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Simulations in Bulk Solids Handling
Valuable resource for engineers and professionals dealing with bulk granular or powdered materials across industries using Discrete Element Methods (DEM)
In many traditional university engineering programmes, no matter whether undergraduate or postgraduate, the behavior of granular materials is not covered in depth or at all. This omission leaves recent engineering graduates with little formal education in the major industrial area of bulk solids handling. This book teaches young professionals and engineers to find appropriate solutions for handling granular and powdered materials. It also provides valuable information for experienced engineers to gain an understanding and appreciation of the most significant simulation methods–DEM chief amongst them.
For any student or professional involved with bulk solids handling, this book is a key resource to understand the most efficient and effective stimulation methods that are available today. Its comprehensive overview of the topic allows for upcoming professionals to ensure they have adequate knowledge in the field and for experienced professionals to improve their skills and processes.
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Veröffentlichungsjahr: 2023
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Table of Contents
Cover
Title Page
Copyright
Preface
1 Calibration of DEM Parameters
Abbreviations and Acronyms
1.1 Introduction
1.2 Basic DEM Theory
1.3 DEM Application and Calibration Philosophies
1.4 Physical Bulk Properties
1.5 DEM Parameters and Their Relation to Bulk Properties
1.6 Overview of Calibration Tests
1.7 Recommended Calibration Procedure for Non‐cohesive and Slightly Cohesive Materials
1.8 Outlook on the Calibration of Cohesive Materials
1.9 Optimisation Approaches Applied to the Calibration Process
1.10 Conclusion
References
2 Simulation of Transfer Chutes
2.1 Introduction
2.2 Practicalities – Balancing Conflicting Objectives
2.3 The Suggested Approach
2.4 Basic Design Principles – The Continuum Approach
2.5 DEM Simulation of Transfer Chutes – General Comments
2.6 General Flow Analysis and Validation
2.7 Quantitative Validation of Forces in DEM Simulation
2.8 Belt Mistracking
2.9 Simulation of Build‐Up and Blockage of Cohesive Material
2.10 Prediction of Wear
2.11 Prediction of Dust
2.12 Interrelationships Between Wear, Build‐Up, and Flow
2.13 Conclusion
References
3 Belt Conveyor Design and Troubleshooting
3.1 Introduction
3.2 Belt Conveyor Design
3.3 Belt Conveyor Troubleshooting
References
4 Multibody Dynamics and Discrete Element Method Co‐Simulations for Large‐Scale Industrial Equipment
4.1 Introduction
4.2 Categorisation and Publications on DEM–MBD
4.3 Developing a DEM and MBD Coupling
4.4 How DEM–MBD Models Can be Used
4.5 Outlook
References
5 Simulation of Pneumatic Conveying
5.1 Introduction
5.2 Single Fluid Model
5.3 Two Fluid Models
5.4 Coupled DEM–CFD Models
5.5 Summary
Nomenclature
References
Further Reading
6 Modelling and Simulation of Erosive Wear and Particle Breakage in Pneumatic Conveying
6.1 Introduction
6.2 One‐dimensional Particle Breakage Modelling of the Conveying Pipeline
6.3 One‐dimensional Surface Erosion Modelling of the Conveying Pipeline
6.4 Conclusion
References
7 Discrete Element Modelling of Pharmaceutical Powder Handling Processes
7.1 Introduction
7.2 Discrete Element Method
7.3 DEM Modelling of Powder Mixing/Segregation
7.4 DEM Modelling of Continuous Blending
7.5 DEM Modelling of Powder Filling and Hopper Discharging
7.6 DEM Modelling of Twin Screw Granulation
7.7 DEM Modelling of Milling
7.8 DEM Modelling of Dry Powder Inhalation
7.9 Summary and Perspectives
Nomenclature
References
8 Algorithms and Capabilities of
Solidity
to Simulate Interactions and Packing of Complex Shapes
8.1 Introduction
8.2 Mathematical Models
8.3 Application of Cube Packing
8.4 Application of the Packing of Platonic and Archimedean Solids
8.5 Conclusions
Acknowledgements
References
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1 Relation between DEM parameters and non‐cohesive bulk properties....
Table 1.2 A summary and graphic representation of typical calibration tests...
Chapter 4
Table 4.1 Detailed overview of literature on load‐bearing terramechanics us...
Table 4.2 Detailed overview of literature on load‐loosening terramechanics ...
Table 4.3 Detailed overview of literature on bulk material processing using...
Table 4.4 Detailed overview of literature on bulk material handling using D...
Table 4.5 Detailed overview of literature on vibration attenuation by parti...
Table 4.6 Detailed overview of literature on DEM–MBD coupling development a...
Chapter 5
Table 5.1 Comparison of mixture and Eulerian models.
Chapter 6
Table 6.1 Simulation conditions.
Table 6.2 Summary of collision characteristic functions.
Table 6.3 Empirical parameters for the crushing force model.
Table 6.4 Equivalence model empirical parameters.
Table 6.5 Breakage function empirical parameters.
Chapter 8
Table 8.1 Packing density.
List of Illustrations
Chapter 1
Figure 1.1 DEM computation cycle.
Figure 1.2 Typical elements of a contact model.
Figure 1.3 AoR simulation results according to Wensrich and Katterfeld et al...
Figure 1.4 Comparison of AoR simulation results with varying particle–partic...
Figure 1.5 Combination of draw down test results for gravel with considerati...
Figure 1.6 Calibration procedure for non‐cohesive materials.
Figure 1.7 Overview of optimisation algorithm. SQP = sequential quadratic pr...
