Fragments spawning and interaction models for DEM breakage simulation

Particles breakage occurs in many industrial applications. During the last decade many works have been devoted for modelling and simulating such processes. A new and innovative procedure of empirical comminution functions for Discrete Element Method (DEM) simulations (Kalman et al. in Granul Matter 11(4):253–266, 2009) posed the question how to introduce the fragments of the broken particle back into the computational domain. Daughter particles (Fragments) spawning and interaction imposes several problems during DEM simulation. Some of the main problems are: seeding (allocating) daughter particles and their initial conditions i.e. fragments locations, velocities and physical properties. This work focuses on the daughter particles seeding and the interaction between “sibling” particles for spherical particles. Fragments spawning and interaction algorithm for particle breakage during DEM simulation was developed. The algorithm enables prediction of particle comminution/attrition processes using DEM applications. The new algorithm can utilize any breakage function allowing unlimited fragment size fractions. In the proposed model, sibling particles can overlap without increasing the energy of the system in the simulation. Particle-particle and particle-wall interactions are calculated using the standard DEM calculations. Daughter particles interactions were calculated using the developed temporary contact radius model. The model was utilized to predict particle comminution in jet milling and particle attrition during pneumatic conveying with great successes.     

A discrete element method-based approach to predict the breakage of coal

Pulverization is an essential pre-combustion technique employed for solid fuels, such as coal, to reduce particle sizes. Smaller particles ensure rapid and complete combustion, leading to low carbon emissions. Traditionally, the resulting particle size distributions from pulverizers have been determined by empirical or semi-empirical approaches that rely on extensive data gathered over several decades during operations or experiments, with limited predictive capabilities for new coals and processes. This work presents a Discrete Element Method (DEM)-based computational approach to model coal particle breakage with experimentally characterized coal physical properties. The effect of select operating parameters on the breakage behavior of coal particles is also examined.     

A new method to implement comminution functions into DEM simulation of a size reduction system due to particle-wall collisions

The ability to design a size reduction system prior to full scale experiments and to optimize existing systems has long been a goal of designers. Such a design and optimization could be achieved by correctly simulating any system under any operating condition. In this paper we present a new and innovative procedure to implement empirical comminution functions into DEM–CFD simulations. The paper is focused on the implementation procedures and not the DEM/CFD simulations, which deserve full attention. Therefore, this paper is not aimed to study any specific mill. The comminution functions include: initial strength distribution, selection function, breakage function and fatigue function. First, the traditional comminution functions (strength distribution, selection and breakage functions) and the recently investigated fatigue function are briefly described and modified. Then a procedure for implementing the functions into a DEM–CFD model or any other source to provide impact velocities and number of impacts, is described in detail. The implementation involves converting the probability comminution functions into individual particle properties by a random method and then converting the velocity dependent comminution functions into strength dependent ones. In this way, and mainly owing to the use of the fatigue function (which defines the weakening of those particles that are not breaking), a real size reduction system, in which each particle is subjected to multiple impacts at various velocities can be simulated. Three case studies for multiple impact conditions at the same average velocity (several impacts at the same velocity, various velocities at each impact and randomly selected velocities) are presented and analyzed in order to confirm qualitatively the procedure, although the comminution functions need to be further quantitatively modified. It should be emphasized that although the new procedure presents a step towards the final goal, some limitations do exist and some questions remain open.     

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 general approach for the characterization of fragmentation problems

A general approach for the quantitative and systematic characterization of fragmentation problems, which is based on the Weibull statistics, is presented. A model, initially developed for materials stressed under impact with respect to their breakage probability, has been successfully applied to the characterization of compressive comminution, fragmentation of nanoparticle agglomerates and destroying of adhesive bonds. The experimental results from the slow compression comminution and from the comminution by falling weight match for various materials and particle sizes exactly to the master curve deduced for impact comminution. However, the material parameters determined for compression comminution are not identical for one and the same material to that determined by impact comminution. This indicates that the two model parameters are not pure material characteristics as assumed from the impact experiments, but depend on the stress mechanism. The dependence of the fragmentation degree on the particle size and the energy input observed when impacting particles in the micrometer to millimeter range has been proven also for nanoparticle agglomerates. Furthermore, a model analogous to that for breakage has been deduced for the quantification of the failure of adhesive bonds.     

