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EXPERIMENTALANDNUMERICALANALYSISOFLADLETEEMINGPROCESSGASTNMMAZZAFERROA,1,MARCELOPIVAB,2,SERGIOPFERROA,3,PABLOBISSIOB,4,MARINAIGLESIASB,ADRIANACALVOB,5,MARCELABGOLDSCHMITA,6ACENTERFORINDUSTRIALRESEARCH,FUDETECDRSIMINI250,2804CAMPANA,ARGENTINABPOROUSMEDIAGROUP,ENGINEERINGSCHOOL,UNIVERSIDADDEBUENOSAIRES,PASEOCOLN850,1063,BUENOSAIRES,ARGENTINA1EMAILSIDGSMSIDERCACOM2EMAILMPIVAFIUBAAR3EMAILSIDFESSIDERCACOM4EMAILPABLOBISSIOCIUDADCOMAR5EMAILACALVOFIUBAAR6EMAILSIDGLDSIDERCACOMABSTRACTINTHECONTINUOUSCASTING,THEMOLTENSTEELISPOUREDFROMTHELADLETOTHETUNDISHTHROUGHANOZZLELOCATEDATTHEBOTTOMOFTHELADLETHISPROCESS,HOWEVER,MUSTBESTOPPEDBEFORETHELADLEISCOMPLETELYEMPTIEDTOAVOIDSLAGCARRYOVERTOTHETUNDISHTHEAMOUNTOFSTEELTHATREMAINSUNTEEMEDINTHELADLEISUSUALLYSIGNIFICANTSOSTEELPLANTSAREHIGHLYINTERESTEDINSTUDYINGDIFFERENTWAYSTOIMPROVETHEPROCESSINTHEPRESENTWORK,EXPERIMENTALSTUDIESONWATERMODELSANDNUMERICALSIMULATIONSAREUSEDTOANALYZETHECONDITIONSNEEDEDFORVORTEXFORMATIONANDTHEINFLUENCEOFGEOMETRICALANDFLOWPARAMETERSINTHEAMOUNTOFWASTEDSTEELBOTHEXPERIMENTALANDNUMERICALRESULTSLEADTOTHECONCLUSIONTHATNOVORTEXFORMATIONISEXPECTEDTOTAKEPLACEDURINGLADLEDRAINAGEUNDERINDUSTRIALCONDITIONS1INTRODUCTIONDURINGTHECONTINUOUSCASTINGPROCESS,MOLTENSTEELISPOUREDFROMLADLETOTUNDISHTHROUGHANOZZLELOCATEDINANECCENTRICPOSITIONOFLADLEFLOORALADLEISAVESSELOFGENERALLYCYLINDRICALSHAPEWITHADIAMETEROF23METERSANDAHEIGHTOFAPPROXIMATELY3METERSITCONTAINSBETWEEN100AND200TONSOFLIQUIDSTEELWHICHAREDRAINEDTHROUGHA5/10CMDIAMETERNOZZLEMOLTENSTEELINLADLEISCOVEREDBYASLAGLAYERWHICHTHICKNESSVARIESBETWEEN5AND20CMWHICHPREVENTSITSOXIDATIONBYAIRCONTACTASTHEDRAININGPROCESSPROGRESSES,THEINTERFACETHATSEPARATESTHESTEELFROMTHESLAG,EVENTUALLYDEFLECTSTOWARDSTHEDRAINAGENOZZLEANDADOPTSTHEFORMOFA“FUNNEL”FUNNELFORMATIONLEADSTOSLAGCARRYOVERFROMLADLETOTUNDISHTHEDRAINAGEISSTOPPEDWHENFIRSTTRACESOFSLAGAREDETECTEDINTHENOZZLE,LEAVINGASIGNIFICANTAMOUNTOFSTEELUPTO3TONSUNTEEMEDINTHELADLEFUNNELFORMATIONEFFECTHASBEENANALYZEDBYSEVERALSTUDIES17,GENERALLYBASEDONEXPERIMENTSPERFORMEDONPHYSICALMODELSWHEREWATERISUSEDINSTEADOFSTEELINTHESEEXPERIMENTSWATERDRAINAGEFROMCYLINDRICALORSQUARESHAPEDVESSELSWITHFLATHORIZONTALFLOORSISSTUDIEDFORDIFFERENTNOZZLEDIAMETERS054CMTO8CMANDECCENTRICITIESUPTO07THESUBJACENTFLUIDDYNAMICSOFTHEPHENOMENONHASALSOBEENANALYZEDBYSEVERALAUTHORS814ACCORDINGTOBIBLIOGRAPHY18TWODIFFERENTMECHANISMSCANLEADTOTHEDEFLECTIONOFTHESTEELSURFACEVORTEXSINKORDRAINSINKVORTEXSINKISCHARACTERIZEDBYHIGHTANGENTIALVELOCITIESINTHENEIGHBORHOODOFTHENOZZLESEELEFTSCHEMEONFIGURES1AND2ANDCANBEDEVELOPEDEVENWITHAHIGHCOLUMNOFSTEELINTHELADLEVORTEXFORMATIONCANTAKEPLACEINVESSELSWHERETHEFLUIDHASIMPORTANTINITIALTANGENTIALVELOCITIESESPECIALLYIFTHEDISCHARGENOZZLEISCENTEREDTHEAMOUNTOFLIQUIDINLADLEWHENVORTEXSINKREACHESTHENOZZLEDEPENDSONINITIALROTATIONALVELOCITYANDONNOZZLEECCENTRICITYONTHEOTHERHAND,THEDRAINSINKISCHARACTERIZEDBYRADIALFLOWRIGHTSCHEMEONFIGURES1AND2ANDDEVELOPSINTHELASTSTAGEOFTHETEEMINGPROCESS,WHENLESSLIQUIDSTEELISLEFTINTHELADLEDRAINSINKISALWAYSPRESENTATTHEENDOFTHEPROCESSANDDOESNOTDEPENDONTHEPREVIOUSFORMATIONOFAVORTEXSINKTHEHEIGHTOFTHELIQUIDCOLUMNLEFTUNTEEMEDINLADLEWHENDRAINSINKIRRUPTSINTHENOZZLE,ISAPPROXIMATELYEQUALTOTHEDIAMETEROFTHENOZZLEDRAINSINKIRRUPTIONINTHENOZZLE,UNLIKEVORTEXSINKIRRUPTION,LEADSTOSIGNIFICANTPROPORTIONOFSLAGCARRYOVER1,4,6TAKINGINTOACCOUNTTHESECONSIDERATIONSFOUNDINLITERATURE,ITSEEMSTHATDUETONOZZLEECCENTRICITYANDTHEABSENCEOFPREFERREDROTATIONSENSE,VORTEXSINKISNOTEXPECTEDTOTAKEPLACEUNDERGENERALPLANTCONDITIONSTHEAMOUNTOFSTEELUSUALLYDOWNGRADEDINPLANTSDUETOSLAGCARRYOVERISCONSISTENTWITHTHISHYPOTHESISINTHISWORKWEFIRSTPRESENTWATERMODELEXPERIMENTS–SECTION2–CARRIEDOUTTOCONFIRMTHELASTASSUMPTIONBYESTIMATINGTHEPROBABILITYOFVORTEXFORMATIONINACTUALCASTINGPRACTICEINSECTION3WEPRESENTNUMERICALSIMULATIONSOFINDUSTRIALLADLEDRAINAGEPROCESS,WITHFOCUSONDRAINSINKFORMATIONANDPOSSIBLEINFLUENCEOFLADLEFLOORGEOMETRYANANALYSISOFEXPERIMENTALANDNUMERICALRESULTSISPRESENTEDINSECTION4ANDCONCLUSIONSAREPRESENTEDINSECTION52WATERMODELEXPERIMENTSWATERMODELEXPERIMENTSWERECARRIEDOUTBYTHEPOROUSMEDIAGROUP,ATTHEENGINEERINGSCHOOLOFBUENOSAIRESUNIVERSITYTHEEXPERIMENTALSETUPUSEDTOANALYZETHEFLOWOFWATERDURINGTHEDRAININGPROCESSISPRESENTEDINFIGURE3ACYLINDRICALCONTAINEROFDIAMETERD20CMISPARTIALLYFILLEDWITHWATERUPTOACONSTANTHEIGHTH0,THROUGHTWOTANGENTIALPIPESLOCATEDATOPPOSITESIDESOFTHECONTAINERBOTTOMANDAT1CMOFTHEWALLTHISWAYOFFILLINGPROVIDESTHEFLUIDTHETANGENTIALVELOCITYNECESSARYTOINDUCEVORTEXFORMATIONWATERISDRAINEDTHROUGHANOZZLEOFDIAMETERDN05