Mathematical modeling of solidification phenomena in electromagnetically stirred melts.

摘要

A methodology is presented to simulate the electromagnetic, heat transfer, and fluid flow phenomena for two dimensional electromagnetic solidification processes. For computation of the electromagnetic field, the model utilizes the mutual inductance technique to limit the solution domain to the molten metal and magnetic shields, commonly present in solidification systems. The temperature and velocity fields were solved using the control volume method in the metal domain. The developed model employs a two domain formulation for the mushy zone. Mathematical formulations are presented for turbulent flow in the bulk liquid and the suspended particle region, along with rheological behavior. An expression has been developed---for the first time---to describe damping of the flow in the suspended particle region as a result of the interactions between the particles and the turbulent eddies. The flow in the fixed particle region is described using Darcy's law. Calculations were carried out for globular and dendritic solidification morphologies of an electromagnetically-stirred melt in a bottom-chill mold. The coherency solid fraction for the globular solidification morphology was taken to be 0.5, while the coherency for dendritic morphology was 0.25. The results showed the flow intensity in the suspended particle region was reduced by an order of magnitude. The effect of the heat extraction rate on solidification time was investigated using three different heat transfer coefficients. The results showed that the decrease in solidification time is nonlinear with respect to increasing heat transfer coefficient. The influence of the final grain size on the damping of the flow in the suspended particle region was examined, and it was found that larger grain sizes reduce the extent of flow damping.