A fast strategy for simulation of phase change phenomena at multiple length scales

Abstract

Solid–liquid phase change phenomena are commonly encountered in many material processing operations, such as, crystal growth, casting, welding, laser processing, metal joining and so on. The physics of solid–liquid phase transition is highly complex involving many phenomena at many spatial and temporal scales, such as, fluid flow, heat transfer, undercooling, nucleation, atomic attachment and so on. Modeling of phenomena at a particular scale needs an appropriate computational strategy to capture the physics. In this paper, we present a brief overview on the various strategies for mathematical modeling of transport phenomena during solidification at macroscopic, mesoscopic and microscopic levels. This is followed by an algorithmic representation of an appropriate multiscale simulation strategy for solid–liquid phase change. At the macroscopic level, a modified mixture continuum model has been adopted where the turbulence fields have been appropriately modeled for evolution of solidification and coupled with the mass, momentum, energy and species conservation fields. At mesocopic level, transport phenomena within a grain envelope has been modeled following Rappaz and Thevoz. At microscopic level, the grain density, nucleation rate and the solidification path has been modeled with the help of a Gaussian distribution function, following Rappaz and Thevoz. A novel concept of fractal measure of the dendritic microstructure has been introduced and improved correlations for dendritic arm spacing and the permeability of the porous dendritic network have been derived and successfully validated with data from published literature for directional solidification of various alloy systems. The algorithm is arguably easier and faster to implement than other algorithms for macro–micro coupling published in the literature. The implementation of various aspects of this algorithm to problems of alloy solidification will be discussed elsewhere.