DEM Simulation of Particle Comminutionin Jet Milling

A combined discrete element method (DEM) and CFD numerical model was developed to simulate particle comminution in a jet mill. The DEM was used to simulate the motion of the particles in the gas flow. For this, the compressible Reynolds Averaged Navier-Stokes (RANS) equations were used to describe the gas flow field inside a given size's jet mill. Ghadiri's models for breakage and chipping were implemented in the simulation to define the reduction of the particle's size during jet milling. The size distributions of the particles after grinding were obtained numerically. The prediction of the numerical simulation for the median particle size d 50 after grinding was qualitative compared with experimental results for the different operating conditions (i.e., feed rate, angle of grinding nozzles, volumetric rate of grinding air, etc.). The comparison shows good agreement with the experimental observation. The results shows that the feed rate, angle of feeding nozzle, and feeding air's flow rate have more influence on the breakage and chipping of particles in jet milling. In addition, a parametric study was performed to obtain the desired operation conditions.     

DEM investigation of particle anti-rotation effects on the micromechanical response of granular materials

The importance of particle rotation to the mechanical behavior of granular materials subject to quasi-static shearing has been well recognized in the literature. Although the physical source of the resistance to particle rotation is known to lie in the particle surface topography, it has been conveniently studied using the rolling resistance model installed typically on spherical particles within the DEM community. However, there has been little effort on assessing the capability of the rolling resistance model to produce more realistic particle rotation behavior as exhibited by irregular-shaped particles. This paper aims to eliminate this deficiency by making a comprehensive comparison study on the micromechanical behavior of assemblies of irregular-shaped particles and spherical particles installed with the rolling resistance model. A variety of DEM analysis techniques have been applied to elucidate the full picture of micromechanical processes occurring in the two types of granular materials with different particle-level anti-rotation mechanisms. Simulation results show that the conventional rheology-type rolling resistance models cannot reproduce the particle rotation and strain localization behavior as displayed by irregular-shaped materials, although they demonstrate clear effects on the macroscopic strength and dilatancy behavior, as have been adequately documented in the literature. More insights into the effects of particle-level anti-rotation mechanism are gained from an in-depth inter-particle energy dissipation analysis.     

Degradation model of Gladstone Port Authority's coal using a twin-pendulum apparatus

Single-particle breakage tests of South Blackwater and Ensham coal were conducted by using a computer-monitored twin-pendulum device to determine a parameter which will describe the product size distribution of the breakage product. The size distribution parameter ‘t’₅₀ related to the specific comminution energy [defined as the comminution energy per unit mass which transmitted to a particle during breakage (kWh/t)] of breakage coal particles and described the breakage characteristics of two types of coal. At a specific comminution energy level, the t₅₀ parameter of South Blackwater coal was higher than the t₅₀ parameter of Ensham coal. A degradation model was developed with several parameters for the coal-handling circuits of Gladstone Port. In the degradation model, the raw data of the non-cushioned curve deviates from the model data after a few initial drops because the mass of the sample reduces in successive drops and produced more fines.     

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 Simulation of Particle Comminutionin Jet Milling

A combined discrete element method (DEM) and CFD numerical model was developed to simulate particle comminution in a jet mill. The DEM was used to simulate the motion of the particles in the gas flow. For this, the compressible Reynolds Averaged Navier-Stokes (RANS) equations were used to describe the gas flow field inside a given size's jet mill. Ghadiri's models for breakage and chipping were implemented in the simulation to define the reduction of the particle's size during jet milling. The size distributions of the particles after grinding were obtained numerically. The prediction of the numerical simulation for the median particle size d 50 after grinding was qualitative compared with experimental results for the different operating conditions (i.e., feed rate, angle of grinding nozzles, volumetric rate of grinding air, etc.). The comparison shows good agreement with the experimental observation. The results shows that the feed rate, angle of feeding nozzle, and feeding air's flow rate have more influence on the breakage and chipping of particles in jet milling. In addition, a parametric study was performed to obtain the desired operation conditions.     

