Pr. Cha et al., NUMERICAL-ANALYSIS ON COLD CRUCIBLE USING 3D H-PHI METHOD AND FINITE-VOLUME METHOD WITH NON-STAGGERED BFC GRID SYSTEM, ISIJ international, 36(9), 1996, pp. 1157-1165
Generally, numerical analysis of MHD systems including cold crucible r
equires much amounts of calculating resources. These systems often inc
lude 3D electromagnetic field, fluid flow in irregular boundaries, sol
idification, even coupling between electromagnetic field and fluid flo
w. Two kinds of basically different simulation techniques are necessar
y for effective calculation of these MHD systems. These are FEM (Finit
e Element Method) for calculation of electromagnetic field and FVM (Fi
nite 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 crucib
le do not include the analysis of fluid flow. For calculation of elect
romagnetic field, 2D axisymmetric wire model, it's improved model or B
oundary Element Method have been widely used instead of fully 3D FEM.
In this study, 3D H-phi formulation for electromagnetic field by FEM a
nd a technique using non-staggered grid system for fluid flow by FVM w
ith BFC were employed to save the memory space and calculation time in
numerical analysis of cold crucible. A package of numerical models in
cluding electromagnetic, fluid dynamic, heat transfer and solidificati
on model was constructed and applied to the numerical simulation of co
ld crucible. Validity of the electromagnetic model was confirmed by co
mparison between the results from calculation and those from direct me
asurement. Verification of the developed code on fluid dynamic calcula
tion was carried out by its comparison with the commercial code PHOENI
CS. Influence of some important operating parameters on the meniscus s
hape and solidification front were investigated using the developed pa
ckage. Temperature distribution in the molten tin was uniform because
of the circulating flow induced by non-uniform distribution of electro
magnetic force and the heat transfer through mold wall at the melt-mol
d contacted region was noticeably reduced as a result of magnetic pres
sure.