Computations of phase change.

Abstract

A computational methodology based on a front tracking/finite difference method is developed for the direct simulation of two-dimensional, time-dependent; phase change processes involving: (1) pure material solidification, (2) alloy solidification and (3) liquid-vapor phase change with fluid flow. The method is general in the sense that large interface deformations, topology change, latent heat, interfacial anisotropy and discontinuities in material properties between the phases are directly incorporated into the problem formulation and solution technique. For simulations of solidification of pure materials the accuracy of the front tracking method is verified through comparison with exact solutions. Convergence under grid refinement is demonstrated for unstable solidification problems. Experimentally observed complex dendritic structures such as liquid trapping, tip-splitting, side branching and coarsening are reproduced. It is also shown that a small increase in the liquid to solid volumetric heat capacity ratio markedly increases the solid growth rate and interface instability. For the directional solidification of binary alloys, the coupled solute and energy equations are considered. Convergence under grid refinement is demonstrated and results for the growth of instabilities is shown to be in close agreement with a linear stability analysis. During the transient development of cellular and dendritic structures realistic phenomena such as liquid trapping, coarsening and droplet detachment from deep cellular grooves are observed. These simulations also predict a variety of microstructural solute segregation patterns such as necking, coring and banding. For liquid-vapor phase change with fluid flow the coupled Navier-Stokes and energy equations with interphase mass transfer are solved. The method is validated through comparison with an exact one-dimensional solution and by grid resolution studies. In film boiling a vapor layer-adjacent to a heated surface undergoes a Rayleigh-Taylor instability with vaporization at the interface. Pinch off of a vapor bubble causes hot vapor from regions near the wall to be convected upward in the rising bubble. Heat transfer results are compared with a correlation of experimental data. Simulations of the rapid evaporation of a highly superheated liquid under microgravity conditions demonstrate the energetic growth of instabilities from planar and circular interfaces. The formation of highly convoluted interfaces leads to enhanced evaporation and explosive growth.