion ofthematrix[I-hBBF/By].Forlargesystemsofequations thisprocedure isverytime0consuming. InLSODES,theJacobianisevaluated andthesubsequent inversion of[I-h8BF/By]iscarriedoutonlywhenconvergence ofthefinitedifference 0Iequations becomesslow.Thistechnique iscalledchorditeration (ref.5) PP8,LEorm24'>0>83>Ca<e9uco> SE-B-NA-046Re..0g'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETandismuchmoreefficient thantheconventional Newton'siteration scheme.Also,forverylargesystemsofequations thatresultintheNMOLsolutionofpartialdifferential equations, mostoftheelementsoftheJacobianarezero.IfMF222,LSODESdetermines thesparsitystructure oftheJacobianandusesspecialmatrixinversion techniques designedforsparsesystems.IfMF=13or23adiagonalapproximation totheJacobianisused,thatis,onlythediagonalelementsoftheJacobianareevaluated, allotherentriesaretakenaszero.(MF=13corresponds toAdam'smethodandMF=23corresponds toGear'smethod). Pp<<LFOrm2<<A<1583)Gal,<<91340lSF--B-NA-046Rev.QgDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER5LIGHTCOMPANYERNo.CALCULATION SHEET3.DESCRIPTION OFCODEINPUTSThissectiongivesinstructions forpreparing aninputdatasetforCOTTAP.Thedatacardsthataredescribed mustbesuppliedintheorderthattheyareshown.Commentlinesmaybeinsertedinthedatasetbyputtinganasteriskinthefirstcolumnoftheline.However,commentlinesshouldnotbeinsertedwithinblocksofdata:theyshouldonlybeusedbetweenthevarioustypesofinputdatacards.Forexample,commentcardscanbesuppliedafterthelastroomdatacardandbeforethefirstventillation flowdatacardbutnotwithintheroomdatacardsandnotwithintheventillation flowdatacards.Thefirstlineintheinputdatasetisthetitlecard.Thiscardisprintedatthebeginning oftheCOTTAPoutput.Alistingofalltheinputdatacardsfollowing thetitlecardisgivenbelow.Thewordsthatmustappearoneachcardarelistedinorder:Wlisword1,W2isword2,etc.ThelettersIandRindicatewhethertheitemistobeenteredinintegerorrealformat. ppaLForm2a5anor83)Cara9rwo> ~E-8-NA-046Rev0)'ept.DateDesignedbyApprovedby19PROJECTSht.No.~GofPENNSYLVANIA POWER&LIGHTCOMPANY-ERNo.CALCULATION SHEET3.1ProblemDescritionData(Card1of3)Wl-INROOM=Numberofrooms(compartments) contained inthemodel(maximumvalueis300).NROOMdoesnotincludetime-dependent rooms.W2-INSLB1=Numberofthickslabs(maximumvalueis1200).Theseareslabsforwhichtheone-dimensional, time-dependent heatconduction equationissolved.W3-INSLB2=Numberofthinslabs(maximumvalueis1200).Theseareslabswhichhavenegligible thermalcapacitance. W4-INFLOW=Numberofventilation flowpaths(maximumvalueis500).W5-INHEAT=Numberofheatloads(maximumvalueis750).W6-INTDR~Numberoftime-dependent rooms(maxvalueis50).W7-INTRIP~Numberofheatloadtrips(maximumvalueis500). ppsLForm2454nsallCa4N97340lSE-B-NA-046P"0~Dept.Date19DesignedbyApprovedbyPENNSYLVANIA POWER8LIGHTCOMPANYERNo.CALCULATION SHEETCPROJECTSht.No.~ofW8-INPIPE~Numberofhotpipes(maximumvalueis750).W9-INBRK~Numberofpipebreaks(maximumis20).W10-INLEAK=Numberofleakagepaths(maximumis500).Wll-INCIRC~Numberofcirculation paths(maximumvalueis500).W12-INEC=Numberofeditcontrolcards.(Atleastonecardmustbesupplied, andamaximumof10cardsmaybesupplied). 3.2ProblemDescritionData(Card2of3)Wl-INFTRIP~Numberofflowtrips(maximumvalueis300).Flowtripscanactonventilation flows,leakageflows,andcirculation flows.W2-IMASSTR~Mass-tracking flag.0~>Masstrackingisoff.Inthiscase,compartment massbalancesarenotsolvedrthetotalmassineachcompartment isheldconstant. Incaseswherethisoptioncanbeused,itresultsinlargesavingsin ppLLForm245'01s3) Cat,<<973401SE-B-NA-046Rev.0Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETcomputertime.Inordertousethisoption,thefollowing inputvariables mustbespecified as:NBRK=NLEAK=NCIRC=NFTRIP=O =1=>Masstrackingison;massbalancesaresolvedforeachcompartment. W3-IMFNumerical solutionflag.MF=222shouldonlybeusedifMASSTR~O. IfMASSTR~1, therecommended methodsareMF=13andMF23.MF=10andMF20usefunctional iteration methodstosolvethefinitedifference equations andgenerally requiresmallertimestepsandlargercomputation timesthanMF~13andMF=23.~10~>ImplicitAdam'smethod.Difference equations solvedbyfunctional iteration (predictor-corrector scheme).~13~>ImplicitAdam'smethod.Difference equations solvedbyNewton'smethodwithchorditeration. AnII PP4LForm245'or83l Car.<<973401SE-B-NA-046Rev.Q$'ept.PENNSYLVANIA POWER8rLIGHTCOMPANYCALCULATION SHEETDesignedbyPROJECTApprovedbyERNo.Sht.No.~Sofinternally generated diagonalapproximation totheJacobianmatrixisused.=20~>Zmplicitmethodbasedonbackwarddifferentiation formulas(Gear'smethod).Difference equations aresolvedbyfunctional iteration; Jacobianmatrixisnotused.=23=>Zmplicitmethodbasedonbackwarddifferentiation formulas. Difference equations aresolvedbyNewton'smethodwithchorditeration. Aninternally-generated diagonalapproximation totheJacobianmatrixisused.~222~>Zmplicitmethodbasedonbackwarddifferentiation formulas. Difference equations aresolvedbyNewton'smethodwithchorditeration. Aninternally-generated sparseJacobianmatrixisused.Thesparsity-structure oftheJacobianisdetermined bythecode. ppdLForm2<<5<<n0I83) Cw,<<973401'8E-B-NA-046Rev.Q]Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~~of.PENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETW4-RCP1Parameter usedincalculation ofleakageflows.Xncreasing CP1increases theleakageflowrateforagivenpressuredifference. Therecommended valueofCPl4islx10.LargervaluesofCPlcanbeusedifcompartment pressures increaseaboveatmospheric pressureduringrapidtemperature transients. W5-RCP2~Parameter usedincalculating maximumallowedvaluesforleakageflows.Therecommended valueofCP2is150.Increasing CP2increases themaximumleakageflowrates.W6-RCR1Parameter usedinrainoutcalculation. Increasing thisparameter increases therainoutratewhenrainoutisinitiated. Therecommended valueofCR1is10.W7-IXNPUTF~Flagcontrolling theprintingofinputdata.~0~>Summaryofinputdatawillnotbeprinted.=1<<<<>Summaryofinputdatawillbeprinted. pphLForm2454n0/83)Cat.4973401SE-8-NA-046Rev.Oy'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~EofPENNSYLVANIA POWER&LIGHTCOMPANY-ERNo.CALCULATION SHEETW8-IIFPRT=Ventilation-flow editflag.=0=>Ventilation-flow editswillnotbeprinted.=1=>Ventilation-flow editswillbeprinted.W9-RRTOL=Errorcontrolparameter. RTOListhemaximumrelativeerrorinthesolution. Therecommended valueofRTOLislxlo3.3ProblemDescritionData(Card3of3)W1-INSH=Numberoftimestepsbetweenre-evaluation ofslabheattransfercoefficients. Ifapipebreakisbeingmodelled, thisparameter mustbesettozero.Iftherearenopipebreaksincludedinthemodel,NSHmayhaveavalueaslargeas10withoutintroducing significant errorsintothesolution. Forproblemsinvolving alargenumberofslabs(butnopipebreaks),avalueof10isrecommended. PPAt.Form2454t1$83)Cat,197340ISE,-B-NA"046Rev.0y'ept.Date19DesignedbyApprovedbyPROJECTSht.No.4OofPENNSYLVANIA POWER8LIGHTCOMPANYERNo.CALCULATION SHEETW2-RTFC=massfractionthreshold value.Ifthemassfractionofairorwatervapordropsbelowthevaluespecified forTFC,thatcomponent isessentially neglected duringthe-5calculation. Arecommended valueforTFCis10-5Specifying TFCmuchsmallerthan10shouldbeavoidedbecauseitcansometimes leadtonegativemassofthesmallcomponent. 3.4ProblemRun-TimeandTri-Tolerance DataWl-RT=Problemstarttime(hr).W2-RTEND=Problemendtime(hr).W3<<RTRPTOLTriptolerance (hr).AlltripsareexecutedatthetripsetpointplusorminusTRPTOL.W4-RTRPEND~ThemaximumtimestepsizeislimitedtoTRPTOLuntiltheproblemtimeexceedsTRPEND(hr).NotethatalargevalueofTRPENDandasmallvalueofTRPTOLwillleadtoexcessively largecomputation times. PPCLForm2454n0'83)Col.4973401SE-B-NA-046I'"..0yDept.Date19DesignedbyApprovedbyPROJECTSht.No.~4ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET3.5ErrorTolerance forComartmentVentilation-Flow MassBalanceOmitthiscardifNFLOW0.Wl-RDELFLOmThemaximumallowable compartment ventilation flowimbalance (cfm),i.e.,thefollowing condition mustbesatisfied foreach"compartments NetVentilation Flow(cfm)intoCompartment <DELFLO.Therecommended valueofDELFLOislx10.Itis-5particularly important toensurethattherearenoventilation flowimbalances whenthemass-tracking optionisnotused(MASSTRm0) becauseinthiscasethecodeassumesthatthemassinventory ineachcompartment remainsconstantthroughout thetransient. 3.6EditControlDataNECeditcontroldatacardsmustbesupplied2 oneachcardthefollowing threeitemsmustbespecified. PP0(.Form245'0t03) Cht.N972l0(SSF--8-NA-046Rev.O>'ept.Date19DesignedbyApprovedbyPROJECTSht.No..CWofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETW1-IIDEC~IDnumberoftheeditcontrolparameter set.TheIDnumbersmuststartwith1andtheymustbesequential, i.e.,IDEC1,2,3,...,NEC. W2-RTLAST~Time(hr)uptowhichtheeditparameters apply.WhentimeexceedsTLAST,thenextsetofeditcontrolparameters willcontrolprintoutofthecalculation results.W3-RTPRNTPrintintervalforcalculation results(hr),i.e.,resultswillbeprintedeveryTPRNThours.3.7EditDimension DataWl-INRED~Totalnumberofroomsforwhichthecalculation resultswillbeprinted.Thisincludesboth,standardroomsandtime-dependent rooms.W2-INS1ED~Numberofthickslabswhichwillbeedited.Associated heattransfercoefficients areeditedalongwiththeslabtemperature profiles. 'PPE,LFOcm2454IIO/83)Cat,s97340ISE-B-NA-046Rev.01IDept.Date19DesignedbyApprovedbyPROJECTSht.No.~~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETW3-INS2ED=Numbersofthinslabswhichwillbeedited.3.8Selection ofRoomEditsOnthiscard(s)entertheIDnumbersoftheroomstobeedited.Includeboth,standardroomsandtime-dependent rooms(notethattime-dependent roomshavenegativeIDnumbers). EntertheIDnumbersacrossthelinewithatleastonespacebetweeneachitem.Thedatacanbeenteredonasmanylinesasnecessary. Roomeditswillbeprintedintheorderthattheyarespecified here.Foreachroomspecified, calculation resultssuchastemperature,

pressure, relativehumidity, andmassandenergyinventories willbeprintedalongwiththevariousheatloadscontained withintheroom.OmitthiscardifNRED~O.3.9Selection ofThickSlabEditsEntertheIDnumbersofthethickslabstobeedited.EachIDnumbershouldbeseparated byatleastonespace.IftheIDnumberscannotfitononeline,additional linesmaybeusedasnecessary.

