Journal of Fluid Mechanics

Rapids

Kinetic-theory predictions of clustering instabilities in granular flows: beyond the small-Knudsen-number regime

Peter P. Mitranoa1, John R. Zenka1, Sofiane Benyahiaa2, Janine E. Galvina2, Steven R. Dahla1 and Christine M. Hrenyaa1 c1

a1 Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309, USA

a2 National Energy Technology Laboratory, Morgantown, WV 26507, USA

Abstract

In this work we quantitatively assess, via instabilities, a Navier–Stokes-order (small-Knudsen-number) continuum model based on the kinetic theory analogy and applied to inelastic spheres in a homogeneous cooling system. Dissipative collisions are known to give rise to instabilities, namely velocity vortices and particle clusters, for sufficiently large domains. We compare predictions for the critical length scales required for particle clustering obtained from transient simulations using the continuum model with molecular dynamics (MD) simulations. The agreement between continuum simulations and MD simulations is excellent, particularly given the presence of well-developed velocity vortices at the onset of clustering. More specifically, spatial mapping of the local velocity-field Knudsen numbers () at the time of cluster detection reveals due to the presence of large velocity gradients associated with vortices. Although kinetic-theory-based continuum models are based on a small- (i.e. small-gradient) assumption, our findings suggest that, similar to molecular gases, Navier–Stokes-order (small-) theories are surprisingly accurate outside their expected range of validity.

(Received September 26 2013)

(Revised November 05 2013)

(Accepted November 09 2013)

(Online publication December 04 2013)

Key words

  • granular media;
  • kinetic theory;
  • nonlinear instability

Correspondence

c1 Email address for correspondence: hrenya@colorado.edu

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