# Thermal Rayleigh-Marangoni convection in a three-layer liquid-metal-battery model

## TL;DR

This study investigates the combined effects of Rayleigh-Bénard and Marangoni convection in a three-layer liquid metal battery model, revealing how these instabilities interact and influence heat transfer and flow patterns.

## Contribution

It provides a linear stability analysis and direct numerical simulations of convection modes in a liquid metal battery model, highlighting the role of Marangoni effects and layer thickness.

## Key findings

- Marangoni effects increase instability growth rates.
- Critical Grashof and Marangoni numbers decrease with thicker middle layer.
- Convection thresholds are realistic for laboratory-sized batteries.

## Abstract

The combined effects of buoyancy-driven Rayleigh-B\'{e}nard convection (RC) and surface tension-driven Marangoni convection (MC) are studied in a triple-layer configuration which serves as a simplified model for a liquid metal battery (LMB). The three-layer model consists of a liquid metal alloy cathode, a molten salt separation layer, and a liquid metal anode at the top. Convection is triggered by the temperature gradient between the hot electrolyte and the colder electrodes, which is a consequence of the release of resistive heat during operation. We present a linear stability analysis of the state of pure thermal conduction in combination with three-dimensional direct numerical simulations of the nonlinear turbulent evolution on the basis of a pseudospectral method. Five different modes of convection are identified in the configuration, which are partly coupled to each other: RC in the upper electrode, RC with internal heating in the molten salt layer, MC at both interfaces between molten salt and electrode as well as anti-convectionin the middle layer and lower electrode. The linear stability analysis confirms that the additional Marangoni effect in the present setup increases the growth rates of the linearly unstable modes, i.e. Marangoni and Rayleigh-B\'{e}nard instability act together in the molten salt layer. The critical Grashof and Marangoni numbers decrease with increasing middle layer thickness. The calculated thresholds for the onset of convection are found for realistic current densities of laboratory-sized LMBs. The global turbulent heat transfer follows scaling predictions for internally heated RC. The global turbulent momentum transfer is comparable with turbulent convection in the classical Rayleigh-B\'{e}nard case.