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Fog Inerting Analysis for PWR Ice Condenser Plants.
	ML17320A791
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Site:	Cook
Issue date:	11/30/1981
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.FOGINERTIHGANALYSISFORPMRICECONDENSERPLANTSBYS.S.TSAICOREANDCONTAINMEHTANALYSISNUCLEARSAFETYDEPARTMENTWESTINGHOUSEELECTRICCORP.NOYEHBER19818310140042831010PDRADOCK050003i5PPDR0430Q:1 ABSTRACT.TherecenthydrogenburntestconductedattheLawrenceLivermoreNationalLaboratoryhasraisedtheNRCandtheicecondenserplant'ownersconcernaboutfoginertingprobabilityandconsequencesinicecondenserplants.Thepresentinvestigationisaimedatresolvingthisfoginertingissue.Inthisreport,majorfogformationandremovalmechanismsthatexistinthepost-accidenticecondensercontainmentareidentifiedandquyntified.Methodologieshavebeendevelopedforpre-dictingfogformatiopandremovalratesandforpredictingfogconcen-trationsinvariouscompartmentsinanicecondensercontainment.Thismethodologydevelopmenthasresultedintwocomputerprograms,FOGandFOGMASS.TheFOGcomputerprogramemploystheHijikata-Moriboun-darylayerfogformationtheory,andcalculatesthefogformationratesduetoboundarylayerandbulkstreamcondensation.Thecomputerpro-gramFOGMASSsolvesthemassconservationequationsforfogdropletsandcalculatesthefogconcentrationsinvariouscompartments.Bothcompu-terprogramshavebeenusedtopredictfogconcentrationsinthe'equoyah,McGuire,andD.C.Cookcontainments,usingtheCLASIXoutputdataforaS>Daccidentsequence.Inordertoutilizethec'alculationalresults-fromthestudy,afoginertingcriterionhasbeenestablished.Thiscriterionusesthehydro-genconcentration,volumemeandropsize,andfogconcentrationtodefinethefoginertingregime.Foragivenhydrogenconcentration,theminimumfoginertingconcentrationwasfoundtovarywiththesquareofthevolumemeandropsize.ThiscriterionhasbeenverifiedbytheFactoryMutualrecentfoginertingtestdata.Theapplicationofthefoginertingcriteriontothethreeicecondenserplantsshowsthatfoginertingwouldnotexistintheupperandlowercompartments.Foginertingintheicecondenserupperplenumathydro-genconcentratonsatwhichglowplugignitersaredesignedtooperateisveryunlikely.0430Q:I TABLEOFCONTENTSSectionTftle~PaeABSTRACTTABLEOFCONTENTSLISTOFTABLESLISTOFFIGURES1V1.02.03.0',BACKGROUNDINTRODUCTIONFOGGENERATINGMECHANISMSINAHICECONDENSERCONTAINMENT3.1FogGeneratedbyBreakFlow3.1.1AmountofFogGeneratedbyBreakFlow3.1.2DropSizesGeneratedbyBreakFlow3.2HucleationofFogDropletsinContainmentAtmosphere3.2.1NucleationTheories3.2.1.1ClassicalTheoryofHomogeneousNucleation3.2.1.2HeterogeneousNucleationTheory3.2.2FogFormationConditions3.2.3ConditionsforFogFormationNearaColdSurface.3.2.4RateofFogFormation3.2.5FogDropSizes3.3FineMistDropletsFromContainmentSprays2-13-13-13-33-53-63-73-73-93-103-123-153-193-194.0FOGREMOVALMECHANISMSIHAHICECONDENSERCONTAIHMEHT4.1SettlingDuetoGravity4.2Agglomeration4.3Vaporization4.4RemovalbySprayDrops4.5OtherRemovalMechanisms4-10430Q:1 TABLEOFCONTENTS(Continued)SectionTitle~Pae5.0FOGINERTIHGCRITERIA5.1PreviousMork5.2PresentTheory5.3VerificationofTheoriesbyExperiments5-15-25-66.0ASSESSMENTOFFOGINERTINGPROBABILITYIHICECONDENSERCOHTAINMEHTS6.1DeterminationofVolumeFractionofFogDropletsinIceCondenserContainmentSubcompartments6.1.1Calculationofmbreak6.1.2Calculationof6.1.3Calculationofmset6.1.4Ca1culationofmsP6.2FogInertingProbabilityintheSequoyahPlant6.3FogInertingProbabilityintheMcGuirePlant6.4FogInertingProbabilityintheD.C.CookPlant6.5EffectofFogonGlobalCombustion6-16-16-56-66-66-76-76-236-376-507.0SUMMARYANDCONCLUSIONS7-1ACKNOWLEDGMENTS7-3REFERENCESR-1APPENDIXAA-1APPENDIX8B-10430Q:1 ifl LISTOFTABLESTableNo.Title~Pae6.1FOGInputDataforSequoyahLowerCompartment6-18'.26.3FOGInputDataforSequoyahIceCondenserGeometricDataforSequoyahContainment6-196-206.4MARCHPredictionofReactorCoolantMassandEnergyReleaseRatefortheS20Sequence.6-216.5IntercompartmentalFlowRates(ft/sec)3PredictedbyCLASIXforSequoyah6-226.6FOGInputDataforMcGuireLowerCompartment6-336.7FOGInputDataforHcGuireIceCondenser6-346.8GeometricDataforMcGuireContainment6-356.9IntercompartmentalFlowRates(ft/sec)PredictedbyCLASIXforHcGuire6-366.10FOGInputDataforD.C.CookLowerCompartment6-466.11FOGInputDataforD.C.CookIceCondenser6-476.12GeometricDataforD.C.CookContainment6-486.13IntercompartmentalFlowRates(ft/sec)PredictedbyCLASIXforD.C.Cook6-49iv0430Q:1 LISTOFFIGURES~FiureNo.Title~Pae3.1T-SDiagramforReactorCoolantDischargedFromBreak3-43.2~VaporPressureandTemperatureProfileHearaColdSurface3-143.3FormationofFogHearaColdSurface3-163.4DropSizeDistributionPredictedbyHeiburgerandChien3-203.5ParticleSizeDistributionfor50PSIPressureDropAcrossHozzleNo.17133-214.1TerminalVelocityasaFunctionofDropRadiusinSteam-AirAtmospheres4-54.2AgglomerationRatesinAirBetweenEqual-SizedDrops5.1MinimumIgnitionEnergiesandQuenchingDistance5-3forHydrogen-OxygenInertGasMixturesatAtmo-sphericcPressure5.2TheEffeetofDropletSpacingonFlameQuenching5-45.3SchematicRepresentationofTemperatureProfileThroughtheFlameFront5-7TheParameterWe.gasaFunctionof1(Y-Yf)/e~forDifferentValuesofKei5-70430Q:1 f)i' LISTOFFIGURES(Continued)~FiureNo.Title~Pae5.5(K).te.attheFlammabilityLimitasaFunctionof(Yu-Yf)/ei5-85.65.7ComparisonBetweenTheoriesandFactoryMutualFogInertingExperimentson4.76PercentH2r'IComparisonBetweenthePresentTheoryandFactoryMutualFogInertingExperimentson7.2PercentH25-105-115.8ComparisonBetweenthePresentTheoryandFactoryMutualFogInertingExperimentson7.9PercentH25-126.1SequoyahCLASIXContainmentModel6-86.2FogFormationinTVASequoyahLowerCompartment6-106.3FogFormationinTVASequoyahIceCondenser6-116.46.5FogConcentrationinSequoyahContainmentMcGuireCLASIXContainmentModel6-146-246.6FogFormationinDukeMcGuireLowerCompartment6-256.7FogFormationinDukeMcGuireIceCondenser6-266.8FogConcentrationinMcGuireContainment6-296.9D.C.CookCLASIXContainmentModel6-380430Q:1 LISTOFFIGURES(Continued)Title~PaeFogFormationinAEPCookLowerCompartment6-29FogFormationinAEPCookIceCondenser6-406.12FogConcentrationinD.C.CookContainment6-43vii0430(}:I 1.0BACKGROUNDTheincidentatThreeMileIslandhasdemonstratedthatasignificantamountofhydrogencouldbegeneratedduringcoredegradation.ThisexperienceraisedHRCconcernaboutthesafetyofnuclearpowerplants,intermsoftheircapabilitytocontrolhydrogenduringsevereacci-dents.Sinceicecondenserplantshavearelativelysmallvolumeandlowcontainmentdesignpressure,theproblemismagnified.Therefore,theNRChasrequestedtheicecondenserplantownerstostudyhydrogencontrolmethodsforuseintheirplants.Inthisregard,theTennesseeValleyAuthority(TVA),DukePowerandAmericanElectricPower(AEP)haveproposedtheuseofglowplugignitersatvariouslocationsinsidetheiricecondensercontainmentstoignitehydrogenatlowconcentration.Recently,theNRCrequestedLawrenceLivermoreNationalLaboratory(LLNL)tocarryoutexperimentsontheseigniterstodeterminetheireffectiveness.Intheseexperiments,twotestswithhighsteamconcentrationseemedtoindicatethatsubstantialfogformationcouldoccurwhensaturatedsteamis'ischargedintoaunheatedvesselandundersomeconditionsfogcouldeffectivelyprecludehydrogenfromcombustionTheLLHLtestsraisedsomedoubtsabouttheeffectivenessofglowplugignitersunderfogformationconditions.Inarecentreviewofhydrogenrelatedissuesforicecondenserplants,theHRChasraisedseveralquestionsconcerningtheprobabilityandconsequencesoffogformationandsteamsupersaturationinicecondenserplants.Inresponseto'theNRCquestions,TVA,AEP,andDukeestablishedexperi-mentalandtheoreticalanalysisprogramstostudythefoginertingprob-lem.TheexperimentalprogramwascontractedtoFactoryMutual.Theexperimentsweredesignedtotestglowplugigniter'sperformanceunder4differentfoggingconditions.Atthesametime,theplantowners.requestedWestinghousetoperformfoginertinganalysesfortheSequoyah,McGuire,andD.C.Cookplants.ThisreportpresentstheresultsoftheWestinghousestudies.0430Q:1 ae

2.0INTRODUCTION

Fromthepost-testanalysisoftheLLNLfpdrogenburntests,itappearsthatsubstantialfogformationoccurredinsidethetestvessel.Gen-erally,fogdropletsareonlyfewmicronsindiameter.Thesesizesofdropletshavepotentialtopreventafl'ammablegasmixturefromcombus-tionorquenchapropagatingflame.Thisisbecausethesesizesofdropletsvaporizeveryfast(ontheorderofmiliseconds),absorbinganenormousamountoftheheatreleasedfromcombustionifasubstantialquantityofthesedropletsispresentintheatmosphere.Incomparison,largewaterdropletsintherangeoffewhundredmicronsorlarger(e.g.spraydroplets)havenoinertingeffectoncombustionandhencehaveinsignificanteffectonglowplugigniter'sperformance.There-fore,thepresentanalysiswillbeconcentratedonthegenerationandremovaloffog(mist),anditsimpactontheglowplugignitersystem.Thereareanumberoffoggenerationandremovalmechanismspresentinapost-accidenticecondensercontainmentatmosphere.Thefoggenerationmechanismsincludefoggeneratedbythebreakflow(ifitistwo-phase),fogformationneartheiceandstructuralheatsinksurfaces(sincethesurfacetemperaturescouldbewellbelowthedewpoint),andfoggenera-tionduetohomogeneousandheterogeneousnucleationincondensingbulkstreams.Thefogremovalmechanismsincludegravitationalsettling,agglomera-tion,vaporizationandremovalbyspraydroplets.Inordertoestimatethepost-accidentfogconcentrationsinicecondensercontainments,thesecompetingmechanismsmustbestudied,andevaluated.Tosolvethisproblem,itrequiresanumericalintegrationofthemassconserva-.tionequationsforthemistdropletsinthevariouscontainmentsubcom-partments.Bymakingsomesimplifyingassumptionsthetransientfogconcentrationinthevarioussubcompartmentshavebeenestimated.0430QI2-1 Theanalysispresentedhereconsidersallthefogremovalandgenerationmechanismspreviouslydescribed.Inaddition,itconsidersthefogentrainmentintheintercompartmentalflows(includingfanflows)inthefogmassconservationequations.InordertoperformthisanalysisitwasnecessarytouseCLASIXresultsforaS2Deventasboundarycondi-tionstotheproblem.Inadditiontocalculationoffogconcentrationsin'variouscontainmentcompartments,itwasnecessarytoestablishafog'inertingcriterion.AfoginertingcriterionhasbeenproposedbyBermanetal.,whichpre-dictstheminirpumfogconcentrationrequiredtoinertagivenhydrogenconcentrationandgivenvolumemeanfogdropsize.Thiscriterionseemstooverpredicttheminimumfoginertingconcentration,whencomparedwithexperimentaldata.Amorerealisticfoginertingtheoryispresentedinthepresentstudy.Thefoginertingmethodology,analysis,andresultsarepresentedinthefollowingsectionsofthisreport.Sections3and4presentthe,method-ologyforcalculatingthefogformationandremovalrates.Section5givesthefoginertingcriteria,andSection6presentstheresults.0430Q:I2-2 i'0 3.0FOGGENERATINGMECHANISMSIHAHICECONDENSERCOHTAINMEHTTheinertingcapabilityoffogdropletsdependsontheirsizesandcon-centrationinthecontainmentatmosphere,aswellasthehydrogencon-centration.Thissectionisintendedtoidentifyvariousfoggenerationmechanismspresentinanicecondensercontainmentandtodeterminethedropsizesandtheratesoffoggenerationfromthesemechanisms.Threefoggenerationmechanismsarediscussedinthissectionandthedominantfoggenerationmechanismsareidentified.3.1FOGGENERATEDBYBREAKFLOWThepost-LOCAcontainmentatmosphereismostlikelytobeadrop-ladenatmosphere.Thelarge-scalesimulatedLOCAexperimentsconductedtodatehavedirectlyorindirectlyconfirmedthepresenceoftwo-phaseatmospheres.Forexample,MarvikkenandBattelle-Frankfurt(3)experimentswereinstrumentedtomeasurefluiddensitiesandwaterlevelsinvariouspartsofthecontainment.Therefore,foggenerationbythebreakflowcannotbeneglected.ThefollowingdiscussionofthisphenomenonpertainstosmallLOCAs.IntheearlystageofasmallLOCAtransient,asubstantial.portionoftheprimarycoolantdischargedfromthebreakwillremainasliquid.Becauseofthesuperheatandhighvelocity,thisliquidwillbeframen-tedbyaerodynamicforcesandhomogeneousnucleationmechanisminto'malldroplets.Thesedropletsareexpectedtobeentrainedbytheintercompartmentalandfanflowsandspreadtootherpartsoftheicecondensercontainment.Duringtheirtravelthroughoutthecontainment,thefogdropletswillberemovedbygravitationalsettling,sprays,andvaporization.Thefoggene'rationperiodlastsuntilthewaterlevelinthereactorvesselfallstothebreakelevationandthebreakflowisnolongertwo-phase.'ortheparticularS<Dsequenceanalyzedby0430Q:I3-1 CLASIX,thisperiodlastsforabout36minutesandabout4.2x(5)10lbsofwaterhasbeendischargedintothelowercompartmentduring5thisperiodof-time.Afterthewaterlevelinthereactorvesselfallsbelowthebreakeleva-tion,thebreakflowrateissubstantiallyreduced.Theflowisessen-'iallysteamandnofogdropletswillbegenerated.Asaresult,thelowercompartmentbecomessuperheatedafterward.Fogdropletsmayvaporizeduringtheirtravelthroughthiscompartmentandsubstantialremovalofmistdropletsareexpected.Largesuspendeddropsgeneratedbythebreakflowwillberemovedveryquickly.bygravitationalsettlingandimpingement.Forthedropslargerthan20u,theremovalrateishighandcompleteremovalonlytakesafewseconds.Forthesmallestdrops(lessthan1u)theterminalveloc-ityissosmallthattheyvirtuallyremainsuspendedintheatmosphereindefinitely.Theonlyeffectiveremovalmechanismsforthesesizesofdropsarevaporization,andcollisionwithlargerspraydrops.Theweightfractionofthesesizesofdropsisestimatedtobe1per-centgeneratedbythebreakflow.Thepopulationofthesesmall(3)dropscanincreaseifnucleationofembryosoccursinasaturatedatmo-sphere.0430Q:13-2l 3.1.1AMOUNTOFFOGGENERATEDBYBREAKFLOW~~Asdiscussedpreviously,theexistenceofatwo-phasedrop-ladenregimehasbeenobservedexperimentally.Ina.smallLOCA,flashingofprimarycoolantatthebreakandsubsequentvaporizationofblowdownliquidrepresentaseriesofchangesofthermodynamicstates.Sincethereac-torcoolantpressureishigh,thebreakflowwillbechoked.Theaccel-erationofprimarycoolanttothebreaklocationisessentiallyanisen-tropicprocess,inwhichthepressuredecreasestothepointatwhichsubstantialhomogeneousnucleationoccurs.Whentheflowleavesthebreak,theliquidisframentedbyboththeaerodynamicforcesandthenucleationmechanismintosmallfogdroplets.Thesefogdropletscon-tinuetovaporize,becauseofthesuperheatinthedroplets,untilathermodynamicequilibriumstateisreached.Becauseofthehighsuper-heatandlargeaerodynamicforces,itisexpectedthatthefogdropletsgeneratedareverysmall.Thisvaporizationprocessisessentiallyisenthalpic.Theexistenceofatwophasedrop-ladenregimecanalsobeexplainedbyuseofaT-SdiagramforsteamasshowninFigure3,1(Figure1ofReference6).Itisshowninthisfigurethattheblowdownliquidgoesthroughaseriesofthermodynamicstates,startingfromthesubcooledliquidstateB.Theliquidexpandsisentropicallyfromthesubcooled0state8tothestateB>atthebreak,whereatwo-phasecriticalflowisdeveloped.Atthesametime,temperaturechangesfromTtoTI.Afterleavingthebreak,thedropletscontinuetovaporizebecauseofexcessivesuperheatuntilfinallyanequilibriumstateB<isreachedatwhichthedropletsareinthermalequilibriumwiththeirsurroundings.Thisvaporizationprocessisessentiallyisenthalpic.Atthistime,thedroplettemperaturedropstoT>andtheatmospherictemperaturealsorisestoT>.ForasmallLOCA,theequilibriumtem-peraturevarieswithtime.AccordingtotheCLASIXanalysisoftheSequoyahplant,thelowercompartmentgastemperaturerisesquicklyfrom100"Ftoapproximately200"Fandthenstayatthistemperatureforanextendedperiodoftime.Usingthesetemperaturesasfinalequilibrium0430QI3-3

