Numerical prediction of solidified shell thicknesses obtained in continuous casting with different billet shapes

Thermal physics of continuous casting is strongly dependent on the velocity of the molten metal, surface heat extraction rate and also on the mold shapes. In the present numerical study, both the moving front and the geometric boundaries of non-rectilinear molds are modeled using Immersed Boundary Method (IBM) which reduces computational time and provides simplicity as compared to the body confirming grid approaches. A second order accurate finite difference method is used to solve unsteady heat conduction equation along with lateral convection to predict the solidified shell thickness during continuous casting. This methodology shows good agreement with the reported data for a rectangular billet. A quantitative study has been performed to report the effects of casting velocity and heat extraction rate on the solidified shell thickness for different mold shapes such as circular, elliptic and I-shaped. Chipman-Fondersmith correlations for solidified shell thickness during continuous casting are assessed for these three different mold shapes and improved correlations are suggested to take into account the variations in the heat extraction rate.