PERTURBATION MODEL FOR THREE-DIMENSIONAL THERMOCAPILLARY CONVECTION IN LASER MELT POOL.

A three-dimensional model of the thermocapillary flow during laser surface heating is developed. This physically corresponds to the process of a stationary laser beam irradiating on the surface of a moving work-piece. A molten pool is formed by the laser heating. Due to the high temperature gradient on the surface, a surface tension gradient is created. Being a decreasing function of temperature for most metal, the surface tension therefore pulls the liquid metal from the hot central region to the cold outer region. Return flow is set up because of the existence of the solid-liquid interface. This recirculating flow, as it turns out, 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.