Numerical and experimental modelling of the melt flow in a travelling magnetic field for Vertical Gradient Freeze crystal growth

A traveling magnetic field (TMF) driven convection and its transition from a laminar to a time-dependent flow is studied by means of ultrasonic Doppler velocimetry and numerical simulations.
The experimental setup comprises a cylindrical cavity containing the electrically conducting model fluid GaInSn and a system of six equidistant coils, which are fed by an out-of-phase current to create an up- or downward directed TMF. Hence, a Lorentz force is induced in the melt which leads to meridional flow patterns. For numerical simulations commercial codes (Opera/Fidap) and a spectral code are used. The characteristic parameters of the magnetohydrodynamic model system are chosen close to the conditions used for Vertical Gradient Freeze (VGF) crystal growth.
The axisymmetric basic flow and its dependence on the dimensionless shielding parameter S are examined. It is shown that, for S>10, the flow velocity decreases significantly, whereas almost no influence is found for a smaller shielding parameter. The critical Reynolds number for the onset of instability is found in the range of 300-450. Good agreement between experimental results and the numerical simulations is achieved.