Granular flow around a cylindrical obstacle in an inclined chute

Shock waves and granular vacua are important phenomena for studying the behavior of granular materials due to the dramatic change in flow properties across shock wave and the particle-free feature at the boundary of granular vacuum. In this paper, we use experiment and numerical simulation to study the granular free-surface flow past a cylindrical obstacle in an inclined chute, where the time-dependent development of the granular flow impacting the obstacle is analyzed at both microscopic and macroscopic scales using the discrete element method (DEM) and the depth-averaged granular model, respectively. Using high-speed camera results as a benchmark solution, the shock solutions are compared between experiment and simulation. The DEM simulation shows better agreement for its shock formation as it is capable of capturing solid, liquid, and gas behaviors for the shock region, while the depth-averaged model provides closer and simpler agreement for the jump solution across the shock. It is shown from the experiment and simulation that the granular shock wave can give rise to a solid-liquid-gas behavior following the propagation of the flow around the obstacle, where, at the front of the obstacle, the shock region can be regarded as a solid regime as the flow becomes stationary during the primary course of the granular flow. With the flow propagating to the downstream, the shock region extends significantly and exhibits strong liquid and gas behavior. Another mixed liquid and gas behavior of granular flow is also observed following the appearance of the granular vacuum, where a localized μ (I)-rheology is shown to be effective in resolving the vacuum boundary in the numerical simulation.