A Transient Unified Model of Arc-Weld Pool Couplings during Pulsed Spot Gas Tungsten Arc Welding
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1 A Transint Unifid Modl of Arc-Wld Pool Couplings during Pulsd Spot Gas Tungstn Arc Wlding A. Traidia 1, 2, F. Rogr *, 1 1 ENSTA Paristch, Dpartmnt of Mchanics UME 2 AREVA NP, Tchnical Cntr *Corrsponding author: ENSTA Paristch, Dpartmnt of Mchanics UME, Chmin d la hunièr, Palaisau, FRANCE, frdric.rogr@nsta-paristch.fr Abstract: A transint finit lmnt modl has bn dvlopd to study th hat transfr and fluid flow during pulsd spot GTA wlding on stainlss stl. Tmpratur fild, fluid vlocity and lctromagntic filds ar computd insid th cathod, arc- and anod using a unifid MHD formulation. Th volution of th hat flux and currnt dnsity at th top surfac of th anod ar studid during th wlding procss. Th lctric hating flux at th anod which rprsnts th nrgy absorbd by th workpic from th lctrons coming from th cathod is found to b th major mchanism of hating. Th proposd numrical modl also prmits to study th tim volution of th wld pool dimnsions for both constant and pulsd currnt. A comparison shows that th us of a pulsd currnt wlding givs a widr and dpr wld shap than th man constant currnt wlding. Th prsnt work lays a foundation for th futur dvlopmnt of a thr-dimnsional modl for moving torch arc wlding. Kywords: Hat transfr, Fluid flow, Arc, Unifid modl, Marangoni ffct. 1. Introduction Du to th widsprad us of GTA wlding in th manufacturing industry, th numrical simulation of such a procss is currntly in grat progrss. Th main goal is to study th impact of th wlding paramtrs (wlding currnt, arc lngth, puls frquncy, wlding spd ) on th final wld shap in ordr to improv th wlding quality and incras productivity. Th complxity of th numrical modling is du th strong couplings btwn many physics involvd in this procss. Th ionization of th shilding gas nsurs th currnt flow btwn th two lctrods, thn th hating Joul ffct crats a thrmal composd of lctrons, ions and nutral spcis at a larg tmpratur rang; from 300 K to mor than K. Th workpic is thn hatd from both th arc- conduction, and th lctrons flow at th top surfac. Dpnding on th mlting tmpratur of th workpic, a wld pool is formd in which th fluid flow is govrnd by th Marangoni ffct at th top surfac, th buoyancy forcs and th lctromagntic forcs cratd by th currnt flow. Th fluid flow insid th wld pool is also strongly coupld to th tmpratur fild and th dformation of th top fr surfac. Many numrical modls of spot GTAW ar availabl in th litratur [1-5]. Most of thm considr only on part of th wlding procss [1- ] (ithr th cathod, or th arc, or th anod) which lads to fix som boundary conditions that do not rprsnt th ral situations. Th bst way to dal with th problm is to tak into account th thr parts (anod, cathod and arc-) in a unifid formalism. Th intrfacs btwn th and th lctrods ar thn considrd as intrnal boundaris. This approach was proposd by Lowk and Tanaka t al [5] and givs satisfying rsults for constant currnt wlding. In th prsnt work, a unifid finit lmnt modl is introducd taking into account th thr parts of th wlding procss. Th tim-dpndnt modl can simulat pulsd currnt wlding in which th wlding currnt varis with tim at a givn frquncy btwn two constant valus; th pak currnt and th background currnt. This prmits to study th transint volution of som physical quantitis at th transition btwn th pak and background tims but also to compar wlding undr pulsd currnt with wlding undr th man corrsponding constant currnt. 2. Mathmatical formulation 1.1 Govrning quations
