Numerical and experimental modeling of melt flow in a directional solidification configuration under the combined influence of electrical current and magnetic field

One of the key issues in the directional solidification (DS) process of multi-crystalline silicon is the control of the melt flow in order to achieve a higher quality of the crystallized material. The combination of a static magnetic field BB and an electrical current II, giving rise to an electromagnetic force has a significant melt stirring effect, even for small values of II and BB. In order to understand the basic features of the melt flow in a DS-like configuration under electromagnetic stirring, an isothermal model experiment in a rectangular crucible filled with a room temperature GaInSn melt and a corresponding STHAMAS3D time-dependent numerical model, were developed. Experimental velocity profiles measured by UDV confirmed the flow structure obtained in the numerical simulations. A parametrical study for a range of II and BB values was performed, in the case of a symmetrical electrode positioning along the diagonal of the free melt surface. The resulting flow structure was analyzed and described in terms of a vortex or a poloidal recirculation domination and a transition between the two. A characteristic parameter was defined to quantify the different flow structures. Through the use of scaling analysis, two dimensionless numbers corresponding to the two Lorentz force components were identified and a good correlation between their values, flow structure and maximal velocity was observed. This correlation makes possible the prediction of the flow structure for any set of the system parameters II and BB and a characteristic crucible length. The same conclusions would hold for a silicon melt if the dimensionless numbers are conserved by choosing different II and BB in respect with the different material constants.