Figure 1.8 Component structure and process of generalised surrogate modellin...
Chapter 2
Figure 2.1 Transfer chute examples.
Figure 2.2 Trajectory model.
Figure 2.3 Chute flow models.
Figure 2.4 (a) Flow and (b) qualitative wear pattern analysis in a DEM simul...
Figure 2.5 Conveyor belt transition geometry.
Figure 2.6 Discharge of free‐flowing and cohesive materials (a to b).
Figure 2.7 Free‐flowing (a) and cohesive (b) burden at discharge ‐ compariso...
Figure 2.8 Free‐flowing (a) and cohesive (b) material discharge comparison....
Figure 2.9 Comparison of continuum mechanics and DEM flow simulation.
Figure 2.10 Hood and loading spoon DEM flow simulation.
Figure 2.11 Comparison of force measurements on a vertical impact wall in a ...
Figure 2.12 Comparison of the deformation data (diagram to the left) and gen...
Figure 2.13 Off‐centred loading of bulk material on a belt conveyor causes m...
Figure 2.14 The change of centred and off‐centred loading of bulk material o...
Figure 2.15 Comparison of DEM simulation results of a hood and spoon transfe...
Figure 2.16 Material flow of wet gypsum (moisture content 23%, bulk density ...
Figure 2.17 Comparison of the remaining bulk material in experiment and DEM ...
Figure 2.18 Wear of transfer chutes.
Figure 2.19 Abrasive sliding (a) and impact wear (b).
Figure 2.20 Qualitative wear comparison (from left to right) of shear and im...
Figure 2.21 Qualitative wear analysis of a transfer chute from [57] using an...
Figure 2.22 Ring wear test rig for the determination of abrasive glider wear...
Figure 2.23 Impact wear test rig as described by [58]. A bucket wheel transp...
Figure 2.24 DEM simulation of the ring wear tester for sliding wear (a) and ...
Figure 2.25 DEM simulation of a 90° transfer chute (a) and vis...
Figure 2.26 DEM simulation of the two transfer chute designs with commented ...
Figure 2.27 Steep loading chute.
Figure 2.28 Relative abrasive wear (AWI) comparison of different chute and c...
Figure 2.29 Transfer chute and belt velocity, wear, and flow relationships....
Chapter 3
Figure 3.1 Steady‐state belt tension distribution for a horizontal belt conv...
Figure 3.2 A stress field graph superimposed over an idler roll.
Figure 3.3 Diagram of a finite element analysis mesh for a viscoelastic roll...
Figure 3.4 Shear relaxation moduli.
Figure 3.5 Measurement technique for determination of rubber relaxation prop...
Figure 3.6 Approximate mass distribution (a) and indentation rolling resista...
Figure 3.7 Strand7 FEM model of a 6 mm belt loaded with coal under 5 kN tens...
Figure 3.8 DEM belt conveyor model in LIGGGHTS. (a) DEM simulation showing p...
Figure 3.9 The FEM–DEM coupling scheme based on a Python programmed interfac...
Figure 3.10 Two‐way coupling.
Figure 3.11 Two‐way coupling at first iteration. (a) Particle velocities in ...
Figure 3.12 Two‐way coupling at final iteration. (a) Particle velocities in ...
Figure 3.13 Detailed finite element model of a conveyor belt [15].
Figure 3.14 Mathematical representation of the finite element model [15].
Figure 3.15 Free body diagram of a belt element [15].
Figure 3.16 S‐type starting procedures as given by Harrison [12] and Nordell...
Figure 3.17 Belt velocity at the head and tail.
Figure 3.18 Counterweight behaviour.
Figure 3.19 Dynamic tensions along the conveyor.
Figure 3.20 ANSYS FEM equivalent (von Mises) pulley shaft stress.
Figure 3.21 ANSYS FEM, total shaft deformation.
Figure 3.22 ANSYS FEM, equivalent (von Mises) pulley shell stress.
Figure 3.23 ANSYS FEM, equivalent (von Mises) pulley end disk stress.
Figure 3.24 ANSYS FEA, lip seal mesh.(a) Finalised finite element model ...
Figure 3.25 ANSYS FEM, lip seal interaction with idler shaft.(a) Equival...
Figure 3.26 Isometric view of Rocky 4.0 DEM simulation showing particle inte...
Figure 3.27 Wear output from DEM software package showing impact and abrasiv...
Figure 3.28 Orthographic view of Rocky 4.0 DEM simulation showing non‐centra...
Figure 3.29 Scale model transfer chute showing CFD simulation of dust emissi...
Chapter 4
Figure 4.1 Real‐scale physical prototype is built to be tested at a bulk ter...
Figure 4.2 Virtual model of the grabbing process by the DEM–MBD co‐simulatio...
Figure 4.3 Electric loader, an example of DEM–MBD coupling.
Figure 4.4 Publications that develop or apply DEM–MBD co‐simulation.
Figure 4.5 (a) Single‐Wheel test bed [42], and (b) Simulation of helically d...
Figure 4.6 Seabed miner (a) and its MBD model (b).
Figure 4.7 (a) Tamping operation, and (b) Tamping co‐simulation.
Figure 4.8 High‐pressure grinding rolls (HPGR) schematics (left) and model (...
Figure 4.9 Footprint of the grabbing process on two types of iron ore: (a) C...
Figure 4.10 Comparing filling situations of the mobile excavator in experime...
Figure 4.11 Schematic diagram of modelling driver, walking motor, transmissi...
Figure 4.12 Schematic of the coupling server sharing information between usi...
Figure 4.13 Particle cube collision test.
Figure 4.14 Comparison of theory and co‐simulation results of velocity and d...