Thetemperature profilethatisprintedforeachthickslabconsistsofseventemperatures atequallyspacedpointsthroughout theslab.Ingeneral,thesetemperatures aredetermined byquadratic interpolation sinceinmostcases ppLLForm2454(10/83)Cal.N973401SE-~-NA-046Rev.Q>'ept.Datet9DesignedbyApprovedbyPROJECTSht.No.~~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETthelocations donotcorrespond togridpoints.OmitthiscardifNS1EDmO.3.10Selection ofThinSlabEditsSpecifytheIDnumbersofthethinslabstobeedited.Entertheitemsacrosseachlineanduseasmanylinesasnecessary. Thinslabeditswillbeprintedintheorderthattheyarelistedhere.Foreachthinslabspecified, theheatflowthroughtheslabandthedirection ofheatflowwillbeprinted.OmitthiscardifNS2ED=O.3.11Reference TemeratureandPressureforVentilation FlowsOmitthiscardifNFLOWmO.Wl-RTREF=Temperature (F)usedbycodetocalculate areference 0airdensity.Thereference densityisusedbythecodetoconvertventilation flowsfromCFMtoibm/hr.W2-RPREPPressure(psia)usedtocalculate thereference density ppht.Form2a54n0i83>C4I.N913l01SE-B-NA-046R..V.O1'ept.DateDesignedbyApprovedby19PROJECTSht.No.4~ofPENNSYLVANIA POWER8LIGHTCOMPANYERNo.CALCULATION SHEET3.12StandardRoomDataWl-IIDROOM=RoomIDnumber.TheIDnumbersmuststartwith1andmustbesequential. W2-RVOL=Roomvolume(ft).Inordertomaintainconstant3properties inacompartment throughout thecalculation, 15enteralargevalueforVOL(e.g.1xlO).W3>>RPRES=Initialroompressure(psia).W4-RTR=Initialroomtemperature (F).0W5-RRHUM=Initialrelativehumidity(decimalfraction) .ForthecaseofMASSTR~O, thisparameter isonlyusedincalculating heattransfercoefficients forthickslabs.W6-RRMHT=Roomheight(ft).Thisparameter isusedinthecalculation ofcondensation coefficients forthickslabs. pphLForm2454nOI83lCat.%13401~-B-NA-046Rev.QpDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER8LIGHTCOMPANYERNo.CALCULATION SHEET3.13Ventilation FlowDataOmitthiscard(s)ifNFLOW0.Wl-IZDFLOW=ZDnumberoftheventilation flowpath.Valuesmuststartwith1andbesequential. W2>>IIFROMIDnumberofroomthatsuppliesventilation flow.Thiscanbeastandardroomoratime-dependent. room.W3-ZZTO=IDnumberofroomthatreceivesflow.Thiscanbeastandardroomoratime-dependent room.W4>>RVFLOW=Ventilation flowrate(ft/min).Thisvolumetric flowis3converted toamassflowrateusingTREFandPREFsuppliedabove.Themassflowrateisheldconstantthroughout thecalculation unlesstheflowisacteduponbyatrip. PP4LForm2ISln0r83)Cat.99%401Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~7ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET3.14LeakaeFlowDataOmitthiscard(s)ifNLEAK=O.Wl-IIDLEAK=IDnumberoftheleakagepath.Valuesmuststartwith1andmustbesequential. W2-RARLEAK=Areaofleakagepath(ft).W3-RAKLEAK=pressurelosscoefficient forleakagepathbasedonflowareaARLEAK.Specifya-1forAKLEAKifthesimple,proportional controlmodelisdesired,seeSection2.1.3.2.W4-ILRM1IDnumberofroomtowhichleakagepathisconnected. Thiscanbeastandardroomoratime-dependent room.W5-ILRM2-IDnumberoftheotherroomtowhichtheleakagepathisconnected. Thiscanbeastandardroomoratime-dependent room.eW6-ILDIRNAlloweddirection forleakageflow. PPtLt.Form2c5cn0/83)Cat.tr073401SE"B"NA-046Rev.O>:Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~4ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET1=>leakagefromcompartment LRM1tocompartment, LRM2only.2=>leakagecanbeinbothdirections: fromLRM1toLRM2andfromLRM2toLRM13.15Circulation FlowDataOmitthiscard(s)ifNCZRC~O.Wl-IZDCIRCIDnumberofcirculation flowpath.Valuesmuststartwith1andmustbesequential. W2-IKRM1~IDnumberofroomtowhichcirculation pathisconnected. Thiscanbeastandardroomoratime-dependent room.W3-IKRM2~ZDnumberofotherroomtowhichthecirculation pathisconnected. Thiscanbeastandardroom"oratime-dependent room.W4-RELVL~Elevation ofthelowerflowpath(ft).aWS-RELVU~Elevation oftheupperflowpath(ft). pp6LForm296anar831Cal.9976401SE-B-NA-046Rev.0Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~4ofPENNSYLVANIA POWER&LIGHTCOMPANY'R No.CALCULATION SHEETW6-RARL~Flowareaofthelowerflowpath(ft).2W7-RARU=Flowareaoftheupperflowpath(ft).2WB-RAKL=Losscoefficient forlowerflowpathreferenced toARL.W9>>RAKU=Losscoefficient fortheupperflowpathreferenced toARU.3.16Air-FlowTriDataOmitthiscard(s)ifNFTRIP=O. Wl-IIDFTRPTripIDnumber.The1Dnumbersmuststartwith1andmustbesec(uential. W2-IKFTYP1Typeofflowpath.~1~>Ventilation 2>Leakage3>-Circulation PP<<,LFarm2<<5<<{10/831 Cat.<<913<<01ItSE-B-NA-046Rev.QPDept.Date19DesignedbyApprovedbyPROJECTSht.No.~OofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETW3-IKFTYP2=Typeoftrip.1>tripoff~2=>triponNotethatallairflowsareinitially onunlesstrippedoff.W4-RFTSET~Timeoftripactuation (hr).W5-IIDFPIDnumberofflowpathuponwhichthetripisacting.3.17HeatLoadDataOmitthiscard(s)ifNHEAT=O.Wl-IIDHEAT~HeatloadIDnumber.IDnumbersmuststartwith1andmustbesecpxential. W2-INUMR~IDnumberofroomcontaining heatload.W3-IITYPTypeofheatload.~1~>Lighting~2=>Electrical panela PPdLFontt2954n$83)Cat.e91340lDept.Date19DesignedbyApprovedbyPROJECTSht.No.~lofPENNSYLVANIA POWER8LIGHTCOMPANYERNo.CALCULATION SHEET=3=>Motor=4=>RoomCooler=5=>Hotpiping=8=>Miscellaneous I~~tW4-RQDOT=Magnitude ofheatload(Btu/hr). Ifthisisapipingheatload(ITYP=5)enter0.0forthisparameter; thevalueofQDOTwillbecalculated bythecode.IfITYP=4,QDOTshouldbenegative. W5-RTC=Temperature (F)ofcoolingwaterenteringcoolerifITYP-4.IfITYPisnotequalto4enteravalueof-1".W6-RWC-Coolingwaterflowrate(ibm/hr)ifITYP=4.IfITYPisnotequalto4enteravalueof0.3.18HotPiinDataOmitthiscard(s)ifNPIPE=O.Wl-IIDPIPE-IDnumberofpipe.TheIDnumbersmuststartwith1andmustbesequential' PPdLForm24MttiattCat,tt973lOINA-046RevP):Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETW2-IZPREFIDnumberofassociated heatload.W3-RPOD~Outsidediameterofpipe(in).W4-RPZD~Insidediameterofpipe(in).W5-RAZNOD~Outsidediameterofpipeinsulation (in).Ifthepipeisnotinsulated setAZNODequaltoPOD.W6-RPLENLengthofpipe(ft).W7-RPEMEmissivity ofpipesurface.IW8-RAINK~Thermalconductivity ofpipeinsulation (Btu/hrftF).Zfthepipeisnotinsulated setAZNK~O.O. W9-RPTEMP~Temperature (F)offluidcontained inpipe.0W10-IZPHASE~1ifpipeisfilledwithsteam.2ifpipeisfilledwithliquid. pp&LForm24MnSN>Cht.4973401SE-B-NA-046Rev.0]lDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET3.19HeatLoadTriDataOmitthiscard(s)ifNTRZP0.Wl-IZDTRIP=TripZDnumber.ZDTRIPmuststartwith1andallvaluesmustbesequential. W2<<ZZHREF=ZDnumberofheatloadthatistobetripped.W3-IITMD~Typeoftrip.~1~>Heatloadisinitially onandwillbetrippedoff.m2~>Heatloadisinitially offandwillbetrippedon.W3-RTSET~Time(hr)atwhichtripisactivated. W4-RTCON~Timeconstantforheatloadtrip.Thefollowing optionsareavailable ifITMD~1:~ZfTCON~O.O, theentireheatloadistrippedoffat ppKLForm2c54nOI831Cat.4973401aSE-S-NA-046.,Rev.QgDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET~Zftheheatloadisapipingheatload(ITYP~5), TCONcanbesetto-1andatimeconstantwillbecalculated bythecode.Thistimeconstantwillthenbeusedtoexponentially decaytheheatloadwhenitistrippedoff.~AtimeconstantcanbesuppliedbysettingTCONequaltothedesiredtimeconstant(hr).'hen theheatloadistrippedoff,itwillexponentially decaywiththeuser-supplied timeconstant. Thisoptioncanbeusedwithanyheatloadsitisnotrestricted tojustpipingheatloads.0.0ifITMD~2.3.20PieBreakDataOmitthiscard(s)ifNBRK~O.Wl-I,ZDBK~IDnumberofbreak.ZDBKmuststartwith1andallvaluesmustbesequential. PPSLForm2454(1SN)C4l.N973l01SE-B-NA-046Rev.0$Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~SofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETW2-IZBRM=IDnumberofroominwhichpipebreakoccurs.W3-RBFLPR=Fluidpressurewithinpipe(psia).W4-IZBFLGFluidStateflag.=1~>fluidinpipeissteam=2=>fluidinpipeislicpxidwaterW5-RBDOT=Totalmassflowexitingthebreak(1bm/hr).W6-RTRZPONTimeatwhichbreakoccurs(hr).W7-RTRZPOF=Timeatwhichbreakflowisturnedoff(hr).W8-RRAMP~Timeperiod(hr)overwhichthebreakdevelops. Thetotalmassexitingthebreakincreases linearlyfromavalueofzeroattMRZPONtoavalueofBDOTatt-ZRIPON+RAMP. 3.21ThickSlabData(card1of3)Omitthiscard(s)ifNSLB10. PPAt.Fotm2454(tDt83)Cat.tt97340ISE-8-NA-046Rev.0>tDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETW1-IIDSLBl=SlabZDnumber.IDSLB1muststartwith1andallvaluesmustbesequential. W2-IZRM1=ZDnumberofroomonside1ofslab.Astandardroomoratime-dependent roomcanbespecified. Ifside1oftheslabisincontactwithgroundenteravalueofzero.W3-IZRM2IDnumberofroomonside2ofslab.Astandardroomora"time-dependent zoomcanbespecified. Zfside2oftheslabisincontactwithgroundenteravalueofzero.W4-IZTYPE~Typeofslab.=1ifslabisaverticalwall=2ifslabisafloorwithrespecttoroomZRM1.=3ifslabisaceilingwithrespecttoroomZRM1.W5-INGRIDF=Numberofgridpointsperfootusedinthefinite-difference solutionoftheunsteadyheatconduction equation. Aminimumof6gridpointsperslabisusedbythecode,andthemaximumnumberofgridpointsusedperslabis100.Zfthespecified valueoftNGRZDFcausesthetotalnumberofgridpointsfortheI ppdLForm2454n$83)Ca1,t973401Dept.Date19DesignedbyApprovedbyPROJECTSht.No.17ofIPENNSYLVANIA POWER8LIGHTCOMPANYERNo.CALCULATION SHEETslabtobeoutsideoftheselimits,theappropriate limitwillbeusedbythecode.W6-IIHFLAG=Heattransfercoefficient calculation flag.Heattransfercoefficient datamustbesuppliedforanyslabsidethatisincontactwithatimedependent room.0ifnoheattransfercoefficient datawillbesuppliedfortheslab.Thecodewillcalculate natural-convection andradiation heattransfercoefficients forbothsidesoftheslab.-1ifheattransfercoefficient datawillbesuppliedforside1oftheslab.Thecodewillcalculate natural-convection andradiation heattransfercoefficient forside2.2ifheattransfercoefficient datawillbesuppliedforside2oftheslab.Thecodewillcalculate natural-convection andradiation heattransfercoefficients forside1.-12ifheattransfercoefficient datawillbesuppliedforboth,side1andside2oftheslab. pp&LForm2454no/MrC4t.I@13401SE-B-NA-046Rev.a>'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANY'RNo.CALCULATION SHEETAllowthecodetocalculate filmcoefficients forslabsurfacesincontactwithground.W7-RCHARLmcharacteristic lengthoftheslab(ft).=heightoftheslabifITYPEml.=theheattransferareadividedbytheperimeter ifITYPEm2or3.IfthevalueofCHARLissetto0.0,thecodewillcalculate avalueforthecharacteristic length.Inthisecase,thecodeassumesthattheslabisintheshapeofasguare.3.22ThickSlabData(Card2of3)Omitthiscard(s)ifNSLB1=0.Wl-IIDSLB1=SlabIDnumber.W2-RALS~Thickness ofslab(ft). pp<<t.Form2<<5<<n0/83) C<<l,<<97340'tISE-B-NA-046Rev.ogDept.Date19DesignedbyApprovedbyPROJECTSht.No.~oiPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETW3-RAREAS1=Slabheat,transferarea(ft).Thisisthesurfacearea2ofonesideoftheslab.W4-RAKS=Thermalconductivity ofslab(Btu/hrftF).0W5-RROS=Densityofslab(ibm/ft).3W6-R,CPS=Slabspecificheat(Btu/ibm-F).0W7-REMZSS=Slabemissivity 3.23ThickSlabData(Card3of3)ZfZHFLAG=Oforaslab,thendonotsupplyacardinthissectionforthatparticular slab.IfIHFLAG1or2,onlysupplytherequireddata;leavetheotherentriesblank.ZfZHFLAG=12, supplyalltheheattransfercoefficient dataforthatslab.Omitthiscard(s)ifNSLB10.Wl-IZDSLB1=SlabIDnumber.W2-RHTC1(1)Heattransfercoefficient forside1ofslabifITYPE=1(Btu/hr-ft -F).20 pphLForm2<<5an0/80)Cat.<<973<<01SE-B-NA-046Rev,Pg'ept. Date19DesignedbyApprovedbyPROJECTSht.No.~OofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET=Heattransfercoefficient forupwardflowofheatbetweenslabandroomIRM1ifITYPE~2or3(Btu/hr-ft -F).20W3-RHTC2(1)~Heattransfercoefficient forside2ofslabifITYPE=1(Btu/hr-ft -F).20=Heattransfercoefficient forupwardflowofheatbetweenslabandroomIRH2.ifITYPE~2or3(Btu/hr-ft -F).2oW4-RHTCl(2)~Heattransfercoefficient fordownwardflowofheatbetweenslabandroomIRM1ifITYPE~2or3(Btu/hr-ft -F).DonotsupplyavalueifITYPE=1.20W5-RHTC2(2)'Heattransfercoefficient fordownwardflowofheatbetweenslabandroomIRH2ifITYPE~2or3(Btu/hr-ft -F).DonotsupplyavalueifITYPE=1.203.24ThinSlabData(Card1of2)Omitthiscard(s)ifNSLB2~0. ppaLFotttt2454nDt83tCat.tt97340tSE-B-N-A-046Rev.pg'ept.Datet9DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETWl-IZDSLB2=SlabZDnumber.ZDSLB2muststartwith1andallvaluesmustbesequential. W2-IJRM1=ZDnumberofroomonside1ofslab.Astandardroomoratime-dependent roomcanbespecified. Athinslabcannotbeincontactwithg'round,i.e.,donotspecifyJRM1orJRM2equaltozero.W3-IJRM2=IDnumberofroomonside2ofslab.Astandardroomoratime-dependent roomcanb'especified. W4-IJTYPE=1ifslabisaverticalwall.=2ifslabisafloorwithrespecttoroomJRM1.=3ifslabisaceilingwithrespectto"roomJRM1.W5-RAREAS2~Slabheattransferarea(ft).Thisisthesurfacearea2ofonesideoftheslab.3.25ThinSlabData(Card2of2)Omitthiscard(s)ifNSLB2~0. pprLLForm2<<5<<norN) C<<r.<<973401\SE-B-NA-046Rev.ODept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETWl-IIDSLB2SlabIDnumber.W2-RUHT(1)Overallheattransfercoefficient forslabisJTYPE=1(Btu/hr>>ft -F).20~Overallheattransfercoefficient forupwardflowofheat'IthroughslabifJTYPEm2or3(Btu/hr-ft -F).20W3-RUHT(2)=Overallheattransfercoefficient fordownwardflowofheatthroughslabifJTYPEm2or3(Btu/hr-ft -F).Do20notsupplyavalueofJTYPEml.3,.26Time-DeendentRoomData(Card1of2)Omitthiscard(s)ifNTDR~O.Wl-IIDTDRIDnumberoftime-dependent room.IDTDRmuststartwith-1andproceedsecgxentially (i.e.,IDTDR~1<<2<<3<<~~~<<NTDR)W2-IIRMFLG~1iftemperature,

pressure, andrelativehumiditydatawillbesupplied.

