The onset of instabilities and finite amplitude waves in a model of aluminum reduction cells with nonuniform cathode current

In aluminum reduction cells, the electric current density at the cathode is seldom uniform. This may be due to a variety of reasons. One of the reasons is that a mass of undissolved alumina may get enrobed by the cryolitic bath, and this mix freezes due to the decrease in temperature below the liquidus point. Thus, an electrically resistive solid layer ("mud") is formed at a part of the cathode. This leads to horizontal electric currents in the liquid aluminum layer, and their magnetohydrodynamic (MHD) interaction with the vertical magnetic field induces a rotating flow of aluminum. This may cause undesirable MHD instabilities. A quasi-two-dimensional model for the laboratory facility has been presented. The results show that the dominating feature of the flow is a depression of the free surface of the liquid metal above the mud spot. This is due to strong rotation of the liquid metal around the mud spot, which causes the centrifugal force. Other effects may include superimposed conventional MHD instability, which manifests itself in a rotating interface, modulated waves, reflection of the waves from the corners of the domain, sloshing, etc. It has been shown that small mud spots do not affect the cell stability, while the large ones may cause such deep depressions that the centrifugal force completely removes the liquid metal above the spot