-Kg/cm210010'r450400350300025020015010050600400300g200100ijI/tA200.00.2~0.40.60.8X=1FIGURE3.1T-SDIAGRAMFORREACTORCOOLANTDISCHARGEDFROMBREAK

.temperaturesforwaterdroplets,theweightfractionofwaterdropletsinthebreakflowisapproximately50percent,whichisconsistentwiththeMARCHcalculations~7~ofthebreakflowrateanditsenergyreleaserate.Thediscussiongivenaboveisvalidonlywhentheinitialstate'ofthebreakflowissubcooledorsaturatedliquid.Afterthewaterlevelinsidethereactorvesselfallsbelowthebreakelevation,thebreakflowwillbesteam.Themoisturecontentofthesteamwillbeverylow,eventhoughisentropicexpansionmayleadtohomogeneousnucleationandsubsequentcondensationinthevaporstream.Dependingonthesuper-saturationthatcanbeachievedinthisisentropicexpansion,aconden-sationshockispossiblewhencritical'supersaturationisreached.However,itisbelievedthatthefogdropletsgeneratedbyhomogeneousnucleationinthissupersonicjetisnegligibleascomparedtootherfoggeneratingmechanisms.Hence,itwillbeneglectedinthispresentanalysis.Therefore,thefoggenerationbythebreakflowisconsideredpossibleonlywhenthewaterlevelinthereactorvesselisabovethebreakelevation.AccordingtotheMARCH~"~calculationat2172secondsintotheacci-dent,thewaterlevelinsidethereactorvesselfallsbelowthebreakelevationfortheS2DcaseanalyzedinReference7.Bythistimeapproximately421,000lbsofwaterhasbeendischargedfromthebreakand56percentofthisdischargedfluid,i.e.,236,000lbs,willbesus-pendedintheatmosphereascondensate.However,mostofthesedropletswilllaterberemovedbygravitationalsettling,sprays,andvaporiza-tion.3.1.2DROPSIZESGENERATEDBYBREAKFLOWTheflashingjetexperimentconductedbyBrownandYork~B~hasindi-catedthatthedropsizesproducedbyflashing.liquidaresmall.Theyderivedacorrelationforthelinearmeandropsizebasedonthetestdata.Thecorrelationshowsthatthemeandropsizeisinverselypro-portionaltotheWebernumberanditdecreaseslinearlywithincreasing0430Q:I3-'5 superheat.However,thiscorrelationisapplicableforliquidsuperheatlessthan75'Fanditcannotbeextrapolatedtothelargesuperheatofthereactorcoolant.However,someconclusionconcerningthedropsizesproducedbyblowdownofthereactorcoolantcanbedrawnforthiscondi-tion.,ThebreakflowhasmuchlargersuperheatandWebernumberthanthoseusedinthisexperiment;therefore,thedropsizesproducedbythebreakflowshouldbemuchsmallerthan-50'bservedinthisexperi-ment.GidoandKoestelhavedevelopedamethodforestimatingthe.drop(9)sizeleavingthefragmentation/evaporationzoneofablowdownjet.Thismodelisbasedontheassumptionthatdropswithan'internal.temperaturedifferenceoflessthan5Kwillescapefragmentation.Thismodelhasbeenverifiedbythelowsuperheat,dataofBrownandYork.ApplicationofthismethodtotheLOCAconditionshowsthatthemaximumattainabledropsizeis7p(thismeansthatarlydropsizelargerthan7pwillnotescapeframentationbyhomogeneousnucleation).Thecorrespondingmeandropsizeisabout4p,basedontheobservationofthelargestdropsizeandmeandropsizeintheexperimentreportedinReference8.However,thisvolumemeandropsizeisnotusedinthepresentanalysis.Instead,thepresentanalysisuses10pmeandropsize,.consideringthedropagglomerationeffect.3.2NUCLEATIONOFFOGDROPLETSINCONTAINMENTATMOSPHERENucleationofwaterembryosfromthehomogeneousvaporphaseplaysanimportantroleinmistgenerationinicecondenserplants.Nucleationisaprocessbywhichtinywaterembryosorcondensationnucleiareformedfromapurevaporphaseatarapidrate.Inincipienthomogene-ousnucleation,thelocalgastemperaturedropsbelowthedewpointcorrespondingtothelocalsteampartialpressureandsomedegreeoflocalsupersaturationisneeded.Thedegreeofsupersaturationneededtostartnucleationdependsonthenumberofcondensationnucleipresentinthecontainment.Thesecondensationnucleicouldbeverysmallwaterdropletsordustparticles.Ifsufficientnumberofcondensationnuclei0430Q:I3-6 exist,supersaturationcouldbesmall.Itislikelythattheicecon-densercontainmentcontainsasubtantialnumberofdustparticlessuchthatlittlesupersaturationisneededfornucleation.Thissectionisdevotedtothediscussionoffogformationbyhomogene-ousorheterogeneousnucleation.Theclassicalnucleationtheoriesareusedtoexplainthenucleationphenomenon.3.2.1NUCLEATIONTHEORIESTheprocessofn0cleationofanembryowaterdropisimportantinunder-standingthemechanismoffogformationinicecondenserplants.Twotypesofnucleationprocess,namely,homogeneousandheterogeneousnucleations,andtheirtheorieswillbediscussedinSection3.2.1.3.2.1.1CLASSICALTHEORYOFHOMOGENEOUSNUCLEATIONl)Whenanembryodroplet,usuallyassumedspherical,isformedfromcon-densationofwatervapormolecules,itsfreeenergychanges.ThechangeoffreeenergycanbeexpressedasaG=4xra"(4/3)xrnLKTZn(p/p)whereaisthesurfacefreeenergyperunitarea,orsurfacetension,risthedropradius,Pisthevaporpressure,P;sthesaturation0PressureatthedroPlettemPerature,nLisnumberofmoleculesper,unitvolume,KistheBoltzmanconstant,andTisthedroptemperature.ThesupersaturationS,isdefinedasP/P.Equation(3.1)representsafreeenergybarriertothegrowthofthedropsatagivensuprsaturation.AtmaximumaG,thecriticalradiusr"canbeobtainedfromEquation3.1asr*200430/:13-7 r1',i~I Thedropsofthecriticalsizecanbeconsideredascondensationnuclei~~~~~~~~~~~~~~~sinceatthissizethedropswillgrowwithnochangeinfreeenergy.Thiscriticalsizerepresentsanequilibriumsizeatwhichasupersatu-ratedvaporatvaporpressurePisinequilibriumwiththiscriticaldropatalowersaturationpressureP.However,thisequilibriummodeisunstable.Forexample,ifadropofthecriticalsizeorigi-nallyinequilibriumwiththesurroundingvaporsuffersasuddensmallincreaseinsizeduetocondensation,then(ifthedroptemperaturedoesnot,change),Equation3.2showsthattheequilibriumpressure,P,onitssurfacewilldecrease.Therefore,theactualvaporpressurewillthenbegreaterthantheequilibriumvalueandfurthercondensationwilloccur.Thisiswhythedropofthiscriticalsizeiscalledcondensa-tionnucleus.Thenucleationrateofcritical-sizedembryoscanbeobtainedfromthekineticsofanonequilibriumdistributionofembryos.Theclassicalnucleationtheoryshowsthatthereisaverysuddenincreaseinthenucleationratewhenpastacertaincriticalvalueofsupersatura-tion.AnextensivevalidationofthenucleationtheorywasconductedbyVolmerandFloodinanexperimentinwhichanumberofvaporswereexpandedtovisiblecondensationinacylinder.Theobservedcriticalsupersaturationsagreedsuprisinglywellwiththeoryinnearlyallcases,includingwatervapor.Criticalcondensationnucleisizestypicallyrangefrom10to100atoms.Thesesizesareconsiderablysmallerthanthemeanfreepathofthevapormoleculesandthereforetheratesofmassandheattransferat'thedropsurfacecannotbepredictedbybulktransporttheories.Inthiscase,thekinetictheoryofgasshouldbeusedtopredicttheratesofmassandheattransferatthedropsurface.Startingfromthekinetictheoryofgasandtheenergyconservationequation,therateofgrowthofacondensationnucleuswasobtainedbyHilletal.Itwasfoundthatthegrowthrateisontheorderof10ft/sec.Therefore,ittakesonlyaboutImilisecondforthecondensationnucleustogrowtoafogdropletsizeofIp.0430QI3-8 3.2.1.2HETEROGENEOUSNUCLEATIONTHEORYAnothermechanismofformingembryosisheterogeneousnucleationonforeignparticlesthatcouldsuspendinthecontainmentatmosphere.Theseparticlesmayserveasnucleationsitesforvaporandthusenhancethenucleationrate.Thesourceofforeignparticlesinthecontainmentfollowingcoredegradationcouldcomefromfissionproductaerosolsanddustparticles.Thesizedistributionoftheseparticlesareimportantbecausethesupersaturationrequiredtoformembryosdependsonparticlesizes.AtypicalsizedistributionofatmosphericaerosolsisthatofeJunge,takenfromsurveysmadenearFrankfurtA.H.,German.Thesurveysfoundthatthesizerangeofdustparticlesisfrom0.01toIIntherangefrom0.01to0.5p,therearebetween100and10,000particlespercubiccentimeter.Amajorityofparticleshavesizessmallerthan1micron.Atthesmallestsizeof0.01p,thecriticalsupersaturationisabout1.02andatthelargestsizethesupersatura-tionisonly1.001.~~Theothersourceofaerosolparticulatesisfission,products.Duringnormaloperation,theprimarycoolantcontainsverylittlefissionpro-ducts.However,alargereleaseoffissionproducts,suchasthegaprelease,couldoccurataboutthesametimethehydrogenreleases.Theamountoffissionproductsreleasedtothecontainmentdependsonacci-dentscenarios.ThedistributionandtransportoffissionproductsinthecontainmentcanbepredictedbytheCORRALcode~~.Thesizedistributionoffissionproducts.inthecontainmentcanbeextrapolatedfromtheCSEexperiments~4~.Theseexperimentsindicatedthatsoonafterfissionproductrelease,themeanparticlediameterwas15p.Afewhourslater,themeandiameterdecreasedtoabout5pbecauseofsettlingoflargeparticlesontothefloor.Thesesizesaresubstan-tiallylargerthanthoseofdustparticlesandtherefore,criticalsupersaturationisevensmallerthanvaluesquotedaboveforthedustparticles.0430Q:13-9 Theatmosphericaerosolsconsistofparticulatesofvarioussizes,vari-ouschemicalcomponents,andvariouselectrostaticcharges.Theaerosolparticulatescouldbesolubleorinsolubleinwater.Alltheseproper-tiescouldaffecttherequiredsupersaturationfornucleation.Inthecaseofinsolubleparticulates,thecontactangle,6,betweenthe"embryoandtheparticlesurfaceisimportant.Iftheparticleiscom-pletelywettable,6="0,itformsabaseonwhichasmallamountofwatercan.formadropoflargeradiusofcurvatureandthussatisfytheHemholtzequation(Eq.3.2)atamuchlowersupersaturationthanwouldbethecaseifsamenumberofmoleculesformadropwithaparticlecore.FletcherdevelopedarelationshipbetweenthesupersIatura-(I')tionanddropradiusforseveralvaluesofcontactangle,assumingthattheparticleisspherical.Competelywettable,aparticleof1micronorso,whencoveredwithafilmofwater,istheoreticallyatthecrit-icalradius,anditneedsonly1.001criticalsupersaturation.Thepost-accidentcontainmentatmosphereislikelytocontainasubstan-~~~~~tialamountofaerosolparticles.Theseparticleswillactascondensa-i)tionnucleiandtherefore,littlesupersaturationisrequiredtopre-cipitatecondensation.3.2.2FOGFORlCTIONCONDITIONSFogformationinamixture'fvaporandnoncondensiblegaseshasbeenofinteresttometeorologists,andturbineandcondenserdesigners.Fogisformedbyhomogeneousorheterogeneousnucleationasaresultoftem-peraturedropbelowthedewpoint(sometimeswithconcommitantpressuredrop).Duringthetemperaturedrop,alocalgaselementwillgothroughaseriesofthermodynamicstates.Eventually,astateisreachedatwhichincipientfogformationoccurs.Somedegreeofvaporsupersatura-t'ionisneededtoprecipitatefogformation.Thevaporsupersaturationatwhichrapidnucleationofvaporfirstappearsiscalledcriticalsupersaturation.Thecriticalsupersaturation,ingeneral,isa0430Q:13-10 efunctionoftemperature,vaporproperties,mixingtime(ifamixingprocessisinvolved),andconcentrationandsizesofforeignparticles.ThecriticalsupersaturationdataforwaterhasbeengiveninReference15.Fogformationinanicecondensercontainmentasaresultofhomogeneousorheterogeneousnucleationcouldoccur:(i)insidethethermalboun-darylayernearacoldsurface,(ii)inadiabaticornearlyadiabaticexpansionofvaporjet,and(iii)inmixingofahotvaporstreamwithanothercoolergas.Surfacecoolingmaycreatearegionoflocalsupersaturationwithinthethermalboundarylayer,eventhoughthebulkstreamisstillsuper-heated.Ifthelocalsupersaturationreachesthecriticalsupersatura-tion,incipientfogformationwillcommence.Thiscondensationmecha-nismmayexistinanycompartmentswithinthecontainmentespeciallyintheicecondenserwhereicetemperatureiswellbelowthedewpoint.Whenahighspeedvapor-noncondensiblegasmixturejetgoesthroughanadiabaticornearlyadiabaticexpansion,thegasmixt'uretemperatureandpressurewilldroprapidlysuchthatcondensationmayoccursomewhereintheexpansionprocess.Thisisthecasewhenahydrogen-steammixturejetexitsfromabreakatasupersonicspeed.Thejetexperiencesarapidexpansionandifcriticalsupersaturationisreached;condensationshockmayoccursomewherewithintheexpandingjet.Thiscondensationmechanismcanonlyoccurinacompartmentinwhichthehydrogen-steammixturejetexists.Condensationinafastexpandingvapor-noncondensiblegasjetisalocalizedphenomenon.Usuallyverylittlemoistureisgeneratedintheexpansionprocessevenifacondensationshockdoesexist.Therefore,thepresentstudydoesnotattempttotreatthecondensationshockasasourceoffogformation.0430Q:I3-11 P

