Modelling of instabilities in aluminium electrolysis cells
The physical phenomena governing the behavior of aluminium electrolysis
cells are complicated and couple fluid mechanics, magnetic, chemical
In our work, we focus on the magnetohydrodynamic modelling of cells.
An electrolysis cells is composed of some anods, which drive a very
electric current through a bath (cryolite) and aluminium, both molten,
towards the cathod. We are especially interested in the modelling of
movements of the interface between the two liquids (the bath and the
These movements are created by huge magnetic fields, due to the
conductors bringing the current to the cells.
For the mathematical and numerical questions raised by the modelling
of this phenomenon, we refer to :
PhD thesis of Jean-Frédéric Gerbeau
- (with J-F. Gerbeau, C. Le Bris and N. Ligonesche)
pad roll instabilities, proceeding of the 2002 TMS Annual Meeting
- (with J-F. Gerbeau and C. Le Bris) Simulations of MHD flows with moving
interfaces, Journal of Computational Physics, volume 184, pp
- (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
MHD flows, Fundamental and Applied MHD. Proceedings of the Fifth
PAMIR Conference, p. I.101-I.105, 2002.
- (with J-F. Gerbeau et C. Le Bris) Modeling and simulation of
in aluminium reduction cells, Proceedings of the fourth
Conference on Electromagnetic Processing of Materials, EPM 2003,
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
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.
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
the right, the interface obtained with this circuit.
Velocity (left) and magnetic (right) fields obtained with the same
circuit as above.
Here are some movies showing instabilities in a cylindrical cell.
instabilities are due to a too much intense vertical component of the
field (see above the proceeding
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
the same subject : http://www-rocq.inria.fr/bang/MHD/
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Last update: May 3rd 2006.