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Characterization of the flow past a truncated square cylinder in a duct under a spanwise magnetic field

Published online by Cambridge University Press:  05 December 2011

Vincent Dousset  and
Alban Pothérat
Vincent Dousset*
Affiliation:
Applied Mathematics Research Centre, Faculty of Engineering and Computing, Coventry University, Priory Street, Coventry CV15FB, UK
Alban Pothérat
Affiliation:
Applied Mathematics Research Centre, Faculty of Engineering and Computing, Coventry University, Priory Street, Coventry CV15FB, UK
*
†Email address for correspondence: vincent.dousset@voila.fr
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Abstract

We study the flow of an electrically conducting fluid past a truncated square cylinder in a rectangular duct under the influence of an externally applied homogeneous magnetic field oriented along the cylinder axis. Our aim is to bridge the gap between the non-magnetic regime, where we previously found a complex set of three-dimensional recirculations behind the cylinder (Dousset & Pothérat, J. Fluid Mech., vol. 653, 2010, pp. 519–536) and the asymptotic regime of dominating Lorentz force analysed by Hunt & Ludford (J. Fluid. Mech., vol. 33, 1968, pp. 693–714). The latter regime is characterized by a remarkable structure known as Hunt’s wake in the magnetohydrodynamics community, where the flow is deflected on either side of a stagnant zone, right above the truncated cylinder as if the latter would span the full height of the duct. In steady flows dominated by the Lorentz force, with negligible inertia, we provide the first numerical flow visualization of Hunt’s wake. In regimes of finite inertia, a thorough topological analysis of the steady flow regimes reveals how the Lorentz force gradually reorganizes the flow structures in the hydrodynamic wake of the cylinder as the Hartmann number (which gives a non-dimensional measure of the magnetic field) is increased. The nature of the vortex shedding follows from this rearrangement of the steady structures by the magnetic field. As is increased, we observe that the vortex street changes from a strongly symmetric one to the alternate procession of counter-rotating vortices typical of the non-truncated cylinder wakes.

JFM classification

MHD and Electrohydrodynamics: High-Hartmann-number flows Wakes/Jets: Vortex streets Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 691 , 25 January 2012 , pp. 341 - 367
Copyright
Copyright © Cambridge University Press 2011

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Dousset and Potherat supplementary movie

Animation of the vortex street at $Re=600$ and $Ha=50$: iso-surfaces of $\lambda_2=-20$ for $1212\le t \le1266$. One observes the formation and release of almost symmetric rib-like vortices

Download Dousset and Potherat supplementary movie(Video)
Video 2 MB

Dousset and Potherat supplementary movie

Animation of the vortex street at $Re=600$ and $Ha=50$: iso-surfaces of $\lambda_2=-20$ for $1212\le t \le1266$. One observes the formation and release of almost symmetric rib-like vortices

Download Dousset and Potherat supplementary movie(Video)
Video 7.1 MB

Dousset and Potherat supplementary movie

Caption: Animation of the vortex street at $Re=800$ and $Ha=100$: iso-surfaces of $\lambda_2=-30$ for $640\le t \le664$. Note the change in the direction along which the vortices are released in the wake

Download Dousset and Potherat supplementary movie(Video)
Video 942.1 KB

Dousset and Potherat supplementary movie

Caption: Animation of the vortex street at $Re=800$ and $Ha=100$: iso-surfaces of $\lambda_2=-30$ for $640\le t \le664$. Note the change in the direction along which the vortices are released in the wake

Download Dousset and Potherat supplementary movie(Video)
Video 2.7 MB

Dousset and Potherat supplementary movie

Caption: Animation of the vortex street at $Re=1000$ and $Ha=200$: iso-surfaces of $\lambda_2=-30$ for $429\le t \le567$. Note the alternance between the modes of vortex shedding.

Download Dousset and Potherat supplementary movie(Video)
Video 2.9 MB

Dousset and Potherat supplementary movie

Caption: Animation of the vortex street at $Re=1000$ and $Ha=200$: iso-surfaces of $\lambda_2=-30$ for $429\le t \le567$. Note the alternance between the modes of vortex shedding.

Download Dousset and Potherat supplementary movie(Video)
Video 8 MB