Magnetohydrodynamic stability of large scale liquid metal batteries

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...

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Bibliographic Details
Published in:Journal of fluid mechanics 2018-10, Vol.852, p.453-483
Main Authors: Tucs, A., Bojarevics, V., Pericleous, K.
Format: Article
Language:English
Subjects:
Aluminium
Aluminum
Batteries
Boundary conditions
Carbon
Computational fluid dynamics
Damping
Eigenvalues
Electric currents
Electrodes
Electrolysis
Electrolytes
Fluid flow
Gravitational waves
Intermetallic compounds
JFM Papers
Linearization
Magnetic field
Magnetic fields
Magnetohydrodynamic stability
Magnetohydrodynamics
Mathematical models
Metals
Perturbation methods
Stability
Stability analysis
Stability criteria
Three dimensional models
Velocity distribution
Viscous damping
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2018.482