First experimental results of applying the contactless inductive flow tomography to a thermally driven convection problem motivated by Czochralski crystal growth


First experimental results of applying the contactless inductive flow tomography to a thermally driven convection problem motivated by Czochralski crystal growth

Wondrak, T.; Pal, J.; Stefani, F.; Eckert, S.

In Czochralski crystal growth (CZ) the flow structure of the liquid silicon in the crucible and especially below the meniscus plays an important role for the quality of the grown crystal, because it controls the mass flow and the temperature gradient. A direct measurement of the flow would be highly desirable. However, the melt temperature of more than 1420°C, its corrosive impact on most materials, and the high demands on its purity, makes the flow measurement a complicated task. The contactless inductive flow tomography (CIFT) is able to reconstruct the approximate flow structure in conducting liquids [1]. Exposing the liquid to one or multiple applied magnetic fields and measuring the flow induced magnetic field around the fluid volume, it is possible to infer the velocity field by solving a linear inverse problem with appropriate regularization techniques. Great challenges for applying CIFT to the Cz process are, first, the small poloidal melt velocities in the order of a few cm/s and, second, the large distance between the liquid silicon and the magnetic field sensors which are located outside the puller. After having carried out successfully some preliminary magnetic field measurements at a real industrial Cz puller, we are presently evaluating the applicability of CIFT for small velocities.
A modified Rayleigh-Bénard (RB) setup has been chosen, which was already used to model and control temperature fluctuations in a Cz setup [2]. The growing crystal rod is simulated by a “cold finger” placed on the top of the cylindrical geometry. The diameter of the cold finger is about one third smaller than the heated bottom part. As working fluid GaInSn was used. Large efforts were made to adapt CIFT to the experimental setup in order to compensate thermal expansion during the measurement.
We will present preliminary results which demonstrate the applicability of CIFT on thermally driven convection systems. Typical features of the thermally driven turbulent flow were detected in the magnetic field measurements and were also verified by simultaneous temperature measurements recorded by small thermocouples placed in the vicinity of the rim of the cold finger.

References
1. F. Stefani, G. Gerbeth, T. Gundrum, Physical Review E, 70 (2004), 056306
2. A. Cramer, M. Röder, J. Pal, G. Gerbeth, Magnetohydrodynamics, 46 (2010), 353-361

  • Poster
    1st German Czechoslovak Conference on Crystal Growth - GCCCG-1, 16.-18.03.2016, Dresden, Deutschland

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Publ.-Id: 24646