The influence of flow asymmetry on refractory erosion in the vacuum chamber of a RH degasser.

(1)

w w w . j m r t . c o m . b r

Availableonlineatwww.sciencedirect.com

Original

Article

The

inﬂuence

of

ﬂow

asymmetry

on

refractory

erosion

in

the

vacuum

chamber

of

a

RH

degasser

Pedro

Henrique

Resende

Vaz

de

Melo

a,∗

_,

_Johne

_Jesus

_Mol

_Peixoto

a

_,

Gustavo

Santos

Galante

a

_,

_Bruna

_Helena

_Malovini

_Loiola

a

_,

_Carlos

_Antônio

_da

_Silva

a

_,

Itavahn

Alves

da

Silva

a

_,

_Varadarajan

_Seshadri

b

a_Department_of_{Metallurgical}_Engineering_and_Materials,_Federal_University_of_Ouro_Preto_(UFOP),_Ouro_Preto,_Brazil b_Department_of_{Metallurgical}_Engineering_and_Materials,_Federal_University_of_Minas_Gerais_(UFMG),_Belo_Horizonte,_Brazil

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received13February2019 Accepted22June2019 Availableonline12July2019

Keywords: RHdegasser Flowasymmetry Refractoryerosion Modeling

a

b

s

t

r

a

c

t

NozzleblockageinRHreactorsisaseriousoperationalproblemsinceitcancausean asym-metricdistributionofthesteelflowinboththeup-legaswellasthelowerregionofthe vacuumchamber.Thisanomalycanalterthecirculationrateinadditiontoaffectingthe erosionprofileofthelowerpartofvacuumchamberrefractorylining.Inthisstudy,the effectofnozzleobstructiononliquidcirculationrate,wallshearstress,velocityprofilesand flowpatternhavebeenevaluated.Inaddition,refractoryerosioninthevacuumchamber hasbeenestimatedthroughphysicalmodelingandmathematicalsimulationresults.Four blockageconditionswerestudiedfordifferentgasflowrates.Therewasagoodagreement inphysicalandmathematicalmodelsresults.Asymmetricflowwasobservedinvacuum chamberlowerregioninasymmetricblockagecases,whichresultedinpreferentialwear ononechambersideinphysicalmodelingexperiments.Thewallshearstressanalysisin thevacuumchamberusingafluiddynamicmodelalsoindicatespreferentialerosion.When compared,refractoryerosionresultsinphysicalmodelingandshearstressinmathematical modelingpresentedgoodcorrelation.

1. Introduction

Refractorywearcostsinvolvedintheproductionofsteel rep-resentsasigniﬁcantproportionoftheoverallmanufacturing cost.Hencethechoiceofthemostsuitablerefractorytypefor eachapplicationisofutmostimportance,consideringaspects

∗ _{Corresponding}_author.

E-mail:[email protected](P.H.Melo).

suchasresistancetohigh-temperatureandtoerosion.These notonlydependsonrefractorytypebutalsotheﬂuiddynamic conditionsofmoltensteelincontactwiththerefractory lin-ing.Inaddition,thechemicalpropertiesoftheslagandsteel, atmosphereandtemperatureofprocessarefactorsthataffect refractory linings. Hencethe refractorystructure zoningis important and thechoice ismade takinginto account the physicochemicalcharacteristicsoftherefractoryandthe envi-ronmenttowhichitisexposed.Someaspectsofpredominant refractoriesusedinmetallurgyhavebeendiscussedinRef.[1].

https://doi.org/10.1016/j.jmrt.2019.06.036

(2)

Fig.1–(a)AcrylicmodelmaindimensionsoftheRHreactor;(b)setupforRHreactorCFDsimulation;(c)boricacidtablets

distribution/areasforwallshearstressanalysis(CFD)inthevacuumchamber.

TheRHreactoriswidelyusedinsecondarysteelreﬁning duetoitsﬂexibilityinrespectofmetallurgicalfunctionssuch asdecarburization,degassing,homogenization, desulfuriza-tion,removalofnonmetallicinclusionsandalloyingadditions

[2].ThenozzleblockageisarecurrentproblemintheRHand maydirectlyinfluencethefluidbehavior,especiallyinthe vac-uum chamber(VC).The uniformgas distributionand flow patterngetsaltered,incaseofasymmetricobstruction,and consequently,thecirculationratealsoisadverselyaffected

[3–5].