Figure 4.15 Motorised pendulum with mass
m
according to Eq. (4.6), consistin...
Figure 4.16 Schematic of translational spring damper system.
Figure 4.17 System response by the co‐simulation compared to the analytical ...
Figure 4.18 System response by the co‐simulation compared to the analytical ...
Figure 4.19 A comprehensive approach to develop and used DEM–MBD co‐simulati...
Figure 4.20 Main components of a generic DEM calibration procedure.
Figure 4.21 Overview of validating a DEM–MBD co‐simulation for the grab appl...
Figure 4.22 (a) Generated 3D surface mesh, including grab geometry and colle...
Figure 4.23 Load comparison between co‐simulation and experiment for a grab....
Figure 4.24 Simulating the grabbing process on flat (a) and irregular bulk s...
Figure 4.25 Hybrid grab system: creating a variable and controllable power f...
Chapter 5
Figure 5.1 Outline of a pneumatic conveying system.
Figure 5.2 Simplified illustration of pneumatic conveying modes. (a) Dilute ...
Figure 5.3 Example performance map or conveying characteristic of a product ...
Figure 5.4 Example of pressure contour plot.
Figure 5.5 Example of Eulerian volume fraction plot of a plug entering a ben...
Figure 5.6 CFD–DEM simulation of one plug in the pipeline with particles of ...
Figure 5.7 Schematic diagram of the pneumatic conveying test Rig at Glasgow ...
Figure 5.8 OpenModelica schematic of pipeline.
Figure 5.9 Comparison of experimental and modelled line pressure.
Figure 5.10 Finite volume schematic, centres labelled upper case and faces l...
Figure 5.11 Origin of the Magnus force for a ball.
Chapter 6
Figure 6.1 Solid particles impact on target wall.
Figure 6.2 Modes of particle impact on component wall producing erosion. (a)...
Figure 6.3 Schematic definition of particle breakage.
Figure 6.4 Schematic flow diagram of the ODBA.
Figure 6.5 Illustration of particle volume fraction and the equivalent break...
Figure 6.6 Schematic of the pneumatic conveying system adopted for numerical...
Figure 6.7 Definition of geometric parameters for P–W collision in bend and ...
Figure 6.8 Broken ratio of particles after every conveying cycle.
Figure 6.9 ODBA simulation duration in each cycle in terms of particle numbe...
Figure 6.10 Schematic flow diagram of the ODEM.
Figure 6.11 Erosion rate of straight sections: blue dotted line for ODEM res...
Figure 6.12 Erosion rate contour of the second bend in mm/kg: A – ODEM, B – ...
Chapter 7
Figure 7.1 Flowchart of particles' dynamics calculations in DEM modelling.
Figure 7.2 Schematic of particles interacting with each other in DEM.
Figure 7.3 Schematic of the artificial overlap between the contacting partic...
Figure 7.4 The powder discharge process from (a) Flodex device and (b) DEM m...
Figure 7.5 Comparison of the powder discharge time obtained from the experim...
Figure 7.6 Qualitative and quantitative validation of the DEM simulation of...
Figure 7.7 Die filling of a binary mixture of large particles (shown in red)...
Figure 7.8 DEM modelling of the continuous blending process.
Figure 7.9 Evolution of hold‐up mass in the blender.
Figure 7.10 Residence time distribution for a continuous blender.
Figure 7.11 DEM modelling of linear die filling.
Figure 7.12 Variation of the filling ratio with the filling velocity.
Figure 7.13 A shoe feeder assembled with different stirrer designs.
Figure 7.14 Effect of stirrer speed on the fill ratio for different stirrer ...
Figure 7.15 DEM modelling of the rotary tableting process.
Figure 7.16 Schematic diagram of twin screw granulation.
Figure 7.17 Model twin screw granulators with various screw elements: (a) lo...
Figure 7.18 Residence time distributions obtained with twin screw granulator...
Figure 7.19 Snapshots of carrier and drug particles during vibration at diff...
Figure 7.20 Comparison of the contact number during mixing process governed ...
Chapter 8
Figure 8.1 Three hundred rocks depositing in a container, element number: 18...
Figure 8.2 Speedup achieved by the Solidity, Workstation specification: Inte...
Figure 8.3 Left column: deposition sequence for cube packing using deformabl...
Figure 8.4 Simulation of deposition leading to a packed structure of cubes w...
Figure 8.5 Numerical simulation of cube packing for friction coefficient (a)...
Figure 8.6 Sample window for packing density calculations.
Figure 8.7 Packing density of cubes at rest.
Figure 8.8 The five Platonic solids: tetrahedron P1, icosahedron P2, dodecah...
Figure 8.9 The 13 Archimedean solids: truncated tetrahedron A1, truncated ic...
Figure 8.10 Final simulated packing structure for the truncated dodecahedron...
Figure 8.11 Packing density versus friction coefficient for truncated tetrah...
Figure 8.12 Packing structures for (a) rhombicosi dodecahedron A5, (b) trunc...
Figure 8.13 Probability density function, P of normalised contact number.
