Analysis of the symmetry of 3D silicon melts flow generated by a bitter traveling magnetic field in a cylindrical crucible

Abstract

Full 3D numerical simulation and experimental characterization of the topology and sensitivity of a magnetohydrodynamic flow pattern driven by a travelling magnetic field generated by a specifically designed cylindrical Bitter coil have been carried out. This Bitter coil has six windings composed of multiple circular copper plates and insulator separators disposed in a specific way for an optimum round circulation of electric currents, which are three-phase currents at a network frequency. For experimental characterization, experimental measurement data of radial components of the induced magnetic field (Br) at different z-positions were used without any liquid metal for different applied electric currents, and ultrasound Doppler velocimetry was employed to acquire the vertical velocity component along the beam axis in the centre and at different azimuthal positions for a fixed radial coordinate in the liquid GaInSn alloy. On the other hand, for numerical characterization, a numerical model has been developed using the Comsol MultiphysicsTM software to resolve the set of magnetohydrodynamic equations, fundamentally based on low frequency and low magnetic induction, and on an averaged expression of the Lorentz force. The results clearly show that the choice of 3D modelling and the Bitter coil design, which generates instabilities, can change significantly the usually expected axisymmetric torus-type magnetohydrodynamic flow topology and result in a distinct 3D flow configuration. Figs 8, Refs 16.