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Numerical simulations of swirling electrovortex flows in cylinders

Published online by Cambridge University Press:  25 October 2022

S. Bénard Open the ORCID record for S. Bénard [Opens in a new window] ,
W. Herreman Open the ORCID record for W. Herreman [Opens in a new window] ,
J.L. Guermond  and
C. Nore Open the ORCID record for C. Nore [Opens in a new window]
S. Bénard*
Affiliation:
Université Paris-Saclay, CNRS, LISN, 91400 Orsay, France
W. Herreman
Affiliation:
Université Paris-Saclay, CNRS, LISN, 91400 Orsay, France
J.L. Guermond
Affiliation:
Department of Mathematics, Texas A&M University 3368 TAMU, College Station, TX 77843-3368, USA
C. Nore
Affiliation:
Université Paris-Saclay, CNRS, LISN, 91400 Orsay, France
*
†Email address for correspondence: [email protected]
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Abstract

We study swirling electrovortex flows in a cylinder filled with GaInSn metal using axisymmetric and large-scale three-dimensional numerical simulations. In our set-up electrical currents enter and exit the cell symmetrically through wires and the result is a von Kármán-like flow. Three inductionless and an inductive flow regimes are identified. Scaling laws for the magnitude of the velocity in each of these regimes are obtained both numerically and explained theoretically. We study how the aspect ratio of the cell affects the flow and how symmetrically wired cells are different from asymmetrical wired cells. We vary the radius of the connecting wires and propose a simple model that captures how the flow's intensity varies with the wire radius.