Guide
Cover
Table of Contents
Title Page
Copyright
Preface
Begin Reading
Index
WILEY END USER LICENSE AGREEMENT
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Simulations in Bulk Solids Handling
Applications of DEM and other Methods
Edited by
Don McGlinchey
The Editor
Prof. Don McGlinchey
Glasgow Caledonian University
Department of Mechanical Engineering
Cowcaddens Road
G4 0BA Glasgow
United Kingdom
Cover Image: © your/Shutterstock
All books published by WILEY‐VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Library of Congress Card No.: applied for
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© 2023 WILEY‐VCH GmbH, Boschstraße 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Print ISBN: 978‐3‐527‐35010‐0
ePDF ISBN: 978‐3‐527‐83591‐1
ePub ISBN: 978‐3‐527‐83592‐8
oBook ISBN: 978‐3‐527‐83593‐5
Preface
The field associated with Bulk Solids Handling has always been open to a variety of science and engineering disciplines, and important contributions have come from Chemical, Civil, and Mechanical Engineering and Physics – all have contributed to the growth in simulation methods and technologies. Arguably the most important development in the past 20 years has been the progress in discrete element modelling (DEM) which has reached wide industrial use through commercially available codes, along with two‐fluid models and the integration with computational fluid dynamics and multibody motion codes. Options for the high‐fidelity simulation of bulk solids are now open to engineers with access to small HPC facilities or a reasonable workstation, and relevant software, both open source and commercial, can be accessed by all via an internet link through web services and cloud computing.
This book is intended to be of interest both to practicing engineers who may have had little or no exposure to the simulation of bulk solids during their formal education, and to graduate and post‐graduate researchers in this area to provide background and perhaps a springboard for new ideas and areas for investigation. There is wide (and growing) use of simulation in science and engineering research, and industry practice; therefore, it is essential for students and practitioners alike to develop an understanding of relevant simulation techniques and methods. Knowledge of the capabilities and limitations of these techniques will lead to a better understanding of their potential to solve problems on various bulk solids handling applications and suggest potential research direction. Although covering the fundamentals in some sections, the book is not introductory in the sense of a first text in bulk solids handling or the discrete element method. However, the mathematics used in this book is generally undergraduate‐level calculus applied to the underlying physics involved in particle technology and bulk solids handling operations and should be accessible to graduate engineers.
A simulation of a bulk solids handling process or operation may be performed for different reasons, for example:
to reproduce in a virtual environment the behaviours of a physical system so that such behaviours may be ‘recorded’.
to generate simulated behaviours which can be used as ideal behaviours of a perfectly well‐behaved physical system to aid identify degraded performance or problems.
to predict problems, e.g. erosion, before they occur on a physical system to allow mitigating action.
to validate design or operational choices in the virtual environment before instantiating in a physical system.
as the basis for the development of a reduced order model to form a component of a Digital Twin of the process or operation.
The bulk solids handling operations and areas covered include chute design, belt conveying, pneumatic conveying, scoops and grabs, port side operations, pharmaceuticals, particle shape, and simulation calibration.
Chapter 1 summarises different DEM calibration philosophies, the most important DEM parameters of the most commonly used contact models, as well as different calibration tests to determine the DEM parameters efficiently and unambiguously.
Chapter 2 discusses the main relevant aspects of transfer chute design to minimise problems in practice and shows how simulations can be used to improve the design. Modelling and evaluation issues for typical transfer chute problems like the simulation of build‐up, the determination of impact forces, and the prediction of belt mis‐tracking, abrasive wear, and dust emission are presented.
In Chapter 3 Finite and Discrete Element Methods are described to calculate the static and dynamic belt tensions within the conveyor belt during starting, steady‐state running, and stopping, with the aim to improve performance and reliability of the system.
Chapter 4 presents the developments in the use of coupled Discrete Element Method and MultiBody Dynamics (DEM–MBD) in particle‐based systems related fields with a particular focus on the applications in design of bulk handling and processing equipment.
Chapter 5 outlines the fundamentals of gas–solids flow in pipelines and details three simulation methods, Single‐ and Two‐Fluid Models and combined CFD–DEM. The principal theories and equations commonly available in commercial off‐the‐shelf and open source software packages are given.
Chapter 6 introduces different methodologies for computationally capturing erosive wear and particle breakage in pneumatic conveying. A detailed discussion of one‐dimensional two‐phase flow modelling of the industrial conveying pipeline for particle breakage and erosion prediction, including the algorithm for breakage and erosion modelling, is included.
Chapter 7 presents a brief introduction of DEM modelling, including principles, parameter calibration, and model validation, and its application in pharmaceutical processing. For this purpose, an overview of DEM modelling of several key unit operations in pharmaceutical manufacturing, including powder mixing, continuous blending, twin screw granulation, die filling and dry powder inhalation, is presented.
Chapter 8 covers recent code optimisation for the contact force calculation with arbitrary body shape, parallelisation performance, and discussion of results showing both deformable and rigid‐body versions of the code in the application of cube packing.
I am deeply grateful to all the authors for their excellent contributions to this book which provides a width and depth of knowledge in one volume I haven't seen elsewhere.
Glasgow, Scotland, UK
Professor Don McGlinchey
21st November 2022
1Calibration of DEM Parameters
Corné Coetzee1 and André Katterfeld2
1Stellenbosch University, Department of Mechanical and Mechatronic Engineering, Granular Materials Research Group, Joubert Street, Stellenbosch, 7600, South Africa
2Otto von Guericke University Magdeburg, Chair of Material Handling, Institute of Logistics and Material Handling Systems, Universitätsplatz 2, 39106 Magdeburg, Germany
Abbreviations and Acronyms
AoR
Angle of Repose
BCA
Bulk Calibration Approach
CFD
Computational Fluid Dynamics
CoR
Coefficient of Restitution
CPU
Central Processing Unit
DEM
Discrete Element Method/Discrete Element Modelling
DMA
Direct Measurement Approach
FEM
Finite Element Method
GPR
Gaussian Process Regression
GPU
Graphical Processing Unit
GSMC
Generalised Surrogate Modelling‐based Calibration
MPM
Material Point Method
PSD
Particle Size Distribution
UCT
Uniaxial Compression Test
1.1 Introduction
Mesh‐based simulation techniques in continuum mechanics, such as the Finite Element Method (FEM) or Computational Fluid Dynamics (CFD), require the body or volume of interest to be discretised by a mesh. The mesh closely represents the real object with small differences or idealisations, mostly directly proportional to the size of the mesh. These approaches show the convergence of the results with mesh refinement. However, Lagrangian approaches, such as FEM, suffer from severe mesh distortion when the body experiences large deformation. In these cases, the solution can become unstable, and the results inaccurate. The so‐called meshless continuum‐based methods such as the Material Point Method (MPM) are capable of modelling larger deformation [1]. However, these methods still assume a continuum body and might still rely on a non‐deforming mesh. As a result, these methods cannot model the discrete nature of granular materials such as mixing and segregation or single particles separated from the bulk of the material in a screening process, for example.
