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Velocity distribution function and correlations in a granular Poiseuille flow

Published online by Cambridge University Press:  06 May 2010

MEHEBOOB ALAM  and
V. K. CHIKKADI
MEHEBOOB ALAM*
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bengaluru 560064, Karnataka, India
V. K. CHIKKADI
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bengaluru 560064, Karnataka, India
*
†Email address for correspondence: meheboob@jncasr.ac.in
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Abstract

Probability distribution functions of fluctuation velocities (P(ux) and P(uy), where ux and uy are the fluctuation velocities in the x- and y-directions, respectively; the gravity is acting along the periodic x-direction and the flow is bounded by two walls parallel to the y-direction) and the density and the spatial velocity correlations are studied using event-driven simulations for an inelastic smooth hard disk system undergoing gravity-driven granular Poiseuille flow (GPF). It is shown that for GPF with smooth and/or perfectly rough walls the Maxwellian/Gaussian is the leading-order distribution over a wide range of densities in the quasi-elastic limit, which is a surprising result, especially for a dilute granular gas for which the Knudsen number belongs to the transitional flow regime. The signature of wall-roughness-induced dissipation mainly shows up in the P(ux) distribution in the form of a sharp peak for negative velocities in the near-wall region. Both P(ux) and P(uy) distributions become asymmetric with increasing dissipation at any density, and the emergence of density waves, which appear in the form of sinuous wave/slug at low-to-moderate values of mean density, makes these asymmetries stronger, especially in the presence of a slug. At high densities, the flow degenerates into a dense plug (where the density approaches its maximum limit and the shear rate is negligibly small) around the channel centreline and two shear layers (where the shear rate is high and the density is low) near the walls. The distribution functions within the shear layer follow the characteristics of those at moderate mean densities. Within the dense plug, the high-velocity tails of both P(ux) and P(uy) appear to undergo a transition from Gaussian in the quasi-elastic limit to power-law distributions at large inelasticity of particle collisions. For dense flows, it is shown that although the density correlations play a significant role in enhancing the velocity correlations when the collisions are sufficiently inelastic, they do not induce velocity correlations when the collisions are quasi-elastic for which the distribution functions are close to Gaussian. The combined effect of enhanced density and velocity correlations around the channel centreline with increasing inelastic dissipation seems to be responsible for the emergence of non-Gaussian high-velocity tails of distribution functions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 653 , 25 June 2010 , pp. 175 - 219
Copyright
Copyright © Cambridge University Press 2010

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References

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