Boundary Conditions for Planar Granular Flows
Publication: Journal of Engineering Mechanics
Volume 115, Issue 6
Abstract
Boundary conditions are formulated for planar, smooth, rapidly sheared granular flows. The formulation allows the slip at the wall to be large compared to the local mean particle fluctuation speed. In previous work by Jenkins and Richman, slip was assumed small. In order to allow for large slip and obtain tractable results, a simple approximation to the particle velocity distribution is employed in the formulation for the traction forces and energy dissipation rate at the wall. The theory is applied to the Couette flow of granular material and shown to compare well to numerical simulations, and to Jenkins and Richman in the limit of small slip.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ahmadi, G., and Ma, D. (1986). “A kinetic model for granular flows including interstitual fluid effects.” Int. Symp. on Slurry Flows, M. C. Roco and W. Wiedenroth, eds., FED Vol. 38, Amer. Soc. Mech. Engrg., New York, N.Y.
2.
Babić, M., and Shen, H. H. (1989). “A simple mean free path theory for stresses in a rapid granular flow.” J. Engrg. Mech., ASCE, 115(6).
3.
Bagnold, R. A. (1954). “Experiments on a gravity‐free dispersion of large solid spheres in a Newtonian fluid under shear.” Proc. Roy. Soc. London A225, 49–63.
4.
Campbell, C. S., and Gong, A. (1986). “The stress tensor in a two‐dimensional granular shear flow.” J. Fluid Mech. 164, 107–125.
5.
Chapman, S., and Cowling, T. G. (1970). The mathematical theory of non‐uniform gases, 3rd Ed., Cambridge Univ. Press, London and New York.
6.
Hanes, D. M., and Inman, D. L. (1985). “Observations of rapidly flowing granular fluid materials.” J. Fluid Mech. 150, 357–380.
7.
Hopkins, M. A. (1987). “Granular flow simulations.” Rep. No. 87‐7, Clarkson Univ., Potsdam, N.Y.
8.
Hui, K., Haff, P. K., and Ungar, J. E. (1984). “Boundary conditions for high‐shear grain flows.” J. Fluid Mech. 145, 223–233.
9.
Jeans, J. (1967). An introduction to the kinetic theory of gases. Cambridge Univ. Press, London and New York.
10.
Jenkins, J. T., and Richman, M. W. (1986). “Boundary conditions for plane flows of smooth, nearly elastic, circular disks.” J. Fluid Mech. 171, 53–69.
11.
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.
12.
Lun, C. K. K., Savage, S. B., Jeffrey, D. J., and Chepurniy, N. (1984). “Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield.” J. Fluid Mech. 140, 223–256.
13.
Pasquarell, G. C. (1987). “Boundary value problems for planar, smooth, rapidly sheared granular flows including phase changes,” thesis presented to Clarkson University, Potsdam, N.Y., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
14.
Pasquarell, G. C., and Ackermann, N. L. (1988). “Collisional stress in granular flows: Bagnold revisited.” J. Engrg. Mech., ASCE, 114(1), 49–64.
15.
Pasquarell, G. C., and Babić, M. (1988). “On the form of the velocity distribution for collisional constitutive relations.” Abstracts from the 7th Specialty Conf. Engrg. Mech. Div., ASCE, at Virginia Polytechnic Inst. and State Univ., Blacksburg, Virginia, May 23–25, 1988.
16.
Savage, S. B., and Jeffrey, D. J. (1981). “The stress tensor in a granular flow at high shear rates.” J. Fluid Mech. 110, 255–272.
17.
Savage, S. B., and Sayed, M. (1984). “Stresses developed by dry cohesionless granular materials sheared in an annular shear cell.” J. Fluid Mech. 142, 391–430.
18.
Shen, H., and Ackermann, N. L. (1984). “Constitutive equations for a simple shear flow of disk shaped granular mixtures,” Int. J. Engrg. Sci. 22, 829–843.
19.
Walton, O. R., and Braun, R. L. (1986). “Viscosity, granular‐temperature, and stress calculations for shearing assemblies of inelastic, frictional disks.” J. Rheol. 30, 949–980.
Information & Authors
Information
Published In
Copyright
Copyright © 1989 ASCE.
History
Published online: Jun 1, 1989
Published in print: Jun 1989
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.