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Tayler instability in liquid metal columns and liquid metal batteries

Published online by Cambridge University Press:  15 April 2015

W. Herreman ,
C. Nore ,
L. Cappanera  and
J.-L. Guermond
W. Herreman*
Affiliation:
Laboratoire d’Informatique pour la Mécanique et les Sciences de l’Ingénieur, CNRS UPR 3251, BP 133, 91403 Orsay CEDEX and Université Paris-Sud 11, France
C. Nore
Affiliation:
Laboratoire d’Informatique pour la Mécanique et les Sciences de l’Ingénieur, CNRS UPR 3251, BP 133, 91403 Orsay CEDEX and Université Paris-Sud 11, France
L. Cappanera
Affiliation:
Laboratoire d’Informatique pour la Mécanique et les Sciences de l’Ingénieur, CNRS UPR 3251, BP 133, 91403 Orsay CEDEX and Université Paris-Sud 11, France Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX 77843-3368, USA
J.-L. Guermond
Affiliation:
Laboratoire d’Informatique pour la Mécanique et les Sciences de l’Ingénieur, CNRS UPR 3251, BP 133, 91403 Orsay CEDEX and Université Paris-Sud 11, France Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX 77843-3368, USA
*
†Email address for correspondence: wietze.herreman@limsi.fr
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Abstract

In this paper we investigate the Tayler instability in an incompressible, viscous and resistive liquid metal column and in a model of a liquid metal battery (LMB). Detailed comparisons between theory and numerics, both in linear and nonlinear regimes, are performed. We identify the timescale that is well adapted to the quasi-static (QS) regime and find the range of Hartmann numbers where this approximation applies. The scaling law $\mathit{Re}\sim \mathit{Ha}^{2}$ for the amplitude of the Tayler destabilized flow is explained using a weakly nonlinear argument. We calculate a critical electrolyte height above which the Tayler instability is too weak to disrupt the electrolyte layer in a LMB. Applied to present day Mg-based batteries, this criterion shows that short circuits can occur only in very large batteries. Finally, preliminary results demonstrate the feasibility of direct numerical multiphase simulations of the Tayler instability in a model battery.

JFM classification

MHD and Electrohydrodynamics: MHD and Electrohydrodynamics Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Multiphase flow

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 771 , 25 May 2015 , pp. 79 - 114
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© 2015 Cambridge University Press 

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