Effects of Solutal Undercooling on Three-Dimensional Double-Diffusive Convection and Macrosegregation during Solidification of a Binary Alloy

A three-dimensional transient numerical model is developed for simulation of double-diffusive convection duping binary alloy solidification processes, taking into account nonequilibrium effects due to solutal undercooling. Such an effect arising from microscopic convection near the diffusion boundary layer adjacent to the mushy region is captured by devising a macroscopic model based on a fixed-grid, enthalpy-based, control-volume approach. Microscopic features pertaining to solutal undercooling are incorporated through a modification of the partition coefficient by means of a number of macroscopically observable parameters. Numerical simulations are performed for solidification of a metallic alloy system kept in a side-cooled cubic enclosure. Typical curvatures of the streamlines and their nonequidistant characteristics, as projected on various cross-sectional planes, show an element of three-dimensionality in the double-diffusive convection (originating from the solidification process itself) and its interaction with the progressing solidification front. The three-dimensional transport leads to a global macrosegregation, with significant composition variations across the longitudinal planes, as dictated by the modified partition coefficient and thermosolutal convection mechanisms