Detachment of strong shocks in confined granular flows

Abstract

Granular flows are highly dissipative due to frictional resistance and inelasticity in collisions among grains. They are known to exhibit shock waves at velocities that are easily achieved in industrial and nature-driven flows such as avalanches and landslides. This experimental work investigates the formation of strong shock waves on triangular obstacles placed in a dry rapid granular stream in a confined two-dimensional set-up. Oblique attached shock waves are formed for mild turning angles and higher flow velocities, whereas strong bow shock waves are formed for higher turning angles and slower granular streams. A shadowgraph imaging technique elucidates interesting characteristics of the shock waves, especially in the vicinity of shock detachment. Velocity distributions in the form of scatter plots and probability distribution functions are calculated from the flow field data obtained by particle imaging velocimetry. The flow field around the granular shock wave region represents a bimodal distribution of velocities with two distinct peaks, one representing the supersonic flow within the free stream, and the other corresponding to the subsonic faction downstream of a shock wave. Connecting the two is a population that does not directly belong to either of the modes, constituting the non-equilibrium shock wave region. The effect of grain size and scaling, for fixed free-stream conditions and fixed channel width, on the shock detachment is presented. The mechanisms of the static heap formation and the shock detachment process in a confined environment are discussed.

Shocked confined-granular flow over obstacles

“…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.…”

“…The set-up consists of two parallel rectangular glass sheets of dimension 300 × 900 mm 2 separated by a gap of 5 mm, creating a thin rectangular channel that can be inclined at different angles. The experimental set-up is similar to the one used in earlier studies by Khan et al (2022), which may be referred to for more details. Figure 1(a) shows the schematic of the array of three identical wedge obstacles placed in line with symmetrical spacing (S) at a distance of l = 500 mm downstream from the hopper opening.…”

“…The separation between the calculated and experimental curves reduces as φ increases because the energy loss due to the basal friction and inelastic collisions decreases with an increase in the channel inclination. An equivalent Mach number can also be defined for these flows based on the gas dynamic analogy, which is not presented here but the reader is referred to Khan et al (2022), where a similar set-up and flow conditions are used.…”

“…The experimental set-up is similar to the one used in earlier studies by Khan et al. (2022), which may be referred to for more details. Figure 1( a ) shows the schematic of the array of three identical wedge obstacles placed in line with symmetrical spacing () at a distance of mm downstream from the hopper opening.…”

“…Therefore, granular flows easily become supersonic, even at speeds as low as 1 m s −1 , and exhibit shock waves (Heil et al 2004;Amarouchene & Kellay 2006;Khan et al 2020). Granular shocks can be produced in laboratories by placing obstacles, such as a triangular wedge, in a stream of granular material (Gray et al 2003;Gray & Cui 2007;Garai, Verma & Kumar 2019;Khan et al 2019Khan et al , 2022Patel et al 2022). These shock waves are characterised by abrupt change in velocity and packing fraction of grains across a shock front.…”