Thethirdmechanism,condensationduetomixing,mayexistinacompart-mentwhereahothydrogen-steammixturemixeswitharelativelycoldcontainmentatmosphere.Duringthemixingprocess,localcriticalsupersaturationwithinthemixinggascouldbereachedandcondensationwouldensue.Thismechanismcouldexistinthelowercompartmentinwhichrelativelycoldgasfromtheuppercompartmentisreturnedbythedeckfansandmixedwiththehothumidair.Thus,themixingofcoldandhotvaporstreamswillbetreatedinthepresentstudy.'owever,onlybulkcondensationisconsidered.Thatis,itisnotintendedto'computethetemperatureprofiletopredictthelocalcondensationrate.Instead,thebulkgasisassumedatoneuniformtemperature,andbulkcondensationwilloccurwhenmixingresultsinsaturationconditions.ThisisconsistentwiththeCLASIXcodeassumptionofuniformgastemperature.Becauseoftimerestriction,itisalmostimpossibletotreatallthecondensationmechanisms.However,majorcondensationmechanismswillbeidentifiedandtreatedinthepresentstudy.Beforeenteringintothediscussionofthemethodologytocalculatethefogformationratesfromvariousfogformationmechanisms,adiscussionoffogformationconditionsisnecessary.Sincethebulkcondensationapproachforthemixingprocesshasbeenadopted,thefogformationconditionsforthemixingprocessaresimplythatcriticalsupersatura-tionisreachedinthebulkstream.Forpracticalpurposes,thecrit-icalsupersaturationisassumedtobeonesinceitislikelythatplentyofcondensationnucleiexistintheatmospherebeforemixingcondensa-tiontakesplace.3.2.3CONDITIONSFORFOGFORMATIONNEARACOLDSURFACEFogstartstoformatafastratenearacoldsurfacewhenlocalvaporsupersaturationreachesthecriticalsupersaturation.Nearthecoldsurface,athermalboundarylayerisformed,withinwhichlocalvaporpressureandsaturationpressurevary.Typicalvaporpressureand0430Q:I3-12 r

temperatureprofiles,whentheincipienthomogenousnucleationfirstappears,areshowninFigure3.2.Itisseeninthisfigurethatwhenthelocalvaporpressurereachesthecriticalvaporpressurethereisasuddenappearanceoffogintheboundarylayerduetothefastnuclea-tionrate.RosnerandEpsteinhavederivedfogformationcondi-(ll)tionsnearacoldsurface,assumingthatthelocalvaporpressurecurveistangenttothecriticalvaporpressurecurveatthefogincipientpoint.Amoregeneralfog-formationcriterionwasgivenbyHijikataandMori1shW~(dW)Wharwall(3.3)wherehW=W-WwhT=T-Twandtheweightfractionofcondensingvapor,W,canberelatedtothepartialpressureofthecondensingvaporPasvW=1-(Pgp)(v/v)Pvg(3.4)wherePHNtotalpressurevapormolecularweightnoncondensiblegasmolecularweightEquation(3.3)mayberewrittenasn>2(3.5)whereM)(Qd)wal10430Q:I3-13

211233Pv,crit(T)Pv,eq(T~)Pcrit(Tw)Pv,wIIIIIIIllIIII0OOSUPERSATURATEDREGIONPv,ooBOUNDARYLAYERTHERMALSUPERHEATEDOKDCOzO0O1DZOOISUPERSATURATEDREGIONFOGVAPORTooTwFIGURE3.2VAPORPRESSUREANDTEMPERATUREPROFILESNEARACOLDSURFACE3-14 Theparameternisusedinthefollowingsectiontocalculatethefog~~formationrate.Itwillbedemonstratedthatwhenn<2,nofogforma-tionispossible.3.2.4RATEOFFOGFORMATIONHEARACOLO-SURFACEAshasbeendiscussedinSection3.2.3,fogwillformnearcoldsurfaces(e.g.,intheicecondenserearlyinthetransient.)AsdiscussedinSection3.2.1,oncewaterembryosareformedittakesonlyafewmili-secondsforthemtogrowtothemicronsize.Afterthesemicronsizefogdropletsareformed,itneedsverylittlesupersaturationforfur-thergrowth.Therefore,inthepresentanalysis,itisassumedthatvaporanddropletsareinthermalequilibriumandlocalvaporpressureisequaltothelocalsaturationpressure.Thissectionisconcernedwiththetransportofthesemicron-sizefogdropletswithinthethermalboundarylayer.TheboundarylayerfogformationratecanbedeterminedusingtheHijikata-Moritheoryoffogformationinthethermalboundarylayer.Itwasassumedthatathinliquidfilm,havingathicknessofe<onacoldsurface,coexistswithagas-dropletflowinatwo-phaseboundarylayerofthickness6outsidetheliquidfilmasshowninFigure3.3.Itwasfurtherassumedthatthesaturationconditionexistswithinthetwo-phaseboundarylayerandtheboundarylayerapproximationisappli-cable.Numericalsolutionswereobtainedforthemassfractionoffogdroplets,Y,atthegas-liquidfilminterface.ThefogdropletflowotrateatadistanceXalongtheplatemaybeexpressedintermsofYasf'6mf=LpJYudy(3.6)0430(}:I3-15 hfainFlow~0~ieCoolingSurfaceTwoPleaseBoundarylayerInterfaceLiquidFilmFIGURE3.3FORtljATIOHOFFOGHEARACOLDSURFACE

