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Metal pad roll in cylinders: perturbation theory vs. DNS

Herreman, W.; Nore, C.; Guermond, J.-L.; Cappanera, L.; Weber, N.


Liquid metal batteries (LMBs) structurally have much in common with electrolysis cells that are used in the Al-industry and therefore it can be expected that they are prone to similar magneto-hydrodynamical instabilities. Metal pad rolling is one of many instabilities that is currently in the spotlight.

The physical origin of this metal pad roll instability in reduction cells is well described in a furnished literature that goes back to the 70’s. Most theoretical insights have however been found within the restrictive context of quite a number of supplementary assumptions (shallow layers, inviscid, magneto-static, negligible terms in Lorentz force). In lab-scale devices, fluid layers are however not necessarily shallow and the set-up is also small enough for viscous dissipation to become important. Finally, also the magnetic dissipation cannot be ignored given that stronger magnetic fields are necessary to trigger the instability. A critical
comparison between theory and experiments or direct numerical simulation (DNS) dedicated to lab-scale devices requires a more detailed stability model.

In this talk, I present a theoretical stability analysis dedicated to cylindrical reduction cells (2 layers). Using a perturbative approach we find explicit formula for the growth rate of the metal pad roll instability and without making the most common assumptions. We deal with fluid layers of arbitrary heights and incorporate both magnetic and viscous damping effects. We confront our theory to direct numerical simulations (DNS) that are done with two different multiphase MHD solvers (SFEMaNS and OpenFOAM). This comparison also allows us to measure what precision really is required to obtain converged three-dimensional numerical simulations.

  • Lecture (Conference)
    International workshop on liquid metal battery fluid dynamics, 16.-17.05.2017, Dresden, Deutschland


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