Efficient mixing in liquid metal batteries by swirling electrovortex flows
Résumé
Using direct numerical simulations, we study the flow and composition of the bottom alloy layer of a discharging liquid metal battery (LMB). This layer is submitted to a uniform vertical magnetic field Bz and it is electrically connected from below to a thinner solid copper wire. The current is deviated towards the wire and creates a mainly azimuthal Lorentz-force always localized near the electrical contact. This force generates a swirling electrovortex flow that pumps the material downwards in a spiral motion prior to ejecting it radially. By studying the flow in various parameter regimes, we identify and explain a novel scaling law for the intensity of these swirling electrovortex flows. Using this scaling law and the model described in Herreman et al.,Phys. Rev. Fluids 5(7),(2020), we estimate the minimal intensity of the external magnetic field that is needed for the swirling electrovortex to enhance the mixing of the alloys in the bottom electrode of arbitrary liquid metal batteries. Mixing is very intense and three-dimensional. However axisymmetric simulations provide good estimates of the mixing capabilities of the swirling electrovortex flow. More details can be found in Herreman et al.,J. Fluid Mech. 915, A17 (2021).