MHD stability of large scale liquid metal batteries

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.

arXiv comment31 pages, 10 figures

References in corpus (5)

• Thermal convection in a liquid metal battery
• Current-driven flow instabilities in large-scale liquid metal batteries, and how to tame them
• Sloshing instability and electrolyte layer rupture in liquid metal batteries
• The influence of current collectors on Tayler instability and electro-vortex flows in liquid metal batteries
• Shallow water modeling of rolling pad instability in liquid metal batteries

Cited by in corpus (5)

• Simulation of potential and species distribution in a Li||Bi liquid metal battery using coupled meshes
• Numerical simulation of rolling pad instability in cuboid liquid metal batteries
• Anode-metal drop formation and detachment mechanisms in liquid metal batteries
• Fractality of metal pad instability threshold in rectangular cells
• Numerical solutions of an accurate diffuse interface model of the incompressible resistive MHD free surface flow