Perturbation theory for metal pad roll instability in cylindrical reduction cells. (10th November 2019)

• Record Type: Journal Article
• Authors: Herreman, W.; Nore, C.; Guermond, J.-L.; Cappanera, L.; Weber, N.; Horstmann, G. M.
• Is Part Of: Journal of fluid mechanics. Volume 878(2019)
• Page Start: 598
• Page End: 646
• Publication Date: 2019-11-10
• Subjects: multiphase flow; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2019.642
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : We propose a new theoretical model for metal pad roll instability in idealized cylindrical reduction cells. In addition to the usual destabilizing effects, we model viscous and Joule dissipation and some capillary effects. The resulting explicit formulas are used as theoretical benchmarks for two multiphase magnetohydrodynamic solvers, OpenFOAM and SFEMaNS. Our explicit formula for the viscous damping rate of gravity waves in cylinders with two fluid layers compares excellently to experimental measurements. We use our model to locate the viscously controlled instability threshold in cylindrical shallow reduction cells but also in Mg–Sb liquid metal batteries with decoupled interfaces.