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Publication# Simulation numérique des phénomènes thermiques et magnétohydrodynamiques dans une cellule de Hall-Héroult

Abstract

This work is concerned with a numerical simulation of the thermal behaviour of an electrolysis cell for the production of the aluminium. Aluminium is produced by an electrolytic reduction of alumina dissolved in a bath of molten cryolite. In this reduction process, called Hall-Héroult process, the metal is produced at about 965 °C. A frozen bath layer, called ledge, arises in the boundary region and protects the side walls of the cell from corrosive electrolyte. This ledge may change the magnetohydrodynamical equilibrium of the cell and reduce the heat loss through the walls. The ledge is thus playing a significant role in both the thermal and magnetohydrodynamical behaviour of the cell. A precise knowledge of the ledge is thus an imporant ingredient in the optimization process of the cell. The temperature field and the ledge shape in a whole smelter are obtained by simultaneously solving the system of equations formed by: a non-linear convection-diffusion heat equation, which can be considered as a Stephan problem in enthalpy and temperature in the domain of the cell occupied by fluids and ledge, Navier-Stokes equations with a free interface in the fluid domains and Maxwell equations in the whole space. The source term of the heat equation results from the Joule effect due to the electrical current crossing the cell. A Chernoff scheme is used to numerically solve Stephan problem. Three dimensional numerical calculations showing ledge shape, temperature and velocity fields as well as electrical potential for an operating cell are obtained. The effect of thermal field on the electrical current and the effect of fluid motions on the ledge shape in the aluminium cells are presented.

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Metallic aluminium plays a key role in our modern economy. Primary
metallic aluminium is produced by the transformation of aluminium
oxide using the Hall-Héroult industrial process. This process, which
requires enormous quantities of energy, consists in performing the
electrolysis of an aluminium oxide solute in large pots and with
hundreds of thousands of amperes of electrical current.
The topic of this thesis is the study of some selected aspects of the
modelisation of the electrolysis process from the point of view of
numerical simulation. This thesis is divided in two parts.
The first part is focused on the numerical modelisation of the alumina
powder dissolution and transport in the electrolytic bath as a
function of the bath temperature. We provide a mathematical model for the
transport and dissolution of the alumina powder, followed by its time
and space discretisation by means of a finite element
method. Finally, we study the behavior of this numerical model in
the case of an industrial electrolysis pot.
The second part is devoted to the development of a numerical scheme for
the approximation of the fluid flows in an electrolysis pot. The
scheme relies on a Fourier basis decomposition of the unknowns. The amplitude
of each Fourier component satisfies a partial differential equation
which is explicitely derived. The solution of this equation is
approximated by means of a finite element method. Finally, the
approximate fluid flow obtained with this new method is compared
with the solution provided by the reference model in an industrial

The purpose of this thesis is the study, from the numerical simulation point of view, of the aluminum electrolysis process. Navier-Stokes equations for the computation of a two fluids flow with free interface are coupled with Maxwell equations describing the electric current repartition and the magnetic induction field in an electrolysis reduction cell. The emphasis is set on an efficient method for the computation of the magnetic induction in an unbounded domain. The algorithm is based on a Schwarz domain decomposition method and on the Poisson integral representation formula for harmonic functions. The partial differential equations that rule the phenomena are discretized in space and time and implemented in an existing numerical simulation software. This code is then tested on an academic test case and also in a more realistic situation. The key parts of the mathematical model are emphasized. Finally the time-evolution model is compared with another approach, dealing with stationary situations and their linear stability.