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Statistics of shock waves in a two-dimensional granular flow
1The Center for Chaos and Turbulence Studies, The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark.
Summary
Kinematic shock waves move against the flow in a narrow funnel, with their speed and frequency increasing away from the outlet. New shocks form where balls pack tightly across the funnel.
Area of Science:
- Physics
- Fluid Dynamics
- Granular Materials
Background:
- Granular materials exhibit complex flow behaviors, including shock wave phenomena.
- Understanding shock wave dynamics in confined geometries is crucial for various applications.
Purpose of the Study:
- To investigate the dynamics and statistics of kinematic shock waves in a 2D funnel.
- To analyze the factors influencing shock wave propagation and formation.
Main Methods:
- Utilized high-speed video equipment for data acquisition.
- Employed image analysis techniques to study shock wave statistics.
- Experimentally examined a single layer of uniform balls in a small-angle funnel (0° < β < 2°).
Main Results:
- Observed intermittent flow with kinematic shock waves propagating against the flow.
- Shock wave speed and frequency increase with distance from the outlet.
- Shock speed scales with the ratio of local to outlet funnel width.
- Identified shock wave repulsion and new shock formation at close-packed triangular sites.
Conclusions:
- Shock wave behavior in this granular system is strongly dependent on funnel geometry.
- The formation of new shocks is linked to specific packing configurations of the balls.
- The findings provide insights into the fundamental physics of granular flow and shock waves.