A combined physical and DEM modelling approach to investigate particle shape effects on load movement in tumbling mills

The discrete element method (DEM) which is used to simulate granular flows often assumes spherical shape for particles. This assumption is legitimized by the added complexity of non-spherical shape representation, contact detection and computational cost. In this work, the difference between the dynamics of non-spherical and spherical particles was studied in detail by a combined physical and DEM modeling approach. An in-house developed DEM software called KMPC_DEM©, which was coded to handle non-spherical particles, was used to simulate the behavior of particles. To calibrate the model parameters, a model tumbling mill (100 cm diameter and 10.8 cm length) with one transparent end was used which made accurate photography possible. The tests were performed at filling of 20% and mill speed of 85% of critical speed with steel balls and wood cubes. In the simulation, each cubical particle was represented with clusters of spheres (with identical size) by particle packing algorithm for contact detection and contact-force calculation. Comparison of the simulation and experimental results showed that the difference between the measured and predicted impact toe, shoulder angle and bulk toe angle were 3, 4 and 5°, respectively. The significant change in the charge movement and structure on account of non-spherical particles was reflected in the amount of in-flight charge, and positions of shoulder, impact toe and bulk toe. It found that there was a 17% difference in the amount of in-flight of charge between cubical and spherical particles. The marked difference was attributed to higher interlocking of non-spherical particles in comparison to spherical balls. The results showed that cubical particles participated 5% more in the high energy impact action compared to that of the spherical particles. The simulation computation time increased by 35 times when the shape of particles changed from spherical to cubical.     

DEM investigations of failure mode of sands under oedometric loading

It will be practically useful to explore the evolutions of the failure modes of sand grains within a sand specimen subject to compression for the particle breakage research. This paper attempts to deal with this challenge by conducting a discrete element method (DEM) simulation study on oedometric compression of two kinds of sands (spherical and non-spherical particles). In this study, particle morphologies reconstructed by the spherical harmonic (SH) analysis were created using the agglomerate method, and the micro-parameters used to define the contact model and the properties of walls and balls were adopted based on the single particle crushing tests. The effects of particle shape on the crushing behavior of granular materials and on the evolutions of failure modes of sand grains were captured, and the experimental data was used to evaluate the feasibility and reliability of the proposed DEM modelling strategy. The simulation results show that particle shape affects not only the number, type and orientation of cracks but also the evolution of the particle failure modes. The failure mode of chipping is the most common way to crush for both spherical and non-spherical particles. The particles that have less aspect ratio, sphericity and convexity are more likely to experience the failure mode of comminution. These findings shed light on the key role of particle shape in the investigation of the failure mode of sand grains and facilitate a better understanding of grain-scale behavior of granular materials.     

A modelling and verification approach for soybean seed particles using the discrete element method

To build a discrete element method (DEM) model of soybean seed particles, the shape and size of soybean seed particles were measured and analysed. The results showed that the shape of a soybean seed particle could be approximated to an ellipsoid and that the dispersity in size could be approximated by a normal distribution. Additionally, a certain functional relationship between the primary dimension and secondary dimensions was determined. On this basis, an approach for modelling soybean seed particles based on the multi-sphere (MS) method was proposed. The soybean seed particle was simplified to an ellipsoid with the averaged size of one hundred randomly selected soybean seeds. The model of a single soybean seed particle was built by filling spheres within the ellipsoid. For modelling soybean seed assembly, the primary dimension was generated according to the normal distribution, and the other secondary dimensions were calculated based on their relationships with the primary dimension. In this way, the model of soybean seed assembly with different sizes and distributions was built. In this paper, four varieties of soybean seed were used. By comparing the simulated results and experimental results both in piling tests and “self-flow screening” tests, when the number of filling spheres was five, the simulated results were close to those obtained experimentally. Therefore, the feasibility and validity of the modelling method for soybean seed particles that we proposed were verified. Finally, an application case was employed to show how to use the soybean seed particle model and the discrete element method to analyse the discharging process of a silo.     

