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1、Study of Fluid Flow and Heat Transfer of a Moving GTA Weld Pool in Longitudinal Magnetic Field Li Yongbing Shanghai Jiaotong University Wang Yasheng Xian Jiaotong University Lin Zhongqin Shanghai Jiaotong University Abstract Compared with general Gas Tungsten Arc Welding (GTAW), substantial change h
2、appens to liquid metal in external longitudinal magnetic field GTA weld pool. In the paper, mathematical models of fluid flow and heat transfer of external longitudinal magnetic field moving GTAW three-dimensional weld pool are established. Using the multi-coupled analysis function of ANSYS, distrib
3、utions of current density and magnetic field as well as fluid flow and heat transfer of three-dimensional moving weld pool are systematically studied to understand and reveal the effect of external longitudinal magnetic field on liquid metal in moving GTA weld pool and supply basis for the applicati
4、on of external longitudinal magnetic field welding technique. Introduction During GTA welding process, the behavior of weld pool can be changed by an external axisymmetric magnetic field parallel to welding arc centerline. It was found that applying a magnetic field of this type will result in annul
5、ar flow of liquid metal in weld pool and produce significant influences on fluid flow and heat transfer, as a result, also influence the melting and solidification of weld metal. From 1960s (Reference 1), some researchers began to study this kind of welding technique. They found that applying this k
6、ind of magnetic field could control the crystallizing process of weld metal and refine weld metal grain, as well as improve structure property of welding joint. At that time, the main means to study the behaviors of fluid flow and heat transfer of weld pool is experiments (Reference 2,3,4). However,
7、 it is very difficult to study fluid flow and heat transfer of moving weld pool and also impossible to essentially reveal external magnetic field distribution rule. From 1997 to 1999 (Reference 5), Luo jian studied the quasi three- dimensional fixed weld pool in external longitudinal magnetic field.
8、 Obviously, the simulation of spot weld pool could not reflect the real status of moving welding process, therefore, study on external longitudinal magnetic field moving welding process is very necessary and significant. Description of Three-dimensional Mathematical Model According to practical cond
9、itions of external longitudinal magnetic field welding process, following assumptions are given 1) Liquid metal in weld pool is incompressible viscous Newtonian fluid. Fluid flow belongs to laminar flow. There is no slipping velocity on liquid-solid interface. 2) Under weak external magnetic field (
10、TB1 . 0) and low welding current (), heat flux of welding arc on weld pool surface is considered as Gaussian distribution (Reference 5). AI120 3) Under weak external magnetic field (TB1 . 0) and low welding current (), arc plasma force and surface tension on weld pool surface as well as free surface
11、 are ignored. AI120 4) External longitudinal magnetic field has no influence on current density distribution in weld pool. 5) Not dealing with high-energy density, vaporization loss of weld metal and change of chemical constitution are ignored. 6) Under low-speed welding condition, transfer rate of
12、arc energy are ignored. Figure 1 shows the calculation model of external longitudinal magnetic field welding process. Excitation coil producing magnetic field is fixed at welding torch to ensure the external longitudinal magnetic field coaxial and synchronous with welding arc. The model uses Cartesi
13、an coordinate system. Welding heat source moves at constant speed u in X-axis direction. 0 Force Equation Motion of liquid metal in weld pool under external longitudinal magnetic field is very complex. According to above assumptions, the dominant driving force for weld pool motion in external longit
14、udinal magnetic field GTA welding is electromagnetic forces and rotation drag force of welding arc. (1) Electromagnetic Forces In external longitudinal magnetic field GTA welding, there are two kinds of electromagnetic forces to drive liquid metal. One is self-electromagnetic force; the other is add
15、itional electromagnetic force. Interaction of current density vector in weld pool and its self-induced magnetic field results in self-electromagnetic force. It can be given by smsm BJF rrr = r （1） Where, is self-electromagnetic force, J sm F r current density vector in weld pool and Bself-induced ma
16、gnetic field. sm r Additional magnetic force, which results in the annular flow of liquid metal in weld pool, is produced by the interaction of longitudinal magnetic field and weld current in weld pool. It can be given by amam BJF rrr = （2） Where, is additional magnetic force, am F r am B r is exter
