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Stability of aluminium reduction cells with mean flow

Kurenkov, A. and Thess, A. and Zikanov, O. and Segatz, M. and Droste, Ch. and Vogelsang, D. (2004):
Stability of aluminium reduction cells with mean flow.
In: Magnetohydrodynamics, Institute of Physics, University of Latvia, pp. 203-212, 40, (2), ISSN 0024-998X, [Online-Edition: http://www.mhd.sal.lv/contents/2004/2/MG.40.2.6.R.html],
[Article]

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.

Item Type: Article
Erschienen: 2004
Creators: Kurenkov, A. and Thess, A. and Zikanov, O. and Segatz, M. and Droste, Ch. and Vogelsang, D.
Title: Stability of aluminium reduction cells with mean flow
Language: English
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.

Journal or Publication Title: Magnetohydrodynamics
Volume: 40
Number: 2
Publisher: Institute of Physics, University of Latvia
Divisions: 16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
16 Department of Mechanical Engineering
Date Deposited: 23 Aug 2011 14:59
Official URL: http://www.mhd.sal.lv/contents/2004/2/MG.40.2.6.R.html
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