Tayler instability in liquid metal colums and liquid metal batteries
Résumé
In this paper we investigate the Tayler instability in an incompressible,
viscous and resistive liquid metal column and in a model of liquid
metal battery (LMB). Detailed comparisons between theory and numerics,
both in linear and nonlinear regimes, are performed. We identify the
timescale that is well adapted to the quasi-static regime and find
the range of Hartmann numbers where this approximation applies. The
scaling law $\Re \sim \Ha^2$ for the amplitude of the Tayler
destabilized flow is explained using a weakly nonlinear argument.
We calculate a critical
electrolyte height above which the Tayler instability is too weak
to disrupt the electrolyte layer in a LMB. Applied to present day Mg-based
batteries, this criterion shows that short-circuits can occur only
in very large batteries. Finally, preliminary results demonstrate
the feasibility of direct numerical multiphase simulations of the
Tayler instability in a model battery.