Skip to main content
SpringerLink
Log in

Spin-up of electro-vortex flows under external magnetic field

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

Electro-vortex flows (EVFs) occur in many industrial devices, in which strong electric current passes through liquid metal. It is known that the structure of such flows can be significantly changed by applying the external magnetic field. Moreover, even a relatively weak magnetic field (say, the magnetic field of Earth) can be sufficient to influence the flow structure. In this paper, we study the influence on the EVF of the “spin-up” of either electric current or the external magnetic field on the EVF, and analyze the inhomogeneous magnetic field of the electric current conductors (power supply unit). Here, the term “spin-up” means a gradual increase in the flow driving force. These factors are inevitable in laboratory experiments, but usually neglected in numerical studies. It is shown that the spin-up of either poloidal or azimuthal driving force reduces the flow energy in the transient regime. At the same time, the spin-up factor does not influence the resulting flow structure. The inhomogeneous magnetic field of the power supply is shown to have a significant impact on the EVF. It can be a major factor to consider when simulating devices, in which the suppression of the poloidal EVF is the essential pre-requisite for their operation.

Graphical abstract

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data Availability Statement

The data are available from corresponding author on reasonable request. This manuscript has associated data in a data repository. [Authors’ comment: The data are available on reasonable request.]

References

  1. V. Bojarevics, J.A. Freibergs, E.I. Shilova, E.V. Shcherbinin, Electrically Induced Vortical Flows Mechanics of Fluids and Transport Processes (Springer, Berlin, 1989)

    Book  Google Scholar 

  2. S.Y. Khripchenko, Generation of large-scale vortical structures by small-scale helical turbulence in a flat layer. Magnetohydrodynamics 27(4), 77–83 (1991)

    Google Scholar 

  3. A.D. Sneyd, A. Wang, MHD driven instabilities in aluminium reduction cells. Magnetohydrodynamics 32(4), 487–493 (1996)

    Google Scholar 

  4. I. Kolesnichenko, S. Khripchenko, D. Buchenau, G. Gerbeth, Electrovortex flows in a square layer of liquid metal. Magnetohydrodynamics 41(1), 39–51 (2005)

    Article  ADS  Google Scholar 

  5. O.V. Kazak, A.N. Semko, Electrovortex motion of a melt in DC furnaces with a bottom electrode. J. Eng. Phys. Thermophys. 84(1), 223–231 (2011). https://doi.org/10.1007/s10891-011-0464-1

    Article  Google Scholar 

  6. D.A. Vinogradov, I.O. Teplyakov, Y.P. Ivochkin, I.B. Klementeva, Influence of the external magnetic field on hydrodynamic structure of the electrovortex flow in hemispherical container. J. Phys: Conf. Ser. 899(8), 082006 (2017)

    Google Scholar 

  7. S. Mandrykin, I. Kolesnichenko, P. Frick, Electrovortex flows generated by electrodes localized on the cylinder side wall. Magnetohydrodynamics 55, 115–124 (2019)

    Article  Google Scholar 

  8. S. Mandrykin, V. Ozernykh, I. Kolesnichenko, Electro-vortex flow of liquid metal in a cylindrical cell with localized current supply and variable aspect ratio. Magnetohydrodynamics 56, 81–90 (2020).

    Article  Google Scholar 

  9. A. Chudnovsky, Y. Ivochkin, A. Jakovics, S. Pavlovs, I. Teplyakov, D. Vinogradov, An electrovortex flow around two fully submerged electrodes. IOP Conf. Series: Mater. Sci. Eng. 950, 012002 (2020). https://doi.org/10.1088/1757-899x/950/1/012002

    Article  Google Scholar 

  10. S. Dement’ev, A. Chaikovskii, A. Chudnovskii, Generation of electrovortex flows liquid-metal baths with a multielectrode current input. Magnetohydrodynamics 24(1), 45–49 (1988)

    Google Scholar 

  11. O. Kazak, Modeling of vortex flows in direct current (DC) electric arc furnace with different bottom electrode positions. Metall. and Mater. Trans. B. 44(5), 1243–1250 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  12. P.A. Davidson, D. Kinnear, R.J. Lingwood, D.J. Short, X. He, The role of Ekman pumping and the dominance of swirl in confined flows driven by Lorentz forces. Eur. J. Mech. B. Fluids 18(4), 693–711 (1999). https://doi.org/10.1016/s0997-7546(99)00106-5

