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A numerical study of granular shear flows of rod-like particles using the discrete element method

Published online by Cambridge University Press:  12 October 2012

Y. Guo*
Affiliation:
Chemical Engineering Department, University of Florida, Gainesville, FL 32611, USA
C. Wassgren
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
W. Ketterhagen
Affiliation:
Pfizer, Inc., Groton, CT 06340, USA
B. Hancock
Affiliation:
Pfizer, Inc., Groton, CT 06340, USA
B. James
Affiliation:
Chemical Engineering Department, University of Florida, Gainesville, FL 32611, USA
J. Curtis
Affiliation:
Chemical Engineering Department, University of Florida, Gainesville, FL 32611, USA
*
Email address for correspondence: guoyu03@hotmail.com

Abstract

The effect of particle aspect ratio and surface geometry on granular flows is assessed by performing numerical simulations of rod-like particles in simple shear flows using the discrete element method (DEM). The effect of particle surface geometry is explored by adopting two types of particles: glued-spheres particles and true cylindrical particles. The particle aspect ratio varies from one to six. Compared to frictionless spherical particles, smaller stresses are obtained for the glued-spheres and cylindrical particle systems in dilute and moderately dense flows due to the loss of translational energy, which is partially converted to rotational energy, for the non-spherical particles. For dilute granular flows of non-spherical particles, stresses are primarily affected by the particle aspect ratio rather than the surface geometry. As the particle aspect ratio increases, the effective particle projected area in the plane perpendicular to the flow direction increases, so that the probability of the occurrence of the particle collisions increases, leading to a reduction in particle velocity fluctuation and therefore a decrease in the stresses. Hence, a simple modification is made to the kinetic theory for granular flows to describe the stress tensors for dilute flows of non-spherical particles by incorporating a normalized effective particle projected area to account for the effect of particle collision probability. For dense granular flows, the stresses depend on both the particle aspect ratio and the surface geometry. Sharp stress increases at high solid volume fractions are observed for the glued-spheres particles with large aspect ratios due to the bumpy surfaces, which impede the flow. However, smaller stresses are obtained for the true cylindrical particles with large aspect ratios at high solid volume fractions. This trend is attributed to the combined effects of the smooth particle surfaces and the particle alignments such that the major/long axes of particles are aligned in the flow direction. In addition, the apparent friction coefficient, defined as the ratio of shear to normal stresses, is found to decrease as the particle aspect ratio increases and/or the particle surface becomes smoother at high solid volume fractions.

