Interfacial instability due to MHD mode coupling in aluminium reduction cells

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.

Theoretical Investigation of the Inclined Sidewall Design on Magnetohydrodynamic (MHD) Forces in an Aluminum Electrolytic Cell

“…The strong interplay between MHD forces and the metal flow results in complex dynamics in the cell. In recent times, significant work has been done toward understanding cell instability resulting from MHD forces, [5][6][7] but little progress has been made in understanding the effect of current direction in different parts of the cell and cell lining.…”

“…Significant progress in the theoretical modeling of the instability has been achieved through the investigations of Sneyd and Wang [6] and Davidson and Lindsay. [8,9] The findings from these studies indicate that long wavelength interfacial waves could be amplified by the electromagnetic Lorentz forces resulting from interaction between the horizontal current perturbations in the aluminum layer and the external imposed vertical magnetic field.…”

“…Most early works have computed MHD forces only in the molten metal to tackle the stability and heave issues and ignored its effect in the side channel and cathode lining. [2,6,8,14] Moreover, the effect of the Lorentz force on titanium boride penetration or sodium diffusion into the cathode neither have been emphasized nor clearly understood in a situation of large current density within the cathode lining and in the side channel. Thus, the main objective of the article is to show the Lorentz force distribution throughout the cell and its effects resulting from the change in sidewall design.…”

Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field

“…It has been recognized, however, that the most dangerous component of the field is vertical. It destabilizes the cell even if it is uniform [6].…”

“…The so-called MHD noise [18] involving waves of 0.5-2m in length and of finite but small amplitude is always present during the smelting process, but it does not affect the stability of the cells and thus is of no concern here. Several scenarios of the MHD instability have ng [6] jarevics and Romerio [7] have independently proposed a model, later explored by Davidson and Lindsay [10], whereby the instability occurs owing to the magnetic coupling of gravity waves inside the whole domain occupied by the fluids. The interface becomes unstable owing to an internal resonance of these waves.…”