Numerical analysis on cold crucible using 3D H-phi method and finite volume method with non-staggered BFC grid system

Abstract

Generally, numerical analysis of MHD systems including cold crucible requires much amounts of calculating resources. These systems often include 3D electromagnetic field, fluid flow in irregular boundaries, solidification, even coupling between electromagnetic field and fluid flow. Two kinds of basically different simulation techniques are necessary for effective calculation of these MHD systems. These are FEM (Finite Element Method) for calculation of electromagnetic field and FVM (Finite Volume Method) with BFC (Body Fitted Coordinate) for fluid flow. But many researchers have been tried to solve these problems by other methods because the use of the combined method consumes large quantity of memory and computing time. Most of numerical models on cold crucible do not include the analysis of fluid flow. For calculation of electromagnetic field, 2D axisymmetric wire model, it's improved model or Boundary Element Method have been widely used instead of fully 3D FEM. In this study, 3D H-phi formulation for electromagnetic field by FEM and a technique using non-staggered grid system for fluid flow by FVM with BFC were employed to save the memory space and calculation time in numerical analysis of cold crucible. A package of numerical models including electromagnetic, fluid dynamic, heat transfer and solidification model was constructed and applied to the numerical simulation of cold crucible. Validity of the electromagnetic model was confirmed by comparison between the results from calculation and those from direct measurement. Verification of the developed code on fluid dynamic calculation was carried out by its comparison with the commercial code PHOENICS. Influence of some important operating parameters on the meniscus shape and solidification front were investigated using the developed package. Temperature distribution in the molten tin was uniform because of the circulating flow induced by non-uniform distribution of electromagnetic force and the heat transfer through mold wall at the melt-mold contacted region was noticeably reduced as a result of magnetic pressure.