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A numerical investigation of granular shock waves over a circular cylinder using the discrete element method

Published online by Cambridge University Press:  07 February 2022

Akhil K. Mathews Open the ORCID record for Akhil K. Mathews [Opens in a new window] ,
Aqib Khan Open the ORCID record for Aqib Khan [Opens in a new window] ,
Bhanuday Sharma Open the ORCID record for Bhanuday Sharma [Opens in a new window] ,
Sanjay Kumar Open the ORCID record for Sanjay Kumar [Opens in a new window]  and
Rakesh Kumar Open the ORCID record for Rakesh Kumar [Opens in a new window]
Akhil K. Mathews
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
Aqib Khan
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
Bhanuday Sharma
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
Sanjay Kumar
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
Rakesh Kumar*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
*
†Email address for correspondence: rkm@iitk.ac.in
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Abstract

Numerical simulation based on the discrete element method (DEM) is used to investigate the flow field generated when a cylindrical obstacle is placed in a supersonic granular stream. Robust validation of the simulation model is performed by comparing numerical results with experiments. Experiments are performed using a two-dimensional set-up generating rapid granular flow owing to gravity. DEM simulations demonstrate that a rapid gas-like stream of grains suddenly decelerates across the shock wave and finally collapses into a slow-moving heap at the cylinder. The volume fraction suddenly increases across the shock layer and remains constant thereafter. The flow physics of the shock wave and the granular heap is elucidated through fundamental fluid dynamic quantities such as the velocity, volume fraction, pressure and granular temperature. It is shown that the interaction of grains with a cylindrical obstacle results in the generation of pressure, which is responsible for sustaining static granular heaps on the cylinder. The total pressure is resolved into collisional and streaming components. A streaming pressure is generated owing to velocity fluctuations, and is found to be significant only in the shock wave region. The observations show that the rheological complexity offered by granular shock waves is a direct manifestation of the dissipative and frictional nature of granular collisions. The new insight into the granular heaps could be relevant to a variety of applications involving granular-fluid–solid interactions.

JFM classification

Granular media: Granular media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 936 , 10 April 2022 , A11
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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