Comparisons between different models for thermal simulation of GTAW process

Comparisons between dilerent models for thermal simulation of GTAW process125Comparisons between different models for thermalsimulation of GTAW processXu Yanli and Wei Yanhong徐艳利,魏艳红”Abstract Tuo mathematical models are built to study the efets of the fluid flowo on thermal distributions of ithe gas tungstenare welding( GTAW) proces. One model is buased on the heat conduciity equation, wohich doesn' t take the efs of the fluidflow into account, and the other couples the laminar heat transfer and fluid flow in the weld pool, which is called laminarfluid flow model in shor. The simulated rsuls of the two models show that the patten and velocity of the fluid flow play acritical role in determining the thermal distribution and the weld pool shape. For the laminar fluid flow model, is highesttemperature is 400 K lover than that calculated with the other model and the depth of is weld pool is shallower too, twhich ismainly caused by the main vortex of the floww in the weld poo.Key words thermal distribution, gas tungsten arc welding, heat transfer and fluid flow0 Introductiontive representation of heat transfer and fluid flow phenome-In are welding processes, final microstructure andna in the weld pool[3-61.mechanical properties of the weldments mainly depend onIn order to know the effects of the weld pool on thethe thermal cycle undergoing during the heating and cool-workpiece thermal distribution, and get a quantitative rep-ing process. The accurate analysis of the welding thermalresentation of the differences between whether the effectsprocess is the foundation of metallurgical analysis, struc-of the fluid flow take into account, two models are built toture stress and strain analysis as well as the weldingsimulate the thermal distributions of the stainless steelprocess control. So far, experimental determination ofSUS310 GTAW process by the Computational Fluid Dy-temperature profile and fluid field in the weld pool is ex-namics ( CFD) software PHOENICS. One is the heat con-tremely dificult due to the small weld pool, the high tem-ductivity equation model, and the other is the laminar flu-perature involved and the presence of the welding arc.id flow model. The results of the temperature distributionMathematical modeling provides an effective way to over-and the shape of the weld pool simulated by these twocome these problems. The welding processes simulatedmodels are compared, and the efects of the molten metalstarted in the 1940's, in the first few decades, the wholevelocity on the shape of the weld pool and the temperatureworkpiece was treated as a solid workpiece and solved bydistribution are analyzed.the heat conductivity equation. This method is easy to un-derstand and master, so many people still use it to simu-1 Mathematical modellate the weld process 1.2] with finite element method soft-1.1The heat conductivity equation model and itsware packages. Since the effects of the velocity and tem- boundary conditionsperature distribution of the molten pool could be consid-In this model, the thermal distribution of the GTAWered, researchers show significant interest in the quantita- process is calculated by the heat conductivity equation,中国煤化工Project (No. 50375038) supprted by National Science Foundation of ChiMHC N M H Gndation of Habin Intituteof Technology ( HIT.2002.41).** Xu Yanli and Wei Yanhong, State Key Laboratory of Advanced Welding Production Technology, Harbin Institute of Technology,Harbin, 150001. E-mail: xuyanli@ hit. edu. cn (Xu Yanli)126CHINA WELDING Vol. 14 No. 2 November 2005and the governing equation is:opment of the weld pool are the continuity , momentum anda(K四+(x哥)az dz' ax(kgaT)(puoH) +Sp =0energy equations.ax“ax'8The continuity equation is represented as:(1)K-Thermal conductivity, W/(m. K)8(pu,)=0(5)ax;T-Temperature, KThe momentum equation is described as:uo- -Welding speed, m/sa(pu,u.)