Flow Phenomena in Liquid Metal Batteries

Liquid metal batteries (LMBs) are high temperature systems consisting of liquid metal electrodes and a molten salt ionic conductor. The densities are chosen in such a way that a stable density stratification of the inmiscible layers results. LMBs were considered mainly as part of energy conversion systems in the 1960s \ and have only recently received renewed interest for economic large-scale storage. Our work concentrates on the fluid dynamic aspects of this cell type with a special focus on the effects and properties of the Tayler instability (TI).
Due to the completely liquid interior of LMBs, fluid flow is an important aspect of their operation. It can be beneficial, when enhancing mass transfer in the cathode, or it might have harmful consequences, if the integrity of the electrolyte layer is disrupted.
The latter case can result form the action of the current-driven TI. We therefore studied the characteristics of the TI depending on the cell's aspect ratio using an integro-differential approach implemented in the open source library OpenFOAM. The TI occurs if a critical value of a dimensionless parameter Ha is exceeded. Ha, the Hartmann number, is in our case solely determined by the total current I and the material properties density, kinematic viscosity, and electrical conductivity. The critical Ha is lowest for an infinitely high cuboid and corresponds to a total current of approx. 1 kA in the case of Na. Decreasing the aspect ratio increases Hacrit since the wavelength selection for the TI becomes more and more restricted.
Current densities in LMBs are typically very high. A current density of 10 kA/m2 is a characteristic value for a Na|NI-NaCl-NaF|Bi-system and results in an approximately 10 mm thick sodium layer transferred per hour from the anodic to the cathodic compartment. Depending on the design capacity and cell area, aspect ratios of the anodic compartment up to one seem imaginable.