Application of DEM to evaluate and compare process parameters for a particle failure under different loading conditions

The paper presents an application of Discrete Element Modelling (DEM) in understanding the micro-process parameters of a particle failure under different loading conditions. A composite particle has been modelled using many primary particles to represent a quasi-homogeneous particle. Some of the examples of quasi-homogeneous particles are constituents of tablets, pellets, granules and concrete. These particles can behave differently under identical loading conditions even though they consist of same primary particles and proportions. This is a typical behaviour of such particles which is governed by the imperfections present in the particles. A DEM has been used to model the composite particle consisting of bi-modal distribution (smaller particles—matrices and larger particles—aggregates) of primary particles. The particle has been loaded under single plate compression, double plate compression and normal impact on different types of target. The single plate compression and normal impact experiments have also been performed. Process parameters like, fracture pattern, particle size distribution, liberation degree and new surface generation have been evaluated and compared. The results are applicable in understanding the particle failure under different processing operations like, transportation, handling and comminution. The results are also useful in selecting the better loading method for liberating aggregates from cheaper matrices for recycling.     

A combined approach for modeling particle behavior in granular impact damper using discrete element method and cellular automata

A particle impact damper is a vibration absorber type that consists of a container attached to a primary vibrating structure. It also contains many particles that are constrained to move inside the container, whereby the damping effect can be obtained by collision between particles and the container. The discrete element method (DEM) has been developed for modeling granular systems, where the kinematics of each particle are calculated numerically using the equations of motion. However, the computational time is significant since the algorithm checks for particle contacts for all possible particle combinations. The use of a cellular automata (CA) modeling technique may provide increased computational efficiency due to the local updating of variables, and the discrete treatment of time and space. In this study, we propose a new approach combining DEM with CA for modeling a granular damper under a forced excitation. We use DEM to describe the particle motion according to the equations of motion, while CA is introduced for the particle contact checks in discrete space. We also investigate the effect of simplification in the contact force model, which allows the unit time step of numerical integration to become larger than that used in the strict model. It is shown that the suggested particle contact scanning method and the force approximation model contribute to the reduction of the computational time, and neither degenerates the calculation accuracy nor causes the numerical instability.     

A new GPU-based DEM simulator for polydispersed granular systems with wide size distribution and its application in the silo discharge

While discrete element method (DEM) has been successfully established in many studies, serious problems have limited its industrial-scale applications. Considerably long runtime is one of the most critical bottlenecks of the DEM simulation applicability. Despite extensive efforts on the parallelization of DEM on the CPU or GPU, DEM runtime on the current generation of computers is so long that further improvements are demanded. Moreover, while many real-world granular systems consist of polydispersed particles with a relatively wide size distribution, the majority of DEM simulation studies have assumed monodispersed particle assemblies. Few have studied the parallelization of polydispersed systems, and fewer have developed GPU-based codes for these systems. The main purpose of this study is to provide a novel solver, NP-DEM, which is optimized for GPU-based simulation of polydispersed particle systems with a wide size distribution. Silo discharge is chosen as the case study to examine the applicability of the code.     

Discrete element modelling of under sleeper pads using a box test

It has recently been reported that under sleeper pads (USPs) could improve ballasted rail track by decreasing the sleeper settlement and reducing particle breakage. In order to find out what happens at the particle–pad interface, discrete element modelling (DEM) is used to provide micro mechanical insight. The same positive effects of USP are found in the DEM simulations. The evidence provided by DEM shows that application of a USP allows more particles to be in contact with the pad, and causes these particles to transfer a larger lateral load to the adjacent ballast but a smaller vertical load beneath the sleeper. This could be used to explain why the USP helps to reduce the track settlement. In terms of particle breakage, it is found that most breakage occurs at the particle–sleeper interface and along the main contact force chains between particles under the sleeper. The use of USPs could effectively reduce particle abrasion that occurs in both of these regions.     

Study of the Comminution Characteristics of Coal by Single Particle Breakage Test Device

Single-particle breakage tests of South Blackwater and Ensham coal from the Bowen Basin area in Queensland were conducted by a computer-monitored twin-pendulum device to measure the energy utilization pattern of the breakage particles. Three particle sizes (-16.0 + 13.2 mm, -13.2 + 11.2 mm, -11.2 + 9.5 mm) of each coal were tested by a pendulum device at five input energy levels to measure the specific comminution energy. When particles were tested at constant input energy, the variation of comminution energy between the same size broken particles of Ensham coal was minimal, because Ensham coal is a softer and higher friability coal, which absorbs more input energy than harder coal during breakage tests. For different particle sizes, the specific comminution energy increases linearly with the input energy and the fineness of the breakage products increases with the specific comminution energy.The size distribution graphs are curved but approach linearity in the finer region. At a constant input energy, the twin pendulum breakage product results show that the fineness of the products increases with decrease in particle size and South Blackwater coal produced finer products than the Ensham coal. The t-curves are the family of size distribution curves, which can describe the product size distribution of the breakage particles during single-particle breakage tests.     