Influence of particle shape on mixing rate in rotating drums based on super-quadric DEM simulations

Fundamental research on the flow and mixing of non-spherical particles is critical for industrial production and design. In this paper, the Discrete Element Method (DEM) is used to study the flow and mixing of granular materials in the horizontal rotating drum, and the periodic boundary condition is employed to eliminate end wall effect. Super-quadric elements are adopted to describe spherical and non-spherical particles. The influences of rotating speed, blockiness, and aspect ratio on the mixing rate are investigated by the Lacey mixing index. The results show that the rotating speed has a primary effect on the mixing rate, whereas the effect of the particle shape on the mixing rate is a secondary factor for non-spherical granular systems. Moreover, the mixing rate of spherical and non-spherical particle systems is significantly different. The mixing rate of spheres is the lowest, and the cubes have a higher mixing rate than the cylinders. As the blockiness decreases or aspect ratio deviates from 1.0, the mixing rate decreases. Ordered face-to-face contacts and dense packing structures result in a higher mixing rate. The analysis of kinetic energy shows that particle shape affects the transfer efficiency of external energy to the granular systems. The translational kinetic energy of non-spherical particles is higher than that of spherical particles, and their rotational kinetic energy is lower than that of spheres. Meanwhile, the blockiness enhances the transfer efficiency of external energy to the non-spherical systems; in contrast, the aspect ratio reduces the energy conversion efficiency.     

A method to model realistic particle shape and inertia in DEM

A simple and fast original method to create irregular particle shapes for the discrete element method using overlapping spheres is described. The effects of its parameters on the resolution of the particle shape are discussed. Overlapping spheres induce a non-uniform density inside the particle leading to incorrect moments of inertia and therefore rotational behaviour. A simple method to reduce the error in the principal moments of inertia which acts on the individual densities of the spheres is also described. The pertinence of the density correction is illustrated by the case of free falling ballast particles forming a heap on a flat surface. In addition to improve behaviour, the correction reduces also computational time. The model is then used to analyse the interaction between ballast and geogrid by simulating pull-out tests. The pulling force results show that the model apprehends better the ballast geogrid interlocking than models with simple representation of the shape of the particles. It points out the importance of modelling accurately the shape of particles in discrete element simulations.     

The influence of particle orientation on the loading condition of pebbles in fluvial gravel

The loading conditions of pebbles in fluvial gravel deposits were studied with different degrees of preferred particle orientation. Sediments that are comprised of non-spherical particles often show a preferred particle orientation, due to dynamic sedimentation. Here, the impact of this effect on the loading conditions of the particles and its implication on particle breakage was investigated by using discrete element simulations in three dimensions. The numerical models are based on the size and shape distribution of pebbles from a natural gravel sample. In addition, the particle size in some of the models was chosen to be uniform, to study the influence of the particle size distribution on the loading condition. Fluvial pebbles, whose shapes can be at best approximated by ellipsoids, were efficiently simulated in the discrete element models by the use of clumps. The results show that a preferred orientation of approximate ellipsoidal sedimentary particles has only a minor effect on the number and the position of particle contacts but leads to a significant load transfer from the rim to the centre of the oblate sides of the ellipsoidal particles, in comparison to an assembly of arbitrarily oriented particles. The comparison of the different particle size models indicates that the influence of the particle size distribution on the loading condition is relatively low. The results have significant implications for the breakage rate of non-spherical particles in sediments under load.     

Modelling sheet-flow sediment transport in wave-bottom boundary layers using discrete-element modelling

Sediment transport in oscillatory boundary layers is a process that drives coastal geomorphological change. Most formulae for bed-load transport in nearshore regions subsume the smallest-scale physics of the phenomena by parametrizing interactions amongst particles. In contrast, we directly simulate granular physics in the wave-bottom boundary layer using a discrete-element model comprised of a three-dimensional particle phase coupled to a one-dimensional fluid phase via Newton's third law through forces of buoyancy, drag and added mass. The particulate sediment phase is modelled using discrete particles formed to approximate natural grains by overlapping two spheres. Both the size of each sphere and the degree of overlap can be varied for these composite particles to generate a range of non-spherical grains. Simulations of particles having a range of shapes showed that the critical angle--the angle at which a grain pile will fail when tilted slowly from rest--increases from approximately 26 degrees for spherical particles to nearly 39 degrees for highly non-spherical composite particles having a dumbbell shape. Simulations of oscillatory sheet flow were conducted using composite particles with an angle of repose of approximately 33 degrees and a Corey shape factor greater than about 0.8, similar to the properties of beach sand. The results from the sheet-flow simulations with composite particles agreed more closely with laboratory measurements than similar simulations conducted using spherical particles. The findings suggest that particle shape may be an important factor for determining bed-load flux, particularly for larger bed slopes.     

