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Gravity granular flows of slightly frictional particles down an inclined bumpy chute

Published online by Cambridge University Press:  26 April 2006

J. Cao ,
G. Ahmadi  and
M. Massoudi
J. Cao
Affiliation:
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699-5725, USA
G. Ahmadi
Affiliation:
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699-5725, USA
M. Massoudi
Affiliation:
US Department of Energy, Pittsburgh Energy Technology Center, PO Box 10940, Pittsburgh, PA 15236-0940, USA
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Abstract

Gravity-driven granular flow of slightly frictional particles down an inclined, bumpy chute is studied. A modified kinetic model which includes the frictional energy loss effects is used, and the boundary conditions for a bumpy wall with small friction are derived by ensuring the balance of momentum and energy. At the free surface, the condition of vanishing of the solid volume fraction is used. The mean velocity, the fluctuation kinetic energy and the solid volume fraction profiles are evaluated. It is shown that steady granular gravity flow down a bumpy frictional chute could be achieved at arbitrary inclination angles. The computational results also show that the slip velocity may vary considerably depending on the granular layer height, the surface boundary roughness, the friction coefficient and the inclination angles. The model predictions are compared with the existing experimental and simulation data, and good agreement is observed. In particular, the model can well predicate the features of the variation of solid volume fraction and fluctuation energy profiles for different particle–wall friction coefficients and wall roughnesses.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 316 , 10 June 1996 , pp. 197 - 221
Copyright
© 1996 Cambridge University Press

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References

Abu-Zaid, S. & Ahmadi, G. 1990 Simple kinetic model for rapid granular flows including frictional losses. J. Engng Mech. ASCE 116, 379–389.Google Scholar
Abu-Zaid, S. & Ahmadi, G. 1993 Analysis of rapid shear flows of granular materials by a kinetic model including frictional losses. Powder Technol. 77, 7–17.Google Scholar
Ahmadi, G. & Ma, D. 1986 A Kinetic model for granular flows of nearly elastic particles in grain-inertia regime. Intl J. Bulk Solids Storage in Silos 2, 8–16.Google Scholar
Anderson, K. G. & Jackson, R. 1992 A comparison of the solutions of some proposed equations of motion of granular materials for fully developed flow down inclined planes. J. Fluid Mech. 241, 145–168.Google Scholar
Augenstein, D. A. & Hogg, R. 1978 An experimental study of dry powders on inclined surfaces. Powder Technol. 19, 205–215.Google Scholar
Bailard, J. 1978 An experimental study of granular-fluid flow. PhD Dissertation, Univ. Calif., San Diego, La Jolla.
Campbell, C. S. & Brennen, C. E. 1985 Chute flows of granular material: some numerical simulations. Trans. ASME J. Appl. Mech. 172, 172–178.Google Scholar
Campbell, C. S., Brennen, C. E. & Sabersky, R. H. 1985 Flow regimes in inclined open-channel flows of granular materials. Powder Technol. 41, 77–82.Google Scholar
Campbell, C. S. & Gong, A. 1986 The stress tensor in a two-dimensional granular shear flow. J. Fluid Mech. 164, 107–125.Google Scholar
Cao, J. & Ahmadi, G. 1995 Numerical simulation of frictional granular Couette flows between two bumpy parallel plates. Particulate Sci. Tech. 13, 133–147.Google Scholar
Drake, T. G. 1990 Structural features in granular flows. J. Geophys. Res. 95, 8681–8696.Google Scholar
Drake, T. G. 1991 Granular flow: physical experiments and their implications for microstructural theories. J. Fluid Mech. 225, 121–152.Google Scholar
Drake, T. G. & Shreve, R. L. 1986 High-speed motion pictures of nearly steady, uniform, two-dimensional, inertial flows of granular material. J. Rheol. 50, 981–993.Google Scholar
Gudhe, R., Rajagopal, K. R. & Massoudi, M. 1994 Fully developed flow of granular materials down a heated inclined plane. Acta Mechanica 103, 63–78.Google Scholar
Hanes, D. M., Jenkins, J. T. & Richman, M. W. 1988 The thickness of steady plane shear flows of circular disks driven by identical boundaries. Trans. ASME J. Appl. Mech. 55, 969–974.Google Scholar
Hui, K., Haff, P. K., Ungar, J. E. & Jackson, R. 1984 Boundary conditions for high shear grain flows. J. Fluid Mech. 145, 223–233.Google Scholar
Jenkins, J. T. 1992 Boundary conditions for rapid granular flow: flat, frictional walls. Trans. ASME J. Appl. Mech. 59, 120–127.Google Scholar
Jenkins, J. T. & Hanes, D. M. 1993 The balance of momentum and energy at an interface between colliding and freely flying grains in a rapid granular flow. Phys. Fluids A 5, 781–783.Google Scholar
Jenkins, J. T. & Richman, M. W. 1985 Grad's 13-moment systems for a dense gas of inelastic spheres. Arch. Rat. Mech. Anal. 87, 355–377.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. 1987 A simple kinetic theory for granular flow of rough, inelastic, spherical particles. Trans. ASME J. Appl. Mech. 54, 47–53.Google Scholar
Oyediran, A. A., Richman, M. W., Martin, R. E. & Alexandrou, A. N. 1994 Granular flows down bumpy inclines: numerical solutions. Acta Mechanica (in press).Google Scholar
Pasquarell, G. C., Ackermann, N. L., Shen, H. H. & Hopkins, M. A. 1988 Collisional stress in granular flows, bagnold revisited. J. Engng Mech. ASCE 114, 49–64.Google Scholar
Patton, J. S., Brennen, C. E. & Sabersky, R. H. 1987 Shear flows of rapidly flowing granular materials. Trans. ASME J. Appl. Mech. 54, 801–805.Google Scholar
Richman, M. W. 1988 Boundary conditions based upon a modified Maxwellian velocity distribution for flow of identical, smooth, nearly elastic spherical. Acta Mechanica 75, 227–240.Google Scholar
Richman, M. W. & Marciniec, R. P. 1990 Gravity-driven granular flows of smooth, inelastic spheres down bumpy inclines. Trans. ASME J. Appl. Mech. 57, 1036–1043.Google Scholar
Ridgway, K. & Rupp, R. 1970 Flows of granular material down chutes. Chem. Process Engng 51, 82–85.Google Scholar
Savage, S. B. 1978 Experiments on shear flows of cohesionless granular material. In Proc. US-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Material, pp. 241–254. Gakujutsu Bunken Fukyukai. Tokyo.
Savage, S. B. 1979 Gravity flows cohesionless granular materials in chutes and channels. J. Fluid Mech. 92, 53–96.Google Scholar
Savage, S. B. & Dai, R. 1991 Some aspects of bounded and unbounded shear flows of granular materials. In Micromechanics of Granular Materials, US-Japan Seminar. Potsdam, New York.
Shook, C. A., Daniel, S. M., Scott, J. A. & Holgate, J. P. 1968 Flow of suspensions in pipelines part II: mechanisms of particle suspension. Can. J. Chem. Engng 46, 238–244.Google Scholar
Walton, O. R. 1992 Numerical simulation of inclined chute flows of monodisperse, inelastic, frictional spheres. In Advances in Micromechanics of Granular Materials (ed. H. H. Shen et al.), pp. 453–461. Elsevier.
Walton, O. R., Braun, R. L., Mallon, R. G. & Cervelli, D. M. 1988 Particle-dynamics calculations of gravity flow of inelastic frictional spheres. In Micromechanics of Granular Materials (ed. M. Satake & J. T. Jenkins), pp. 152–162. Elsevier.