Modelling Rayleigh-B\'enard convection and electro-vortex flow in liquid metal batteries.

Liquid Metal Batteries (LMBs) are a promising grid-scale energy storage technology that offer low costs per kilowatt-hour, high energy and current densities, as well as low fade rates. The all-liquid composition of LMBs, as well as the presence of temperature gradients and electric and magnetic fields, results in the occurrence of multiple fluid phenomena. These fluid phenomena can affect the hydrodynamic stability and resulting operation of the battery, making it critical to understand how they interact. In this work, the interaction of Rayleigh-B\'enard convection (RBC) and Electro-vortex flow (EVF) is considered as these flow types will be present in LMBs from lab to grid-scale. A single-layer electrode is simulated, and the computed results compared to experimental data. It is found that Rayleigh-B\'enard convection will take a pattern representative of the cell structure due to the presence of non-isothermal walls. The introduction of a 2 A current is found to stabilise the central convection cell, while the introduction of a 40 A current leads to the dominance of Electro-vortex flow at the centre of the electrode. The interaction of Rayleigh-B\'enard convection and Electro-vortex flow characterised in this work is indicative of the flow that will be found in the anodes of all discharging LMBs.