Simple Kinetic Model for Rapid Granular Flows Including Frictional Losses
Publication: Journal of Engineering Mechanics
Volume 116, Issue 2
Abstract
A simple kinetic model for flows of nearly elastic granular materials in the grain‐inertia regime is presented, which includes the effects of frictional‐energy dissipation during collision. It is shown that frictional losses have the same effects as energy dissipation due to the inelasticity of granular particles. The special case of granular simple shear flow is treated in detail. Variations of stress components with solid volume fraction, coefficient of restitution, and friction coefficient are studied. The results are compared with the available experimental data for rapid shearing of glass and polystyrene beads and good agreement is observed. For small values of the coefficient of friction, it is shown that the shear and normal stresses decrease as frictional‐energy dissipation increases. The decrease in normal stress is more noticeable than that of the shear stress.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ackermann, N. L., and Shen, H. (1982). “Stresses in rapid sheared fluid‐solid mixtures.” J. Engrg. Mech. Div., ASCE, 108, 748–763.
2.
Ahmadi, G., and Shahinpoor, M. (1983). “A note on collision operators in rapid granular flows of rough inelastic particles.” Power Tech., 35, 119–122.
3.
Ahmadi, G., and Ma, D. N. (1986). “A kinetic model for granular flows of nearly elastic particles in grain‐inertia regime.” Int. J. Bulk Solid Storage in Silos, 2, 8–16.
4.
Chapman, S., and Cowling, T. G. (1970). “The mathematical theory of non‐uniform gasses.” Cambridge University Press, London, England.
5.
Haff, P. K. (1983). “Grain flow as a fluid mechanical phenomenon.” J. Fluid Mech., 134, 401–430.
6.
Jenkins, J. T., and Savage, S. B. (1983). “A theory for the rapid flow of identical smooth, nearly elastic particles.” J. Fluid Mech., 130, 187–202.
7.
Jenkins, J. T., and Richman, M. W. (1985a). “Grad's 13‐moment system for a dense gas of inelastic spheres.” Archive for Rational Mech. and Analysis, 87, 355–377.
8.
Jenkins, J. T., and Richman, M. W. (1985b). “Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks.” Physics of Fluids, 28, 3485–3494.
9.
Lun, C. K. K., and Savage, S. B. (1987). “A simple kinetic theory for granular flow of rough, inelastic, spherical particles.” J. Appl. Mech., 54, 47–53.
10.
Lun, C. K. K., et al. (1984). “Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flow field.” J. Fluid Mech., 140, 223–256.
11.
Ma, D. N., and Ahmadi, G. (1986). “An equation of state for dense rigid sphere gases.” J. Chemical Physics, 84, 3449–3350.
12.
Ogawa, S., Umemura, A., and Oshima, N. (1983). “On the equations of fully fluidized granular materials.” Zeitschrift Fuer Angewaadte Mathemtie und Physik, 31, 483–493.
13.
Savage, S. B., and Sayed, M. (1984). “Stresses developed by dry cohesionless granular materials in an annular shear cell.” J. Fluid Mech., 142, 391–430.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 116 • Issue 2 • February 1990
Pages: 379 - 389
Copyright
Copyright © 1990 ASCE.
History
Published online: Feb 1, 1990
Published in print: Feb 1990
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.