Three-dimensional GSMAC-FEM simulations of the deformation process and the flow structure in the floating zone method

Abstract

This paper presents an improved level set method (LSM) for the analysis of a free surface deformed in an alternating current magnetic field. Three-dimensional numerical simulations are carried out based on the generalized simplified marker and cell—finite element method (GSMAC-FEM) algorithm to investigate the deformation processes of a silicon liquid bridge similar to the floating zone (FZ) configuration with the coil position, width, and the magnitude of surface tension changed under microgravity. The A- ϕ method is adopted to calculate the physical quantities of the magnetic field, and it is solved by the hybrid finite element method–boundary element method (FEM–BEM). The liquid part at the coil position becomes largely squeezed by the Lorentz force if the magnitude of surface tension is small, and the radius of a liquid bridge varies when a coil moves from the upper position in height to the middle one. However, the deformation becomes greatly suppressed if the magnitude of surface tension is large because the outward force in proportion to the magnitude of curvature increases. From these results, it is expected that the deformation quantity of a liquid bridge will be rather small in the real FZ process because of large surface tension and a high frequency which causes the skin effect.