Chemical non-equilibrium modelling of columnar solidification

Abstract

This paper deals with the macroscopic modeling and numerical simulation of columnar dendritic solidification of binary alloys. The macroscopic governing equations and associated effective transport properties were previously derived using a volume averaging technique with local closure. The macroscopic model takes into account the spatial variation of the pore-scale geometry within the mushy zone, which leads to additional terms involving porosity gradients. The second important feature concerns solute mass conservation, which is described by considering a macro-scale non-equilibrium accounting for chemical exchanges at the solid–liquid interface. A simplified version of the model is validated through a comparison of the numerical solution to three experiments available in the literature. Porosity extra terms are systematically estimated on the basis of these numerical simulations, and the influence on solidification of effective transport properties such as permeability and interfacial solute exchange coefficients is investigated.