pplLForm2454n0rajjCat.l97340ISE,-B-NA-046Rev.QyDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET=2ifasinusoidal temperature variation willbeusedforthisroom.Zfthisoptionischosentherecannotbeanyflowtoorfromthisroom.W3-INPTS~NumberofdatapointsthatwillbesuppliedifZRMFLG=1. Eachdatapointconsistsofavalueoftime,temperature,

pressure, andrelativehumidity.

NPTSmustbelessthanorequalto500.Sinceoutputisdetermined byinterpolation, time-dependent-room datamustbesuppliedatleastonetimestepbeyondtheproblemendtime.~0ifZRMFLG~2. W4-RTDRTO~Initialroomtemperature (F)ifIRMFLG=2. 0~0.0ifZRMFLG~1W5-RAMPLTDAmplitude (F)oftemperature oscillation ifIRMFLG=2. 0~0.0ifZRMFLG=1. W6-RFREQ~Frequency (rad/hr)oftemperature oscillation ifZRMFLG2.~0.0ifZRMFLGm1. PPKLForm2<<5<<n0IMI C<<t,<<91340lSE-B-NA-046Rev.0y'ept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET3.27Time-DeendentRoomData(Card2of2)Supplythefollowing dataforeachtime-dependent roomthathasavalueofZRMFLG=l. Omitthiscard(s)ifNTDR=O.Wl-ZZDTDRZDnumberoftime-dependent roomW2-RTTZME~Time(hr).W3-RTTEMP~Temperature (F).0W4-RTRHUM~Relativehumidity(decimalfraction) .WS>>RTPRES~Pressure(psia).Repeatwords2through5untilNPTSdatapointsaresupplied. Thenstartanewcardforthenexttime-dependent room. t~pp&LForm2i54nOIN)Cat.l973401SE-B-N,A=046Rev.O.ODept.Date19DesignedbyApprovedbyPROJECTSht.No.S~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET4.SAMPLEPROBLEMS4.1ComarisonofCOTTAPResultswithAnalticalSolutionforConduction throuhaThickSlab(SamleProblem1)Adescription ofthisproblemisshowninFigure4.1.Astandardroomisonside1oftheslabandatime-dependent roomisincontactwithside2.Thetemperature inthetime-dependent roomoscillates withamplitude A0andfrequency Q.Therearenoheatloadsorcoolerswithinthestandardroomyheatisonlytransferred toorfromtheroomby'onduction throughtheslab.Theequations describing thisproblemareaT/at=a8T/ax,22ss(4-1)3Ts3xx=0-h[T(t)-T(Opt)]g-1rlks(4-2)-h[T(L,t)-T(0)-Asin(W)],-2skr20(4-3)T(x0)sax+b,(4-4)P1C1VldTAh[T(0gt)T(t)]dt(4-5) PPSLForm24'10r83) Cat.rr973c0>SE-B-NA-046Rev0I!Dept.Date19DesignedbyApprovedbyPENNSYLVANIA POWER&LIGHTCOMPANYCALCULATION SHEETPROJECTERNo.Sht.No.+6ofRoom1StandardRoomRoom2Time-Dependent RoomRoomtemp,T(t)rlVolume,VlAirdensity,pSpecificheat,C1vl~Initialpressure, PFilmcoefficient, hlSlabTelllPrT(x,t)s"'Roomtemp,T2(t)-T2(0)+Asin(00t)r2r20Filmcoefficient, hSide1ofslabSide2ofslabX=OX=LeFigure4.1Description ofSampleProblem1 ppct.Form2l5in183)Cst.l973l01$f-8-NA-046Rev.00Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER8LIGHTCOMPANYERNo.CALCULATION SHEETwhereaandbaregivenbyequations (2-30)and(2-31)~Itisassumedthatbothroomshavebeenattheirinitialtemperatures longenoughfortheslabtoattainaninitialsteady-state temperature profile.Thegeneralsolutiontothisproblemisrathercomplicated, butthesolutiontakesamuchsimplierformforlargevaluesoft.ThisproblemwasalsosolvedwithCOTTAP.Valuesfortheinputparameters usedinthecalculation aregiveninTable4.1andacopyoftheCOTTAPinputdatafileisgiveninTable4.2.Theslabtemperature profilesat900and2000hours,calculated withCOTTAP,arecomparedwiththeasymptotic formoftheanalytical solutioninFigures4.2and4.3.Theresultsshowgoodagreement. TheCOTTAPresultsforthetemperature inroom1arecomparedwiththeanalytical solutioninFigure4.4ragain,theresultsshowgoodagreement. PPdLForm24$4{10/N)Cat.NQ73401SE-B-AA-046Rev.pgDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETTable4.1ValuesofParameters usedinSampleProblem1Parameters ValueT0)rlT(0)A0hhVA80F200F100F0.5rad/hr1.46Btu/hrftF6.00Btu/hrftF200.0325ft/hr21.0Btu/hrftF800ft300ft2ft1014.7psia TSOFOREGROUND HARDCOPY0~~~PRINTED89284.1100 JSNAME=EAMAC.COTTAP.SAMPLI.DATA MOL=DSK533 COTTAPSAMPLEPROBLEMI-"RUNIt1~~1~1~~0~~~~10~~~~~~011~~00~11~~~0040000000 PROBLEMDESCRIPTION DATA(CARDIOF3)NROOMNSLAB'INSLAB2NFLOWNHEATNTDRNTRIPII000I0~1~1~0~00400~000~~~~~~0~~~00~0~~~00~000~00000~PROBLEMDESCRIPTION DATA(CARD2OF3)NFTRIPMASSTRMFCPICP2CRI002222.D42.010.~41~~10~~~~4~~~0~~~~~0~~~~~1~~~~~~~~~~00~00~~PROBLEMDESCRIPTION DATA(CARD3OF4~NSHTFC01.0-54~0~~0~~~~~~0~~11~~~1~1~~~~~~~0~~~0~0~~~~~~~~PROBLEMTIMEANDTRIPTOLERANCE 0040004004141411040410040~~NPIPENBRKNLEAKNCIRCNEC0000I04014~4444010444410~11~0400RTOLI.D-5INPUTFIFPRTII'10~~100~1~~~~~~~~00~~0~~~~~000~~1~010~~~0100~1~~~4~~~1DATA+41~TTENDTRPTOLTRPEND.02000.010.000.004~~~~~~~~~401~0~~~~~~~~~~~00000000~~000~~~0~~~~~40~00~0~0~00~1~TOLERANCE FORCOMPARTMENT-AIR-FLOW MASSBALANCE(OMITTHISCARDIFNFLOW=0)44110DELFLOI.D-5~0~~1~444~~~1~04~~~0~~~~~0~~0~00~00~0~00~~00100~~~1~00~0100~01~~00~0EDITCONTROLDATACARDSIOECTLASTTPRNTI2000.100.4~0410~1144~0~~~~~1~0~~0~~0~~0~~00~010~0000~~0~1~10~0~0400114~~0001~0EDITDIMENSION CARD144NREONSLEONS2ED2I014~~~~~0~~1~~~~~~~~~~~~~~~~~1I~~~~~0~11~I~011~1~1I~111004144~1114~~0I~44~ROOMEDITDATACARO(S)I-I~44444440~1~~~1000~~0~01~~~~00~0010~I~0~440444040440440004444404000000444 EDITCARD(S)FORTHICKSLABS444444440 ~0401~1~~10~~01~~~~~~0~0~~~~~0~4~~00~1400~~014111~40414111~01~1EOITCARDSFORTHINSLABS44440444441~1~000~40~~1~0~10~0~~~~~00~~~~1~1~'REFERENCE PRESSUREFORAIRF(OMITTHISCARDIFNFLOW=O001101411444440441014401141LOWSTREF100.~1~~11~~~~PREF14.7~~~~1~~4~~~~~~~~1~~~~1~1~14~111~~01ROOMDATACARDS(DONOTINCLUDETIME-DEPENDENT ROO1~00011~1~01414111~14~1~4~1MS)~IUROOMI~444444444VOLPRESTRRELHUMRMHT800.14.780.00.510.01~11~~1~111~~~~~411~~~10~~4'~1~~410AIRFLOWDATACARDS(OMITTHISCAROIFNFLOW=0)0001~~11~1~1414~141~~~11~11IIIFIAWIFROMITOVFLOW s44~4~0~0~~~~~4~~~~~~~~~~~~0~00~~~~~~~40~~44~00~~04~~~4440~44~444\440000LEAKAGEPATHDATA(OMITTHISCARDIFNLEAK=0)JRM2IDLEAKARLEAKAKLEAKLRMILRM2LDIRN~~~4~~~~~~~~~4~~~~~~4~000~4~~~~~000~00~0~~0~~4444~~~~~~~~~0~4~~004444AIRFLOWTRIPDATAIDFTRPKFTYPIKFTYP2FTSETIDFP~444~0~~~00~~0~0~~~~~~~~~00~~~~0~~0~~00~0~~~~~~4~~00~0~00~~0~~~00~0~~HEATLOADDATACARDS~IDHEATNUMRITYPQOOTTCWCOOL~4400~00~~0~0~~4~~0~00~~~0~~~0000~00~~0~~00~~~~~~0~~~~0~~0~4444444444PIPINGDATACARDSr~IDPIPEIPREFPOOPIDAIODNPLENPEMAINKPTEMPIPHASE4444~4400~~4~~4~~4~~~~4~~4~~~0000~~04~00000~~0~000~4~04~~404F4'4444HEATLOADTRIPCARDSIOTRIPIHREFITMOTSETTCON~~~44~~~~~~~~4~4~~~~040~~~0~000~00~0~0~0000~0~~0~00~~~~~~~~4~~4~440~~STEAMLINEBREAKDATACARDS4~IDBRKIBRMBFLPRIBFLGBOOTTRIPDNTRIPOFRAMP4~444~44~4~~4044~~44~~0~~4~04000~00~00~00000000~0000~0~0~00000~44444~0THICKSLABDATACARO(CARDIOF3)4IDSLBIIRMIIRLI2ITYPENGRI0IHFLAGCHARLII-II'I51210.~444~4~0~4~4~~4~0~4~4400004000~0000~0~4~~00440~~~~~~~4440~~00~4400444THICKSLABDATACARD(CARO2OF3)0IOSLBIALSAREASIAKSROSCPSEMISI2.0300.I.00140.0.220.8~4~4~~~404~4~~~0004~~~~~000~40040~0000~00~00004~4~~~~~00~044~~000~0~4THICKSLABDATACARD(CARD3OF3)~IDSLBIHTCI(1)HTC2(l)HTCI(2)HTC2(2)I1.466.00~44444~0~4~0~~440~0~~~0~~00~~~~00000444~0~~~04444~~44~~~4~044444~440~THINSLABDATACARO(CARDIOF2)4IDSLB2JRMIJTYPEAREAS24~4~0404000000000~0~0~00~0~0~40000400~40040000000~00404404400044040400THINSLABDATACARO(CARO2OF2)4IDSL82UHT(l)UHT(2)444~044~~~04~~~~~040~00~~~~~0~00~~0~~04004~4~004~000440F4'4404444440 4TIME-DEPENDENT ROOMDATAIDTORIRMFLGNPTSTDRTOAMPLTOFREQ-I20200.0100.00.50~44~44~~~~~~4~~~~~~~44~~~~~4~~04~440~~4~~4~~0~4~~~~004~4~~44~4440~44~TIMEVERSUSTEMPERATURE DATA~Il)TDRTTCMETTEMPTTIMETTEMPTTIMETTEMP~t~4~444~~~~~~~~~~4~~44~~44~~~444444~~44~44~44~~~4~4~~~444~40~4444444~~44~~~~~~44~~~~~~~44~44~4~~~444444~4404~4~~4~44444444444~44~~44~~4~40444~~4040440440~004044~444444444 TSOFOREGROUND HAROCOPY~~~0PRINTED89284.1045 SNAME=EAMAC.COTTAP.SAMPLI.DATA DL=DSK533 (OTTAPSAMPLEPROBLEMI--RUN2o00000~~~0~100000~0~1~~~~~~00~~~00~00~0~0~0~~~1000000101~~~~~~0~~~~010~PROBLEMDESCRIPTION DATA(CARDIOF3)NROOMNSLAB'INSLA82NFLOWNHEATNTORNTRIPNPIPENBRKNLEAKNCIRCNECII000I000002~01~0~00000000~00~00~~~~~~~~~~~~110~00100000~~~11~~00~~~~0~~00~~000~0~0PROBLEMDESCRIPTION DATA(CARO2OF3)NFTRIPMASSTRMFCPICP2CRIINPUTFIFPRTRTOL002222.042.010.III.D-5~010~~~~0~00~000~~~00~~0~000~0~~~~~1~~000010~~0~~0~1~00~0100000~01~00~0PROBLEMDESCRIPTION DATA(CARD3OF3)NSHTFC0I.D-5~101~0~I~0~0~0I~~~0~~~~0~~0~~~~~0~0000000001000~000~0~1001~0~00011000010~PROBLEMTIMEANDTRIPTOLERANCE DATATTENDTRPTOLTRPENO0.01520.0IO.DO0.001~~0~0~~1~11~~~00~~~0~~0~~~~~0~~~~~~0~~~0~~~01~~1TOLERANCE FORCOMPARTMENT-AIR-FLOW MASSBA(OMITTHISCARDIFNFLOW=0)~~~0~~~00000~0~~000110LANCEDELFLO1.0-5~00100~0~1~~10~~~0~~~~~~~~~~1~~~0~~~00~0~~0~0~0~~~~~~~~1~1~~~1~~~~00001EDITCONTROLDATACARDSIDECIt~~110~00TLASTTPRNT1500.1500.1520.I.0~~~~~~00~~1~0~~~~~~11~00000~0000~~~~~~~EOITDIMENSION CARD~~~~~~~~~~~0~~01~~~~1~NREO2~a0~10~011~~~~NS00~0~10~0ROOMIEDNS2EDI00000~00~000000000010~00~0~00~~~1~1~0~00~~00000011EDITDATACARD(S)000-I~00~~~1~00111~~~~~~~EDIT~0~~~~0~00000~~~~~1~0100~~~~0~~01~~00~~0000000000CARO(S)FORTHICKSLABS~0~~0~0~000000~1~~00~~~~~01~1~0~1001000000000~000000~~1000100100~0101111EDITCARDSFORTHINSLABS~1~10000~0~~111~~~~10~1~0~~~000~000000100~~0~0~1010~~~~100~~000000~0000~REFERENCE PRESSUREFORAIRFLOWS(OMITTHISCARDIFNFLOW=O)TREF1(10.