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

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.

[1]  Joseph F. Pekny,et al.  Effect of system size on particle-phase stress and microstructure formation , 2004 .

[2]  R. Jackson,et al.  Frictional–collisional constitutive relations for granular materials, with application to plane shearing , 1987, Journal of Fluid Mechanics.

[3]  Paul W. Cleary,et al.  DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge , 2002 .

[4]  D. Vescovi,et al.  Constitutive relations for steady, dense granular flows. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Jennifer S. Curtis,et al.  Cylindrical object contact detection for use in discrete element method simulations, Part II—Experimental validation , 2010 .

[6]  Y. Forterre,et al.  Flows of Dense Granular Media , 2008 .

[7]  M. Shapiro,et al.  Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations , 1995, Journal of Fluid Mechanics.

[8]  J. Jenkins,et al.  Kinetic theory for identical, frictional, nearly elastic spheres , 2002 .

[9]  J. Jenkins Dense shearing flows of inelastic disks , 2006 .

[10]  Charles S. Campbell,et al.  Granular shear flows at the elastic limit , 2002, Journal of Fluid Mechanics.

[11]  R. L. Braun,et al.  Viscosity, granular‐temperature, and stress calculations for shearing assemblies of inelastic, frictional disks , 1986 .

[12]  C. Wassgren,et al.  Stress results from two-dimensional granular shear flow simulations using various collision models. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  S S C A M P B E,et al.  Granular shear flows at the elastic limit , 2022 .

[14]  S. Edwards,et al.  The computer study of transport processes under extreme conditions , 1972 .

[15]  K. E. Starling,et al.  Equation of State for Nonattracting Rigid Spheres , 1969 .

[16]  Charles S. Campbell,et al.  The stress tensor for simple shear flows of a granular material , 1989, Journal of Fluid Mechanics.

[17]  Jennifer S. Curtis,et al.  Some computational considerations associated with discrete element modeling of cylindrical particles , 2012 .

[18]  H. Hertz Ueber die Berührung fester elastischer Körper. , 1882 .

[19]  C. Campbell Stress-controlled elastic granular shear flows , 2005, Journal of Fluid Mechanics.

[20]  James T. Jenkins,et al.  Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks , 1985 .

[21]  Prabhu R. Nott,et al.  A frictional Cosserat model for the slow shearing of granular materials , 2002, Journal of Fluid Mechanics.

[22]  Jennifer S. Curtis,et al.  Cylindrical object contact detection for use in discrete element method simulations. Part I ― Contact detection algorithms , 2010 .

[23]  Mohammad Hossein Abbaspour-Fard,et al.  Theoretical Validation of a Multi-sphere, Discrete Element Model Suitable for Biomaterials Handling Simulation , 2004 .

[24]  C. Campbell Elastic granular flows of ellipsoidal particles , 2011 .

[25]  Paul W. Cleary,et al.  The effect of particle shape on simple shear flows , 2008 .

[26]  Prabhu R. Nott,et al.  Frictional–collisional equations of motion for participate flows and their application to chutes , 1990, Journal of Fluid Mechanics.

[27]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[28]  Ailing Gong,et al.  The stress tensor in a two-dimensional granular shear flow , 1986, Journal of Fluid Mechanics.

[29]  Hertz On the Contact of Elastic Solids , 1882 .

[30]  H. J. Herrmann,et al.  Influence of particle shape on sheared dense granular media , 2006 .

[31]  J. Talbot,et al.  Dynamics of sheared inelastic dumbbells , 2010, Journal of Fluid Mechanics.

[32]  D. Jeffrey,et al.  Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield , 1984, Journal of Fluid Mechanics.

[33]  Charles S. Campbell,et al.  Granular material flows – An overview , 2006 .

[34]  V. Garzó,et al.  Kinetic theory of simple granular shear flows of smooth hard spheres , 1999, Journal of Fluid Mechanics.