Theincreaseinliquidsteelcirculationrateisalsorelatedto theaccelerationofrefractoryliningerosion.Amongthe possi-blerefractoryweartypes,erosionisthemostaggressivetothe lininglife,especiallyintheupanddownlegsaswellastheVC lowerregion.Theerosionisduetoliquidsteelandslagﬂow, whichgraduallyremovestherefractorybrickssurfacelayer

[6].

Evaluationofwallshearstressdistribution,via mathemat-icalmodeling,helpstopredictrefractoryliningerosion.The maximumshearstresspointisthepreferentialpointofwear

[7].Luoetal.[8]alsousedmathematicalmodeling,validated bysimulationsinacoldmodel,tocalculatecirculationrate andmixingtime,aswellaswallshearstresstopredict pref-erentialrefractorieswearintheRHreactor.Thepresentwork aimstoanalyzeandcharacterizetheinﬂuenceofnozzle block-age,leadingtoasymmetricﬂowanditseffectoncirculation rateandrefractoryerosion.

2. Materials

and

methods

2.1. Physicalmodeling

Fig.1givesthe maindimensionsofthe RHreactormodel, builtinacrylicwithascale factor=1:7.5.The

dimension-lessparameters,namelytheFroudenumber(Fr)andﬂow(NVa)

serve assimilarity criteria betweenprototype andphysical model.Thegasinjectionnozzlesdiameterwascalculatedby modiﬁedFroudenumber(Frm).Adiscussionofsimilarity

cri-teriaasappliedtoRHdegassercanbefoundinSeshadriand Costa[9].

Fr=V2_/gD;_N

Va=G/D2V;Frm=U2g/Dgl (1)

whereVisliquidvelocity;gandlarethedensityoftheliquid

andgas;Disthelegsinnerdiameter;gisthegravity acceler-ation;UisthegasvelocityinthenozzleandGisthegasﬂow rateinthenozzles.

Forboththephysicalandmathematicalsimulations,aRH reactormodelwith16gasinjectionnozzles(2.4mminternal diameter),distributedsymmetricallyintworingshavebeen considered.Fourdifferentconditionswere studied,namely: Condition1:noblockage;Condition2:asymmetricblockage of8nozzles;Condition3:asymmetric4-nozzleblockage; Con-dition4:symmetricalblockageof8nozzles.Fig.2showsthe simulatedblockageconditions.

2.1.1. Circulationrate

Thecirculation ratein the RHdegasser hasbeen assessed bytheconductimetrytechnique,asshowninprevious stud-ies[4,9–11].Itconsistsofinjectingapulse-shapedpotassium chloridesolutionintotheVCintheportionnearofthe up-leg.Aconductivitysensorwaspositionedinthedown-legfor continuouslymeasuringthesaltconcentrationvariation. Con-centrationvalueswereevaluatedbyadataacquisitionboard connectedtoacomputer,whichstoresandprocessesthedata

[4].ThecirculationratewascomputedusingEq.2.Thefour cloggingconditionsweresimulatedforgasﬂowratesof80,

(3)

Fig.2–(a)Condition1;(b)Condition2;(c)Condition3;(d)

Condition4.

90,100,110, 120,140L/min.Thereportedcirculationrateis theaverageof10experiments.

Q=C·Mwater/Ar (2)

whereQisthecirculationrate(kg/s);Cistheconcentration variationingofKCl/kgofwater;Mwateristheamountofliquid

inthereactorinkg;Aristheareaoftheregioncorresponding

tothepassageoftheﬁrsttracerpulseundertheconcentration versustimecurve(gofKCl.s/kgofwater).

2.1.2. Flowproﬁlepattern

TocharacterizetheﬂowinsidetheVC,200mlofdyetracer,was injected50mmbelowtheRHup-leg.Acamerawaspositioned abovetheVCtovisualizethechamberbottom.Frameswere selectedinordertoevaluateandcomparethedyescattering andpathintheVCfortheproposedblockageconditions.The conditionsC1andC3forthe100L/mingasﬂowwere simu-lated.

2.1.3. Refractoryerosionsimulationinthevacuum chamber

Boricacid(7g)pressed(3000kgf)onmetallicplateswereused tosimulaterefractoryerosion.Boricacidissolubleinwater. Asthewaterpassesthroughthetabletsurface,boricacidis graduallyremoved,whichsimulatestherefractorieserosion accordingtothetechniqueproposedbySuetal.[12].

