ML17320A791

Fog Inerting Analysis for PWR Ice Condenser Plants.

ML17320A791
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Site:	Cook
Issue date:	11/30/1981
From:	TSAI S S WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP.
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.FOGINERTIHGANALYSISFORPMRICECONDENSER PLANTSBYS.S.TSAICOREANDCONTAINMEHT ANALYSISNUCLEARSAFETYDEPARTMENT WESTINGHOUSE ELECTRICCORP.NOYEHBER19818310140042 831010PDRADOCK050003i5PPDR0430Q:1 ABSTRACT.Therecenthydrogenburntestconducted attheLawrenceLivermore NationalLaboratory hasraisedtheNRCandtheicecondenser plant'ownersconcernaboutfoginertingprobability andconsequences inicecondenser plants.Thepresentinvestigation isaimedatresolving thisfoginertingissue.Inthisreport,majorfogformation andremovalmechanisms thatexistinthepost-accident icecondenser containment areidentified andquyntified.

Methodologies havebeendeveloped forpre-dictingfogformatiop andremovalratesandforpredicting fogconcen-trationsinvariouscompartments inanicecondenser containment.

Thismethodology development hasresultedintwocomputerprograms, FOGandFOGMASS.TheFOGcomputerprogramemploystheHijikata-Mori boun-darylayerfogformation theory,andcalculates thefogformation ratesduetoboundarylayerandbulkstreamcondensation.

Thecomputerpro-gramFOGMASSsolvesthemassconservation equations forfogdropletsandcalculates thefogconcentrations invariouscompartments.

Bothcompu-terprogramshavebeenusedtopredictfogconcentrations inthe'equoyah, McGuire,andD.C.Cookcontainments, usingtheCLASIXoutputdataforaS>Daccidentsequence.

Inordertoutilizethec'alculational results-from thestudy,afoginertingcriterion hasbeenestablished.

Thiscriterion usesthehydro-genconcentration, volumemeandropsize,andfogconcentration todefinethefoginertingregime.Foragivenhydrogenconcentration, theminimumfoginertingconcentration wasfoundtovarywiththesquareofthevolumemeandropsize.Thiscriterion hasbeenverifiedbytheFactoryMutualrecentfoginertingtestdata.Theapplication ofthefoginertingcriterion tothethreeicecondenser plantsshowsthatfoginertingwouldnotexistintheupperandlowercompartments.

Foginertingintheicecondenser upperplenumathydro-genconcentratons atwhichglowplugignitersaredesignedtooperateisveryunlikely.

0430Q:I TABLEOFCONTENTSSectionTftle~PaeABSTRACTTABLEOFCONTENTSLISTOFTABLESLISTOFFIGURES1V1.02.03.0',BACKGROUND INTRODUCTIONFOGGENERATING MECHANISMS INAHICECONDENSER CONTAINMENT 3.1FogGenerated byBreakFlow3.1.1AmountofFogGenerated byBreakFlow3.1.2DropSizesGenerated byBreakFlow3.2Hucleation ofFogDropletsinContainment Atmosphere 3.2.1Nucleation Theories3.2.1.1Classical TheoryofHomogeneous Nucleation 3.2.1.2Heterogeneous Nucleation Theory3.2.2FogFormationConditions3.2.3Conditions forFogFormation NearaColdSurface.3.2.4RateofFogFormation 3.2.5FogDropSizes3.3FineMistDropletsFromContainment Sprays2-13-13-13-33-53-63-73-73-93-103-123-153-193-194.0FOGREMOVALMECHANISMS IHAHICECONDENSER CONTAIHME HT4.1SettlingDuetoGravity4.2Agglomeration 4.3Vaporization4.4RemovalbySprayDrops4.5OtherRemovalMechanisms 4-10430Q:1 TABLEOFCONTENTS(Continued)

SectionTitle~Pae5.0FOGINERTIHGCRITERIA5.1PreviousMork5.2PresentTheory5.3Verification ofTheoriesbyExperiments 5-15-25-66.0ASSESSMENT OFFOGINERTINGPROBABILITY IHICECONDENSER COHTAINMEHTS 6.1Determination ofVolumeFractionofFogDropletsinIceCondenser Containment Subcompartments 6.1.1Calculation ofmbreak6.1.2Calculationof6.1.3Calculation ofmset6.1.4Ca1culationofmsP6.2FogInertingProbability intheSequoyahPlant6.3FogInertingProbability intheMcGuirePlant6.4FogInertingProbability intheD.C.CookPlant6.5EffectofFogonGlobalCombustion 6-16-16-56-66-66-76-76-236-376-507.0SUMMARYANDCONCLUSIONS 7-1ACKNOWLEDGMENTS 7-3REFERENCES R-1APPENDIXAA-1APPENDIX8B-10430Q:1 ifl LISTOFTABLESTableNo.Title~Pae6.1FOGInputDataforSequoyahLowerCompartment 6-18'.26.3FOGInputDataforSequoyahIceCondenser Geometric DataforSequoyahContainment 6-196-206.4MARCHPrediction ofReactorCoolantMassandEnergyReleaseRatefortheS20Sequence.

6-216.5Intercompartmental FlowRates(ft/sec)3Predicted byCLASIXforSequoyah6-226.6FOGInputDataforMcGuireLowerCompartment 6-336.7FOGInputDataforHcGuireIceCondenser 6-346.8Geometric DataforMcGuireContainment 6-356.9Intercompartmental FlowRates(ft/sec)Predicted byCLASIXforHcGuire6-366.10FOGInputDataforD.C.CookLowerCompartment 6-466.11FOGInputDataforD.C.CookIceCondenser 6-476.12Geometric DataforD.C.CookContainment 6-486.13Intercompartmental FlowRates(ft/sec)Predicted byCLASIXforD.C.Cook6-49iv0430Q:1 LISTOFFIGURES~FiureNo.Title~Pae3.1T-SDiagramforReactorCoolantDischarged FromBreak3-43.2~VaporPressureandTemperature ProfileHearaColdSurface3-143.3Formation ofFogHearaColdSurface3-163.4DropSizeDistribution Predicted byHeiburger andChien3-203.5ParticleSizeDistribution for50PSIPressureDropAcrossHozzleNo.17133-214.1TerminalVelocityasaFunctionofDropRadiusinSteam-Air Atmospheres 4-54.2Agglomeration RatesinAirBetweenEqual-Sized Drops5.1MinimumIgnitionEnergiesandQuenching Distance5-3forHydrogen-Oxygen InertGasMixturesatAtmo-sphericcPressure5.2TheEffeetofDropletSpacingonFlameQuenching 5-45.3Schematic Representation ofTemperature ProfileThroughtheFlameFront5-7TheParameter We.gasaFunctionof1(Y-Yf)/e~forDifferent ValuesofKei5-70430Q:1 f)i' LISTOFFIGURES(Continued)

~FiureNo.Title~Pae5.5(K).te.attheFlammability LimitasaFunctionof(Yu-Yf)/ei5-85.65.7Comparison BetweenTheoriesandFactoryMutualFogInertingExperiments on4.76PercentH2r'IComparison BetweenthePresentTheoryandFactoryMutualFogInertingExperiments on7.2PercentH25-105-115.8Comparison BetweenthePresentTheoryandFactoryMutualFogInertingExperiments on7.9PercentH25-126.1SequoyahCLASIXContainment Model6-86.2FogFormation inTVASequoyahLowerCompartment 6-106.3FogFormation inTVASequoyahIceCondenser 6-116.46.5FogConcentration inSequoyahContainment McGuireCLASIXContainment Model6-146-246.6FogFormation inDukeMcGuireLowerCompartment 6-256.7FogFormation inDukeMcGuireIceCondenser 6-266.8FogConcentrationinMcGuireContainment 6-296.9D.C.CookCLASIXContainment Model6-380430Q:1 LISTOFFIGURES(Continued)

Title~PaeFogFormation inAEPCookLowerCompartment 6-29FogFormation inAEPCookIceCondenser 6-406.12FogConcentration inD.C.CookContainment 6-43vii0430(}:I

1.0 BACKGROUND

TheincidentatThreeMileIslandhasdemonstrated thatasignificant amountofhydrogencouldbegenerated duringcoredegradation.

Thisexperience raisedHRCconcernaboutthesafetyofnuclearpowerplants,intermsoftheircapability tocontrolhydrogenduringsevereacci-dents.Sinceicecondenser plantshavearelatively smallvolumeandlowcontainment designpressure, theproblemismagnified.

Therefore, theNRChasrequested theicecondenser plantownerstostudyhydrogencontrolmethodsforuseintheirplants.Inthisregard,theTennessee ValleyAuthority (TVA),DukePowerandAmericanElectricPower(AEP)haveproposedtheuseofglowplugignitersatvariouslocations insidetheiricecondenser containments toignitehydrogenatlowconcentration.

Recently, theNRCrequested LawrenceLivermore NationalLaboratory (LLNL)tocarryoutexperiments ontheseigniterstodetermine theireffectiveness.

Intheseexperiments, twotestswithhighsteamconcentration seemedtoindicatethatsubstantial fogformation couldoccurwhensaturated steamis'ischarged intoaunheatedvesselandundersomeconditions fogcouldeffectively precludehydrogenfromcombustion TheLLHLtestsraisedsomedoubtsabouttheeffectiveness ofglowplugignitersunderfogformation conditions.

Inarecentreviewofhydrogenrelatedissuesforicecondenser plants,theHRChasraisedseveralquestions concerning theprobability andconsequences offogformation andsteamsupersaturation inicecondenser plants.Inresponseto'theNRCquestions, TVA,AEP,andDukeestablished experi-mentalandtheoretical analysisprogramstostudythefoginertingprob-lem.Theexperimental programwascontracted toFactoryMutual.Theexperiments weredesignedtotestglowplugigniter's performance under4different foggingconditions.

Atthesametime,theplantowners.requested Westinghouse toperformfoginertinganalysesfortheSequoyah, McGuire,andD.C.Cookplants.ThisreportpresentstheresultsoftheWestinghouse studies.0430Q:1 ae

2.0INTRODUCTION

Fromthepost-test analysisoftheLLNLfpdrogenburntests,itappearsthatsubstantial fogformation occurredinsidethetestvessel.Gen-erally,fogdropletsareonlyfewmicronsindiameter.

Thesesizesofdropletshavepotential topreventafl'ammable gasmixturefromcombus-tionorquenchapropagating flame.Thisisbecausethesesizesofdropletsvaporizeveryfast(ontheorderofmiliseconds),

absorbing anenormousamountoftheheatreleasedfromcombustion ifasubstantial quantityofthesedropletsispresentintheatmosphere.

Incomparison, largewaterdropletsintherangeoffewhundredmicronsorlarger(e.g.spraydroplets) havenoinertingeffectoncombustion andhencehaveinsignificant effectonglowplugigniter's performance.

There-fore,thepresentanalysiswillbeconcentrated onthegeneration andremovaloffog(mist),anditsimpactontheglowplugignitersystem.Thereareanumberoffoggeneration andremovalmechanisms presentinapost-accident icecondenser containment atmosphere.

Thefoggeneration mechanisms includefoggenerated bythebreakflow(ifitistwo-phase),

fogformation neartheiceandstructural heatsinksurfaces(sincethesurfacetemperatures couldbewellbelowthedewpoint),andfoggenera-tionduetohomogeneous andheterogeneous nucleation incondensing bulkstreams.Thefogremovalmechanisms includegravitational

settling, agglomera-tion,vaporization andremovalbyspraydroplets.

Inordertoestimatethepost-accident fogconcentrations inicecondenser containments, thesecompeting mechanisms mustbestudied,andevaluated.

Tosolvethisproblem,itrequiresanumerical integration ofthemassconserva-.

tionequations forthemistdropletsinthevariouscontainment subcom-partments.

Bymakingsomesimplifying assumptions thetransient fogconcentration inthevarioussubcompartments havebeenestimated.

0430QI2-1 Theanalysispresented hereconsiders allthefogremovalandgeneration mechanisms previously described.

Inaddition, itconsiders thefogentrainment intheintercompartmental flows(including fanflows)inthefogmassconservation equations.

Inordertoperformthisanalysisitwasnecessary touseCLASIXresultsforaS2Deventasboundarycondi-tionstotheproblem.Inadditiontocalculation offogconcentrations in'various containment compartments, itwasnecessary toestablish afog'inerting criterion.

Afoginertingcriterion hasbeenproposedbyBermanetal.,whichpre-dictstheminirpumfogconcentration requiredtoinertagivenhydrogenconcentration andgivenvolumemeanfogdropsize.Thiscriterion seemstooverpredict theminimumfoginertingconcentration, whencomparedwithexperimental data.Amorerealistic foginertingtheoryispresented inthepresentstudy.Thefoginertingmethodology,

analysis, andresultsarepresented inthefollowing sectionsofthisreport.Sections3and4presentthe,method-ologyforcalculating thefogformation andremovalrates.Section5givesthefoginertingcriteria, andSection6presentstheresults.0430Q:I2-2 i'0

3.0 FOGGENERATING

MECHANISMS IHAHICECONDENSER COHTAINMEHT Theinertingcapability offogdropletsdependsontheirsizesandcon-centration inthecontainment atmosphere, aswellasthehydrogencon-centration.

Thissectionisintendedtoidentifyvariousfoggeneration mechanisms presentinanicecondenser containment andtodetermine thedropsizesandtheratesoffoggeneration fromthesemechanisms.

Threefoggeneration mechanisms arediscussed inthissectionandthedominantfoggeneration mechanisms areidentified.

3.1FOGGENERATED BYBREAKFLOWThepost-LOCA containment atmosphere ismostlikelytobeadrop-laden atmosphere.

Thelarge-scale simulated LOCAexperiments conducted todatehavedirectlyorindirectly confirmed thepresenceoftwo-phase atmospheres.

Forexample,Marvikken andBattelle-Frankfurt (3)experiments wereinstrumented tomeasurefluiddensities andwaterlevelsinvariouspartsofthecontainment.

Therefore, foggeneration bythebreakflowcannotbeneglected.

Thefollowing discussion ofthisphenomenon pertainstosmallLOCAs.IntheearlystageofasmallLOCAtransient, asubstantial

.portionoftheprimarycoolantdischarged fromthebreakwillremainasliquid.Becauseofthesuperheat andhighvelocity, thisliquidwillbeframen-tedbyaerodynamic forcesandhomogeneous nucleation mechanism into'mall droplets.

Thesedropletsareexpectedtobeentrained bytheintercompartmental andfanflowsandspreadtootherpartsoftheicecondenser containment.

Duringtheirtravelthroughout thecontainment, thefogdropletswillberemovedbygravitational

settling, sprays,andvaporization.

