MHD stability of large scale liquid metal batteries

TL;DR

This paper develops a stability theory and numerical model for large-scale liquid metal batteries, analyzing the effects of magnetic fields and viscosity on their stability, with implications for similar electrochemical systems.

Contribution

It introduces a new analytical stability criterion for stratified liquid layers under magnetic fields, incorporating viscous damping effects, validated by numerical solutions.

Findings

Derived new stability criteria accounting for viscous damping.

Validated criteria through numerical simulations for battery-relevant materials.

Applicable to aluminium electrolysis cell MHD stability analysis.

Abstract

The aim of this paper is to develop a stability theory and a numerical model for the three density-stratified electrically conductive liquid layers. Using regular perturbation methods to reduce the full 3d problem to the shallow layer model, the coupled wave and electric current equations are derived. The problem set-up allows the weakly non-linear 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 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 variety of materials used in the batteries. The new criteria are equally applicable to the aluminium electrolysis cell MHD stability estimates.