Theregionselectedforthis studywasthelowerportion ofthe VC,asit hasashorterrefractorylifeifcomparedto otherreactorregions[13].Ineachexperiment,6tabletswere used(A–F),distributedsymmetricallybytheVCataheight of3.5cm(Fig.1c).Thetabletswereweighedbeforeandafter theexperimenttoquantifytheweightloss. Photosofeach tabletweretakenbeforetheexperimentstomeasurethearea ofthetablet’scontactfacewithwaterwhichweremeasured andanalyzedthroughthefreesoftwareImageJ.Theresultsin termsoferosionrate(mm/min),wasgivenaccordingtoEq.3. ErosionRate= m/(_b·A0·t) (3)

wheremisthetabletsmasschange(g);bistheboricacid

density(g/mm3_);_A

0istheinitialarea(mm2)andtisthe

exper-imentaltime(min).

After tablets positioning into the VC, the test has been started, promoting liquid circulation between the VC and the ladle.Thefour blockageconditionstogasﬂowratesof 100 and 140L/min were simulated. Three tests were per-formedforeachﬂowrate.Thetimeofeachexperimentwas 2min.

2.2. Mathematicalmodeling

Thegeometryusedinthesimulationswasbuiltusingthe soft-wareDesignModeler.Itsdimensionsarecompatiblewiththe physicalmodeldimensions.Themeshindependencestudy was performed bycomparingthe resultsofthe circulation rate obtained with meshes ofvaried sizes. Themesh was constructedbytheMeshingModelersoftware,themesh ele-mentsizingusedwas18mminthelowervessel,4mmmesh in the up-leg and rest of the VC and 5mm mesh in the down-leg.Therefore,themeshwasabout1millionelements and413,000gridpoints.Themathematicalsimulationswere performedthroughCFX18.2software(Ansys®).Inthe math-ematical model was assumedturbulent three-dimensional ﬂow;incompressibleNewtonianﬂuids(theexpansionofthe gaswasdisregarded);isothermalsystem(at25◦C);ambient pressureequalto1atmandwaterandairstandardphysical propertiesat25◦C.Theturbulencemodeladoptedwasthek–␧ modelforthecontinuousphase(liquid),whileforthediscrete phase (gas), the dispersedphase zeroequation model was adopted.Itwasassumedthatthediscretephasehadthesame turbulent kinematicviscosity ofthecontinuous phase[14]. Theturbulencetransferbetweenthe phaseswasestimated bytheSatomodel[14].

Thefollowingconservationequationsweresolved:ofmass conservation ofeach phase, namely, waterand air;of vol-ume considered that the volumetric fractions sum of air and water is equal to 1; of turbulent kinetic energy and the rate ofdissipationofturbulencekinetic energy(model k–␧);ofthemomentumofeachphase(turbulentformofthe Navier–Stokesequations),inthethreeCartesiancoordinates (x,y,andz).FormoredetailsseePeixotoetal.[10].Basedon Ref.[10],theIshii–Zubermodelwasadoptedfordragforces, which ismoreappropriateforhigh particle concentrations

[14];themodelbasedontheFavreaverage(ormass-weighted average)wasusedtoevaluatethedragforcefortheturbulent dispersioninsituationsofknownvaluesofturbulent disper-sioncoefﬁcient(CTD)[14]andforthewalllubricationforce,

Frank’smodelhasbeenused[10].

Theboundaryconditionsappliedtotheproblemare(see

Fig. 1b) asfollows. Non-slip condition appliedto all walls, regionswherethefluidhaszerovelocity.Injectioncondition: Gasisinjectedthroughnozzles(flowratesof80,90,100,110, 120and140(L/min)convertedinmassflowrates(kg/s)).The selectedflowregimeissubsonic,withaturbulenceintensity of5%(average).Freeslipconditionontheladlesurface.VC surface:with10cmairlayer-openingcondition,withpressure equaltoappliedvacuum.

Itisassumedthatthegasbubblediameterisconstant(the deformation,aswellasthebreakingandcoalescenceofthe gasbubbles,areneglected).Asinothercontributions[7,8,11], thecorrelationgivenbyEq.4(adaptedforladleagitationwith

(4)

gas[15],originallyfromRef.[16])isusedtoestimatethebubble diameter.

db=0.35

G2_/g

0.2

₍₄₎

whereGisthegasﬂow(Nm3_/s)_and_g_is_the_gravity_acceleration

(m/s2_).

