Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Numerical simulation of electrovortex flows in cylindrical fluid layers and liquid metal batteries

W. Herreman*, C. Nore, and P. Ziebell Ramos

L. Cappanera

J.-L. Guermond

N. Weber

  • Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur, LIMSI, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât 507, Campus Universitaire F-91405 Orsay, France

  • Department of Computational and Applied Mathematics, Rice University, 6100 Main MS-134 Houston, Texas 77005, USA

  • Department of Mathematics, Texas A&M University 3368 TAMU, College Station, Texas 77843-3368, USA

  • Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstrasse 400, 01328 Dresden, Germany

  • *wietze.herreman@limsi.fr

Phys. Rev. Fluids 4, 113702 – Published 6 November, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.113702

Abstract

We use the multiphase magnetohydrodynamic code SFEMaNS to study the generation of electrovortex flows in liquid metal batteries. We first reproduce some well known results in a single-phase liquid metal column and then we characterize the electrovortex flow in layered multiphase fluid systems. A simple energy density balance argument accurately estimates the typical interface deformation caused by the electrovortex flow. When applied to Mg-Sb liquid metal batteries, we find that the electrovortex flows may have the capacity to cause short circuits even in moderate size batteries with radii in the range [10,20]cm.

Physics Subject Headings (PhySH)

Article Text

References (41)

