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Interfacial instability due to MHD mode coupling in aluminium reduction cells

Published online by Cambridge University Press:  26 April 2006

A. D. Sneyd  and
A. Wang
A. D. Sneyd
Affiliation:
University of Waikato, Hamilton, New Zealand
A. Wang
Affiliation:
University of Waikato, Hamilton, New Zealand
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Abstract

This paper analyses instabilities on the cryolite/aluminium interface in an aluminium reduction cell. The simplified cell model is a finite rectangular tank containing the two fluid layers, and carrying a uniform normal current. The magnetic field is assumed to be a linear function of position. Several previous studies have considered waves consisting of a single Fourier component but here we consider perturbations which are a general combination of the normal gravity-wave modes. We derive a system of coupled ordinary differential equations for the time-development of the mode amplitudes, and show that instability can occur via mode interactions, the electromagnetic perturbation force due to one mode feeding energy into the other. Growth rates are determined by computing the eigenvalues of an interaction matrix, and an approximate method using only the three leading diagonals is developed. If two modes have similar frequencies they may resonate and become unstable at a very low threshold current. We consider the influence of various cell parameters and draw some general conclusions about cell design.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 263 , 25 March 1994 , pp. 343 - 360
Copyright
© 1994 Cambridge University Press

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References

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