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Two-fluid flow under the constraint of external magnetic field: Revisiting the dam-break benchmark

Luca Marioni (Transvalor S.A., Mougins, France and MINES ParisTech, PSL – Research University, CEMEF – Centre for Material Forming, Sophia Antipolis, France)
Mehdi Khalloufi (MINES ParisTech, PSL – Research University, CEMEF – Centre for Material Forming, Sophia Antipolis, France)
Francois Bay (MINES ParisTech, PSL – Research University, CEMEF – Centre for Material Forming, Sophia Antipolis, France)
Elie Hachem (MINES ParisTech, PSL – Research University, CEMEF – Centre for Material Forming, Sophia Antipolis, France)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 6 November 2017

97

Abstract

Purpose

This paper aims to develop a robust set of advanced numerical tools to simulate multiphase flows under the superimposition of external uniform magnetic fields.

Design/methodology/approach

The flow has been simulated in a fully Eulerian framework by a {\it variational multi-scale} method, which allows to take into account the small-scale turbulence without explicitly model it. The multi-fluid problem has been solved through the convectively re-initialized level-set method to robustly deal with high density and viscosity ratio between the phases and the surface tension has been modelled implicitly in the level-set framework. The interaction with the magnetic field has been modelled through the classic induction equation for 2D problems and the time step computation is based on the electromagnetic interaction to guarantee convergence of the method. Anisotropic mesh adaptation is then used to adapt the mesh to the main problem’s variables and to reach good accuracy with a small number of degrees of freedom. Finally, the variational multiscale method leads to a natural stabilization of the finite elements algorithm, preventing numerical spurious oscillations in the solution of Navier–Stokes equations (fluid mechanics) and the transport equation (level-set convection).

Findings

The methodology has been validated, and it is shown to produce accurate results also with a low number of degrees of freedom. The physical effect of the external magnetic field on the multiphase flow has been analysed.

Originality/value

The dam-break benchmark case has been extended to include magnetically constrained flows.

Keywords

Citation

Marioni, L., Khalloufi, M., Bay, F. and Hachem, E. (2017), "Two-fluid flow under the constraint of external magnetic field: Revisiting the dam-break benchmark", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 11, pp. 2565-2581. https://doi.org/10.1108/HFF-09-2016-0371

Publisher

:

Emerald Publishing Limited

Copyright © 2017, Emerald Publishing Limited

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