~00101000~~~~(00PREF14.710~0001~~RNOTINCL~~~~1~00~0~0~0~0000~0~~~~~~~1~~~~~01~~~0111100110OOMDATACARDSUDETIME-DEPENDENT ROOMS)I(>ROOMIVOL800.~~0\001101110~PRESTRRELHUMRMHT14.780.00.510.00~110~~0~~~~0~~1~~~0~1001~01~10~~0~0AIRFLOWDATACARDSOMITTHISCARDIFNFLOW=0)~~00~~~~10~1~~~1~11001 TSETJRM2e~I~I~~~~~~0011~~I~~~0~~~~~~~I~11~~I~~~010011~I~~~~LEAKAGEPATHDATA(OMITTHISCAROIFNLEAK-"0)IOLEAKARLEAKAKLEAKLRM1LRM2LOI~IIII~~I~~I~~~~I~~~~~~~~~~III~~IIIIII~I~IIIIIII~I~~AIRFLOWTRIPDATA~IDFTRPKFTYP1KFTYP2FTSETIOFP~~I~~~~I~I~I~~~~~~~~~~~~~~~10~00~10~~~~~~III~I~0000~HEATLOADDATACARDS~IDHEATNUMRITYPQOOTTCWCOOL~t~11~I~~01~~~~~~I~~I~I~~I~~~~~~~~I~~I~~~I~~~I~I~I~PIPINGDATACARDS~IDPIPEIPREFPODPIOAIOONPLENPEMAtIIII~~I~II~~~~~III~~III~I~I~~~I~~~I~II~IIIIIIIIIIIHEATLOADTRIPCARDSIOTRIPIHREFITMDTCONt~~~~~010~~~I~I~00~~~~I~~~~I~~I~~00~~~01~I~0000~~~~tSTEAMLINEBREAKDATACARDS~IDBRKIBRMBFLPRIBFLG~~III~II~~I~~~~II~~~~0~~~0~IIII~IIII~~~~I~IIIII~0~ITHICKSLABDATACARO(CARO1OF3)IDSJBlIRMlIRM2ITYPENGRIDI1-1I15~I~tt~~~11~~I~I~~~~~~~~01~~10011~~I~~~I~000~~~~00~~THICKSLABDATACARD(CARO2OFIDSLB1ALSAREAS)AKSROS12.0300.1.00140.~t~~I~01~~~~~~~I~1001~~I~~~~~~10~10~~~~~~~~100~01~~THICKSLABDATACARO(CARO3OF3tIIJSL81HTC1(1)HTC2(1)HTC1(2)HTC211.466.00~t~~~~~~~t~~~I~I~~~~~~I~~~I~~00~~~~~~~I~~10100~~~~~tTHINSLABDATACARD(CARO1OF2)t~IOSL82JRM1JTYPEAREAS2t~III~~~~IIII~I~III~~~I~~IIIII~~~III~~~I~~~II~IIIIIITHINSLABDATACARO(CARO2OFt~IDSL82UHT(1)UHT(2)~~tt~IIII~I~~~~00~~~~~~I~~~I~~001~~I~I~011111000 ~I~TIME-DEPENDENT ROOMDATA~~I~01111111100 ~I~~~IRNI~010000000001 ~~~~~I~I~~~0000~00~~00100~I~~~~~~~~II~I~~~~I~~~I~INKPTEMPIPHASEIIIIIIIIIIIIIII~~IIII~I~1110~1001~01~I~111FRAMPI~01~~I~I~~0101~10~I~IHFLAGCHARL1210.00~~I~~I~I~I~~I~100~I3)CPSEMIS0.220.8~~~~~~11101~I~~I~~~)(2)I~~I~1111~100~~~I~~I~~I~I~111111~01~00~1002)IIIIIIIIIII~~III~~~II1010RIRMFLGNPTSTORTOAMPLTD-12-0200.0100.0~~tt~~I~~~~~~~~I~I~I~~~~I~~~tt~~~~~~~~I~11~11~I~111TIMEVERSUSTEMPERATURE DATA~IDTDRTTIMETTEMPTTIMETTEMPt~1tt~~~~~I~~~~~~~~01~~~I~I~101~I~~~I~I~1101~11~~~~~~t~11~~I~~~~~~~~~I~~~~~~~1111~11~~~I~~I~000~~111TTIMETTEMP10~1101~11~I~II~I~I~~11~~~I~~~11t~I~~~IFREQ0.50~~~11~I~~ttt~I~~~~I~~gI RGURE4.2COMPARISON OFCOTTAPCALCULATED TEMPERATURE PROFILEWITHANALYTICAL SOLUTION(t=900hr)FORSAMPLEPROBLEMt220210QlQ)200I~190180LegendANALYIICAL 4COTTAP1700.5x(tt)1.5o(CC) FIGURE4.3COMPARISON OFCOTTAPCALCULATED TEMPERATURE PROFILEWITHANALYTICAL SOLUllON(t-2000hr)FORSAMPLEPROBLEM1250240Q)230220l~50-210200Legend~WALVTlCAL ~COTTAP1901800.5x(tt)1.5'IOCgCD FIGURE4.4COMPARISON OFCOTlAPCALCULATED TEMPERATURE OSCILLATION WITHANALYTICAL SOLUTIONFORSAMPLEPROBLEM1IM4OLJCIMKOOOO4JCLI-!L4JI-200.6200A200.2200199.8199.6199A15015051510TIME(hr)LegendANALYTICAL ~COTTAP15151520cC) PP8LForm24S4(!N83)Cat.l973401VSE-B-NA-046Rev.agDept.Date19DesignedbyApprovedbyPROJECTSht.No.~9ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET4.2ComarisonofCOTTAPResultswithAnalticalSolutionforComartmentHeatUduetoTriedHeatLoads(SamleProblem2)Thisproblemconsistsoftwocompartments separated byathinwall.Oneofthecompartments ismaintained ataconstanttemperature (COTTAPtimedependent room)gthetemperature intheothercompartment iscalculated bythecode.Thecompartment forwhichthetemperature iscalculated contains4heatloadsand5associated heatloadtrips.Thetimingofthesetripsmatchestheplotinfigure4.5.Theanalytical solutionfortheroomtemperature isT(t)=T(0)e+T(1-e)rrcont-tB/a~yB/a()0a(4-6)wheretheconstants aandBaredefinedinAppendixB,Tistheconcompartment temperature ontheoppositesideofthethinwall,andQisthefunctionshowninFigure4.5. Q>ookW<000IIIOlX7QIO(2aaOO'CA'0~'D@ry0o3AIP~30QQS~aOoo+/Oo&/oi~LO~->a~>LaxTi:po~HPC,+lI0agLTbPO~Ogpu+J~aQQ.TiI)PO~~OHcakLo~dt3Tvp-g~~/L<c.dg&pDCCC~/g20T>~g(Hrs)0mOCAZ00mXXCOCIn~rZo>C0I0~mOmZgyIIIrm~xm-l~A=0D'Xm37Z0'ICDCCD PPKLForm2iSl(1$N)Cat.t970401L$F9lqA.-046RevQiDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER8cLIGHTCOMPANYERNo.CALCULATION SHEETBecauseofthecomplexity ofthisfunction, aFORTRANprogramwaswrittentoperformthenecessary numerical integration andtoevaluatetheanalytical solutions TheCOTTAPinputdeckisgiveninTable4.3.Comparison oftheCOTTAPresultswiththeanalytical solutionisshowninfigure4.6.Ascanbeseen,theCOTTAPresultsagreewiththeanalytical solution. 4.3COTTAPResultsforComartmentCoolinbNaturalCirculation (SamleProblem3)Inthisproblem,acompartment containing aheatsourceof10Btu/hris5initially cooledbyforcedventilation flowdrawnfromoutsideair(outsideconditions arerepresented bytime>>dependent compartment, -1).Ventilation flowistrippedoffatt~1hr.Sincethe'compartment isnotairtight, airleakagebetweenthecompartment andtheenvironment occurswhichmaintains thecompartment atatmospheric pressure. Thisairtransferprocessismodeledbymeansofaleakagepath.Noairflowtothecompartment occursfromt~1hrtot~2hr(exceptforleakageflow)ratt~2hr,twoventsatdifferent elevations areopenedallowingnaturalcirculation flowthroughthecompartment. Inordertosimulatethis,anaturalcirculation flowpathistrippedonatt=2hr,andatthesametime,theleakageflowistrippedoffbecausethecirculation flowmodelalreadyallowsforairleakage. ~~4TSOFOREGROUND HAROCOPY111~PRINTED89284.1412SNAME=EAMAC.COTTAP ~SAMPL2.DATA ~OL=OSK534 COTTAPSAMPLEPROBLEM241~~1~~4444141I11 ~4~~4~~~I~~4~~4~~4~~~1~1~44I4~~~44I~~4411~~~4~~~~1~441~44~PROBLEMDESCRIPTION DATA(CARD1OF3)NROOMNSLA81NSLA82NFLOWNHEATNTDRNTRIPNPIPENBR101041500144~1144~~4~~I4~4~~~4~4~~~~~~I~14444~14~~4I44~41444I~~~~4PROBLEMDESCRIPTION DATA(CARD2OF3)KNLEAKNCIRCNEC0014~~~14~4~4~44444~~NFTRIPMASSTRMFCP1CP2CR1INPUTFIFPRTRTOL002222.042.010.I11.0-514~~4~~~~4444~44~~1~~~~~~~~~~4~4~44~~~~414444~441~~441~4~~~1~~~444144~~PROBLEMDESCRIPTION DATA(CARO3OF3)NSHTFC0'I.0-5411~14~~~444~~1~~~14~~4~~~~~~~~~444~41~4144444~44~4444~~~~~44~4~~4~~444PROBLEMTIMEANOTRIPTOLERANCE DATATTENDTRPTOLTRPEND0.040.00.00540.0~4~4~44414444~44444~~~~~~44~~~~4~4~~I4~4I~~I~4~~4~41~~~~TOLERANCE FORCOMPARTMENT-AIR-FLOW MASSBALANC(OMITTHISCAROIFNFLOW=0)4~4~41414~4~~44441DELFLO~~4~1~~~4414~4~~44~~4~~~~4~14~444~~4444144~444444414~~44~~~~~4~~~~41441EDITCONTROLDATACARDSIDECTLASTTPRNT160.2.0~4~~44444414~44~~44~~~~~~~4~4~~~41~44414~414~4444444144 ~~~4~41~44~4~11~EOITDIMENSION CARONRED2441444414 NS1EDNS2ED01~1~~~~44~~41~~~44~~1~4~4~11411444~44444~4~~~~~4444~~~~~~44~~44ROOMEDITDATACARO(5)~44-14444444~444~4~444444~~4~4~~44~4~~4~~1~1~41~41~~~4444~~4~4~44~14~414~4EDITCARO(S)FORTHICKSLABS~444444444 ~14444~~~1444~~~~444~~1~~~~44441441444444~4~~~~4~~1~1~~~~44\41EDITCARDSFORTHINSLABS~~1~~~~1~441444~444444~~~~~444414~44444444~4444~REFERENCE PRESSUREFORAIRFLOW(OMITTHISCARDIFNFLOW=O)4~4414~414~41~~44~4~4444TREFPREFf4414~444144444~~444~~~1~~~444~~1~414444~14~1~44144~441~~4411~~~41144441ROOMDATACARDS(DONOTINCLUDETIME-DEPENDENT ROOMS)~IDROOM10~~1114~444VOLPRESTRRELHUMRMHT000.14.7100.00.510.041~44~1~~44~~~~~~~~1~~444~414441~14~44AIRFLOWDATACARDS(OMITTHISCAROIFNFLOW=0)4~4411~~~444~~1~41~141441nrinwIFROMITOVFLOW 1~~~000~10~~~0~~~0~1~1~~~~0~0~10~1~1~~~11111~11~1111~~1~~~111~0~10~~~~~LEAKAGEPATHDATA(OMITTHISCAROIFNLEAK=0)IOLEAKARLEAKAKLEAKLRMILRM2LDIRN~~~0~~~~~~01010~~000~0~~0~~1~~0000~000000~000~0~00111001~0110~1100~~~~0AIRFLOWTRIPDATAIDFTRPKFTYPIKFTYP2FTSETIDFP1~~~~00000~~00~0~0~~~~0~~~~~~~0~~~~~0~0~00~0~0~0~~~~1~~~~~~~~~~~~~~~~~~HEATLOADDATACARDSIDHEATNUMRITYPQDOTTCWCOOLII2'I000.