2 Th mathmatical formulation is basd on th following assumptions: Th study is rstrictd to spot GTAW; an axisymmtric coordinat systm is usd. Th arc column is assumd to b pur argon at Local Thrmodynamic Equilibrium. Th gas and moltn mtal ar incomprssibl. A wak coupling is considrd btwn th fr surfac dformation and th Magnto Hydrodynamic (MHD) calculations. Th tmpratur, vlocity and prssur filds ar calculatd in th thr domains using th classical consrvation quations writtn in a unifid transint formalism as follows: (1) Consrvation of mass v 0 (2) Consrvation of momntum v t t v v p v v + j g 1 w T T (3) Consrvation of nrgy p rf q T 5k cp v T kt j E j T t 2 (1 w ) Whr v is vlocity, T is tmpratur, p is prssur, ρ is dnsity, q dfl cp cp wpl is an f dt quivalnt spcific hat that taks into account th latnt hat of fusion L f, f L is th liquid fraction assumd to vary linarly with tmpratur in th mushy zon and w p quals 1 in th wld pool and 0 lswhr. k is thrmal conductivity and μ is th viscosity. Th oussinsq approximation is usd to comput th convction forcs insid th wld pool. β is th mtal thrmal xpansion and T rf is takn as th solidus tmpratur. In th wld pool th volumtric hat sourc is th Joul ffct and th nthalpic flux, and in th arc w tak in addition th radiation losss, usually approximatd by, whr is th N N p N nt mission cofficint of argon that varis with tmpratur. Th dtrmination of th lctromagntic forcs and th joul ffct in both arc and work pic rquirs th computation of th currnt dnsity j and th magntic flux. To achiv this, th coupld currnt continuity and th magntic potntial quations ar computd as function of th lctric potntial V and th magntic potntial vctor A as follows: A V 0 t A 1 A V 0 t 0 Th currnt dnsity, lctric fild and magntic flux ar thn computd from V and A as follows: A A E V ; j V ; A t t It is important to notic that th ddy currnt A j cratd by th tim variation of th t wlding currnt is takn into account in th abov xprssions. Th fr surfac dformation φ(r) is dscribd by th following PDE obtaind from [2]: 1 r 2 rrr r r Pa g r 1 Whr φ is th fr surfac dprssion, Pa is th arc prssur, γ is th moltn mtal surfac tnsion and λ is a Lagrangian multiplir usd to tak into account th mass consrvation constraint: 2 ( rr ) dr oundary conditions Th computational domain is shown in Figur 1. As sn th worpic is mad of two subdomains in ordr to us a finr msh siz for th wld pool formation. All th boundary conditions ar listd in Tabl 1; th most important points ar discussd blow; At th intrfac btwn arc and th anod (GD) th following conditions must b satisfid [5]: k T n k T n j n T ( ) ( ) a anod ( v s) T a f L n T s
3 Along th intrfac btwn th arc and th cathod (HIJ), th normal discontinuity of th hat flux is xprssd as follows: k T ( n ) k T ( n ) jv j T i i c cathod Whr V and i c ar rspctivly th argon ionization potntial and th cathod work function. j and i j ar rspctivly th ion currnt and lctron currnt calculatd from: j jr j n jr 0 j n j n jr 0 j j n j i 2 jr ArT xp kt A r, and ar rspctivly th Richardson s constant, th ffctiv work function for thrmionic mission and th lmntary charg. Tabl 1: oundary conditions Figur 1. Computational domain (dimnsions in mm) Th first condition shows that th normal hat flux at th anod is composd by th hating conduction flux from th, th hating lctric flux (which rprsnts th nrgy transfrrd from th lctrons to th anod) and th cooling radiation losss. is th anod work function and is th Stfan-oltzmann constant. Th scond condition mans that th total shar strss is th sum of th arc drag forc and th Marangoni forc. s and n ar rspctivly a local tangnt vctor and th normal vctor to th top fr surfac ( n is dirctd toward th domain). / T is th surfac tnsion cofficint, which has bn rportd to hav a big impact on th flow dirctions insid th wld pool [1-]. Its dpndnc on tmpratur T and sulfur activity a s is considrd using th xprssion dvlopd by Sahoo and DbRoy t al [6] as follows: Kas H 0 A Rg s ln 1 Kas s T 1Ka T K T H 0 k1 xp RT g a s T T ; j n It () A 0 2 Rc T T ; v n Ugaz ; j n 0; An C CD T T ; j n 0; p p ; 0 0 n n 0; A n 0 DE EF q n hc ( T T0 ); v 0; V 0; An 0 FA q n 0; v n 0; j n 0; 0 GD H kt ( n) kt ( n) j n T anod ( v s) T a fl n T s v n 0; j n 0 k T ( n ) k T ( n ) jv j T cathod v 0; j n 0 3. Numrical simulation rsults a i i c Th numrical modl is applid to an AISI 30 stainlss stl disk containing 290 ppm sulfur with 8 mm thicknss. Th thrmophysical proprtis of AISI 30 ss ar listd in th appndix. Th proprtis of pur argon ar takn from [7]. Th gas inflow rat is fixd to 30 L/min. Tabl 2 lists th othr wlding paramtrs.
