Numerical modeling of a benchmark experiment on equiaxed solidification of a Sn–Pb alloy with electromagnetic stirring and natural convection

Abstract

A three-phase volume averaged equiaxed model is applied to simulation of an experiment on solidification of the binary alloy Sn-10 wt.% Pb subjected to the electromagnetic stirring. The experiment, whose description was published earlier, was performed in a parallelepiped cavity under controlled cooling conditions and with real-time two-dimensional temperature measurement over a lateral surface of the cavity co-planar with direction of solidification. Applied numerical model treats motion of the liquid and equiaxed grains whose growth kinetics is taken into account and uses a double time step scheme to accelerate solution. Growth of columnar dendrite is not considered. It is shown that electromagnetic force acting in a direction opposite to the natural convection flow creates moderately turbulent flow in pure liquid which is treated with a realizable kε−ε model. It is demonstrated that calculated temperature distribution in the cavity well reproduces temperature maps reconstructed from thermocouples measurements throughout the experiment. Final macrosegregation map and distribution of density grain number are qualitatively similar to those obtained in the experiment. Variation of intensity of electromagnetic stirring in numerical model shows that this affects shape and localization of positive segregation region at the bottom of the cavity.