A truncated-Scheil-type model for columnar solidification of binary alloys in the presence of melt convection

Abstract

A two-phase truncated-Scheil-type model is developed for columnar solidification of binary alloys in the presence of melt convection and liquid undercooling ahead of the primary dendrite tips. The model is derived from a three-phase model, which takes into account liquid undercooling ahead and behind the primary tips. These models are used to simulate a numerical solidification benchmark problem, and their predictions are compared with those of a Scheil-type model that disregards liquid undercooling and solute diffusion in solid. Simulation results reveal that the predictions of the truncated-Scheil-type and three-phase models are nearly identical, indicating that undercooling behind the primary tips can be disregarded and the truncated-Scheil-type model can replace the significantly more complex three-phase model. The truncated-Scheil-type and three-phase models smoothly recover the Scheil-type model as the value of the dendrite tip selection parameter is increased. Taking into account liquid undercooling changes the melt convection pattern around the columnar front and the form of channel segregates but does not change the overall macrosegregation pattern.