17、nal longitudinal magnetic field. It can be easily found that the two forces, in nature, are all produced by the interaction of magnetic field and current density vector. According to Ref.6, wherever there exists current, ANSYS will automatically calculate the electromagnetic force applied in the reg
18、ion. If no external longitudinal magnetic field, ANSYS will calculate self-electromagnetic force, otherwise, additional magnetic force. Therefore, before solving the forces，current density vector must be obtained firstly. In cylinder coordinate system ),(zr，the current density is calculated from (Re
19、ference 7) = = rr j zr j e z e r 11 11 0 0 （3） Where, 0 is the permeability of air and e is defined as (Reference 8) = e + + r c c c c c L z rdr k rr k rr k I 0 2200 )1 ()(2exp)(2exp 2/ j （4） Where,is workpiece thickness,current density constant of weld pool surface, kcentralized coefficient of curr
20、ent density on weld pool surface, L 0 j c I welding current and r radial distance of current density peak value. c According to finite difference method, Equation (3) can be expanded as = = rr j zr j zrezre z zrezre r , 1|,| 0 1,|,| 0 11 11 （5） Where and zr are difference step size in z and r direct
21、ions respectively. zre ,| , 1,|zre and zre, 1| are respectively the value of e at coordinates (),zr, ), 1,(zr and (), 1zr. Based on Finite Difference Method and ANSYS Parameter Design Language (APDL), a program designed to calculate current density distribution of weld pool is embedded in electromag
22、netic field calculation program as boundary condition to complete electromagnetic force calculation. In the paper, a hollow cylinder coil excited by a constant-current source produces external longitudinal magnetic field. During the magnetic field analysis, the helicity of coil turn and the non-unif
23、ormity of the whole coil current are ignored to greatly reduce computation time. Practice shows the method only produces minimal error between calculation value and practical measurement value (Reference 9). Figure 2 shows the calculation model of external longitudinal magnetic field. Involved media
24、 have welding workpiece, excitation coil and air. Because tungsten electrode has the same permeability as air, air property is assigned to tungsten electrode region to simplify calculation model complexity. The calculation of external longitudinal magnetic field in the paper deals with an open infin
25、ite domain. Because Magnetic Vector Potential (MVP) at the boundary of welding workpiece and excitation coil cannot be obtained by experiment, and all the air surrounding the model also cannot be included into the model, this paper define a layer of far-field elements simulate the open infinite doma
26、in (Reference 6). Assuming all the media are isotropic, according to electromagnetic field theory, Maxwell equation set, which external longitudinal magnetic field follows, is given by = = = = = 0 0 0 B J JH D E e r r rr r r （6） r Where,E(v/m) is electric field intensity,B r ( ) magnetic induction i
27、ntensity, DT r (c/m2) electric displacement vector, H r (A/m) magnetic intensity,J r (A/m2) current density, e (C/m3) charge density. The following equations are given to describe the macro-electromagnetic character of media in external longitudinal magnetic field. = = = ED HB EJ rr rr rr （7） Where,
28、 is permeability and electric conductivity. (2) Arc Rotation Drag Force to Weld Pool Surface In external longitudinal magnetic field, welding arc rotates at high speed and at the same time drags weld pool surface to rotate (Reference 5). The force is from the interaction of external longitudinal mag
29、netic field and welding current density vector in arc region. It can be given approximately by (Reference 8) rBsm jkF rrr = （8） Where, is arc rotation drag force, which has the same direction with external longitudinal magnetic field and approximately equal to magnetic induction intensity of weld po
30、ol surface. is the r direction component of weld pool surface current density. sm F r r j r Continuity Equation Liquid metal in weld pool is incompressible fluid, that is to say, metal density is invariable during welding process. Therefore, the continuity equation is given by 0= + + z w y v x u （9）
31、 Where,( are fluid velocity component in direction respectively. ),wvu),(zyx Momentum Equation In view of the incompressibility and Newtonianism of weld pool liquid metal, the momentum equation is given by x F z u y u x u z u w y u v x u uu+ + + = + + )()( 2 2 2 2 2 2 0 y F z v y v x v z v w y v v x
32、 v uu+ + + = + + )()( 2 2 2 2 2 2 0 （10） z F z w y w x w z w w y w v x w uu+ + + = + + )()( 2 2 2 2 2 2 0 where,is liquid density, viscous coefficient，and components of body force in weld pool fluid in directions respectively. ),( zyx FFF ),(zyx Energy Equation Energy equation is given by )()()()( 0
