Skip to main content
SpringerLink
Log in

Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field

  • Original Article
  • Published:
Theoretical and Computational Fluid Dynamics Aims and scope Submit manuscript

Abstract

A unified view on the interfacial instability in a model of aluminium reduction cells in the presence of a uniform, vertical, background magnetic field is presented. The classification of instability modes is based on the asymptotic theory for high values of parameter β, which characterises the ratio of the Lorentz force based on the disturbance current, and gravity. It is shown that the spectrum of the travelling waves consists of two parts independent of the horizontal cross-section of the cell: highly unstable wall modes and stable or weakly unstable centre, or Sele’s modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Sele’s modes are characterised by a distributed disturbance over the whole horizontal extent of the cell. As β increases these modes are stabilized by the field.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Sele T.: Instabilities of the metal surface in electrolytic aluminium reduction cells. Metall. Trans. B 8, 613–618 (1977)

    Article  Google Scholar 

  2. Gerbeau J.-F., Le Bris C., Lelievre T.: Mathematical Methods for the Magnetohydrodynamics of Liquid Metals. Oxford University Press, New York (2006)

    MATH  Google Scholar 

  3. Davidson P.A.: Overcoming instabilities in aluminium reduction cells: a route to cheaper aluminium. Mater. Sci. Technol. 16, 475–479 (2000)

    Google Scholar 

  4. Lukyanov, A., El, G., Molokov, S.: Stabilisation of the liquid metal–electrolyte systems. Int. Patent Application No. PCT/GB2003/00072 (2003)

  5. Urata, N.: Magnetics and metal pad instability. Light Metals, 581–591 (1985)

  6. Sneyd A.D., Wang A.: Interfacial instability due to MHD mode coupling in aluminium reduction cells. J. Fluid Mech. 236, 111–126 (1994)

    Article  Google Scholar 

  7. Bojarevics V., Romerio M.V.: Long wave instability of liquid metal-electrolyte interface in aluminium reduction cells: a generalisation of Sele’s criterion. Eur. J. Mech. B 13, 33–56 (1994)

    MathSciNet  MATH  Google Scholar 

  8. Bojarevics V.: Nonlinear waves with electromagnetic injection in aluminium electrolysis cells. Prog. Astronaut. Aeronaut. 182, 833–848 (1998)

    Google Scholar 

  9. Droste, Ch., Segatz, M., Vogelsang, D.: Improved 2-dimensional model for magnetohydrodynamic stability analysis in reduction cells. Light Metals, 419–428 (1998)

  10. Davidson P.A., Lindsay R.L.: Stability of interfacial waves in aluminium reduction cells. J. Fluid Mech. 362, 273–295 (1998)

    Article  MATH  Google Scholar 

  11. Zikanov, O., Thess, A., Davidson, P.A., Ziegler, D.P.: Nonlinear shallow water model of the interfacial instability in aluminium reduction cells. In: Proceedings of 3rd International Symposium on Electromagnetic Processing of Materials, Nagoya, Japan, 2000, pp. 109–114 (2000)

  12. Lukyanov A., El G., Molokov S.: Instability of MHD-modified interfacial waves revisited. Phys. Lett. A 290, 165–172 (2001)

    Article  MATH  Google Scholar 

  13. Morris S.J.S., Davidson P.A.: Hydromagnetic edge waves and instability in reduction cells. J. Fluid Mech. 493, 121–130 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Molokov, S., El, G., Lukyanov, A.: On the nature of interfacial instability in aluminium reduction cells. Coventry University, Internal Report AM-01/2003 (2003)

  15. Sun S., Zikanov O., Finlayson B.A.: Effect of background melt flow and interface distorsion on the stability of Hall— Heroult cells. Magnetohydrodynamics 41, 273–287 (2005)

    Google Scholar 

  16. Kohno H., Molokov S.: Finite element analysis of interfacial instability in aluminium reduction cells in a uniform, vertical magnetic field. Int. J. Eng. Sci. 45, 644–659 (2007)

    Article  Google Scholar 

  17. Pedcenko A., Molokov S., Thomas P.J., Lukyanov A., Priede J.: Experimental model of the interfacial instability in aluminium reduction cells. Europhys. Lett. 88, 24001 (2009)

    Article  Google Scholar 

  18. Dupuis, M., Bojarevics, V., Freibergs, J.: Demonstration thermo-electric and MHD mathematical models of a 500 kA Al electrolysis cell. In: Proceedings of 42nd Conference on Metallurgists COM 2003, Vancouver, Canada, pp. 1–18 (2003)

  19. Sneyd A.D.: Interfacial instabilities in aluminium reduction cells. J. Fluid Mech. 236, 111–126 (1992)

    Article  MATH  Google Scholar 

  20. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Nat. Bureau of Standards (1964)

Download references

Author information

Authors and Affiliations

  1. Applied Mathematics Research Centre, Coventry University, Priory Street, Coventry, CV1 5FB, UK

    Sergei Molokov

  2. Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK

    Gennady El

  3. Department of Mathematics, University of Reading, 9 Whiteknights, PO Box 220, Reading, RG6 6AX, UK

    Alexander Lukyanov

Authors
  1. Sergei Molokov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gennady El
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexander Lukyanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sergei Molokov.

Additional information

Communicated by O. Zikanov

Rights and permissions

Reprints and permissions

About this article

Cite this article

Molokov, S., El, G. & Lukyanov, A. Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field. Theor. Comput. Fluid Dyn. 25, 261–279 (2011). https://doi.org/10.1007/s00162-010-0201-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00162-010-0201-y

Keywords

Search

Navigation