Comparison of solid particle erosion predictions using the dense discrete phase and discrete element models

A numerical procedure involving the dense discrete phase model (DDPM) is used to calculate solid particle erosion. DDPM works in two mechanisms. First, the discrete particles are treated as a pseudofluid, and the interaction among particles is evaluated by solving the governing equations of the pseudofluid. Second, the equivalent pressure of the pseudofluid is applied to a single particle to reflect the blocking effect of high-concentration particles. The numerical procedure is well verified by comparison with the experimental data picked from a direct impact test. In addition, the DDPM predictions are compared with the discrete element model (DEM) predictions in detail. Both methods show that the predicted mass loss caused by sand per unit mass decreases with an increase in sand concentration. DDPM indirectly considers the influence of particle interactions on solid particle erosion, and the predicted erosion contours are more uniform and smoother than the DEM-predicted contours.     

Reduction of discrete element models by Karhunen–Loève transform: a hybrid model approach

The term “discrete element method” (DEM) in engineering science comprises various approaches to model physical systems by agglomerates of free particles. While shapes, sizes and properties of particles may vary, in most DEM models, particles are not confined by constraints, but subject to applied forces derived from potential fields and/or contact laws. This general approach allows for widespread use of DEM models for physical phenomena including gas dynamics, granular flow, fracture and impact analysis. However, its characteristic feature, combining particle restraints and forces into applied forces, does not only provide for flexible adaption of DEM to different physics, but also creates the most limiting restriction: Evaluation of the applied forces for each particle is computational expensive restraining the time sequence and sample size for numerical analyses. As an ansatz to circumvent this obstacle for a class of DEM models, we propose a model order reduction method based on coherency in the dynamics of particles. While initial flexibility of DEM is conserved, computational effort can be reduced significantly.     

A new algorithm for contact detection between spherical particle and triangulated mesh boundary in discrete element method simulations

In discrete element method (DEM) simulations of real scale, the spherical particles are commonly employed for increasing the computation speed, and the complex boundary models are represented by triangle meshes with controllable accuracy. A new contact detection algorithm has been developed to resolve the contacts between the spheres and the triangle mesh boundaries. The application of the barycentric coordinates makes this algorithm more efficient to identify contacts in the intersection test. As a particle probably collides with several triangles at the same time, the multiple contacts would be reported as face contacts, edge contacts, or vertex contacts. Moreover, the particle embedding in a triangle can be also contact with the edges or vertices of the next triangles. These contacts should be considered as invalid for updating contact forces in the DEM. To exclude invalid records from the multiple contacts, the algorithm gives attention to the mesh structure nearby contacts and analyzes all possible collision situations. Numerical experiments have been conducted to verify this algorithm by using the algorithm in the DEM simulation framework. The numerical results suggest that the algorithm can resolve all contacts precisely and stably when the spherical particles collide on the complex boundary circumstances. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Evaluation of Particle Degradation Due to High-Speed Impacts in a Pneumatic Handling System

Particle degradation can be a significant issue in particulate solids handling and processing, particularly in pneumatic conveying systems, in which high-speed impact is usually the main contributory factor leading to changes in particle size distribution (comparing the material to its virgin state). However, other factors may strongly influence particles breakage as well, such as particle concentrations, bend geometry, and hardness of pipe material. Because of such complex influences, it is often very difficult to predict particle degradation accurately and rapidly for industrial processes. In this article, a general method for evaluating particle degradation due to high-speed impacts is described, in which the breakage properties of particles are quantified using what are known as “breakage matrices.” Rather than a pilot-size test facility, a bench-scale degradation tester has been used. Some advantages of using the bench-scale tester are briefly explored. Experimental determination of adipic acid has been carried out for a range of impact velocities in four particle size categories. Subsequently, particle breakage matrices of adipic acid have been established for these impact velocities. The experimental results show that the “breakage matrices” of particles is an effective and easy method for evaluation of particle degradation due to high-speed impacts. The possibility of the “breakage matrices” approach being applied to a pneumatic conveying system is also explored by a simulation example.