Numerical simulation of deformation-induced segregation in continuous casting of steel

The deformation-induced macrosegregation in continuous casting of steel has been simulated using a finite-volume scheme. For that purpose, a two-dimensional heat-flow computation was first performed in a Eulerian reference frame attached to the mold, assuming a unique solidification path, i.e., a unique relationship between temperature and enthalpy. This gave the stationary enthalpy field in the longitudinal section of the slab. On the other hand, bulging of the slab between two rolls was calculated in the same section, assuming plane-strain deformation and using the ABAQUS code. The Lagrangian reference frame was attached to the slab, and the rolls were moved at the surface until a stationary, bulging deformation profile was reached. The bulging of the surface was then used as an input condition for the calculation of the velocity and pressure fields in the interdendritic liquid. Using a fairly simple hypothesis for the deformation of the solid skeleton, the mass conservation and Darcy equations were solved in a Eulerian reference frame. This calculation was performed in an iterative loop, within which the solute conservation equation was also solved. At convergence and using the enthalpy field, this calculation allowed to obtain the temperature, the volume fraction of solid, and the average concentration fields, in addition to the fluid velocity and pressure. It is shown that the positive centerline segregation of carbon in the slab is well reproduced with this model. The effects of shrinkage and soft reduction were also investigated.