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

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 (Knu) at the time of cluster detection reveals Knu » 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.
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Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0022-1120; applab
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Fluid Mechanics; Journal Volume: 738
Cambridge University Press
Research Org:
National Energy Technology Laboratory - In-house Research; National Energy Technology Laboratory (NETL), Pittsburgh, PA, and Morgantown, WV (United States); Albany Research Center (ARC), Albany, OR (United States)
Sponsoring Org:
USDOE Office of Fossil Energy (FE)
Country of Publication:
United States
42 ENGINEERING granular media, kinetic theory, nonlinear instability