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Velocity distribution for a two-dimensional sheared granular flow.

M Bose1, V Kumaran

  • 1Department of Chemical Engineering, Indian Institute of Science, Bangalore, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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This study examines granular flow in a channel, revealing how particle collisions and wall interactions affect velocity distributions across various Knudsen numbers. Findings show complex velocity patterns, with temperature dissipation at walls, impacting flow dynamics.

Area of Science:

  • Physics
  • Granular Mechanics
  • Fluid Dynamics

Background:

  • Understanding granular flow in confined geometries is crucial for various industrial applications.
  • Previous theoretical models predict bimodal velocity distributions in high Knudsen number regimes.
  • The influence of inelastic particle-wall collisions on granular temperature and slip velocity requires detailed investigation.

Purpose of the Study:

  • To investigate the velocity distribution of two-dimensional granular flow in a channel.
  • To analyze the effects of inelastic particle-particle and particle-wall collisions on flow behavior.
  • To explore the relationship between Knudsen number, restitution coefficients, and flow characteristics.

Main Methods:

  • Simulated a two-dimensional collection of disks with varying number density and radius.

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  • Incorporated inelastic particle-particle collisions (coefficient e) and inelastic particle-wall collisions (coefficients e(t), e(n)).
  • Varied the Knudsen number (Kn) from <<1 to >>1 to cover different flow regimes.

    • Main Results:

    • High Kn regime: Streamwise velocity distribution is bimodal, consistent with theory, with moments scaling as predicted.
    • Low Kn regime: Distribution is Gaussian for restitution close to 1, and 'composite Gaussian' otherwise.
    • Intermediate regime: Complex distribution with three maxima near the wall and bimodal at the center; significant temperature dissipation at the wall.
    • Slip velocity at the wall exhibits a power-law dependence on Kn, with the exponent influenced by restitution coefficients.

    Conclusions:

    • Kinetic theory accurately predicts granular temperature at the channel center.
    • Inelastic particle-wall collisions cause significant temperature dissipation, even at high restitution coefficients.
    • Slip velocity at the wall is strongly dependent on both Knudsen number and restitution coefficients.