Thermocapillary convection in laser melted pools during materials processing

Abstract

A numerical study was undertaken in order to understand the complex heat transfer encountered during laser welding of metals. Melting and resolidification of the material occurs when the metal undergoes intense, non-uniform irradiation from a concentrated energy source, such a laser. Motion of the liquid metal in the molten region is induced by buoyancy and surface tension (thermocapillary) forces. This motion of the liquid metal causes heat to be redistributed (convective heat transfer) which in turn effects the melt pool shape (solid/liquid interace), local temperature gradients, and ultimately, the microstructure of the resolidified material. In order to better understand the importance of thermocapillary convection within the melted region during the laser welding process, both two-dimensional and three-dimensional steady-state finite difference models were developed. The governing mass, momentum, and energy transport equations were discretized using a control volume formulation which incorporated variables mesh and variable thermophysical property capabilities. Results from both the two-dimensional and three-dimensional models indicate that convection of the molten metal within the melt region during laser welding plays an important role in the overall heat transfer of the process. Surface tension (thermocapillary) forces are shown to be the predominant driving mechanism of the flow in the molten metal region. Both two-dimensional and three-dimensional models show the development of recirculating flow patterns in the melt pool due to thermocapillary convection. Three-dimensional results indicate that at higher substrate scanning speeds complex recirculating flow patterns occur which can not be predicted using two-dimensional models. Maximum free surface velocities on the order of 1 m/s occur in the melt region due to the severe thermal gradients induced by the concentrated energy source. The melt pool aspect ratios (width/depth) are shown to increase (compared to conduction models) for low Prandtl materials (Steel $\sim$0.1, Aluminium $\sim$0.01) due to the redistribution of heat by thermocapillary induced convection. Surface active agents (elements which modify the local values of surface tension) are shown to dramatically influence the convective flow patterns (and therefore convective heat transfer) in the molten region. Three-dimensional dynamic free surface boundary conditions were derived from first principles for the welding simulations. The welding codes were then modified to allow dynamic movement of the molten free surface during the simulations. Initial free surface calculations reveal surface deflections which are small compared to the characteristic length of the melt pool. Thermocapillary driven square cavity calculations were initiated in order to examine the concentrated temperature gradient region developed in (generic) thermocapillary flows. High Ma flows were found to exhibit a singular behavior which decreased with decreasing Pr. Surface contaminants were found to inhibit the development of this singular region.