The mathematical simulation has been carried out in steady state conditions. The ﬁrst order advection scheme (Upwind)wasusedtosolvetheproposeddifferential equa-tions.Toreduceresiduesﬂuctuation,thephysicaltimescale controlof0.01sandamaximumof2100iterationswereused, whichweredividedinto300iterationswithoutturbulent dis-persionforce,300iterationsafterturbulentdispersionforce insertionand1500iterationswithadvancedsolutioncontrol option,coupledvolumetricfraction.Theconvergencecontrol was10−5(RMS,rootmeansquare).ThisprocedurefollowsRef.

[10].

Transient simulations were performed to evaluate the tracerdispersionintheVC.Tracerisrepresentedbythe Addi-tionalVariablesfunction,usingthevolumetricscalaroption (kg/m3_). _The_tracer _injection _point _is _shown _in _Fig. ₁_b, _by

SourcePointtool,whichisasourcetermsimplyaddedtoa generalscalarequation[14].Thesteady-stateflowfieldisthen usedinordertoevaluatetracerdispersion.Atransient simu-lationlasting35sisenoughtodescribethedispersionasitcan beconfirmedbyphysicalmodelresults.

3. Results

and

discussion

3.1. Circulationrate

Fig.3showsthecirculationrateresultsfordifferentgasﬂow ratesinthephysicalandmathematicalmodels.

Itcanbeseenthat, asthe gasflowinthe injector noz-zlesincreases, the circulationrate alsoincreases, which is inaccordancewiththeresultsreportedpreviously[4,17,18]. Thecirculationrate,incaseofasymmetricblockages(C2and C3),showed a considerable decrease relativeto the condi-tionwithoutblockages(C1).Insymmetricblockagescondition (C4),therewasnosignificantchangeinthecirculationrate. Theseresultsarecompatiblewithpreviousworks[3–5].There is good agreement between the experimental results and the valuespredicted bythe CFD model. This supportsthe assumptionthatthe mathematicalmodelisabletopredict thebiphasicflowbehaviorintheRHreactorandcouldbeused toevaluateotherparameters, suchasthewallshearstress ofthe reactorandcorrelateit withtherefractories erosion rate.

3.2. Flowandvelocityproﬁle

Thetracerflowpatternanalysisasafunctionoftimeforthe (C1)conditionindicatedsymmetricalscatteringbytheVC.The tracerpresentedthetendencytoflowalongtheVCsidewall. Theasymmetric4-nozzleblockage(C3)presentedpreferential flowthroughoneVCside.Inthiscase,thetracerscattering occurredasymmetrically.Theresultsobtainedinthe physi-calmodelexperimentsshowedagoodcorrelationwiththe

resultsobtainedthroughCFD,againsupportingthe mathe-maticalmodel.Fig.4showsthetracerdispersionintheVCas afunctionoftimeforblockageconditionsC1andC3via(a) physicalmodeland(b)mathematicalmodel.

Thepreferentialflowalongthewallcanbeexplainedby the higher velocityoftheliquid phasein thisregion com-paredtotheVCcentralregion(Fig.5).Theliquidentersthe VC athigh speed,carried by the gasinjected into the up-leg,and,asitspreadsandgetsinrecirculationzones,loses speed.The liquidonlyregainsspeed inthe impact region, thetransitionzonebetweenVCanddown-leg.Fig.5shows velocityvectors,calculatedintheVCcross-section,at3.5cm height.ConditionsC1andC4indicateasymmetrical distri-butionofthevectors.Ontheotherhand,conditionsC2and C3indicate highervelocityononeVCside,whichexplains the preferential flow.The symmetricalflow foundforcase C1andthefluidscatteringpatternbytheVCaresimilarto thepreviousflowcharacterizationresultsintheRHdegasser

[19–21].

