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Numerical simulation of inelastic frictional spheres in simple shear flow

Published online by Cambridge University Press:  26 April 2006

C. K. K. Lun  and
A. A. Bent
C. K. K. Lun
Affiliation:
Department of Engineering, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
A. A. Bent
Affiliation:
Department of Engineering, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
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Abstract

A numerical program is developed to simulate an assembly of inelastic frictional spheres inside a control volume undergoing rapid shearing motion induced by the top and bottom moving periodic boundaries. A sticking–sliding collision model is used to emulate binary collisions of real particles. After the flow has reached a steady state, ensemble averages of macroscopic properties such as translational and rotational granular temperatures, and kinetic and collisional stresses at different solids concentrations are obtained. The present results are compared with previous theoretical, numerical and experimental works, and favourable agreement is found among them. The simulation results show that the stresses are anisotropic and decrease with decreasing coefficient of restitution and increasing friction coefficient. At high solids fraction, above about 0.5, there exists a critical concentration where the layering effects of particles, the formation of high-density microstructures and the increase in correlation of particle velocities are the major causes of abrupt changes in flow properties.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 258 , 10 January 1994 , pp. 335 - 353
Copyright
© 1994 Cambridge University Press

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References

Allen, M. P. & Tildesley, D. J. 1987 Computer Simulation of Liquids. Oxford University Press.
Babic, M. 1992 Particle clustering: an instability of rapid granular flows. In Advances in Micromechanics of Granular Materials (ed. H. Shen, M. Satake, M. Mehrabadi, C. S. Chang & C. S. Campbell).Elsevier.
Campbell, C. S. 1986 Computer simulation of rapid granular flows. Proc. US Natl Congr. Appl. Mech., 10th Austin, TX, pp. 327–338.
Campbell, C. S. 1989 The stress tensor for simple shear flows of a granular material. J. Fluid Mech. 203, 449–473.Google Scholar
Campbell, C. S. 1990 Rapid granular flows. Ann. Rev. Fluid Mech 22, 57–92.Google Scholar
Campbell, C. S. & Brennen, C. E. 1985 Computer simulation of granular shear flows. J. Fluid Mech. 151, 167–188.Google Scholar
Carnahan, N. F. & Starling, K. E. 1969 Equations of state for non-attracting rigid spheres. J. Chem. Phys. 51, 635–636.Google Scholar
Craig, K., Buckholz, R. H. & Domoto, G. 1986 An experimental study of the rapid flow of dry cohesionless metal powders. Trans. ASME E: J. Appl. Mech. 53, 935–942.Google Scholar
Craig, K., Buckholz, R. H., & Domoto, G. 1987 Effects of shear surface boundaries on stress for shearing flow of dry metal powders–an experimental study. Trans. ASME K: J. Tribol. 109, 232–237.Google Scholar
Goldsmith, W. 1960 Impact: The Theory and Physical Behavior of Colliding Solids. E. Arnold.
Hanes, D. M. & Inman, D. L. 1985 Observations of rapidly flowing granular-fluid materials. J. Fluid Mech. 150, 357–380.Google Scholar
Hoover, W. G. & Ree, F. H. 1968 Melting transition and communal entropy for hard spheres. J. Chem. Phys. 49, 3609–3617.Google Scholar
Hopkins, M. A., Jenkins, J. T. & Louge, M. Y. 1992 On the structure of 3D shear flows. In Advances in Micromechanics of Granular Materials (ed. H. Shen, M. Satake, M. Mehrabadi, C. S. Chang & C. S. Campbell).Elsevier.
Hopkins, M. A. & Louge, M. Y. 1991 Inelastic microstructure in rapid granular flows of smooth disks. Phys. Fluids A 3, 47–57.Google Scholar
Jenkins, J. T. 1987 Rapid flows of granular materials. In Non-classical Continuum Mechanics: Abstract Techniques and Applications (ed. R. J. Knops & A. A. Lacey). Cambridge University Press.
Jenkins, J. T. & Richman, M. W. 1985 Grad's 13-moment system for a dense gas of inelastic spheres. Arch. Rat. Mech. Anal. 87, 355–377.Google Scholar
Johnson, K. L. 1982 One hundred years of Hertz contact. Proc. Inst. Mech. Engrs 196, 363–378.Google Scholar
Lees, A. W. & Edwards, S. F. 1972 The computer study of transport processes under extreme conditions. J. Phys. C: Solid State Phys. 5, 1921–1929.Google Scholar
Lun, C. K. K. 1991 Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres. J. Fluid Mech. 233, 539–559.Google Scholar
Lun, C. K. K. & Savage, S. B. 1987 A simple kinetic theory for granular flow of rough, inelastic, spherical particles. Trans. ASME E: J. Appl. Mech. 54, 47–53.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 flowfield. J. Fluid Mech. 140, 223–256.CrossRefGoogle Scholar
Maw, N. 1976 A theoretical and experimental investigation into the impact and rebound of elastic bodies PhD Thesis, CNAA, Sunderland Polytechnic, UK
Maw, N., Barber, J. R. & Fawcett, J. N. 1976 The oblique impact of elastic spheres. Wear 38, 101–114.Google Scholar
Maw, N., Barber, J. R. & Fawcett, J. N. 1981 The role of elastic tangential compliance in oblique impact. Trans ASME F: J. Lubrication Technol. 103, 74–80.Google Scholar
Nakagawa, M. 1988 Kinetic theoretical approach for rapidly deforming granular material. In Micromechanics of Granular Materials (ed. M. Sataka & J. T. Jenkins).Elsevier.
Richman, M. W. 1986 Kinetic theories for rate dependent granular flows. Proc. US Natl Congr. Appl. Mech, 10th Austin, TX pp. 339–366.
Richman, M. W. 1989 The source of 2nd moment in dilute granular flows of highly inelastic spheres. J. Rheol. 33, 1293–1306.Google Scholar
Savage, S. B. 1989 Flow of granular materials. In Theoretical and Applied Mechanics (ed. P. Germain, M. Piau & D. Caillerie).Elsevier.
Savage, S. B. 1992 Numerical simulations of Couette flow of granular materials; spatio-temporal coherence and 1/f noise. In Physics of Granular Media (ed. J. Dodds & D. Bideau), pp. 343–362. New York: Nova Science.
Savage, S. B. 1993 Disorder, diffusion and structure formation in granular flows. In Disorder and Granular Media (ed. D. Bideau). North-Holland.
Savage, S. B. & Sayed, M. 1984 Stresses developed by dry cohesionless granular materials sheared in an annular shear cell. J. Fluid Mech. 142, 391–430.Google Scholar
Walton, O. R. 1988 Granular solids flow project quarterly report. Rep UCID-20297–88–1. Lawrence Livermore Lab., University of California.
Walton, O. R., & Braun, R. L. 1986a Stress calculations for assemblies for inelastic spheres in uniform shear. Acta Mech. 63, 73–86.Google Scholar
Walton, O. R., & Braun, R. L. 1986b Viscosity and temperature calculations for shearing assemblies of inelastic, frictional disks. J. Rheol. 30, 949–980.Google Scholar
Walton, O. R., Kim, H. & Rosato, A. D. 1991 Micro-structure and stress difference in shearing flows of granular materials. Proc. ASCE Engng Mech. Div. Conf., Columbus. Ohio, May 19–21, 1991.