_ (pu4o4)_. a (.aPp-Density, kg/m'dx;xx+S:(6)H-Enthalpy, J/kgThe energy equation is given by:SH- -Source term, here is the latent heat, J/m'a(pu,H) a(pugH)2(K2)+Sp (7)The boundary conditions of the heat conductivity e-dx)xx;quation model are :The source terms of the momentum equation are:On the top surface, arc heat input is conducted intoIn x, y directions:the workpiece, and part of it loses to the surrounding be-C(1-cause of the convection and radiation. It is expressed ass.=(9-)u; +(jxB)。(8)following formula:In z direction:=-qa +h.(T-T,) +σoe(T^-T°) (2)，C(1-f)2-)w+(jxB)。+pgB(T-T_) (9)s,=( f:+b。q% -Heat flux from welding arc, W/m2j-Curent itensit, A/m2h。- -Convective heat transfer coefficient, W/(m2●K)B- -Magnetic fux intensity , Weber/m2T。- Surrounding temperature, Kf- -Liquid fractionε--Radiation emissivityC- -Empirical constantσo一Stefan-Boltzmann cofficient, W/(m2●K*)b,- -Small positive number to avoid the denominator to beThe symmetric surface is the adiabatic surface, andzerothe expression is ;g -Gravitational constant, 9. 8 m/s?T=0(3)β- -Ceoficient of thermal expansion, W/(m2●K*)8Tm -Melting temperature, KAt the other surfaces, heat lost to the surrounding byThe first part of the source terms is the enthalpy-po-the convection and radiation, just as formula:rosity term!", by which the solid/liquid interface comes-Ko=h.(T-T)+σoe(r*-T() (4)out as a part of solution. The second part of the equationis the Lorentz force tem and the value of J and B can be1.2 The laminar fluid flow model and its boundaryobtained through solution of Mxwell' s equation based onconditionsthe assumption of the J and B fields are axisymmetric.In the model，electromagnetic ，surface tension andThe third part in z direction is the buoyancy force term.buoyancy forces are considered as driving forces, and fol-The source term of the energy equation is:lowing assumptions are made: (1) The welding process isrestricted to the stationary GTAW process and the system中国煤化工H) + (puAH)+)z Pis symmetrie; (2) The flow in the weld pool is Newtoni-MYHCNMH G(10)an, incompressible and laminar; (3) Surface deformationaxV0-of the weld pool is ignored. Based on the assumptions stat-AH-Latent heat, J/kged above, the governing functions that describe the devel-The boundary conditions for solving the energy equa-.Comparisons between different models for thermal simulation of GTA W process127tion are the same as those in the conductive equation mod-el described above，and those for the momentum equationare as follows:/oyAt the top surface of the workpiece: .au_ ayaTdv_ ayaT(11)az aTax ’az aTayγ- -Surface tension, N/may/ aT- -Constant in surface tension coefficient,N/(m.K)μ- -Viscosity, kg/(m.s)At the symmetry surface of the workpiece:Fig. 1 Schematic diagram of double llipsoial model(8]au=0，w_=0， v=0(12)Table 1 Values of parameters in double llipsoidal model3ya,/ mma2/ mmb/ mmc/mmf1.3 The heat source8.86.01.40.6The double llipsoidal model is used to represent theare heat fux distribution[8)(Fig. 1) and the values of the1.4 Material properties used for modelingparameters in the model are shown in Table 1.Properties of stainless SUS310 are shown in Table 2.Table 2 Material properties data used for modelingp/kg.m~C/] .kg-'.K-'T/KT,/Kh./W.m-2●K-'lμkg.m-' .sI7 8005731 67315231006.0x 10-T。/Kβ/K-'σ:/W .m-2.K-+AH/] . keay/8T(N.m".K~')0.929310-5.7x 10-82.47x10'5.0x10-4A nonuniform grid system is used here within the do-TMP1: 398 798 1198 1598 1998 2398main size (50 mm x 25 mm x 10 mm). The welding volt-age is 13 V, the current is 200A, and the speed is 2 mm/s.0.010.023 0.010.000.00.000.042 Results and discussionx/mFig. 2 shows the temperature distributions of GTAW(a) Simulated by the heat conductivity equation modelprocess simulated by the conductivity equation model andthe laminar fluid flow model. As Fig. 2 shows, the highesttemperature of the results calculated by the heat conductiv-ity equation model is 400 K higher than that calculated bylaminar fluid flow model. That verifes the behavior of themolten metal in the weld pool has significant effects on thethermal distribution.中国煤化工Fig. 