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 B and an electrical current I, giving rise to an electromagnetic force has a significant melt stirring effect, even for small values of I and B. 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 I and B 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 I and B and a characteristic crucible length. The same conclusions would hold for a silicon melt if the dimensionless numbers are conserved by choosing different I and B in respect with the different material constants. (C) 2015 Elsevier Masson SAS. All rights reserved.