Computational modeling of phase fronts, free surfaces and convective heat transfer during solidification processing

A methodology has been developed to simulate fluid flow, heat transfer, free surface, and phase change dynamics in the context of solidification processing. Special attention has been given to float zone processing of single crystals due to its increasing technological importance in growing high quality single crystals and due to the complex physical phenomena involved--free surface flow, thermocapillary and buoyancy driven convection, phase change and the nonlinear coupling amongst these physical phenomena. The SIMPLE algorithm in body fitted coordinates has been chosen for fluid flow and heat transfer computations. Issues of accuracy and implementation of convection schemes have been addressed in the context of buoyancy driven convection. Accurate simulations of transient natural convection around an enclosed vertical channel have been conducted since it is an important heat transfer mechanism in solidification as well as a host of other applications such as electronics cooling. The issues of existence, multiplicity and non-uniqueness of float zone menisci have been dealt with in the context of a free energy minimization principle. Steady, thermocapillary convection has been simulated in a liquid bridge which yields useful information on heat transfer characteristics in a float zone configuration. Both single phase flows and flows with phase change have been computed in this study. Alternative formulations of enthalpy porosity models have been developed and assessed for the computation of phase change dynamics in the presence of melt convection. These methods have been applied to compute and assess the impact of interacting natural and thermocapillary convection on solid-liquid interfaces during float zone growth. A moving boundary algorithm has been developed to simulate the nonlinear coupling between the unknown shape and location of the free surface, the unknown shape and location of the solid-liquid interfaces, and the convective heat transfer processes in the float zone. This computational model has also been applied to assess the impact of both, normal gravity as well as microgravity conditions, on the dynamics within the float zone. It has been found that whereas buoyancy induced convection is negligible under microgravity conditions, significant levels of thermocapillary convection exist and have a profound impact on the solid-liquid interface morphology at the macroscopic scales. It has also been found that under normal gravity conditions, the counteracting effect of natural and thermocapillary convection can actually result in reduced convection strength in the lower half of the zone and lead to a flatter solid-liquid interface shape. The calculation procedures developed in this study constitute a predictive capability for float zone single crystal growth.