A fully implicit method for diffusion-controlled solidification of binary alloys

Abstract

A recently developed numerical method for single-component phase-change problems is extended to treat some existing multi-domain models for diffusion-controlled solidification of binary alloys. The multi-domain models invoke a special difficulty associated with the unknown interface location and phase-transition temperature. Such a difficulty is efficiently resolved here by defining corrections similar to those used in single-phase convection problems. The field equations and the interfacial conditions are treated fully implicitly through the correction equations that are developed from the conservation of the interfacial fluxes. In addition, when a high disparity occurs between thermal and solutal mass diffusivities, renormalization of the length scales is suggested to improve spatial resolution of both the temperature and concentration fields. As a verification, several diffusion models that allow for analytical solutions are considered. Numerical solutions agree well with the available analytical solutions. The widely used assumption of a constant latent heat is found to be thermodynamically inconsistent under certain conditions and is clarified and corrected. A unique iteration procedure suggested in this study proves to be remarkably efficient and leads to fast convergence.