.whereYmassfractionoffogdropletsintheboundarylayerfogdropletdensityPvvapordensityPgnoncondensiblegasdensityYo.~fly=ok~v+~g)y=coordinateperpendiculartotheplatefogboundarylayerthicknesswidthofboundarylayerPv+pg=Y0(1-y/e)(3.7)u=U(<(~)-~(~))~(x)=ax1<<(3.g)4u=e(x)(1-6)(3.10)whereaknownconstantknownconst'antfreestreamvelocity0430Q:13-17 I0 SubstitutingEqs.(3.7)through(3.10)intoEq.(3.6),wehavetherateoffogformationmf=pL6YU0.250.025(3.11)oerivationofexpressionsfora,YandgisgiveninAppendixEventhoughboundarylayerfogformationmayoccurinanycontainmentsubcompartment,thefogformationrateislikelytobesmallexceptintheicecondenser.Forfogformationintheicecondenser,Listhetotallengthoftheperipheryandxistheheightoftheicebed.Duringfogformationintheboundarylayer,heattransfertothecoldsurfacewilldecreasethebulkfluidtemperature.Ifthebulkfluidtemperaturedropsbelowthedewpointcorrespondingtothefreestreamvaporpressure,thenbulkstreamcondensationcouldoccur.Inthiscase,itisassumedthattheboundarylayerthickness,s,willgrowsothickthatLeU~becomesthegasvolumetricflowrateQthroughthecon-densingcompartment.Thisisaveryconservativeassumptionintermsofthefogformationrate.UnderthisassumptionEquation(3.11)becomes0.250.025condo~"o1:g(1-g).(3.12)wheremdisthesumofboundaryandbulkstreamfogformationrates.cond0430Q13-18 3.2.5FOGDROPSIZESAsmentionedearlier,whenhomogeneousnucleationcommences,alargenumberofcondensationnucleiareformedandtheygrowtothemicronsizewithinafewmilliseconds.Inheterogeneousnucleation,fogdrop-letsgrowonaerosalparticles,whichareusuallylessthan1p.Inanycase,thefinaldropsizesaredeterminedbytheatmosphericconditionswithwhichthedropsareinthermalequilibrium.NeiburgerandChien(18)studiedthegrowthofclouddropsbycondensa-tionandcalculateddropletsizedistributionbasedonacloudcoolingrateof6c/hr.Theinitialsizedistributionofcondensationnuclei(sodiumchloride)werechosentocorrespondtoavailableobservationsasshowninFigure3.4(designatedas0second).Thecalculateddropsizedistributionsat3000and6000secondsareshowninFigure3.4.Itisseenthatthesizesoffogdropletsrangefrom0.01pto20p.Thevolumemeandropsizeis8pat3000second.Thevolumemeandropsizeforhomogeneousnucleationisexpectedtobesmallerthanthisvalue.Fogsofvolumemeandropsizesrangingfrom9to14p(30)havebeenobservedtoexistinanaturalenviroment,e.g.valley.InthepresentstuQ,avolumemeanfogdropsizeof10pischosenforfogdeposition-andinertingcalculations.3.3FINEMISTDROPLETSFROMCONTAINMENTSPRAYSThecontainmentspraysproduce-fairlylargedropsizes.A-typicalcon-tainmentspraynozzle,e.g.,Spraco1713nozzle,producesthesizedis-tributionasshowninFigure3.5,usingapressuredifferenceof50psiacrossthenozzle().Itisseenthatwaterdropletsproducedfromcontainmentrangefrom100pto2000p.Theselargedropshavelittleeffectonhydrogencombustionandflammabilitylimits,asalreadydemon-stratedintheFenwaltests()andmorerecenttestsatFactoryMutual(21).Toaffectthecombustioncharacteristicsofahydrogenmixture,thedropsizeshavetobesmallerthanabout20p,namelyinthefogdropsizeranges.Sincecontainmentspraysessentiallydonotproducedropsinthissizerange,containmentsprayswillnotbecon-sideredasameanstoproducefogdroplets.Rather,itwillbecon-sideredasameanstoremovethefogdroplets.0430Q:I3-19

~~~~~j~~)

I<lOI20lnOCD80ED609020200000600800l000l200l900l600l80020002200PARTICLEDIAllETER(MlCROHS)FIGURE3.5PARTICLESIZEDISTRIBUTIOHFOR50PSIPRESSUREDROPACROSSNOZZLEHO.1713

.J"s1~0 4.0FOGREMOYALMECHANISMSINANICECONDENSERCOHTAIHMEHTInSection3,themechanismsofgeneratingfogdropletswerediscussed.Afterthesedropletsaregenerated,theycanberemovedfromthecon-tainmentatmosphereby.gravitationalsettling,vaporization,containmentsprays,andimpingementonstructures.Theycanalsocoalescewithotherdropsduringcollisionandformbiggerdrops.Thesebiggerdropscouldeasilysettleoutoftheatmosphereundergravity.Thesefogdropletremovalmechanismswillbediscussedinthissection.4.1SETTLINGDUETO'RAVITYDropremovalratesduetogravitationalsettlingdependstronglyondropradius.Theremovalrateincreaseslinearlywithdropterminalveloc-ity,dropconcentration,andsettlingarea.Therelationshipmaybeexpressedasmsett"r(4.I)whereqisthemassofmistdropletsperunit.volume,andAistheset-tlingarea.Theterminalvelocity,Yt,isastrongfunctionofdropradiusandtherelationshipisshowninFigure4.1.Itisseenthattheterminalvelocityisapproximatelyalinearfunctionofdropradiusinbothlami-nartheturbulentregimes.Fora1000pdrop,itsterminalvelocityisaboveIm/s,whilefora10pdrop,whichisthetypicalfogdropsize,itsterminalvelocityisonlyaboutIcm/s.Therefore,thereisverylittleremovalbygravityforfogdroplets.0430Q:I

4.2AGGLOMERATIONAfterthefogdropletsareproduced,thedropletswillundergochangesinthenumberdensityandsizedistributionwithtime,whendropscol-lidewitheachotherandcoalesce.The.agglomerationrate(No.ofpar-ticleperunitvolumeperunittime)hasbeenfoundtobeproportionaltothesquareofthedroppopulationdensityandthecoagulationmecha-nismsdependentrateconstantKFordropslargerthan1g,thedominantmechanismisthedifferencein'Ivelocitiesbetweendropsinadjacentstreamlines.Thisisusuallytermedthevelocitygradientcoagulation.Fordropssmallerthan1g,thevelocitygradienteffectbecomessmall,anddropsarebrought'ogetherbyBrownianmotion.Thisleadstogreatlydifferentagglomera-tionratesfordifferentinitialdropsizes.AtypicalagglomerationrateasafunctionofdropsizeinamoderatelyturbulentatmosphereisshowninFigure4.2.InFigure4.2,thesharpriseoftheagglomerationratewithdropdiameterlargerthan1pimpliesthatthelargerdropsagglomeratequicklytothemaximumstablesizesupportedbytheatmo-sphericturbulerce.Theagglomerationratesfordropslessthan1pareverysmall.Sincemostofthefogdropletsarein.micronsizeranges,theagglomerationrateisnotlarge.Itisassumedinthepresentanalysisthattheinitial4ublowdownmeandropsizewillgrowto10g(SeeSection3.2.5).Agglomerationasaseparatemechanismforfoggrowthhas'beenconservativelyneglected.4.3VAPORIZATIONFogdropletssuspendedinthecontainmentatmosphereisconsideredtobeinthermodynamicequilibriumwiththesurroundinggas.Mhenthesur-roundingatmospherebecomessuperheatedorwhenthedropletsareentrainedintoasuperheatedsubcompartment,itcanundergovaporizationorcondensation.0430Q:14-2 Inthepresentanalysis,itisassumedthatwatervaporandmistdrop-letsareinthermalequilibriumatalltimes.Therefore,theamountofvaporizationorcondensationwillbedeterminedbythethermalequilib-riumstatereachedbythevaporanddrops.Inotherwords,itisnotintendedtomodelheattransferbetweenthedropsandthesurroundinggas,andthusdeterminethevaporizationrate.Thisisagoodassump-tionforthesmallfogdropsizes.4.4REMOVALBYSPRAYDROPSAsmentionedabove,thecontainmentspraydropletsrangefrom100u-2000p,whicharesubstantiallylargerthanthefogdroplets.Iffogdropletsenterthesprayzone,theywillprobablyberemovedbythespraydropletsbycollidingwiththem,sincethespraydropmassismuchlargerthanthefogdropmass.AsimpleanalyticalmodelisusedinthepresentstudywhichassumesthatallthefogdropletsresidinginthesprayzonewillbesweptbythespraystothefloorwiththespraydropremovalefficiencyE.Thesprayremovalratemaybeexpressedasm=EQM/qV(4.2)whereEQspspMspraydropremovalefficiencyvolumetricflowrateofspraysvolumefractionofspraydropletsinthesprayzonemassoffogincompartmentvolumeV4.5OTHERREMOVALMECHANISMSAnothersimilarmechanismforfogremovalistheformationofdropletsintheicecondenser.Thesedropletswhichwouldbegeneratedintheicebedwhentheicemelts,wouldfallthroughtheicebed,andremovefogdropletsfromtheflowthroughtheicecondenser.Thislargequan-tityofwaterwouldbeeffectiveinremovingfogdroplets.However,duetodifficultyinmodelingthisremovalmechanism,itisconservativelyneglectedinthepresentanalysis.0430Q:I4-3 I

Inadditiontotheremovalmechanismsmentionedabove,fogcanalsoberemovedbyimpactingstructuralsurfaces.Ouetotheinertiaoffogdroplets,substantialfogremovalbyimpactingstructuralsurfacescouldoccur,whenthedrop-ladenmixtureflowpassesthroughlong,narrow,curvedpaths,suchasicebasketflowpaths,andfanducts.Moreover,thecentrifugalforceexertingonthefogdroplets,whentheypassthroughthefans,couldcausethefogdropletstoimpactthebladesur-facesorotherpartsofthefans.Theseremovalmechanismsarebelievedtobesignificant;however,theyareconservativelyneglectedinthepresentanalysis.Itis,therefore,believedthatthepresentanalysisisveryconservative.4-40430Q:1 I,

121273110TERMINALDROPFALLINGVELOCITIESINSTEAM.AIRATMOSPHERESp~1.0COZ0.10TURBULENTAMINARREGIMEREGIMEHATCHEDREGIONINDICATES:50<Re<550.011.00.001001'1DROPRADIUS(CM)FIGURE4.1TERHINALVELOCITYASAFUNCTIONOFDROPRADIUSINSTEAH-AIRATHOSPHERE104~~7u103O102ROI-o101GRADIENTAGGLOMERATIONn10CM100Sdvdy8ROWNIANAGGLOMERATIONn10CMNETRATE1000.010.11.0DROPDIAMETER(pM)FIGURE4.2AGGLOHERATIONRATESINAIRBETWEENEQUAL-SIZEDDROPS4-5 T,

5.0FOGINERTINGCRITERIARecenthydrogenburnexperimentsconductedatLawrenceLivermoreLabora-toryindicatedthatsubstantialfogformationcouldoccurwhensaturatedsteamisdischargedintoanunheatedvessel.Itappearedthatthisfogpreventedaglowplugigniterfromsuccessfullyignitingthehydrogenmixtureinthevessel.Theabilityoffogininhibitingandquenchingofhydrogencombustioncanbeexplainedasfollows.Thefogdropletssuspendedinthehydrogen-air-steammixtureactasaheatsinkthatcouldabsorbalargeamountofcombustionheat,greatlyreducingthepressureandtemperaturerisesresultingfromhydrogencombustion.Ifdropletsaresufficientlysmallsuchthattheycouldvaporizeinsidethethin(Imm)flamefront,theflamemaybequenchedorinhibited.Foraflamespeedof2m/s,thedropresidencetimeisoftheorderof0.5x10seconds.Insuchashortperiodoftime,thedropletsofinitialradiuslessthanabout4pwillvaporizeentirelyintheflamefront.Thequenchingofapropagatingflameisalsogovernedbythedistancebetweendroplets.Asthedropletsbecomecloselypacked,thetotaldropletsurfaceareaavailableforenergylossincreases.Acriticalspacingbetweendropletsexistssuchthatalargefractionofth'eheatreleasedisabsorbed,thuspreventingflamepropagation.Thiscriticalspacingisknownasthe"quenchingdistance",whichisusuallydeter-minedbypropagatingflamesintubes.5.1PREVIOUSWORKTheeffectivenessoffogdropletsininhibitingorquenchingaflamedependsonitsquenchingdistance,wasdeterminedbyBermanetal.asd=[4VIS3(5.1)whereVisthegasvolumeandSistheheattransfersurfacearea.Forahydrogen-airmixture,thedataonthequenchingdistanceisshownin04300:I5-1

Figure5.1.Inthesuspendedfogdroplets,thisvolume-to-surfaceratio~~~~(i.e.,V/S)isequalto1d(1-n)wheredisthemeandropletdiameterandnisthevolumefractionofwater.Whenfourtimesthisratioapproachesthequenchingdistance,acriticaldropletdiametercanbeobtainedasqdc2(5.2)Usingthiscriterionforquenchingaflame,foragivenvolumefractionofwaterandgascomposition,dcanbedetermined.Thecriticaldropletdiameterthencanbedeterminedfromtheaboveequation.Thedropsizeslessthanthecriticaldropsizeiscapableofquenchingaf1arne.AplotofEq.(5.2)fortwohydrogenconcentrationsisshowninFigure5.2.5.2PRESENTTHEORYTheprevioustheoriesdonotmodeltheheattransferandcombustionprocessesoccurringbetweentheburnedgasandthesuspendeddroplets.Anewtheoryhasbeendeveloped,whichmodelstheheatlossandcombus-tion.0430Q:15-2 t~"t0V FEG.5.1MINIMUMIGNITIONENERGIESANDQUENCHINGDISTANCEFORKYDROGEN-OXYGENINERTGASMIXTURESATATMOSPHERICPRESSURE5-3

&ALIIS~mS'REER~~~~~~~~~MR~~ESESR~~~RSRES~~~m~~EEI~~~RRRE~ERSRSRSRSR~EEERR~~~WMRE~SEERS~~~BESSER~~~~~~~~RRRR~~~EERRRRERRE~EEEE~ERRSR~EERRE~~~~~RA~WE~E~iFsSHSIWI0~~~lI~~ERIIESECEEEEEESSWRERRREMRS~~SEERSEREEE~~~~ESSES~~~SEERS~

Considerahydrogen/air/steam/mistdropletsmixtureinwhichaflameisgropagating.Theflamemaybedividedintothreezones:heatingzone,,reactionzone,andpost-reactionzoneasshowninFigure5.3.TheunburnedgasattemperatureTmoveinthereactonzonewiththeUlaminarburningvelocityS.Iftheunburnedgasdensityisp,UthentheconstantmassflowratemisequaltopS.TheunburnedgasisheatedtoignitiontemperatureT.andburnedinthereaction1zonetoreachtheflametemperatureTf.Thefogdropletswillactasaheat'sinkthatreducestheflametemperature.TheproblemhasbeenformulatedandsolvedbyvonKarman.Inhisformulation,three(25)energyequations,whichincorporatetheheatlossterms,werewrittenforthethreezonesdescribedabove.Thesolutiontotheseequationsyieldsthefollowingrelationship2Ke.=1-exp(-TIi)(Y-Yf)121U1((~~((()(-~Ii1+K/Ii(5.3)wheree.1C(T.-T)/qpiU~Z/iwmPKei(S/Cw)eiPtheratioofheatlossrateperunitvolumetotheheatreleaseratebychemicalreactionperunitvolumeheatofcombustionCmeanspecificheat0430Q:15-5 VJ0 heatconductivityreactionrate(massoffuelconsumedperunittimeperunitvolume)YuhydrogenmassfractionintheheatingzoneYfhydrogenmassfractioninthereactionzone'u'uAplotof,Eq.(5.3)isshowninFigure5.4.ItisseenthatforagivenKe,thereisaminimumvalueof(Yu-Yf)/e,-.Belowthismini-mumvalue,thereisnosolutionfortheve,.p.Therefore,thisvalueisconsideredastheflammabilitylimit.Attheflammabilitylimit,thevalueofKe.canbedeterminedfromFigure5.4orfromEq.(5.3)as)critejf((uYf)/Gi)(5.4)'Aplotof(K)cr,.te;asafunctionof(Yu-Yf)/eiisshowninFigure5.5.Equation(5.4)maybeexpressedas2(YuqpuSu(Y-Yf)f(e-Cp212i(T,.-Tu)(5.5)DetailedderivationprocedureforEq.(5.5),isgiveninAppendixB.UsingthedataonSfromReference(26)wecancalculatetherightuhandsideofEq.(5.5)foragivencompositionandinitialgastempera-ture.5.3YERIFICATIOHOFTHEORIESBYEXPERIMENTSExperimentshavebeenconductedatFactoryMutualtostudytheeffectsofwaterfogdensity,dropletdiameter,andtemperatureonthelower0430Q:I Tempore~,7m~~zone(Dljt=m(r<-Vgw~~<a>xa0xa(Deltonce,x~FIGURE5.3SCHEMATICREPRESENTATIONOFTEMPERATUREPROFILETHROUGHTHEFLAMEFRONTA',a0'(i0200'ye0300.2.46l012(Yv-YrVdtFIGURE5.4THEPARAMETERA.pASAFUNCTIONOF(Y-Y)/0FORDIFFERENTVALUESOFKO5-7 1t 0.30.2UlICO0.10.00(Y-Y))/0;FIGURE5.5(K)t8ATTHEFLA50BIL1'TYLINITASAFUNCTIONOF~Yuf~i 4

flammability1imitofhydrogen-air-steammixtures.Theresultsindicatedthatmostofthefognozzlestestedat20Conlychangedthelimitfrom4.03volumepercentto4.76percent,correspondingtofogconcentrationintherangeof0.028-0.085volumepercent,andaveragedropsizerangingfrom45-90microns.Forthe50'Ccase,thelowerflammabilitylimitincreasesto7.2percent,correspondingto0.01-0.04volumepercentoffogand20-50micronaveragedropsizes.Theresultsdemonstratedthatthefoginertingeffectismorepronouncedatsmalldropsizes.Figures5.6through5.8showthecomparisonbetweenthetestdataandthetheoreticalpredictions.Forthiscomparison,thepresenttheoryusedthefreestreamtemperaturetocalculatethethermodynamicproper-tiesusedinEquation(5.5).Thisyieldedsomewhathigherfogcorcen-trationsthanthosecalculatedbyuseofthemean'oftheflameandfreestreamtemperatures.InFigures5.6and5.7,thedatasuggestsalinearrelationshipbetweenthevolumeconcentrationandvolumemeandropsizeonthelog-logplot.Italsosuggeststhattheminimumfoginertingconcentrationvariesapproximatelywiththesquareofthevolumemeandropsize.Inthisregard,thepresenttheoryisconsistentwiththedatawhiletheBermanetal.theoryisnot.-ThepresenttheoryisingoodagreementwiththeFactoryMutualdataat476percentH2',however,itoverpredict'stheminimumfoginertingconcentrationat7.2percentH2.Thecauseofthisdiscrepancyisstillunknown.Thediscrepancymaybecausedbytheuncertaintyofthedata.Thefollowingdiscussionsupportsthisclaim.Thefogdropletsareverysmallandtheyvaporizeveryfastinaflame.Therefore,thefogdropletsbehaveassteamexceptfortheirlargerheatabsorptioncapability.Whenthefogdropletsvaporize,theyabsorbtheheatofvaporizationwhichismuchlargerthanthesteamsensibleheat.Typ-ically,theheatofvaporizationofwaterisabout1000Btu/lbandtheaveragespecificheatofsteaminthetemperaturerangeofinterestisabout0.48Btu/lb.Itiswellknownthatatydrogenflamecannotpropa-gateinsteamhigherthanabout64percentinasteam-airmixture.At7.9H2,theadiabaticflametemperatureisabout1240Fandtherefore0430Q:I5-9

oSpracoZI63LSpracol405-0604.GSpraco2020"l704v'Spracol806-l605l0~CDNNON-FLAMMABLE.ZONECDPRESENTTHEORYBERMANETAL.THEORYFLAMMABLEZONEloIOIOO200VOLUMEMEANDIAMETER,MICRONSFIGURE5.6COMPARISONBETWEENTHEORIESANDFACTORYMUTUALFOGINERTINGEXPERIMENTSON4.76PERCENTH~5-10

I0'80Spraco2I63-7604vSpraco2020-I704OSonicore035HXIONon-FlammableZonePRESENTTHEORYFlammable.Zone72%HzInAirAt50'CIOIO20405060708090.VOLUMEb]EANDIAMETER,MICRONS.FIGURE5.7COMPARISONBETWEENTHEPRESENTTHEORYANDFACTORYMUTUALFOGINERTINGEXPERIMENTSON7.2PERCENTH2'"5-11' I