Type
Papers
Copyright
©2012 Cambridge University Press

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References

Abbaspour-Fard, M. H. 2004 Theoretical validation of a multi-sphere, discrete element model suitable for biomaterials handling simulation. Biosystems Engineering 88 (2), 153161.Google Scholar
Berzi, D., di Prisco, C. G. & Vescovi, D. 2011 Constitutive relations for steady, dense granular flows. Phys. Rev. E 84, 031301.Google Scholar
Campbell, C. S. 1989 The stress tensor for simple shear flows of a granular material. J. Fluid Mech. 203, 449473.CrossRefGoogle Scholar
Campbell, C. S. 2002 Granular shear flows at the elastic limit. J. Fluid Mech. 465, 261291.Google Scholar
Campbell, C. S. 2005 Stress-controlled elastic granular shear flows. J. Fluid Mech. 539, 273297.Google Scholar
Campbell, C. S. 2006 Granular material flows: an overview. Powder Technol. 162, 208229.Google Scholar
Campbell, C. S. 2011 Elastic granular flows of ellipsoidal particles. Phys. Fluids 23, 013306.CrossRefGoogle Scholar
Campbell, C. S. & Gong, A. 1986 The stress tensor in a two-dimensional granular shear flow. J. Fluid Mech. 164, 107125.Google Scholar
Carnahan, N. F. & Starling, K. E. 1969 Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51, 635636.CrossRefGoogle Scholar
Cleary, P. W. 2008 The effect of particle shape on simple shear flows. Powder Technol. 179, 144163.CrossRefGoogle Scholar
Cleary, P. W. & Sawley, M. L. 2002 DEM modeling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Appl. Math. Model. 26, 89111.CrossRefGoogle Scholar
Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assemblies. Geotechnique 29, 4765.CrossRefGoogle Scholar
Forterre, Y. & Pouliquen, O. 2008 Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 124.Google Scholar
Goldshtein, A. & Shapiro, M. 1995 Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations. J. Fluid Mech. 282, 75114.Google Scholar
Guo, Y., Wassgren, C., Ketterhagen, W., Hancock, B. & Curtis, J. 2012 Some computational considerations associated with discrete element modelling of cylindrical particles. Powder Technol. 228, 193198.Google Scholar
Hertz, H. 1882 Über die Berührung fester elastischer Körper. J. Reine Angew. Math. 92, 156171.CrossRefGoogle Scholar
Jenkins, J. T. 2006 Dense shearing flows of inelastic disks. Phys. Fluids 18, 103307.Google Scholar
Jenkins, J. T. & Richman, M. W. 1985 Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks. Phys. Fluids 28 (12), 34853494.Google Scholar
Jenkins, J. T. & Zhang, C. 2002 Kinetic theory for identical, frictional, nearly elastic spheres. Phys. Fluids 14 (3), 12281235.Google Scholar
Johnson, P. C. & Jackson, R. 1987 Frictional–collisional constitutive relations for granular materials with applications to plane shearing. J. Fluid Mech. 176, 6793.Google Scholar
Johnson, P. C., Nott, P. & Jackson, R. 1990 Frictional–collisional equations of motion for particulate flows and their applications to plane shearing. J. Fluid Mech. 210, 501535.Google Scholar
Ketterhagen, W. R., Curtis, J. S. & Wassgren, C. R. 2005 Stress results from two-dimensional granular shear flow simulations using various collision models. Phys. Rev. E 71, 061307.Google Scholar
Kodam, M., Bharadwaj, R., Curtis, J., Hancock, B. & Wassgren, C. 2010a Cylindrical object contact detection for use in discrete element method simulations. Part 1. Contact detection algorithms. Chem. Engng Sci. 65, 58525862.CrossRefGoogle Scholar
Kodam, M., Bharadwaj, R., Curtis, J., Hancock, B. & Wassgren, C. 2010b Cylindrical object contact detection for use in discrete element method simulations. Part 2. Experimental validation. Chem. Engng Sci. 65, 58635871.Google Scholar
Lasinski, M. E., Curtis, J. S. & Pekny, J. F. 2004 Effect of system size on particle-phase stress and microstructure formation. Phys. Fluids 16 (2), 265272.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, 19211929.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, 223256.Google Scholar
Mitarai, N., Hayakawa, H. & Nakanishi, H. 2002 Collisional granular flow as a micropolar fluid. Phys. Rev. Lett. 88, 174301.Google Scholar
Mohan, L. S., Rao, K. K. & Nott, P. R. 2002 A frictional Cosserat model for the slow shearing of granular materials. J. Fluid Mech. 457, 377409.Google Scholar
Montanero, J. M., Garzo, V., Santos, A. & Brey, J. J. 1999 Kinetic theory of simple granular shear flows of smooth hard spheres. J. Fluid Mech. 389, 391411.Google Scholar
Peña, A. A., García-Rojo, R. & Herrmann, H. J. 2007 Influence of particle shape on sheared dense granular media. Granul. Matt. 9, 279291.Google Scholar
Reddy, K. A., Kumaran, V. & Talbot, J. 2009 Orientational ordering in sheared inelastic dumbbells. Phys. Rev. E 80, 031304.Google Scholar
Reddy, K. A., Talbot, J. & Kumaran, V. 2010 Dynamics of sheared inelastic dumbbells. J. Fluid Mech. 660, 475498.Google Scholar
Walton, O. R. & Braun, R. L. 1986 Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks. J. Rheol. 30 (5), 949980.Google Scholar
Yoon, D. K. & Jenkins, J. T. 2005 Kinetic theory for identical, frictional, nearly elastic disks. Phys. Fluids 17, 083301.Google Scholar