Thefoggene'ration periodlastsuntilthewaterlevelinthereactorvesselfallstothebreakelevation andthebreakflowisnolongertwo-phase.'or theparticular S<Dsequenceanalyzedby0430Q:I3-1 CLASIX,thisperiodlastsforabout36minutesandabout4.2x(5)10lbsofwaterhasbeendischarged intothelowercompartment during5thisperiodof-time.Afterthewaterlevelinthereactorvesselfallsbelowthebreakeleva-tion,thebreakflowrateissubstantially reduced.Theflowisessen-'iallysteamandnofogdropletswillbegenerated.

Asaresult,thelowercompartment becomessuperheated afterward.

Fogdropletsmayvaporizeduringtheirtravelthroughthiscompartment andsubstantial removalofmistdropletsareexpected.

Largesuspended dropsgenerated bythebreakflowwillberemovedveryquickly.bygravitational settlingandimpingement.

Forthedropslargerthan20u,theremovalrateishighandcompleteremovalonlytakesafewseconds.Forthesmallestdrops(lessthan1u)theterminalveloc-ityissosmallthattheyvirtually remainsuspended intheatmosphere indefinitely.

Theonlyeffective removalmechanisms forthesesizesofdropsarevaporization, andcollision withlargerspraydrops.Theweightfractionofthesesizesofdropsisestimated tobe1per-centgenerated bythebreakflow.Thepopulation ofthesesmall(3)dropscanincreaseifnucleation ofembryosoccursinasaturated atmo-sphere.0430Q:13-2l 3.1.1AMOUNTOFFOGGENERATED BYBREAKFLOW~~Asdiscussed previously, theexistence ofatwo-phase drop-laden regimehasbeenobservedexperimentally.

Ina.smallLOCA,flashingofprimarycoolantatthebreakandsubsequent vaporization ofblowdownliquidrepresent aseriesofchangesofthermodynamic states.Sincethereac-torcoolantpressureishigh,thebreakflowwillbechoked.Theaccel-erationofprimarycoolanttothebreaklocationisessentially anisen-tropicprocess,inwhichthepressuredecreases tothepointatwhichsubstantial homogeneous nucleation occurs.Whentheflowleavesthebreak,theliquidisframented byboththeaerodynamic forcesandthenucleation mechanism intosmallfogdroplets.

Thesefogdropletscon-tinuetovaporize, becauseofthesuperheat inthedroplets, untilathermodynamic equilibrium stateisreached.Becauseofthehighsuper-heatandlargeaerodynamic forces,itisexpectedthatthefogdropletsgenerated areverysmall.Thisvaporization processisessentially isenthalpic.

Theexistence ofatwophasedrop-laden regimecanalsobeexplained byuseofaT-SdiagramforsteamasshowninFigure3,1(Figure1ofReference 6).Itisshowninthisfigurethattheblowdownliquidgoesthroughaseriesofthermodynamic states,startingfromthesubcooled liquidstateB.Theliquidexpandsisentropically fromthesubcooled 0state8tothestateB>atthebreak,whereatwo-phase criticalflowisdeveloped.

Atthesametime,temperature changesfromTtoTI.Afterleavingthebreak,thedropletscontinuetovaporizebecauseofexcessive superheat untilfinallyanequilibrium stateB<isreachedatwhichthedropletsareinthermalequilibrium withtheirsurroundings.

Thisvaporization processisessentially isenthalpic.

Atthistime,thedroplettemperature dropstoT>andtheatmospheric temperature alsorisestoT>.ForasmallLOCA,theequilibrium tem-peraturevarieswithtime.According totheCLASIXanalysisoftheSequoyahplant,thelowercompartment gastemperature risesquicklyfrom100"Ftoapproximately 200"Fandthenstayatthistemperature foranextendedperiodoftime.Usingthesetemperatures asfinalequilibrium 0430QI3-3

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

.temperatures forwaterdroplets, theweightfractionofwaterdropletsinthebreakflowisapproximately 50percent,whichisconsistent withtheMARCHcalculations~7~

ofthebreakflowrateanditsenergyreleaserate.Thediscussion givenaboveisvalidonlywhentheinitialstate'ofthebreakflowissubcooled orsaturated liquid.Afterthewaterlevelinsidethereactorvesselfallsbelowthebreakelevation, thebreakflowwillbesteam.Themoisturecontentofthesteamwillbeverylow,eventhoughisentropic expansion mayleadtohomogeneous nucleation andsubsequent condensation inthevaporstream.Depending onthesuper-saturation thatcanbeachievedinthisisentropic expansion, aconden-sationshockispossiblewhencritical'supersaturation isreached.However,itisbelievedthatthefogdropletsgenerated byhomogeneous nucleation inthissupersonic jetisnegligible ascomparedtootherfoggenerating mechanisms.

Hence,itwillbeneglected inthispresentanalysis.

Therefore, thefoggeneration bythebreakflowisconsidered possibleonlywhenthewaterlevelinthereactorvesselisabovethebreakelevation.

According totheMARCH~"~calculation at2172secondsintotheacci-dent,thewaterlevelinsidethereactorvesselfallsbelowthebreakelevation fortheS2DcaseanalyzedinReference 7.Bythistimeapproximately 421,000lbsofwaterhasbeendischarged fromthebreakand56percentofthisdischarged fluid,i.e.,236,000lbs,willbesus-pendedintheatmosphere ascondensate.

However,mostofthesedropletswilllaterberemovedbygravitational

settling, sprays,andvaporiza-tion.3.1.2DROPSIZESGENERATED BYBREAKFLOWTheflashingjetexperiment conducted byBrownandYork~B~hasindi-catedthatthedropsizesproducedbyflashing.

liquidaresmall.Theyderivedacorrelation forthelinearmeandropsizebasedonthetestdata.Thecorrelation showsthatthemeandropsizeisinversely pro-portional totheWebernumberanditdecreases linearlywithincreasing 0430Q:I3-'5 superheat.

However,thiscorrelation isapplicable forliquidsuperheat lessthan75'Fanditcannotbeextrapolated tothelargesuperheat ofthereactorcoolant.However,someconclusion concerning thedropsizesproducedbyblowdownofthereactorcoolantcanbedrawnforthiscondi-tion.,Thebreakflowhasmuchlargersuperheat andWebernumberthanthoseusedinthisexperiment; therefore, thedropsizesproducedbythebreakflowshouldbemuchsmallerthan-50'bserved inthisexperi-ment.GidoandKoestelhavedeveloped amethodforestimating the.drop(9)sizeleavingthefragmentation/evaporation zoneofablowdownjet.Thismodelisbasedontheassumption thatdropswithan'internal.

temperature difference oflessthan5Kwillescapefragmentation.

Thismodelhasbeenverifiedbythelowsuperheat, dataofBrownandYork.Application ofthismethodtotheLOCAcondition showsthatthemaximumattainable dropsizeis7p(thismeansthatarlydropsizelargerthan7pwillnotescapeframentation byhomogeneous nucleation).

Thecorresponding meandropsizeisabout4p,basedontheobservation ofthelargestdropsizeandmeandropsizeintheexperiment reportedinReference 8.However,thisvolumemeandropsizeisnotusedinthepresentanalysis.

Instead,thepresentanalysisuses10pmeandropsize,.considering thedropagglomeration effect.3.2NUCLEATION OFFOGDROPLETSINCONTAINMENT ATMOSPHERE Nucleation ofwaterembryosfromthehomogeneous vaporphaseplaysanimportant roleinmistgeneration inicecondenser plants.Nucleation isaprocessbywhichtinywaterembryosorcondensation nucleiareformedfromapurevaporphaseatarapidrate.Inincipient homogene-ousnucleation, thelocalgastemperature dropsbelowthedewpointcorresponding tothelocalsteampartialpressureandsomedegreeoflocalsupersaturation isneeded.Thedegreeofsupersaturation neededtostartnucleation dependsonthenumberofcondensation nucleipresentinthecontainment.

Thesecondensation nucleicouldbeverysmallwaterdropletsordustparticles.

Ifsufficient numberofcondensation nuclei0430Q:I3-6 exist,supersaturation couldbesmall.Itislikelythattheicecon-densercontainment containsasubtantial numberofdustparticles suchthatlittlesupersaturation isneededfornucleation.

Thissectionisdevotedtothediscussion offogformation byhomogene-ousorheterogeneous nucleation.

Theclassical nucleation theoriesareusedtoexplainthenucleation phenomenon.

3.2.1NUCLEATION THEORIESTheprocessofn0cleation ofanembryowaterdropisimportant inunder-standingthemechanism offogformation inicecondenser plants.Twotypesofnucleation process,namely,homogeneous andheterogeneous nucleations, andtheirtheorieswillbediscussed inSection3.2.1.3.2.1.1CLASSICAL THEORYOFHOMOGENEOUS NUCLEATION l)Whenanembryodroplet,usuallyassumedspherical, isformedfromcon-densation ofwatervapormolecules, itsfreeenergychanges.Thechangeoffreeenergycanbeexpressed asaG=4xra"(4/3)xrnLKTZn(p/p)whereaisthesurfacefreeenergyperunitarea,orsurfacetension,risthedropradius,Pisthevaporpressure, P;sthesaturation 0PressureatthedroPlettemPerature, nLisnumberofmolecules per,unitvolume,KistheBoltzmanconstant, andTisthedroptemperature.

Thesupersaturation S,isdefinedasP/P.Equation(3.1)represents afreeenergybarriertothegrowthofthedropsatagivensuprsaturation.

AtmaximumaG,thecriticalradiusr"canbeobtainedfromEquation3.1asr*200430/:13-7 r1',i~I Thedropsofthecriticalsizecanbeconsidered ascondensation nuclei~~~~~~~~~~~~~~~sinceatthissizethedropswillgrowwithnochangeinfreeenergy.Thiscriticalsizerepresents anequilibrium sizeatwhichasupersatu-ratedvaporatvaporpressurePisinequilibrium withthiscriticaldropatalowersaturation pressureP.However,thisequilibrium modeisunstable.

Forexample,ifadropofthecriticalsizeorigi-nallyinequilibrium withthesurrounding vaporsuffersasuddensmallincreaseinsizeduetocondensation, then(ifthedroptemperature doesnot,change),

Equation3.2showsthattheequilibrium

pressure, P,onitssurfacewilldecrease.

Therefore, theactualvaporpressurewillthenbegreaterthantheequilibrium valueandfurthercondensation willoccur.Thisiswhythedropofthiscriticalsizeiscalledcondensa-tionnucleus.Thenucleation rateofcritical-sized embryoscanbeobtainedfromthekineticsofanonequilibrium distribution ofembryos.Theclassical nucleation theoryshowsthatthereisaverysuddenincreaseinthenucleation ratewhenpastacertaincriticalvalueofsupersatura-tion.Anextensive validation ofthenucleation theorywasconducted byVolmerandFloodinanexperiment inwhichanumberofvaporswereexpandedtovisiblecondensation inacylinder.

Theobservedcriticalsupersaturations agreedsuprisingly wellwiththeoryinnearlyallcases,including watervapor.Criticalcondensation nucleisizestypically rangefrom10to100atoms.Thesesizesareconsiderably smallerthanthemeanfreepathofthevapormolecules andtherefore theratesofmassandheattransferat'thedropsurfacecannotbepredicted bybulktransport theories.

Inthiscase,thekinetictheoryofgasshouldbeusedtopredicttheratesofmassandheattransferatthedropsurface.Startingfromthekinetictheoryofgasandtheenergyconservation

equation, therateofgrowthofacondensation nucleuswasobtainedbyHilletal.Itwasfoundthatthegrowthrateisontheorderof10ft/sec.Therefore, ittakesonlyaboutImilisecond forthecondensation nucleustogrowtoafogdropletsizeofIp.0430QI3-8 3.2.1.2HETEROGENEOUS NUCLEATIONTHEORYAnothermechanism offormingembryosisheterogeneous nucleation onforeignparticles thatcouldsuspendinthecontainment atmosphere.

Theseparticles mayserveasnucleation sitesforvaporandthusenhancethenucleation rate.Thesourceofforeignparticles inthecontainment following coredegradation couldcomefromfissionproductaerosolsanddustparticles.

Thesizedistribution oftheseparticles areimportant becausethesupersaturation requiredtoformembryosdependsonparticlesizes.Atypicalsizedistribution ofatmospheric aerosolsisthatofeJunge,takenfromsurveysmadenearFrankfurt A.H.,German.Thesurveysfoundthatthesizerangeofdustparticles isfrom0.01toIIntherangefrom0.01to0.5p,therearebetween100and10,000particles percubiccentimeter.

Amajorityofparticles havesizessmallerthan1micron.Atthesmallestsizeof0.01p,thecriticalsupersaturation isabout1.02andatthelargestsizethesupersatura-tionisonly1.001.~~Theothersourceofaerosolparticulates isfission,products.

Duringnormaloperation, theprimarycoolantcontainsverylittlefissionpro-ducts.However,alargereleaseoffissionproducts, suchasthegaprelease,couldoccurataboutthesametimethehydrogenreleases.

Theamountoffissionproductsreleasedtothecontainment dependsonacci-dentscenarios.

Thedistribution andtransport offissionproductsinthecontainment canbepredicted bytheCORRALcode~~.Thesizedistribution offissionproducts.inthecontainment canbeextrapolated fromtheCSEexperiments~

4~.Theseexperiments indicated thatsoonafterfissionproductrelease,themeanparticlediameterwas15p.Afewhourslater,themeandiameterdecreased toabout5pbecauseofsettlingoflargeparticles ontothefloor.Thesesizesaresubstan-tiallylargerthanthoseofdustparticles andtherefore, criticalsupersaturation isevensmallerthanvaluesquotedaboveforthedustparticles.

0430Q:13-9 Theatmospheric aerosolsconsistofparticulates ofvarioussizes,vari-ouschemicalcomponents, andvariouselectrostatic charges.Theaerosolparticulates couldbesolubleorinsoluble inwater.Alltheseproper-tiescouldaffecttherequiredsupersaturation fornucleation.

Inthecaseofinsoluble particulates, thecontactangle,6,betweenthe"embryoandtheparticlesurfaceisimportant.

Iftheparticleiscom-pletelywettable, 6="0,itformsabaseonwhichasmallamountofwatercan.formadropoflargeradiusofcurvature andthussatisfytheHemholtzequation(Eq.3.2)atamuchlowersupersaturation thanwouldbethecaseifsamenumberofmolecules formadropwithaparticlecore.Fletcherdeveloped arelationship betweenthesupersIatura-(I')tionanddropradiusforseveralvaluesofcontactangle,assumingthattheparticleisspherical.

Competely

wettable, aparticleof1micronorso,whencoveredwithafilmofwater,istheoretically atthecrit-icalradius,anditneedsonly1.001criticalsupersaturation.

