Columnar-equiaxed transition in continuous casting based on a micro-macro solidification model with long-range solutal mixing

A novel model is proposed to describe the columnar to equiaxed transition (CET) in continuous casting. The model bases on Rappaz and Thevoz's solute diffusion model for equiaxed dendritic growth, combined with a 1-Dimensional solidification model normal to the slab surface. The unique feature of the proposed model is the combination with a mixing term between interdendritic and extradendritic melt, representing long-range solutal mixing by convection. The model can also be applied to predict equiaxed to columnar transition (ECT), i.e. the chill zone thickness. The model consists of modules such as nucleation, growth kinetics, solute and heat balance, and a solute mixing module. Nucleation is considered with a fixed nucleation undercooling. The growth kinetics of the dendrites are treated according to the LGK model. A finite difference scheme is employed for solving 1-Dimensional heat transfer equations and finally, volume averaged solute balance equations are solved in a staggered scheme. Mixing of inter- and extradendritic liquid is, as a first step, treated ideally fast. When applied to Fe-C binary system with the thermo-physical properties obtained from literature and CALPHAD simulations, the model successfully predicts recalescence, phase fraction evolution, and concentration profiles in different phases. Realistic boundary conditions of the continuous casting process are obtained from macroscopic FEM simulation.