MHD stability of large scale liquid metal batteries

This paper presents the development of a stability theory and a numerical model for three density-stratified electrically conductive liquid layers relevant to liquid metal batteries (LMBs). The objective is to analyze the stability under the influence of an arbitrary vertical magnetic field. Utilizing regular perturbation methods, the complex three-dimensional problem is reduced to a shallow layer model, from which the coupled wave and electric current equations are derived. Further linearization enables a comprehensive linear stability analysis within the framework of a uniform vertical magnetic field. The study introduces new analytical stability criteria that incorporate viscous damping, and these criteria are validated against numerical solutions for various materials commonly used in LMBs. The findings indicate that the derived criteria are applicable not only to the specific case of LMBs but also to MHD stability estimates for aluminium electrolysis cells. Overall, this research contributes valuable insights into the fluid dynamics of LMBs and lays the groundwork for enhancing their practical application in future renewable energy systems.