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

Published online by Cambridge University Press:  04 December 2013

Peter P. Mitrano ,
John R. Zenk ,
Sofiane Benyahia ,
Janine E. Galvin ,
Steven R. Dahl  and
Christine M. Hrenya
Peter P. Mitrano
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309, USA
John R. Zenk
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309, USA
Sofiane Benyahia
Affiliation:
National Energy Technology Laboratory, Morgantown, WV 26507, USA
Janine E. Galvin
Affiliation:
National Energy Technology Laboratory, Morgantown, WV 26507, USA
Steven R. Dahl
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309, USA
Christine M. Hrenya*
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309, USA
*
†Email address for correspondence: hrenya@colorado.edu
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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 ($K{n}_{u} $) at the time of cluster detection reveals $K{n}_{u} \gg 1$ due to the presence of large velocity gradients associated with vortices. Although kinetic-theory-based continuum models are based on a small-$Kn$ (i.e. small-gradient) assumption, our findings suggest that, similar to molecular gases, Navier–Stokes-order (small-$Kn$) theories are surprisingly accurate outside their expected range of validity.

JFM classification

Granular media: Granular media Rarefied Gas Flow: Kinetic theory Instability: Nonlinear instability
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 738 , 10 January 2014 , R2
Copyright
©2013 Cambridge University Press 

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