Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-19T15:19:04.364Z Has data issue: false hasContentIssue false
  • English
  • Français

Frictional–collisional equations of motion for granular materials and their application to flow in aerated chutes

Published online by Cambridge University Press:  26 April 2006

P. Nott  and
R. Jackson
P. Nott
Affiliation:
Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA
R. Jackson
Affiliation:
Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Equations of motion and boundary conditions for a flowing granular material, developed in earlier publications, are here extended to allow for drag forces resulting from relative motion of the material and interstitial air. These are solved for fully developed flow down an inclined plane, through which a constant flow of air passes upward. The results are compared with measurements from an experimental aerated chute, in which the inclination of the chute, the flow rate of the granular material, and the flow of air are all varied. Using parameter values from independent measurements, as far as possible, the theory is found to give a good qualitative account of the observed behaviour. With a reasonable assigned value for the one parameter that cannot be determined independently the quantitative agreement is also satisfactory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 241 , August 1992 , pp. 125 - 144
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

Doedel E. 1986 Software for Continuation and Bifurcation Problems in Ordinary Differential Equations. (AUTO Software Package user's manual.)
Jenkins J. T. 1987 Rapid shear flows of granular materials. In Non-classical Continuum Mechanics: Abstract Techniques and Applications (ed. R. J. Knops & A. A. Lacey). Cambridge University Press.
Johnson, P. C. & Jackson R. 1987 Fractional-collisional constitutive relations for granular materials, with application to plane shearing. J. Fluid Mech. 176, 67–93.Google Scholar
Johnson P. C., Nott, P. & Jackson R. 1990 Frictional-collisional equations of motion for particulate flows and their application to chutes. J. Fluid Mech. 210, 501–535.Google Scholar
Lun C. K. K., Savage S. B., Jeffrey, D. J. & Chepurniy N. 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.Google Scholar
Nott P. 1991 Analysis of granular flow in aerated and vibrated chutes. Ph.D. dissertation, Princeton University.
Richardson J. F. 1971 Incipient fluidization and particulate systems. In Fluidization (ed. J. F. Davidson & D. Harrison). Academic.
Savage S. B. 1982 Granular flow down rough inclines - review and extension. In Proc. US-Japan Seminar on New Models and Constitutive Relations in the Mechanics of Granular Materials (ed. J. T. Jenkins & M. Satake). Elsevier.
Scarlett, B. & Todd A. C. 1969 The critical porosity of free flowing solids. Trans. ASME B: J. Engng Ind. 91, 477–488.Google Scholar