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On the role of the Knudsen layer in rapid granular flows

Published online by Cambridge University Press:  07 August 2007

J. E. GALVIN ,
C. M. HRENYA  and
R. D. WILDMAN
J. E. GALVIN
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309-0424, USA United States Department of Energy National Energy Technology Laboratory (NETL), Morgantown, WV 26507-0880, USA
C. M. HRENYA*
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309-0424, USA
R. D. WILDMAN
Affiliation:
Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK
*
† Author to whom correspondence should be addressed: hrenya@colorado.edu.
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Abstract

A combination of molecular dynamics simulations, theoretical predictions and previous experiments are used in a two-part study to determine the role of the Knudsen layer in rapid granular flows. First, a robust criterion for the identification of the thickness of the Knudsen layer is established: a rapid deterioration in Navier–Stokes order prediction of the heat flux is found to occur in the Knudsen layer. For (experimental) systems in which heat flux measurements are not easily obtained, a rule-of-thumb for estimating the Knudsen layer thickness follows, namely that such effects are evident within 2.5 (local) mean free paths of a given boundary. Secondly, comparisons of simulation and experimental data with Navier–Stokes order theory are used to provide a measure as to when Knudsen-layer effects become non-negligible. Specifically, predictions that do not account for the presence of a Knudsen layer appear reliable for Knudsen layers collectively composing up to 20% of the domain, whereas deterioration of such predictions becomes apparent when the domain is fully comprised of the Knudsen layer.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 585 , 25 August 2007 , pp. 73 - 92
Copyright
Copyright © Cambridge University Press 2007

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