3.3. Refractoryerosionsimulationinthevacuum

chamber

Fig. 6 presents the average erosionrates of the boric acid tablets,positionedinthe VC,forthe 4blockageconditions studied.Preferentialerosionwearisnotedonthetablets posi-tionedclosetotheup-leg.Intablet Ä¨therewasgreaterwear, whilein ¨D¨justabovethedown-leg,wearseemstobe mini-mal.UnderconditionsC1andC4,erosionratesbetweenthe ¨B änd ¨F äswellasbetween ¨C änd Ë¨tabletsweresimilar,which indicatesflowsymmetryinthechamber.InthecasesC2and C3, the resultspresented preferential wearof the ¨B¨tablets comparedto ¨F ¨whichsuggestsasymmetricalflow.Astatistical hypothesis testconfirmingeneral,the tabletsaverage ero-sionintestswith140L/minwashigher thanincaseswith 80L/min,whichmayberelatedtotheincreaseoftheliquid localvelocity.

The wall shear stress distribution in the VC has been evaluated through computer simulation for the different obstructionconditions(Fig.7).AtconditionsC1andC4, sym-metrycanbeseeninthewallshearstressdistributioninthe VC,whichsignifiesflowsymmetry.InthecasesC2andC3, theshearstressdeviationtooneoftheVCsidesisdetected, thehighershearstressisobservedintheregion correspon-dent to the point ¨Bïn the physical model. Thewall shear stressdistributiondeviationindicatesasymmetricflowinthe VC.Inallcases,thewallshearstresswashigherinregions near the up-leg, due to the higher liquid velocity values, therefore,theyaremoresusceptibletoerosiondegradation. The increase in the gas flow rate and, consequently, the localliquid velocity,increases theshearstress on thewall surface

For analyzing the correlation between the erosion rate (physicalsimulations)andthewallshearstressintheVC, cal-culatedviaCFDintheregionsshowninFig.1c,the ¨A ¨position results were disregarded, due tothe impact ofair bubbles on the tablet’ssurface, which increase the erosionrate in the physicalmodel. For theother regions,the liquidphase isresponsibleforremovingmaterialfromthetablets.Itwas

(5)

Fig.3–Circulationrateasafunctionofthegasﬂowratefordifferentobstructionconditions.(a)Physicalmodeland(b)

mathematicalmodel.

Fig.4–DispersionandtrajectoryofthetracerasafunctionoftimeforC1andC3,gasﬂowof100L/min,via(a)physical

modeland(b)mathematicalmodel.

Fig.5–Velocityvectorsinthevacuumchambercross-section,attheheightof3.5cmfortheblockageconditions(a)C1;(b)

(6)

Fig.6–Erosionwearresultsonthephysicalmodelasafunctionofthepositioninthevacuumchamberfortheconditions

(a)C1;(b)C2;(c)C3and(d)C4.

Fig.7–WallshearstressintheVCfortheconditions(a)C1;(b)C2;(c)C3;(d)C4.

foundagoodcorrelationbetweentheparametersWallShear StressandErosionRate(Eq.5):

WallShearStress (Pa)=5.47ErosionRate(mm/min)r2₌_0,₇₆₍₅₎

whichvalidatestheuseofwallshearstressdistribution anal-ysistopredictpreferentialerosionwearpoints.

Thedistributionofwallshearstressoftheupanddown legswasanalyzed(Fig.8).TheC1andC4casesshowed sym-metryinthestressdistribution,whichindicatessymmetrical ﬂowinbothlegs.Ontheotherhand,thecasesC2andC3

pre-sentedanaccumulationofstressesintheregionoppositethe nozzleblockages,whichindicatesapreferentialﬂowofliquid ononesideoftheup-leg.Theﬂowdeviationisalsoindicated fordown-leg.Theup-legpresentshigherlevelsofwallshear stressthanthedown-leg,sinceitisthemomentumtransfer regionbetweengasandliquidbubbles.TheC2andC3cases presentedlowerlevelofwallshearstressinthedown-legdue tothelowercirculationrateresultingfromtheobstruction.

Thewallshearstressvaluesshown inFig.8aare about one order of magnitude higher than the results reported in thework ofLuo et al.[8], who performed a

(7)

mathemat-Fig.8–Wallshearstressoftheupanddownlegsforthe

100L/mingasﬂowratefortheconditions(a)C1;(b)C2;(c)

C3;(d)C4.

ical simulation of a physical model on a 1:5 scale. This difference is due to the fact that Luo et al. [8] worked withgasﬂowsbetween15L/minand35L/min,muchlower than the values adopted in this study, from 100L/min to 140L/min.