Thepost-accident containment atmosphere islikelytocontainasubstan-~~~~~tialamountofaerosolparticles.

Theseparticles willactascondensa-i)tionnucleiandtherefore, littlesupersaturation isrequiredtopre-cipitatecondensation.

3.2.2FOGFORlCTION CONDITIONS Fogformation inamixture'f vaporandnoncondensible gaseshasbeenofinteresttometeorologists, andturbineandcondenser designers.

Fogisformedbyhomogeneous orheterogeneous nucleation asaresultoftem-peraturedropbelowthedewpoint(sometimes withconcommitant pressuredrop).Duringthetemperature drop,alocalgaselementwillgothroughaseriesofthermodynamic states.Eventually, astateisreachedatwhichincipient fogformation occurs.Somedegreeofvaporsupersatura-t'ionisneededtoprecipitate fogformation.

Thevaporsupersaturation atwhichrapidnucleation ofvaporfirstappearsiscalledcriticalsupersaturation.

Thecriticalsupersaturation, ingeneral,isa0430Q:13-10 efunctionoftemperature, vaporproperties, mixingtime(ifamixingprocessisinvolved),

andconcentration andsizesofforeignparticles.

Thecriticalsupersaturation dataforwaterhasbeengiveninReference 15.Fogformation inanicecondenser containment asaresultofhomogeneous orheterogeneous nucleation couldoccur:(i)insidethethermalboun-darylayernearacoldsurface,(ii)inadiabatic ornearlyadiabatic expansion ofvaporjet,and(iii)inmixingofahotvaporstreamwithanothercoolergas.Surfacecoolingmaycreatearegionoflocalsupersaturation withinthethermalboundarylayer,eventhoughthebulkstreamisstillsuper-heated.Ifthelocalsupersaturation reachesthecriticalsupersatura-tion,incipient fogformation willcommence.

Thiscondensation mecha-nismmayexistinanycompartments withinthecontainment especially intheicecondenser whereicetemperature iswellbelowthedewpoint.Whenahighspeedvapor-noncondensible gasmixturejetgoesthroughanadiabatic ornearlyadiabatic expansion, thegasmixt'uretemperature andpressurewilldroprapidlysuchthatcondensation mayoccursomewhere intheexpansion process.Thisisthecasewhenahydrogen-steam mixturejetexitsfromabreakatasupersonic speed.Thejetexperiences arapidexpansion andifcriticalsupersaturation isreached;condensation shockmayoccursomewhere withintheexpanding jet.Thiscondensation mechanism canonlyoccurinacompartment inwhichthehydrogen-steam mixturejetexists.Condensation inafastexpanding vapor-noncondensible gasjetisalocalized phenomenon.

Usuallyverylittlemoistureisgenerated intheexpansion processevenifacondensation shockdoesexist.Therefore, thepresentstudydoesnotattempttotreatthecondensation shockasasourceoffogformation.

0430Q:I3-11 P

Thethirdmechanism, condensation duetomixing,mayexistinacompart-mentwhereahothydrogen-steam mixturemixeswitharelatively coldcontainment atmosphere.

Duringthemixingprocess,localcriticalsupersaturation withinthemixinggascouldbereachedandcondensation wouldensue.Thismechanism couldexistinthelowercompartment inwhichrelatively coldgasfromtheuppercompartment isreturnedbythedeckfansandmixedwiththehothumidair.Thus,themixingofcoldandhotvaporstreamswillbetreatedinthepresentstudy.'owever,onlybulkcondensation isconsidered.

Thatis,itisnotintendedto'computethetemperature profiletopredictthelocalcondensation rate.Instead,thebulkgasisassumedatoneuniformtemperature, andbulkcondensation willoccurwhenmixingresultsinsaturation conditions.

Thisisconsistent withtheCLASIXcodeassumption ofuniformgastemperature.

Becauseoftimerestriction, itisalmostimpossible totreatallthecondensation mechanisms.

However,majorcondensation mechanisms willbeidentified andtreatedinthepresentstudy.Beforeenteringintothediscussion ofthemethodology tocalculate thefogformation ratesfromvariousfogformation mechanisms, adiscussion offogformation conditions isnecessary.

Sincethebulkcondensation approachforthemixingprocesshasbeenadopted,thefogformation conditions forthemixingprocessaresimplythatcriticalsupersatura-tionisreachedinthebulkstream.Forpractical

purposes, thecrit-icalsupersaturation isassumedtobeonesinceitislikelythatplentyofcondensation nucleiexistintheatmosphere beforemixingcondensa-tiontakesplace.3.2.3CONDITIONS FORFOGFORMATION NEARACOLDSURFACEFogstartstoformatafastratenearacoldsurfacewhenlocalvaporsupersaturation reachesthecriticalsupersaturation.

Nearthecoldsurface,athermalboundarylayerisformed,withinwhichlocalvaporpressureandsaturation pressurevary.Typicalvaporpressureand0430Q:I3-12 r

temperature

profiles, whentheincipient homogenous nucleation firstappears,areshowninFigure3.2.Itisseeninthisfigurethatwhenthelocalvaporpressurereachesthecriticalvaporpressurethereisasuddenappearance offogintheboundarylayerduetothefastnuclea-tionrate.RosnerandEpsteinhavederivedfogformation condi-(ll)tionsnearacoldsurface,assumingthatthelocalvaporpressurecurveistangenttothecriticalvaporpressurecurveatthefogincipient point.Amoregeneralfog-formation criterion wasgivenbyHijikataandMori1shW~(dW)Wharwall(3.3)wherehW=W-WwhT=T-Twandtheweightfractionofcondensing vapor,W,canberelatedtothepartialpressureofthecondensing vaporPasvW=1-(Pgp)(v/v)Pvg(3.4)wherePHNtotalpressurevapormolecular weightnoncondensible gasmolecular weightEquation(3.3)mayberewritten asn>2(3.5)whereM)(Qd)wal10430Q:I3-13

211233Pv,crit(T)Pv,eq(T~)Pcrit(Tw)Pv,wIIIIIIIllIIII0OOSUPERSATURATED REGIONPv,ooBOUNDARYLAYERTHERMALSUPERHEATED OKDCOzO0O1DZOOISUPERSATURATED REGIONFOGVAPORTooTwFIGURE3.2VAPORPRESSUREANDTEMPERATURE PROFILESNEARACOLDSURFACE3-14 Theparameter nisusedinthefollowing sectiontocalculate thefog~~formation rate.Itwillbedemonstrated thatwhenn<2,nofogforma-tionispossible.

3.2.4RATEOFFOGFORMATION HEARACOLO-SURFACE Ashasbeendiscussed inSection3.2.3,fogwillformnearcoldsurfaces(e.g.,intheicecondenser earlyinthetransient.

)Asdiscussed inSection3.2.1,oncewaterembryosareformedittakesonlyafewmili-secondsforthemtogrowtothemicronsize.Afterthesemicronsizefogdropletsareformed,itneedsverylittlesupersaturation forfur-thergrowth.Therefore, inthepresentanalysis, itisassumedthatvaporanddropletsareinthermalequilibrium andlocalvaporpressureisequaltothelocalsaturation pressure.

Thissectionisconcerned withthetransport ofthesemicron-size fogdropletswithinthethermalboundarylayer.Theboundarylayerfogformation ratecanbedetermined usingtheHijikata-Mori theoryoffogformation inthethermalboundarylayer.Itwasassumedthatathinliquidfilm,havingathickness ofe<onacoldsurface,coexistswithagas-droplet flowinatwo-phaseboundarylayerofthickness 6outsidetheliquidfilmasshowninFigure3.3.Itwasfurtherassumedthatthesaturation condition existswithinthetwo-phase boundarylayerandtheboundarylayerapproximation isappli-cable.Numerical solutions wereobtainedforthemassfractionoffogdroplets, Y,atthegas-liquid filminterface.

ThefogdropletflowotrateatadistanceXalongtheplatemaybeexpressed intermsofYasf'6mf=LpJYudy(3.6)0430(}:I3-15 hfainFlow~0~ieCoolingSurfaceTwoPleaseBoundarylayerInterface LiquidFilmFIGURE3.3FORtljATIOH OFFOGHEARACOLDSURFACE

.whereYmassfractionoffogdropletsintheboundarylayerfogdropletdensityPvvapordensityPgnoncondensible gasdensityYo.~fly=ok~v+~g)y=coordinate perpendicular totheplatefogboundarylayerthickness widthofboundarylayerPv+pg=Y0(1-y/e)(3.7)u=U(<(~)-~(~))~(x)=ax1<<(3.g)4u=e(x)(1-6)(3.10)whereaknownconstantknownconst'ant freestreamvelocity0430Q:13-17 I0 Substituting Eqs.(3.7)through(3.10)intoEq.(3.6),wehavetherateoffogformation mf=pL6YU0.250.025(3.11)oerivation ofexpressions fora,YandgisgiveninAppendixEventhoughboundarylayerfogformation mayoccurinanycontainment subcompartment, thefogformation rateislikelytobesmallexceptintheicecondenser.

Forfogformation intheicecondenser, Listhetotallengthoftheperiphery andxistheheightoftheicebed.Duringfogformation intheboundarylayer,heattransfertothecoldsurfacewilldecreasethebulkfluidtemperature.

Ifthebulkfluidtemperature dropsbelowthedewpointcorresponding tothefreestreamvaporpressure, thenbulkstreamcondensation couldoccur.Inthiscase,itisassumedthattheboundarylayerthickness, s,willgrowsothickthatLeU~becomesthegasvolumetric flowrateQthroughthecon-densingcompartment.

Thisisaveryconservative assumption intermsofthefogformation rate.Underthisassumption Equation(3.11)becomes0.250.025condo~"o1:g(1-g).(3.12)wheremdisthesumofboundaryandbulkstreamfogformation rates.cond0430Q13-18 3.2.5FOGDROPSIZESAsmentioned earlier,whenhomogeneous nucleation commences, alargenumberofcondensation nucleiareformedandtheygrowtothemicronsizewithinafewmilliseconds.

Inheterogeneous nucleation, fogdrop-letsgrowonaerosalparticles, whichareusuallylessthan1p.Inanycase,thefinaldropsizesaredetermined bytheatmospheric conditions withwhichthedropsareinthermalequilibrium.

Neiburger andChien(18) studiedthegrowthofclouddropsbycondensa-tionandcalculated dropletsizedistribution basedonacloudcoolingrateof6c/hr.Theinitialsizedistribution ofcondensation nuclei(sodiumchloride) werechosentocorrespond toavailable observations asshowninFigure3.4(designated as0second).Thecalculated dropsizedistributions at3000and6000secondsareshowninFigure3.4.Itisseenthatthesizesoffogdropletsrangefrom0.01pto20p.Thevolumemeandropsizeis8pat3000second.Thevolumemeandropsizeforhomogeneous nucleation isexpectedtobesmallerthanthisvalue.Fogsofvolumemeandropsizesrangingfrom9to14p(30)havebeenobservedtoexistinanaturalenviroment, e.g.valley.InthepresentstuQ,avolumemeanfogdropsizeof10pischosenforfogdeposition

-andinertingcalculations.

3.3FINEMISTDROPLETSFROMCONTAINMENT SPRAYSThecontainment spraysproduce-fairlylargedropsizes.A-typical con-tainmentspraynozzle,e.g.,Spraco1713nozzle,producesthesizedis-tribution asshowninFigure3.5,usingapressuredifference of50psiacrossthenozzle().Itisseenthatwaterdropletsproducedfromcontainment rangefrom100pto2000p.Theselargedropshavelittleeffectonhydrogencombustion andflammability limits,asalreadydemon-stratedintheFenwaltests()andmorerecenttestsatFactoryMutual(21).

Toaffectthecombustion characteristics ofahydrogenmixture,thedropsizeshavetobesmallerthanabout20p,namelyinthefogdropsizeranges.Sincecontainment spraysessentially donotproducedropsinthissizerange,containment sprayswillnotbecon-sideredasameanstoproducefogdroplets.

Rather,itwillbecon-sideredasameanstoremovethefogdroplets.