-1.0.2I3'I000.-I.0.3I33000.-1.0.4I82000.-I.0.-~~1~~000~0~I~~Ol~~0~0~0~0~~~~~00~0000~00~0~00~eeel~~00~~~~10000~~~~~000~0~PIPINGDATACARDSIDPIPEIPREFPODPIDAIODNPLENPEMAINKPTEMPIPHASE1~1000~~~~01~10~~~~~~0011~0~~~~~~~00000~~0000010~~~01~11~1~0~0~~~~10~~1HEATLOADTRIPCARDSIDTRIPI2345s\00000000IHREFITMDTSETTCON'I21.00.0TRIPONII5.00.0TRIPOFF2I10.00.0TRIPOFF3215.00.0TRIPON4I20.05.0EXPONDECAY~~~~~~011~0~0~~~0~~~010~~~~10~~110~~~~0~~~0~~00000000~~0~1~~~~STEAMLINEBREAKDATACARDS~IOBRKIBRMBFLPRIBFLGBOOTTRIPONTRIPOFRAMPI1000000000 IIOSLBIoeooooo~00IDSLBIt~~~~~0000o~IOSLBI1~~1~100~0ITYPENGRIOIHFLAGCHARLIRM2IRMI~1~~0~~0~1~0~010~~~~00~~~~0~0~~11~~~~~~~~~~~0000~0~~0~~~~0~00~THICKSLABDATACARD(CARD2OF3)ROSCPSEMISALSAREASIAKS00001~~~000~1~0010~~~~~~~~~~0~0~00000~~0~00~1~1~0KSLABDATACARD(CARO3OF30000~~~~0~~THICHTCI(2)HTC2(2)HTCI(I)HTC2(I)0~0~~~~~0~~111~00001~111~100~~0010~0~000000~1~0~~10~~~101~000~THINSLABDATACARO(CAROIOF2)~~~~~~~0~~0~~0~~0~00~0~~~~~~~~~000~~~00~00~~1~~~111~1~~0~0~~~1THICKSLABDATACARD(CAROIOF3)IDSL82I~11111111~JRMIJRM2JTYPEAREAS2I-II500.~oo~~~~~1~1~~1~~~~~1~11~01~~~~~~~~0~0~~~1THINSLABDATACARD(CARO2OF.~~1~1~111~111~~1111~2)IOSIt11111~~IDTDR-I01111111IRMFLGNPTSTORTOAMPLTDFREDI30.00.00.00ooooo~o~~~oooo~~1~~~~1111~ooooeo~ooooooe~ooeoeooooeoo ~~~1~1~IMF<ERSIISTEMPFRATURE DATAnnF(LB2UHI(I)UHT(2)0.33~111~1~~~~~~~1~~~1~1~11~~~1~1~~~111~~~~~1~111~~1~11~~~111111~111TIME-DEPENDENT ROOMDATA -10.00100.00.5014.7050.00100.00.5014.70100.00100.00.5014.70~~~~~~~~~Ij44~I1~0~~~0440I~~0~~0~0~~14I0~0~~~~~10~00~I~0~I444440~00i44~i00~41J44~40~~~0~04044~0~0t4~100~~~4l~~i1~0~~~0~0~~~~00~~l~4044~444~~0~~~0~ FIGURE4.6COMPARISON OFCOTTAPCALCULATEO COMPARTMENT TEMPERATURE WITHANALYTICAL SOLUTIONFORSAMPLEPROBLEM2135130OOOLLILJJ,0125120115110105LegendANALYTICAL ~COTTAP10001020TIME(hr)3040 PP8,LForm24'10/N)Ca).t973401SE-9-.NA=046Rev.0gDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER8cLIGHTCOMPANYERNo.CALCULATION SHEETThewallsofthecompartment consistof3slabs:averticalwall(slabl),aceiling(slab2),andafloor(slab3)whichisincontactwiththeoutsideground.Thetemperature, relativehumidity, andpressurewithinthetime-dependent compartment areheldconstantthroughout thetransient. TheCOTTAPinputdatafileforthisproblemisshowninTable4.4.TheCOTTAPresultsforthisproblemaregiveninFigure4.7.4.4COTTAPResultsforComartmentHeat-UResultinfromaHihEnerPieBreak(SamleProblem4)AhighenergypipebreakismodeledusingastandardCOTTAPcompartment thatisconnected viaaleakagepathtoatimedependent volume.Thepipebreakisinitiated inthestandardcompartment attime0.5hrandisterminated attime2.5hr.Thetimedependent volumeismaintained at095Fand14.7psia.Theleakagepathmaintains constantpressureinthestandardcompartment byallowingflowbetweenitandthetimedependent compartment. TheCOTTAPinputfileisshowninTable4.5andresultsoftheCOTTAPrunaregiveninFigure4.8~ TSOFOREGROUND HARDCOPY~~10PRINTED89304.0951 OSNAME=EAMAC.COTTAP.SAMPL3.DATA VOL=OSK533 COTTAPSAMPLE01101000000000 ~PROBLEMOESC0NROOM,NSLABI I3~~~~1~0~~~~~~~PROBLEMOESCPROBLEM3~0000000~0~1000000000~000010000100~0000000000~0~0101~0~000RIPTIONDATA(CARDIOF3)NSLA82NFLOWNHEATNTDRNTRIPNPIPENBRKNLEAKNCIRCNEC02'II'I00II8~0000~1~00011101000~0~~0~~~0000~~010~~0~~0~~011~11~0~11011RIPTIONDATA(CARD2OF3)MASSTRMFCPICP2CR'IINPUTFIFPRTRTOLI102.04150.5.III.D-5010~100000000000000000~~0~~000~~~~000~00100~10~~000~~~0100~01ESCRIPTION DATA(CARO3OF3)NFTRIP5~001~00OBLEM0~~00PR10NSH1001100~0~10TFC1.0-5000000~0000101000000000000000001~0~000000000000010000~~1~1~~~~11PROBLEMTIMEANDTRIPTOLERANCE DATATENDTRPTOLTRPENO3.00.0053.0~~I~110100~~~~~11~~0~0~~10~~1~~I~~1~001~~~~~~~~I~~~11111111~1~~lI1~~TOLERANCE FORCOMPARTMENT-AIR-FLOW MASSBALANCE(OMITTHISCARDIFNFLOW=0)00.0111111011111DELFLOI.D-511110101~1~~~111~~0~1~1111~1111111~~1~~0101~11~1011~~11~11~11~~0~~11EDITCONTROLDATACARDS~11111[OECI235678100010~TLAST0.11.01.12.2.210.024.0500.00~000101TPRNT0.010.100.010.100.010.100.205.0011011~0110101~111111~~00~~1~0~11~0100011~11~~~1~~1111EOIT0IMENSIONCARO0111011NREDNSIEONS2ED220110~00~~000~~00~~11~~10~00010001111~111~~~1~1~1~~1~00~00110111~0~~011ROOMEDITDATACARO(S)11~00I11~0I111111~1111-I~11~~110111~1~0~~1~1~1~~101~~1~~1~1~1~1~01111~~111~1~~~11~1~1~~11~111EDITCARD(S)FORTHICKSLABS21111~0~~~1~~~~011~111100~001~~11~~~~~11111~0~111~1111111111~11~1~1~11EDITCARDSFORTHINSLABS1~11111~1~~~~11111~1~11~11~1111~1~~1~1~111~~11~~~~~1111111111111~~111REFERENCE PRESSUREFORAIRFLOWS(OMITTHISCAROIFNFLOW=O)ROOMDATACARDSNOTINCLUDETIME-DEPENDENl'OOMS) 1iissci)IIM vwcSiwl(tIHIIMIIMHTTREFPREF100.14.70~00~1~01~1~111~~~1~1111~101111001~~1~~~11~11110~~~1~11~111111111~1~0~~0 11111130000.14.780.00.527.51110110010~~~01~~11101~11101110~1~110000~~11~0~~000~~0~010011~1110110AIRFLOWDATACARDS(OMITTHISCAROIFNFLOW=0)IDFLOWIFROMITOVFLOWI-II'I.D4FAN2I-II.D40FAN11011111~11~1~000~1100100000000000001 ~00000LEAKAGEPATHDATA(OMITTHISCARDIFNLEAK=0)1110000~~~~000~00~0~0~~1~0001001111001IDCIRCKRMIKRM2ELEVIELEV2ARINAROUTAKINAKOUTII-I3.12.50.50.5.5.~0000000101010 ~10001'00~0~~~0~0~0000~011~0~~0~000~001~000011111100 AIRFLOWTRIPDATA00100IDFTRPKFTYPIKFTYP2FTSETIDFPI3I0.0I0TRIPCIRCFLOWOFF.AT2II1.0I0TRIPFANOFF3II1.020TRIPFANOFF42I2.0I0TRIPLEAKAGEPATHOFF5322.0I0STARTNATURALCIRC~111~1101~110~10010111~1~110~0~0~~00~00~00100000000~0000000000011111HEATLOADDATACARDS1IDHEATNUMRITYPOOOTTCWCOOLII3100000.-1.0.~111111~~110~01~011~01~0~110~~~1~1~0~00000~~~0~010~0111110~11~~1~1~1PIPINGDATACARDS1IDPIPEIPREFPODPIDAIODNPLENPEMAINKPTEMPIPHA1100001000~10010~000~1000~011~00~001000~~~1~0000~0000010100~~000~00HEATLOADTRIPCARDSSTART0110001111SEIDLEAKARLEAKAKLEAKLRMILRM2LDIRNI1.0-1.0I-'I200000010100000000~0000000000010000001001001000000010~00~0001110000000CIRCULATION PATHDATAIHREFITMDTSETTCONII10.00.11010000001~0~~01~~~~100001101~1~00000011001100110101000STEAMLINEBREAKDATACARDSIRMIIRM2ITYPENGRIDIHFLAGCHARLI-II10230.I-I310230.I02'I0030.~1~~1110~11~1~~~~~~~11~~~~1~~~11~~~~0~~~~111~~~~1110~101THICKSLABDATACARD(CARO2OF3)11111EMIS0.800.800.801111111111110 HTCI(I)HTC2(1)HTCI(2)3.73.73.711111~11II111~1~~~01~~~11~1~10~~~~I~0~1000~0011~THINSLABDATACARD(CAROIOF2)HTC2(2)~1~1111~110~~00IDTRIPI00111100000 0001100IDBRKIBRMBFLPRIBFLGBOOTTRIPONTRIPOFRAMP0~1000001101~~00011~111~~1~~10100001100000~~0~~10~0~~~~~~~001~001~0001101THICKSLABDATACARD(CARDIOF3)IDSLBII2310010101111 01IDSLBIALSAREASIAKSROSCPSI3.03800.'I.0140.0.2222.0960.1.0140.0.2234.0960.1.0140.0.221~~~~~~~~1~111~1~1111101~11~11~~111~1~11~100011~1111~~00~1THICKSLABDATACARO(CARD3OF3)IDSLBII21~1~1~11111lRMlIRM'7ITVPFARFaS'P 1~111100010000IOT-1~~00~~IOT-I00~01010~~~10~1101~~0001~1001~~~~01~10~11~00~000~1THINSLABDATACARD(CARD00~0011100011100011100000002OF2)IDSLB2UHT(1)UHT(2)OR11010111IRMFLGNPTSTDRTOAMPLTOFREQ'I480.00.00.000OUTSIDEAIR~~~~~~II~~0I~I~~I~1I~01~~~0I~~~0I~~10~0~~00~~~100000101~00~0~0~~1~1TIMEVERSUSTEMPERATURE DATADRTT01250010111~000~0010IME.00.00.00.000~0~0~~0~~0~110~0~TTEMP80.080.080.080.00000~000~~~~~000RHUM0.500.500.500.50~~00000~0~0~000~~~00~~00~~~000PR14.14.14.14.0~00~0~0ES7070707000~100001~1~~01011~11~~~0~00~~~00~~~00~~~11~~~0~0~0110010~0~00~0~1~~~~000~0001~00000~00~0~00001000110~01111~00~~0TIME-DEPENDENT ROOMDATA figure4.7COTTAPTEMPERATURE PROFlLEFORSAMPLEPROBLEM3100CDI-I-CLOOOCk'-CLLIJCLI-9590858000.51.5TIME(hr)2.5 TSOFOREGROUND HAROCOPY1~~0PRINTED89285.1301OSNAME=FAMAC.CQTTAP.SAMPL4.DATA VOL=DSK540 