In industrial practice, the preferred wear points of the refractoryliningarepositionedintheimpactzone,justabove thedown-leg,differentfromtheresultsuggestedbythewall shearstressanalysis.Thisfactindicatesthatinadditionto erosion,otherwearphenomenamayactintheregion,such asthedissolution(MgOandCr2O3oftherefractory),resulting

fromchemicalreactionsbetweenrefractory,slagandalloying elements(corrosionwear).Theslagformedinfunctionofthe oxygenblowthroughalanceinaVC,likeinRH-TOPprocess

[22], is certainly unsaturated in respect of the main con-stituentsoftherefractorybricks,andextremelyfluid,which shouldfavordissolutionofsomecomponentsoftherefractory intheslag.Consideringthatthisprocessathightemperatures (withoutkineticrestrictionregardingthe chemicalreaction stage)iscontrolledbymasstransfer,themasstransfer coef-ficientin the slag can be used toevaluate the dissolution potential.Thisisproportionaltotherelativerefractoryslag velocityiftheinterfacerenewaltheoryisadopted(Eq.6)[23]. Thisway,onecanrelatethemasstransferratewithavelocity index(I)asgivenbyEq.6,definedbytheratiooflocal veloc-itytothemaximumvelocityoftheliquidinapredetermined regionforthefourconditionsstudied.Whiledeterminingthe

velocityindexinashellintheVClocatedabovethe down-leg, 1cm away from the wall (Fig. 9), it can be seen that, in casesC1 and C4, the point of maximum velocityindex (region sensitiveto greater masstransfer),is inthe region oftransitionbetweentheVCandthedown-legandisgiven byEq.7.IntheC2andC3cases,thepointsofgreatestvalue of Iare shifted to the chamberside. For this analysis, the ¨shell ¨was selected onlyforhalf ofthe VCabove the down-leg,asitistheregionwiththehighestprobabilityofcontact betweenrefractoryand materialsthat causeits dissolution (FeO,slag,etc.).

k=2

Div L (6) I= v vmax (7) wherekisthemasstransfercoefﬁcient;Di isthediffusion

coefﬁcientoftheconstituentsoftherefractoryintheslag;Iis theliquidvelocityindex;Listhecharacteristiclengthandvis theliquidvelocity,givenbyCFDresults.

4. Conclusions

The refractory erosion in the vacuum chamber of the RH reactorwasanalyzedthroughphysicalandmathematical sim-ulations.Itcanbeconcludedthat:

The circulation rate presented asigniﬁcant decrease in casesofasymmetricblockages(C2andC3)whencompared tothecasewithoutblockage(C1);

ThetracerflowpatternforconditionC1indicated symmet-ricalscatteringbythe VC.However,C3conditionpresented preferential flow through one side of the VC, indicating asymmetricflow.BothbehaviorsarereproducedbyCFD cal-culations;

Inthephysicalmodel,preferentialerosionwasnotedon thetabletinsertspositionedneartheup-leg.Underconditions C1andC4,erosionratesatsymmetricalpositionswere sim-ilarasexpected.InC2andC3cases,preferentialwearofthe tabletswasobservedononesideoftheVC,resultingfromthe asymmetricﬂow;

Themathematicalsimulation,throughwallshearstress, wasabletopredictpointsofhighererosionwearintheVC;

Itissuggestedthatabovethedown-leg,thereisanother wearmechanismacting,namelychemicalattackofthe refrac-tory(corrosion).Thus,thisisacriticalpointtothelininglife oftheRHreactor.

Fig.9–Liquidvelocityindex(I=v/vmax)toindicatepreferredregionsforcorrosionwearinashellabovethedownlegfor

(8)

Conﬂicts

of

interest

Theauthorsdeclarenoconﬂictsofinterest.

Acknowledgments

Theauthors wishtoacknowledgethehelpprovidedbythe research institutions in Brazil, namely CNPq, CAPES and FAPEMIG.

r

e

f

e

r

e

n

c

e

s

[1]Ertu ˘gB.Classiﬁcationandcharacteristicsofpredominant refractoriesusedinmetallurgy.AdvEngForum2018;26:9–21.

[2]TembergenD,TeworteR,RobeyR.RHmetallurgy. MillenniumSteel2008:104–8.

[3]ZhuB,LiuQ,ZhaoD,RenS,XuM,YangB,etal.Effectof nozzleblockageoncirculationﬂowrateinup-snorkelduring theRHdegasserprocess.SteelResInt2016;87:136–45.

