Advertisement

Fluid Dynamics

, Volume 50, Issue 3, pp 351–360 | Cite as

Convective interactions and flow stability in the czochralskimodel in the case of crystal rotation

  • O. A. Bessonov
Article

Abstract

The results of a numerical investigation of the crystal rotation effect on the flow stability are presented on a wide Prandtl number (Pr) range. For low Pr the regimes with an elevated stability threshold are determined and the mechanisms of the loss of stability, as the critical values of the Grashof number (Gr) and the rotation velocity are exceeded, are considered. For medium and high Pr the tables of flow regimes are given, the special features of stable nonaxisymmetric helical flows are considered, and the zones of partial flow stabilization are established.

Keywords

thermal gravitational convection crystal growth from a melt hydrodynamic Czochralski model numerical modeling convective stability convective interactions stabilization of oscillations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    N.V. Nikitin, S.A. Nikitin, and V.I. Polezhaev, “Convective Instabilities in the Hydrodynamic Czochralski Model of Crystal Growth,” Usp. Mekh. 2(4), 63 (2003).Google Scholar
  2. 2.
    A.A. Wheeler, “Four Test Problems for the Numerical Simulation of Flowin Czochralski Crystal Growth,” J. Crystal Growth 102, 691 (1991).ADSCrossRefGoogle Scholar
  3. 3.
    N. Crnogorac, H. Wilke, K.A. Cliffe, A.Yu. Gelfgat, and E. Kit, “Numerical Modelling of Instability and Supercritical Oscillatory States in a Czochralski Model System of Oxide Melts,” Cryst. Res. Technol. 43, 606 (2008).CrossRefGoogle Scholar
  4. 4.
    P. Hintz and D. Schwabe, “Convection in a Czochralski Crubicle-Part 2: Rotating Crystal,” J. Crystal Growth 222, 356 (2001).ADSCrossRefGoogle Scholar
  5. 5.
    M. Teitel, D. Schwabe, and A.Yu. Gelfgat, “Experimental and Computational Study of Flow Instabilities in a Model of Czochralski Growth,” J. Crystal Growth 310, 1343 (2008).ADSCrossRefGoogle Scholar
  6. 6.
    V.S. Bernikov, V.A. Vinokurov, V.V. Vinokurov, and V.A. Gaponov, “Mixed Convection in the Czochralski Method with a Fixed Crubicle,” in: Proc. 4th Russian Nat. Conf. Heat Transfer. Vol. 3 [in Russian], Moscow Energy Institute (2006), p. 76.Google Scholar
  7. 7.
    V. Polezhaev, O. Bessonov, N. Nikitin, and S. Nikitin, “Convective Interactions and Instabilities in GaAs Czochralski Model,” J. Crystal Growth 230, 40 (2001).ADSCrossRefGoogle Scholar
  8. 8.
    O.A. Bessonov and V.I. Polezhaev, “Modeling of Three-Dimensional Supercritical Thermocapillary Flows in the Czochralski Method,” Izv. Vuzov Sev.-Kavkaz. Region. Estestv. Nauki. Special Issue’ Mathematics and Continuum Mechanics’ p. 60 (2004).Google Scholar
  9. 9.
    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).zbMATHADSCrossRefGoogle Scholar
  10. 10.
    O.A. Bessonov and V.I. Polezhaev, “Instabilities of Thermal Gravitational Convection and Heat Transfer in the Hydrodynamic Czochralski Model at Different Prandtl Numbers,” Fluid Dynamics 48(1), 23 (2013).zbMATHADSCrossRefGoogle Scholar
  11. 11.
    O.A. Bessonov and V.I. Polezhaev, “Regime Diagram and Three-Dimensional Effects of Convective Interactions in the Hydrodynamic Czochralski Model,” Fluid Dynamics 49(2), 149 (2014).zbMATHCrossRefGoogle Scholar
  12. 12.
    Z. Zeng, J. Chen, H. Mizuseki, K. Shimamura, T. Fukuda, and Y. Kawazoe, “Three-Dimensional Oscillatory Convection of LiCaAlF6 Melts in Czochralski Crystal Growth,” J. Crystal Growth 252, 538 (2003).ADSCrossRefGoogle Scholar
  13. 13.
    A.Yu. Gelfgat, “Numerical Study of Three-Dimensional Instabilities of Czochralski Melt Flow Driven by Buoyancy Convection, Thermocapillarity and Rotation, ” in: A.Yu. Gelfgat (ed.), Studies on Flow Instabilities in Bulk Crystal Growth. 37/661(2) (2007), p. 1.Google Scholar
  14. 14.
    O.A. Bessonov, “Effective Method for Calculating Incompressible Flows in Regions of Regular Geometry,” Russian Academy of Sciences, Institute for Problems in Mechanics, Preprint No. 1021 (2012).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Ishlinsky Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia

Personalised recommendations