Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T05:14:26.559Z Has data issue: false hasContentIssue false
  • English
  • Français

A Monte Carlo solution for rapidly shearing granular flows based on the kinetic theory of dense gases

Published online by Cambridge University Press:  26 April 2006

Mark A. Hopkins  and
Hayley H. Shen
Mark A. Hopkins
Affiliation:
US Army Corps of Engineers Cold Regions Research and Engineering Laboratory, 72 Lyme Road, Hanover, NH 03755. USA
Hayley H. Shen
Affiliation:
Department of Civil and Environmental Engineering, Clarkson University, Potsdam, NY 13676, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A Monte Carlo simulation is developed for the study of rapidly deforming, steady, simple shear flows of inelastic disks or spheres. The simulation is based on the theoretical framework of the kinetic theory of dense gases. In the simulation, space is discarded in an explicit sense and replaced by an isotropic, homogeneous, and uncorrelated space based on the assumption of a state of simple shear, a uniform concentration field, and molecular chaos. The simulation generates a distribution of particle velocities which corresponds to the parameters of the flow. The velocity distribution is a numerical solution to the Boltzmann equation under these conditions. The Monte Carlo simulation defines the limits to the accuracy of analytical granular flow theories based on the kinetic theory and the assumption of molecular chaos.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 244 , November 1992 , pp. 477 - 491
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bagnold R. A. 1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear Proc. R. Soc. Lond. A 225, 49–63.Google Scholar
Campbell C. S. 1986 The effect of microstructure development on the collisional stress tensor in a granular flow. Acta Mech. 63, 61–72.Google Scholar
Campbell C. S. 1989 The stress tensor for simple shear flows of a granular material. J. Fluid Mech. 203, 449–473.Google Scholar
Carnahan, N. F. & Starling K. E. 1969 Equations of state for non-attracting rigid spheres. Chem. Phys. 51, 635–636.Google Scholar
Chapman, S. & Cowling T. G. 1970 The Mathematical Theory of Non-Uniform Gases, 3rd ed. Cambridge University Press.
Hopkins M. A. 1987 Constitutive relations for rapidly sheared granular flows: a Monte Carlo form based on the kinetic theory of dense gases. PhD dissertation. Clarkson University, Potsdam, New York.
Hopkins, M. A. & Louge M. Y. 1991 Inelastic micro-structure in rapid granular flows of smooth disks Phys. Fluids A 3 (1), 47–57.Google Scholar
Jeans J. 1948 An Introduction to the Kinetic Theory of Gases. Cambridge University Press.
Jenkins, J. T. & Richman M. W. 1988 Plane simple shear of smooth, inelastic circular disks: the anisotropy of the fluctuation energy in the dilute and dense limits. J. Fluid Mech. 192, 313–328.Google Scholar
Jenkins, J. T. & Savage S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles, J. Fluid Mech. 130, 187–202.Google Scholar
Lun C. K. K., Savage S. B., Jeffrey, D. J. & Chepurniy N. 1984 Kinetic theories for granular flow: inelastic particles in a couette flow and slightly inelastic particles in a general flow field. J. Fluid Mech. 140, 223–256.Google Scholar
Richman, M. W. & Chou C. S. 1992 Constitutive theory for homogeneous granular shear flows of highly inelastic spheres. J. Rheol. (submitted).Google Scholar
Savage, S. B. & Jeffrey D. J. 1981 The stress tensor in a granular flow at high shear rates. J. Fluid Mech. 110, 255–272.Google Scholar
Walton O. R. 1983 Particle-dynamics calculations of shear flow. Mechanics of Granular Materials – New Models and Constitutive Relations (ed. J. T. Jenkins & M. Satake), pp. 327–338. Elsevier.
Walton, O. R. & Braun R. L. 1986 Stress calculations for assemblies of inelastic spheres in uniform flow. Acta Mech. 63, 73–86.Google Scholar