MHD driven istabilities in aluminium reduction cells

A. D. Sneyd - A. Wang

University of Waikato, Hamilton, New Zealand

Abstract
This paper describes a scheme for analyzing MHD driven instabilities of aluminum/cryolite interface in an aluminium reduction cell. There are two principal sources of instability: the current flow perturbation due to the interface distortion, and the discontinuity in steady-state velocity between the cryolite and aluminum layers, which gives rise to a Kelvin-Helmgoltz type instability. The first mechanism can be analyzed relatively simply by means of a set of evolution equations for the coefficients in a Fourier series expansion of the free surface displacement. In practice stability can be determined approximately by analyzing the resonant interaction of the two Fourier modes whose natural frequencies are closest together. The second mechanism is more difficult to analyze, requiring detailed representation of the flow in each layer. Growth rates are determined by solving a generalized eigenvalue problem. We find that both mechanisms destabilize the cell when the current exceeds a critical value. Increasing the thickness of the cryolite layer tends to stabilize mechanism and destabilize mechanism, and we also present typical results for the combined effects of both. The method of analysis accommodates arbitrary current distributions, magnetic fields and steady flows, which are calculated numerically in industrial applications. Figs 3, refs 10.