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

Abstract

The combined effects of buoyancy-driven Rayleigh-Bénard 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-Bénard 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-Bénard case.

References in corpus (3)

• Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection
• Global and local statistics in turbulent convection at low Prandtl numbers
• The influence of current collectors on Tayler instability and electro-vortex flows in liquid metal batteries

Cited by in corpus (6)

• Competing forces in liquid metal electrodes and batteries
• Cell voltage model for Li-Bi liquid metal batteries
• Layer coupling between solutal and thermal convection in liquid metal batteries
• Anode-metal drop formation and detachment mechanisms in liquid metal batteries
• Predicting transition ranges to turbulent viscous boundary layers in low Prandtl number convection flows
• Steady state detection for computational fluid dynamics