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theincreaseofthesteamsensibleheatisabout540Btu/lb.Conse-quently,forthesameamountoffogdropletsandsteam,thefogdropletsheatabsorptioncapabilityisabout1.9timeshigher.Thismeansthatthefogconcentrationwhichisequivalentto22.1percentsteaminsteamandairiscapableofinerting7.9percentH2.lhisfoginertingconcentrationwascalculatedtobe1.61x10-4.Toinert7.2percentH2,aminimumfogconcentrationwhichcorrespondstoabout21.3per-centsteaminsteamandairisrequired.Thisgivesaminimumfogincrtingconcentrationof1.56x10for7.2percentH2.estimatesshowthatthepresentpredictionsarereasonableandconserva-tive.Thepresenttheoryisconservativebecauseitneglectsconvectiveandradiativeheattransferandthusunderpredictstheheatloss.TheestimatesareconsistentwithFactoryMutualdataon7.9percentH2butnoton7.2percentH2.Itshouldbenotedthatintheteststhreefogconcentrationmeasuringtechniqueswereused.Thesethreetechniquesgavesubstantiallydif-ferentresults.Thediscrepancyisatleastoneorderofmagnitudedifference.ThefogconcentrationdatapresentedinFigures5.6through5.8wereobtainedfromoneofthetechniques.Inviewoftheuncer-taintyofthedata,caremustbeexercisedinusingthemforinertinganalysispurposes.Theyshouldbeusedinconjunctionwiththepresentfoginertingcriterionintheassessmentoffoginertingpotentialin=theicecondenserplants.Someuncertaintyalsoexistsinthepresentfoginertingtheory.Theuncertaintyassociatedwiththeunderpredic-tionoftheheatlossandtemperaturedependenceofthethermophysicalpropertiesisestimatedtobe+63percent.ItshouldalsobepointedoutthattheFactoryMutualdataandthepre-senttheorycanonlypredicttheminimumfoginertingconcentration.Toinsurehydrogenburninalldirectionsintheicecondenserupperplenum,furtherworkinthisareamayberequired.0430Q:I5-13 Pr 6.'0ASSESSMENTOFFOGINERTINGPROBABILITYINICECONDENSERCONTAINMENTSAsdiscussedintheprevioussections,thereexistsseveralmechanismsofgeneratingandremovingfogdropletsfromtheicecondensercontain-ment.Inaddition,fogdropletsarealsotransportedfromonesubcom-partmenttoanotherbyentrainmentinthegasstream.Thefogentrain-mentrateisdifficulttoassesswithoutknowingthevelocityfieldanddropsizedistribution.Forsimplifyingpurposes,itispresentlyassumedthat,themassfractionofmistdropletsintheintercompart-mentalandfanflowsisthesameasthatwithinthesubcompartmentfromwhichtheflowsareoriginated.'hisisagoodassumptionsincethefogdropletsaresmall.Theamountoffogdropletsinasubcompartmentdependsonallthesemechanisms.Thetotalamountoffogdropletsisimportantin-determiningthevolumefractionofsuspendedcondensateinasubcompartment.Thisvolumefrac-tion,inturn,isusedinthefoginertingcriteriatodeterminewhetheraparticularhydrogenmixturecompositionformedinasubcompartmentatanytimeisflammableornot.Inotherwords,byknowingthehydrogenconcentrationandthemeanfogdropsize,wecandeterminewhetherthecalculatedvolumefractionoffogdropletsishighenoughtopreventthemixturefromcombustion.6.1DETERMINATIONOFVOLUMEFRACTIONOFMISTDROPLETSINICECONDENSERCONTAINMENTSConsiderasubcompartmentintheicecondensercomtainmentasshowninFigure6.1.Thereexistseveralmechanismsbywhichmistdropscanbegeneratedorremoved.Fogdropletscanbegeneratedbyhomogeneousorheterogeneousnucleationinthethermalboundarylayerand/orinthebulkstreamandtheycanincreaseinsizebycondensationordecreaseinsizebyvaporization.Therateofgenerationofmistdropletsbycon-densationandtheircontinuedgrowth(orshrinkageduetovaporization)isrepresentedbymd.Theothermechanismofgeneratingmistdrop-condletsconsideredinthisanalysisistheprimarycoolantdischargefromthebreakandtherateofgeneratingfogdropletsfromthismechanismis0430Q:I6-1 dj1 representedbymk.Twofogdropletremovalmechanismsareconsid-oreak~~edinthisanalysis:oneisgravitationalsettlingandtheotherismovalbycontainmentspray.Thefogdropletremovalratebygravita-tionalsettlingisrepresentedbymtandthatbysprayisrepresen-settedbym.Inadditiontothegeneratingandremovalmechanismsdiscussedabove,themistdropletconcentrationinasubcompartmentisalsoaffectedbytheintercompartmentalandfanflows.Intheintercom-partmentalandfanflows,themassfractionoffogdropletsentrainedisqandthegasmixtureflowrateism.Thereforetheratesoffogdrop-letsmassintoandoutofasubcompartmentaregqimiandgntmt,respectively.Itshouldbenotedthatgn~m.and$noutmoutincludethefogmassentrainmentratesinalltheintercompartmentalandfanflowsintoandoutofasubcompartment.ThemassconservationequationforthefogdropletsinasubcompartmentmaybeexpressedasdM1t~inin~outoutbreakcondsetspwhere(is'asummationoveralltheflowpaths..InEq.(6.1),ifmdisnegative,thenitbecomestherateofvaporization.Eq.(6.1)canbeintegratedtogivethetotalmassofcondensateattimetc~"inin~"outoutbreak0condŽsetsp11ii+i~"inin~"outoutbreak1111condsetspi(6.2)0430Q:I6-2 r

ThepresentanalysiswillemploytheCLASIXcalculationsofcontainment4ransientduringasmallLOCA.IntheCLASIXanalysis,theentireicecondensercontainmentisusuallydividedintofiveorsixsubcompart-mentsforanalysispurposes.Temperatures,totalpressure,steampartialpressures,andintercompartmentalflowratesarecalculatedduringtransients.ThisinformationisusedinEq.(6.2)todeterminefogdropletmass.WhenapplyingEq.(6.1)toeachindividualsubcompartment,wehavethefollowingfogmass,conservationequationsinfinitedifferenceform:UerComartmentNUC(t+at)=NUC(t)+()e.m(t)UC,set4C,sLowerComartmentNC(t+st)=NLC(t)+()n.m(~"outoutLC,break(6.4)LC,condLC,setLC,f)st0430Q:16-3 PC IceCondenserUerPlenumMUP(t+at)=MUP(t)+'(7ninmin(t)-~"outmout(t)UP,cond()UP,set())IceCondenserLowerPlenumsMLPt+st)MLPt(gn(m.(t)(6.5)~sootout(LPd()LP,set)DeadEndedReionM()E(t+at)=MUE(t)+(pn;m;(t)(6.6)e~sootout"bEcondDEset)Fan/AccumulatorRooms*MEA(t+st)ŽEA(t)+(Pn(nm.(t)e~"outoutFAcond(6.7)4WAsetFAspInthepresentanalysis,thefogconcentrationsintheintercompart-mentalandfan'flowsareassumedtobethesameasthoseinthecompart-mentfromwhichtheflowsareorginated.*TheseroomswereanalyzedonlyfortheD.C.Cookplant(SeeFigure~~6.S).0430Q:16-4 iI' Intheequationsgivenabove,theintercompartmentalandfanflowratesm.andmtareprovidedbyCLASIXcalculationalresults.Theinoutproceduresofcalculatingfogdropletsgeneratingandremovalratesarebasedonthediscussionsintheprevioussectionsandthedetailsaregiveninthefollowingsections.6.1.1CALCULATIONOFHBREAKTodatelittleexperimentaldataisavailabletoestimatetheamountoffogdropletsgeneratedbythebreakflow.ForalargeLOCA,AlmenasandMarchelloestimatedthat13percentofthetotalblowdowndroppopulation(byweight)hasdropradiusrangefrom1pto20pandonly1percentlessthan1p.Thisestimateissomewhatlargerthanthe4pmeandropsizesitedinSection3.1.2,whichisbelievedtobeconserva-tivee.Sinceweareonlyinterestedinfogdropssmallerthan20p,andonlythesedropscanremainsuspendedinairuntilthetimewhenthehydrogenisreleased,weassumethattheestimateofAlmenasandMarchelloisapplicableinsmallLOCAsand14percentofthesuspendedliquidarefogdropletswhichhaveapotentialinertingeffect.ThefractionofreactorcoolantdischargedfromthebreakremainsassuspendedliquidhasbeendeterminedinSection3.KnowingthebreakflowratesfromacomputercodesuchasMARCH,wecancalculatetheamountofliquidsuspendedintheatmosphere.Thenfromthedropsizedistributionwecancalculatetheamountoffogdropletssuspendedintheatmosphere.Oefiningtheblowdownrateasm,theliquidfractionofthebreakflowasgb,thefractionoffogdropletssmallerthan20pasfb,wehavebreakbb~b(6.8)0430Q:16-5 j(

Inthepresentanalysisfb=0.14isused.fbbecomeszerowhenthewaterlevelinthe'eactorvesselfallsbelowthebreakelevation.6.1.2CALCULATIONOFMCONDAsdiscussedpreviously,mdistherateofformationofmistdrop-letsbynucleation,condensation,orvaporization.Nucleationoffogdropletscantakeplaceinthethermalboundarylayerandinthebulkfluid.Weconservativelyassumethatlittlesupersaturationisneededfornucleationinthebulkstreamandfogwillformwhenthebulkstreamsteampartialpressurereachesthesaturationsteampressurecorrespond-ingtothegasstreamtemperature.Therefore,thebulkstreamfogformationratescanbedeterminedfromtheequilibriumthermodynamicstatesofthegasmixture.TheboundarylayerfogformationratecanbedeterminedusingtheHijikata-MoritheoryoffogformationinthethermalboundarylayerasdiscussedinSection3.2.4.ThefogformationrateinthethermalboundarylayerandthebulkstreamisgivenbyEq.(3.12).Boundarylayerandbulkstreamfogformationrateswillbecalculatedfortheicecondenserandlowercompartment.Acomputerprogramcalled'FOGhasbeendevelopedtocalculatemcond'hiscomputerprogramrequiresinputofthevolumetricgasflowrate,gasandwalltemperatures,totalpressure,andsteampartialpressure.ThisinformationcanbeobtainedfromtheCLASIXoutput.6.1.3CALCULATIONOFMSETTherateofsettlingofthefogdropletsdependsontheirterminalvelocity,concentrationandcompartmentcrosssectionalarea.Thedropletterminalvelocityisafunctionofdropsize.Inthepresentstudy,Equation(4.1)willbeusedtocalculatethefoggravitationalsettlingrate.0430Q:I6-6

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6.1.4CALCULATIONOFMSpThemassofafogdropletismuch'mallerthanthatofaspraydroplet.Therefore,whenaspraydropletcollideswithafogdroplet,thefogdropletwillcoalescewiththespraydropandfalltothesump.Inthepresentstudy,thefogremovalratebyspraysisgivenbyEquation(4.2).Itisexpectedthatthespraydropcollectionefficiencyisveryhigh,andthereforea100percentdropcollectionefficiencyisassumedintheanalysis.AsensitivitystudyisneededtobecarriedouttostudytheeffectofEonthevolumefractionoffogdroplets.AcomputerprogramcalledFOGMASShasbeendevelopedtosolveEqs.(6.3)through(6.7).Thisprogramusesafinitedifferencenumericalschemetocarryoutintegration.ThisprogramtakesinputfromFOGandCLASIXoutputdata.SpecificoutputdatafromCLASIXaretimehistoriesofgastemperature,walltemperature,totalpressure,steampartialpressure,andintercompartmental.andfanflowrates.6.2FOGINERTINGPROBABILITYINTHESEQUOYAHPLANTThecomputercodes,FOGandFOGMASS,wereusedtoperformfoginertinganalysisfortheSequoyahplant.FOGwasusedtocalculatetheratesoffogformationduetoboundarylayerandbulkstreamcondensation.intheSequoyahicecondenserandlowerplenum.ThenthesefogformationrateswereusedinFOGMASStocomputethefogconcentrationsineachoftheSequoyahcontainmentsubcompartments.Tocomputethefogformationratesintheicecondenserupperplenumand'owercompartment,someoutputdatafromtheSequoyahCLASIXanaly-(27)sisareneeded.Thesedataincludetimehistoriesofgastempera-ture,walltemperature,totalpressure,andsteampartialpressureineachcontainmentsubcompartment,aswellastheintercompartmentalandfanflowrates.InordertoutilizetheCLASIXoutputdata,theicecondensercontainmentissubcompartmentalizedintheFOGMASSprograminexactlythesamemannerasinReference27.Thesubcompartmentaliza-ionmodelusedintheSequoyahCLASIXanalysisisshowninFigure6.1.InthisstudyonlytheS2Daccidentscenariohasbeenanalyzed.0430Q:I6-7 J-'4'e~II FIGURE6.1SEQUOYAHCLASIXCONTAINMENTMODELICECONDENSERUPPERPLENUhhUPPERCOMPARTMENTICEBEDICECONDENSERLOWERPLENUMCOMPARTMENTDEADENDEDREGIONAIRRETURNFAN/HYDROGENSKIMMERSYSTEMFLOWPATHCONTAINSDQORSFLOWALLOWEDINBOTHDIRECTIONSFLOWALLOWEDINONEDIRECTIONSPRAYHEADER S'

TheFOGinputdataforSequoyahS20CaseIaregiveninTables6.1and6.2,andthecaIculationalresultsareshowninFigures6.2and6.3.InFigure6.2,thefogformationrateinthelowercompartmentisshown.Forthefirstfewhundredsecondsthewalltemperatureislowerthanthe'dewpointcorrespondingtothesteampartialpressureandthereforefogstartstoform.Afterabout600seconds,thefogformationratebecomesnegligiblysmallsincethewalltemperatureisonlyafewdegreesbelowthedewpoint.Thereisnofogformationinth'elowercompartmentafterabout,1800seconds.ThefogformationrateintheicecondenserisshowninFigure6.3.Itisseenthatthefogformationrateintheicecondenserismuchlargerthanthatinthelowercompartment.Itincreaseswiththeicecondensersteamflowrateandreachesapeakof14lb/secatabout1800,seconds.Thefogformationrateintheicecondenserthenbeginstodecreaseandislowatthetimeofsignificanthydrogenrelease.TheninefogformationratesinthelowercompartmentandintheicecondenserareinputtoFOGNSSinatabularformandthereisabuilt-ininterpolationschemeinFOGtQSStoobtainvaluesfortheintermediatetimesteps.FOGNSScomputestherateoffoggenerationbythebreakflow,th'efog'ettlingrateduetogravity,andthefogremovalrateduetosprays,aswell'astheratesoffogentrainmentbyintercompartmentalandfanflows.Theinputdataneededtocalculateeachoftheseratesaredis-cussedasfollows.TherateofreactorcoolantreleasetothecontainmentandthecoolantenthalpywereobtainedfromtheMARCHoutput'orasmallLOCA.The(7)qualityofthebreakflowwascalculatedusingtheenthalpyandthelowercompartmentgastemperature.AccordingtotheMARCHpredic-tionthedischargeofliquidbythebreakflowintothelowercom-0)partmentlastsforonly2172seconds.Afterward,thewaterlevelinthereactorvesseldropsbelowthebreakelevationandthefluiddischarged0430(:I6-9

IIIIIII00IlIIIIIIIII K'

ggIIIIIIIII1IIIIIIiIIIII'IIIII 48 fromthebreakisessentiallysteam.Therefore,inthepresentstu@,itisassumedthatnofogisgeneratedbythebreakflowafter2172seconds.Forfogremovalbygravitationalsettling,avolumemeandropsizeof10pwasassumed.Theterminalvelocityofa10pdropisaboutI.cm/sec.Becauseofthislowterminalvelocity,gravitationalsettlingisnotaneffectivefogremovalmechanism.Theassumptionof10pvolumemeandropsizeisthereforeconservative,consideringthefactthatforafewthousandsecondsthedropagglomerationmechanismwouldbeabletoincreasevolumemeandropsizesubstantially.Itshouldalsobenotedthatasmallervolumemeandropsizemeansthattheminimumfoginertingconcentrationwouldbereducedandthusmakesthepresentanalysisconservative.Furthermore,noconsiderationwasgiventothedepositionoffogonthewallsandverticalsurfacesofthestructure,orforfogremovalinthefanflowswhenitpassesthroughductsandfans.Alltheassumptionsmentionedabovemakethepresentanalysisveryconservative.ThecontainmentgeometricdataneededincomputingthesettlingratearegiveninTable6.3.fForfogremovalbysprays,asprayflowrateof9500gpmwasusedforSequoyah.AccordingtotheSequoyahCLASIXanalysis~27~,thespraysareinitiatedat142seconds.Avolumefractionofsprays(volumeofspraysdividedbyvolumeofthesprayzone)of3.3x10-4was.used,whichwasobtainedusingaspraydropfallheightof107ft,asprayzonevolumeof485,500ft3,andavolumemeandropsizeof700p.Aspreviouslydiscussedasprayremovalofa100percentwasused.InFigure6.1,thedirectionsoftheintercompartmentalfl'owsareshown.Theintercompartmentalflowratesforthesix.flowpathsandninetimestepswereobtainedfromtheOPSCLASIXanalysisandaregiveninTable6.5.Thepresentanalysisconsiderstheintercompartmentalflows'asthemechanismsoftransportingfogfromonecompartmenttoanother.Itwasassumedinthepresentanalysisthatthefogconcen-trationsintheintercompartmentflowsarethesameasthoseinthecompartmentsfromwhichtheflowsareoriginated.0430Q:I6-12 r

ItisseeninFigure6.1thattwotrainsoftheairreturnfanandhydrogenskinnersystemtakesuctionfromthedeadendedregionandfromtheuppercompartmentanddischargeintothelowercompartment.Thefansareinitiatedat712seconds.Thefanhead-flowcurvereportedinReference27wasusedtocomputethefanflowrates.Fanflowratesof1645ft/secand10ft/secwereusedfortheairreturnfanandthe33hydrogenskimmersystem,respectively.Theseflowrateswerecalculatedusingaverageap'sbetweentheuppercompartmentandthelowercompart-ment,andbetweenthedeadendedregionandthelowercompartment.Itwasalsoassumed.thatthefogconcentrationsinthefanflowsarethesameasthoseinthecompartmentsfromwhichtheflowsareoriginated.TheresultsoftheFOGMASScalculationareshowninFigure6.4.Itisseenthatforthefirstfewhundredsecondsthefogconcentrationsinthelowercompartment,icecondenserlowerandupperplenumsareaboutthesameandincreasing.Atabout700seconds,thelowercompartment.fogconcentrationreachesitspeakof2.2x10.Afterward,theintercompartmentalflowstransportmorefogdropletsoutofthelowercompartmentthanaregeneratedbythebreakflowandcondensationand,therefore,thelowercompartmentfogconcentrationdecreases.However,-theupperplenumfogconcentrationkeepsrisinguntilabout900seconds,duetoanincreasingfogformationintheicecondenserandmorefogentrainedintheintercompartmentalflowintotheupperplenum.Theupperplenumfogconcentrationreachesitspeakof5.4x10atabout900seconds.Thelowerplenumfogconcentrationisalmostthesameasthelowercompartmentfogconcentrationbecauseoflittledifferenceintheintercompartmentalflowratesintoandoutoftheicecondenserlowerplenum.-Therefore,thesetwovolumesbehaveasasinglevolumefntermsoffogconcentration.At2172seconds,thebreakflowinthelowercompartmentstopsgenera-tingfogand,therefore,thefogconcentrationsdropsharplythere-after.Theeffectismorepronouncedforthelowercompartmentandlowerplenumfogconcentrations.Thehighestfogconcentrationexistsintheicecondenserupperplenumwhilethelowestexistsintheuppercompartment.Theeffectof.sprayson.theuppercompartmentfogconcen-trationisclearlyseeninFigure6.4.At142seconds,thespraysare0430Q:I6-13 t

IrII<IllIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIflIIIIIIIIIIllIIIIIIIIIIII>>I>>I>>I>>IIIlI>>I~IIIMTHI>>0gII~~~~I~I>>I~~IaI~~~

