Strong oblique shock waves in granular free-surface flows

Strong oblique shock waves of granular flow are a steady-state solution formed when a granular free-surface flow deflects around a wedge-shaped obstacle at a supercritical speed, but they do not usually occur because their formation requires specific conditions to be satisfied downstream of the shock wave. This paper discusses the method of generating the strong oblique shock wave in a laboratory experiment and numerical simulation. The experiment is conducted on a plexiglass chute inclined at an angle to the horizontal, in which a dry granular material is released from a hopper at the top of the chute to form a channelized flow that passes a wedge at a downslope location. In order to generate a strong oblique shock wave, a second gate is established at the downstream of the wedge to control the material to flow out only at the designed time and height. Such a granular flowing process is simulated with a depth-averaged granular flow model, where the above two-gate system is mirrored into the inlet and outlet boundaries, respectively. The formation of the strong oblique shock is investigated through the transient solution of the flow field, and a good agreement is observed between the experiment and the simulation. Then, the steady-state solution of the interaction between the weak and strong oblique shocks is analyzed in the experiment and simulation. This result can be regarded as the third solution of granular shock because it can be formed by just changing the opening time of the second gate. With the dramatic change in flow thickness and velocity across the strong oblique shock, the bulk inertial number, used to quantify the rheological relation of granular materials, becomes extremely small, but it does not seem to affect the behavior of the flow discussed in this paper.

What is it about?

Granular shock waves bear much analogy and distinction to its gasdynamic counterpart, and are particularly important for understanding fundamental physics that pertains to modelling and simulation of granular flows. Strong oblique shock waves of granular flow are a steady-state solution formed when a granular free-surface flow deflects around a wedge-shaped obstacle at a supercritical speed, but they do not usually occur because their formation requires specific conditions to be satisfied downstream of the shock wave. This paper discusses the method of how to generate a strong oblique shock wave in laboratory experiment and numerical simulation with a good agreement. The experiment is conducted on a plexiglass chute inclined at an angle to the horizontal, in which a dry granular material is released from a hopper at the top of the chute to form a channelized flow that passes a wedge at a downslope location. In order to generate a strong oblique shock wave, a second gate is established at the downstream of the wedge to control the material to flow out only at the designed time and height. Such a granular flowing process is simulated with a depth-averaged granular flow model, where the above two-gate system is mirrored into the inlet and outlet boundaries, respectively. Finally, a steady-state shock solution formed between the weak and strong oblique shocks is generated in experiment and simulation by only adjusting the opening time of the second gate, which can be regarded as the third solution of granular shock waves.

Why is it important?

This paper explains methodologies of generating a strong oblique shock wave in laboratory experiment and numerical simulation, where a good agreement has been maintained. It will allow other researchers to conduct experimental and numerical studies for similar or different problems, or for a wider range of conditions and applications related to strong granular shock waves. One important area would be the study of the rheological behaviours that undergo dramatic change across a strong oblique shock. The suggestion of the third type of granular shock solution is a novel concept which has enriched the granular shock theory based on the similar conditions used for generating a strong oblique shock wave.