Discrete particle simulation of particulate systems: A review of major applications and findings

Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves

This paper describes a model to predict the flow of an initially stationary mass of cohesion-less granular material down rough curved beds. This work is of interest in connection with the motion of rock and ice avalanches and dense flow snow avalanches. The constitutive behaviour of the material making up the pile is assumed to be described by a Mohr-Coulomb criterion while the bed boundary condition is treated by a similar Coulomb-type basal friction law assumption. By depth averaging the incompressible conservation of mass and linear momentum equations that are written in terms of a curvilinear coordinate system aligned with the curved bed, we obtain evolution equations for the depthh and the depth averaged velocityū. Three characteristic length scales are defined for use in the non-dimensionalization and scaling of the governing equations. These are a characteristic avalanche lengthL, a characteristic heightH, and a characteristic bed radius of curvatureR. Three independent parameters emerge in the non-dimensionalized equations of motion. One, which is the aspect ratio e-H/L, is taken to be small. By choosing different orderings for the other two, the tangent of the bed friction angle δ and the characteristic non-dimensional curvature λ=L/R, we can obtain different sets of equations of motion which appropriately display the desired importance of bed friction and bed curvature effects. The equations, correct to order e for moderate curvature, are discretized in the form of a Lagrangian-type finite difference representation which proved to be successful in the earlier studies of Savage and Hutter [24] for granular flow down rough plane surfaces. Laboratory experiments were performed with plastic particles flowing down a chute having a bed made up of a straight, inclined portion, a curved part and a horizontal portion. Numerical solutions are presented for conditions corresponding to the laboratory experiments. It is found that the predicted temporal-evolutions of the rear and front of the pile of granular material as well as the shape of the pile agree quite well with the laboratory experiments.

The dynamics of avalanches of granular materials from initiation to runout. Part I: Analysis

A constitutive equation appropriate for flow of cohesionless granular materials at high deformation rates and low stress levels is proposed. It consists of an extension and a reinterpretation of the theory of Goodman & Cowin (1972), and accounts for the non-Newtonian nature of the flow as evidenced by Bagnold's (1954) experiments. The theory is applied to analyses of gravity flows in inclined chutes and vertical channels. Experiments were set up in an attempt to generate two-dimensional shear flows corresponding to these analyses. Velocity profiles measured by a technique which makes use of fibre optic probes agree qualitatively with the theoretical predictions, but direct comparison is inappropriate because of unavoidable side-wall friction effects in the experiments. The existing measure of agreement suggests that the most prominent effects have been included in the proposed constitutive relations. Tests in the inclined chute revealed the possible existence of surge waves and granular jumps analogous to hydraulic jumps.

Gravity flow of cohesionless granular materials in chutes and channels

Publisher Summary This chapter discusses the mechanics of rapid granular flows. A “bulk solid” or “granular fluid” may be defined as an assembly of discrete solid components dispersed in a fluid, such that the solid constituents are in contact or near contact with their neighbors. Bulk solids comprise one member of a larger class of two-phase disperse systems made up of solids and fluids; dilute suspensions form another related member, which is more familiar to fluid mechanicists. The section II of this chapter presents a review of the classical papers of Bagnold and a discussion of the various modes and regimes of granular flow. A dimensional analysis provides a physical background to the detailed review of experimental and theoretical work that follows. Section III reviews flows in vertical channels and inclined chutes; it deals primarily with experimental observations of stress, velocity, and bulk-density fields. Laboratory devices and viscometric type experiments designed to determine the stress-strain-rate behavior are discussed in Section IV. Quasi-static testers, suspension viscometers, and high-shear-rate devices are described. Section V reviews theories for high-shear-rate granular flows. It includes continuum models as well as analytical and numerical microstructural models that consider the details of collisions between particles.

The Mechanics of Rapid Granular Flows

The influence of granular vortex motion on the volumetric performance of enclosed screw conveyors

With the growing increase in the bulk handling of grain, the grain-auger type elevator is now being widely used. While some theoretical analyses of the grain auger have been made and performance data for particular size augers have been obtained, little information is available for general design purposes. This work, which is based on an experimental approach, is aimed at producing such information. The investigation has been carried out using a small scale model auger which allowed a comprehensive range of tests to be conducted on a more manageable basisIn the first part of the investigation, a study is made of the auger performance characteristics with the aim of determining the conditions for most efficient operation. An examination is made of output and volumetric efficiency in relation to speed, angle of elevation and choke length (the length of exposed screw projecting from the lower end of the casing). The effect of casing clearance on auger output is also partially examined. In addition, the varia...

Performance of Grain Augers

Many industrial chute applications are characterised by rapid flow conditions in which the bulk solid stream thickness or depth is less than the chute width. Under these conditions, it is possible to describe the stream flow by means of a lumped parameter model which takes into account the frictional drag around the chute boundaries as well as making allowance for inter-particle friction. Equations of motion to describe the chute flow are presented and their application to the determination of chute profiles to achieve optimum flow is illustrated. By means of design examples, the problems associated with the feeding of bulk solids onto belt conveyors and conveyor transfers are discussed. Criteria for the selection of the most appropriate chute geometry to minimise chute wear and belt wear at the feed point are presented. The determination of optimum chute profiles to achieve specified performance criteria is outlined.

Chute Performance and Design for Rapid Flow Conditions

Chapters in this book discuss: storage and flow of bulk solids; determination of flow properties of bulk solids; determination of hopper geometry; analytical solutions for parameters used in bin design; wall loads in mass-flow bins; the Jenike method for predicting bin wall loads; flow rate of bulk solids from mass-flow bins; segregation and blending; estimating feeder loads; and flow of solids through transfer chutes.

Alan W. Roberts

Papers

The influence of granular vortex motion on the volumetric performance of enclosed screw conveyors

Performance of Grain Augers

Chute Performance and Design for Rapid Flow Conditions

Bulk solids: storage, flow and handling

An Investigation of the Gravity Flow of Noncohesive Granular Materials Through Discharge Chutes