3 and Fig. 4 show the shape of the weld pool sim-MHCNMH Gulated by these two models. From these figures it can be(b) Simulated by the laminar fluid flow modelseen that the width and length of the weld pool simulatedby the laminar fluid flow model are larger than that simula-Fig.2 Temperature distributions in three dimension128CHINA WELDING Vol. 14 No. 2 November 20050.0075 0.2 m/s0.005 00.002 50.0150.020 0.0250.030x/m(a) In top view(a) Simulated by the heat condutivity equation model0.0100.009LIQF: 0.1 03 0.4 二0.6 0.8 090.0080.2 m/st ..wwL.................会0.0040 0.001 0.002 0.003 0.004 0.005 0.006y/m0.099100.0200.025(b) In cross- sectional view(b) Simulated by the laminar fluid flow model0.006Fig.3 Width and length of the weld poolsted by the conductivity equation model, but the depth of(c) In sectioned view along weld axisweld pool simulated by the fluid flow model are much shal-lower because of the pattern of the flow inside the moltenFig.5 Velocity feld in the weld poolspool.show the directions of the fluid flow clearly, unifrm-LIQF: 0.0.3 0.0.6 0.8 0.9length velocity vectors are used in Fig. 5. As the tempera-ture is highest under the heat source, and the surface tem-ξ 0.008perature of the weld pool decreases outward，the fluid flowat the weld pool surface is radically outward when the tem-0.015 0.0200.025 0.030perature surface tension gradient, dy/dT, is negative. InFig. 5b, a large clockwise vortex is caused by the surface(a) Simulated by the heat conductivity equation modeltension gradient on the top of the weld pool. Under thisvortex, another small counterclockwise vortex is driven by0.01IQF: 0.1 0.3 0.4 0.6 0.8 0.Selectromagnetic force. As the surface tension pulls the hotmolten metal at the weld pool surface outward, the coldξ0.008molten metal is driven to the center of the weld pool sur-face, where it will be heated. This process makes the hotmolten metal disperse to the whole weld pool and tempera-中国煤化工orm than just consideringFig.4 Depth of the weld poolsYHCNMHGshows, and the depth ofweld pool becomes shallower as the main fluid flow is fromFig. 5 shows the patterm of the fuid flow in the weldthe center of the surface to the edge of the weld pool, aspool simulated by the laminar fluid flow model. In order to .Fig. 5 shows.Comparisons between different models for thermal simulation of GTAW process1293 Conclusionand Mass Transfer, 2003, 46: 4553 - 4559The conductivity equation model and the laminar fuid[3] KimIS, Basu A. A mathematical model of heat transfer andfuid flow in the gas metal arc welding process. Jourmal offlow model are built to simulate the thermal distribution ofMaterials Processing Technology, 1998, 77: 17-24the GTAW process. From the comparison of the results it4] Lu Fenggui, Yao Shun, Lou Songnian, et al. Modeling andcan be seen that the pattern of the fuid flow affect not onlyfinite element analysis on GTAW arc and weld pool. Compu-the thermal distribution, but also the shape of the weldtational Materials Science, 2004, 29: 371 -378pool. The highest temperature simulated by the laminar5] He X, Fuerschbach P W, DebRoy T. Heat transfer and fluidfluid flow model is 400 K lower than that calculated by theflow during laser spot welding of 304 stainless steel. Jourmalconductivity equation model. As the main vortex flows out-of Plhysics D: Applied physics, 2003, 36(12): 1388 - 1398ward, the weld pool becomes shallower simulated by the[6] Phanikumar Gandham， Dutta Pradip, Chattopadhyay Kar~laminar fuid flow model than that simulated by the heatnanio. Computational modeling of laser welding of Cu-Ni dis-conductivity model.similar couple. Metallurgical and Materials Transactions B:Process Metllurgy and Materials Processing Science, 2004,35(2): 339 -350References[7] Jaidi J, Dutta P. Three -dimensional tubulent weld pool con-[1] Murthy Y V L N, Venkata Rao G, Krishna lyer P. Numericalvection in gas metal arc welding process. Science and Tech-simulation of welding and quenching processes using transientnology of Welding and Joining, 2003, 8(5):407 -414thermal and thermo-elasto-plastic formulations. Computers &8] Goldak J. A new finite element model for welding heatStructures, 1996, 60(1): 131-154 .sources. Melallurgical Transactions B, 1984, 15B: 587 -[2] Couedel D, Rogeon P, Lemasson P, et al. 2D-heat transfer600modeling within limited regions using moving sources: appli-cation to electron beam welding. International Joumal of Heat中国煤化工MYHCNMHG