A front-tracking method for three-phase computations of solidification with volume change

Abstract

We use a front-tracking method to simulate solidification with volume change of a droplet on a fixed cooling plate. The problem includes temporal evolution of three interfaces, i.e., solid-liquid, solid-air, and liquid-air, that are explicitly tracked under the assumption of axisymmetry. The solid-liquid interface is propagated with a normal velocity that is calculated from the normal temperature gradient across the front and the latent heat. The liquid-air front is advected by the velocity interpolated from nearest bulk fluid flow velocities. Accordingly, the evolution of the solid-air front is simply the temporal imprint of the triple point at which simple and straightforward conditions are imposed. The governing Navier-Stokes equations are solved for the whole domain, setting the velocities in the solid phase to zero and with the non-slip condition on the solid-liquid interface. Computational results are compared with exact solutions for two-dimensional Stefan problems and with corresponding experimental results, and show good agreement. © 2013 The Society of Chemical Engineers, Japan.