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

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.

Shocked confined-granular flow over obstacles

“…(2022) and Mathews et al. (2022). When rapid granular flow strikes an obstacle, grains undergo numerous collisions and start accumulating near the obstacle.…”

“…This image (figure 5) reveals the internal structures of the heap that were previously hidden in dark shades of shadowgraphs (shown in figure 2). The process and mechanism of the formation of detached shock waves and associated granular heaps on a single obstacle have been discussed in earlier studies, for example Amarouchene, Boudet & Kellay (2001), Khan et al (2022) and Mathews et al (2022). When rapid granular flow strikes an obstacle, grains undergo numerous collisions and start accumulating near the obstacle.…”

“…For slender bodies, which offer less deflection to the free stream, oblique attached shock waves may be formed, whereas, for bluff bodies that offer larger deflection to the incoming grains, detached bow shock waves are formed. Salient features of these shock waves are studied and modelled using a continuum approach (Gray et al 2003;Gray & Cui 2007;Johnson & Gray 2011;Cui & Gray 2013;Johnson 2020;Tregaskis et al 2022) and particle-based simulations such as the molecular dynamics and discrete element methods (Goldshtein et al 1995;Buchholtz & Pöschel 1998;Rericha et al 2001;Boudet, Amarouchene & Kellay 2008;Pudasaini & Kröner 2008;Padgett, Mazzoleni & Faw 2015;Mathews et al 2022).…”

“…2001; Boudet, Amarouchene & Kellay 2008; Pudasaini & Kröner 2008; Padgett, Mazzoleni & Faw 2015; Mathews et al. 2022).…”