  1. D. J. Bradwell, H. Kim, A. H. C. Sirk, and D. R. Sadoway, Magnesium-antimony liquid metal battery for stationary energy storage, J. Am. Chem. Soc. 134, 1895 (2012).
  2. H. Kim, D. A. Boysen, T. Ouchi, and D. R. Sadoway, Calcium-bismuth electrodes for large-scale energy storage (liquid metal batteries), J. Power Sources 241, 239 (2013).
  3. K. Wang, K. Jiang, B. Chung, T. Ouchi, P. J. Burke, D. A. Boysen, D. J. Bradwell, H. Kim, U. Muecke, and D. R. Sadoway, Lithium-antimony-lead liquid metal battery for grid-level energy storage, Nature 514, 348 (2014).
  4. D. H. Kelley and D. R. Sadoway, Mixing in a liquid metal electrode, Phys. Fluids 26, 057102 (2014).
  5. Y. Shen and O. Zikanov, Thermal convection in a liquid metal battery, Theor. Comput. Fluid Dyn. 30, 275 (2016).
  6. T. Köllner, T. Boeck, and J. Schumacher, Thermal Rayleigh-Marangoni convection in a three-layer liquid-metal-battery model, Phys. Rev. E 95, 053114 (2017).
  7. R. F. Ashour, D. H. Kelley, A. Salas, M. Starace, N. Weber, and T. Weier, Competing forces in liquid metal electrodes and batteries, J. Power Sources 378, 301 (2018).
  8. P. Personnettaz, P. Beckstein, S. Landgraf, T. Köllner, M. Nimtz, N. Weber, and T. Weier, Thermally driven convection in LiBi liquid metal batteries, J. Power Sources 401, 362 (2018).
  9. N. Weber, V. Galindo, F. Stefani, and T. Weier, Current-driven flow instabilities in large-scale liquid metal batteries, and how to tame them, J. Power Sources 265, 166 (2014).
  10. N. Weber, V. Galindo, J. Priede, F. Stefani, and T. Weier, The influence of current collectors on Tayler instability and electrovortex flows in liquid metal batteries, Phys. Fluids 27, 014103 (2015).
  11. W. Herreman, C. Nore, L. Cappanera, and J.-L. Guermond, Tayler instability in liquid metal columns and liquid metal batteries, J. Fluid Mech. 771, 79 (2015).
  12. O. Zikanov, Metal pad instabilities in liquid metal batteries, Phys. Rev. E 92, 063021 (2015).
  13. N. Weber, P. Beckstein, W. Herreman, G. M. Horstmann, C. Nore, F. Stefani, and T. Weier, Sloshing instability and electrolyte layer rupture in liquid metal batteries, Phys. Fluids 29, 054101 (2017).
  14. N. Weber, P. Beckstein, V. Galindo, W. Herreman, C. Nore, F. Stefani, and T. Weier, Metal pad roll instability in liquid metal batteries, Magnetohydrodynamics 53, 129 (2017).
  15. V. Bojarevics and A. Tucs, MHD of large scale liquid metal batteries, Light Metals 2017 (Springer, Cham, 2017), pp. 687–692.
  16. G. M. Horstmann, N. Weber, and T. Weier, Coupling and stability of interfacial waves in liquid metal batteries, J. Fluid Mech. 845, 1 (2018).
  17. S. Molokov, The nature of interfacial instabilities in liquid metal batteries in a vertical magnetic field, Europhys. Lett. 121, 44001 (2018).
  18. O. Zikanov, Shallow water modeling of rolling pad instability in liquid metal batteries, Theor. Comput. Fluid Dyn. 32, 325 (2018).
  19. W. Herreman, C. Nore, J.-L. Guermond, L. Cappanera, N. Weber, and G. M. Horstmann, Perturbation theory for metal pad roll instability in cylindrical reduction cells, J. Fluid Mech. 878, 598 (2019).
  20. N. Weber, M. Nimtz, P. Personnettaz, A. Salas, and T. Weier, Electromagnetically driven convection suitable for mass transfer enhancement in liquid metal batteries, Appl. Therm. Eng. 143, 293 (2018).
  21. D. H. Kelley and T. Weier, Fluid mechanics of liquid metal batteries, Appl. Mech. Rev. 70, 020801 (2018).
  22. V. Bojarevics, J. A. Freibergs, E. I. Shilova, and E. V. Shcherbinin, Electrically Induced Vortical Flows, (Kluwer Academic Publishers, Dordrecht, 1989).
  23. J. A. Shercliff, Fluid motions due to an electric current source, J. Fluid Mech. 40, 241 (1969).
  24. L. Cappanera, J.-L. Guermond, W. Herreman, and C. Nore, Momentum-based approximation of incompressible multiphase fluid flows, Int. J. Numer. Methods Fluids 86, 541 (2018).
  25. R. P. Millere, V. I. Sharamkin, and É. V. Shcherbinin, Effect of a longitudinal magnetic field on electrically driven rotational flow in a cylindrical vessel, Magnetohydrodynamics 16, 66 (1980).
  26. J.-L. Guermond, R. Laguerre, J. Léorat, and C. Nore, An interior penalty Galerkin method for the MHD equations in heterogeneous domains, J. Comput. Phys. 221, 349 (2007).
  27. J.-L. Guermond, R. Laguerre, J. Léorat, and C. Nore, Nonlinear magnetohydrodynamics in axisymmetric heterogeneous domains using a Fourier/finite element technique and an interior penalty method, J. Comput. Phys. 228, 2739 (2009).
  28. C. Nore, D. Castanon Quiroz, L. Cappanera, and J.-L. Guermond, Direct numerical simulation of the axial dipolar dynamo in the Von Kármán sodium experiment, Europhys. Lett. 114, 65002 (2016).
  29. A. Giesecke, C. Nore, F. Stefani, G. Gerbeth, J. Léorat, W. Herreman, F. Luddens, and J.-L. Guermond, Influence of high-permeability discs in an axisymmetric model of the Cadarache dynamo experiment, New J. Phys. 14, 053005 (2012).
  30. N. Weber, P. Beckstein, V. Galindo, M. Starace, and T. Weier, Electrovortex flow simulation using coupled meshes, Comput. Fluids 168, 101 (2018).
  31. A. Bonito and J.-L. Guermond, Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements, Math. Comp. 80, 1887 (2011).
  32. A. Giesecke, C. Nore, F. Stefani, G. Gerbeth, J. Léorat, F. Luddens, and J.-L. Guermond, Electromagnetic induction in nonuniform domains, Geophys. Astrophys. Fluid Dyn. 104, 505 (2010).
  33. A. Bonito, J.-L. Guermond, and F. Luddens, Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains, J. Math. Anal. Appl. 408, 498 (2013).
  34. I. E. Butsenieks, D. E. Peterson, V. I. Sharamkin, and E. V. Sherbinin, Magnetohydrodynamic fluid flows in a closed space with a nonuniform electric current, Magnetohydrodynamics 12, 70 (1976).
  35. V. K. Vlasyuk, Effects of fusible-electrode radius on the electrovortex flow in a cylindrical vessel, Magnetohydrodynamics 23, 434 (1987).
  36. A. Y. Chudnovskii, Evaluating the intensity of a single class of electrovortex flows MHD, Magnetohydrodynamics 25, 406 (1989).
  37. P. A. Nikrityuk, K. Eckert, R. Grundmann, and Y. S. Yang, An impact of a low voltage steady electrical current on the solidification of a binary metal alloy: A numerical study, Steel Res. Int. 78, 402 (2007).
  38. C. Kasprzyk, Numerische Untersuchung zur strömungsmechanik in flüssigmetallbatterien, Master thesis, Technische Universität Dresden, 2015.
  39. V. G. Zhilin, Y. P. Ivochkin, A. A. Oksman, G. R. Lurin'sh, A. I. Chaikovskii, A. Y. Chudnovskii, and E. V. Shcherbinin, An experimental investigation of the velocity field in an axisymmetric electrovortical flow in a cylindrical container, Magnetohydrodynamics 22, 323 (1986).
  40. L. A. Volokhonskii, F. I. Gamzaev, S. B. Dement'ev, K. A. Zvyagin, and E. V. Shcherbinin, Dynamic boundary layer of electrovortex flow in a cylindrical volume with axisymmetric current supply, Magnetohydrodynamics 27, 467 (1991).
  41. A. Kharicha, I. Teplyakov, Yu. Ivochkin, M. Wu, A. Ludwig, and A. Guseva, Experimental and numerical analysis of free surface deformation in an electrically driven flow, Exp. Therm. Fluid Sci. 62, 192 (2015).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation