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Magnetohydrodynamic stability of large scale liquid metal batteries

Published online by Cambridge University Press:  07 August 2018

A. Tucs ,
V. Bojarevics Open the ORCID record for V. Bojarevics [Opens in a new window]  and
K. Pericleous
A. Tucs
Affiliation:
University of Greenwich, Park Row, London SE10 9LS, UK
V. Bojarevics*
Affiliation:
University of Greenwich, Park Row, London SE10 9LS, UK
K. Pericleous
Affiliation:
University of Greenwich, Park Row, London SE10 9LS, UK
*
†Email address for correspondence: V.Bojarevics@gre.ac.uk
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Abstract

The aim of this paper is to develop a stability theory and a numerical model for three density-stratified electrically conductive liquid layers. Using regular perturbation methods to reduce the full three-dimensional problem to the shallow layer model, the coupled wave and electric current equations are derived. The problem set-up allows for weakly nonlinear velocity field action and an arbitrary vertical magnetic field. Further linearisation of the coupled equations is used for the linear stability analysis in the case of a uniform vertical magnetic field. New analytical stability criteria accounting for the viscous damping are derived for particular cases of practical interest and compared to the numerical solutions for a variety of materials used in batteries. These new criteria are equally applicable to the aluminium electrolysis cell magnetohydrodynamic (MHD) stability estimates.

JFM classification

Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Surface gravity waves

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 453 - 483
Copyright
© 2018 Cambridge University Press 

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