Direct Simulation of Mhd Instabilities in Aluminum Reduction Cells

Introduction. Magnetohydrodynamic (MHD) instabilities in aluminum reduction cells (see Fig. 1) have been the subject of several studies, since the pioneering work of Urata et al. [1]. The interaction between the electrolysis current in the cell and the background magnetic field due to remote currents gives rise to a strong magnetic force acting on the fluids inside the cell. Different kinds of waves thus appear at the interface between a liquid aluminum layer and an electrolytic bath lying on its top. These disturb the current distribution inside the cell so that certain modes become unstable. It has been shown by means of linear analysis [2, 3] that the longest waves tend to be more unstable, and that resonance may occur between waves propagating along perpendicular horizontal directions and coupled together by the magnetic force. On the other hand, numerical simulations were performed either with industrial codes [4] or a research code using finite elements [5]. These authors mainly focused on obtaining the well-known metal pad roll, a particular instability of which manifests itself as a rotating wave at the aluminum–electrolyte interface. In order to solve the non-stationary magnetohydrodynamic equations in a three-dimensional two-fluid system such as the aluminum reduction cell, we have designed a novel numerical method by combining a level set technique together with a finite volumes discretization. Moreover, our equations are written in terms of the magnetic vector potential, thus ensuring the magnetic field to remain exactly divergence-free. Not only we found, as was done already by [4, 5], that the metal pad roll becomes unstable for some critical value of the background vertical magnetic field but we also simulated a different configuration which resulted in a vertical jet of aluminum. These new results are backed up by a physical explanation of the instability mechanism.