Skip to main content
Log in

Instabilities of thermal gravitational convection and heat transfer in the Czochralski model at different Prandtl numbers

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The results of the calculations of critical Grash of numbers, at which flowfield and temperature fluctuations originate in the axisymmetric and three-dimensional models of crystal growth by pulling from a melt, are presented. The salient features of the convection and heat transfer structure in the zones of stabilization and changeover of dangerous modes are studied over a wide Prandtl number range under different boundary conditions on the melt surface and compared with the experimental data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. G.Z. Gershuni and E.M. Zhukhovitskii, “Mechanisms of Instability of Plane-Parallel Convective Flows,” in: L.I. Sedov et al. (eds.) Mechanics and Progress in Science and Engineering. Vol. 2, Fluid Mechanics [in Russian], Nauka, Moscow (1987), p. 211.

    Google Scholar 

  2. “Thermal Convection Instabilities Relevant to Crystal Growth from Liquids,” in: W.R. Wilcox and R.A. Lefever(eds.), Preparation and Properties of Solid State Materials. Vol. 3, Marcel Dekker, New York & Basel (1977), p. 1.

  3. J.R. Ristorcelli and J.L. Lumley, “Instabilities, Transition and Turbulence in the Czochralski Crystal Melt,” J. Crystal Growth 116, 447 (1992).

    Article  ADS  Google Scholar 

  4. H.J. Scheel, “Theoretical and Experimental Solutions of the Striation Problem,” in: H.J. Scheel and T. Fukuda (eds.), Crystal Growth Technology,Wiley, New York (2004), p. 69.

    Google Scholar 

  5. N.V. Nikitin and V.I. Polezhaev, “Three-Dimensional Convective Instability and Temperature Oscillations in Czochralski Crystal Growth,” Fluid Dynamics 34(3), 322 (1999).

    MATH  Google Scholar 

  6. N.V. Nikitin and V.I. Polezhaev, “Three-Dimensional Effects in Transitional and Turbulent Czochralski Thermal Convection Regimes,” Fluid Dynamics 34(6), 843 (1999).

    MATH  Google Scholar 

  7. V.I. Polezhaev, “Modeling of Technologically Important Hydrodynamics and Heat/Mass Transfer Processes during Crystal Growth,” in: H.J. Scheel and T. Fukuda (eds.), Crystal Growth Technology,Wiley, New York (2004), p. 155.

    Google Scholar 

  8. N.V. Nikitin, S.A. Nikitin, and V.I. Polezhaev, “Convective Instabilities in the Hydrodynamic Model of the Czochralski Crystal Growth,” Usp. Mekh. 2(4), 63 (2003).

    Google Scholar 

  9. Z. Zeng, J. Chen, H. Mizuseki, et al., “Three-Dimensional Oscillatory Convection of LiCaAlF6 Melt in Czochralski Crystal Growth,” J. Crystal Growth 252, 538 (2003).

    Article  ADS  Google Scholar 

  10. 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).

    Article  Google Scholar 

  11. V.I. Polezhaev, N.V. Nikitin, S.A. Nikitin, and M.N. Myakshina, “Convective Instabilities in the Hydrodynamic Czochralski Model,” Russian Academy of Sciences, Institute for Problems in Mechanics, Preprint No. 809 (2006), p. 40.

  12. V.I. Polezhaev and S.A. Nikitin, “Distinctive Features of Heat Transfer on Free Convective Interactions in Enclosures. Engineering and Technological Applications,” in: Problems of Gas Dynamics and Heat and Mass Transfer in Aerospace Technologies. Vol. 2 [in Russian], Moscow Energy Inst., Moscow (2009), p. 15.

    Google Scholar 

  13. V.I. Polezhaev, S.A. Nikitin, and M.N. Myakshina, “Heat Transfer and Temperature Stratification under Free Convective Interactions in Enclosures,” in: Proc. 5th Russian National Conf. on Heat Transfer. Vol. 2 [in Russian], Moscow Energy Inst., Moscow (2010), p. 55.

    Google Scholar 

  14. V.I. Polezhaev and S.A. Nikitin, “Interaction of the Basic Mechanisms of Buoyancy-Driven Convection: Fundamentals, Technical and Material Sciences Applications,” Int. J. Transport Phenomena 12, 113 (2011).

    Google Scholar 

  15. V.I. Polezhaev, M.N. Myakshina, and S.A. Nikitin, “Heat Transfer Due to Buoyancy-Driven Convection in Enclosures: Fundamentals and Applications,” Int. J. Heat Mass Transfer, 55, 156 (2012).

    Article  Google Scholar 

  16. 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).

    Article  ADS  MATH  Google Scholar 

  17. 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).

    Article  ADS  Google Scholar 

  18. O. Bessonov, “OpenMP Parallelization of a CFD Code for Multicore Computers: Analysis and Comparison,” in: Parallel Computing Technologies. Proc. 11th Int. Conf. — PaCT-2011. Vol. 6873 (2011), p. 13

  19. V.S. Berdnikov, V.A. Vinokurov, V.V. Vinokurov, and V.A. Gaponov, “Heat Transfer in the Regimes of Thermal Gravitational-Capillary Convection in the Czochralski Method Version with a Fixed Crubicle,” in: Proc. 4th Russian National Conf. on Heat Transfer. Vol. 3 [in Russian], Moscow Energy Inst., Moscow (2006), p. 63.

    Google Scholar 

  20. O.A. Bessonov and V.I. Polezhaev, “Modeling Three-Dimensional Supercritical Thermocapillary Flows in the Czochralski Method,” Izv. Vuzov Sev.-Kavkaz. Region. Est. Nauki. Special Issue Mathematics and Continuum Mechanics p. 60 (2004).

  21. A.D.W. Jones, “The Temperature Field of a Model Czochralski Melt,” J. Crystal Growth 69, 165 (1984).

    Article  ADS  Google Scholar 

  22. A.D.W. Jones, “Spoke Patterns,” J. Crystal Growth 63, 70 (1983).

    Article  ADS  Google Scholar 

  23. O.A. Bessonov, V.G. Kosushkin, S.A. Nikitin, N.V. Nikitin, and V.I. Polezhaev, “Convective Instability and Terrestrial Alternatives to Microgravitation in GaAs Crystal Growth Using the Czochralski Method,” in: Proc. 7th Russian Workshop ‘Weightlessness Mechanics. Results and Prospects of Fundamental Research of Gravitationally Sensitive Systems’ [in Russian], Russian Academy of Sciences, Institute for Problems in Mechanics, Moscow (2001), p. 404.

    Google Scholar 

Download references

Authors

Additional information

Original Russian Text © O. A. Bessonov and V. I. Polezhaev, 2013, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2013, Vol. 48, No. 1, pp. 26–40.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bessonov, O.A., Polezhaev, V.I. Instabilities of thermal gravitational convection and heat transfer in the Czochralski model at different Prandtl numbers. Fluid Dyn 48, 23–35 (2013). https://doi.org/10.1134/S0015462813010043

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462813010043

Keywords

Navigation