Numerical Study of Convection in the Directional Solidification of a Binary Alloy Driven by the Combined Action of Buoyancy, Surface Tension, and Electromagnetic Forces

Directional solidification of a dilute electrically conducting binary alloy driven by the combined action of buoyancy, surface-tension, and electromagnetic forces is considered. A numerical methodology using a moving finite element technique is proposed for the simulation of the above phase change process. The melt is modeled as a Boussinesq fluid and the transient Navier–Stokes equations are solved simultaneously with the transient heat and solute transport equations. The location of the advancing solid–liquid interface is numerically determined using an energy preserving weak form of the Stefan condition. The standard SUPG/PSPG method for the simulation of incompressible fluid flow is here extended to flows driven by the combination of buoyancy, surface tension, and electromagnetic forces. A reference problem of directional solidification of a dilute germanium alloy in a horizontal open-boat configuration is considered. The relative influence of thermocapillary convection and buoyancy-driven convection on the solidification process is investigated by varying the Bond number. Thermocapillary convection is shown to have a significant influence on various solidification parameters, such as the shape of the solid–liquid interface and the solute segregation, especially under low gravity conditions. The influence of an external magnetic field on the reference solidification problem is investigated both in a normal and a reduced gravity environment. It is demonstrated that the application of an appropriate strong magnetic field significantly damps the melt flow and improves the solute segregation pattern. The relative influence of an external magnetic field on the solidification process is also studied by independently varying the orientation and magnitude of the applied magnetic field.