COTTAPSAMPLEPROBLEM4~~~~1~~~I~~00~~~0000~00~~~~~0~001~1~0~~~000I~00110I~10~1101~11010~0~1~~~000PROBLEMDESCRIPTION DATA(CARO1QF3)NROOMNSLAB'INSLA82NFLOWNHEATNTORNTRIPNPIPENBRKNLEAKNCIRCNEC13000100'II06~1~1~~~~~~00~1~~10~~~~0~~'~0~~~~~~~0~~~1~~010000~~1~~~0111110~00011~100~PROBLEMDESCRIPTION DATA(CARD2OF3)0~NFTRIPMASSTRMF'PICP2CRIINPUTFIFPRT0113S.D4150.50.I'I~1~~0~000000~00~~00~0~00~0~00~0~0~000~00~0~00000000000 ~~0F00PROBLEMDESCRIPTION DATA(CARO3OF3)NSHTFC0I.0-50010I~000~0~~0000000001000000 ~~0~~00~~0~00~~00~000000~01010000PROBLEMTIMEANOTRIPTOLERANCE DATARTOLI.D-5~~1000~10100~011~00000~0TRPTOLTRPEND0.0056.00~000000010 ~001001~00001000~~00000~00~COMPARTMENT-AIR-FLOW MASSBALANCECARDIFNFLOW=0)TTEND0.06.0~1~~000~1~10~0~~00~~~10TOLERANCE FOR(OMITTHIS1OELFLO1.0-5~~10~0~~0011~110~~0F010EDI00111000000000 0~00100~~~100101~~~~000001100~~~~~0~01~~1~0~010111TCONTROLDATACARDSTLASTTPRNT0.50.100.60.0052.50.102.60.0056.00.2025.00.500001~00~00~001000~~0001~~00100000000000 ~1000~000~I~~1F1'00000EDITDIMENSION CAROOECI23456000000000~000NREONS1EDNS2ED230~~~0~~~~~~0000000100~00~00~00~0~00~00~00000ROOMEDITDATACARD(S)0~~~00011~0~000~10~00001000000I010~10I~01~00011~10~111110ID-I000~0~000010001~011110~0~0~000~00000~001001EDITCARD(S)FORTHICKSLABS~00~00011000~0~~0~~0000~~~~~I~~111111~~1111~I~0111~100I~~~1~~~1~01~0111~~~0I~1I~~~~11~1~00000000I~0REFERENCE PRESSUREFORAIRFLOWS(OMITTHISCARDIFNFLOW=O)TREFPREF100.14.7~~~01Ol~~~~1~01I~I~~00I~0~~110~I~~~101~~00I~~1~I~1ROOMDATACARDS(00NOTINCLUDETIME-DEPENDENT ROOMSROOM~PRESTRRELHUMI105~14.795.01.011~11'1~0a~~1111~~~1~10~~111~~~~~11~~1~1~~~11,~1123010~~~0~10100010~011~0~~1100000000~~~00~0001~~01101000~01~11100~0100EOITCARDSFORTHINSLABS AIRFLOWDATACARDS(OMITTHISCAROIFNFLOW=0)ttttttttttttIDFLOWIFROMITO'FLOWttttttttttttttttttttttttttttttttttttttttttt NLEAK=0)ttttt~~tttttttttttttttttttLEAKAGEPATHDATA(OMITTHISCARDIFTCWCOOLITMDTCONROS140.140.140.CPSEMIS0.220.800.220.800.220.80AKS'1.001.001.00AREAS11000.800.800.ALS2.754.002.75IDLEAKARLEAKAKLEAKLRM1LRM2LDIRN1.0-1.0I-12~ttt~ttt~~ttt~ttttttttttt~ttttttt~t~~~tt~ttttttt~tttttttttt~t't~~t~t~ttt~tCIRCULATION PATHDATAtIDCIRCKRM1KRM2*ELEV1ELEV2ARINAROUTAKINAKOUTttttttttttttttttttttttttttttt ~t~~ttt~ttt~tttt~t~t~ttttttt~~ttttt~~t~ttttttAIRFLOWTRIPDATAIOFTRPKFTYP1KFTYP2FTSETIDFPttttt~t~ttt~tttttttttt~ttttt~tt~tttttt~~tt~~tttttt~t~ttt~~~~~~t~t~tttttttHEATLOADDATACARDSIOHEATNUMRITYPQDOTtt'tt~tttttt~t~ttt~tttt~ttttt~tttt~ttt~tt~tttttttttttttttttttttttttt~~t~ttPIPINGDATACARDStIOPIPEIPREFPODPIDAIOONPLENPEMAINKPTEMPIPHASE~~~~~tt~~~~ttt~~ttt~tttt~~ttttt~tttt~~ttttt~ttttttttt~ttttttttttttt~tt~ttHEATLOADTRIPCARDStIDTRIPIHREFTSETttttt~~tt~ttt~~~tttttttttttttttt~~tt~~ttt~ttttttttttttttt~~~ttttt~~ttt~t~tSTEAMLINEBREAKDATACARDStIDBRKIBRMBFLPRIBFLGBOOTTRIPONTRIPOFRAMP111000.21800.0.52.50.5tttt~tt~ttt~ttttttttttttt ~ttttttt~t~~tt~t~t~~t~ttttttttttttt ~ttt~~ttt~t~THICKSLABDATACARD(CARO1OF3)IDSLBIIRM1IRM2ITYPENGRIDIHFLAGCHARL11-111520.2102'I500.31-131520.t~tt~~tt~t~tttttttt~tttttt~ttttttt~t~~ttt~t~tt~t~tttttttttttt~t~ttttttttTHICKSLABDATACARD(CARD2OF3)tIDSL81123~)0 01000000tt~10001000~01~10~000~010~10000~00t10101000 tf0~101~000THICKSLABDATACARD(CARD3OF3)HTCI(i)HTC2(i)HTCI(2)HTC2(2)0.60.90~00~0000101~1f100100~00001100000~110~~THINSLABDATACARD(CARDIOF2)00000000IDSLBII3111100100IDSLB2JRMI1000000000IOSL820101000000IDTDR-I00101000100IDTDR-I.400~1101~100t0001000111 0JRM2JTYPEAREAS2UHT(1)UHT(2)1tttftf000000~00101010000~0000~01000~0101~~011011110000110011100 TIME-DEPENDENT ROOMDATAIRMFLGNPTSTORTOAMPLTDFREQI30.00.00.000OUTSIDEAIR00000000~tf000000000~0000000~000f000000000000~000000100000010000TIMEVERSUSTEMPERATURE DATATTIME0.0010.0050.0010100110000001000000000000TTEMPRHUMPRES95.00.60'14.795.00.6014.795.00.6014.70000t0~0tt000000ttf000000000010010100000000000000~0000000tf00f000000000000110101010100000000001~00000~1000010001f 0000001~0000000000000 00000~0000000000~0~0~00010000~100010t00000011010 THINSLABDATACARD(CARD2OF2) FIGURE4.8COTTAPTEMPERATURE PROFILEFORSAMPLEPROBLEM4180CAI-Z:IJJOOZ'-I-LxJCLI-160140120100803TIME(hrs)o7cQClCDnO ppdLForm2<<5<<nar83) c<<r.<<073<<0rSE-B-NA-046Rev.01Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET4.5COTTAPResultsforComartmentHeat-ufromaHotPieLoad(SamleProblem5)ThistestproblemconsistsofastandardCOTTAPcompartment thatcontainsalargehotpipeandaroomcooler.ACOTTAPleakagepath,whichallowsflowbetweenconnected roomswhenapressuredifferential exists,linksthestandardcompartment toaninfinitely largecompartment. Thelargecompartment maintains steadypressureintheconnected compartment. Thehotpipebeingmodeledcontainssteamataconstanttemperature of0550F.Itisa20inchdiameterinsulated pipehavingawallthickness ofonehalfinchandaninsulation thickness 'of2inches.Thepipingheatloadistrippedoffat1hour.Atthistimetheheatloadexponentially decays.Thethermaltimeconstantassociated withthedecayiscalculated bythecode.Theunitcoolerisratedat20,000Btu/hrwithacoolingwaterinlettemperature of75F.0TheinputfileforthisrunislistedinTable4.6andresultsareshowninfigure4.9. TSOFOREGROUND HARDCOPY0000PRINTED89285.1403OSNAME=EAMAC.COTTAP.SAMPLS.DATA VOL=DSK536 COTTAPSAMPLEPROBLEM514~~0~4000000~000000~011~00~11~~0~004000000100000 ~0104~400014PROBLEMDESCRIPTION DATA(CAROIOF3)0=NROOMNSLABINSLAB2NFLOWNHEATNTDRNTRIPNPIPENBRKNLEAK200020I.10I0010000000~00~0~00~~00~00t00~00~00~010~00~0~0~1~~~0~0~~0000000PROBLEMDESCRIPTION DATA(CARO2OF3)440100000 NCIRCNEC0I0000000000 NFTRIPMASSTRMF'PICP2CRIINPUTFIFPRT01235.D4150.10.III410000100000100000400001100 ~00000010400 ~~00000~~~~004t40400 ~~1PROBLEMDESCRIPTION DATA(CARO3OF3)0RTOL.0-5000044000t NSHTFC01.0-5011404110004110~0001010PROBLEMTTEND0.04.0001400t10111000000ttt TOLERANCE FOR1(OMITTHIS0~DELFLOI.D-S~44~40000440~1~Ot~0~000EDI~~0401~0~10040000000~~4~~44~10~~4~4~111441440140~~TIMEANOTRIPTOLERANCE DATATRPTOLTRPEND0.054.0~00~0010010~~Ottttt~0~01~0~0~0~0000000~~COMPARTMENT-AIR-FLOW MASSBALANCECARDIFNFLOW=0)0000100000 ~111~t~11111~0040t0~~~0~4~~00~410111110~~01011040~TCONTROLDATACARDSIDECI~411141014444 40TLASTTPRNT25.00.10~040'00104tt1'1100~11~1001100100000110~EDITDIMENSION CARD1~1~001104001104~14401NRED2011411100400101I201404044400140~0410~~~000~010~0410~000~0400TREF100.11111104111114IDROOMVOI100002I.D15441141444404414~1nc~nial000000~000400~040~~~0440t04t040000004~00~~4~440110110441000EDITCARD(S)FORTHICKSLABS0~01~~00000010~0000~000~100000~00~~~~~00111~0~~10010~~~~100EDITCARDSFORTHINSLABS40000~~0~404~~0404~01~010t101t11~101~11~400~0~4441$11111110REFERENCE PRESSUREFORAIRFLOWS(OMITTHISCAROIFNFLOW=O)PREF14.7141~111~~~1~4t~~~110104~1~1~~41114~1~ROOMDATACARDS0NOTINCLUDETIME-DEPENDENT ROOMS)4~11~11411111~1~~40041LPRESTRRELHUMRMHT14.7100.00.510.014.7100.00.510.004~1110~4~0100010101144100000~40010~0AIRFLOWDATACARDS(OMITTHISCARDIFNFLOW=0)1~110110011~010010~44tvvn$cnnaoNSIEDNS2ED001011110401104~0~401101~1100~0000~400~~111~~0~00000100000001ROOMEDITDATACARD(S) 0400000~OO0I0444I0OOO004IDSLB2JRMIJRM2JTYPEAREAS2OOOIOt4004 ~4000~~OJ4410040004041 ~OIOl~~I~~4000~~~04~0000000~044~404~0TIME-DEPENDENT ROOMDATADTDRIRMFLGNPTSTDRTOAMPLTDFREQ~~~004~04~~0~0000~0~0004~~0~~01~1~0014~~~44~4~~~~~~~004~040~404440~00TIMEVERSUSTEMPERATURE DATADTDRTTIMETTEMPRHUMPRES4000~lO~400000000000 ~000~0~0010000I~Oi0000100104000000004J ~OOJJOOOOOJOO ~1~~0~~~0~01440~0~~00400~~~~0~0~0~001004~~~00ii004~000~~00414~~0044~0Ol~~44~~~4044000~0~~~00~4004~00~0401~44~~004~400~~~~0~OOOP01~J40~IIf0THINSLABDATACARD(CARD2OF2)IDSLB2UHT(1)UHT(2) 0000000000 ~00~~~00~000~0000~00~00~0~~~00~000000000~0~~~00000~00~0~0000~0~00LEAKAGEPATHDATA(OMITTHISCARDIFNLEAK=0)IOLEAKI~~~~~~0~0~0IDCIRC0000000000 0A0IDFTR0000000000 H0IOHEATI20000~~000000IDPIPEI00~0~~000~0ARLEAKAKLEAKI.RMlLRM2LO!RN'I.0-1.0I2'I00000000000000~~~~0000~0~~~00~0~0~0~~~000~000000000~000000~00~CIRCULATION PATHDATAKRMIKRM2ELEVIELEV2ARINAROUTAKINAKOUT0000'00~'00000000000000000 ~00~000~0000t0000~0~0~~~~00~00000000IRFLOWTRIPDATAPKFTYPIKFTYP2FTSETIDFP000000000000000000000000000000000 '00F000000000000t00000000ttt EATLOADDATACARDSNUMRITYPQDOTTCWCOOLI4-20000.75.2000.5O.DO-1.0.00000~00~~0000000~~00000000000000 ~~000000000000000000000~PIPINGDATACARDS00000IPREFPODPIDAIODNPLENPEMAINKPTEMPIPHA220.I9.24.50..85.05550.I000'000000000000000tttttt00000 F0000000000t00000000000000 HEATLOADTRIPCARDSSE00~00IDTRIPI~~0~~0~000IOBRKI0000~~0000IOSLBI00000'0IDSLBI~~~~00~00~00IDSLBI0OOOO~~00~~0IHREFITMDTSETTCON2Il.