Three-Dimensional Model for Convection in Laser Weld Pool

"Two three-dimensional models of a surface tension gradient driven flow during laser surface heating are developed. The first model is based on a perturbation solution. The basic solution corresponds to the stationary axisynwnetric case and perturbation is based on a small scanning velocity. The advantage of seeking a perturbation solution, as it turns out, is that the three-dimensional flow is modeled by two sets of two-dimensional equations which are presumably much more tractable than the original three-dimensional equations. Numerical solutions are obtained and discussed. The second model is a full three-dimensional numerical solution of the Navier-Stokes equations, using a point-by-point partially vectorized iteration scheme. Surface shape is also determined in a self-consistent manner. The effect of the presence of convection on pool geometry, cooling rate and solute redistribution is presented and discussed.IntroductionThe existence of fluid flow and convection and their effects were first reported in the fifties (1,2). The role of convection in controlling pool geometry such as pool shape, undercut and ripples, and defects such as variable penetration, porosity and lack of fusion and weld properties such as weld homogeneity and bead formation is studied by a number of researchers and is reviewed by the authors in a recent paper (3).Recently, surface tension gradient driven flow has been identified as one of the forces responsible for convection within the molten pool (4,5). It is postulated that surface tension gradient driven flow is responsible for the surface ripple formation in the weld pool (6-8). Oreper, et al. (9) developed a two-dimensional convection model. Buoyancy, electromagnetic and surface tension gradient forces were considered. The formulation was based on a specified pool profile. It was found that the surface tension gradient is the dominant force in most cases. However, the solid-liquid interface is not known a priori. In fact, the solid-liquid interface, i.e. the pool shape, is a piece of information that the model should be able to predict. A two-dimensional transient self-consistent (i.e. the solid-liquid interface is solved as part of the solution] model for laser surface melted pool was first developed by Chan, Mazumder, and Chen (3)). This model predicted a non-uniform cooling rate, hence non-uniform microstructure. Depending on the Prandtl number (i.e. material) and surface tension number, the shape of the molten region as well as the cooling rate changes. It was also predicted that the recirculating velocity is of one or two order of magnitude higher than that of the scanning velocity. This model provides the detail of the flow field and heat transfer on a plane perpendicular to the scanning direction. However, the front-to-back motion and its effect on heat transfer also play important roles in the physical process, especially for the fact that the recirculating velocity is so much higher than the scanning velocity. Such a motion cannot be obtained from two-dimensional models."