Experimental and numerical study of Rayleigh-Bénard convection affected by a rotating magnetic field

Abstract

In the present paper we experimentally study the effects of a rotating magnetic field (RMF) on the fluid flow in an electrically conducting melt (Gallium), kept in a cylindrical container heated from below (Rayleigh-Bénard configuration). The experimental data are compared to results obtained from three-dimensional, time-dependent numerical calculations. The paper presents the influence of the magnetic induction B, the frequency of the RMF Ω, and the temperature difference ΔT between the hot bottom and cold top of the melt on heat transport and fluid flow, respectively. The results can be summarized in terms of the parameter Nrot, which is defined as the ratio of magnetic Taylor number (∝B2⋅Ω) to Grashof number (∝ΔT). It is shown that for 0.003<Nrot<0.1 large-scale regular thermal waves exist, which travel azimuthally in the same direction as the rotation direction of the RMF. These thermal waves are connected with large-scale temperature fluctuations (amplitude 6%–10% of ΔT). The amplitude decreases with increasing Nrot, whereas the mean frequency increases from 0.001 Hz up to 0.1 Hz for 0.003<Nrot<0.1. For Nrot>0.1 temperature fluctuations with amplitudes smaller than 1%–2% of ΔT and frequencies greater than 0.1 Hz are observed. These oscillations can be attributed to Taylor vortices generated at the vertical cylinder walls. The regions of the different oscillation modes within the parameter space are shown in a stability diagram.

A brief history of defect formation, segregation, faceting, and twinning in melt-grown semiconductors

“…For instance it is well known that alternating magnetic fields can also help very effectively to damp convection and, hence, temperature oscillations also. This requires only a low magnetic field strength of some millitesla [61]. Rotating fields were first used by Hulme and Mullin [62] in 1959 to homogenise an InSb melt.…”

Exact analytical results for the thermosolutal MHD Marangoni boundary layers

“…Hainke et al [24] investigated the basic interactions between magnetic fields and natural and Marangoni convections for crystal growth and alloy solidification. The influence of steady magnetic fields [25][26][27] as well as of rotating magnetic fields [28][29][30][31] on the buoyant flow was analyzed intensively by using so-called convection cells filled with liquid Gallium to which different boundary conditions can be applied. In such systems, different studies can be made to select proper parameters of the magnetic field in which a beneficial effect on the crystal growth process can be expected.…”

The suppression of temperature fluctuations by a rotating magnetic field in a high aspect ratio Czochralski configuration

“…Still, the fluctuation suppression is observed over a wide range of parameters: From Gr % 2 Â 10 5 in Ref. [4] to Gr % 7 Â 10 7 in the current experiment.…”

“…A higher initial melt level, in turn, enables the growth of larger crystals in the same crucible. The stabilizing effect of an RMF has been studied so far in relatively small cylinders only [3][4][5][6]. Can this tendency be extrapolated to higher parameters characteristic for medium size Czochralski techniques?…”

“…This limits the initial melt depth since the thermo-gravitational instability depends mainly on the vertical scale [2]. Being itself turbulent, a sufficiently strong rotating magnetic field (RMF) driven flow is able to suppress significantly the amplitude of the buoyancy driven temperature fluctuations [3][4][5]. The mechanical rotation usually applied in Czochralski growth is also suppressing the thermo-gravitational instability [2].…”