Numerical simulation on the Marangoni convection in the molten metal pool

Melting process of metal is found in various nuclear engineering fields, such as melting phenomena on the first wall in a fusion reactor and the atomic vapor laser isotope separation process. In this process, it is important to know the shape of the molten pool and its melting mechanism. A set of the Navier-Stokes equation and the energy equation is applied to simulate the transient melting process of metal irradiated by electron beam. A time evolution of the liquid-solid interface is predicted using the latent heat model. The validity of this model is confirmed by using the two-phase Stefan problem. The upwind and the higher order finite difference method for nonlinear terms of the convection equation are studied for various parameters, such as the mesh size and the Courant number. The shape of the molten region, which is calculated using a higher order finite difference method, is in good agreement with measured ones. The Marangoni convection in a long rectangular cavity, which is a model of the flow observed in the pool, is simulated in detail as a function of the Reynolds number. It is found that two vortices in the periphery of the pool play a decisive role in forming the molten region. (author)