0430Q:I3-19

~~~~~j~~)

I<lOI20lnOCD80ED609020200000600800l000l200l900l600l80020002200PARTICLEDIAllETER(MlCROHS)FIGURE3.5PARTICLESIZEDISTRIBUTIOH FOR50PSIPRESSUREDROPACROSSNOZZLEHO.1713

.J"s1~0

4.0 FOGREMOYALMECHANISMS

INANICECONDENSER COHTAIHMEHT InSection3,themechanisms ofgenerating fogdropletswerediscussed.

Afterthesedropletsaregenerated, theycanberemovedfromthecon-tainmentatmosphere by.gravitational

settling, vaporization, containment sprays,andimpingement onstructures.

Theycanalsocoalescewithotherdropsduringcollision andformbiggerdrops.Thesebiggerdropscouldeasilysettleoutoftheatmosphere undergravity.Thesefogdropletremovalmechanisms willbediscussed inthissection.4.1SETTLINGDUETO'RAVITY Dropremovalratesduetogravitational settlingdependstronglyondropradius.Theremovalrateincreases linearlywithdropterminalveloc-ity,dropconcentration, andsettlingarea.Therelationship maybeexpressed asmsett"r(4.I)whereqisthemassofmistdropletsperunit.volume,andAistheset-tlingarea.Theterminalvelocity, Yt,isastrongfunctionofdropradiusandtherelationship isshowninFigure4.1.Itisseenthattheterminalvelocityisapproximately alinearfunctionofdropradiusinbothlami-nartheturbulent regimes.Fora1000pdrop,itsterminalvelocityisaboveIm/s,whilefora10pdrop,whichisthetypicalfogdropsize,itsterminalvelocityisonlyaboutIcm/s.Therefore, thereisverylittleremovalbygravityforfogdroplets.

0430Q:I

4.2AGGLOMERATION Afterthefogdropletsareproduced, thedropletswillundergochangesinthenumberdensityandsizedistribution withtime,whendropscol-lidewitheachotherandcoalesce.

The.agglomeration rate(No.ofpar-ticleperunitvolumeperunittime)hasbeenfoundtobeproportional tothesquareofthedroppopulation densityandthecoagulation mecha-nismsdependent rateconstantKFordropslargerthan1g,thedominantmechanism isthedifference in'Ivelocities betweendropsinadjacentstreamlines.

Thisisusuallytermedthevelocitygradientcoagulation.

Fordropssmallerthan1g,thevelocitygradienteffectbecomessmall,anddropsarebrought'ogetherbyBrownianmotion.Thisleadstogreatlydifferent agglomera-tionratesfordifferent initialdropsizes.Atypicalagglomeration rateasafunctionofdropsizeinamoderately turbulent atmosphere isshowninFigure4.2.InFigure4.2,thesharpriseoftheagglomeration ratewithdropdiameterlargerthan1pimpliesthatthelargerdropsagglomerate quicklytothemaximumstablesizesupported bytheatmo-sphericturbulerce.

Theagglomeration ratesfordropslessthan1pareverysmall.Sincemostofthefogdropletsarein.micronsizeranges,theagglomeration rateisnotlarge.Itisassumedinthepresentanalysisthattheinitial4ublowdownmeandropsizewillgrowto10g(SeeSection3.2.5).Agglomeration asaseparatemechanism forfoggrowthhas'beenconservatively neglected.

4.3VAPORIZATION Fogdropletssuspended inthecontainment atmosphere isconsidered tobeinthermodynamic equilibrium withthesurrounding gas.Mhenthesur-roundingatmosphere becomessuperheated orwhenthedropletsareentrained intoasuperheated subcompartment, itcanundergovaporization orcondensation.

0430Q:14-2 Inthepresentanalysis, itisassumedthatwatervaporandmistdrop-letsareinthermalequilibrium atalltimes.Therefore, theamountofvaporization orcondensation willbedetermined bythethermalequilib-riumstatereachedbythevaporanddrops.Inotherwords,itisnotintendedtomodelheattransferbetweenthedropsandthesurrounding gas,andthusdetermine thevaporization rate.Thisisagoodassump-tionforthesmallfogdropsizes.4.4REMOVALBYSPRAYDROPSAsmentioned above,thecontainment spraydropletsrangefrom100u-2000p,whicharesubstantially largerthanthefogdroplets.

Iffogdropletsenterthesprayzone,theywillprobablyberemovedbythespraydropletsbycolliding withthem,sincethespraydropmassismuchlargerthanthefogdropmass.Asimpleanalytical modelisusedinthepresentstudywhichassumesthatallthefogdropletsresidinginthesprayzonewillbesweptbythespraystothefloorwiththespraydropremovalefficiency E.Thesprayremovalratemaybeexpressed asm=EQM/qV(4.2)whereEQspspMspraydropremovalefficiency volumetric flowrateofspraysvolumefractionofspraydropletsinthesprayzonemassoffogincompartment volumeV4.5OTHERREMOVALMECHANISMS Anothersimilarmechanism forfogremovalistheformation ofdropletsintheicecondenser.

Thesedropletswhichwouldbegenerated intheicebedwhentheicemelts,wouldfallthroughtheicebed,andremovefogdropletsfromtheflowthroughtheicecondenser.

Thislargequan-tityofwaterwouldbeeffective inremovingfogdroplets.

However,duetodifficulty inmodelingthisremovalmechanism, itisconservatively neglected inthepresentanalysis.

0430Q:I4-3 I

Inadditiontotheremovalmechanisms mentioned above,fogcanalsoberemovedbyimpacting structural surfaces.

Ouetotheinertiaoffogdroplets, substantial fogremovalbyimpacting structural surfacescouldoccur,whenthedrop-laden mixtureflowpassesthroughlong,narrow,curvedpaths,suchasicebasketflowpaths,andfanducts.Moreover, thecentrifugal forceexertingonthefogdroplets, whentheypassthroughthefans,couldcausethefogdropletstoimpactthebladesur-facesorotherpartsofthefans.Theseremovalmechanisms arebelievedtobesignificant; however,theyareconservatively neglected inthepresentanalysis.

Itis,therefore, believedthatthepresentanalysisisveryconservative.

4-40430Q:1 I,

121273110TERMINALDROPFALLINGVELOCITIES INSTEAM.AIRATMOSPHERES p~1.0COZ0.10TURBULENT AMINARREGIMEREGIMEHATCHEDREGIONINDICATES:

50<Re<550.011.00.001001'1DROPRADIUS(CM)FIGURE4.1TERHINALVELOCITYASAFUNCTIONOFDROPRADIUSINSTEAH-AIR ATHOSPHERE 104~~7u103O102ROI-o101GRADIENTAGGLOMERATION n10CM100Sdvdy8ROWNIANAGGLOMERATION n10CMNETRATE1000.010.11.0DROPDIAMETER(pM)FIGURE4.2AGGLOHERATION RATESINAIRBETWEENEQUAL-SIZED DROPS4-5 T,

5.0FOGINERTINGCRITERIARecenthydrogenburnexperiments conducted atLawrenceLivermore Labora-toryindicated thatsubstantial fogformation couldoccurwhensaturated steamisdischarged intoanunheatedvessel.Itappearedthatthisfogprevented aglowplugigniterfromsuccessfully ignitingthehydrogenmixtureinthevessel.Theabilityoffogininhibiting andquenching ofhydrogencombustion canbeexplained asfollows.Thefogdropletssuspended inthehydrogen-air-steam mixtureactasaheatsinkthatcouldabsorbalargeamountofcombustion heat,greatlyreducingthepressureandtemperature risesresulting fromhydrogencombustion.

Ifdropletsaresufficiently smallsuchthattheycouldvaporizeinsidethethin(Imm)flamefront,theflamemaybequenchedorinhibited.

Foraflamespeedof2m/s,thedropresidence timeisoftheorderof0.5x10seconds.Insuchashortperiodoftime,thedropletsofinitialradiuslessthanabout4pwillvaporizeentirelyintheflamefront.Thequenching ofapropagating flameisalsogovernedbythedistancebetweendroplets.

Asthedropletsbecomecloselypacked,thetotaldropletsurfaceareaavailable forenergylossincreases.

Acriticalspacingbetweendropletsexistssuchthatalargefractionofth'eheatreleasedisabsorbed, thuspreventing flamepropagation.

Thiscriticalspacingisknownasthe"quenching distance",

whichisusuallydeter-minedbypropagating flamesintubes.5.1PREVIOUSWORKTheeffectiveness offogdropletsininhibiting orquenching aflamedependsonitsquenching

distance, wasdetermined byBermanetal.asd=[4VIS3(5.1)whereVisthegasvolumeandSistheheattransfersurfacearea.Forahydrogen-air mixture,thedataonthequenching distanceisshownin04300:I5-1

Figure5.1.Inthesuspended fogdroplets, thisvolume-to-surface ratio~~~~(i.e.,V/S)isequalto1d(1-n)wheredisthemeandropletdiameterandnisthevolumefractionofwater.Whenfourtimesthisratioapproaches thequenching

distance, acriticaldropletdiametercanbeobtainedasqdc2(5.2)Usingthiscriterion forquenching aflame,foragivenvolumefractionofwaterandgascomposition, dcanbedetermined.

Thecriticaldropletdiameterthencanbedetermined fromtheaboveequation.

Thedropsizeslessthanthecriticaldropsizeiscapableofquenching af1arne.AplotofEq.(5.2)fortwohydrogenconcentrations isshowninFigure5.2.5.2PRESENTTHEORYTheprevioustheoriesdonotmodeltheheattransferandcombustion processes occurring betweentheburnedgasandthesuspended droplets.

Anewtheoryhasbeendeveloped, whichmodelstheheatlossandcombus-tion.0430Q:15-2 t~"t0V FEG.5.1MINIMUMIGNITIONENERGIESANDQUENCHING DISTANCEFORKYDROGEN-OXYGEN INERTGASMIXTURESATATMOSPHERIC PRESSURE5-3

&ALIIS~mS'REER~~~~~~~~~MR~

~ESESR~~~RSRES~~~m~~EEI~~~RRRE~ERSRSRSRSR~

EEERR~~~WMRE~SEERS~~~BESSER~~~~~~~

~RRRR~~~EERRRRERRE~EEEE~ERRSR~EERRE~

~~~~RA~WE~E~iFsSHSIWI 0~~~lI~~ERIIESECEEEEEESSW RERRREMRS

~~SEERSEREEE~~~~ESSES~~~SEERS~

Considerahydrogen/air/steam/mist dropletsmixtureinwhichaflameisgropagating.

Theflamemaybedividedintothreezones:heatingzone,,reaction zone,andpost-reaction zoneasshowninFigure5.3.Theunburnedgasattemperature TmoveinthereactonzonewiththeUlaminarburningvelocityS.Iftheunburnedgasdensityisp,UthentheconstantmassflowratemisequaltopS.Theunburnedgasisheatedtoignitiontemperature T.andburnedinthereaction1zonetoreachtheflametemperature Tf.Thefogdropletswillactasaheat'sinkthatreducestheflametemperature.

Theproblemhasbeenformulated andsolvedbyvonKarman.Inhisformulation, three(25)energyequations, whichincorporate theheatlossterms,werewrittenforthethreezonesdescribed above.Thesolutiontotheseequations yieldsthefollowing relationship 2Ke.=1-exp(-TIi)(Y-Yf)121U1((~~((()(-~Ii1+K/Ii(5.3)wheree.1C(T.-T)/qpiU~Z/iwmPKei(S/Cw)eiPtheratioofheatlossrateperunitvolumetotheheatreleaseratebychemicalreactionperunitvolumeheatofcombustion Cmeanspecificheat0430Q:15-5 VJ0 heatconductivity reactionrate(massoffuelconsumedperunittimeperunitvolume)YuhydrogenmassfractionintheheatingzoneYfhydrogenmassfractioninthereactionzone'u'uAplotof,Eq.(5.3)isshowninFigure5.4.ItisseenthatforagivenKe,thereisaminimumvalueof(Yu-Yf)/e,-.Belowthismini-mumvalue,thereisnosolutionfortheve,.p.Therefore, thisvalueisconsidered astheflammability limit.Attheflammability limit,thevalueofKe.canbedetermined fromFigure5.4orfromEq.(5.3)as)critejf((uYf)/Gi)(5.4)'Aplotof(K)cr,.te;asafunctionof(Yu-Yf)/eiisshowninFigure5.5.Equation(5.4)maybeexpressed as2(YuqpuSu(Y-Yf)f(e-Cp212i(T,.-Tu)(5.5)Detailedderivation procedure forEq.(5.5),isgiveninAppendixB.UsingthedataonSfromReference (26)wecancalculate therightuhandsideofEq.(5.5)foragivencomposition andinitialgastempera-ture.5.3YERIFICATIOH OFTHEORIESBYEXPERIMENTS Experiments havebeenconducted atFactoryMutualtostudytheeffectsofwaterfogdensity,dropletdiameter, andtemperature onthelower0430Q:I Tempore~,

7m~~zone(Dljt=m(r<-Vgw

~~<a>xa0xa(Deltonce, x~FIGURE5.3SCHEMATIC REPRESENTATION OFTEMPERATURE PROFILETHROUGHTHEFLAMEFRONTA',a0'(i0200'ye0300.2.46l012(Yv-YrVdtFIGURE5.4THEPARAMETER A.pASAFUNCTIONOF(Y-Y)/0FORDIFFERENT VALUESOFKO5-7 1t 0.30.2UlICO0.10.00(Y-Y))/0;FIGURE5.5(K)t8ATTHEFLA50BIL1'TY LINITASAFUNCTIONOF~Yuf~i 4

flammability 1imitofhydrogen-air-steam mixtures.Theresultsindicated thatmostofthefognozzlestestedat20Conlychangedthelimitfrom4.03volumepercentto4.76percent,corresponding tofogconcentration intherangeof0.028-0.085 volumepercent,andaveragedropsizerangingfrom45-90microns.Forthe50'Ccase,thelowerflammability limitincreases to7.2percent,corresponding to0.01-0.04 volumepercentoffogand20-50micronaveragedropsizes.Theresultsdemonstrated thatthefoginertingeffectismorepronounced atsmalldropsizes.Figures5.6through5.8showthecomparison betweenthetestdataandthetheoretical predictions.

Forthiscomparison, thepresenttheoryusedthefreestreamtemperature tocalculate thethermodynamic proper-tiesusedinEquation(5.5).Thisyieldedsomewhathigherfogcorcen-trationsthanthosecalculated byuseofthemean'oftheflameandfreestreamtemperatures.

InFigures5.6and5.7,thedatasuggestsalinearrelationship betweenthevolumeconcentration andvolumemeandropsizeonthelog-logplot.Italsosuggeststhattheminimumfoginertingconcentration variesapproximately withthesquareofthevolumemeandropsize.Inthisregard,thepresenttheoryisconsistent withthedatawhiletheBermanetal.theoryisnot.-Thepresenttheoryisingoodagreement withtheFactoryMutualdataat476percentH2',however,itoverpredict's theminimumfoginertingconcentration at7.2percentH2.Thecauseofthisdiscrepancy isstillunknown.Thediscrepancy maybecausedbytheuncertainty ofthedata.Thefollowing discussion supportsthisclaim.Thefogdropletsareverysmallandtheyvaporizeveryfastinaflame.Therefore, thefogdropletsbehaveassteamexceptfortheirlargerheatabsorption capability.

Whenthefogdropletsvaporize, theyabsorbtheheatofvaporization whichismuchlargerthanthesteamsensibleheat.Typ-ically,theheatofvaporization ofwaterisabout1000Btu/lbandtheaveragespecificheatofsteaminthetemperature rangeofinterestisabout0.48Btu/lb.Itiswellknownthatatydrogenflamecannotpropa-gateinsteamhigherthanabout64percentinasteam-air mixture.At7.9H2,theadiabatic flametemperature isabout1240Fandtherefore 0430Q:I5-9

oSpracoZI63LSpracol405-0604.

GSpraco2020"l704v'Spracol806-l605l0~CDNNON-FLAMMABLE

.ZONECDPRESENTTHEORYBERMANETAL.THEORYFLAMMABLE ZONEloIOIOO200VOLUMEMEANDIAMETER, MICRONSFIGURE5.6COMPARISON BETWEENTHEORIESANDFACTORYMUTUALFOGINERTINGEXPERIMENTS ON4.76PERCENTH~5-10

I0'80Spraco2I63-7604 vSpraco2020-I704OSonicore 035HXIONon-Flammable ZonePRESENTTHEORYFlammable

.Zone72%HzInAirAt50'CIOIO20405060708090.VOLUMEb]EANDIAMETER, MICRONS.FIGURE5.7COMPARISON BETWEENTHEPRESENTTHEORYANDFACTORYMUTUALFOGINERTINGEXPERIMENTS ON7.2PERCENTH2'"5-11' I

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theincreaseofthesteamsensibleheatisabout540Btu/lb.Conse-quently,forthesameamountoffogdropletsandsteam,thefogdropletsheatabsorption capability isabout1.9timeshigher.Thismeansthatthefogconcentration whichisequivalent to22.1percentsteaminsteamandairiscapableofinerting7.9percentH2.lhisfoginertingconcentration wascalculated tobe1.61x10-4.Toinert7.2percentH2,aminimumfogconcentration whichcorresponds toabout21.3per-centsteaminsteamandairisrequired.

