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Dense, bounded shear flows of agitated solid spheres in a gas at intermediate Stokes and finite Reynolds numbers

Published online by Cambridge University Press:  10 January 2009

HAITAO XU ,
ROLF VERBERG ,
DONALD L. KOCH  and
MICHEL Y. LOUGE
HAITAO XU
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
ROLF VERBERG
Affiliation:
School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
DONALD L. KOCH*
Affiliation:
School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
MICHEL Y. LOUGE
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
*
‡Email address for correspondence: dlk15@cornell.edu
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Abstract

We consider moderately dense bounded shear flows of agitated homogeneous inelastic frictionless solid spheres colliding in a gas between two parallel bumpy walls at finite particle Reynolds numbers, volume fractions between 0.1 and 0.4, and Stokes numbers large enough for collisions to determine the velocity distribution of the spheres. We adopt a continuum model in which constitutive relations and boundary conditions for the granular phase are derived from kinetic theory, and in which the gas contributes a viscous dissipation term to the fluctuation energy of the grains. We compare its predictions to recent lattice-Boltzmann (LB) simulations. The theory underscores the role played by the walls in the balances of momentum and fluctuation energy. When particle inertia is large, the solid volume fraction is nearly uniform, thus allowing us to treat the rheology using unbounded flow theory with an effective shear rate, while predicting slip velocities at the walls. When particle inertia decreases or fluid inertia increases, the solid volume fraction becomes increasingly heterogeneous. In this case, the theory captures the profiles of volume fraction, mean and fluctuation velocities between the walls. Comparisons with LB simulations allow us to delimit the range of parameters within which the theory is applicable.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 618 , 10 January 2009 , pp. 181 - 208
Copyright
Copyright © Cambridge University Press 2008

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References

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