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-turnedonandtheuppercompartmentfogconcentrationdropssharplyuntilabout600seconds.Atabout600seconds,theuppercompartmentfogconcentrationstartstoincreaseagainbecausetheintercompartmen-talflowintothecompartmentincreasessharplyatthattime.Apeak-6concentrationof7x10intheuppercompartmentisreachedatabout1200seconds.Hydrogenstartstoreleaseintothecontainmentatabout3804seconds,accordingtotheMARCHcalculation.Itreaches4volumepercent(27)atabout4300,',4400,and4670secondsinthelowercompartment,upperplenum,anduppercompartment,respectively.At4300seconds,thecalculatedlowercompartmentfogconcentrationis9.7x10,whichisaboutanorderofmagnitudesmallerthanthe-7minimumfogconcentrationsrequiredforinerting4percentH2.At4670seconds,theuppercompartmentfogconcentrationis1.35x10whichisaboutafactoroffivesmallerthantheminimumfogconcen-trationrequiredforinerting4percentH2*.Atthetimesofreaching8.5percentH2,thefogconcentrationsintheloweranduppercompart-mentsareevenlowerthanthefiguresgivenabove.Therefore,itisconcludedthatthefogconcentrations'ntheloweranduppercompart-mentsaretoolowtohaveanyinertingeffect.Theuseofthepresenttheoryonfoginertingalsoleadstothesameconclusion...However,at4400seconds,thecalculatedfogconcentrationintheupper-5plenumis6.1x10whichishigherthantheFactoryMutualfoginertingdataextrapolatedto10pdropsandthepresenttheoreticalprediction.Thedatashowsthatinordertoinert4.76percentH2thefogconcentrationmustbe8.4x10orhigherfor10pvolumemeandropsize.At4600seconds,theupperplenumhydrogenconcentrationreachesabout7percentandthefogconcentrationis5.5x10Again,anextrapolationoftheFactoryMutualdatato10pshowsthatfogconcentrationof2.1x10orhigherisrequiredtoinert7.2percentH.Incomparison,thepresenttheoryonfoginertingpre-dicts1.02x10for7.2percentH2.ThefoginertingcriterionusedisdescribedinSection5.2.0430Q:16-15 Therefore,itappearsthatitispossibletoinert7percentH2butunlikely.However,at8percentH2intheupperplenum,whichoccursatabout4650seconds,thefogconcentrationis5.5x105,whichistoolowtoinert8percentH2.AnextrapolationoftheFactoryMutual8percentH2datato10pvolumemeandropsizeandthepresentpre-dictiongive1.9x10-4andl.2x10-4fortheminimumrequiredfoginertingconcentration,respectively.Thereforeboththetheoryandtheextrapolationoftestdatashowthatfoginertingwillnotoccurintheupperplenum.PgTheglowplugigniterswhichhavebeeninstalledintheSequoyahcon-tainmentweredesignedtoburnhydrogenlowerthan8.0percent.Asdiscussedpreviously,nofoginertingeffectswillbeexpectedintheSequoyahloweranduppercompartments.Therefore,theglowplugigni-tetsareexpectedtofunctionasdesignedinthesetwocompartments.Itmaybepossiblethatfogpresentintheicecondenserupperplenummaypreventtheglowplugignitersfromignitinghydrogenbelow7percent.However,itseemsveryunlikelythatthesameigniterswouldfailtoignite8.0percentH2asdesigned,consideringthefactthatconsider-ableconservatismhasbeenexercisedinthepresentanalysis.Sensitivitystudiesofthesprayremovalefficiencyandthefractionofblowdowndropletssmallerthan20pfortheSequoyahplanthavebeenperformed.Acaseof10percentsprayremovalefficiencywasrunusingFOGMASS.Thecalculationalresultsshowedthatthefogconcentrationsinthelowercompartment,lowerplenum,andupper.compartmentat4600secondswereincreasedapproximatelybyafactorof10.However,theseconcentrationsarestilltoolowtoinert8percenthydrogen-Incom-parison,thefogconcentrationintheupperplenumisincreasedbyonly20percentbecausetheconcentrationatthistimeisprimarilydeter-minedbythefogformationrateintheicecondenser.Thisincreaseistoosmalltochangetheconclusiongivenpreviouslyontheinertingprobabilityintheupperplenum.Anothercaseinwhichalltheblowdowndropletswereassumedtobesmallerthan20pwasrunusingFOGMASS.Thecalculationalresultsshowedthatat4600secondsthefogconcentra-tionsinthelowercompartmentandlowerplenumwereincreasedby150430QI6-16

(\

percentwhiletheincreasesintheupperplenumanduppercompartmentwerenegligiblysmall.Theinsensitivityofthefogconcentrationstotheparameterofthefractionofblowdowndropletssmallerthan20uisduetotheeffectivenessofthesprayremoval.At4600seconds,almostalltheblowdowndropletsareremovedbythesprays.Thesensitivitystudiesshowedthatthefogconcentrationintheupperplenumatthetimeofsignificanthydrogenreleaseisnotsensitivetothesprayremovalefficiencyandthefractionofblowdowndropletssmallerthan20g.0430(:16-17 L'jI TABLE6.1FOGIHPUTQATAFORSfgUOYAHLOWERCOMPARTMENTTime(sec)LowerCompartmentGasflowRate(ft/sec)Temp.('F)Temp('F)GasWallSteamTotalPartialPressurePressure~(sia)~(s(a)6061012101810241030103510401045101404.5646.73157.23115.52913.72871.?,2739.32755.92848.815021518818818017917817519711816.720221.617620.417620.517320.1169'9.916919.9164.19.417319.815.38.98.87.57.26.95.54.80430Q:16-18 TABLE6.2FOGINPUTDATAFORSEQUOYAHICECONDENSERIceCondenserGasFlowRateTime(sec)(ft/sec)GasTemp.('F)IceTemps('F)SteamTotalPartialPressurePressure~(sia)~(sia)606101210181024103010351040104510108296.4'265427992679262925022594262812013218618818217917817118732323232323232323216.621.820.420.520.019.919.919.419.82.52.38.18.87.67.27.05.74.70430Q16-19 (P

TABLE6.3GEOMETRICDATAFORSEgUOYAHCONTAIHMEHTVolume(ft)3FloorArea(ft)LowerCompartment289,0005,410IceCondenserLowerPlenum24,2003,100IceCondenserUpperPlenum47,0003,200UpperCompartment651,00010,390DeadEndedRegion94,0003,3500430(:16-20

k.

-TABLE6.4MARCHPREDICTIONOFREACTORCOOLANTMASSANDENERGYRELEASERATEFORTHES2DSEQUENCETime(seconds)H20MassRe1easeRate(Ibm/sec)H20EnergyRe1easeRate(Btu/sec)0.021722478318038044428475257006012696070627206197.2190.544.8553.5334.8221.4048.4219.4214.07-5.2534.7184.0601.167x101.097x105.230x106.547x104.262x102.842x105.558x102.182x101.583x105.989x1035.388'x1034.693x100430Q:16-21 Ig TABLE6.5IHTERCOMPARTHENTALfLOMRATES(ft/sec)PREDICTEDBYCLASIXFORSEQUOYAHTime(sec)FlowFromFlowFromFlowFromflowFromflowFromLCtoLPLPtoUPUPtoUCUCtoLCDEtoLC6.001E16.100E21.210E31.810E32.410E33.010E33.510E34.010E34.510E31.175E33.580E22.864E32.828E3'.695E32.654E32.528E32.613E32.694E31.082E39.641E12.654E32.799E32.679E32.629E32.502E32.594E32.628E37.029E2-3.931E11.272E31.323E31.375E31.407E31.352E31.537E31.627E3-1.095E2-1.106E2-,3.348E1-4.426E1-9.905E1-1.304E2-2.113E1-2.676E2-1.838E2-1.094E2-1.793E2-1.088E2-1.502E2-6.855E1-1.634E2-6.326E1-1.643E2-4.699E10430Q:I6-22 46.3FOGIHERTIHGPROBABILITYIHTHEMcGUIREPLAHTIThecomputercodes,FOGandFOGMASS,wereusedtoperformfoginertinganalysisfortheMcGuireplant.FOGwasusedtocalculatetheratesoffogformationduetoboundarylayerandbulkstreamcondensationintheMcGuireicecondenserandlowerplenum.ThenthesefogformationrateswereusedinFOGMASStocomputethefogconcentrationsineachoftheMcGuirecontainmentsubcompartments.Tocomputethefogformationratesintheicecondenserupperplenumandlowercompartment,'someoutputdatafromtheMcGuireCLASIXanaly-sisareneeded.Thesedataincludetimehistoriesofgastempera-(28)ture,walltemperature,totalpressure,andsteampartialpressureineachcontainmentsubcompartment,aswellastheintercompartmentalandfanflowrates.InordertoutilizetheCLASIXoutputdata,theicecondensercontainmentissubcompartmentalizedintheFOGMASSprograminexactlythesamemannerasinReference28.Thesubcompartmentaliza-tionmodelusedintheMcGuireCLASIXanalysisisshowninFigure6.5.InthisstudyonlytheS20accidentscenariohasbeenanalyzedbyCLASIXforMcGuire.4~TheFOGinputdataforMcGuireS2DCaseIaregiveninTables6.6and6.7,andthecalculationalresultsareshowninFigures6.6and6.7.InFigure6.6,thefogformationrateinthelowercompartmentisshown.Forthefirstfewhundredsecondsthewalltemperatureislowerthanthedewpointcorrespondingtothesteampartialpressureandthereforefogstartstoform.Thefogformationrateislowbecausethewalltempera-'ureisonlyafewdegreesbelowthedewpoint.Fogformationinthelowercompartmentbecomeszeroafterabout600seconds.Thefogforma-tionrateintheicecondenserisshowninFigure6.7.Itisseenthatthefogformationrateintheicecondenserismuchlargerthanthatinthelowercompartment.Thefogformationrateincreaseswiththeicecondensersteamflowrateandreachesthefirstpeakatabout1510sec-onds.Thentheratedecreasesbecauseofthedecreaseinthesteamflowrate.Thefogformationandthesteamflowratesstarttoincreaseagainatabout2510seconds.Thefogformationratereachesthesecond0430Q:I6-23

II~l~~r<~~~00~~~~~~~~~~~~~~~'~'~~~~I "e4

~~

peakofI0.21b/secatabout3260seconds.Theeightfogformation'ratesinthelowercompartmentandintheicecondenserareinputtoFOGNSSinatabularform.FOGNSScomputestherateoffoggenerationbythebreakflow,thefogsettlingrateduetogravity,andthefogremovalrateduetosprays,aswellastheratesoffogentrainmentbyintercompartmentalandfanflows.Theinputdataneededtocalculateeachoftheseratesaredis-cussedasfollows.0)'TherateofreactorcoolantreleasetothecontainmentandthecoolantenthalpywereobtainedfromtheNRCHoutputforasmallLOCA.TheP)qualityofthebreakflowwascalculatedusingtheenthalpyandthelowercompartmentgastemperature.AccordingtotheNRCHpredic-tionthedischargeofliquidbythebreakflowintothelowercom-partmentlastsforonly2172seconds.Afterward,thewaterlevelinthereactorvesseldropsbelowthebreakelevationandthefluiddischargedfromthebreakisessentiallysteam.Therefore,inthepresentstudy,itisassumedthatnofogisgeneratedbythebreakflowafter2172seconds.Forfogremovalbygravitationalsettling,avolumemeandropsizeof10pwasassumed.Theassumptionof10pvolumemeandropsizeiscon-servative,consideringthefactthatforafewthousandsecondsthedropagglomerationmechanismwouldbeabletoincreasevolumemeandropsizesubstantially.Itshouldalsobenotedthatasmallervolumemeandropsizemeansthattheminimumfoginertingconcentrationwouldbereducedandthusmakesthepresentanalysisconservative.Furthermore,nocon-siderationwasgiventothedepositionoffogonthewallsandverticalsurfacesofthestructure,orforfogremovalinthefanflowswhenitpassesthroughductsandfans.Alltheassumptionsmentionedabovemakethepresentanalysisveryconservative.ThecontainmentgeometricdataneededincomputingthesettlingratearegiveninTable6.8.0430QI6-27 C4 Forfogremovalbysprays,asprayflowrateof6800gpmwasusedforRcGuire.AccordingtotheHcGuireCLASIXanalysis,thespraysareinitiatedat124seconds.Avolumefractionofsprays(volumeofspraysdividedbyvolumeofthesprayzone)of3.3x10wasused.Aspre-viouslydiscussedasprayremovalefficiencyofa100percentefficiencywasused.InFigure6.5,thedirectionsoftheintercompartmentalflowsareshown.TheintercompartmentalflowratesforthesixflowpathsandeighttimestepswereobtainedfromtheOPSCLASIXanalysisandaregiveninTable6.9.Thepresentanalysisconsiderstheintercompart-mentalflowsasthemechanismsoftransportingfogfromonecompartmenttoanother.Itwasassumedinthepresentanalysisthatthefogconcen-trationsintheintercompartmentflowsarethesameasthoseinthecompartmentsfromwhichtheflowsareoriginated.Figure6.5showstwotrainsoftheairreturnfanandhydrogenskimmersystemandthefanflowdirections.Thefansareinitiatedat694sec-onds.Thefanhead-flowcurvereportedinReference28wasusedto3computethefanflowrates.Fanflowratesof1000ft/secand100ft/secwereusedfortheairreturnfanandthehydrogenskimmer3system,respectively.Theseflowrateswerecalculatedusingaverageap'sbetweentheuppercompartmentandthelowercompartment,andbetweenthedeadendedregionandtheuppercompartment.Itwasalsoassumedthatthefogconcentrationsinthefanflowsarethesameasthoseinthecompartmentsfromwhichtheflowsareoriginated.TheresultsoftheFOGMASScalculationareshowninFigure6.8.Itisseenthatforthefirstfewhundredsecondsthefogconcentrationsinthelowercompartment,icecondenserlowerandupperplenumsareaboutthesameandincreasing.Atabout600seconds,thelowercompartmentfogconcentrationreachesitspeakof1.6x10.Afterward,theintercompartmentalflowstransportmorefogdropletsoutofthelowercompartmentthanaregeneratedbythebreakflowandcondensationand,therefore,thelowercompartmentfogconcentrationdecreases.However,theupperplenumfogconcentrationkeepsrisinguntilabout800seconds,0430Q:I6-28

~~0I~I~~I'II~~~0WCa~~~~.~0~0~4~0~~~

)

duetoanincreasingfog.formationintheicecondenserandmorefogentrainedintheintercompartmentalflowintotheupperplenum.Theupperplenumfogconcentrationreachesitspeakof6.4x10atabout800seconds.Thelowerplenumfogconcentrationisalmostthesameasthelowercopartmentfogconcentrationbecauseoflittledifferenceintheintercompartmentalflowratesintoandoutoftheicecondenserlowerplenum.Therefore,thesetwovolumesbehaveasasinglevolumeintermsoffogconcentration.At2172seconds,thebreakflowinthelowercompartmentstopsgenera-tingfogand,'herefore,thefogconcentrationsdropsharplythere-after.Theeffectismorepronouncedforthelowercompartmentandlowerplenumfogconcentrations.Thehighestfogconcentrationexistsintheicecondenserupperplenumwhilethelowestexistsintheuppercompartment.Theeffectofspraysontheuppercompartmentfogconcen-trationisclearlyseeninFigure6.8.At124seconds,thespraysareturnedonandtheuppercompartmentfogconcentrationdropssharplyuntilabout600seconds.Atabout600seconds,theuppercompartmentfogconcentrationstartstoincreaseagainbecausetheintercompart-mentalflowintothecompartmentincreasessharplyatthattime.Apeakconcentrationof7.5x10intheuppercompartmentisreachedatabout1500seconds.Hydrogenstartstoreleaseintothecontainmentatabout3804seconds,accordingtotheMARCHcalculation.Itreaches4volumepercentatabout4300,4400,and4850secondsinthelowercompartment,upperplenum,anduppercompartment,respectively.At4300seconds,thecalculatedlowercompartmentfogconcentrationis84x10,whichisaboutanorderofmagnitudesmallerthantheminimumfogconcentrationsrequiredforinerting4percentH2.At4850seconds,theuppercompartmentfogconcentrationis1.47x10whichisaboutafactoroffivesmallerthantheminimumfogconcen-trationrequiredforinerting4percentH2*.=Atthetimesof*ThefoginertingcriterionusedisdescribedinSection5.2.0430Q:16-30 reaching8.5percentH2,thefogconcentrationsintheloweranduppercompartmentsareevenlowerthanthefiguresgivenabove.Therefore,itisconcludedthatthefogconcentrationsintheloweranduppercompart-mentsaretoolowtohaveanyinertingeffect.Theuseofthepresenttheoryonfoginertingalsoleadstothesameconclusion.However,at4400seconds,thecalculatedfogconcentrationintheupperplenumis9.8x10whichishigherthantheFactoryMutualfoginertingdataextrapolatedto10pdropsandthepresenttheoreticalprediction.Thedatashowsthatinordertoinert4.76percentH2thefogconcentrationniustbe8.4x10orhigherfor10pvolumemeandropsize.At4500seconds,theupperplenumhydrogenconcentration-5reachesabout7percentandthefogconcentrationis9.3x10Again,anextrapolationoftheFactoryMutualdatato)0pshowsthatfogconcentrationof2.1x10orhigherisrequiredtoinert7.2percentH2.Incomparison,thepresenttheoryonfoginertingpre-dicts1.02x10for7.2percentH2.Therefore,itappearsthatitispossibletoinert7percentH2,butunlikely.However,at8per-centH2intheupperplenum,whichoccursatabout4600seconds,thefogconcentrationis9.1x10,whichistoolowtoinert8percentAnextrapolationoftheFactoryMutual8percentH2datato104uvolumemeandropsizeandthepresentpredictiongive1.9x10and1.2x10fortheminimumrequiredfogincrtingconcentration,respectively.Therefore,boththetheoryandtheextrapolationofthe'estdataindicatethatfoginertihgwillnotoccur.TheglowplugigniterswhichhavebeeninstalledintheMcGuirecontain-mentweredesignedtoburnhydrogenlowerthan8.5percent.Asdiscus-sedpreviously,nofoginertingeffectswillbeexpectedintheMcGuireloweranduppercompartments.Therefore,theglowplugignitesareexpectedtofunctionasdesi'gnedinthesetwocompartments.Itmaybepossiblythatfogpresentintheicecondenserupperplenummaypreventtheglowplugignitesfromignitinghydrogenbelow7percent.However,itseemsveryunlikelythatthesameigniterswouldfailtoignite8.5"Thefoginerting'criterionusedisdescribedSection5.2.0430Q:16-31 percentH2asdesigned,consideringthefactthatconsiderableconser-vatismhasbeenexercisedinthepresentanalysis.0430Q:16-32 TABLE6.6FOGINPUTDATAFORMcGUIRELOWERCOMPARTMENTLowerCompartmentGasGasFlowRateTemp.Time(sec)(ft/sec)('F)WallTotalTemp.PressureSteamPartialPressure~(sia)605101510201025103260376045101624.61248.12387.82393.81940.72055.-51801.71919.316014916.522521522.220519821.920519822195193'21.520019521.6200,1942125022221.218.312.612.410.410.89.37.30430/:16-33 TABLE6.7FOGIHPUTDATAFORHcGUIREICECOHDEHSERIceCondenserGasFlowRateTime(sec)(ft/sec)SteamGasIceTotalPartialTemp.Temp.PressurePressure60510151020102510326037604510820.5107.119261637114516301514146490130190193188195193192323232323232323216.522.2"21.92221.421.621.122.12.39.38.610.38.17.10430Q:16-34 TABLE6.8GEOMETRICDATAFORMcGUIRECONTAINMENT'IVolume(ft)FloorArea(ft)LowerCompartment237,4005,410IceCondenserLowerPlenum24,2003,100IceCondenserUpperPlenum47,0003,200UpperCompartment670,00010,390DeadEndedRegion130,9003,3500430Q:1~6-35 l

TABLE6.9IHTERCOMPARTMEHTALFLOWRATES(ft/sec)3PREDICTEDBYCLASIXFORMcGUIRETime(sec)FlowFromflowFromFlowFromFlowFromFlowfromLCtoLPLPtoUPUPtoUCUCtoLCDEtoLC6.001E15.100E21.510E32.010E32.510E33.260E33.760E34.510E31.351E38.716E22.008E32.010E31.722E31.713E31.546E31.634E38.205E21.071E21.926E31.637E31.145E31.630E31.514E31.464E3-1.198E2-1.538E2-2.863E1-3.479E2-1.900E2-1.898E2-2.266E2,-1.572E25.783E2,-2.269E18.635E26.869E24.807E26.666E27.231E2-1.410E2-2.087E2-7.767E1-1.338E2-1.289E2-1.268E27.640E2-1.328E2-1.515E20430Q:16-36 6.4FOGINERTINGPROBABILITYINTHED.C.COOKPLANTf'hecomputercodes,FOGandFOGMASS,wereusedtoperformfoginertinganalysisfortheD.C.Cookplant.FOGwasusedtocalculatetheratesoffogformationduetoboundarylayerandbulkstreamcondensationintheD.C.Cookicecondenserandlowerplenum.ThenthesefogformationrateswereusedinFOGMASStocomputethefogconcentrationsineachoftheD.C.Cookcontainmentsubcompartments.Tocomputethe,fogformationratesintheicecondenserupperplenumandlowercompartment,some'outputdatafromtheCookCLASIXanalysis(29)areneeded.Thesedataincludetimehistoriesofgastemperature,walltemperature,totalpressure,andsteampartialpressureineachcontain-mentsubcompartment,aswellastheintercompartmentalandfanflowrates.InordertoutilizetheCLASIXoutputdata,theicecondensercontainmentissubcompartmentalizedintheFOGMASSprograminexactlythesamemannerasinReference29.ThesubcompartmentalizationmodelusedintheCookCLASIXanalysisisshowninFigure6.9.InthisstudyonlytheS20accidentscenariohasbeenanalyzed.TheFOGinputdataforCookS2DCase.1aregiveninTables6.10and6.11,andthecalculationalresultsareshowninFigures6.10and6.11.'nFigure6.10,thefogformationrateinthelowercompartmentisshown.Itisseenthatthefogformationrateisnegligiblysmall.Itshouldbenotedthatthecalculationofthelowercompartmentfogconcentrationinthe0.C.Cookplantstartsat600secondsinsteadof60secondsusedfortheothertwoplants.Thefogformationrateinthelowercompartmestartstoincreaseatabout4200secondsbecauseoftheincreaseinthesteampartialpressure.Itreaches0.017lb/secatabout4590seconds.Fogformationinthelowercompartmentwillstopafter4700secondsbecauseofthehydrogenburnthereafter.ThefogformationrateintheicecondenserisshowninFigure6.11.Itisseenthatthefogformationrateintheicecondenserismuchlargerthanthatinthelowercompartment.Itincreaseswiththeicecondensersteamflowrateandreachesapeakofabout15.6lb/secatabout1200seconds.Thefogformationrateintheicecondenserthenbeginstodecreaseandislowatthetimeofsignificanthydrogenrelease.0430Q16-37