Thisgivesaminimumfogincrtingconcentration of1.56x10for7.2percentH2.estimates showthatthepresentpredictions arereasonable andconserva-tive.Thepresenttheoryisconservative becauseitneglectsconvective andradiative heattransferandthusunderpredicts theheatloss.Theestimates areconsistent withFactoryMutualdataon7.9percentH2butnoton7.2percentH2.Itshouldbenotedthatintheteststhreefogconcentration measuring techniques wereused.Thesethreetechniques gavesubstantially dif-ferentresults.Thediscrepancy isatleastoneorderofmagnitude difference.

Thefogconcentration datapresented inFigures5.6through5.8wereobtainedfromoneofthetechniques.

Inviewoftheuncer-taintyofthedata,caremustbeexercised inusingthemforinertinganalysispurposes.

Theyshouldbeusedinconjunction withthepresentfoginertingcriterion intheassessment offoginertingpotential in=theicecondenser plants.Someuncertainty alsoexistsinthepresentfoginertingtheory.Theuncertainty associated withtheunderpredic-tionoftheheatlossandtemperature dependence ofthethermophysical properties isestimated tobe+63percent.ItshouldalsobepointedoutthattheFactoryMutualdataandthepre-senttheorycanonlypredicttheminimumfoginertingconcentration.

Toinsurehydrogenburninalldirections intheicecondenser upperplenum,furtherworkinthisareamayberequired.

0430Q:I5-13 Pr 6.'0ASSESSMENT OFFOGINERTINGPROBABILITY INICECONDENSER CONTAINMENTS Asdiscussed intheprevioussections, thereexistsseveralmechanisms ofgenerating andremovingfogdropletsfromtheicecondenser contain-ment.Inaddition, fogdropletsarealsotransported fromonesubcom-partmenttoanotherbyentrainment inthegasstream.Thefogentrain-mentrateisdifficult toassesswithoutknowingthevelocityfieldanddropsizedistribution.

Forsimplifying

purposes, itispresently assumedthat,themassfractionofmistdropletsintheintercompart-mentalandfanflowsisthesameasthatwithinthesubcompartment fromwhichtheflowsareoriginated.

'hisisagoodassumption sincethefogdropletsaresmall.Theamountoffogdropletsinasubcompartment dependsonallthesemechanisms.

Thetotalamountoffogdropletsisimportant in-determining thevolumefractionofsuspended condensate inasubcompartment.

Thisvolumefrac-tion,inturn,isusedinthefoginertingcriteriatodetermine whetheraparticular hydrogenmixturecomposition formedinasubcompartment atanytimeisflammable ornot.Inotherwords,byknowingthehydrogenconcentration andthemeanfogdropsize,wecandetermine whetherthecalculated volumefractionoffogdropletsishighenoughtopreventthemixturefromcombustion.

6.1DETERMINATION OFVOLUMEFRACTIONOFMISTDROPLETSINICECONDENSER CONTAINMENTS Considerasubcompartment intheicecondenser comtainment asshowninFigure6.1.Thereexistseveralmechanisms bywhichmistdropscanbegenerated orremoved.Fogdropletscanbegenerated byhomogeneous orheterogeneous nucleation inthethermalboundarylayerand/orinthebulkstreamandtheycanincreaseinsizebycondensation ordecreaseinsizebyvaporization.

Therateofgeneration ofmistdropletsbycon-densation andtheircontinued growth(orshrinkage duetovaporization) isrepresented bymd.Theothermechanism ofgenerating mistdrop-condletsconsidered inthisanalysisistheprimarycoolantdischarge fromthebreakandtherateofgenerating fogdropletsfromthismechanism is0430Q:I6-1 dj1 represented bymk.Twofogdropletremovalmechanisms areconsid-oreak~~edinthisanalysis:

oneisgravitational settlingandtheotherismovalbycontainment spray.Thefogdropletremovalratebygravita-tionalsettlingisrepresented bymtandthatbysprayisrepresen-settedbym.Inadditiontothegenerating andremovalmechanisms discussed above,themistdropletconcentration inasubcompartment isalsoaffectedbytheintercompartmental andfanflows.Intheintercom-partmental andfanflows,themassfractionoffogdropletsentrained isqandthegasmixtureflowrateism.Therefore theratesoffogdrop-letsmassintoandoutofasubcompartment aregqimiandgntmt,respectively.

Itshouldbenotedthatgn~m.and$noutmoutincludethefogmassentrainment ratesinalltheintercompartmental andfanflowsintoandoutofasubcompartment.

Themassconservation equationforthefogdropletsinasubcompartment maybeexpressed asdM1t~inin~outoutbreakcondsetspwhere(is'asummation overalltheflowpaths..In Eq.(6.1),ifmdisnegative, thenitbecomestherateofvaporization.

Eq.(6.1)canbeintegrated togivethetotalmassofcondensate attimetc~"inin~"outoutbreak0condŽsetsp11ii+i~"inin~"outoutbreak1111condsetspi(6.2)0430Q:I6-2 r

ThepresentanalysiswillemploytheCLASIXcalculations ofcontainment 4ransient duringasmallLOCA.IntheCLASIXanalysis, theentireicecondenser containment isusuallydividedintofiveorsixsubcompart-mentsforanalysispurposes.

Temperatures, totalpressure, steampartialpressures, andintercompartmental flowratesarecalculated duringtransients.

Thisinformation isusedinEq.(6.2)todetermine fogdropletmass.WhenapplyingEq.(6.1)toeachindividual subcompartment, wehavethefollowing fogmass,conservation equations infinitedifference form: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 IceCondenser UerPlenumMUP(t+at)=MUP(t)+'(7ninmin(t)-~"outmout(t)UP,cond()UP,set())IceCondenser LowerPlenumsMLPt+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/Accumul atorRooms*MEA(t+st)ŽEA(t)+(Pn(nm.(t)e~"outoutFAcond(6.7)4WAsetFAspInthepresentanalysis, thefogconcentrations intheintercompart-mentalandfan'flows areassumedtobethesameasthoseinthecompart-mentfromwhichtheflowsareorginated.

• TheseroomswereanalyzedonlyfortheD.C.Cookplant(SeeFigure~~6.S).0430Q:16-4 iI' Intheequations givenabove,theintercompartmental andfanflowratesm.andmtareprovidedbyCLASIXcalculational results.Theinoutprocedures ofcalculating fogdropletsgenerating andremovalratesarebasedonthediscussions intheprevioussectionsandthedetailsaregiveninthefollowing sections.

6.1.1CALCULATION OFHBREAKTodatelittleexperimental dataisavailable toestimatetheamountoffogdropletsgenerated bythebreakflow.ForalargeLOCA,AlmenasandMarchello estimated that13percentofthetotalblowdowndroppopulation (byweight)hasdropradiusrangefrom1pto20pandonly1percentlessthan1p.Thisestimateissomewhatlargerthanthe4pmeandropsizesitedinSection3.1.2,whichisbelievedtobeconserva-tivee.Sinceweareonlyinterested infogdropssmallerthan20p,andonlythesedropscanremainsuspended inairuntilthetimewhenthehydrogenisreleased, weassumethattheestimateofAlmenasandMarchello isapplicable insmallLOCAsand14percentofthesuspended liquidarefogdropletswhichhaveapotential inertingeffect.Thefractionofreactorcoolantdischarged fromthebreakremainsassuspended liquidhasbeendetermined inSection3.KnowingthebreakflowratesfromacomputercodesuchasMARCH,wecancalculate theamountofliquidsuspended intheatmosphere.

Thenfromthedropsizedistribution wecancalculate theamountoffogdropletssuspended intheatmosphere.

Oefiningtheblowdownrateasm,theliquidfractionofthebreakflowasgb,thefractionoffogdropletssmallerthan20pasfb,wehavebreakbb~b(6.8)0430Q:16-5 j(

Inthepresentanalysisfb=0.14isused.fbbecomeszerowhenthewaterlevelinthe'eactor vesselfallsbelowthebreakelevation.

6.1.2CALCULATION OFMCONDAsdiscussed previously, mdistherateofformation ofmistdrop-letsbynucleation, condensation, orvaporization.

Nucleation offogdropletscantakeplaceinthethermalboundarylayerandinthebulkfluid.Weconservatively assumethatlittlesupersaturation isneededfornucleation inthebulkstreamandfogwillformwhenthebulkstreamsteampartialpressurereachesthesaturation steampressurecorrespond-ingtothegasstreamtemperature.

Therefore, thebulkstreamfogformation ratescanbedetermined fromtheequilibrium thermodynamic statesofthegasmixture.Theboundarylayerfogformation ratecanbedetermined usingtheHijikata-Mori theoryoffogformation inthethermalboundarylayerasdiscussed inSection3.2.4.Thefogformation rateinthethermalboundarylayerandthebulkstreamisgivenbyEq.(3.12).Boundarylayerandbulkstreamfogformation rateswillbecalculated fortheicecondenser andlowercompartment.

Acomputerprogramcalled'FOG hasbeendeveloped tocalculate mcond'hiscomputerprogramrequiresinputofthevolumetric gasflowrate,gasandwalltemperatures, totalpressure, andsteampartialpressure.

Thisinformation canbeobtainedfromtheCLASIXoutput.6.1.3CALCULATION OFMSETTherateofsettlingofthefogdropletsdependsontheirterminalvelocity, concentration andcompartment crosssectional area.Thedropletterminalvelocityisafunctionofdropsize.Inthepresentstudy,Equation(4.1)willbeusedtocalculate thefoggravitational settlingrate.0430Q:I6-6

~/~

6.1.4CALCULATION OFMSpThemassofafogdropletismuch'maller thanthatofaspraydroplet.Therefore, whenaspraydropletcollideswithafogdroplet,thefogdropletwillcoalescewiththespraydropandfalltothesump.Inthepresentstudy,thefogremovalratebyspraysisgivenbyEquation(4.2).Itisexpectedthatthespraydropcollection efficiency isveryhigh,andtherefore a100percentdropcollection efficiency isassumedintheanalysis.

Asensitivity studyisneededtobecarriedouttostudytheeffectofEonthevolumefractionoffogdroplets.

AcomputerprogramcalledFOGMASShasbeendeveloped tosolveEqs.(6.3)through(6.7).Thisprogramusesafinitedifference numerical schemetocarryoutintegration.

ThisprogramtakesinputfromFOGandCLASIXoutputdata.SpecificoutputdatafromCLASIXaretimehistories ofgastemperature, walltemperature, totalpressure, steampartialpressure, andintercompartmental.

andfanflowrates.6.2FOGINERTINGPROBABILITY INTHESEQUOYAHPLANTThecomputercodes,FOGandFOGMASS,wereusedtoperformfoginertinganalysisfortheSequoyahplant.FOGwasusedtocalculate theratesoffogformation duetoboundarylayerandbulkstreamcondensation.

intheSequoyahicecondenser andlowerplenum.Thenthesefogformation rateswereusedinFOGMASStocomputethefogconcentrations ineachoftheSequoyahcontainment subcompartments.

Tocomputethefogformation ratesintheicecondenser upperplenumand'owercompartment, someoutputdatafromtheSequoyahCLASIXanaly-(27)sisareneeded.Thesedataincludetimehistories ofgastempera-ture,walltemperature, totalpressure, andsteampartialpressureineachcontainment subcompartment, aswellastheintercompartmental andfanflowrates.InordertoutilizetheCLASIXoutputdata,theicecondenser containment issubcompartmentalized intheFOGMASSprograminexactlythesamemannerasinReference 27.Thesubcompartmentaliza-ionmodelusedintheSequoyahCLASIXanalysisisshowninFigure6.1.InthisstudyonlytheS2Daccidentscenariohasbeenanalyzed.

0430Q:I6-7 J-'4'e~II FIGURE6.1SEQUOYAHCLASIXCONTAINMENT MODELICECONDENSER UPPERPLENUhhUPPERCOMPARTMENT ICEBEDICECONDENSER LOWERPLENUMCOMPARTMENT DEADENDEDREGIONAIRRETURNFAN/HYDROGEN SKIMMERSYSTEMFLOWPATHCONTAINSDQORSFLOWALLOWEDINBOTHDIRECTIONS FLOWALLOWEDINONEDIRECTION SPRAYHEADER S'

TheFOGinputdataforSequoyahS20 CaseIaregiveninTables6.1and6.2,andthecaIculational resultsareshowninFigures6.2and6.3.InFigure6.2,thefogformation rateinthelowercompartment isshown.Forthefirstfewhundredsecondsthewalltemperature islowerthanthe'dewpointcorresponding tothesteampartialpressureandtherefore fogstartstoform.Afterabout600seconds,thefogformation ratebecomesnegligibly smallsincethewalltemperature isonlyafewdegreesbelowthedewpoint.Thereisnofogformation inth'elowercompartment afterabout,1800 seconds.Thefogformation rateintheicecondenser isshowninFigure6.3.Itisseenthatthefogformation rateintheicecondenser ismuchlargerthanthatinthelowercompartment.

Itincreases withtheicecondenser steamflowrateandreachesapeakof14lb/secatabout1800,seconds.

Thefogformation rateintheicecondenser thenbeginstodecreaseandislowatthetimeofsignificant hydrogenrelease.Theninefogformation ratesinthelowercompartment andintheicecondenser areinputtoFOGNSSinatabularformandthereisabuilt-ininterpolation schemeinFOGtQSStoobtainvaluesfortheintermediate timesteps.FOGNSScomputestherateoffoggeneration bythebreakflow,th'efog'ettlingrateduetogravity,andthefogremovalrateduetosprays,aswell'astheratesoffogentrainment byintercompartmental andfanflows.Theinputdataneededtocalculate eachoftheseratesaredis-cussedasfollows.Therateofreactorcoolantreleasetothecontainment andthecoolantenthalpywereobtainedfromtheMARCHoutput'orasmallLOCA.The(7)qualityofthebreakflowwascalculated usingtheenthalpyandthelowercompartment gastemperature.

According totheMARCHpredic-tionthedischarge ofliquidbythebreakflowintothelowercom-0)partmentlastsforonly2172seconds.Afterward, thewaterlevelinthereactorvesseldropsbelowthebreakelevation andthefluiddischarged 0430(:I6-9

IIIIIII00IlIIIIIIIII K'

ggIIIIIIIII1IIIIIIiIIIII'IIIII 48 fromthebreakisessentially steam.Therefore, inthepresentstu@,itisassumedthatnofogisgenerated bythebreakflowafter2172seconds.Forfogremovalbygravitational

settling, avolumemeandropsizeof10pwasassumed.Theterminalvelocityofa10pdropisaboutI.cm/sec.Becauseofthislowterminalvelocity, gravitational settlingisnotaneffective fogremovalmechanism.

Theassumption of10pvolumemeandropsizeistherefore conservative, considering thefactthatforafewthousandsecondsthedropagglomeration mechanism wouldbeabletoincreasevolumemeandropsizesubstantially.

