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Model for density waves in gravity-driven granular flow in narrow pipes
Simen A Ellingsen1, Knut S Gjerden, Morten Grøva
1Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
Density waves in granular flow through pipes form when wall collisions are more dissipative than particle collisions. Counterintuitively, higher flow rates occur with more grains per wave, approaching a constant in simulations.
Area of Science:
- Physics
- Granular Flow Dynamics
- Statistical Mechanics
Background:
- Granular materials exhibit complex flow behaviors, particularly in confined geometries.
- Understanding density wave formation is crucial for predicting flow rates and stability.
Purpose of the Study:
- To investigate the formation criteria of density waves in gravity-driven granular flow through a narrow pipe in a vacuum.
- To analyze the relationship between flow rate, wave characteristics, and collisional dissipation.
Main Methods:
- Utilized a one-dimensional model incorporating two coefficients of restitution.
- Performed numerical simulations to observe and analyze density wave phenomena.
Main Results:
- Density waves emerge when wall-particle collision dissipation exceeds inter-particle collision dissipation.
- Maximal flow rates correlate with an increasing number of grains per density wave.
- The number of grains per wave tends towards a constant as particle count increases.
Conclusions:
- A simple criterion governs density wave formation in this granular flow system.
- The observed wave collapse in previous studies may be attributed to insufficient particle numbers for multiple wave development.
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