Modelling of instabilities in aluminium electrolysis cells

with Jean-Frédéric Gerbeau, Claude Le Bris and Antonin Orriols.

The physical phenomena governing the behavior of aluminium electrolysis cells are complicated and couple fluid mechanics, magnetic, chemical reactions... In our work, we focus on the magnetohydrodynamic modelling of cells.

An electrolysis cells is composed of some anods, which drive a very intense electric current through a bath (cryolite) and aluminium, both molten, towards the cathod. We are especially interested in the modelling of the movements of the interface between the two liquids (the bath and the aluminium). These movements are created by huge magnetic fields, due to the electric conductors bringing the current to the cells.

For the mathematical and numerical questions raised by the modelling of this phenomenon, we refer to :

The PhD thesis of Jean-Frédéric Gerbeau
(with J-F. Gerbeau, C. Le Bris and N. Ligonesche) Metal pad roll instabilities, proceeding of the 2002 TMS Annual Meeting and Exhibition.
(with J-F. Gerbeau and C. Le Bris) Simulations of MHD flows with moving interfaces, Journal of Computational Physics, volume 184, pp 163-191, 2003.
(with J-F. Gerbeau and C. Le Bris) Modelling and simulation of the industrial production of aluminium: the nonlinear approach, Computers and Fluids, volume 33, pp 815-820, 2004.
(with J-F. Gerbeau et C. Le Bris) Numerical simulations of two-fluids MHD flows, Fundamental and Applied MHD. Proceedings of the Fifth international PAMIR Conference, p. I.101-I.105, 2002.
(with J-F. Gerbeau et C. Le Bris) Modeling and simulation of MHD phenomena in aluminium reduction cells, Proceedings of the fourth International Conference on Electromagnetic Processing of Materials, EPM 2003, C3-10.4, p. 57-62, 2003.
(with T. Tomasino, M. Le Hervet et O. Martin) Stability analysis of simplified electrolysis cells with Mistral, proceeding of the 2006 TMS Annual Meeting and Exhibition, Light Metals, p. 335-340, 2006.
(with J-F. Gerbeau et C. Le Bris) Mathematical methods for the Magnetohydrodynamics of liquid metals, to appear in Numerical Mathematics and Scientific Computation, Oxford University Press.

Jean-Frédéric Gerbeau, Claude Le Bris and I received the Prix CS 2002 of the company Communications & Systèmes for our work about the numerical simulation of aluminium electrolysis cells (pdf).

Some numerical results :

The shape of the interface : on the left, the electric circuit and on the right, the interface obtained with this circuit.

Velocity (left) and magnetic (right) fields obtained with the same electric circuit as above.

Here are some movies showing instabilities in a cylindrical cell. These instabilities are due to a too much intense vertical component of the magnetic field (see above the proceeding article about Metal pad roll instabilities). First a case with a small magnetic field and no instability (mpeg), and then a case with an instability (mpeg).

A link to the site of Jean-Frédéric Gerbeau about the same subject : http://www-rocq.inria.fr/bang/MHD/