~~~~~~~0o~0~~0~l~0~~~~~~~c~+j~~~~~~'J~'~~~

IIIIIIIIIIIIIIIIIIIeI I

II'IIIIIIIIIIIlIIIIIII Theeightfogformationratesinthelowercompartmentandintheice.condenserareinputtoFOGMASSinatabularform..:FOGMASScomputestherateoffoggenerationbythebreakflow,thefogsettlingrateduetogravity,andthefog-removalrateduetosprays,aswellastheratesoffogentrainmentbyintercompartmentalandfanflows.Theinputdataneededtocalculateeachoftheseratesaredis-cussedasfollows.Therateofreactorcoolantreleasetothecontainmentandthecoolant'IP)enthalpywereobtainedfromtheMARCHoutputforasmallLOCA.Thequalityofthebreakflowwascalculatedusingtheenthalpyandthelowercompartmentgastemperature.AccordingtotheMARCHpredic-tionthedi,schargeofliquidbythebreakflowintothelowercom-P)partmentlastsforonly2172seconds.Afterward,thewaterlevelinthereactorvesseldropsbelowthebreakelevationandthefluiddischargedfromthebreakisessentiallysteam.Therefore,inthepresentstudy,itisassumedthatnofogisgeneratedbythebreakflowafter2172seconds.Forfogremovalbygravitationalsettling,avolumemeandropsizeof10pwasassumed.Theassumptionof10pvolumemeandropsizeiscon--servative,consideringthefactthatforafewthousandsecondsthedropagglomerationmechanismwouldbeabletoincreasevolumemeandropsizesubstantially.Itshouldalsobenotedthatasmallervolumemeandropsizemeansthattheminimumfoginertingconcentrationwouldbereducedandthusmakesthepresentanalysisevenmoreconservative.Further-more,noconsiderationwasgiventothedepositionoffogonthewallsandverticalsurfacesofthestructure,orforfogremovalinthefanflowswhenitpassesthroughductsandfans.Alltheassumptionsmen-tionedabovemakethepresentanalysisveryconservative.Thecontain-mentgeometricdataneededincomputingthesettlingratearegiveninTable6.12.0430Q:I6-41 C

Forfogremovalbysprays,sprayflowratesof4000,1800,and528gpmwereusedfortheuppercompartment,lowercompartment,andfan/accumulatorrooms,respectively.AccordingtotheCookCLASIXanalysis~~,thespraysareinitiatedat141seconds.Avolumefractionofsprays'(volumeofspraysdividedbyvolumeofthesprayzone)of3.3x10-4wasused.Aspreviouslydiscussedasprayremovalefficiencyofa100percentefficiencywasused.InFigure6.9,thedirectionsoftheintercompartmentalflowsareshown.Theintercompartmentalflowratesforthesixflowpathsandeighttimesteps'wereobtainedfromtheOPSCLASIXanalysisandaregiveninTable6.13.Thepresentanalysisconsiderstheintercompart-mentalflowsasthemechanismsoftransportingfogfromonecompartmenttoanother.Itwasassumedinthepresentanalysisthatthefogconcen-trationsintheintercompartmentflowsarethesameasthose:inthecompartmentsfromwhichtheflowsareoriginated.Figure6.9showstwotrainsoftheairreturnfanandhydrogenskimmersystemandthefanflowdirections.Thefansareinitiatedat711sec-onds.Thefanhead-flowcurvereportedinReference29wasusedtocomputethefanflowrates.Fanflowratesof1388,61.76,and4.13ft3/secwereusedfortheflowsfromtheuppercompartment,lowercompartment,anddeadendedregiontothefan/accumulatorrooms,respectively.Theseflowrateswerecalculatedusingthehp'sbetweenthethefan/accumulatorroomsandthreeothercompartments.Itwasalsoassumedthatthefogconcentrationsinthefanflowsarethesameasthoseinthecompartmentsfromwhichtheflowsareoriginated.TheresultsoftheFOGMASScalculationareshowninFigure6.12.Itisseenthatforthefirstfewhundredsecondsthefogconcentrationsinthelowercompartment,andtheicecondenserlowerplenumarehigh.Atabout140seconds,thelowercompartmentfogconcentrationreachesitspeakof1x10-4.Afterthespraysareinitiatedat141seconds,thefogconcentrationsinthelowercompartment,uppercompartment,andfan/accumulatorroomsdropsharply.However,theupperplenumfogconcentrationkeepsrisinguntilabout1200seconds,'uetoanincreasing0430Q:16-42 III~T~~I~~I~III~T~~~I

'l fogformationintheicecondenserandmorefogentrainedintheintercompartmentalflowintotheupperplenum.Theupperplenumfogconcentrationreachesitspeakof2.4x10atabout1200seconds.Afterabout1200seconds,thelowerplenumfogconcentrationisalmostthesameasthelowercopartmentfogconcentrationsincetheintercompartmentalflowsquicklymakethefogconcentrationsinthesetwocompartmentsuniform.Therefore,thesetwovolumesbehaveasasinglevolumeintermsoffogconcentration.At2172seconds,thebreakflowinthelowercompartmentstopsgenera-tingfogand,therefore,thefogconcentrationsdropsharplythere-after.Theeffectismorepronouncedforthelowercompartmentandlowerplenumfogconcentrations.Thehighestfogconcentrationexistsintheicecondenserupperplenum.TheeffectofspraysontheuppercompartmentfogconcentrationisclearlyseeninFigure6.12.At141seconds,thespraysareturnedonandtheuppercompartmentfogconcentrationdropssharplyuntilabout300seconds.Atabout300seconds,theuppercompartmentfogconcentrationstartstoincreaseagainbecausetheintercompartmentalflowintothecompartmentincreases-6sharplyatthattime.Apeakconcentrationof9.5x10intheuppercompartmentisreachedatabout1400seconds.Hydrogenstartstoreleaseintothecontainmentatabout3804seconds,accordingtotheHARCHcalculation.Itreaches4volumepercentatabout4350,4370,and4700secondsinthelowercompartment,upperplenum,anduppercompartment,respectively.At4350seconds,thecalculatedlowercompartmentfogconcentrationis10,whichisabouttwoordersofmagnitudesmallerthantheminimumfogconcentrationsrequiredforinerting4percentH.At4700-6seconds,theuppercompartmentfogconcentrationis2.4x10,whichisaboutafactoroftwosmallerthantheminimumfogconcentrationrequiredforinerting4percentH*.Atthetimesofreaching8.5*ThefoginertingcriterionusedisdescribedinSection5.2.0430Q:16-44 percentH,thefogconcentrationsintheloweranduppercompartmentsareevenlowerthanthefiguresgivenabove.Therefore,itisconcludedthatthefogconcentrationsintheloweranduppercompartmentsaretoolowtohaveanyinertingeffect.Theuseofthepresenttheoryonfoginertingalsoleadstothesameconclusion.However,at4370seconds,thecalculatedfogconcentrationintheupperplenumis6.5x10which'shigherthantheFactoryMutualfoginertingdataextrapolatedto10pdropsandthepresenttheoreticalprediction.Thedatashowsthatinordertoinert4.76percentH2thefogconcentrationmustbe8.4x10orhigherfor10pvolumemeandropsize.At4530seconds,theupperplenumhydrogenconcentration-5reachesabout7percentandthefogconcentrationis5.5x10Again,anextrapolationoftheFactoryMutualdatato10pshowsthatfogconcentrationof2.1x10orhigherisrequiredtoinert7.2percentH2.Incomparisonthepresenttheoryoffoginertingpredicts1.02x10for7.2percentH2.Therefore,itappearsthatitispossibletoinert7percentH2,butunlikely.However,at8percentH2intheupperplenum,whichoccursatabout4600sec'onds,thefog-5concentrationis5.1x10,whichistoolowtoinert8percentH2.AnextrapolationoftheFactoryMutual8percentHdatato104uvolumemeandropsizeandthepresentpredictiongive1.9x10and1.2x10fortheminimumrequiredfoginertingconcentration,respectively.TheglowplugigniterswhichhavebeeninstalledintheCookcontainmentweredesignedtoburnhydrogenlowerthan8percent.Asdiscussedpre-viously,nofoginertingeffectswillbeexpectedintheCookloweranduppercompartments.Therefore,theglowplugignitersareexpectedtofunctionasdesignedinthesetwocompartments.Itmaybepossiblethatfogpresentintheicecondenserupperplenummaypreventtheglowplugignitersfromignitinghydrogenbelow7percent.However,itseemsveryunlikelythatthesameigniterswouldfailtoignite8percentH2asdesigned,consideringthefactthatconsiderableconservatismhasbeenexercisedinthepresentanalysis.0430Q16-45 TABLE6.10FOGINPUTDATAFORD.C.COOKLOWERCOMPARTMENTTime(sec)LowerCompartmentGasWal1TotalGasFlowRateTemp..Temp.Pressure(ft/sec)('F)('F)~(sia)SteamPartialPressure.~(sia)6001200180024003000360042004590799.42798.2,2805.82513.62448.52359.72272.32482.7222190190180178175165168215.2183.5180.3177.2170.4169.321.820.22019.619.319.2161.918.816119,517.49.49.17.67.26.45.35.80430Q:16-46

