Publikationsrepositorium - Helmholtz-Zentrum Dresden-Rossendorf

The operation of a liquid metal battery (LMB) produces Ohmic losses in the electrolyte layer that separates both electrodes. As a consequence, temperature gradients will be established making the system prone to thermal convection since density and interfacial tension depend on the local temperature. The knowledge of convective transport mechanisms in LMBs is necessary for their design, e.g. preventing short-circuits and controlling the temperature.
Our numerical investigations follow recent studies of Shen and Zikanov that considered a three-layer model consisting of a liquid metal alloy cathode, a molten salt separation layer, and a liquid metal anode at the top. Both electrodes are held at a fixed ambient temperature. The model of Shen and Zikanov based on the Navier-Stokes-Boussinesq and heat transport equations, is extended by including interfacial tension gradients (the Marangoni effect) and completely accounting for all differences in the transport properties between phases.
We analyzed the linear stability of pure thermal conduction and performed three-dimensional direct-numerical simulations by a pseudospectral method, where we probed different: electrolyte layer heights, overall heights, and current densities.
Four instability mechanisms are identified, which are partly coupled to each other: buoyant convection in the upper electrode, buoyant convection in the molten salt layer, and Marangoni convection at both interfaces between molten salt and electrode.
The linear stability analysis confirms that the additional Marangoni effect 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 (based on the bottom electrode properties) decrease with increasing middle layer thickness. The calculated thresholds for the onset of convection are found to appear at practical current densities of laboratory-sized LMBs. The global turbulent heat transfer follows scaling predictions for internally heated buoyant convection. 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.