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.