The Discrete Element Method (DEM) was developed by Cundall and Strack [2] in the 1970s in order to solve problems associated with rock mechanics. The potential of DEM was quickly recognised for research purposes in a number of areas such as physics, nanotechnology, chemical engineering, and materials handling. DEM is completely meshfree (or meshless) and can easily model the large deformation typically associated with the handling and flow of bulk granular materials (particulate matter). DEM can also model the discrete nature of the individual particles, during screening for example.
To use DEM to analyse the behaviour of bulk materials, for example, in conveyor systems, during transportation and storage and flow through processing equipment, an accurate simulation model should be generated. A DEM model should define the geometric properties of the particles, such as the size and shape distributions, as well as the geometry of any structure or equipment. The interaction or contact properties (particle–particle and particle–wall) also need to be defined, which is a major component of the modelling process. As in all the numerical simulation methods, the experience (know‐how) and sometimes the art applied by the user are critical to define and create a model capable of producing the most accurate simulation results in the shortest possible time frame.
In a DEM model, the discretisation of the bulk material is directly related to the size of the considered particles, which have a significant influence on the behaviour of the modelled material. DEM is also computationally intensive, and for this reason, most practical models are simplified in terms of particle size, shape, and contact properties. This idealisation is the reason why established bulk material properties (e.g. the angle of internal friction and the angle of repose [AoR]) cannot be directly used as input parameters. Hence, it is necessary to reverse engineer the parameters by comparing the modelled bulk behaviour to that observed in the experimental tests. This procedure is called the ‘calibration of DEM parameters’ and is the key to produce realistic simulation results.
1.2 Basic DEM Theory
A typical DEM model consists of particles and walls. The particles can make contact with one another and with walls, but wall–wall contact is usually undefined. The particles represent the granular material and can in theory take on any shape and size. However, in practice, spherical and multi‐sphere particles are the most commonly used. Walls are used to define all the structures with which the particles can interact, such as the walls of equipment and machines. Contact models are used to calculate the contact forces and moments based on the contact kinematics.
Figure 1.1 DEM computation cycle.
1.2.1 The Calculation Cycle
A DEM calculation cycle consists of four steps as illustrated in Figure 1.1, namely (1) contact detection, (2) contact resolution, (3) solving the equation of motion, and (4) updating of the particle velocity and position.
The contacting pieces (particles and walls) are allowed to overlap, and in the first step of the computation cycle, all particle–particle and particle–wall contacts are identified. The overlap is assumed to be relatively small compared to the particle size. Although contact detection happens automatically, without any user intervention, the particle shape selected by the user has a significant effect on the efficiency of this step. Spherical particles are computationally the best, followed by multi‐sphere particles and more complex shape representations such as super‐quadrics and polyhedra.
In the second step, the force and moment vectors are calculated at each contact, based on one of a number of available contact models selected by the user. The contact force and moment are dependent on the relative contact displacement or overlap (elastic force), velocity (viscous force) and the contact parameter values specified by the user.
In the third step, the resultant force and moment acting on each particle are calculated. This includes the forces, Fc, and moments, Mc, due to the contacts and the body force due to gravity Fg. Based on the particle's mass, m, and moment of inertia, Ig, the translational acceleration, , and the rotational acceleration, , can be calculated using the equations of motion,
In the fourth and last step, the particle velocity (translational and rotational ) is first updated using an explicit time integration scheme,
where Δt is the timestep. This is followed by the particle's position and orientation update,
The explicit time integration scheme is conditionally stable and requires a timestep smaller than the critical timestep. Using the analogy of a single degree‐of‐freedom mass‐spring system, it can be shown that the stable timestep is proportional to the particle mass and inversely proportional to the effective contact stiffness. For slight variations in the explicit time integration scheme and the calculation of the timestep, see O'Sullivan [3] for example.
This step concludes the basic time cycling sequence, after which the time is incremented, followed by a new contact detection step.
1.2.2 Contact Models
A contact model defined at each contact describes the force–displacement relation. There are a number of contact models from which the user can select. Figure 1.2 shows the basic elements of a contact model, namely springs, dashpots, frictional sliders, and tension elements. A combination of these elements act in each of the normal and shear (tangential) directions.
The spring elements define the elastic force component and can have linear behaviour (as in the linear model) or non‐linear behaviour (as in the Hertz–Mindlin model). The viscous dashpots dissipate energy, and the frictional slider allows for Coulomb‐like frictional behaviour in the shear direction. For the modelling of spheres, rolling resistance models are very important; however, they are not visualised in Figure 1.2. Cohesive behaviour can be modelled by allowing tensile forces in the normal direction. The details of the different contact models are not presented here, and the interested reader should consult other sources such as O'Sullivan [3] and Thornton [4].
