The shallow water approximation applied to the aluminium electrolysis process

The industrial production of aluminium is an electrolysis process where two superposed horizontal liquid layers are subjected to a mainly vertical electric current supplied by carbon electrodes. The lower layer consists of molten aluminium and lies on the cathode. The upper layer is the electrolyte and is covered by the anode. The interface between the two layers is often perturbed, leading to oscillations, or waves, similar to the waves on the surface of seas or lakes. The presence of electric currents and the resulting magnetic field are responsible for electromagnetic (Lorentz) forces within the fluid, which can amplify these oscillations and have an adverse influence on the process. The electrolytic bath vertical to horizontal aspect ratio is such, that it is advantageous to use the shallow water equations to model the interface motion. These are the depth-averaging the Navier-Stokes equations so that nonlinear and dispersion terms may be taken into account. Although these terms are essential to the prediction of wave dynamics, they are neglected in most of the literature on interface instabilities in aluminium reduction cells where only the linear theory is usually considered. The unknown variables are the two horizontal components of the fluid velocity, the height of the interface and the electric potential. In this application, a finite volume resolution of the double-layer shallow water equations including the electromagnetic sources has been developed, for incorporation into a generic three-dimensional computational fluid dynamics code that also deals with heat transfer within the cell.

Computational modelling of freeze layers in smelting processes

The use of computational modelling in examining process engineering issues is very powerful. It has been used in the development of the HIsmelt process from its concept. It is desirable to further water-cool the HIsmelt vessel to reduce downtime for replacing refractory. Water-cooled elements close to a metal bath run the risk of failure. This generally occurs when a process perturbation causes the freeze and refractory layers to come away from the water-cooled element, which is then exposed to liquid metal. The element fails as they are unable to remove all the heat. Modelling of the water-cooled element involves modelling the heat transfer, fluid flow, stress and solidification for a localised section of the reaction vessel. The complex interaction between the liquid slag and the refractory applied to the outside of thewater-cooled element is also being examined to model the wear of this layer. The model is being constructed in Physica, a CFD code developed at the University of Greenwich. Modelling of this system has commenced with modelling solidification test cases. These test cases have been used to validate the CFD code’s capability to model the solidification in this system. A model to track the penetration of slag into refractory has also been developed and tested.