[4]SilvaCA,SilvaIA,deCastroMartinsEM,SeshadriV,Perim CA,VargasFilhoGA.Fluidﬂowandmixingcharacteristicsin RHdegasserofCompanhiaSiderúrgicadeTubarão,and inﬂuenceofbottomgasinjectionandnozzleblockage throughphysicalmodellingstudy.IronmakSteelmak 2004;31:37–42.

[5]LinL,BaoY,YueF,ZhangL,OuH.Physicalmodeloffluid flowcharacteristicsinRH-TOPvacuumrefiningprocess.IntJ MinerMetalMater2012;19(6):483–9.

[6]KumayasuT.Damageofrefractoriesinsecondary steel-reﬁning.JTechAssocRefrac2016;36(3):158–64.

[7]LingH,ZhangL,LiuC.Effectofsnorkelshapeontheﬂuid ﬂowduringRHdegassingprocess:mathematicalmodelling. IronmakSteelmak2016;1:1–12.

[8]LuoY,LiuC,RenY,ZhangL.Modelingontheﬂuidﬂowand mixingphenomenainaRHsteeldegasserwithoval down-legsnorkel.SteelResInt2018:1–13.

[9]SeshadriV,CostaSLS.ColdmodelofRHdegassing.TransISIJ 1986;26:133–8.

[10]PeixotoJJM,GabrielWV,deOliveiraTAS,SilvaCA,SilvaIA, SeshadriV.Numericalsimulationofrecirculatingﬂowand

physicalmodelofslag–metalbehaviorinanRHreactor: applicationtodesulfurization.MetallMaterTransB 2018;49:2421–34.

[11]KishanPA,DashSK.Predictionofcirculationﬂowrateinthe RHdegasserusingdiscretephaseparticlemodeling.ISIJInt 2009;49(4):495–504.

[12]SuCJ,ChouJM,LiuSH.Effectofbottomblowingconditionon refractoryerosionintheironmakingsmelterbywater modeling.MaterTrans2010;51(9):1586–93.

[13]HubbleDH,RusselRO,VernonHL,MarrRJ.Steelmaking refractories.In:FruehanRJ,editor.Themaking,shapingand treatingofsteel.Pittsburgh(PA):AISESteelFoundation;1998. p.227–90[chapter4].

[14]AnsysInc.ANSYSCFX—SolverTheoryGuide[Internet]. Release18.2.Canonsburg(PA):ANSYS;2017.

[15]JohansenST,BoysanF.Fluiddynamicsinbubblestirred ladles:partII.Mathematicalmodeling.MetallMaterTransB 1988;19B:755–64.

[16]DavidsonJF,SchülerBOG.Bubbleformationatanoriﬁceina viscousliquid.TransInstChemEng1960;38:105–15.

[17]ParkYG,YiKW,AhnSB.Theeffectofoperatingparameters anddimensionsoftheRHsystemonmeltcirculationusing numericalcalculations.ISIJInt2001;41(5):403–9.

[18]MukherjeeD,ShuklaAK,SenkDG.Coldmodel-based investigationstostudytheeffectsofoperationaland nonoperationalparametersontheRuhrstahl-Heraeus degassingprocess.MetallMaterTransB2017;48: 763–71.

[19]ZhuB,ChattopadhyayK,HuX,ZhangB,LiuQ,ChenZ. OptimizationofsamplinglocationintheladleduringRH vacuumreﬁningprocess.Vacuum2018;152:30–9.

[20]ChenG,HeS,LiY,GuoY,WangQ.Investigationofgasand liquidmultiphaseﬂowintheRheinsahl-Heraeus(RH)reactor byusingtheEuler–Eulerapproach.JOM2016;68(8):2138–48.

[21]GengDQ,LeiH,HeJC.Simulationonﬂowﬁeldandmixing phenomenoninRHdegasserwithladlebottomblowing. IronmakSteelmak2012;39(6):431–8.

[22]WangYN,BaoYP,CuiH,ChenB,JiC.Finaltemperature predictionmodelofmoltensteelinRH-TOPreﬁningprocess forIFsteelproduction.JIronSteelResInt2012;19(3):1–5.

[23]TosunI.Modellingintransportphenomena:aconceptual approach.Amsterdam(NL):Elsevier;2002.