Numerical analysis of thermal melt flow and melt/solid interface shapes in the floating zone method

Abstract

Numerical simulation of the thermal melt flow coupled with moving melt/solid interfaces in the floating zone (FZ) method under low gravity is carried out. The novel feature of the proposed algorithm is the application of the arbitrary Lagrangian–Eulerian (ALE) method to the moving melt/solid interface problem. The governing equations are discretized by the finite element method (FEM), and the velocity field is solved by the generalized simplified marker and cell (GSMAC) method. The developed scheme is employed to investigate the two-dimensional (2D) melt flow and melt/solid interface shapes in various conditions of gravity and surface tension. Through computation, it is revealed that the melt/solid interface shape is greatly affected by the flow configuration and the intensity of convection. Moreover, coupled natural and Marangoni convection reduces the stability of the melt zone; for the conditions in the present study, the flow configuration and the melt/solid interface shape are suddenly changed as soon as natural convection is merged into Marangoni convection as a consequence of increased gravity. The usefulness of the transverse magnetic field in control of the melt flow is also clarified through the comparison with the vertical magnetic field.