JFM classification

MHD and Electrohydrodynamics: Magnetic fluids Instability: Transition to turbulence Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 950 , 10 November 2022 , A28
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Ashour, R.F., Kelley, D.H., Salas, A., Starace, M., Weber, N. & Weier, T. 2018 Competing forces in liquid metal electrodes and batteries. J. Power Sourc. 378, 301–310.CrossRefGoogle Scholar
Berhanu, M., et al. 2007 Magnetic field reversals in an experimental turbulent dynamo. Europhys. Lett. 77 (5), 59001.CrossRefGoogle Scholar
Bojarevičs, V., Freibergs, J.A., Shilova, E.I. & Shcherbinin, E.V. 1989 Electrically Induced Vortical Flows. Mechanics of Fluids and Transport Processes, vol. 1. Springer.CrossRefGoogle Scholar
Bojarevics, V., Millere, R. & Chaikovsky, A.I. 1981 Investigation of the azimuthal perturbation growth in the flow due to an electric current point source. In Proceedings of the 10th Riga Conference on MHD, Riga, Latvia, vol. 1, pp. 147–148.Google Scholar
Cappanera, L., Guermond, J.-L., Herreman, W. & Nore, C. 2018 Momentum-based approximation of incompressible multiphase fluid flows. Intl J. Numer. Meth. Fluids 86 (8), 541–563.CrossRefGoogle Scholar
Chudnovskii, A.Y. 1989 Evaluating the intensity of a single class of electrovortex flows MHD. Magnetohydrodynamics 25 (3), 406–408.Google Scholar
Davidson, P.A. 1992 Swirling flow in an axisymmetric cavity of arbitrary profile, driven by a rotating magnetic field. J. Fluid Mech. 245, 669–699.CrossRefGoogle Scholar
Davidson, P.A. 2001 An Introduction to Magnetohydrodynamics. Cambridge Texts in Applied Mathematics. Cambridge University Press.Google Scholar
Davidson, P.A., Kinnear, D., Lingwood, R.J., Short, D.J. & He, X. 1999 The role of Ekman pumping and the dominance of swirl in confined flows driven by Lorentz forces. Eur. J. Mech. (B/Fluids) 18, 693–711.CrossRefGoogle Scholar
Geindreau, C. & Auriault, J.-L. 2002 Magnetohydrodynamic flows in porous media. J. Fluid Mech. 466, 343–363.CrossRefGoogle Scholar
Guermond, J.-L., Laguerre, R., Léorat, J. & Nore, C. 2007 An interior penalty Galerkin method for the MHD equations in heterogeneous domains. J. Comput. Phys. 221 (1), 349–369.CrossRefGoogle Scholar
Guermond, J.-L., Laguerre, R., Léorat, J. & Nore, C. 2009 Nonlinear magnetohydrodynamics in axisymmetric heterogeneous domains using a Fourier/finite element technique and an interior penalty method. J. Comput. Phys. 228, 2739–2757.CrossRefGoogle Scholar
Herreman, W., Bénard, S., Nore, C., Personnettaz, P., Cappanera, L. & Guermond, J.-L. 2020 Solutal buoyancy and electrovortex flow in liquid metal batteries. Phys. Rev. Fluids 5, 074501.CrossRefGoogle Scholar
Herreman, W., Nore, C., Cappanera, L. & Guermond, J.-L. 2021 Efficient mixing by swirling electrovortex flows in liquid metal batteries. J. Fluid Mech. 915, A17.CrossRefGoogle Scholar
Herreman, W., Nore, C., Ziebell Ramos, P., Cappanera, L., Guermond, J.-L. & Weber, N. 2019 Numerical simulation of electrovortex flows in cylindrical fluid layers and liquid metal batteries. Phys. Rev. Fluids 4, 113702.CrossRefGoogle Scholar
Hunt, J.C.R. & Malcolm, D.G. 1968 Some electrically driven flows in magnetohydrodynamics. Part 2. Theory and experiment. J. Fluid Mech. 33 (4), 775–801.CrossRefGoogle Scholar
Hunt, J.C.R. & Stewartson, K. 1965 Magnetohydrodynamic flow in rectangular ducts. II. J. Fluid Mech. 23 (3), 563–581.CrossRefGoogle Scholar
Kelley, D.H. & Sadoway, D.R. 2014 Mixing in a liquid metal electrode. Phys. Fluids 26 (5), 057102.CrossRefGoogle Scholar
Kelley, D.H. & Weier, T. 2018 Fluid mechanics of liquid metal batteries. Appl. Mech. Rev. 70, 020801.CrossRefGoogle Scholar
Kharicha, A., Teplyakov, I., Ivochkin, Y., Wu, M., Ludwig, A. & Guseva, A. 2015 Experimental and numerical analysis of free surface deformation in an electrically driven flow. Exp. Therm. Fluid Sci. 62, 192–201.CrossRefGoogle Scholar
Kolesnichenko, I., Frick, P., Eltishchev, V., Mandrykin, S. & Stefani, F. 2020 Evolution of a strong electrovortex flow in a cylindrical cell. Phys. Rev. Fluids 5 (12), 123703.CrossRefGoogle Scholar
Liu, K., Stefani, F., Weber, N., Weier, T. & Li, B.W. 2020 Numerical and experimental investigation of electro-vortex flow in a cylindrical container. Magnetohydrodynamics 56 (1), 27–42.Google Scholar
Malcolm, D.G. 1970 An investigation of the stability of a magnetohydrodynamic shear layer. J. Fluid Mech. 41 (3), 531–544.Google Scholar
Millere, R.P., Sharamkin, V.I. & Shcherbinin, É.V. 1980 Effect of a longitudinal magnetic field on electrically driven rotational flow in a cylindrical vessel. Magnetohydrodynamics 1, 81–85.Google Scholar
Monchaux, R., et al. 2007 Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium. Phys. Rev. Lett. 98 (4), 044502.CrossRefGoogle Scholar
Moresco, P. & Alboussiere, T. 2004 Experimental study of the instability of the Hartmann layer. J. Fluid Mech. 504, 167–181.CrossRefGoogle Scholar
Nore, C., Tartar, M., Daube, O. & Tuckerman, L.S. 2004 Survey of instability thresholds of flow between exactly counter-rotating disks. J. Fluid Mech. 511, 45–65.CrossRefGoogle Scholar
Nore, C., Tuckerman, L.S., Daube, O. & Xin, S. 2003 The 1:2 mode interaction in exactly counter-rotating von Kármán swirling flow. J. Fluid Mech. 477, 51–88.CrossRefGoogle Scholar
Plevachuk, Y., Sklyarchuk, V., Eckert, S., Gerbeth, G. & Novakovic, R. 2014 Thermophysical properties of the liquid Ga–In–Sn eutectic alloy. J. Chem. Engng Data 59 (3), 757–763.CrossRefGoogle Scholar
Poyé, A., Agullo, O., Plihon, N., Bos, W.J.T., Desangles, V. & Bousselin, G. 2020 Scaling laws in axisymmetric magnetohydrodynamic duct flows. Phys. Rev. Fluids 5, 043701.CrossRefGoogle Scholar
Sutton, G.W. & Sherman, A. 1965 Engineering Magnetohydrodynamics. McGraw-Hill Book Company.Google Scholar
Vernet, M., Pereira, M., Fauve, S. & Gissinger, C. 2021 Turbulence in electromagnetically driven Keplerian flows. J. Fluid Mech. 924, A29.CrossRefGoogle Scholar
Vlasyuk, V.K. 1987 Effects of fusible-electrode radius on the electrovortex flow in a cylindrical vessel. Magnetohydrodynamics 4, 101–106.Google Scholar
Weber, N., Galindo, V., Priede, J., Stefani, F. & Weier, T. 2015 The influence of current collectors on Tayler instability and electro-vortex flows in liquid metal batteries. Phys. Fluids 27 (1), 014103.CrossRefGoogle Scholar
Weber, N., Nimtz, M., Personnettaz, P., Salas, A. & Weier, T. 2018 Electromagnetically driven convection suitable for mass transfer enhancement in liquid metal batteries. Appl. Therm. Engng 143, 293–301.CrossRefGoogle Scholar
Weber, W., Nimtz, M., Personnettaz, P., Weier, T. & Sadoway, D. 2020 Numerical simulation of mass transfer enhancement in liquid metal batteries by means of electro-vortex flow. J. Power Sources Adv. 1, 100004.CrossRefGoogle Scholar

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