33、 z T k zy T k yx T k xz T w y T v x T uuCp + + = + + （11） Where, is time, Cconstant pressure specific heat, t p Ttemperature, and k coefficient of heat transfer. Analysis External longitudinal magnetic field welding process deals with heat transfer, phase transition and the interaction of electromag
34、netic field and flow field, moreover, fluid flow and heat transfer are interacting, therefore, it is very difficult to solve the problem with analytic solution. Based on commercial finite element software ANSYS, the problem is automatically loaded and solved by program designed by APDL. If no specia
35、l statement, in experiments and numerical simulation of this paper, excitation current is 20A, gap between coil and upper surface of workpiece is 10mm, welding current 100A, arc length 2mm, tungsten diameter 3.2mm, tungsten cone angle 60 degree, argon flow quality 8L/min，welding velocity 3mm/s. Dire
36、ct current and normal polarity are adopted. Initial and Boundary Conditions Before solving the coupled field of flow field and thermal field, boundary conditions should be specified. Furthermore, because welding is a transient process, initial condition also should be given in advance. Velocity Boun
37、dary Velocity boundary includes the liquid-solid interface of molten domain and non-molten domain, and also free surface of weld pool. During welding process, the liquid-solid interface, where latent heat of phase change takes place, is moving. During the solution of fluid flow and heat transfer, th
38、e most difficult problem faced with is the moving of the liquid-solid interface. General measure is to assume there is a minute time lag between transferring of heat energy into the interface and its result, moving of the contact surface. That is to say, during a minute time step, liquid-solid inter
39、face is supposed to be stationary. Under the assumption, flow field and thermal field are solved. Then according to the calculated thermal energy transferred into liquid-solid interface, latent heat of phase change and other heat balance conditions, the displacement of every node on the interface is
40、 calculated to obtain new position of the moving interface. Based on the new position, flow field and thermal field of next time step can be calculated. According to the method, the flow field and thermal field of the whole welding process can be calculated. Obviously, the algorithm of this measure
41、is fairly complicated to realize. Moreover, the calculation accuracy is dependant on time step size. The smaller time step is, the higher calculation accuracy is. However, minute time step is at the cost of lots of CPU calculation time. In order to overcome the deficiency of this measure, this paper
42、 adopts Liquid Solid Identity Method. In the method, solid phase is also regarded as liquid phase. That is to say, in the region, where temperature is less than or equal to solidus temperatureT，very great viscosity (about 10 s 9 order) is assigned to ensure flow velocity in the region is zero. Howev
43、er, in the rest region, where temperature is greater than or equal to liquidus temperatureT, real viscosity is used, therefore, when electromagnetic forces are applied, the region with little viscosity will move. With this method, program will automatically handle the moving liquid-solid interface a
44、nd update physical properties of material according to calculated temperature field without artificial intervention. l The other velocity boundary is free surface of weld pool. At present, ANSYS cannot handle three- dimensional free surface, therefore, normal velocity of liquid metal of weld pool su
45、rface is prescribed to be zero. Under low welding current (, the upper surface of general GTA weld pool can be regards as plat surface (Reference 10). Furthermore, according to Reference 5, during external longitudinal magnetic field GTA welding process, the displacement of the upper surface of fixe
46、d weld pool is very small and can be ignored. As a result, this processing method will is reasonable. )120AI FLOTRAN analysis module of ANSYS requests that fluid region must be defined before FLOTRAN analysis. In this paper, solid phase is regarded as liquid phase; therefore, fluid region should be
47、the whole welding workpiece. Therefore, the normal velocities of other five outer surfaces other than free surface also should be assigned a zero value to determine the unique fluid region. Thermal Boundary Heat flux of external longitudinal magnetic field moving GTA welding arc presents Gaussian di
48、stribution (Reference 5). It is given by arc Q= 2 3 q aUI exp( 2 2 3 q r )， q r （12） Where, q is heat flux distribution parameter of welding arc. It is defined as radial distance from arc center to the position where heat flux decays to 5% of heat flux maximum. Uis arc voltage, a coefficient of efficiency of welding heat source, Q heat flux distribution of welding arc. arc Because of the temperature difference between welding workpiece and ambient medium (gas), heat exchange will take place. Convection and radiation are dominating