Itshouldalsobenotedthatasmallervolumemeandropsizemeansthattheminimumfoginertingconcentration wouldbereducedandthusmakesthepresentanalysisconservative.

Furthermore, noconsideration wasgiventothedeposition offogonthewallsandverticalsurfacesofthestructure, orforfogremovalinthefanflowswhenitpassesthroughductsandfans.Alltheassumptions mentioned abovemakethepresentanalysisveryconservative.

Thecontainment geometric dataneededincomputing thesettlingratearegiveninTable6.3.fForfogremovalbysprays,asprayflowrateof9500gpmwasusedforSequoyah.

According totheSequoyahCLASIXanalysis~27~,

thespraysareinitiated at142seconds.Avolumefractionofsprays(volumeofspraysdividedbyvolumeofthesprayzone)of3.3x10-4was.used, whichwasobtainedusingaspraydropfallheightof107ft,asprayzonevolumeof485,500ft3,andavolumemeandropsizeof700p.Aspreviously discussed asprayremovalofa100percentwasused.InFigure6.1,thedirections oftheintercompartmental fl'owsareshown.Theintercompartmental flowratesforthesix.flowpathsandninetimestepswereobtainedfromtheOPSCLASIXanalysisandaregiveninTable6.5.Thepresentanalysisconsiders theintercompartmental flows'asthemechanisms oftransporting fogfromonecompartment toanother.Itwasassumedinthepresentanalysisthatthefogconcen-trationsintheintercompartment flowsarethesameasthoseinthecompartments fromwhichtheflowsareoriginated.

0430Q:I6-12 r

ItisseeninFigure6.1thattwotrainsoftheairreturnfanandhydrogenskinnersystemtakesuctionfromthedeadendedregionandfromtheuppercompartment anddischarge intothelowercompartment.

Thefansareinitiated at712seconds.Thefanhead-flow curvereportedinReference 27wasusedtocomputethefanflowrates.Fanflowratesof1645ft/secand10ft/secwereusedfortheairreturnfanandthe33hydrogenskimmersystem,respectively.

Theseflowrateswerecalculated usingaverageap'sbetweentheuppercompartment andthelowercompart-ment,andbetweenthedeadendedregionandthelowercompartment.

Itwasalsoassumed.thatthefogconcentrations inthefanflowsarethesameasthoseinthecompartments fromwhichtheflowsareoriginated.

TheresultsoftheFOGMASScalculation areshowninFigure6.4.Itisseenthatforthefirstfewhundredsecondsthefogconcentrations inthelowercompartment, icecondenser lowerandupperplenumsareaboutthesameandincreasing.

Atabout700seconds,thelowercompartment

.fogconcentration reachesitspeakof2.2x10.Afterward, theintercompartmental flowstransport morefogdropletsoutofthelowercompartment thanaregenerated bythebreakflowandcondensation and,therefore, thelowercompartment fogconcentration decreases.

However,-

theupperplenumfogconcentration keepsrisinguntilabout900seconds,duetoanincreasing fogformation intheicecondenser andmorefogentrained intheintercompartmental flowintotheupperplenum.Theupperplenumfogconcentration reachesitspeakof5.4x10atabout900seconds.Thelowerplenumfogconcentration isalmostthesameasthelowercompartment fogconcentration becauseoflittledifference intheintercompartmental flowratesintoandoutoftheicecondenser lowerplenum.-Therefore, thesetwovolumesbehaveasasinglevolumefntermsoffogconcentration.

At2172seconds,thebreakflowinthelowercompartment stopsgenera-tingfogand,therefore, thefogconcentrations dropsharplythere-after.Theeffectismorepronounced forthelowercompartment andlowerplenumfogconcentrations.

Thehighestfogconcentration existsintheicecondenser upperplenumwhilethelowestexistsintheuppercompartment.

Theeffectof.sprayson.theuppercompartment fogconcen-trationisclearlyseeninFigure6.4.At142seconds,thespraysare0430Q:I6-13 t

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

t~

-turnedonandtheuppercompartment fogconcentration dropssharplyuntilabout600seconds.Atabout600seconds,theuppercompartment fogconcentration startstoincreaseagainbecausetheintercompartmen-talflowintothecompartment increases sharplyatthattime.Apeak-6concentration of7x10intheuppercompartment isreachedatabout1200seconds.Hydrogenstartstoreleaseintothecontainment atabout3804seconds,according totheMARCHcalculation

.Itreaches4volumepercent(27)atabout4300,',4400, and4670secondsinthelowercompartment, upperplenum,anduppercompartment, respectively.

At4300seconds,thecalculated lowercompartment fogconcentration is9.7x10,whichisaboutanorderofmagnitude smallerthanthe-7minimumfogconcentrations requiredforinerting4percentH2.At4670seconds,theuppercompartment fogconcentration is1.35x10whichisaboutafactoroffivesmallerthantheminimumfogconcen-trationrequiredforinerting4percentH2*.Atthetimesofreaching8.5percentH2,thefogconcentrations intheloweranduppercompart-mentsareevenlowerthanthefiguresgivenabove.Therefore, itisconcluded thatthefogconcentrations'n theloweranduppercompart-mentsaretoolowtohaveanyinertingeffect.Theuseofthepresenttheoryonfoginertingalsoleadstothesameconclusion.

..However, at4400seconds,thecalculated fogconcentration intheupper-5plenumis6.1x10whichishigherthantheFactoryMutualfoginertingdataextrapolated to10pdropsandthepresenttheoretical prediction.

Thedatashowsthatinordertoinert4.76percentH2thefogconcentration mustbe8.4x10orhigherfor10pvolumemeandropsize.At4600seconds,theupperplenumhydrogenconcentration reachesabout7percentandthefogconcentration is5.5x10Again,anextrapolation oftheFactoryMutualdatato10pshowsthatfogconcentration of2.1x10orhigherisrequiredtoinert7.2percentH.Incomparison, thepresenttheoryonfoginertingpre-dicts1.02x10for7.2percentH2.Thefoginertingcriterion usedisdescribed inSection5.2.0430Q:16-15 Therefore, itappearsthatitispossibletoinert7percentH2butunlikely.

However,at8percentH2intheupperplenum,whichoccursatabout4650seconds,thefogconcentration is5.5x105,whichistoolowtoinert8percentH2.Anextrapolation oftheFactoryMutual8percentH2datato10pvolumemeandropsizeandthepresentpre-dictiongive1.9x10-4andl.2x10-4fortheminimumrequiredfoginertingconcentration, respectively

.Therefore boththetheoryandtheextrapolation oftestdatashowthatfoginertingwillnotoccurintheupperplenum.PgTheglowplugigniterswhichhavebeeninstalled intheSequoyahcon-tainmentweredesignedtoburnhydrogenlowerthan8.0percent.Asdiscussed previously, nofoginertingeffectswillbeexpectedintheSequoyahloweranduppercompartments.

Therefore, theglowplugigni-tetsareexpectedtofunctionasdesignedinthesetwocompartments.

Itmaybepossiblethatfogpresentintheicecondenser upperplenummaypreventtheglowplugignitersfromignitinghydrogenbelow7percent.However,itseemsveryunlikelythatthesameigniterswouldfailtoignite8.0percentH2asdesigned, considering thefactthatconsider-ableconservatism hasbeenexercised inthepresentanalysis.

Sensitivity studiesofthesprayremovalefficiency andthefractionofblowdowndropletssmallerthan20pfortheSequoyahplanthavebeenperformed.

Acaseof10percentsprayremovalefficiency wasrunusingFOGMASS.Thecalculational resultsshowedthatthefogconcentrations inthelowercompartment, lowerplenum,andupper.compartment at4600secondswereincreased approximately byafactorof10.However,theseconcentrations arestilltoolowtoinert8percenthydrogen-Incom-parison,thefogconcentration intheupperplenumisincreased byonly20percentbecausetheconcentration atthistimeisprimarily deter-minedbythefogformation rateintheicecondenser.

Thisincreaseistoosmalltochangetheconclusion givenpreviously ontheinertingprobability intheupperplenum.Anothercaseinwhichalltheblowdowndropletswereassumedtobesmallerthan20pwasrunusingFOGMASS.Thecalculational resultsshowedthatat4600secondsthefogconcentra-tionsinthelowercompartment andlowerplenumwereincreased by150430QI6-16

(\

percentwhiletheincreases intheupperplenumanduppercompartment werenegligibly small.Theinsensitivity ofthefogconcentrations totheparameter ofthefractionofblowdowndropletssmallerthan20uisduetotheeffectiveness ofthesprayremoval.At4600seconds,almostalltheblowdowndropletsareremovedbythesprays.Thesensitivity studiesshowedthatthefogconcentration intheupperplenumatthetimeofsignificant hydrogenreleaseisnotsensitive tothesprayremovalefficiency andthefractionofblowdowndropletssmallerthan20g.0430(:16-17 L'jI TABLE6.1FOGIHPUTQATAFORSfgUOYAHLOWERCOMPARTMENT Time(sec)LowerCompartment GasflowRate(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 TABLE6.2FOGINPUTDATAFORSEQUOYAHICECONDENSER IceCondenser GasFlowRateTime(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

TABLE6.3GEOMETRIC DATAFORSEgUOYAHCONTAIHMEHT Volume(ft)3FloorArea(ft)LowerCompartment 289,0005,410IceCondenser LowerPlenum24,2003,100IceCondenser UpperPlenum47,0003,200UpperCompartment 651,00010,390DeadEndedRegion94,0003,3500430(:16-20

k.

-TABLE6.4MARCHPREDICTION OFREACTORCOOLANTMASSANDENERGYRELEASERATEFORTHES2DSEQUENCETime(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 TABLE6.5IHTERCOMPARTHENTAL fLOMRATES(ft/sec)PREDICTED BYCLASIXFORSEQUOYAHTime(sec)FlowFromFlowFromFlowFromflowFromflowFromLCtoLPLPtoUPUPtoUCUCtoLCDEtoLC6.001E16.100E21.210E31.810E32.410E33.010E33.510E34.010E34.510E31.175E33.580E22.864E32.828E3'.695E3 2.654E32.528E32.613E32.694E31.082E39.641E12.654E32.799E32.679E32.629E32.502E32.594E32.628E37.029E2-3.931E11.272E31.323E31.375E31.407E31.352E31.537E31.627E3-1.095E2-1.106E2-,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 46.3FOGIHERTIHGPROBABILITY IHTHEMcGUIREPLAHTIThecomputercodes,FOGandFOGMASS,wereusedtoperformfoginertinganalysisfortheMcGuireplant.FOGwasusedtocalculate theratesoffogformation duetoboundarylayerandbulkstreamcondensation intheMcGuireicecondenser andlowerplenum.Thenthesefogformation rateswereusedinFOGMASStocomputethefogconcentrations ineachoftheMcGuirecontainment subcompartments.

Tocomputethefogformation ratesintheicecondenser upperplenumandlowercompartment,

'someoutputdatafromtheMcGuireCLASIXanaly-sisareneeded.Thesedataincludetimehistories ofgastempera-(28)ture,walltemperature, totalpressure, andsteampartialpressureineachcontainment subcompartment, aswellastheintercompartmental andfanflowrates.InordertoutilizetheCLASIXoutputdata,theicecondenser containment issubcompartmentalized intheFOGMASSprograminexactlythesamemannerasinReference 28.Thesubcompartmentaliza-tionmodelusedintheMcGuireCLASIXanalysisisshowninFigure6.5.InthisstudyonlytheS20accidentscenariohasbeenanalyzedbyCLASIXforMcGuire.4~TheFOGinputdataforMcGuireS2DCaseIaregiveninTables6.6and6.7,andthecalculational resultsareshowninFigures6.6and6.7.InFigure6.6,thefogformation rateinthelowercompartment isshown.Forthefirstfewhundredsecondsthewalltemperature islowerthanthedewpointcorresponding tothesteampartialpressureandtherefore fogstartstoform.Thefogformation rateislowbecausethewalltempera-'ureisonlyafewdegreesbelowthedewpoint.Fogformation inthelowercompartment becomeszeroafterabout600seconds.Thefogforma-tionrateintheicecondenser isshowninFigure6.7.Itisseenthatthefogformation rateintheicecondenser ismuchlargerthanthatinthelowercompartment.

Thefogformation rateincreases withtheicecondenser steamflowrateandreachesthefirstpeakatabout1510sec-onds.Thentheratedecreases becauseofthedecreaseinthesteamflowrate.Thefogformation andthesteamflowratesstarttoincreaseagainatabout2510seconds.Thefogformation ratereachesthesecond0430Q:I6-23

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

~~

~~

peakofI0.21b/secatabout3260seconds.Theeightfogformation

'ratesinthelowercompartment andintheicecondenser areinputtoFOGNSSinatabularform.FOGNSScomputestherateoffoggeneration bythebreakflow,thefogsettlingrateduetogravity,andthefogremovalrateduetosprays,aswellastheratesoffogentrainment byintercompartmental andfanflows.Theinputdataneededtocalculate eachoftheseratesaredis-cussedasfollows.0)'Therateofreactorcoolantreleasetothecontainment andthecoolantenthalpywereobtainedfromtheNRCHoutputforasmallLOCA.TheP)qualityofthebreakflowwascalculated usingtheenthalpyandthelowercompartment gastemperature.

According totheNRCHpredic-tionthedischarge ofliquidbythebreakflowintothelowercom-partmentlastsforonly2172seconds.Afterward, thewaterlevelinthereactorvesseldropsbelowthebreakelevation andthefluiddischarged fromthebreakisessentially steam.Therefore, inthepresentstudy,itisassumedthatnofogisgenerated bythebreakflowafter2172seconds.Forfogremovalbygravitational

settling, avolumemeandropsizeof10pwasassumed.Theassumption of10pvolumemeandropsizeiscon-servative, considering thefactthatforafewthousandsecondsthedropagglomeration mechanism wouldbeabletoincreasevolumemeandropsizesubstantially.

Itshouldalsobenotedthatasmallervolumemeandropsizemeansthattheminimumfoginertingconcentration wouldbereducedandthusmakesthepresentanalysisconservative.

Furthermore, nocon-sideration wasgiventothedeposition offogonthewallsandverticalsurfacesofthestructure, orforfogremovalinthefanflowswhenitpassesthroughductsandfans.Alltheassumptions mentioned abovemakethepresentanalysisveryconservative.

