Free surface problems for static Coulomb-Mohr granular solids

This paper is concerned with some plane strain and axially symmetric free surface problems which arise in the study of static granular solids that satisfy the Coulomb-Mohr yield condition. Such problems are inherently nonlinear, and hence difficult to attack analytically. Given a Coulomb friction condition holds on a solid boundary, it is shown that the angle a free surface is allowed to attach to the boundary is dependent only on the angle of wall friction, assuming the stresses are all continuous at the attachment point, and assuming also that the coefficient of cohesion is nonzero. As a model problem, the formation of stable cohesive arches in hoppers is considered. This undesirable phenomena is an obstacle to flow, and occurs when the hopper outlet is too small. Typically, engineers are concerned with predicting the critical outlet size for a given hopper and granular solid, so that for hoppers with outlets larger than this critical value, arching cannot occur. This is a topic of considerable practical interest, with most accepted engineering methods being conservative in nature. Here, the governing equations in two limiting cases (small cohesion and high angle of internal friction) are considered directly. No information on the critical outlet size is found; however solutions for the shape of the free boundary (the arch) are presented, for both plane and axially symmetric geometries.

Multi-scale modelling of granular avalanches

Avalanches, debris flows, and landslides are geophysical hazards, which involve rapid mass movement of granular solids, water and air as a single-phase system. The dynamics of a granular flow involve at least three distinct scales: the micro-scale, meso-scale, and the macro-scale. This study aims to understand the ability of continuum models to capture the micro-mechanics of dry granular collapse. Material Point Method (MPM), a hybrid Lagrangian and Eulerian approach, with Mohr-Coulomb failure criterion is used to describe the continuum behaviour of granular column collapse, while the micromechanics is captured using Discrete Element Method (DEM) with tangential contact force model. The run-out profile predicted by the continuum simulations matches with DEM simulations for columns with small aspect ratios ('h/r' < 2), however MPM predicts larger run-out distances for columns with higher aspect ratios ('h/r' > 2). Energy evolution studies in DEM simulations reveal higher collisional dissipation in the initial free-fall regime for tall columns. The lack of a collisional energy dissipation mechanism in MPM simulations results in larger run-out distances. Micro-structural effects, such as shear band formations, were observed both in DEM and MPM simulations. A sliding flow regime is observed above the distinct passive zone at the core of the column. Velocity profiles obtained from both the scales are compared to understand the reason for a slow flow run-out mobilization in MPM simulations. © 2013 AIP Publishing LLC.

The role of deposition process on pressure dip formation underneath a granular pile

This paper describes an experimental investigation on the pressure dip phenomenon in a conical pile of granular solids. The roles of different deposition processes such as the pouring rate, pouring height and deposition jet size on the pressure dip formation were studied. Test results confirmed that the pressure dip is a robust phenomenon in a pile formed by top deposition. When the deposition jet radius is significantly smaller than the final pile radius (i.e. concentrated deposition), a dip developed in the centre as shown in previous studies. However, when the deposition jet radius is comparable to the final pile radius (i.e. diffuse deposition), the location of the dip moves towards the edge of deposition jet, with a local maximum pressure developed in the centre. For concentrated deposition, an increase in the pouring rate may enhance the depth of the dip and reduce its width, while an increase in the pouring height has only a negligible effect in the studied range. The results suggest the pressure dip is closely related to the initial location, intensity and form of downslope flows. © 2013 Elsevier Inc. All rights reserved.

Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.

A DEM study of silo discharge of a cohesive solid

Bulk handling of powders and granular solids is common in many industries and often gives rise to handling difficulties especially when the material exhibits complex cohesive behaviour. For example, high storage stresses in a silo can lead to high cohesive strength of the stored solid, which may in turn cause blockages such as ratholing or arching near the outlet during discharge. This paper presents a Discrete Element Method study of discharge of a granular solid with varying levels of cohesion from a flat-bottomed silo. The DEM simulations were conducted using the commercial EDEM code with a recently developed DEM contact model for cohesive solids implemented through an API. The contact model is based on an elasto-plastic contact with adhesion and uses hysteretic non-linear loading and unloading paths to model the elastic-plastic contact deformation. The adhesion parameter is a function of the maximum contact overlap. The model has been shown to be able to predict the stress history dependent behaviour depicted by a flow function of the material. The effects of cohesion on the discharge rate and flow pattern in the silo are investigated. The predicted discharge rates are compared for the varying levels of cohesion and the effect of adhesion is evaluated. The ability of the contact model to qualitatively predict the phenomena that are present in the discharge of a silo has been shown with the salient feature of mixed flow from a flat bottomed hopper identified in the simulation.