DEM simulation and experimental validation for mechanical response of ellipsoidal particles under confined compression

The representation of non-spherical particles in discrete element method (DEM) has not been addressed adequately. Although the multiple sphere method (MSM) is the most popular approach to describe non-spherical particle shape, the validity of the MSM has not been established yet. The purpose of this study is to examine the validity and adequacy of the MSM. A uni-axial confined compression test was designed and set up to study the mechanical behaviour of an ellipsoidal granular assembly under vertical loading and the load transfer to the contacting boundary. Four levels of multi-sphere approximation for an axi-symmetric ellipsoidal particle were employed in DEM simulation to investigate the adequacy of multi-sphere approximation. A comparison on compression characteristics between the numerical and experimental results was made and discussed in this paper. Most of the compared physical properties showed reasonable agreement, indicating that capturing the key linear dimensions of a non-spherical particle may be sufficient to predict reasonable results. A small number of sub-spheres (say, N?≥?5) for representing an axi-symmetric ellipsoidal particle can give plausible results. However, the DEM simulations also produced a certain extent of discrepancy in loading stiffness with experiments. Plausible explanations are provided and require further investigation.     

Particle shape effects in discrete element modelling of cohesive angular particles

This paper investigates the effect of particle angularity on general granular response concentrating on flow and stress-strain behaviour. A 2D polygon DEM model is developed to a 3D polyhedron model. The effect of particle shape on the response of polygons in simple shear and polyhedra under gravity flow is investigated using regular shapes with rounded vertices. The study concentrates on the angularity rather than aspect ratio by comparing circles, near squares and near equilateral triangles in 2D and spheres, tetrahedra and octahedra in 3D. In summary the more angular the particle the greater the resistance to the forcing load and the flowability is reduced. A mix of spheres and octahedra demonstrates an approximate linear combination of effects.     

Angle of repose and stress distribution of sandpiles formed with ellipsoidal particles

The properties of a sandpile such as angle of repose and stress distribution are affected by many variables, among which particle shape is one of the most important. In this work, ellipsoids which can represent a large range of shapes varying from disk- to cylinder-type are used. The discrete element method is employed in order to conduct controlled numerical experiments. The results confirm the general findings reported in the literature. It also shows that with aspect ratios deviating from 1.0, the angle of repose increases significantly, but disk-type shape and cylinder-type shape follow different variation trends. Empirical correlations between the angle of repose and aspect ratio or sphericity are proposed. The analysis on the stress distribution shows that particle shape affects the magnitude of the normal contact force between particles significantly, with spheres being the smallest. The pressure distribution underneath sandpiles is featured with a relatively constant normal pressure in the central region rather than a dip. It is confirmed that non-spherical particles have more pronounced stress dip than spherical particles.     

矿物颗粒形状对球磨机磨矿性能的影响

为了探究矿物颗粒形状对球磨机研磨作业的影响机制,运用离散单元法,采用球体和由球形颗粒凝聚而成的正四面体、平行六面体矿物颗粒模型,数值模拟球磨机的磨矿过程,分析矿物颗粒形状对运动形式、碰撞形式以及球磨机磨矿性能的影响。结果表明,矿物颗粒形状对球磨机磨矿性能的影响很大,相同条件下,球形矿粒碰撞能最大,正四面体矿粒次之,平行六面体矿粒最小。     

Strength of non-spherical particles with anisotropic geometries under triaxial and shearing loading configurations

