Temperature and velocity analysis in vertical melt cylinders
under the influence of rotating magnetic fields and buoyant convection

B. Fischer, U. Hilburger, J. Friedrich^* and G.Müller

Crystal Growth Lab, Dept. of Material Science WW6, University of Erlangen-Nürnberg,
Martensstr. 7, D-91058 Erlangen, Germany
^* Crystal Growth Lab, Fraunhofer Institute IIS-B, Schottkystraße 10, D-91058 Erlangen, Germany

Rotating magnetic fields (RMFs) offer an efficient possibility to control the convective heat and mass transport in electrically conducting fluids, in metallurgy as well as in the field of semiconductor crystal growth. In this study we report on the influence of the magnetic induction and frequency of a RMF on the flow in cylindrical Rayleigh-Benard configurations for various system parameters (thermal boundary conditions, aspect ratio). Both experiments and numerical simulations were carried out.

Cylindrical test cells with diameter D = 34 mm and different heights H or aspect ratios H/D = 0.5, 1.0, 2.0, respectively, are completely filled with liquid gallium (melting point at 30 °C). The test cells consist of a plexiglas tube as the vertical cylinder wall. Copper plates on top and bottom of the cylinder (each connected to a thermostat water circuit) are establishing the thermal boundary conditions, in the case of this study a type of Rayleigh-Benard temperature profile with hot bottom and cold top. NTC temperature sensors are fixed at various positions in the vertical cylinder wall, reaching about 4 mm into the melt. A series of three sensors at the same height (H and H, respectively), which are azimuthally separated by 90°, allows to determine the azimuthal phase shift of the recorded temperature signals. The RMF is generated by a 3-phase stator (number of pole pairs p = 2) with an inner diameter of 16 cm and a height of 17 cm, where the test cells are centered coaxially.

The behaviour of the flow is analysed by using the frequency, amplitude and phase shift of the time-dependent temperature signals at the different positions near the cylinder wall. The chosen parameters are: temperature difference D T = 2, 5, 10, 20 K, frequency W /2p =7.5, 25, 50, 100 Hz, and the magnetic induction was varied from 0 to 10 mT. In addition to the experiments we carried out three-dimensional time-dependent numerical simulations. The combined results of experiments and simulations give a clear picture of the flow regimes, flow patterns, velocities, rotation frequencies, and time-dependent behaviour.We find hybrid flow patterns which are significantly influenced by both buoyancy and RMF with different wave numbers, preceeding in the same azimuthal direction as the RMF. For dominating RMF a nearly axisymmetric rotational motion of the fluid with flattened isotherms results in an axial heat transport similar to the case of pure diffusion.

This study is supported by the german space agency, DLR, contract 50WM9455.