Effect of surface tension gradient driven convection in a laser melt pool: Three-dimensional perturbation model

A three-dimensional model of the thermocapillary flow within the molten region during laser surface heating is developed. This physically corresponds to the process of a stationary laser beam irradiating on the surface of a moving workpiece. The recirculating flow due to the surface tension gradient is much faster than the scanning motion. This allows a perturbation solution. The basic solution corresponds to the stationary axisymmetric case, and the perturbation is based on a small scanning velocity. The advantage of seeking a perturbation solution 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. The solid-liquid interface is determined by an iterative scheme. In the presence of the recirculating flow, the heat transfer becomes convection dominated. The absorbed laser energy is convected sideways so that a wider and shallower molten region is obtained. The molten pool shape is obtained and presented. The effect of various operation parameters (such as laser power, beam radius) on the pool shape are obtained and discussed. The cooling rate of resolidifying materials is also determined. Trajectory of a fluid particle is presented. This provides the most realistic scenario of mixing in a laser melted pool obtained to date. This also gives a semiquantitative understanding of the mechanism of solute redistribution. The effect of alloying elements, which may change the temperature dependence to an increasing function, is also considered. A reverse recirculating vortex is obtained and its effect on pool shape is presented and discussed.