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Propagation of a strong shock over a random bed of spherical particles

Published online by Cambridge University Press:  25 January 2018

Y. Mehta ,
C. Neal ,
K. Salari ,
T. L. Jackson ,
S. Balachandar Open the ORCID record for S. Balachandar [Opens in a new window]  and
S. Thakur
Y. Mehta
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
C. Neal
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
K. Salari
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
T. L. Jackson
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
S. Balachandar*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
S. Thakur
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
*
†Email address for correspondence: bala1s@ufl.edu
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Abstract

Propagation of a strong incident shock through a bed of particles results in complex wave dynamics such as a reflected shock, a transmitted shock, and highly unsteady flow inside the particle bed. In this paper we present three-dimensional numerical simulations of shock propagation in air over a random bed of particles. We assume the flow is inviscid and governed by the Euler equations of gas dynamics. Simulations are carried out by varying the volume fraction of the particle bed at a fixed shock Mach number. We compute the unsteady inviscid streamwise and transverse drag coefficients as a function of time for each particle in the random bed for different volume fractions. We show that (i) there are significant variations in the peak drag for the particles in the bed, (ii) the mean peak drag as a function of streamwise distance through the bed decreases with a slope that increases as the volume fraction increases, and (iii) the deviation from the mean peak drag does not correlate with local volume fraction. We also present the local Mach number and pressure contours for the different volume fractions to explain the various observed complex physical mechanisms occurring during the shock–particle interactions. Since the shock interaction with the random bed of particles leads to transmitted and reflected waves, we compute the average flow properties to characterize the strength of the transmitted and reflected shock waves and quantify the energy dissipation inside the particle bed. Finally, to better understand the complex wave dynamics in a random bed, we consider a simpler approximation of a planar shock propagating in a duct with a sudden area change. We obtain Riemann solutions to this problem, which are used to compare with fully resolved numerical simulations.

JFM classification

Aerodynamics: High-speed flow Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 839 , 25 March 2018 , pp. 157 - 197
Copyright
© 2018 Cambridge University Press 

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