Time dependent electric, magnetic and hydrodynamic interaction in aluminium electrolysis cells

The waves in commercial cells for electrolytic aluminium production originate at the interface between the liquid aluminium and electrolyte, but their effect can spread into the surrounding busbar network as electric current perturbation, and the total magnetic field acquires a time dependent component. The presented model for the wave development accounts for the nonuniform electric current distribution at the cathode and the whole network of the surrounding busbars. The magnetic field is computed for the continuous current in the fluid zones, all busbars and the ferromagnetic construction elements. When the electric current and the associated magnetic field are computed according to the actual electrical circuit and updated for all times, the instability growth rate is significantly affected. The presented numerical model for the wave and electromagnetic interaction demonstrates how different physical coupling factors are affecting the wave development in the electrolysis cells. These small amplitude self-sustained interface oscillations are damped in the presence of intense turbulent viscosity created by the horizontal circulation velocity field. Additionally, the horizontal circulation vortices create a pressure gradient contributing to the deformation of the interface. Instructive examples for the 500 kA demonstration cell are presented.

Determining surface tension using DC magnetic levitation

The values of material physical properties are vital for the successful use of numerical simulations for electromagnetic processing of materials. The surface tension of materials can be determined from the experimental measurement of the surface oscillation frequency of liquid droplets. In order for this technique to be used, a positioning field is required that results in a modification to the oscillation frequency. A number of previous analytical models have been developed that mainly focus on electrically conducting droplets positioned using an A.C. electromagnetic field, but due to the turbulent flow resulting from the high electromagnetic fields required to balance gravity, reliable measurements have largely been limited to microgravity. In this work axisymmetric analytical and numerical models are developed, which allow the surface tension of a diamagnetic droplet positioned in a high DC magnetic field to be determined from the surface oscillations. In the case of D.C. levitation there is no internal electric currents with resulting Joule heating, Marangoni flow and other effects that introduce additional physics that complicates the measurement process. The analytical solution uses the linearised Navier-Stokes equations in the inviscid case. The body force from a DC field is potential, in contrast to the AC case, and it can be derived from Maxwell equations giving a solution for the magnetic field in the form of a series expansion of Legendre polynomials. The first few terms in this expansion represent a constant and gradient magnetic field valid close to the origin, which can be used to position the droplet. Initially the mathematical model is verified in microgravity conditions using a numerical model developed to solve the transient electromagnetics, fluid flow and thermodynamic equations. In the numerical model (as in experiment) the magnetic field is obtained using electrical current carrying coils, which provides the confinement force for a liquid droplet. The model incorporates free surface deformation to accurately model the oscillations that result from the interaction between the droplet and the non-uniform external magnetic field. A comparison is made between the analytical perturbation theory and the numerical pseudo spectral approximation solutions for small amplitude oscillations.