Modeling equiaxed solidification with melt convection and grain sedimentation—I: Model description

Part I of this two part investigation presents a modified volume-averaged equiaxed solidification model which accounts for nucleation, globular grain growth, globular-to-dendritic transition, dendritic growth, formation of extra- and interdendritic eutectic, grain transport and melt convection, and their influence on microstructure and macrosegregation. Globular grain growth is governed by diffusion around a spherical grain. For the dendritic growth, a “natural” grain envelope smoothly enclosing the primary and secondary dendrite tips is assumed to separate the interdendritic melt from the extradendritic melt. The solid dendrites and interdendritic melt, confined in the “natural” grain envelope, combine to form a dendritic grain. Two “hydrodynamic” phases are considered: the extradendritic melt and the equiaxed grains; and three thermodynamic phase regions are distinguished: the solid dendrites, the interdendritic melt and the extradendritic melt. The velocities of the hydrodynamic phases are solved with a two-phase Eulerian approach, and transport of the mass and solute species of each thermodynamic phase region are considered individually. Growth kinetics for the grain envelope and the interdendritic melt solidification are implemented separately. Simplification of the grain dendritic morphology and treatment of the non-uniform solute distribution in the interdendritic melt region are detailed. Illustrative modeling results and model verification are presented in Part II.