Thecontainment geometric dataneededincomputing thesettlingratearegiveninTable6.8.0430QI6-27 C4 Forfogremovalbysprays,asprayflowrateof6800gpmwasusedforRcGuire.According totheHcGuireCLASIXanalysis,thespraysareinitiated at124seconds.Avolumefractionofsprays(volumeofspraysdividedbyvolumeofthesprayzone)of3.3x10wasused.Aspre-viouslydiscussed asprayremovalefficiency ofa100percentefficiency wasused.InFigure6.5,thedirections oftheintercompartmental flowsareshown.Theintercompartmental flowratesforthesixflowpathsandeighttimestepswereobtainedfromtheOPSCLASIXanalysisandaregiveninTable6.9.Thepresentanalysisconsiders theintercompart-mentalflowsasthemechanisms oftransporting fogfromonecompartment toanother.Itwasassumedinthepresentanalysisthatthefogconcen-trationsintheintercompartment flowsarethesameasthoseinthecompartments fromwhichtheflowsareoriginated.

Figure6.5showstwotrainsoftheairreturnfanandhydrogenskimmersystemandthefanflowdirections.

Thefansareinitiated at694sec-onds.Thefanhead-flow curvereportedinReference 28wasusedto3computethefanflowrates.Fanflowratesof1000ft/secand100ft/secwereusedfortheairreturnfanandthehydrogenskimmer3system,respectively.

Theseflowrateswerecalculated usingaverageap'sbetweentheuppercompartment andthelowercompartment, andbetweenthedeadendedregionandtheuppercompartment.

Itwasalsoassumedthatthefogconcentrations inthefanflowsarethesameasthoseinthecompartments fromwhichtheflowsareoriginated.

TheresultsoftheFOGMASScalculation areshowninFigure6.8.Itisseenthatforthefirstfewhundredsecondsthefogconcentrations inthelowercompartment, icecondenser lowerandupperplenumsareaboutthesameandincreasing.

Atabout600seconds,thelowercompartment fogconcentration reachesitspeakof1.6x10.Afterward, theintercompartmental flowstransport morefogdropletsoutofthelowercompartment thanaregenerated bythebreakflowandcondensation and,therefore, thelowercompartment fogconcentration decreases.

However,theupperplenumfogconcentration keepsrisinguntilabout800seconds,0430Q:I6-28

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

)

duetoanincreasing fog.formation intheicecondenser andmorefogentrained intheintercompartmental flowintotheupperplenum.Theupperplenumfogconcentration reachesitspeakof6.4x10atabout800seconds.Thelowerplenumfogconcentration isalmostthesameasthelowercopartment fogconcentration becauseoflittledifference intheintercompartmental flowratesintoandoutoftheicecondenser lowerplenum.Therefore, thesetwovolumesbehaveasasinglevolumeintermsoffogconcentration.

At2172seconds,thebreakflowinthelowercompartment stopsgenera-tingfogand,'herefore, thefogconcentrations dropsharplythere-after.Theeffectismorepronounced forthelowercompartment andlowerplenumfogconcentrations.

Thehighestfogconcentration existsintheicecondenser upperplenumwhilethelowestexistsintheuppercompartment.

Theeffectofspraysontheuppercompartment fogconcen-trationisclearlyseeninFigure6.8.At124seconds,thespraysareturnedonandtheuppercompartment fogconcentration dropssharplyuntilabout600seconds.Atabout600seconds,theuppercompartment fogconcentration startstoincreaseagainbecausetheintercompart-mentalflowintothecompartment increases sharplyatthattime.Apeakconcentration of7.5x10intheuppercompartment isreachedatabout1500seconds.Hydrogenstartstoreleaseintothecontainment atabout3804seconds,according totheMARCHcalculation

.Itreaches4volumepercentatabout4300,4400,and4850secondsinthelowercompartment, upperplenum,anduppercompartment, respectively.

At4300seconds,thecalculated lowercompartment fogconcentration is84x10,whichisaboutanorderofmagnitude smallerthantheminimumfogconcentrations requiredforinerting4percentH2.At4850seconds,theuppercompartment fogconcentration is1.47x10whichisaboutafactoroffivesmallerthantheminimumfogconcen-trationrequiredforinerting4percentH2*.=Atthetimesof*Thefoginertingcriterion usedisdescribed inSection5.2.0430Q:16-30 reaching8.5percentH2,thefogconcentrations intheloweranduppercompartments areevenlowerthanthefiguresgivenabove.Therefore, itisconcluded thatthefogconcentrations intheloweranduppercompart-mentsaretoolowtohaveanyinertingeffect.Theuseofthepresenttheoryonfoginertingalsoleadstothesameconclusion.

However,at4400seconds,thecalculated fogconcentration intheupperplenumis9.8x10whichishigherthantheFactoryMutualfoginertingdataextrapolated to10pdropsandthepresenttheoretical prediction.

Thedatashowsthatinordertoinert4.76percentH2thefogconcentration niustbe8.4x10orhigherfor10pvolumemeandropsize.At4500seconds,theupperplenumhydrogenconcentration

-5reachesabout7percentandthefogconcentration is9.3x10Again,anextrapolation oftheFactoryMutualdatato)0pshowsthatfogconcentration of2.1x10orhigherisrequiredtoinert7.2percentH2.Incomparison, thepresenttheoryonfoginertingpre-dicts1.02x10for7.2percentH2.Therefore, itappearsthatitispossibletoinert7percentH2,butunlikely.

However,at8per-centH2intheupperplenum,whichoccursatabout4600seconds,thefogconcentration is9.1x10,whichistoolowtoinert8percentAnextrapolation oftheFactoryMutual8percentH2datato104uvolumemeandropsizeandthepresentprediction give1.9x10and1.2x10fortheminimumrequiredfogincrtingconcentration, respectively.

Therefore, boththetheoryandtheextrapolation ofthe'estdataindicatethatfoginertihgwillnotoccur.Theglowplugigniterswhichhavebeeninstalled intheMcGuirecontain-mentweredesignedtoburnhydrogenlowerthan8.5percent.Asdiscus-sedpreviously, nofoginertingeffectswillbeexpectedintheMcGuireloweranduppercompartments.

Therefore, theglowplugignitesareexpectedtofunctionasdesi'gned inthesetwocompartments.

Itmaybepossiblythatfogpresentintheicecondenser upperplenummaypreventtheglowplugignitesfromignitinghydrogenbelow7percent.However,itseemsveryunlikelythatthesameigniterswouldfailtoignite8.5"Thefoginerting'criterion usedisdescribed Section5.2.0430Q:16-31 percentH2asdesigned, considering thefactthatconsiderable conser-vatismhasbeenexercised inthepresentanalysis.

0430Q:16-32 TABLE6.6FOGINPUTDATAFORMcGUIRELOWERCOMPARTMENT LowerCompartment GasGasFlowRateTemp.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 TABLE6.7FOGIHPUTDATAFORHcGUIREICECOHDEHSER IceCondenser GasFlowRateTime(sec)(ft/sec)SteamGasIceTotalPartialTemp.Temp.PressurePressure60510151020102510326037604510820.5107.119261637114516301514146490130190193188195193192323232323232323216.522.2"21.92221.421.621.122.12.39.38.610.38.17.10430Q:16-34 TABLE6.8GEOMETRIC DATAFORMcGUIRECONTAINMENT

'IVolume(ft)FloorArea(ft)LowerCompartment 237,4005,410IceCondenser LowerPlenum24,2003,100IceCondenser UpperPlenum47,0003,200UpperCompartment 670,00010,390DeadEndedRegion130,9003,3500430Q:1~6-35 l

TABLE6.9IHTERCOMPARTMEHTAL FLOWRATES(ft/sec)3PREDICTED BYCLASIXFORMcGUIRETime(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 6.4FOGINERTINGPROBABILITY INTHED.C.COOKPLANTf'hecomputercodes,FOGandFOGMASS,wereusedtoperformfoginertinganalysisfortheD.C.Cookplant.FOGwasusedtocalculate theratesoffogformation duetoboundarylayerandbulkstreamcondensation intheD.C.Cookicecondenser andlowerplenum.Thenthesefogformation rateswereusedinFOGMASStocomputethefogconcentrations ineachoftheD.C.Cookcontainment subcompartments.

Tocomputethe,fogformation ratesintheicecondenser upperplenumandlowercompartment, some'output datafromtheCookCLASIXanalysis(29)areneeded.Thesedataincludetimehistories ofgastemperature, walltemperature, totalpressure, andsteampartialpressureineachcontain-mentsubcompartment, aswellastheintercompartmental andfanflowrates.InordertoutilizetheCLASIXoutputdata,theicecondenser containment issubcompartmentalized intheFOGMASSprograminexactlythesamemannerasinReference 29.Thesubcompartmentalization modelusedintheCookCLASIXanalysisisshowninFigure6.9.InthisstudyonlytheS20accidentscenariohasbeenanalyzed.

TheFOGinputdataforCookS2DCase.1aregiveninTables6.10and6.11,andthecalculational resultsareshowninFigures6.10and6.11.'nFigure6.10,thefogformation rateinthelowercompartment isshown.Itisseenthatthefogformation rateisnegligibly small.Itshouldbenotedthatthecalculation ofthelowercompartment fogconcentration inthe0.C.Cookplantstartsat600secondsinsteadof60secondsusedfortheothertwoplants.Thefogformation rateinthelowercompartme startstoincreaseatabout4200secondsbecauseoftheincreaseinthesteampartialpressure.

Itreaches0.017lb/secatabout4590seconds.Fogformation inthelowercompartment willstopafter4700secondsbecauseofthehydrogenburnthereafter.

Thefogformation rateintheicecondenser isshowninFigure6.11.Itisseenthatthefogformation rateintheicecondenser ismuchlargerthanthatinthelowercompartment.

Itincreases withtheicecondenser steamflowrateandreachesapeakofabout15.6lb/secatabout1200seconds.Thefogformation rateintheicecondenser thenbeginstodecreaseandislowatthetimeofsignificant hydrogenrelease.0430Q16-37

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

IIIIIIIIIIIIIIIIIIIeI I

II'IIIIIIIIIIIlIIIIIII Theeightfogformation ratesinthelowercompartment andintheice.condenser areinputtoFOGMASSinatabularform..:FOGMASScomputestherateoffoggeneration bythebreakflow,thefogsettlingrateduetogravity,andthefog-removal rateduetosprays,aswellastheratesoffogentrainment byintercompartmental andfanflows.Theinputdataneededtocalculate eachoftheseratesaredis-cussedasfollows.Therateofreactorcoolantreleasetothecontainment andthecoolant'IP)enthalpywereobtainedfromtheMARCHoutputforasmallLOCA.Thequalityofthebreakflowwascalculated usingtheenthalpyandthelowercompartment gastemperature.

According totheMARCHpredic-tionthedi,scharge ofliquidbythebreakflowintothelowercom-P)partmentlastsforonly2172seconds.Afterward, thewaterlevelinthereactorvesseldropsbelowthebreakelevation andthefluiddischarged fromthebreakisessentially steam.Therefore, inthepresentstudy,itisassumedthatnofogisgenerated bythebreakflowafter2172seconds.Forfogremovalbygravitational

settling, avolumemeandropsizeof10pwasassumed.Theassumption of10pvolumemeandropsizeiscon--servative, considering thefactthatforafewthousandsecondsthedropagglomeration mechanism wouldbeabletoincreasevolumemeandropsizesubstantially.

Itshouldalsobenotedthatasmallervolumemeandropsizemeansthattheminimumfoginertingconcentration wouldbereducedandthusmakesthepresentanalysisevenmoreconservative.

Further-more,noconsideration wasgiventothedeposition offogonthewallsandverticalsurfacesofthestructure, orforfogremovalinthefanflowswhenitpassesthroughductsandfans.Alltheassumptions men-tionedabovemakethepresentanalysisveryconservative.

Thecontain-mentgeometric dataneededincomputing thesettlingratearegiveninTable6.12.0430Q:I6-41 C

Forfogremovalbysprays,sprayflowratesof4000,1800,and528gpmwereusedfortheuppercompartment, lowercompartment, andfan/accumulator rooms,respectively.

According totheCookCLASIXanalysis~

~,thespraysareinitiated at141seconds.Avolumefractionofsprays'(volumeofspraysdividedbyvolumeofthesprayzone)of3.3x10-4wasused.Aspreviously discussed asprayremovalefficiency ofa100percentefficiency wasused.InFigure6.9,thedirections oftheintercompartmental flowsareshown.Theintercompartmental flowratesforthesixflowpathsandeighttimesteps'wereobtainedfromtheOPSCLASIXanalysisandaregiveninTable6.13.Thepresentanalysisconsiders theintercompart-mentalflowsasthemechanisms oftransporting fogfromonecompartment toanother.Itwasassumedinthepresentanalysisthatthefogconcen-trationsintheintercompartment flowsarethesameasthose:inthecompartments fromwhichtheflowsareoriginated.

Figure6.9showstwotrainsoftheairreturnfanandhydrogenskimmersystemandthefanflowdirections.

Thefansareinitiated at711sec-onds.Thefanhead-flow curvereportedinReference 29wasusedtocomputethefanflowrates.Fanflowratesof1388,61.76,and4.13ft3/secwereusedfortheflowsfromtheuppercompartment, lowercompartment, anddeadendedregiontothefan/accumulator rooms,respectively.

Theseflowrateswerecalculated usingthehp'sbetweenthethefan/accumulator roomsandthreeothercompartments.

Itwasalsoassumedthatthefogconcentrations inthefanflowsarethesameasthoseinthecompartments fromwhichtheflowsareoriginated.

TheresultsoftheFOGMASScalculation areshowninFigure6.12.Itisseenthatforthefirstfewhundredsecondsthefogconcentrations inthelowercompartment, andtheicecondenser lowerplenumarehigh.Atabout140seconds,thelowercompartment fogconcentration reachesitspeakof1x10-4.Afterthespraysareinitiated at141seconds,thefogconcentrations inthelowercompartment, uppercompartment, andfan/accumulator roomsdropsharply.However,theupperplenumfogconcentration keepsrisinguntilabout1200seconds,'ue toanincreasing 0430Q:16-42 III~T~~I~~I~III~T~~~I

'l fogformation intheicecondenser andmorefogentrained intheintercompartmental flowintotheupperplenum.Theupperplenumfogconcentration reachesitspeakof2.4x10atabout1200seconds.Afterabout1200seconds,thelowerplenumfogconcentration isalmostthesameasthelowercopartment fogconcentration sincetheintercompartmental flowsquicklymakethefogconcentrations inthesetwocompartments uniform.Therefore, thesetwovolumesbehaveasasinglevolumeintermsoffogconcentration.

At2172seconds,thebreakflowinthelowercompartment stopsgenera-tingfogand,therefore, thefogconcentrations dropsharplythere-after.Theeffectismorepronounced forthelowercompartment andlowerplenumfogconcentrations.

