Consistent description of phase-change processes in substances with density contrast: a finite volume based approach

Abstract

Phase-change is an important phenomenon and usually it causes a concomitant change in the density of the underlying materials. As applications of phase-change grow, it is important to develop numerical tools that can model this phase-change behaviour accurately; many efforts have improved the ability of numerical algorithms to do so; however, with materials in which phase-change causes significant change in density, these approaches are inadequate in predicting the phase-change interface or the temperature profiles during this process. To address these limitations, we present a "moving mesh" method that explicitly accounts for volumetric expansion during the melting (or, evaporation) process by introducing liquidus or vapour cells at appropriate locations adjacent to the interface. This moving mesh approach is used in conjunction with the apparent heat capacity method implemented through a finite volume scheme to represent the one-dimensional propagation of the melting (or, vapour) front during heating. This new algorithm has been validated for the Stefan's analytical solution, in addition to verifying the conservation of energy principle. We subsequently use our approach to investigate phase-change phenomena for a host of materials with a large gamut of density contrasts between the various phases, and compare the results to those obtained using a fixed-grid approach. The moving mesh method forecasts an early commencement of melting (or, evaporation) at a given position, a comparatively rapid movement of the front, and a larger volume fraction of the molten (or, vapour) phase, for substances that expand upon phase change, while the opposite is observed for the melting of ice, considered as a special case in this study. We hope that the proposed scheme will be adopted in addressing phase-change problems involving significant density contrasts.