    Article  MathSciNet  MATH  Google Scholar 

  13. P.A. Davidson Introduction to Magnetohydrodynamics. CAMBRIDGE, ??? (2017)

  14. V.G. Zhilin, Y.P. Ivochkin, I.O. Teplyakov, The problem of swirling of axisymmetric electrovortex flows. High Temp. 49(6), 927–929 (2011). https://doi.org/10.1134/S0018151X11060241

    Article  Google Scholar 

  15. K. Liu, F. Stefani, N. Weber, T. Weier, B.W. Li, Numerical and experimental investigation of electro-vortex flow in a cylindrical container. Magnetohydrodynamics 56, 27–42 (2020).

    Article  Google Scholar 

  16. I. Kolesnichenko, P. Frick, V. Eltishchev, S. Mandrykin, F. Stefani, Evolution of a strong electrovortex flow in a cylindrical cell. Phys. Rev. Fluids 5, 123703 (2020). https://doi.org/10.1103/PhysRevFluids.5.123703

    Article  ADS  Google Scholar 

  17. W. Herreman, C. Nore, L. Cappanera, J.-L. Guermond, Efficient mixing by swirling electrovortex flows in liquid metal batteries. J. Fluid Mech. (2021). https://doi.org/10.1017/jfm.2021.79

    Article  MathSciNet  MATH  Google Scholar 

  18. D.H. Kelley, T. Weier, Fluid mechanics of liquid metal batteries. Appl. Mech. Rev. 70(2), 020801 (2018). https://doi.org/10.1115/1.4038699

    Article  ADS  Google Scholar 

  19. N. Weber, V. Galindo, F. Stefani, T. Weier, Current-driven flow instabilities in large-scale liquid metal batteries, and how to tame them. J. Power Sources 265, 166–173 (2014). https://doi.org/10.1016/j.jpowsour.2014.03.055

    Article  ADS  Google Scholar 

  20. N. Weber, V. Galindo, J. Priede, F. Stefani, T. Weier, The influence of current collectors on Tayler instability and electro-vortex flows in liquid metal batteries. Phys. Fluids 27(1), 014103 (2015). https://doi.org/10.1063/1.4905325

    Article  ADS  Google Scholar 

  21. N. Weber, P. Beckstein, W. Herreman, G.M. Horstmann, C. Nore, F. Stefani, T. Weier, Sloshing instability and electrolyte layer rupture in liquid metal batteries. Phys. Fluids 29(5), 054101 (2017). https://doi.org/10.1063/1.4982900

    Article  ADS  Google Scholar 

  22. D.C. Wilcox, Reassessment of the scale-determining equation for advanced turbulence models. AIAA J. 26(11), 1299–1310 (1988). https://doi.org/10.2514/3.10041

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. R.F. Ashour, D.H. Kelley, A. Salas, M. Starace, N. Weber, T. Weier, Competing forces in liquid metal electrodes and batteries. J. Power Sources 378, 301–310 (2018). https://doi.org/10.1016/j.jpowsour.2017.12.042

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The work was supported by the Ministry of Science and Higher Education of the Russian Federation (theme no. 122030200191-9).

Funding

The authors have no relevant financial or non-financial interests to disclose.

Author information

Author notes

  1. Ilya Kolesnichenko and Sergei Mandrykin these authors contributed equally to this work.

Authors and Affiliations

  1. Institute of Continuous Media Mechanics of the Ural Branch of RAS, Acad. Korolev St., 1, Perm, Perm Krai, Russia, 614013

    Ilya Kolesnichenko & Sergei Mandrykin

Authors
  1. Ilya Kolesnichenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sergei Mandrykin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sergei Mandrykin.

Ethics declarations

Conflict of interest

The authors have no competing interests to declare that are relevant to the content of this article.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kolesnichenko, I., Mandrykin, S. Spin-up of electro-vortex flows under external magnetic field. Eur. Phys. J. Plus 137, 988 (2022). https://doi.org/10.1140/epjp/s13360-022-03186-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-022-03186-5

Search

Navigation