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Mathematical Methods for the Magnetohydrodynamics of Liquid Metals$
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Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre

Print publication date: 2006

Print ISBN-13: 9780198566656

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198566656.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 21 October 2020

MHD MODELS FOR ONE INDUSTRIAL APPLICATION

MHD MODELS FOR ONE INDUSTRIAL APPLICATION

Chapter:
(p.233) 6 MHD MODELS FOR ONE INDUSTRIAL APPLICATION
Source:
Mathematical Methods for the Magnetohydrodynamics of Liquid Metals
Author(s):

Jean-Frédéric Gerbeau

Claude Le Bris

Tony Lelièvre

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566656.003.0006

This chapter is entirely devoted to one industrial application, the simulation of the industrial production of aluminium in electrolytic cells. The simulation of this specific problem has indeed motivated the whole scientific strategy described in the first five chapters. It serves as an illustration of the efficiency of the approach presented throughout this book. A schematic description of the problem is as follows. An electric current of huge intensity runs downwards through two horizontal layers of incompressible non-miscible conducting fluids. Owing to the magnetohydrodynamics coupling, the interface between the fluids moves, and, in view of the very high intensity of the electric current, the system is very sensitive to instabilities. The industrial challenge is to model, understand, and control these instabilities. Numerical simulation of nonlinear systems can help to reach such a goal. Other techniques (such as a stability analysis for the linearized system) are also employed, and are overviewed for comparison.

Keywords:   aluminium electrolysis cells, linear stability analysis, non-linear stability analysis, Sele's criterion, metal pad roll instabilities

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