Heat and mass transfer in gas metal arc welding Part I The arc.docx
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Heat and mass transfer in gas metal arc welding Part I The arc.docx
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HeatandmasstransferingasmetalarcweldingPartIThearc
InternationalJournalofHeatandMassTransfer50(2007)833–846
Heatandmasstransferingasmetalarcwelding.PartI:
Thearc
*
J.Hu1,H.L.Tsai
DepartmentofMechanicalandAerospaceEngineering,UniversityofMissouri–Rolla,1870MinerCircle,Rolla,MO65409,UnitedStates
Received18January2006;receivedinrevisedform22August2006Availableonline24October2006
Abstract
Aunifiedcomprehensivemodelwasdevelopedtosimulatethetransportphenomenaoccurringduringthegasmetalarcweldingprocess.Aninteractivecouplingbetweenarcplasma;meltingoftheelectrode;dropletformation,detachment,transfer,andimpingementontotheworkpiece;andweldpooldynamicsallwereconsidered.Basedontheunifiedmodel,athoroughinvestigationoftheplasmaarccharacteristicsduringthegasmetalarcweldingprocesswasconducted.Itwasfoundthatthedroplettransferandthedeformedweldpoolsurfacehavesignificanteffectsonthetransientdistributionsofcurrentdensity,arctemperatureandarcpressure,whichwerenormallyassumedtobeconstantGaussianprofiles.
�2006ElsevierLtd.Allrightsreserved.
Keywords:
GMAW;Arcplasma;Heattransfer;Fluidflow
1.Introduction
Gasmetalarcwelding(GMAW)isanarcweldingprocessthatusesaplasmaarcbetweenacontinuous,consumablefiller-metalelectrodeandtheweldpool,asshowninFig.1.Thehightemperatureplasmaarcmeltstheelectrodeandformsadropletattheelectrodetip.Thedropletisdetachedandtransferredinthearctotheworkpiece.Aweldpoolformsundertheinfluencesofthearcplasmaandtheperiodicalimpingementofdroplets.Theformationofdroplet,thetransferofdropletinthearc,andthedynamicsofweldpoolaregovernedbythebalanceofforcesandtheheattransferinsidethedropletorwithintheweldpoolandtheheattransferredfromthearcplasma.Theforcesincludegravity,surfacetension,electromagneticforce,arcpressure,andplasmashearstress.Thebalanceoftheforcesatthedropletdeterminestheshape,volume,andfrequencyofthedropletdetachmentandthedropletaccel
*
Correspondingauthor.Tel.:
+15733414945;fax:
+15733414607.E-mailaddress:
tsai@umr.edu(H.L.Tsai).1Currentaddress:
DepartmentofMechanicalEngineering,UniversityofBridgeport,Bridgeport,CT06604,UnitedStates.
0017-9310/$-seefrontmatter�2006ElsevierLtd.Allrightsreserved.doi:
10.1016/j.ijheatmasstransfer.2006.08.025
erationafterthedetachment.Theweldpooldynamicsarenotonlyinfluencedbythebalanceofforcesactingonit,butarealsoaffectedbydropletimpingement.TheheattransferwithinthedropletandweldpoolincludesOhmicheating,conduction,andconvection.Theheattransferredfromthearcplasmaincludesconductionandheatthroughthermaleffectatthesurfaceoftheanodeandcathode.Mostoftheseforcesandheatfluxtermschangeasafunctionoftime.Theydependontheinstantaneouselectrodeandweldpoolconfigurations;thedropletposition;thecurrentdensitydistributionwithinthearc,theelectrode,andtheweldpool;thethermophysicalpropertiesandthefluidflowoftheplasma;andtheenergybalanceoftheplasma,theelectrode,andtheworkpiece.
ModelingtheheattransferandfluidflowinthearcplasmaforGTAW[1–18]hasbeenwelldocumented,butveryfewresearcharticlescanbefoundforGMAW.MckelligetandSzekely[1],Chooetal.[2]andGoodarzietal.