TABLE6.11FOGINPUTDATAFORD.C.COOKICECONDENSERIceCondenserGasFlowRateTime(sec)(ft/sec)3GasTemp.('F)IceTemp~('F)TotalPressure~(sia)SteamPartialPressure~(sia)6001200180024003000360042004590762548257223592256219921262312147190188184187175166163323232323232323221.820.119.919.719.319.218.819'.83.49.39.07.97.16.65.34.30430Q:I6-47 TABLE6.12GEOMETRICDATAFORD.C.COOKCONTAINMENTVolume(ft)FloorArea(ft)LowerCompartment249,6815,410IceCondenserLowerPlenum24,7003,100IceCondenserUpperPlenum47,0103,200UpperCompartment681,28310,390DeadEndedRegionFan/AccumulatorRooms61,10554,8288532,5000430Q:I6-48 TABLE6.13INTERCOMPARTMENTALFLOWRATES(ft/sec)PREDICTEDBYCLASIXFORD.C.COOKTime(sec)FlowFromFlowFromFlowFromFlowFromFlowFromFlowFromLCtoLPLPtoUPUPtoUCUCtoLCDEtoLCF/AtoLC60012001800240030003600420045906.387E22.577E32.600E,32.356E3;2.273E32.202E32.136E32.346E37.600E12.548E3,2.572E32.359E32.256E32.199E32.126E32.312E3-4.410E11.106E31.155E31.145E31.178E31.190E3l.258E31.400E3-3.746E1'1.740E2-1.232E2-4.720E1-1.620E2-4.381E1-1.325E2-2.512E1-1.463E2-2.923E1-1.334E2-2.333E1-1.183E2-1.802E1-1.130E2-2.371E1-1.229E21.509E31.529E31.595E31.553E31.603E31.642E31.650E30430Q:I6-49

6.5EFFECTOFFOGONGLOBALCOMBUSTIONInordertoassesstheeffectoffogonthedeflagrationlimitofhydro-gen,whichisdefinedastheminimumhydrogenconcentrationatwhichtheflamepropagatesin,alldirections,aflametemperaturecriterionwhichconsidersfogdropletsasaheatsinkwasused.Thiscriterionassumesthatthecriticalflametemperatureof710Cisstillapplicabletoahydrogenmixturewhichcontainsfogdroplets.Foragivenfogconcen-tration,theheatrequiredtoheataunitmassofthemixtureto710ccanbecalculated.'henthehydrogenconcentrationneededtosupplythisamountofheat,assuming100percentcombustion,canbedeter-mined.Usingthismethod,thecalculatedfogconcentrationsof5.5x10and5.1x10fortheSequoyahplantat4650secondsandfortheD.C.CookPlantat4600seconds,respectively,werefoundtobecapableofraisingthedeflagrationlimitto10.6vol.percentH2.In-5comparison,thecalculatedfogconcentrationof9.1x10fortheMcGuireplantat4600secondswasfoundtobecapableofraisingthedeflagrationlimitto12vol.percentH2.Thisstudyshowsthatinordertoachieveglobalcombustionintheupperplenum,hydrogenconcen-trationhigherthan8.5percentmayberequired.Theeffectofincreas-inghydrogenconcentrationrequiredtoobtainglobalcombustionin.theupperplenumshouldbeinvestigated.F0430Q:16-50 7.0SUMMARYANDCONCLUSIONSThepresentstudyhasdevelopedasystematicmethodologytostudythepotentialfoginertingproblemforthePWRicecondenserplants.Inthepresentinvestigation,majorfogformationandremovalmechanismsareidentifiedandquantified.Theoreticalmodelsaredevelopedtopredictthefogformationrateduetoboundarylayerandbulkstreamcondensa-tion,thefogremovalratesduetogravitationalsettlingandcontain-mentsprays.Themassconservationequationsforthefogdropletsineachofthecontainmentsubcompertmentsaresolvedsimultaneouslyinordertoobtaintimehistoriesoffogconcentration.Theseequationsincorporatefogformationduetocondensation,foggenerationduetobreakflow,fogremovalduetogravitationalsettlingandsprays,trans-portoffogbytheintercompartmentalflowsandfanflows.ComputerprogramsFOGandFOGMASShavebeendevelopedtocomputefogformationratesandfogconcentrationsineachofthecontainmentsubcompart-ments.ThesetwocomputerprogramshavebeenusedtoanalyzeaS<DaccidentsequencefortheSequoyah,McGuire,andD.C.Cookplants.TheanalysesemployedoutputdatafromtheSequoyahCLASIXanalyses.Speci-fically,timehistoriesofgastemperature,walltemperature,totalpressure,andsteampartialpressureineachcontainmentsubcompartment,aswellastheintercompartmentalandfanflowrateswereusedinthepresentanalysis.Afoginertingcriterionhasbeendevelopedtopredicttheminimumfogconcentrationrequiredtoinertagivenhydrogenconcentrationandvolumemeanfogdropsize.ThepresentfoginertingcriterionhasbeenshowntobeinagreementwiththeFactoryMutualdata.Thecriterionshowsthattheminimumfoginertingconcentrationvarieswiththesquareofthevolumemeanfogdropsize.Thepresentstudyshowsthatthefogconcentrationsintheupperandlowercompartmentsofthethreeplantsanalyzedaretoolowtohaveanyinertingeffectonhydrogenmixtures.Therefore,theproposedglowplugignitersareexpectedtofunctionasdesignedinthesetwocompart-ments.Itmaybepossiblethatfogpresentintheicecondenserupper0430Q:I7-1

plenummaypreventtheglowplugignitersfromignitinghydrogenbelow7~~~percent.However,itseemsveryunlikelythatthesameigniterswouldfailtoignite8.5percentH2asdesigned.Itshouldberecognizedthattheexistingtheoriesanddatacanonlypredicttheminimumfogconcentrationforinerting.Furtherworkmayberequiredtoverifythefoginertingtheoryassociatedwithflamepropagationinalldirections.0430Q:I7-2 ACKNOWLEDGMENTSTheauthorwishestoexpresshissinceregratitudetoMr.N.J.Liparulo,Drs.Y.Srinivas,B.Lewis,andB.Karlovitzforassistance,sugges-tions,andhelpfuldiscussions,particularlyintheareaofthefoginertingcriteriaandtheflametemperaturecriteriaforfog,toMessrs.D.F.Paddleford,R.Bryan,F.G.Hudson,andK.Shiuforvaluab1e.comnents,toMr.K.C.Perry,Mr.S.J.Reiser,andMs.,R.M.Marinerforprovidingdataonthethreeicecondenserplants,andtoMr.T.J.,Mieleforprovidingprogrammingassistance.HealsowouldliketothankTYA,DukePower,andAEPforprovidingthefinancialsupport.0430Q:17-3

REFERENCES1.B.Lowry,"PreliminaryResults:AStudyofHydrogenIgniters,"ENNBO-45;LawrenceLivermoreNationalLaboratory,November17,1980.2."AdditionalguestionsonHydrogenControlSystemforIceCondenserPlants,"NRCmemofromL.RubensteintoR.Tedesco,datedJune26,1981.3."TheMarvikkenFullScaleContainmentExperiments,"MXB-301ABAtomenergi,March,1977.*4.T.F.Kanzleiter,"LOCAExperimentsWithaPWRMulti-CompartmentModelContainment,"Trans.1977LWRSafetyConf.,IdahoFalls,Idaho,1977.5.G.'M.Fuls,"TheCLASIXComputerProgramfortheHydrogenReleaseandDegradation",OPS-07A35,OffshorePowerSystems,1981.6.K.K.Almenas,"ThePhysicalStateofPost-Loss-of-CoolantAccidentContainmentAtmospheres,"Vol.44,NuclearTechnology,pp.411.-427,August,1979.7."SummaryofAnalysisofIceCondenserContainmentResponsetoHydro-genTransients,"OffshorePowerSystemsreportNo.RP-28A52,Septem-ber,1980.8.R.BrownandJ.L.York,"SpraysFormedbyFlashingLiquidJets,"Vol.8,No.2,AICh.EJournal,p.149,May,1962.(9.R.G.Gido,andA.Koestel,"LOCA-GeneratedDropSizePrediction-AThermalFramentationModel,"Trans.Am.Nucl.Soc.,30,p.371.1978.10.P.G.Hill,H.Witting,andE.P.Demetri,"CondensationofMetalVaporsDuringRapidExpansion,"JournalofHeatTransfer,p.303,November,1963.0430/:1R-1 11.M.VolmerandH.Flood,Z.PhysikChemic,A170,p.273,1934.12.C.E.Junge,Advan.Geophys.,H.LandsbergandJ.VanMieghem,ed.,4.1,AcademicPress,NewYork,1958.13.R.J.Burian,andP.Cybulskis,"CORRALIIUserManual,"BattelleColumbusLaboratories,January,1977.14.R.K.HilliardandL.F.Coleman,"NaturalTransportEffectsonFissionProductBehaviorintheContainmentSystemsExperiment,"BNWL-7457,Battelle-Northwest,Richland,Washington,1970.15.N.H.Fletcher,J.Chem.Phys.,29,p.572;31,p.1136,1958.16.D.E.RosnerandM.Epstein,"FogFormationConditionsNearColdSurfaces,"Vol.28,No.1,J.ofColloidandInterfaceSci.,Septem-ber,1968.17.K.Hijikata,andY.Mori,"ForcedConvectiveHeatTransferofaGasWithCondensingVaporAroundaFlatPlate,"Vol.2,No.1,HeatTransfer-Jap.Res.,pp.81-101,January,1973.18.M.NeiburgerandC.W.Chien,"ComputationoftheGrowthofCloudDropsbyCondensationUsinganElectronicDigitalComputer,"Geophys.MonographNo.5,pp.191-209,1960.19.R.M.Kemper,"IodineRemovalbySprayintheSalemStationContain-ment,"WCAP-7952,WestinghouseElectricCorp.,August,1972.20.N.J.Liparulo,J.E.OlhoeftandD.F.Paddleford,"GlowPlugIgnitorTestsinH2Mixtures,"WCAP-5909,WestinghouseElectricCorp.,March6,1981.21.R.G.ZaloshandS.N.Bajpai,"WaterFogInertingofHy'drogen-AirMixtures,"EPRIProjectPreliminaryRp.1932-1,September,1981.0430Q:I

22.J.M.Marchello,"ControlofAirPollutionSource,"MarcelDekker,~~~~~Inc.,HewYork,1976.23.LetterfromB.LewisandB.KarlovitztoL.E.Hochreiter,datedmay5,1980.24.M.Berman,etal.,"AnalysisofHydrogenMitigationforDegradedCoreAccidentsintheSequoyahNuclearPowerPlant,"Sandiadraftreport,December1,1980.25.T.vonKarman',Unpublishednotes,1956.26.S.S.Tsai,"FlameTemperatureCriteriaTests,"HS-CCA-81-039,West-inghouseinternalmemo,datedJune17,1981.27.AttachmenttoOffshorePowerSystemletterPST-HE-109,datedMay22,1981.28.AttachmenttoOffshorePowerSystemletterPST-NE-106,datedMay14,1981.29.AttachmenttoOffshorePowerSystemletterPST-HE-218,datedAugust6,1981.30.M.L.Corrin,J.R.Connel,andA.J.Gero,"AnAssessmentofWarmFog-Nucleation,Control,andRecommendedResearch,"NASACR-2477,November,1974.0430Q:1R-3

APPENDIXAC0MPUTATI0N0FYoANDgINEQUATI0N{312)TheHijikata-MorifogapproximationforthefogconcentrationandassumedinEqs.(3.7)intotheconservationformationtheoryusedtheboundarylayercontinuity,momentum,andenergyequations.Thevelocityprofilesintheboundarylayerareand(3.S).SubstitutingEqs.(3.7)through(3.10)equations,wehave33V-(+)~997Y+v=0Ioca-m'rr<'m"'m<V-'-'371mm".'-'-z"')x311,3I(A-1)(A-2)(A-3)A(n)+B(n)g+C(n)+~EY7'F)Proo=g)p--V-V(1+E)Y0(A-4)whereA(n)-B(n)=C(n)=3(n+5)n+n+3(n+6)n+n+n+3(n+7)bW2hWhE=HrPg0430Q:1A-1 0

6vvl00W0aWSfgCpghTTOOT0weightfractionofvaporatfreestreamweightfractionofvaporatwallW'-WSchmidtnumberkineticviscositycomponentofthefreestreamvelocityperpendiculartothewallheatofvaporizationspecificheatofnon-condensiblegasT-TogastemperatureatfreestreamgastemperatureatwallEquations(A-I)through(A-4)arefouralgebraicequationsforfourunknowns,Y,g,R,andv'TheseequationshavebeensolvedbythecomputerprogramFOG.InFOG,thevaluesofY,g,andRarecomputedandusedinEq.(3.12)tocomputethefogformationrate.0430Q:1A-2 I

.APPENDIXBDERIVATIONOFEQUATION(5.5)ThisappendixgivesdetailedprocedurestoderiveEq.(5.5),startingfromEq.(5.4)criteiu-Yf)/ei)(5.4)Ewheretheratioofheatlossrateperunitvolumetotheheatreleaseratebychemic'alreactionperunitvolume,(K)t,isdefinedasKcrt=S/CwPandtheratioofsensibleheattoheatofcombustion,e;,isdefinedase.=C(T.-T)/q1p1uToarriveatEq.(5.5),itisnecesarytoassumethatalltheheatlossisattributedtoconvectionheattransfertofogdropletsofonlyonedropsize.Underthisassumption,therateofheatlossperunitvolumeperdegree,S,maybeexpressedasS=nxdhwheren=numberofdropsperunitvolumed=volumemeandropsizeh=heat'transfercoefficientItisfurtherassumedthattherelativevelocitybetweenthedropletsandthemixtureflowissosmallthatheattransfercoefficient,h,canbeapproximatedbytheconductionlimit.Underthisassumption,Eq.(B-3)reducestod0430Q:IB-I

~,~4k ATTACHMENT5TOAEP:NRC:0500KFOGINERTINGCRITERIAFORHYDROGEN/AIRMIXTURESDONALDC.COOKNUCLEARPLANTUNITNOS.lAND2 CO

ML17320A791

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2.0INTRODUCTION

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