This paper presents a study on the macroscopic shear strength characteristics of granular assemblies with three- dimensional complex-shaped particles. Different assemblies are considered, with both isotropic and anisotropic particle geometries. The study is conducted using the discrete element method (DEM), with so-called sphero-polyhedral particles, and simulations of mechanical true triaxial tests for a range of Lode angles and confining pressures. The observed mathematical failure envelopes are investigated in the Haigh–Westergaard stress space, as well as on the deviatoric-mean pressure plane. It is verified that the DEM with non-spherical particles produces results that are qualitatively similar to experimental data and previous numerical results obtained with spherical elements. The simulations reproduce quite well the shear strength of assemblies of granular media, such as higher strength during compression than during extension. In contrast, by introducing anisotropy at the particle level, the shear strength parameters are greatly affected, and an isotropic failure criterion is no longer valid. It is observed that the strength of the anisotropic assembly depends on the direction of loading, as observed for real soils. Finally simulations on a virtual shearing test show how the velocity profile within the shear band is also affected by the grain’s shape.     

DEM-aided direct shear testing of granular sands incorporating realistic particle shape

Discrete element method (DEM) of granular sands incorporating the effect of the realistic particle shape has been an important issue for many years. In this context, this study proposed a novel framework for the generation of realistic-shaped particles of natural sands in 3D DEM simulations. The generation framework mainly included micro-CT (μCT) scanning of sand particles, image processing of μCT images, spherical harmonic reconstruction of the particle surface, and clump generation by the overlapping multisphere clump method (OMCM) in DEM simulations. To validate the accuracy of OMCM, the volume and inertia moment of the clump were carefully investigated, and a set of optimized generation parameters was then determined to ensure the accuracy of the clump and the limit number of the filling spheres. Based on the generation framework, a clump sample with realistic particle shapes and a corresponding sphere sample were generated to conduct a series of direct shear testing. The simulation results demonstrated that the realistic particle shape highly increases the particle interlocking rather than the anisotropic intensity of strong contact force chains, and in turn enhances the shear resistance and the shear-induced dilation of the sands. It was also found that the inter-particle contacts of the clump sample have higher friction mobilization than that of the sphere sample, which identified the micromechanism of the shape effect on the particle interlocking.     

CFD–DEM Model for Simulation of Non-spherical Particles in Hole Cleaning Process

During the well drilling process, particles are produced in different shapes. The shape of particles can influence the characteristics of particles transport process. The aim of this work is to analyze the effects of particle shape on the transportation mechanism. For this purpose, a three-dimensional model is prepared for simulation of particle transportation with spherical and non-spherical shapes, during deviated well drilling. The motion of particles and the non-Newtonian fluid flow are simulated via discrete element method and CFD, respectively. The two-way coupling scheme is used to incorporate the effects of fluid–particle interactions. Three different samples of non-spherical shapes are constructed using multi-sphere method. The interactions of particle–particle/wall/drill pipe are taken into account via Hertz–Mindlin model. Simulations are carried out for some laboratory-scale configurations and fair agreements with the experimental data available in the literature are established.     

A contact detection algorithm for multi‐sphere particles by means of two‐level‐grid‐searching in DEM simulations

In discrete element method simulations, multi‐sphere particle is extensively employed for modeling the geometry shape of non‐spherical particle. A contact detection algorithm for multi‐sphere particles has been developed through two‐level‐grid‐searching. In the first‐level‐grid‐searching, each multi‐sphere particle is represented by a bounding sphere, and global space is partitioned into identical square or cubic cells of size D, the diameter of the greatest bounding sphere. The bounding spheres are mapped into the cells in global space. The candidate particles can be picked out by searching the bounding spheres in the neighbor cells of the bounding sphere for the target particle. In the second‐level‐grid‐searching, a square or cubic local space of size (D + d) is partitioned into identical cells of size d, the diameter of the greatest element sphere. If two bounding spheres of two multi‐sphere particles are overlapped, the contacts occurring between the element spheres in the target multi‐sphere particle and in the candidate multi‐sphere particle are checked. Theoretical analysis and numerical tests on the memory requirement and contact detection time of this algorithm have been performed to verify the efficiency of this algorithm. The results showed that this algorithm can effectively deal with the contact problem for multi‐sphere particles. Copyright © 2015 John Wiley & Sons, Ltd.     