Solid transport in a pyrolysis pilot-scale rotary kiln: Preliminary results?stationary and dynamic results

Experiments for the investigation of the flow of granular solids in a pyrolysis pilot-scale rotary kiln are presented. These experiments consisted first in measuring the volumetric filling ratio (steady-state experiences) for several operating conditions and second in recording the exit flow rates after a positive or negative step in one of the operating parameters (dynamic experiences). A dynamical model computing the evolution of the flow rate of granular solids through the kiln has been developed based on Saeman model [Chem. Eng. Prog. 47 (1951) 508]. The simulations are compared with experimental results; the model gives good results for the rolling mode, but for the slipping mode too. (C) 2004 Elsevier B.V. All rights reserved.

Utilising computational fluid dynamics (CFD) for the modelling of granular material in large-scale engineering processes

In this paper, the framework is described for the modelling of granular material by employing Computational Fluid Dynamics (CFD). This is achieved through the use and implementation in the continuum theory of constitutive relations, which are derived in a granular dynamics framework and parametrise particle interactions that occur at the micro-scale level. The simulation of a process often met in bulk solids handling industrial plants involving granular matter, (i.e. filling of a flat-bottomed bin with a binary material mixture through pneumatic conveying-emptying of the bin in core flow mode-pneumatic conveying of the material coming out of a the bin) is presented. The results of the presented simulation demonstrate the capability of the numerical model to represent successfully key granular processes (i.e. segregation/degradation), the prediction of which is of great importance in the process engineering industry.

Micro-mechanical parameterisations for continuum modelling of granular material using the discrete element method

The present work uses the discrete element method (DEM) to describe assemblies of particulate bulk materials. Working numerical descriptions of entire processes using this scheme are infeasible because of the very large number of elements (1012 or more in a moderately sized industrial silo). However it is possible to capture much of the essential bulk mechanics through selective DEM on important regions of an assembly, thereafter using the information in continuum numerical descriptions of particulate processes. The continuum numerical model uses population balances of the various components in bulk solid mixtures. It depends on constitutive relationships for the internal transfer, creation and/or destruction of components within the mixture. In this paper we show the means of generating such relationships for two important flow phenomena – segregation whereby particles differing in some important property (often size) separate into discrete phases, and degradation, whereby particles break into sub-elements, through impact on each other or shearing. We perform DEM simulations under a range of representative conditions, extracting the important parameters for the relevant transfer, creation and/or destruction of particles in certain classes within the assembly over time. Continuum predictions of segregation and degradation using this scheme are currently being successfully validated against bulk experimental data and are beginning to be used in schemes to improve the design and operation of bulk solids process plant.

A computational model of coupled heat and moisture transfer with phase change in granular sugar during varying environmental conditions

As part of a comprehensive effort to predict the development of caking in granular materials, a mathematical model is introduced to model simultaneous heat and moisture transfer with phase change in porous media when undergoing temperature oscillations/cycling. The resulting model partial differential equations were solved using finite-volume procedures in the context of the PHYSICA framework and then applied to the analysis of sugar in storage. The influence of temperature on absorption/desorption and diffusion coefficients is coupled into the transport equations. The temperature profile, the depth of penetration of the temperature oscillation into the bulk solid, and the solids moisture content distribution were first calculated, and these proved to be in good agreement with experimental data. Then, the influence of temperature oscillation on absolute humidity, moisture concentration, and moisture migration for different parameters and boundary conditions was examined. As expected, the results show that moisture near boundary regions responds faster than farther away from them with surface temperature changes. The moisture absorption and desorption in materials occurs mainly near boundary regions (where interactions with the environment are more pronounced). Small amounts of solids moisture content, driven by both temperature and vapour concentration gradients, migrate between boundary and center with oscillating temperature.

Granular Attrition due to Rotary Valve in a Pneumatic Conveying System

The rotary valve is a widely used mechanical device in many solids-handling industrial processes. However, it may also be responsible for most of the attrition effects occurring in a typical process. In this study, the attrition effects occurring in a rotary valve operating as a stand-alone device and as part of a pneumatic conveying system were investigated. In the former case granular attrition was carried out at three different rotary valve speeds and the experimental results obtained were found to be in good agreement with the Gwyn correlation. In the latter case three typical air flow rates were used in the pneumatic conveying system. The size distribution of the attrition product obtained at the lowest air flow rate used was not adequately described by the Gwyn correlation. The attrition process and mechanisms involved were analysed and the minimum size of the attrition product obtained from both modes of operations was found to be similar.