Figure 1.2 Typical elements of a contact model.
At each timestep, the relative motion between two contacting pieces is used, in combination with the elements defined above, to update the contact force components. The user should specify the parameter values for the spring stiffness, for example the damping (dashpot) constants and the coefficient of friction. Obtaining a set of parameter values so that the modelled bulk behaviour of the material is an accurate representation of a physical material is the main focus of the calibration process.
1.3 DEM Application and Calibration Philosophies
In general, the application of DEM can be classified in two groups:
Group 1
focuses on improving our general understanding of the physics (e.g. rheology, constitutive behaviour) of granular materials through applied research [
5
,
6
]. For this purpose, idealised (‘artificial’ or manufactured) bulk materials such as glass beads with a very well‐defined
particle size distribution
(
PSD
) (mono‐disperse or bi‐disperse) and (close to) homogeneous properties are used. Often the particle behaviour is investigated in small‐scale laboratory tests with a relatively small number of particles involved. The DEM model replicates the real application with a scale of 1 : 1, even if it requires a very large computational effort and duration of time.
Group 2
focuses on the modelling of ‘natural’ bulk materials in industrial applications. The materials range from powders to rocks and require an idealisation of the DEM models in terms of particle shape, size distribution, and stiffness.
In the first group of applications, it is possible to use tests to determine the particle or contact micro‐properties and directly use them as DEM input parameters. This approach or philosophy for DEM parameter selection was labelled the ‘Direct Measurement Approach’ (DMA) by Coetzee [7].
In the second group of applications, the DMA can at most be partly used, since there are a number of simplifications required. For these applications, the macroscopic (bulk) material behaviour needs to be replicated by an idealised DEM model. Hence, the microscopic DEM parameters are to be chosen in such a way that the macroscopic behaviour of the material in the simulation is the same as that in reality. According to Coetzee [7], this approach is called the ‘Bulk Calibration Approach’ (BCA) since the process of finding the DEM parameters is an iterative process that involves a series of simulations which replicate at least one experiment. This approach truly earns the name ‘calibration’, and in the sections to follow, the term calibration refers to BCA, unless stated otherwise.
Although the process of parameter selection using the BCA is essential to produce simulations with realistic results, there are only a few works which try to define a systematic approach for the BCA. Especially in the industrial sector, many calibration approaches do not earn the name ‘calibration’. The selection of DEM parameters based on a non‐systematic parameter selection (‘guessing of parameters’) may lead to wrong DEM results and invalid conclusions. This may also be the case when DEM parameters are ‘tuned’ based on simulations of the final application, where the parameters are non‐systematically varied until the flow results look like what is expected.
Furthermore, the kind of applications being modelled can also influence the calibration experiments and DEM parameters to be used (the selection of appropriate contact models, for example). Here the focus is on bulk storage and handling applications where the consolidation pressure is relatively low (less than 10 kPa), and the material is either static (storage in a bin or moving with a conveyor belt, for example) or dynamic and flowing (out of a bin or through a transfer chute, for example). When the material is under higher consolidation pressure, aspects such as plasticity might become important, which is not addressed in this work.
To ensure that the DEM simulation results can be trusted, the user must have a basic understanding of the physical bulk properties and the most important DEM parameters. This is addressed in the next sections, followed by a detailed discussion of the calibration process.
1.4 Physical Bulk Properties
The properties that are important for bulk handling applications are discussed. It is important to consider all these bulk properties during the calibration process.
1.4.1 Bulk Density and Porosity
Bulk density is needed to accurately model the body forces due to gravity and hence the consolidation pressure (even if relatively low) experienced by a bed of material. Bulk density is also important to accurately model the forces exerted by the material on structures or equipment walls. When the material flow rates are considered (modelling the conveying of material, for example), it is important to accurately model not only the mass flow rate but also the volume flow rate. The cross‐sectional area of a transfer chute, for example, should be sufficient to handle the volume flow rate, which is related to the mass flow rate by the bulk density.
1.4.2 Bulk Friction
In this chapter, the term ‘bulk friction’ is used to define and characterise the bulk property related to the material's resistance to shear flow. Physically, the bulk friction is influenced by the PSD, particle shape, and inter‐particle sliding friction. The particle shape leads to mechanical interlocking, which results in shear resistance even under zero normal load. The Coulomb‐type sliding friction at contacts has a significant effect on the bulk friction. On the bulk level, the material can be considered a continuum and described by the Mohr–Coulomb constitutive model, defining a bulk cohesion and internal friction angle (yield locus) which can be measured in a direct shear test, for example.
1.4.3 Dissipation of Energy
In non‐cohesive bulk materials, energy is dissipated in the form of contact friction, inelastic deformation of the particles and walls, particle breakage (fracture energy), and other losses such as wind resistance. Losses due to wind resistance and particle breakage are usually ignored, unless multiphase flow (coupled CFD–DEM modelling) or particle breakage is specifically analysed. Contact friction is responsible for the majority of the energy dissipated and should be accurately accounted for in all DEM models.
Additional contact damping (usually viscous damping) is required to reach a state of static equilibrium, when particles are dropped from a height into a bin, for example. However, appropriate levels of damping are also required for dynamic processes to keep the energy levels realistic and to avoid excessive particle motion.
1.4.4 Bulk Stiffness
When a bed of material is compressed, the relation between the applied force and the displacement (change in bed height) defines bulk stiffness. The stiffness can be measured under confined and unconfined conditions (these two approaches will result in different stiffness values).
