Coupling and stability of interfacial waves in liquid metal batteries

TL;DR

This paper analyzes the complex coupling of interfacial waves in liquid metal batteries, deriving analytical expressions and validating them with simulations to understand stability and potential safety implications.

Contribution

It introduces a potential analysis for coupled interfacial waves in three-layer cylindrical batteries and identifies regimes of wave coupling and stability.

Findings

Wave coupling can be described by two dimensionless parameters.

Decoupling criterion for wave interactions is established.

Novel instabilities in strongly coupled interfaces may enhance safety.

Abstract

We investigate the interfacial wave coupling dynamics in liquid metal batteries and their effects to the battery's operation safety. Similar to aluminum reduction cells, liquid metal batteries can be highly susceptible to magnetohydrodynamical instabilities that excite undesired interfacial waves capable to provoke short-circuits. However, in liquid metal batteries the wave dynamics is far more complex since two metal-electrolyte interfaces are present that may step into resonance. In the first part of this paper, we present a Potential analysis of coupled gravity-capillary interfacial waves in a three-layer battery model of cylindrical shape. Analytical expressions for the amplitude ratio and the wave frequencies are derived and it is shown that the wave coupling can be completely described by two independent dimensionless parameters. We provide a decoupling criterion clarifying that wave coupling will be present in most future liquid metal batteries. In the second part, the theory is validated by comparing it with multiphase direct numerical simulations. An accompanying parameter study is conducted to analyze the system stability for differently strongly coupled interfaces. Three different coupling regimes are identified involving characteristic coupling dynamics. For strongly coupled interfaces we observe novel instabilities that may have beneficial effects on the operational safety.