Abstract
The results of a numerical investigation of the joint effect of crystal and crubicle rotation on the flow stability at low Prandtl numbers (Pr=0.01 to 0.07) are presented. The regimes with an elevated stability threshold are determined for various combinations of crystal and crubicle rotations and the heat flux distributions over the growing crystal endface are obtained. The mechanisms of the loss of stability, as the critical values of the Grashof number and the rotation velocities are exceeded, are considered and a new regime of stable nonaxisymmetric flow is established.
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V. Polezhaev, O. Bessonov, N. Nikitin, and S. Nikitin, “Convective Interactions and Instabilities in GaAs Czochralski Model,” J. Crystal Growth 230, 40 (2001).
N. V. Nikitin, S. A. Nikitin, and V. I. Polezhaev, “Convective Instabilities in the Hydrodynamic Czochralski Crystal Growth Model,” Usp. Mekh. 2 (4), 63 (2003).
A. A. Wheeler, “Four Test Problems for the Numerical Simulation of Flow in Czochralski Crystal Growth,” J. Crystal Growth 102, 691 (1991).
O. A. Bessonov and V. I. Polezhaev, “Modeling Three-Dimensional Supercritical Thermocapillary Flows in the Czochralski Model,” Izv. Vuzov. Sev. Kavkaz Region. Eststv. Nauki. Special Issue, 60 (2004).
O. A. Bessonov and V. I. Polezhaev, “Unsteady Nonaxisymmetric Flows in the Hydrodynamic Czochralski Model at High Prandtl Numbers,” Fluid Dynamics 46 (5), 684 (2011).
O. A. Bessonov and V. I. Polezhaev, “Instabilities of Thermal Gravitational Convection and Heat Transfer in the Czochralski Model at Different Prandtl Numbers,” Fluid Dynamics 48 (1), 23 (2013).
O. A. Bessonov and V. I. Polezhaev, “Regime Diagram and Three-Dimensional Effects in the Hydrodynamic Czochralski Model,” Fluid Dynamics 49 (2), 149 (2014).
O. A. Bessonov, “Convective Interaction and Flow Stability in the Czochralski Model in the Case of Crystal Rotation,” Fluid Dynamics 50 (1), 351 (2015).
P. Capper and D. Elwell, “Crubicle Rotation and Crystal Growth in the Czochralski Geometry,” J. Crystal Growth 30, 352 (1975).
K. Kakimoto, M. Watanabe, M. Eguchi, and T. Hibiya, “The Coriolis Force Effect on Molten Silicon Convection in a Rotating Crubicle,” Int. J. Heat Mass Transfer 35, 2551 (1992).
Y.-R. Li, Y. Akiyama, N. Imaishi, and T. Tsukada, “Global Analysis of a Small Czochralski Furnace with Rotating Crystal and Crubicle,” J. Crystal Growth 255, 81 (2003).
V. S. Berdnikov and V. A. Gaponov, “Mixed Convection in the Regimes of Differential Rotation of Crystal and Crubicle in the Czochralski Model,” in: Works of the 4th Russ. Nat. Conf. on Heat Transfer. Vol. 3 [in Russian], Moscow Energy Institute (2006), p. 71.
O. A. Bessonov, “An Effective Method for Calculating Incompressible Flows in Regions of Regular Geometry,” Russian Academy of Sciences, Institute for Problems in Mechanics, Preprint No. 1021 (2012)
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Original Russian Text © O.A. Bessonov, 2016, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2016, Vol. 51, No. 4, pp. 33–43.
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Bessonov, O.A. Effect of crystal and crubicle rotation on the flow stability in the Czochralski model at low Prandtl numbers. Fluid Dyn 51, 469–477 (2016). https://doi.org/10.1134/S0015462816040050
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DOI: https://doi.org/10.1134/S0015462816040050