A continuum grain attachment model for simulations of equiaxed solidification

Numerical models of equiaxed solidification must consider the effect of free-floating solid grains and their eventual coalescence on the fluid flow and macrosegregation development during processing. Previous models based on a mixture formulation of the governing equations assume that each cell within the computational domain consists of either fully unattached or fully rigid grains. This approach, however, has been found to misrepresent the geometry of the interface between these two regions by forcing it to fall on the boundaries between numerical cells, the effect of which dramatically alters the fluid flow and solute advection during solidification, producing unwanted numerical artifacts. The present study proposes a new continuum model for grain attachment in which cells may be partially rigid. The core of the new model is the introduction of a weighting function that controls the relative magnitude of the appropriate source terms in the momentum conservation equations and a modification of Stokes’ law to account for the flow rate of solid particles in cells that contain both free-floating and rigid solid. A power law form of the weighting function was assumed and a parametric study on the effect of the weighting exponent and the range of solid fraction over which the model is applied was performed. The continuum grain attachment model is shown to effectively suppress the appearance of compositional instabilities and produce a smooth composition field.