Even if the inter‐particle contact stiffness is linear, bulk stiffness is not necessarily linear. The non‐linearity in bulk stiffness is caused by re‐organisation of the position of the particles and contacts in the packing – increasing the number of contacts under increasing load. Due to this phenomenon, initial cyclic loading‐and‐unloading compression of a loosely packed particle bed results in hysteretic behaviour, where the unloading curve shows increased stiffness as compared to the loading curve.
1.4.5 Bulk Cohesion and Adhesion
In general, the term ‘cohesion’ refers to the attractive force between two similar materials, and the term ‘adhesion’ to the attractive force between two dissimilar materials. Here, however, the two terms are used interchangeably. The bulk cohesive behaviour is due to cohesive forces acting at the contact level (particle–particle and particle–wall), where it is mainly caused by one of two mechanisms: liquid‐bridges or Van der Waals forces.
When moisture or liquid (mostly water in the applications considered here) is introduced, a thin liquid film forms on the outer surface of the particles and walls. When a new contact forms, a liquid bridge is formed, resulting in a tensile force due to the capillary effect and liquid surface tension (see Mitarai and Nori [8], for example). The van der Waals force, on the other hand, acts between two macroscopic bodies due to intermolecular cohesion forces, and the effects are significant only for very small particles such as powders (<100 μm, [9]). Independent of the cohesion mechanism at the contact level, an increase in contact cohesion results in an increase in bulk cohesion. Here, the term bulk cohesion refers to the bulk material's resistance to shear flow under zero normal load.
1.5 DEM Parameters and Their Relation to Bulk Properties
The DEM contact parameters discussed in this section are generic and applicable to all non‐cohesive contact models, including linear and non‐linear models. These are the parameters that should in general be considered and calibrated to ensure accurate modelling of the applications considered in this chapter. Although the implementation of these generic parameters is dependent on the specific contact model (and even the software) used, the relation with bulk properties as described here will remain valid.
The DEM parameters and bulk properties considered are listed in Table 1.1. The first three parameters (particle shape, size, and density) are related to the particles, while the other parameters are all related to the contacts (particle–particle and particle–wall). The relation between each parameter and bulk property (as discussed in Section 1.2) is indicated as either ‘strong’, ‘weak’, or ‘negligible’ (insignificant), and the effect of the parameter on the computation time is also indicated. These relations are further discussed below, and typical calibration experiments for each bulk property are listed at the bottom of the table.
1.5.1 Particle Shape
Discrete elements are used in DEM to represent the particles. In general, these elements are referred to as particles, and pioneering DEM codes [2] were used for circular (in 2D) and spherical (in 3D) particles due to the associated computational efficiency in contact detection and overlap calculation. However, with advances in computing power, more complex non‐spherical shapes were introduced using different techniques as discussed below.
The particle shape will influence all the other model parameters that need to be calibrated and should be the first parameter to be decided by the modeller. If, at any later stage, the shape is changed or even slightly modified, all the parameter values should be re‐calibrated. When the physical particles are non‐spherical (which is the case in most industry and practical applications), the user has the option to make use of spherical particles and include rolling resistance or to make use of one (or more) of the available non‐spherical shape models (with or without rolling resistance).
1.5.1.1 Non‐spherical Particles
Any number of spheres can be merged to form a single particle, often referred to as ‘multi‐sphere particles’, ‘clumps’, ‘clusters’, or ‘glued particles’. The constituent spheres can overlap, and their relative position within the particle remains fixed, thus creating a rigid particle. Multi‐sphere particles still allow for efficient contact detection and overlap calculation. However, these particles still have some limitations, and sharp edges or blocky particles cannot be easily created. Multi‐sphere particles also have ‘bumpy’ surfaces, which might introduce higher levels of interlocking and tend to have more contacts with other particles and walls.
Table 1.1 Relation between DEM parameters and non‐cohesive bulk properties.
Bulk material properties
DEM parameters
Bulk density and porosity including changes due to flow (dilatancy)
Bulk friction/shear/interlocking/flow behaviour
Dissipation of energy (damping)
Bulk stiffness
DEM model computation time
Particle shape
Weak
Influences the packing porosity, and hence the bulk density for a given particle (solid) density.
Strong
The more non‐spherical the shape, the higher is the interlocking effect, and thus, the higher the bulk friction.
Negligible
Negligible
Strong
Spherical particles are the most efficient. The more complex the shape, the longer a defined simulation takes to complete.
Particle size distribution (PSD)
Weak
Influences the packing porosity, and hence the bulk density. The wider the PSD, the lower is the porosity and the higher is the bulk density.
Weak
The wider the PSD, the lower is the porosity and the higher is the particle interlocking, thereby increasing the resistance to shear.
Negligible
Negligible
Strong
A reduction in the number of particles, logarithmically reduces the computation time.
Particle density
Strong
The relation between particle density and bulk density is very close to linear for a given porosity (i.e. particle shape and size distribution).
Negligible
Negligible
Negligible
Strong
The time step increases in size with an increase in density, thus reducing the total simulation time.
Contact damping/coefficient of restitution
Negligible
Negligible
Strong
Contact damping (together with sliding and rolling friction) is one of the major mechanisms for the dissipation of energy.
Negligible
Negligible
Contact stiffness
Negligible
Using realistic values, the contact stiffness has a negligible effect on the bulk density. Very low values will increase the contact overlap and the bulk density. However, if this is the case, the stiffness is probably too low for modelling the typical materials considered here.
Negligible
The contact stiffness has an effect on the bulk friction only for unrealistically low stiffness values which should be avoided
[10]
.
