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, and MC at both interfaces between molten salt and electrode as well as anticonvection in 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. In summary, our studies show that incorporating Marangoni effects generates smaller flow structures, alters the velocity magnitudes, and enhances the turbulent heat transfer across the triple-layer configuration.

No abstract

No abstract

Liquid Metal Batteries (LMBs) are a promising concept for cheap electrical energy storage at grid level. These are built as a stable density stratification of three liquid layers, with two liquid metals separated by a molten salt. In order to ensure a safe and efficient operation, the understanding of transport phenomena in LMBs is essential. With this motivation we study thermal convection induced by internal heat generation. We consider the electrochemical nature of the cell in order to define the heat balance and the operating parameters. Moreover we develop a simple 1D heat conduction model as well as a fully 3D thermo-fluid dynamics model. The latter is implemented in the CFD library OpenFOAM, extending the volume of fluid solver, and validated against a pseudo-spectral code. Both models are used to study a rectangular 10×10 cm Li||Bi LMB cell at three different states of charge.