基于概率接触算法的椭球离散元及料仓试验研究

该文提出一种基于概率接触算法,并嵌入到球形颗粒离散元程序中,在保持原有颗粒接触检索效率的基础上,实现了非球形颗粒模拟。以椭球颗粒为例给出了算法推导过程,进行了球形西米、椭球形绿豆和长米的料仓卸料过程模拟,对颗粒体系的流态和流量进行了研究,并开展了相应的试验加以验证。结果表明:基于概率接触算法的非球形颗粒离散元法适用于在椭球颗粒流动特性方面的研究,可以较精确的模拟卸料过程,且计算效率较高。     

A strategy to determine DEM parameters for spherical and non-spherical particles

In Discrete element method (DEM) simulations the choice of appropriate contact parameters is significant to obtain reasonable results. Particularly, for the determination of DEM parameters for non-spherical particles a general straightforward procedure is not available. Therefore, in a first step of the investigation here, methods to obtain the friction and restitution coefficients experimentally for single particles [Polyoxymethylene (POM) spheres and quartz gravel] will be introduced. In the following, these predetermined DEM coefficients are used as initial values for the adjustment of bulk simulations to respective experiments. In the DEM simulations, the quartz gravel particles are represented by non-spherical particles approximated by clustered spheres. The best fit approximation of the non-spherical particles is performed automatically by a genetic algorithm. In order to optimize the sliding and rolling friction coefficients for DEM simulations, the static and dynamic angle of repose are determined from granular piles obtained by slump tests and rotating drum experiments, respectively. Additionally, a vibrating plate is used to obtain the dynamic bed height which is mainly influenced by the coefficient of restitution. The adjustment of the results of the bulk simulations to the experiments is conducted automatically by an optimization tool based on a genetic algorithm. The obtained contact parameters are later used to perform batch-screening DEM simulations and lead to accurate results. This underlines the applicability of the in parts automated strategy to obtain DEM parameters for particulate processes like screening.     

碎石料应力路径大型三轴试验的离散元模拟研究

碎石料在高填方工程中得到广泛应用。由于其粒径较大,对碎石料力学特性的研究通常需要大型的试验设备。该文探索通过离散元数值模拟方法研究碎石料的应力路径相关力学特性。离散元程序可以将若干球形单元粘结成一个捆绑单元,从而模拟可破碎的碎石颗粒。该文首先简要介绍了离散元的计算原理、特点和模拟过程,并建立碎石料试件的离散元模型。通过对比一组恒定围压下的大型三轴试验,确定了各参数,对所建模型进行了标定。进而通过该模型独立预测碎石料试件在三种不同应力路径加载时的应力-应变关系及体变特性,并与相应的应力路径大型三轴试验结果进行对比,验证了离散元方法可以较为准确地计算碎石料沿不同应力路径加载时的力学特性,同时还讨论了碎石料的小应变刚度特性。     

Micromechanical modelling of oval particulates subjected to bi-axial compression

One of the questions that still remain unanswered among researchers dealing with granular materials is how far the particle shape affects the micro-macroscopic features of granular assemblies under mechanical loading. The latest advances made with particle instrumentation allow us to capture realistic particle shapes and size distribution of powders to a fair degree of accuracy at different length scales. Industrial applications often require information on the micromechanical behaviour of granular assemblies having different particle shapes and varying surface characteristics, which still remains largely unanswered. Traditionally, simulations based on discrete element method (DEM) idealise the shape of individual particles as either circular or spherical. In the present investigation, we analyse the influence of particle shape on the shear deformation characteristics of two dimensional granular assemblies using DEM. We prepared the assemblies having nearly an identical initial packing fraction (dense), but with different basic shapes of the individual particles: (a) oval and (b) circular for comparison purposes. The granular assemblies were subjected to bi-axial compression test. We present the evolution of macroscopic strength parameters and microscopic structural/topological parameters during mechanical loading. We show that the micromechanical properties of granular systems are significantly influenced by the shape of the individual particles constituting the granular assemblies.