Liquid metal batteries (LMBs) are discussed today as a cheap grid scale energy storage, as required for the deployment of fluctuating renewable energies. Built as a stable density stratification of two liquid metals separated by a thin molten salt layer, LMBs are susceptible to short-circuit by fluid flows. Using direct numerical simulation, we study a sloshing long wave interface instability in cylindrical cells, which is already known from aluminium reduction cells. After characterising the instability mechanism, we investigate the influence of cell current, layer thickness, density, viscosity, conductivity and magnetic background field. Finally we study the shape of the interface and give a dimensionless parameter for the onset of sloshing as well as for the short-circuit.

A cylindrical container partially filled with a liquid in orbital shaking motion, i.e. in circular translation with fixed orientation with respect to an inertial frame of reference, generates, along with a rotating sloshing wave, a mean flow rotating in the same direction as the wave. Here we investigate experimentally the structure and the scaling of the wave flow and the Lagrangian mean flow in the weakly nonlinear regime, for small forcing amplitude and for forcing frequency far from the resonance, using conventional and stroboscopic particle image velocimetry. The Lagrangian mean flow is composed of a strong global rotation near the center and a non trivial pattern of poloidal recirculation vortices of weaker amplitude, mostly active near the contact line. The global rotation near the center is robust with respect to changes in viscosity and forcing frequency, and its amplitude compares well with the predicted Stokes drift for an inviscid rotating sloshing wave. On the other hand, the spatial structure of the poloidal vortices show strong variation with viscosity and forcing frequency, suggesting that it results from the streaming flow driven by the complex oscillatory boundary layers near the contact line.arXiv:1702.04128v2 [physics.flu-dyn]