USING A FIVE-PHASE VOLUME AVERAGING APPROACH TO MODEL THE MIXED COLUMNAR-EQUIAXED SOLIDIFICATION

A previous mixed columnar-equiaxed solidification model, developed by the current authors, is extended to include the dendritic morphology. Five phase regions (phases) must be considered: the interdendritic melt and solid dendrites in equiaxed grains, the interdendritic melt and solid dendrites in columnar dendrite trunks, the extra melt. The five phase regions are quantified by their volume fractions, and characterized by different solute concentrations. They are transported with the velocities of the so-called ‘hydrodynamic’ phases. Here three ‘hydrodynamic’ phases are distinguished: the extra melt, the equiaxed grains combining the interdendritic melt and solid dendrites, and the columnar trunks combining the interdendritic melt and solid dendrites. The shape of the grain/trunk envelopes, separating the extra melt from the interdendritic melts, are described with the morphological parameters. Evolutions of the envelopes are derived from the growth kinetics: Kurz-Giovanola-Trivedi model for the columnar primary dendrite tips, Lipton-Glicksman-Kurz model for the columnar trunks (radial direction) and the equiaxed dendrites. The solidification of the interdendritic melt is governed by the diffusion in the interdendritic melt region.