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Computer simulation of granular shear flows

Published online by Cambridge University Press:  20 April 2006

Charles S. Campbell
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125 Present address: Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453.
Christopher E. Brennen
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125

Abstract

Detailed understanding of flowing granular materials is severely hampered by the deficiencies of present experimental methods. To help increase the information base, a computer simulation has been developed to describe two-dimensional unidirectional flows of inelastic fully rough particles. This paper presents the results of a Couette shear-flow simulation. The results include distributions of velocity, density and granular temperature (a measure of the kinetic energy contained in the random particle motions). The effects of density and shear rate on the granular temperature are explored. Shear and normal forces on the solid walls are compared with experimental and theoretical results. The behaviour of the particles in the simulated flow is examined and assessments are made of the collision angle and velocity distributions. The development of a distinct, ‘layered’ microstructure is observed in high-density granular flows.

Type
Research Article
Copyright
© 1985 Cambridge University Press

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References

Ackermann, N. L. & Shen H.1979 Stresses in rapidly sheared fluid-solid mixtures. J. Engng Mech. Div. ASCE 108, 95113.Google Scholar
Bagnold R. A.1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear Proc. R. Soc. Lond. A 225, 4963.Google Scholar
Bailard J.1978 An experimental study of granular-fluid flow. Ph.D. thesis, University of California, San Diego.
Blinowski A.1979 On the dynamic flow of granular media. Arch. Mech. 30, 2734.Google Scholar
Campbell C. S.1982 Shear flows of granular materials. Ph.D. thesis (and Rep. E-200.7), Division of Engineering and Applied Science, California Institute of Technology.
Campbell C. S.1984 Work in progress.
Campbell, C. S. & Brennen C. E.1982a Computer simulation of shear flows of granular materials. Proc. 2nd US-Japan Seminar on New Models and Constitutive Relations in the Mechanics of Granular Materials, Ithaca, NY. Elsevier.
Campbell, C. S. & Brennen C. E.1982b Computer simulation of chute flows of granular materials. Proc. IUTAM Symp. on Deformation and Failure of Granular Materials, Delft, Netherlands. Balkema.
Campbell, C. S. & Brennen C. E.1984 Chute flows of granular material: some computer simulations, Trans. ASME E: J. Appl Mech. (to appear).Google Scholar
Chapman, S. & Cowling T. G.1970 The Mathematical Theory of Non-Uniform Gases, 3rd edn. Cambridge University Press.
Cundall P. A.1974 A computer model for rock-mass behaviour using interactive graphics for input and output of geometrical data. US Army Corps of Engrs (Missouri River Div.) Tech. Rep. MRD-2074.Google Scholar
Davis, R. A. & Deresiewicz X. X.1977 A discrete probabilistic model for mechanical responses of a granular medium. Acta Mech. 26, 6989.Google Scholar
Einstein A.1906 On the theory of the Brownian movement. Ann. d. Phys. 19, 371381. (English transl. in Investigations on the Theory of the Brownian Movement. Dover, 1956.)Google Scholar
Ferziger, J. M. & Kaper H. G.1972 Mathematical Theory of Transport Processes in Gases. North-Holland.
Ishida, M. & Shirai T.1979 Velocity distributions in the flow of solid particles in an inclined open channel. J. Chem. Engng Japan 12, 4650.Google Scholar
Jenkins, J. T. & Savage S. B.1983 A theory for the rapid flow of identical, smooth, nearly elastic particles. J. Fluid Mech. 130, 187202.Google Scholar
Kanatani K.1971a A micropolar continuum theory of granular materials. Intl J. Engng Sci. 17, 419432.Google Scholar
Kanatani K.1979b A continuum theory for the flow of granular materials. In Theoretical and Applied Mechanics (ed. Japan Natl Comm. for Theor. Appl. Mech.), vol. 27, pp. 571578.
Kanatani K.1980 A continuum theory for the flow of granular materials (II). In Theoretical and Applied Mechanics (ed. Japan Natl Comm. for Theor. Appl. Mech.), vol. 28, pp. 485497.
Landau, L. D. & Lifshitz E. M.1958 Statistical Physics. Pergamon.
Mctigue D. F.1978 A model for stresses in shear flows of granular material. Proc. US—Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp. 266271.
Mroz A.1980 On hypoelasticity and plasticity approaches to constitutive modeling of the inelastic behaviour of soils. Intl J. Numer. and Anal. Meth. in Geomech. 4, 4555.Google Scholar
Ogawa S.1978 Multi-temperature theory of granular materials. Proc. US—Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp. 208217.
Ogawa, S. & Oshima N.1977 A thermomechanical theory of soil-like materials. In Theoretical and Applied Mechanics (ed. Japan Natl Comm. for Theor. Appl. Mech.), vol. 25, pp. 229244.
Oshima N.1978 Continuum model of fluidized granular media. Proc. US—Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp. 189202.
Oshima N.1980 Dynamics of fluidized granular material. In Theoretical and Applied Mechanics (ed. Japan Natl Comm. for Theor. Appl. Mech.), vol. 28, pp. 475484.
Savage S. B.1979 Gravity flow of cohesionless granular materials in chutes and channels. J. Fluid Mech. 92, 5396.Google Scholar
Savage S. B.1984 The mechanics of rapid granular flows. Adv. Appl. Mech. 24, 000000.Google Scholar
Savage, S. B. & Sayed M.1980 Experiments on dry cohesionless materials in an annular shear cell at high shear rates. Presented at Euromech 133 – Statics and Dynamics of Granular Materials, Oxford University.
Savage, S. B. & Sayed M.1983 Stresses developed by dry cohesionless granular materials in an annular shear cell J. Fluid Mech. 142, 391430.Google Scholar
Spencer A. J. M.1981 Deformation of an ideal granular material. In Mechanics of Solids; Rodney Hill 60th Anniversary Volume (ed. H. G. Hopkins & J. J. Sewell). Pergamon.
Teollope, D. H. & Berma B. C.1980 Physical and numerical experiments with granular wedges. Geotech. 30, 135157.Google Scholar
Walton O. R.1980 Particle dynamic modeling of geological materials. Lawrence Livermore Lab. Rep. UCRL-52915.Google Scholar
Walton O. R.1982a Explicit particle dynamics model for granular materials. Lawrence Livermore Lab. Rep. UCRL-86260.Google Scholar
Walton O. R.1982b Particle-dynamic calculations of shear flows. Lawrence Livermore Lab. Rep. UCRL-88560.Google Scholar