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Shock waves induced by a planar obstacle in a vibrated granular gas

Published online by Cambridge University Press:  07 March 2018

Alexandre Vilquin ,
Hamid Kellay  and
Jean-François Boudet Open the ORCID record for Jean-François Boudet [Opens in a new window]
Alexandre Vilquin
Affiliation:
Laboratoire Onde et Matière d’Aquitaine (UMR CNRS 5798), Université de Bordeaux, 351 cours de la Libération, 33405 Talence, France
Hamid Kellay
Affiliation:
Laboratoire Onde et Matière d’Aquitaine (UMR CNRS 5798), Université de Bordeaux, 351 cours de la Libération, 33405 Talence, France
Jean-François Boudet*
Affiliation:
Laboratoire Onde et Matière d’Aquitaine (UMR CNRS 5798), Université de Bordeaux, 351 cours de la Libération, 33405 Talence, France
*
†Email address for correspondence: jean-francois.boudet@u-bordeaux.fr
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Abstract

The low value of the speed of sound in dilute granular media permits the study of the properties of supersonic flows for a wide range of Mach numbers. In this paper, we report the experimental observation of a subsonic–supersonic transition in a vibrated granular gas. The shock fronts studied are obtained by simply pushing a rectangular obstacle into the granular gas for different obstacle velocities. The supersonic regime is characterized by the formation of normal shock waves whose width increases when the Mach number decreases to values close to 1. The bimodal model proposed by Mott-Smith in the 1950s provides a good description for the velocity distributions as well as the macroscopic quantities for shock waves in molecular gases but remains inadequate for dissipative media like granular gases and plasmas. Here by examining the shock front structure for a wide range of Mach numbers, we adapt the Mott-Smith bimodal description to a dissipative medium. By using balance equations from granular kinetic theory and taking into account different dissipation sources, the proposed model allows us to understand how this dissipation modifies temperature, mean velocity and volume fraction profiles through the shock front.

JFM classification

Granular media: Granular media Rarefied Gas Flow: Kinetic theory Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 842 , 10 May 2018 , pp. 163 - 187
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Copyright
© 2018 Cambridge University Press 

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