Thehighestfogconcentration existsintheicecondenser upperplenum.Theeffectofspraysontheuppercompartment fogconcentration isclearlyseeninFigure6.12.At141seconds,thespraysareturnedonandtheuppercompartment fogconcentration dropssharplyuntilabout300seconds.Atabout300seconds,theuppercompartment fogconcentration startstoincreaseagainbecausetheintercompartmental flowintothecompartment increases

-6sharplyatthattime.Apeakconcentration of9.5x10intheuppercompartment isreachedatabout1400seconds.Hydrogenstartstoreleaseintothecontainment atabout3804seconds,according totheHARCHcalculation

.Itreaches4volumepercentatabout4350,4370,and4700secondsinthelowercompartment, upperplenum,anduppercompartment, respectively.

At4350seconds,thecalculated lowercompartment fogconcentration is10,whichisabouttwoordersofmagnitude smallerthantheminimumfogconcentrations requiredforinerting4percentH.At4700-6seconds,theuppercompartment fogconcentration is2.4x10,whichisaboutafactoroftwosmallerthantheminimumfogconcentration requiredforinerting4percentH*.Atthetimesofreaching8.5*Thefoginertingcriterion usedisdescribed inSection5.2.0430Q:16-44 percentH,thefogconcentrations intheloweranduppercompartments areevenlowerthanthefiguresgivenabove.Therefore, itisconcluded thatthefogconcentrations intheloweranduppercompartments aretoolowtohaveanyinertingeffect.Theuseofthepresenttheoryonfoginertingalsoleadstothesameconclusion.

However,at4370seconds,thecalculated fogconcentration intheupperplenumis6.5x10which'shigherthantheFactoryMutualfoginertingdataextrapolated to10pdropsandthepresenttheoretical prediction.

Thedatashowsthatinordertoinert4.76percentH2thefogconcentration mustbe8.4x10orhigherfor10pvolumemeandropsize.At4530seconds,theupperplenumhydrogenconcentration

-5reachesabout7percentandthefogconcentration is5.5x10Again,anextrapolation oftheFactoryMutualdatato10pshowsthatfogconcentration of2.1x10orhigherisrequiredtoinert7.2percentH2.Incomparison thepresenttheoryoffoginertingpredicts1.02x10for7.2percentH2.Therefore, itappearsthatitispossibletoinert7percentH2,butunlikely.

However,at8percentH2intheupperplenum,whichoccursatabout4600sec'onds, thefog-5concentration is5.1x10,whichistoolowtoinert8percentH2.Anextrapolation oftheFactoryMutual8percentHdatato104uvolumemeandropsizeandthepresentprediction give1.9x10and1.2x10fortheminimumrequiredfoginertingconcentration, respectively.

Theglowplugigniterswhichhavebeeninstalled intheCookcontainment weredesignedtoburnhydrogenlowerthan8percent.Asdiscussed pre-viously,nofoginertingeffectswillbeexpectedintheCookloweranduppercompartments.

Therefore, theglowplugignitersareexpectedtofunctionasdesignedinthesetwocompartments.

Itmaybepossiblethatfogpresentintheicecondenser upperplenummaypreventtheglowplugignitersfromignitinghydrogenbelow7percent.However,itseemsveryunlikelythatthesameigniterswouldfailtoignite8percentH2asdesigned, considering thefactthatconsiderable conservatism hasbeenexercised inthepresentanalysis.

0430Q16-45 TABLE6.10FOGINPUTDATAFORD.C.COOKLOWERCOMPARTMENT Time(sec)LowerCompartment GasWal1TotalGasFlowRateTemp..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.COOKICECONDENSER IceCondenser GasFlowRateTime(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 TABLE6.12GEOMETRIC DATAFORD.C.COOKCONTAINMENT Volume(ft)FloorArea(ft)LowerCompartment 249,6815,410IceCondenser LowerPlenum24,7003,100IceCondenser UpperPlenum47,0103,200UpperCompartment 681,28310,390DeadEndedRegionFan/Accumulator Rooms61,10554,8288532,5000430Q:I6-48 TABLE6.13INTERCOMPARTMENTAL FLOWRATES(ft/sec)PREDICTED BYCLASIXFORD.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

6.5EFFECTOFFOGONGLOBALCOMBUSTION Inordertoassesstheeffectoffogonthedeflagration limitofhydro-gen,whichisdefinedastheminimumhydrogenconcentration atwhichtheflamepropagates in,alldirections, aflametemperature criterion whichconsiders fogdropletsasaheatsinkwasused.Thiscriterion assumesthatthecriticalflametemperature of710Cisstillapplicable toahydrogenmixturewhichcontainsfogdroplets.

Foragivenfogconcen-tration,theheatrequiredtoheataunitmassofthemixtureto710ccanbecalculated.'hen thehydrogenconcentration neededtosupplythisamountofheat,assuming100percentcombustion, canbedeter-mined.Usingthismethod,thecalculated fogconcentrations of5.5x10and5.1x10fortheSequoyahplantat4650secondsandfortheD.C.CookPlantat4600seconds,respectively, werefoundtobecapableofraisingthedeflagration limitto10.6vol.percentH2.In-5comparison, thecalculated fogconcentration of9.1x10fortheMcGuireplantat4600secondswasfoundtobecapableofraisingthedeflagration limitto12vol.percentH2.Thisstudyshowsthatinordertoachieveglobalcombustion intheupperplenum,hydrogenconcen-trationhigherthan8.5percentmayberequired.

Theeffectofincreas-inghydrogenconcentration requiredtoobtainglobalcombustion in.theupperplenumshouldbeinvestigated.

F0430Q:16-50

7.0 SUMMARYANDCONCLUSIONS

Thepresentstudyhasdeveloped asystematic methodology tostudythepotential foginertingproblemforthePWRicecondenser plants.Inthepresentinvestigation, majorfogformation andremovalmechanisms areidentified andquantified.

Theoretical modelsaredeveloped topredictthefogformation rateduetoboundarylayerandbulkstreamcondensa-tion,thefogremovalratesduetogravitational settlingandcontain-mentsprays.Themassconservation equations forthefogdropletsineachofthecontainment subcompertments aresolvedsimultaneously inordertoobtaintimehistories offogconcentration.

Theseequations incorporate fogformation duetocondensation, foggeneration duetobreakflow,fogremovalduetogravitational settlingandsprays,trans-portoffogbytheintercompartmental flowsandfanflows.ComputerprogramsFOGandFOGMASShavebeendeveloped tocomputefogformation ratesandfogconcentrations ineachofthecontainment subcompart-ments.ThesetwocomputerprogramshavebeenusedtoanalyzeaS<DaccidentsequencefortheSequoyah, McGuire,andD.C.Cookplants.TheanalysesemployedoutputdatafromtheSequoyahCLASIXanalyses.

Speci-fically,timehistories ofgastemperature, walltemperature, totalpressure, andsteampartialpressureineachcontainment subcompartment, aswellastheintercompartmental andfanflowrateswereusedinthepresentanalysis.

Afoginertingcriterion hasbeendeveloped topredicttheminimumfogconcentration requiredtoinertagivenhydrogenconcentration andvolumemeanfogdropsize.Thepresentfoginertingcriterion hasbeenshowntobeinagreement withtheFactoryMutualdata.Thecriterion showsthattheminimumfoginertingconcentration varieswiththesquareofthevolumemeanfogdropsize.Thepresentstudyshowsthatthefogconcentrations intheupperandlowercompartments ofthethreeplantsanalyzedaretoolowtohaveanyinertingeffectonhydrogenmixtures.

Therefore, theproposedglowplugignitersareexpectedtofunctionasdesignedinthesetwocompart-ments.Itmaybepossiblethatfogpresentintheicecondenser upper0430Q:I7-1

plenummaypreventtheglowplugignitersfromignitinghydrogenbelow7~~~percent.However,itseemsveryunlikelythatthesameigniterswouldfailtoignite8.5percentH2asdesigned.

Itshouldberecognized thattheexistingtheoriesanddatacanonlypredicttheminimumfogconcentration forinerting.

Furtherworkmayberequiredtoverifythefoginertingtheoryassociated withflamepropagation inalldirections.

0430Q:I7-2 ACKNOWLEDGMENTSTheauthorwishestoexpresshissinceregratitude toMr.N.J.Liparulo, Drs.Y.Srinivas, B.Lewis,andB.Karlovitz forassistance, sugges-tions,andhelpfuldiscussions, particularly intheareaofthefoginertingcriteriaandtheflametemperature criteriaforfog,toMessrs.D.F.Paddleford, R.Bryan,F.G.Hudson,andK.Shiuforvaluab1e.comnents, toMr.K.C.Perry,Mr.S.J.Reiser,andMs.,R.M.Marinerforproviding dataonthethreeicecondenser plants,andtoMr.T.J.,Mieleforproviding programming assistance.

HealsowouldliketothankTYA,DukePower,andAEPforproviding thefinancial support.0430Q:17-3

REFERENCES 1.B.Lowry,"Preliminary Results:AStudyofHydrogenIgniters,"

ENNBO-45; LawrenceLivermore NationalLaboratory, November17,1980.2."Additional guestions onHydrogenControlSystemforIceCondenser Plants,"NRCmemofromL.Rubenstein toR.Tedesco,datedJune26,1981.3."TheMarvikken FullScaleContainment Experiments,"

MXB-301ABAtomenergi, March,1977.*4.T.F.Kanzleiter, "LOCAExperiments WithaPWRMulti-Compartment ModelContainment,"

Trans.1977LWRSafetyConf.,IdahoFalls,Idaho,1977.5.G.'M.Fuls,"TheCLASIXComputerProgramfortheHydrogenReleaseandDegradation",

OPS-07A35, OffshorePowerSystems,1981.6.K.K.Almenas,"ThePhysicalStateofPost-Loss-of-Coolant AccidentContainment Atmospheres,"

Vol.44,NuclearTechnology, pp.411.-427, August,1979.7."SummaryofAnalysisofIceCondenser Containment ResponsetoHydro-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-Generated DropSizePrediction

-AThermalFramentation Model,"Trans.Am.Nucl.Soc.,30,p.371.1978.10.P.G.Hill,H.Witting,andE.P.Demetri,"Condensation ofMetalVaporsDuringRapidExpansion,"

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.Landsberg andJ.VanMieghem,ed.,4.1,AcademicPress,NewYork,1958.13.R.J.Burian,andP.Cybulskis, "CORRALIIUserManual,"BattelleColumbusLaboratories, January,1977.14.R.K.HilliardandL.F.Coleman,"NaturalTransport EffectsonFissionProductBehaviorintheContainment SystemsExperiment,"

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,"FogFormation Conditions NearColdSurfaces,"

Vol.28,No.1,J.ofColloidandInterface Sci.,Septem-ber,1968.17.K.Hijikata, andY.Mori,"ForcedConvective HeatTransferofaGasWithCondensing VaporAroundaFlatPlate,"Vol.2,No.1,HeatTransfer-Jap.Res.,pp.81-101,January,1973.18.M.Neiburger andC.W.Chien,"Computation oftheGrowthofCloudDropsbyCondensation UsinganElectronic DigitalComputer,"

Geophys.Monograph No.5,pp.191-209,1960.19.R.M.Kemper,"IodineRemovalbySprayintheSalemStationContain-ment,"WCAP-7952, Westinghouse ElectricCorp.,August,1972.20.N.J.Liparulo, J.E.OlhoeftandD.F.Paddleford, "GlowPlugIgnitorTestsinH2Mixtures,"

WCAP-5909, Westinghouse ElectricCorp.,March6,1981.21.R.G.ZaloshandS.N.Bajpai,"WaterFogInertingofHy'drogen

-AirMixtures,"

EPRIProjectPreliminary Rp.1932-1,September, 1981.0430Q:I

22.J.M.Marchello, "ControlofAirPollution Source,"MarcelDekker,~~~~~Inc.,HewYork,1976.23.LetterfromB.LewisandB.Karlovitz toL.E.Hochreiter, datedmay5,1980.24.M.Berman,etal.,"Analysis ofHydrogenMitigation forDegradedCoreAccidents intheSequoyahNuclearPowerPlant,"Sandiadraftreport,December1,1980.25.T.vonKarman',Unpublished notes,1956.26.S.S.Tsai,"FlameTemperature CriteriaTests,"HS-CCA-81-039, West-inghouseinternalmemo,datedJune17,1981.27.Attachment toOffshorePowerSystemletterPST-HE-109, datedMay22,1981.28.Attachment toOffshorePowerSystemletterPST-NE-106, datedMay14,1981.29.Attachment toOffshorePowerSystemletterPST-HE-218, datedAugust6,1981.30.M.L.Corrin,J.R.Connel,andA.J.Gero,"AnAssessment ofWarmFog-Nucleation, Control,andRecommended Research,"

NASACR-2477,

November, 1974.0430Q:1R-3

APPENDIXAC0MPUTATI0N0FYoANDgINEQUATI0N{312)TheHijikata-Mori fogapproximation forthefogconcentration andassumedinEqs.(3.7)intotheconservation formation theoryusedtheboundarylayercontinuity,

momentum, andenergyequations.

Thevelocityprofilesintheboundarylayerareand(3.S).Substituting Eqs.(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'-WSchmidtnumberkineticviscositycomponent ofthefreestreamvelocityperpendicular tothewallheatofvaporization specificheatofnon-condensible gasT-Togastemperature atfreestreamgastemperature atwallEquations (A-I)through(A-4)arefouralgebraic equations forfourunknowns, Y,g,R,andv'Theseequations havebeensolvedbythecomputerprogramFOG.InFOG,thevaluesofY,g,andRarecomputedandusedinEq.(3.12)tocomputethefogformation rate.0430Q:1A-2 I

.APPENDIXBDERIVATION OFEQUATION(5.5)Thisappendixgivesdetailedprocedures toderiveEq.(5.5),startingfromEq.(5.4)criteiu-Yf)/ei)(5.4)Ewheretheratioofheatlossrateperunitvolumetotheheatreleaseratebychemic'al reactionperunitvolume,(K)t,isdefinedasKcrt=S/CwPandtheratioofsensibleheattoheatofcombustion, e;,isdefinedase.=C(T.-T)/q1p1uToarriveatEq.(5.5),itisnecesarytoassumethatalltheheatlossisattributed toconvection heattransfertofogdropletsofonlyonedropsize.Underthisassumption, therateofheatlossperunitvolumeperdegree,S,maybeexpressed asS=nxdhwheren=numberofdropsperunitvolumed=volumemeandropsizeh=heat'transfer coefficient Itisfurtherassumedthattherelativevelocitybetweenthedropletsandthemixtureflowissosmallthatheattransfercoefficient, h,canbeapproximated bytheconduction limit.Underthisassumption, Eq.(B-3)reducestod0430Q:IB-I

~,~4k ATTACHMENT 5TOAEP:NRC:0500K FOGINERTINGCRITERIAFORHYDROGEN/AIR MIXTURESDONALDC.COOKNUCLEARPLANTUNITNOS.lAND2 CO