The two-domain model of solute transport in binary alloy

Abstract

A mixed model for micro-macroscopic computer simulation of binary alloy solidification is proposed. It involves a two-domain approach to solute conservation equations in the liquid and solid phases, whereas transport of momentum and energy in the two-phase region is modelled using the phase mixture theory. To distinguish regions of columnar and equiaxed crystal structures evolving in a cast during solidification, the special front tracking technique on non-structural triangular grids is included in the model. In this two-domain approach, solute conservation equations are averaged across solid and liquid phases, and the solute transport at the phase interface is included. Additionally, the microstructure evolution is modelled to capture the development of various complex grain structures and more accurately describe the solute transport between the phases. The accuracy of the proposed model is first verified by a grid refinement analysis, and then the model is used to predict the solute concentration and macro-segregation in the example problem of Pb-48%wt Sn alloy solidification in a 2D mould. The results obtained are next compared with the relevant ones predicted by the fully single-domain model, earlier developed by authors. Thus, the role of finite diffusion in liquid and solid phases is identified and discussed.