A Front-Tracking Method for Three-Phase Computations of Solidification with Volume Change

抄録

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.