[3]havesimulatedthearccolumnbyassumingthecurrentdensitydistributionatthecathodesurfaceinGTAW.Fanetal.[4,5]usedfixedtemperatureboundaryconditionsatthecathodetiptocalculatethearccolumninGTAW.Zhuetal.[6]developedaunifiedmodeltosimulatethe
J.Hu,H.L.Tsai/InternationalJournalofHeatandMassTransfer50(2007)833–846
Nomenclature
Avconstant,definedinEq.(19)ttimeBhself-inducedazimuthalmagneticfieldTtemperaturecspecificheatTarcarcplasmatemperatureclosetotheanodeandCcoefficient,definedinEq.(11)cathodec1permeabilitycoefficient,definedinEq.(10)Ta,Tcanode,cathodesurfacetemperatureddendritearmspacingTlliquidustemperatureeelectronicchargeTssolidustemperatureFvolumeoffluidfunctionT1ambienttemperaturefmassfractionuvelocityinr-directiongvolumefractionorgravitationalaccelerationvvelocityinz-directionhenthalpyVvelocityvectorHlatentheatoffusionVrrelativevelocityvector(Vl�Vs)HevlatentheatofvaporizationVwwirefeedrateIweldingcurrentWmeltevaporationrateJaanodecurrentdensityJrradialcurrentdensityGreeksymbolsJzaxialcurrentdensitybTthermalexpansioncoefficientkthermalconductivitycsurfacetensioncoefficientKpermeability,definedinEq.(10)oc/oTsurfacetensiontemperaturegradientkbStefan–Boltzmannconstantesurfaceradiationemissivitykeffeffectivethermalconductivityatarc-metalinter-jfreesurfacecurvature
facelldynamicviscosity~nvectornormaltothelocalfreesurfacel0magneticpermeabilityppressure/electricpotentialPatmatmosphericpressure/wworkfunctionoftheanodematerialpssurfacetensionpressurereelectricalconductivityQshieldinggasflowrateqdensity
qevsps
evaporationmassrateofmetalvaporplasmashearstressr-zcylindricalcoordinatesystemMarangonishearstress
sMsRgasconstantdlengthoftheanodeorcathodesheathRninternalradiusoftheshieldinggasnozzleDttimeintervalRwradiusoftheelectrode~svectortangentialtothelocalfreesurfaceSubscriptsSaanodesheathenergyheatfluxforthemetal0initialvalueSapanodesheathenergyheatfluxforthearcplasmalliquidphaseSccathodesheathenergyheatfluxforthemetalrrelativetosolidphasevelocityScpcathodesheathenergyheatfluxforthearcplas-ssolidphasemawwireSRradiationheatloss
arccolumn,thecathodeandthecathodesheathinGTAW.Lowkeetal.[7,8]simplifiedtheunifiedmodeltotreattheelectrodeinaspecialwayatthecathodesurfacetoaccountforelectrodeeffects[7]oromittheelectrodesheath[8].Thesimplifiedmodels[7,8]reducedthecomputationtimeto1%oftheoriginalunifiedmodelandgavefairresultsinagreementwithexperimentaldatawhen0.005–0.01cmmeshsizearoundthecathodetipwaschosen.Thesesimplifiedmodelshavebeenusedandfurtherdevelopedbymanyresearchers[9–18]tocalculatetheheattransferandfluidflowinthearccolumn.
BothGTAWandGMAWhaveaplasmaarcstruckbetweenanelectrodeandaworkpiece.Eventhoughthe
GTAWhasaninerttungstencathodeastheelectrodeandtheelectrodeofGMAWisameltingmetalandusuallysetastheanode,theGTAWarcmodelcanbeadoptedtomodeltheGMAWarc.Jonsson[19]adoptedtheGTAWarcmodelofMckelligetandSzekely[1]tocalculatethearccolumnbyassumingacurrentdensitydistributionatthecathodespot.Zhuetal.[20]calculatedtheanodetemperatureprofilebyincorporatingthesimplifiedarcmodelofLowkeetal.[8]intoaone-dimensionalconductionmodelofthemovingelectrodeinGMAW.Theheatinputtotheelectrodewasestimatedfromthearcplasma,andthe‘molten’metalwasdiscardedwhenitstemperaturereachedthemeltingpoint.HaidarandLowke[21]andHaidar[22]
J.Hu,H.L.Tsai/InternationalJournalofHeatandMassTransfer50(2007)833–846
ContacttubeShieldinggasnozzlettAB
CD
R
Anode(+)
Shieldinggasvelocityprofile
Electrode
Z
Metaldroplet
Arc
GFE
Fig.1.AschematicrepresentationofaGMAWsystemincludingtheelectrode,thearc,andtheweldpool(nottoscale).
extendedthesimplifiedarcmodelofLowkeetal.[8]tosimulatethedropletformationinGMAW.Theywerethefirsttosimulatethedynamicinteractionofthearcplasmaandthedroplet.Haidar[13,23,24]furtherdevelopedthisGMAWmodeltotakeintoaccountthesheatheffectattheanodesurface.However,thedropletwaseliminatedimmediatelywhenitwasdetachedfromtheelectrodetip.Theweldpooldynamicswasalsoneglectedandthework-piecewastreatedasaflatplate.Thefluidflowintheweldpoolwasnotcalculatedandonlyconductionwasconsidered.Zhuetal.[25]andFanandKovacevic[26]havedevelopedmodelstosimulatethearccolumn,dropletformation,detachment,transferandimpingementontotheworkpieceandtheweldpooldynamics.However,thesimulatedarcplasmadistributionsmatchedboththeexperimentalresults[27–31]andthesimulationresultsfromaforementionedarcmodels[1–24]poorly.FromthesimulatedfluidflowwithinthedropletsinRef.[25],thecouplingofthearcplasmaandthedropletsseemedtobepoorasthedropletsshowedverylittlesignofbeingsubjectedtotheelectromagneticforce,arcpressure,andplasmashearforce.ThearcplasmaflowinRef.[26]couldnotpushthedetacheddropletsdownandanempiricalformulationwasusedtocalculatetheplasmadragforce.
Inalmostalloftheaforementionedstudies,thearcplasmawasconsideredtobeindependentofelectrodemelting,dropletgenerationandtransfer,orweldpooldynamics.However,inreality,thesurfaceoftheweldpoolishighlydeformable,andtheprofileoftheelectrodechangesrapidly.Also,whentherearedropletsbetweentheelectrodetipandthesurfaceoftheweldingpool,theflowofarcplasmacanbedramaticallydistorted.Inthisarticle,amathematicalmodelemployingthevolumeoffluid(VOF)techniqueandthecontinuumformulationisdevelopedtosimulatethecoupledtransportphenomenainclud
ingthegenerationandchangesofthearcplasma;theelectrodemelting;thedropletformation,detachment,transfer,andimpingementontotheworkpiece;andthedynamicsoftheweldpool.
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