CMANDLENGTHHN10CMLOCATEDATTHEBOTTOMOFTHEVESSELANDATADISTANCERΕFROMITSCENTERONCETHEFILLINGPROCESSHASCONCLUDEDTHEVELOCITYFIELDDECAYSWITHTIMEUNTILTHEFLUIDREMAINSATRESTSO,WECANSELECTTHEINITIALVELOCITYFIELDBYTHEWAITINGTIME,TI,BETWEENTHEENDOFTHEFILLINGANDTHEBEGINNINGOFTHEDRAINAGEASSUMINGTHATTHEFLOWFIELDISESSENTIALLYTANGENTIALANDAXISYMMETRICWECHARACTERIZETHEINITIALFLOWCONDITIONTHROUGHVΘ,DEFINEDASTHEMAXIMUMINITIALTANGENTIALVELOCITYMEASUREDATTHEFREESURFACEONCETHENOZZLEISOPENTHEMASSOFWATERLEAVINGTHELADLE,M,ISCOLLECTEDINASECONDVESSELWHEREITSWEIGHTISMONITOREDASAFUNCTIONOFTIMEWITHAPRECISIONBALANCEINTHISWAYTHEFLOWRATEATTHENOZZLEOUTPUT,QDM/DT,CANBEOBTAINEDTHECRITICALHEIGHTHC,DEFINEDASTHELEVELOFWATERINTHELADLEWHENAIRIRRUPTIONINTHENOZZLETAKESPLACE,WASANALYZEDASFUNCTIONOFTHENOZZLEECCENTRICITYΕ2RΕ/D,ANDINITIALTANGENTIALVELOCITY,VΘINFIGURE4AANEXAMPLESHOWINGTHETIMEEVOLUTIONOFTHEFLOWRATEQTHROUGHTHENOZZLEISPRESENTEDTHEFIGURECORRESPONDSTOTHEDRAINAGEOFAH011CMWATERCOLUMNTHROUGHACENTEREDNOZZLEΕ0ANDLARGEINITIALTANGENTIALVELOCITY,VΘ≈25CM/SITCANBESEENTHATTHEINITIALFLOWRATE,QI≈32G/S,SMOOTHLYDECREASESWITHTIMEUNTILT28SINTHISPERIODTHEFREESURFACEOFTHEFLUIDREMAINSALMOSTFLATEXCEPTINTHEVICINITYOFTHENOZZLEAXISWHERETHEFORMATIONOFASMALLFREESURFACEDEPRESSIONORDIMPLEWASOBSERVEDAFTERFEWSECONDSTHETHEORETICALFLOWRATECALCULATEDFROMBERNOULLILAWWASFOUNDTOFITQUITEWELLTHEEXPERIMENTALDATAINDICATINGTHEINVISCIDNATUREOFTHEDRAINAGEPROCESSINTHISSTAGETHEABRUPTDROPINTHEFLOWRATEATTC≈28SINDICATESTHEBEGINNINGOFTHEVORTEXSINKTHECRITICALHEIGHTISHC86CMWHILETHEDRAINEDPERCENTAGEISABOUT22SIMULTANEOUSLYTHEFREESURFACEDIMPLEEVOLVESDOWNWARDTOFORMALONGVORTEXFUNNELWHICHGOESTHROUGHTHEOUTPUTPRODUCINGTHEIRRUPTIONOFAIRINTHENOZZLEAFTERTHISCRITICALEVENTTHEFLOWRATEMEANVALUEDECREASESSMOOTHLYWITHFLUCTUATIONSDUETOTHEPRESENCEOFAIRINTHENOZZLEINTHEFINALPARTOFTHEDRAINAGE,T≈190S,ITISOBSERVEDTHATTHEFUNNELDISAPPEARSTHEREMAININGCIRCULATIONISNOTENOUGHTOSUSTAINTHEVORTEXSINKANDTHEFREESURFACEOFTHEFLUIDBECOMESFLATTHISPHENOMENONOCCURSATH≈DNTHENOZZLEISAGAINFILLEDWITHWATERANDTHEFLOWRATEINCREASESSUDDENLYDURINGAFEWSECONDSPRODUCINGASIGNIFICANTDRAINAGETHEN,THEDRAINSINKOCCURSATT198SINFIGURE4BANEWEXAMPLEISCONSIDEREDWITHIDENTICALCONDITIONSASTHEPREVIOUSCASEBUTWITHAMUCHLOWERINITIALTANGENTIALVELOCITYMUCHLONGERWAITINGTIMEINTHISCASETHEINITIALCIRCULATIONISNOTLARGEENOUGHTOPRODUCEAVORTEX,THELADLEDRAINSWITHTHEFREESURFACEALMOSTFLATUNTILT109SWHENTHEDRAINSINKOCCURSTHEDRAINEDPERCENTAGEISABOUT85TOANALYZETHEINFLUENCEOFNOZZLEECCENTRICITYWEPERFORMEDEXPERIMENTSINSIMILARCONDITIONSASINFIGURE4AH011CMANDLARGEINITIALTANGENTIALVELOCITYBUTWITHTWODIFFERENTVALUESOFTHENOZZLEECCENTRICITYΕ05ANDΕ09INFIGURE4CTHERESULTSFORΕ05ARESHOWN,ITCANBESEENTHATAVORTEXDEVELOPSATT96STHECRITICALHEIGHTISHC16CMANDTHEDRAINEDPERCENTAGEIS86FORΕ09THEFLOWRATEEVOLUTIONISSIMILARASTHATSHOWNINFIGURE4CTHATIS,NOVORTEXISOBSERVEDINSPITEOFTHECONSIDERABLEAMOUNTOFINITIALCIRCULATIONAGAIN,THEDRAINSINKOCCURSATTHEENDOFTHEDRAINAGEWHENH≈DNACOMPLETESETOFRESULTSAREPRESENTEDINFIGURE5WHERETHECRITICALHEIGHTHCISPLOTTEDASAFUNCTIONOFTHEINITIALTANGENTIALVELOCITYVΘFORΕ0CIRCLES,Ε05DOWNTRIANGLESANDΕ09SQUARESINAGREEMENTWITHPREVIOUSSTUDIES18WEFOUNDTHATTHEROLLPLAYEDBYNOZZLEECCENTRICITYISTODELAYTHEVORTEXFORMATIONANDEVENTOINHIBITITFORTHELARGESTVALUEOFΕTHUS,FORTHELARGESTECCENTRICITYΕ09NOVORTEXWASOBSERVEDINANYOFTHECONSIDEREDVALUESOFVΘAMOREDETAILEDANALYSISOFTHESEEXPERIMENTSCANBEFOUNDELSEWHERE15INORDERTORELATETHERESULTSJUSTSHOWNWITHATYPICALFULLSCALEMOLTENSTEELDRAINAGEONECANUSETHEDIMENSIONALANALYSISPROPOSEDBYGUTHRIEETAL8THEYCONCLUDETHATTHEDIMENSIONLESSCRITICALHEIGHTHC/H0DEPENDSONLYONTWOHYDRODYNAMICSPARAMETERSAREYNOLDSNUMBERDEFINEDASREVOUTH0/ΝVOUTISTHEINITIALOUTPUTVELOCITY,ΝTHEKINETICALFLUIDVISCOSITYANDTHEVORTEXNUMBERDEFINEDASKVVΘR/VOUTDN/2ITWASARGUED6,8THATTHEEXTREMELYLARGEREYNOLDSNUMBERVALUESREACHEDBOTHINPHYSICALMODELLINGANDINACTUALCASTINGPRACTICEMAKETHISPARAMETERIRRELEVANTINVORTEXFORMATIONTHUS,THEVORTEXNUMBERBECOMESTHEKEYPARAMETERTOESTABLISHSIMILARITYCRITERIONSINFIGURE5ITISOBSERVEDTHATFORΕ09NOVORTEXFORMATIONOCCURSEVENFORVALUESOFVΘASLARGEAS10CM/SKV≈3THEREFORE,FORALADLEWITHASIMILARNOZZLEECCENTRICITY,D200CMH0300CMANDDN10CM,ANINITIALTANGENTIALVELOCITYLARGERTHAN60CM/SSHOULDBENECESSARYFORAVORTEXSINKTOAPPEARASSUMINGTHATTHEFILLINGPROCESSINACTUALPRACTICEEXCLUDESTHEPOSSIBILITYOFHAVINGSUCHLARGEINITIALTANGENTIALVELOCITIESWECANCONCLUDETHATNOVORTEXSINKISPRESENTINATYPICALFULLSCALEMOLTENSTEELDRAINAGECONSIDERINGTHEPREVIOUSDISCUSSION,INTHEFOLLOWINGSECTIONWEPRESENTANUMERICALSIMULATIONOFAFULLSCALEDRAINAGEPROCESSFOCUSEDINTHEDRAINSINKPHENOMENON