4 Tabl 2: Wlding paramtrs Pak currnt ackground currnt Pak puls duration Frquncy Total hating tim 160 A 80 A 0.5 s 1 Hz 15 s Figur 2 prsnts th tim volution of th computd solution at th nd of th background tim (lft) and th pak tim (right) vry fiv priods. It is rprsntd th tmpratur fild and tmpratur contours insid th arc and th lctrod, th normalizd vlocity fild and stramlins insid th moltn wld pool. During th pak tim th arc is bll-shapd and th maximum of tmpratur and vlocity filds ar highr than during th background tim. Th obtaind valus for th maximum of -jt vlocity and tmpratur ar in good agrmnt with th litratur, in fact for a 150 A continuous currnt wlding K for th maximum tmpratur and 150 m/s for th maximum vlocity ar rviwd [5]. W can also notic that th variations of tmpratur and vlocity filds insid th column btwn th pak tims ar ngligibl; this is also th cas for th background tims. Th dynamic of th wld pool flow is studid by considring th stramlins of th vlocity fild. W can clarly idntify in ach figur two vortics namd A and. Thy rsults from th Marangoni ffct at th top surfac of th wld pool, th siz of ach vortx is rlatd to both tmpratur distribution at th surfac and sulfur contnt of th workpic. Dtails about th dynamic variation of ths vortics and thir influnc on th wld pool volution ar availabl in our prvious works []. Figur 3 shows th anodic hat flux distribution during th transition from th last pak tim (t=1.5 s) to th last pak tim (15 s). During th background tim th maximum of anodic flux is around 3 W/mm². Th transition is thn vry fast; in approximatly 15 μs th hat flux sms to stabiliz spcially at th cntr of th disk and rachs a maximum of 56.6 W/mm². Th numrical modl prmits to study th nrgy transfr btwn th arc and th workpic. Figur shows th radial volution of th hat flux at th anod at th last pak and background tims (t=1.5 s and t=15 s). In ach figur it is rprsntd th total hat flux and its lmntary contributions, namly; th lctric flux j n a, th conduction from th arc kt n and th radiation losss T. Figur 2. MHD solutions at background tims (lft) and pak tims (right) for diffrnt priods
5 Figur 3. Evolution of th anodic hat flux at th transition btwn th background to th pak tim nrgy transfrrd to th workpic. Th contribution of th conductiv hat flux from th rprsnt around 30 % and th cooling radiation losss ar undr 10 % of th total hat flux. Figur 5 shows th tim volution of th wld pool half-width and dpth for th pulsd currnt 80/160 A and th continuous man currnt 120 A Evn though th two cass ar nrgtically quivalnt, th pulsd cas producs a dpr and widr wld pool than th continuous cas, spcially for th wld pool dpth. This conclusion gos with what is commonly obsrvd by wldrs. Figur 5. Evolution of th wld pool siz for th pulsd currnt 80/160 A and th man currnt 120 A. Conclusions A transint unifid modl of pulsd spot GTAW has bn dvlopd using COMSOL Multiphysics. Th numrical simulation allowd a bttr undrstanding of th hat transfr btwn th arc and th lctrods. Th hating thrmionic mission at th anod was found to b th most important hating ffct. Th rsults showd that for a givn lvl of nrgy, it is mor intrsting to us a pulsd currnt wlding than th man constant currnt to gt a bttr wld siz. Figur. Anodic hat flux and its lmntary contributions at th last priod of hating Th lctric flux is found to b th most significant factor in both pak and background tims. It rprsnts around 80 % of th total 8. Rfrncs 1. W.H. Kim and S.J. Na. Int. J. Hat Mass Tran., 1, (1998) 2. H.G. Fan, H.L. Tsai and S.J. Na. Int. J. Hat Mass Tran.,, (2001)
6 3. F. Lu, S. Yao, S. Lou and Y. Li. Comput. Matr. Sci., 29, (200). A. Traidia, F. Rogr and E. Guyot. Int. J. Thrm. Sci., 9, (2010) 5. M. Tanaka and J.J. Lowk. J. Phys. D: Appl. Phys., 0, R1-R23 (2007) 6. P. Sahoo, T. DbRoy, M.T. McNallan. Mtall. Trans.., 19, (1988) 7. P. Fauchais, M. oulos and E. Pfndr, Thrmal, fundamntals and applications, (199) 9. Acknowldgmnts This rsarch was supportd by th Tchnical Cntr of wlding at AREVA NP, FRANCE. Th authors ar gratful to Lahcn Chrfa, Alxandr Chidly and Cathrin Holm for thir hlp on th rsults procssing. Appndix Tabl 3: Matrial proprtis of th usd matrials. ρ 6080 to 7272 kg.m -3 c p 510 to 796 J.kg -1.K -1 k 15.2 to 2.8 W.m -1.K -1 μ 0.05 kg.m -1.s -1 σ 7.7 x 10 5 Ω -1.m -1 T l 1723 K T s 1673 K a s wt% A γ.3 x 10 - N.m -1.K -1 R g 831 J.kg -1.mol -1.K -1 ΔH x 10 8 J.kg -1.mol -1 Γ s 1.3 x 10-8 J.kg -1.mol -1.m -2 γ m 1.93 N.m V a c.52 V 2.63 V h c 15 W.m -2.K -1 ε 0.
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