-1.000~0~00~0~0000t00~~0~~~~~~~00~000~000~00000~~~000000000~000~STEAMLINEBREAKDATACARDSBRMBFLPRIBFLGBOOTTRIPONTRIPOFRAMP~0000000t0~t0t0~000~~00~0000000~00~~0000~000000000000t00000000THICKSLABDATACARD(CARDIOF3)IRM'IIRM2ITYPENGRIDIHFLAGCHARL0000000I~~~~ttt~~0000~~~0000000000I ~~0~~00~~00~000~000~tl~00~0000THICKSLABDATACARD(CARD2OF3)ALSAREASIAKSROSCPSEMIS0000~00~0~t~00~000000000 ~~0~0~~~~0000~~~0~~0000~0~~00~00~0~~THICKSLABDATACARD(CARO3OF3)HTCI(I)HTC2(1)HTCI(2)HTC2(2)00000~000~~~00t~tt00~~~0~000t~000~00~~00000000000000000t 000\00THINSLABDATACARD(CARDIOF2) FIGURE4.9COTTAPTEMPERATURE PROFILEFORSAMPLEPROBLEM5120115U)CL110I-LIDCLI-1051002TIME(hr) PPdl.Form2cSln0/83jCat,r973401~E-8-NA:-046R(,,0)Dept.Date19DesignedbyApprovedbyPROJECTSht.No.JL7ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET4.6ComarisonofCOTTAPResultswithAnalticalSolutionforComartmentDeressurization duetoLeakae(SamleProblem6)Acompartment isinitially atapressureof14.7psiaandatemperature 0of150F.Theinitialrelativehumidityissetto0.001sothatthecompartment containsessentially pureair.Thiscompartment (compartment 1intheCOTTAPmodel)isconnected toatime-dependent compartment bymeansof.aleakagepath.Thepressureinthetime-dependent compartment -5isfixedat10psia.Theleakageflowareais0.01ftandthe2associated form-loss coefficient hasavalueof4.0.Leakageisinitiated att=0.Table4.7showstheCOTTAPdatafileforthiscase,andtheCOTTAPoutputiscontained inSectionF.6.Figure4.10showsacomparison oftheCOTTAPresultswiththecorresponding analytical solution~ TSOFOREGROUND HARDCOPY+i+iPRINTED89286.1008DSNAME=EAMAC.COTTAP.SAMPL6.DATA VOL=OSK532 COTTAPSAMPLEPROBLEM6~~4~400440~~0004~00004004~4~1~~0I4~~~~000~~0444400~00~40000~04PROBLEMDESCRIPTION DATA(CARDIOF3)NROOMNSLABINSLA82NFLOWNHEATNTDRNTRIPNPIPENBRKNLEAKI0000I000I~~0~~0~~~~0~~~OO~0J~4400~0~~0~000~04~~~40004444~4~~tO~0~~4~~0~PROBLEMDESCRIPTION DATA(CARO2OF3)~NFTRIPMASSTRMFCPICP2CRIINPUTFIFPRT0I235.04150.10.III~40~000~0~~0010~~0000~0~~40~000~010~~~040~000~004004~404404~00PROBLEMDESCRIPTION DATA(CARO3OF3)4NSHTFC0I.0-5~~014~0~~~~44t~ii0~004~~~~~~4000~~004t~~~0~~~00~~~4410~~00~l~~PROBLEMTIMEANOTRIPTOLERANCE DATA0440~~0~404NCIRCNEC03~0~~~~~4~~RTOL.D-54400444400 44144~400~TTENDTRPTOLTRPEND0.00.20.0054.0~~04~~040~~~~~J0~~4~~~~~00~~~~i4t0~~0000~040~TOLERANCE FORCOMPARTMENT-AIR-FLOW MASS(OMITTHISCARDIFNFLOW=0)~40~Oi0~0~4440~04i~40~44BALANCEI~4DELFLO'I.0-54I~440~~~~0040404~~0444004444~~0~0~~~1~04~4~00~'04~~~40~~~~~0~~40~4~~EDITCONTROLDATACARDS04~0IDECTLASTTPRNTI0.50.0120.60.0135.00.100~~44~40~I440400~~~i~0~~4~0~~~~0~0l~~40004444EDITDIMENSION CARD4~4~4440~~~4440I04~044040I~0~4440441440~44-I04~1044~~4~~00~~~~~~~0~40~4044044~~~~0~4~40~4~0~4I4444~444~4~444~~~4~EDITCARO(S)FORTHICKSLABS~~~404~~~~40~0004~0~4440414000000~~I4~4~~~404~~4444I044404414I0~i0iiyEOITCARDSFORTHINSLABSl~~04~10~4~~0~440~4~~~4444404i4044IO40~~I~4~0404~i114~0~4~~400~II0~040~4REFERENCE PRESSUREFORAIRFLOW(OMITTHISCAROIFNFLOW=O)IReF100.~4~~1~~4~4~4PREF14.7~Oi~~~~4~0~i04~f4440~4~~4044~4ll4ROOMDATACARDSNOTINCLUDETIME-DEPENDENT ROOMS)~~0141444~~0~444~401044t(00NREONSIEDNS2ED200~~4400~00~440~4~4~1~0~~~000~~~~~40410~0~~~44~0~~~004~000~4~~0~044441~ROOMEDITDATACARD(S)DROOMVOLI10000.t~40~40~~~~~PRESTRRELHUMRMHT14.7150.00.00110.0~~~4~~4444I44t~4000~4~0440~0~~444AIRFLOWDATACARDS('HARONFLI04~4441444~~44444~444440P IDFLOWIFROMITOVFLOW11010100000~11~10100~0\1~10~0~1~01000011101111~1~01111101~11011111~10101000LEAKAGEPATHDATA(OMITTHISCAROIFNLEAK=0)KARLEAKAKLEAKLRMILRM2LOIRN0.014.0I-II10~111000000110000000~0000000~0100~0011~0000~1110111010~00000000CIRCULATION PATHDATA001000000~01~01~~~00~~0~00000~000001~100000~~~~~~0110~00~0~001~0AIRFLOWTRIPDATAIOFP000100000100011001 ~0~0000~000000001011000 ~~1~1000100100 ~00010~~0HEATLOADDATACARDS~111~00011~~1111100~00000000000000001~~10101~0~00010111111~~01~0PIPINGDATACARDS1~0~110~0100~1~~~01000~0~0~~~0~~00000~~1~0~0~00~~0~~0~0000001110HEATLOADTRIPCARDSTCON11~~1~~~00~0011~00~10~0~~00~~01001~~~~~00~~~0~001~~0~0~~010000~1STEAMLINEBREAKDATACARDS0~11000~0~0~~010000100000001000000000110~00000000~0000~000000100THICKSLABDATACARO(CARDIOF3)NGRIDIHFLAGCHARLIRM2~~00~1~11~~~00~0~11CPSEMISAREASIAKS1111~00~~0~~~~1101~~~~0~~1~111000~00011~~0~00~1~1~111I~~I1~1111~THINSLABDATACARD(CARDIOF2)IDLEAI010000110IDCIRCKRMIKRM2ELEV1ELEV2ARINAROUTAKINAKOUT011~~10001~IDFTRPKFTYPIKFTYP2FTSET0000000001IDHEATNUMRITYPQOOTTCWCOOL1~1111101IDPIPEIPREFPODPIDAIODNPLENPEMAINKPTEMPIPHASE10100001~IDTRIPIHREFITMOTSET01101010IDBRKIBRMBFLPRIBFLGBOOTTRIPONTRIPOFRAMP~10100111IDSLBIIRMIITYPE~11111~111~1~1~~100~0~~0~~~~~0110000~~00~~1111~~~~~~~1THICKSLABDATACARD(CARD2OF3)0IDSLBIALSROS~1~10101111~100~~0~10000~~~0~00~0~~0~~10~0~~10101~11~00~~01~~~10~10111THICKSLABDATACARD(CARD3OF3)1IDSLBIHTCI(I)HTC2(I)HTCI(2)HTC2(2)10010111CAICD"ICQOCD(O 4IDSL8010140000IOS00100000000IDTDR-I0000400400IDTDR-I2JRMIJRM2JTYPEAREAS200040004~~00000441040~~~00~00000~~004~~THINSLA8DATACARD(CARO2~0~~~~10~4440~0~004404~~~OF2)UH1(I)L82UHT(2)0040400RMFLGNPTSTDRTOAMPLTI30.00.04000010040000000 ~~00~~04044~040~TIMEVERSUSTEMPERATURE DATA0FREQ0.0~000~~~0~0440~00~~400~004TTIM0.010.020.0ETTEMPRHUM150.0.01150.0.01150.0.0114040004000041000040~~00000401000000~000000040 ~04000000400010040 PRESI.D-51.D-51.0-5000404411 ~~00~~~1~~~~1~~0~~0004041~~~044~~~40404~01111114040~04104000~000004000000~000~0~01000~~~0I~~~4~00~0000~~~I~1~4~~4001~~0~04~~~~~4114~10440TIME-DEPENDENT ROOMDATA FIGURE4.10COMPARISON OFCOTTAPCALCULATED COMPARTMENT AIRMASSWITHANALYTICAL SOLUTIONFORSAMPLEPROBLEM6700COI-I-CLC)zV)V)0650600550500450400LegendANALYTICAL 0COTTAP3500.000.050.10TIME(HR)0.150.20 PPdLForm2ddd(15831Cdl.9973401SE-B-NA.-O46R~v.0],Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWERII1LIGHTCOMPANYERNo.CALCULATION SHEET5.REFERENCES 1.Gear,C.W.,Numerical InitialValuesProbleminOrdinarDifferential ~Zations, Prentice-Hall, Englewood Cliffs,Hs,1971,Ch.11.2.Pirkle,J.C.Jr.,Schiesser, W.E.,"DSS/2:ATransportable FORTRAN77CodeforSystemsofOrdinaryandOne,TwoandThree-Dimensional PartialDifferential Equations," 1987SummerComputerSimulation Conference,

Montreal, July,1987.3.Schiesser, W.E.,"AnIntroduction totheNumerical MethodofLinesIntegration ofPartialDifferential Equations,"

