Granular Flows: Steady Planar Chute Flow within Slightly Bumpy Walls
Publication: Journal of Engineering Mechanics
Volume 121, Issue 3
Abstract
The Wentzel, Kramers, and Brillouin (WKB) asymptotic approximation is used to produce an analytical solution for the bounded, gravity-driven flow of smooth, uniform disks in the limit where the wall-form roughness is small and slip is large. A unique, steady solution is obtained for all channel slopes, in contrast with previous experiments. However, this apparent contrast can be explained by the fact that the large travel distances required to develop the very rapid flows predicted may exceed the practical limits for experimental observation. The slip speed governs the rate of mass transport, and is shown to be inversely proportional to the wall roughness, and directly proportional to the square root of the channel slope and channel width. The spatial variation in fluctuation speed is primarily governed by the energy dissipative characteristics of the disks. However, the ratio of slip speed to fluctuation speed at the wall is inversely related to both the wall elasticity and wall-form roughness.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Campbell, C. S., and Gong, A. (1986). “The stress tensor in a two-dimensional granular shear flow.”J. Fluid Mech., Vol. 164, 107–125.
2.
Dent, J. D. (1986). “Flow properties of granular materials under large overburden loads.”Acta Mechanica, Vol. 64, 111–122.
3.
Hui, K., Haff, P. K., Ungar, J. E., and Jackson, R. (1984). “Boundary conditions for high-shear grain flows.”J. Fluid Mech., Vol. 145, 223–233.
4.
Jenkins, J. T.(1992). “Boundary conditions for rapid granular flows: Flat, frictional walls.”J. Appl. Mech., 59(1), 120–127.
5.
Jenkins, J. T., and Richman, M. W.(1985). “Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks.”Phys. of Fluids, 28(12), 3485–3494.
6.
Jenkins, J. T., and Richman, M. W. (1986). “Boundary conditions for plane flows of smooth, nearly elastic, circular disks.”J. Fluid Mech., Vol. 171, 53–69.
7.
Johnson, P. C., and Jackson, R. (1987). “Frictional-collisional constitutive relations for granular materials, with application to plane shearing.”J. Fluid Mech., Vol. 176, 67–93.
8.
Lakin, W. D., and Sanchez, D. A. (1970). Topics in ordinary differential equations . Dover Publications, New York, N.Y.
9.
Pasquarell, G. C. (1987). “Boundary value problems for planar, smooth, rapidly sheared granular flows including phase changes,” PhD dissertation, Clarkson Univ., Potsdam, N.Y.
10.
Pasquarell, G. C.(1991). “Granular flows: Boundary conditions for slightly bumpy walls.”J. Engrg. Mech., ASCE, 117(2), 312–328.
11.
Pasquarell, G. C., and Ackermann, N. L.(1989). “Boundary conditions for planar granular flows.”J. Engrg. Mech., ASCE, 115(6), 1283–1302.
12.
Pasquarell, G. C., Ackermann, N. L., Shen, H. H., and Hopkins, M. A.(1988). “Collisional stress in granular flows: Bagnold revisited.”J. Engrg. Mech., ASCE, 114(1), 49–64.
13.
Richman, M. W., and Chou, C. S. (1988). “Boundary effects on granular flows of smooth disks.” ZAMP, Basel, Switzerland, Vol. 39(6), 885–901.
14.
Roberson, J. A., and Crowe, C. T. (1975). Engineering fluid mechanics . Houghton Mifflin, Boston, Mass.
15.
Savage, S. B. (1979). “Gravity flow of cohesionless granular materials in chutes and channels,”J. Fluid Mech., Vol. 92, part 1, 53–96.
16.
Shen, H. H., Hibler, W. D., and Leppäranta, M. (1986). “On applying granular flow theory to a deforming broken ice field.”Acta Mechanica, Vol. 63, 143–160.
17.
Verlet, L., and Levesque, D.(1982). “Integral equations for classical fluids III. The hard discs system.”Mol. Phys., 46(5), 969–980.
Information & Authors
Information
Published In
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Mar 1, 1995
Published in print: Mar 1995
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.