Stability of aluminium reduction cells with mean flow

A. Kurenkov¹ - A. Thess² - O. Zikanov³ - M. Segatz⁴ - Ch. Droste⁴ - D. Vogelsang⁴

¹ Department of Hydromechanics and Hydraulics, Technical University of Darmstadt, 64287 Darmstadt, Petersenstrasse 13, Germany
² Department of Mechanical Engineering, Ilmenau University of Technology, P.O.Box 100565, 98684 Ilmenau, Germany
³ University of Michigan - Dearborn, Department of Mechanical Engineering, Dearborn, MI, 48128-1491, USA
⁴ Hydro Aluminium-Technologie GmbH, 53117 Bonn, Germany

Abstract
We report results of the linear stability analysis undertaken to investigate the effect of the mean flow of liquid metal on the stability of aluminum reduction cells. A simplified model of the cell is considered that consists of thin layers of aluminum and cryolite superimposed in an infinite horizontal channel with electrically non-conducting walls. A vertical uniform magnetic field and an electric current are applied in the opposite directions. In the basic steady state, a uniform flow of aluminum is assumed, while cryolite is at rest. The onset of the instability is caused by the action of two different mechanisms. The first is the Kelvin--Helmholtz instability of the mean flow. The second, essentially the MHD mechanism, is a consequence of destabilizing electromagnetic (Lorentz) forces produced by nonuniformities of the electric current due to interface deflections. We use the shallow water approximation and solve the problem for the cases of pure Kelvin--Helmholtz (zero magnetic field) and pure MHD (zero mean flow) instabilities and for the general case. We compute the stability chart and derive the parameters that determine the stability threshold. It is found that, while both playing a destabilizing role, the instability mechanisms do not affect each other. In particular, a uniform mean flow changes the direction of propagation of interfacial waves but leaves the MHD stability threshold unaltered. Figs 4, Refs 12.