Density waves in the flows of granular media

Abstract

We study density waves in the flows of granular particles through vertical tubes and hoppers using both analytic methods and molecular dynamics (MD) simulations. We construct equations of motion for quasi one-dimensional systems. The equations, combined with the Bagnold's law for friction, are used to describe the time evolutions of the density and the velocity fields for narrow tubes and hoppers. The solutions of the equations can have two types of density waves, kinetic and dynamic. For tubes, we can show the existence of kinetic waves, and obtain the condition for dynamic waves for tubes from the equations. For hoppers, we obtain the solutions of the equations up to the first order of the opening angle, which also show the existence of kinetic waves. We reproduce density waves in the MD simulations for tubes. The waves are believed to be kinetic based on a few evidences, including a well defined flux-density curve. In MD simulations of flows in hoppers, we find density waves, which are also believed to be kinetic. 05.40+j, 46.10+z, 62.20-x Typeset using REVT E X 1

Model for density waves in gravity-driven granular flow in narrow pipes

“…Previous simulations of granular pipe flow have also reported density waves [6,[29][30][31][32][33][34]. Several mechanisms for velocity dissipation through inelastic collisions, damping and static friction have been employed, see, e.g., [35].…”

“…Early papers [6,29] were unable to study sufficiently large numbers of grains and collsions to reach a state independent of initial conditions. The model used by Lee [30] was a 2+1-dimensional time-driven molecular dynamics (MD) simulation, with at least eight significant parameters. In the model of Peng and Herrmann [31,32], a 2+1 dimensional lattice gas automaton is used in which various events are assigned probalistic collision rules.…”

A new strategy for discrete element numerical models: 1. Theory

“…Other advantages of the method come from the very large range of initial geometries which can be investigated, from the methods inherent treatment of porosity and dilatation, and from the amount of deformation allowed. As examples, the Discrete Element Method has been successfully applied in simulations of density waves in tubes and hoppers [Lee, 1994;Ristow and Herrmann, 1994], tumbling mills [Rajamani et al, 2000;Mishra, 2003], the breakup of large aggregates in flows [Higashitani et al, 2001], fluvial sediment transport [Schmeeckle and Nelson, 2003] and large scale landslides [Campbell et al, 1995].…”

An exact method for determining local solid fractions in discrete element method simulations

“…[15][16][17][18][19][20] Some authors, most likely in an effort to save computational cost, use a center of volume (COV) approach. 21,22 Most authors fail to report their method of computing solid fraction profiles entirely. [23][24][25][26][27][28][29][30][31][32][33][34][35] Louge 36 compared the COV and partial volume methods for parallel strips when determining the solid fraction profile in the vicinity of a boundary in a Couette flow.…”