LehighUniversity, Bethlehem, PA,1977.4.Lambert,J.D.,Comutational MethodsinOrdinaDifferential ~Eations,1973.,ChapterB.5.Hindmarsh, A.C.,"GEAR:OrdinaryDifferential EquationSystemSolver,"LawrenceLivermore Laboratory reportUCID-30001, Rev.l,August,1972. PPALForm245l(10I83)Car,l9D40'rSF.-B-.>>a.-04bRev.aqDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANfERNo.CALCULATION SHEET6.Hindmarsh, A.C.,"Construction ofMathematical SoftwarePartIII:TheControlofErrorintheGearPackageforOrdinaryDifferential Equations," LawrenceLivermore Laboratory reportUCID-30050, Part3,August1972.7.Hougen,O.A.,Watson,K.M.,andRagatz,R.A.,ChemicalProcess8.Incropera, F.P.,andDeWitt,D.P.,Fundamentals ofHeatTransfer, Wiley,NewYork,1981.9."RETRAN-02 -AProgramforTransient Thermal-Hydraulic AnalysisofComplexFluidFlowSystems,Volume1:TheoryandNumerics," Revision2,NP-1850-CCM, ElectricPowerResearchInstitute, PaloAltoCalf.,1984.10.Kern,D.Q.,ProcessHeatTransfer, McGraw-Hill, NewYork,1950.11.ASHRAEHandbook1985Fundamentals, AmericanSocietyofHeating,Refrigerating andAir-Conditioning Engineers, Inc.,1791TullieCircle,N.E.,Atlanta,GA. ppCLFormitesen0r83)Cat,e973l01eSE-B-NA.=O46Rev.01Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~of.PENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEET12.CRCHandbookofChemistrandPhsics,56thEdition,R.C.Weast,,editor,CRCPress,Cleveland, Ohio,1975.13.ChemicalEnineer'sHandbook, 5thEdition,R.H.PerryandC.H.Chilton,editors,McGraw-Hill, NewYork,1973.14.ASMESteamTables,5thEdition,TheAmericanSocietyofMechanical Engineers, UnitedEngineering Center,NewYork,N.Y.,1983.15.McCabe,W.L.,Smith,J.C.,Unit0erationsofChemicalEngineering, 3rdEdition,McGraw>>Hill, NewYork,1976.16.Lin,C.C.,Economos, C.,Lehner,J.R.,Maise,L.G.,andNg,K.K.,CONTEMPT4/MOD4 AMulticompartment Containment SystemAnalysisProgram,NUREG/CR-3716, U.S.NuclearRegulatory Commission, Washington, D.C.,1984.17.Fujii,T.,andZmura,H.,"Naturalconvection HeatTransferfromaPlatewithArbitrary Inclination," Znt.J.HeatMassTransfer, 15,755(1972). PP&'Lforam2454n$83)Cat.s91340tDept.Date19DesignedbyApprovedbyPROJECTSht.No./25ofPENNSYLVANIA POWER5LIGHTCOMPANYERNo.CALCULATION SHEET18.Goldstein, R.J.,Sparrow,E.M.,andJones,D.C.,"NaturalConvection MassTransferAdjacenttoHorizontal Plates,"Int.J.HeatMassTransfer, 16,1025(1973).19.Hottel,H.C.andSarofim,A.F.,Radiative

Transfer, McGraw-,Hill,NewYork(1967).20.Uchida,H.,Oyama,A.,andTogo,Y.,"Evaluation ofPost-Incident CoolingSystemsofLight-Water PowerReactors,"

Proceedings oftheThirdInternational Conference onthePeacefulUsesofAtomicEnergy,Geneva,Switzerland, Vol.13,p.93(1964).21.Cess,R.D.,andLian,M.S.,"ASimpleParameterization fortheWaterVaporEmissivity", Transactions, ASMEJournalofHeatTransfer, 98,676,1976.22.Hottel,H.C.,andEgbert,R.B.,"RadiantHeatTransmission fromWaterVapor,"Trans.Am.Inst.Chem.Eng.38,531,1942. ppdLForm2I54n0td3)Cd).t973C01$P-gNA.-046Rev02.Dept.Date19DesignedbyApprovedbyPROJECTSht.No.lg6ofPENNSYLVANIA POWER8LIGHTCQINPANYERNo.CALCULATION SHEETAPPENDIXATHERMODYNAMIC ANDTRANSPORT PROPERTIES OFAIRANDWATERThemethodsusedwithinCOTTAPtocalculate therequiredthermodynamic andtransport properties ofairandwaterarediscussed inthissection.A.lPressureofAir/Water-Va orMixtureThepartialpressure'f airwithineachcompartment iscalculated fromtheidealgasequationofstate,P=p10.731(T+459.67)/Maara'hereP=partialpressureofair(psia),ap=densityofair(ibm/ft),3aTcompartment temperature (F),0(A-1)andM=molecular weightofair=28.8ibm/lbmole.aThepartialpressureofwatervapor,P,isalsocalculated fromthevidealgasequationofstate.Thetotalpressurewithinthecompartment, P,isthenobtainedfromr'=P+Prav(A-2) 0)pp&LForm2lS4(10rN)Clt.t973401$f-B-NA.-046Rev01Dept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofpENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETA.'2SecificHeatofAir/Water-Va orMixtureTheconstant-volume specificheatofairCisgivenbyvaandC=C-R/M(A-3)vapaaC=constant-pressure specificheatofair(Btu/ibmR),0paR=gasconstant(1.9872Btu/lbmoleR).0Theconstant-pressure specificheatofairiscalculated from(TableDofref.7)C=0.2331+1.6309x10 T+3.9826x10 Tparr1.6306x10 TrwhereTiscompartment temperature inK.0r(A-4)Similarly, thespecificheatofwatervaporisobtainedfrom(TableDofref.7)C=0.4278+2.552x10TpvZ-72-113+1.402x10T-4.77lx10TZr(A-5) pphLForm245'043)Cat.4973401$F.-BNA.-046Rev.pgDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER8cLIGHTCOMPANYERNo.CALCULATION SHEETwheretheunitsofCareBtu/ibmF,andTiscompartment temperature 0pvr0inK.Themixturespecificheatistakenasthemolar-average valuefortheairandwatervapor;(A-6)wheregandIIIarethemolefractions ofairandwatervaporavrespectively, andMandMarethemolecular weightsofairandwateravvaporrespectively. A.3Saturation PressureofWaterThesaturation pressureofwater,asafunctionoftemperature, iscalculated fromthesaturation-line functiongiveninSection5ofAppendix1ofref.14. opp&LForm2454nN83)Cat.rQU401SE-g-gA=046Rev.ogDept.Date19DesignedbyApprovedbyPROJECTSht.No.~of'PENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETA.4Saturation EnthalyofLiuidWaterandVaorThesaturation enthalpyofliquidwaterandvapor,asafunctionofpressure, iscalculated fromthepropertyroutinesusedintheRETRAN-02 thermal-hydraulics code(Section1II.1.2.1 ofref.9).Theseroutinesaresimplified approximations tothefunctions givenintheASME1967steamtables.A.SSaturation TemeratureofWaterThesaturation temperature ofwater,asafunctionofsaturation pressureandsaturation

enthalpy, iscalculated fromtheRETRAN-02 propertyroutine(SectionZZI.1.2.2 ofref.9).A.6SecificVolumeofSaturated WaterandVaorThespecificvolumeofsaturated liquidandvaporiscalculated fromtheRETRAN-02 propertyroutines(SectionIZI.1.2.3 ofref.9).Theroutinesgivesaturated specificvolumeasafunctionofsaturation pressureandenthalpy.

PPALForm245'10rLO Cot.N973l01Dept.Date19DesignedbyApprovedbyPROJECTSht.No.LB0ofPENNSYLVANIA POWER8rLIGHTCOMPANYERNo.CALCULATION SHEETA.7Coefficient ofThermalExansionforAir/Water-Va orMixtureThecoefficient ofthermalexpansion, 8,fortheair/water-vapor mixtureisdefinedas9=1BvvBTPrrwherev=specificvolumeofair/water-vapor mixture,(A-7)andP=compartment pressure', rT=compartment temperature (R).0ZEvaluation ofeq.(A-7)withtheassumption ofidealgasbehaviorfortheair/water-vapor mixturegives9=1TZ(A-8)A.SViscositofAir/Water-Va rMixtureTheviscosity oftheair/water-vapor mixtureiscalculated from(ref.13p.3-249)u=(Viri+uP]/[HM+9M]1/21/2(A-9) PP&LForm245'$83)Cal.t973i0rSf,-Q-.ISA=046ReV.PgDept.Date19DesignedbyApprovedbyPENNSYLVANIA POWER8cLIGHTCOMPANYCALCULATION SHEETPROJECTERNo.Sht.No.~3ofwheremviscosity ofairandwatervaporrespectively a'(ibm/hr-ft),andIII,ftI=molefractionofairandwatervaporrespectively, a'M=molecular weightofair(28.8ibm/lbmole),aM=molecular weightofwatervapor(18ibm/lbmole).vandparedetermined byfittingstraightlinestothedatagiveninavTablesA.landA.2.temperature areTheequations whichgiveuandpasfunctions ofavp=0.0413+(7.958x10 )(T-32),ar(A-10)andp=0.0217+(4.479xl0 )(T-32),vr(A-11)wherepandphaveunitsofibm/fthrandTiscompartment temperature avr0inF. PPKLForm2454<1182)C41.4023401,, ia$E-8-.NA=046Rev.PZDept.Date19DesignedbyApprovedbyPROJECTSht.No.~ofPENNSYLVANIA POWER&LIGHTCOMPANYERNo.CALCULATION SHEETTableA.lViscosity ofAirViscosity ofAir*(ibm/fthr)Temperature (F)0.04130.051932165.2*Datafromref.12,p.F-56TableA.2Viscosity ofWaterVaporViscosity ofWaterVapor*(ibm/fthr)Temperature (F)0.02170.029032195*Datafromref.14p.294. PP&LForm24&4(l(VN)Ctt.t973401Bg<.-046Rev.0gDept.Date19DesignedbyApprovedbyPROJECTSht.No.333ofPENNSYLVANIA PONER&LIGHTCOMPANYERNo.CALCULATION SHEETA.9ThermalConductivit ofAir/Water-Va orMixtureThethermalconductivity, k,oftheair/water-vapor mixtureasafunctionoftemperature andcomposition iscalculated from(ref.13,p.3-244)(A-12)wherek,k=thermalconductivity ofairandwatervapora'respectively, andg,Izi=molefractionofairandwatervaporrespectively, a'M=molecular weightofair(28.8ibm/lbmole), aM=molecular weightofwatervapor(18ibm/lbmole) .vThecomponent conductivities aredetermined fromlinearcurvefitsofthedatagiveninTablesA.3andA.4.Thecurve-fit equations forthecomponent thermalconductivities areandk=0.0140+(2.444x10 )(T-32)ga(z-13)k=0.010+(2.00x10)(T-32),-awherekandkhaveunitsofBtu/hrftFandTisinF.00av(A-14) PPE1Form2454n0/N)Cat.N973401A$F.-8NA=046Rev.01Dept.Date19DesIgnedbyApprovedbyPROJECTSht.No.~l~ofPENNSYLVANIA POWERScLIGHTCOMPANYERNo.CALCULATION SHEETTableA.3ThermalConductivity ofAirThermalConductivity ofAir(Btu/hrftF)Temperature (F)0.01400.018432212 pp&LForm24s4n0/s3)Cat.t973401$Q-8-NA=046ReV.QgDept.Date19DesignedbyApprovedbyPROJECTSht.No./~~ofPENNSYLVANIA POWER8LIGHTCOMPANYERNo.CALCULATION SHEETTableA.4ThermalConductivity ofWaterVapor*ThermalConductivity ofWaterVapor(Btu/hrftF)Temperature (F)0.0100.013632212*ValuesfromAppendix12ofref.15andp.296ofref.14. ATTACHMENT 8 "C,iC~,gia~4'ahae1}}

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