Fluid dynamics of a stationary weld pool

Abstract

Flow driven by a combination of thermocapillary, Lorentz, and buoyant forces has been investigated in an axisymmetric and stationary weld pool numerically. By assuming a small value for the capillary number, the top and bottom boundaries can be taken to be flat, and the surface deflections can be calculateda posteriori as a domain perturbation. Owing to thin boundary layers that exist at the top free surface and next to the vertical wall, very fine grids are required in these regions in order to obtain an accurate solution to the Boussinesq form of the Navier-Stokes equations. This was done by solving the governing equations by multigrid methods to which a local grid refinement technique was added. Welding of both aluminum and steel were considered. The essential difference between these two materials for this analysis is that the Prandtl number of aluminum is an order of magnitude smaller than that of steel. Through a parametric study, the thermocapillary forces and Lorentz forces were found to dominate buoyancy forces in a typical welding situation. Although the flows in weld pools include a pronounced recirculating region near the top surface, isotherms could be determined in the case of aluminum to a good approximation by a conduction analysis, owing to the smallness of its Prandtl number and the relative thinness of the welded plate considered. For steel, the isotherms deflect considerably for high current inputs.