Negligible
If the user specifies either the non‐dimensional critical damping ratio or coefficient of restitution, the effect is negligible since the code will calculate the damping constant based on this value in combination with the stiffness.
Strong
The contact stiffness has a strong relation to the bulk stiffness. With an increase in the contact stiffness, the bulk stiffness increases.
Strong
The contact stiffness highly influences the time step: the higher the stiffness, the smaller is the time step. Due to this effect, most DEM simulations make use of a reduced stiffness.
Contact coefficient of sliding friction: particle–particle
Weak
Higher friction values lead to less dense packings (slightly higher porosity).
Strong
The sliding friction is one of the major parameters influencing the bulk shear behaviour. An increase in the friction increases the bulk friction asymptotically: for lower friction coefficients, the bulk friction is more sensitive than for higher friction coefficients (typically 0.7 and higher).
Strong
The sliding friction is one of the major mechanisms for energy dissipation.
Negligible
Negligible
Contact coefficient of sliding friction: particle–wall
Negligible
Strong
The sliding friction is one of the major parameters influencing the bulk shear behaviour against a structure or wall. For example the flow down a chute or out of a bin.
Strong
The sliding friction is one of the major mechanisms for energy dissipation, although quantitatively less than particle–particle friction.
Negligible
Negligible
Contact coefficient of rolling friction (particles and walls)
Negligible
Strong
The rolling friction, in combination with the sliding friction, has a strong influence on the bulk friction (shear) behaviour.
Negligible
Negligible
Negligible
Experiments that are sensitive to the specific bulk material property
Bulk density/porosity: Filled container Dilatancy: Direct shear test
Angle of repose Discharge test Draw down test Direct shear test
Drop test Pendulum test Uniaxial compression
Uniaxial compression
—
Non‐spherical particle shapes can also be modelled using mathematical descriptions such as superquadrics, polyhedra, and faceted particles. The advantages of this technique include the modelling of complex shapes more accurately, including blocky particles and sharp edges; however, it comes with a decrease in computational efficiency.
In general, when non‐spherical particles are used, rolling resistance (friction) can be omitted if the selected shape can be accurately calibrated using only sliding friction [11].
1.5.1.2 Spherical Particles
The contact model for spherical particles should include rolling resistance to realistically model the rotational behaviour of physical non‐spherical particles. Various authors (e.g. [11–14]) have shown that rolling resistance can accurately account for the particle shape in terms of bulk behaviour. Wensrich et al. [15] showed that spherical particles with rolling friction can accurately model the behaviour of non‐spherical particles in both static and dynamic flow conditions with the dilational nature also captured to a reasonable degree. Several rolling resistance models are available as summarised by Ai et al. [16], and according to Wensrich and Katterfeld [17], Type C is the preferred and most stable model.
1.5.1.3 Shape Selection
If the bulk material has a relatively homogeneous particle size and shape, it is suggested to make use of spherical particles with rolling resistance. This is applicable to materials such as sand, crushed gravel, mineral ore, and agricultural grains and seeds. Also, when the material flow is relatively homogeneous, i.e. the material flows in a stream with little variation in particle velocity, the effect of particle shape becomes less significant, and a simple and efficient shape can be selected. In these cases, if non‐spherical particles are used, it is proposed to use simple multi‐sphere particles comprising three spheres in a pyramid shape [18, 19], where rolling resistance can be ignored.
In applications where the material is non‐homogeneous in particle shape and size and where the particles are relatively large in comparison to the model boundaries (interacting with structures, equipment, and machine parts), the particle shape becomes more important. Also, if mixing, screening and sieving, or mechanical arching and bridging are investigated, accurate shape models should be considered [20]. The modelling of materials such as biomaterials might also require more accurate shape modelling if the particles are far from spherical, for example, wood chips and fibres [21, 22].
1.5.2 Particle Size Distribution and Scale
The PSD and scale (size) of calibration experiments are closely related. The PSD of the physical material being modelled can be measured using sorting sieves or screens. Alternative methods include photo analysis and laser diffraction techniques. However, the modeller should decide how the PSD of the physical material will be modelled. Due to computational constraints, the maximum number of particles that can be modelled within a reasonable time frame is limited, depending on the available software and hardware (Central Processing Unit [CPU] versus Graphical Processing Unit [GPU], for example). In most industrial‐scale applications the number of particles can easily be in billions to trillions [23], which cannot be modelled, regardless of the available hardware. In these cases, the number of particles should be reduced by scaling the PSD.
There are several approaches available for this, as described by Roessler and Katterfeld [24] and the references therein, namely exact scaling, coarse graining, scalping, and combined scaling. Mohajeri et al. [25] developed a hybrid scaling technique where the geometry and the particles are scaled in a stepwise manner. This technique requires more simulation runs, but it can be used for the calibration and validation of upscaled particles even if the available experimental setup is too small to accommodate the final upscaled particles and if the experiment is scale‐dependent.
The final selection of the modelled PSD will depend on the physical PSD, the application being modelled, available calibration equipment, and the available computational power. There are no general rules and guidelines that apply to all possible cases. The PSD used in the calibration step should be identical to the PSD used in modelling the (full‐scale) final application. Similar to the particle shape, once a PSD is calibrated, it cannot be modified, unless the calibration steps are repeated. As a general rule, the particle size should be selected so that there are at least 10–20 particles across all dimensions of the geometry. The particle resolution should be high enough to render realistic and accurate results within a reasonable time frame. With larger (fewer) particles, the resolution is reduced, and boundary (wall) effects become significant. When the flow of the material through an orifice is modelled, the ratio of the orifice opening to particle size should be as large as computationally possible to avoid any choking effects.
