Theimpactofthermalnon-equilibriumandlarge-scale2D/3DeffectsondebrisbedrefloodingandcoolabilityOriginalResearchArticle

Duringaseverenuclearaccident,apartofthemoltencoriumresultingfromthecoredegradationmayrelocatedowntothelowerplenumofthereactorvessel.Theinteractionwithresidualwaterinthelowerplenumleadstoafragmentationofthecoriumandformationofparticles(characteristiclength-scale:1–5mm).Inordertopredictthesafetymarginofthereactorundersuchconditions,thecoolabilityofthisporousheat-generatingmediumandthepossibilitytorefloodtheparticlebedarestudiedinthispaperandcomparedwithothertheoreticalorexperimentalresults. Aquickoverviewoftheexistingexperimentalresultsandmodelsisprovidedtoidentifytheremaininguncertaintiesonsomemodellingissuesandthelackofunderstandingofsomeofthephysicalprocessesinvolved.ItalsojustifiestheapproachchosenbyInstitutdeRadioProtectionetdeSûretéNucléaire(IRSN)todealwiththeissuesofdebriscoolabilityandreflooding.Thedetaileddescriptionoftwo-phaseflowinadebrisbedisaddressedinIRSNbyaspecialmoduleoftheICARE/CATHAREcode.Thisthermalhydraulicmoduleisdesignedtodealwithanon-homogeneousdebrisbedofanyshape.ThemomentumbalanceequationforeachfluidphaseisanextensionofDarcyʹslaw.Thisextensiontakesintoaccountthecapillaryeffectsbetweenthetwophases,therelativepermeabilitiesandpassabilitiesofeachphase,theinterfacialdragforcebetweenliquidandgas,andtheporousbedconfiguration(porosity,particlediameter,…).Themodeldevelopedisthree-dimensional,whichisimportanttobetterpredicttheflowinconfigurationssuchasnaturalconvectionco-currentflowsinlargebedsortoemphasizetheimpactofpreferentialpathsinducedbyporousgeometry(existenceofregionswithlowerorhigherporosityandpermeability).Theenergybalanceequationsofthethreephases(liquid,gasandsolidphase)areobtainedbyavolumeaveragingprocessofthelocalconservationequations.Inthismethod,thelocalthermalnon-equilibriumbetweenthethreephasesistakenintoaccountandtheheatexchangecoefficientsaswellasthethermaldispersioncoefficientsarecalculatedasafunctionofthelocalgeometryoftheporousmediumandthelocalphasedistribution.Numericalestimationsofthesethermalpropertiescanbeperformed,whichisquiteconvenient,onapracticalpointofview,sincetheyareverydifficulttodetermineexperimentally.Thisfeatureisagreatadvantageofthisapproach.Examplesofnumericaldeterminationofeffectivepropertiesaregiveninthepaper,withanalyticalsolutionsforasimplegeometry.Thephasechangerateisalsonaturallydeterminedwithoutadditionalphenomenologicalequation. One-dimensionalpredictionsofcriticaldryoutfluxesarepresentedandcomparedwithresultsfromtheliterature.Reasonableagreementisobtained.Calculationsofone-dimensionalreflooding(fromtoporbottom)arecomparedwithexperimentaldata.Theresultsshowtheimportanceofusinganon-equilibriummodelfortemperatures.Theyalsoindicatethatchannelingeffectsmayexistandshouldbetakenintoaccountinthemodelforfurtherimprovements.Two-dimensionalcalculationsarepresentedandshowtheinfluenceoftheporousmediumcharacteristics.Asexpected,watercirculationisimprovedconsideringmulti-dimensionalflowinthebedandthedryoutheatfluxislargerthanpredictedby1Dmodelling.Conditionsforrefloodingarealsomorefavourableiflarge-scalenon-homogeneitiesexistinthedebrisbed.Thisleadstoaflowpatternwheresteamcanexitthedebrisbedinpreferentialchannelsandthereislesslimitationbycounter-currentflow.