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FACULTY MECHANICAL, MARITIME AND MATERIALS ENGINEERING
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Specialization: Transport Engineering and Logistics
Report number: 2015.TEL.7920
Title:
Calibration and Verification
experiments for Discrete Element
Modeling of cohesive materials
Author:
R. Kapelle
Title (in Dutch) Kalibratie en verificatie experimenten voor het Discreet Element Modelleren van cohesieve materialen
Assignment: literature
Confidential: no
Initiator (university): dr. ir. D. L. Schott Initiator (company): TU Delft
Supervisor: dr. ir. D. L. Schott
Delft University of Technology
FACULTY OF MECHANICAL, MARITIME AND MATERIALS ENGINEERING
Department of Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl
Student: R. Kapelle Assignment type: Literature
Mentor: Dr.ir. Dingena Schott Report number: 2015.TEL.7920
Specialization: TEL Confidential: No
Creditpoints (EC): 10
Subject: Calibration and Verification experiments for Discrete Element Modeling of cohesive materials
Within the research theme Dynamics and Interaction of Material and Equipment the simulation tool Discrete Element Method (DEM) is used. DEM is a particle based method to model interaction of particulate material (powders or bulk material) with equipment.
In practice DEM is used to represent realistic material behavior. In our lab we use a set of tests: angle of repose and angle of movement to calibrate material behavior, and penetration to calibrate material-equipment interaction. The chosen tests to validate the material behavior depend on the nature of the process that has to be modeled. For example:
a dynamic process with high particle velocities might is different compared to a quasi-static process such as an angle of movement test where the majority of the particles are in rest. if the contact between material and equipment or tool is not dominant there is no need to use
the penetration test.
The ultimate goal is to have one single experimental setup that gives us enough information to calibrate and verify the material. Therefore first, we would like to have an overview of the ways DEM researchers calibrate and verify their simulated cohesive materials and processes. A previous literature review by Paul Willekens (2014.TEL.7871) has been carried out on this subject but focused on
freeflowing materials and not on cohesive materials.
Your assignment is to investigate and make an overview of the laboratory and/or industrial scale tests that are used to calibrate and verify the modeled cohesive material in DEM.
This assignment comprises amongst others (but is not limited to) the following: Find relevant literature and research groups
Describe and explain experimental setup(s) used by researchers
Describe for which context the laboratory or real scale tests are used (kind of material, kind of application, etc.)
Describe to which extent the calibrated and verified material behavior is validated with (industrial scaled) experiments
Classify and make an overview of the tests found and compare them
Based on your findings propose an experimental setup that can be used to calibrate the material
It is expected that you conclude with a recommendation for further research based on the results of this study.
The report should comply with the guidelines of the section. Details can be found on blackboard. The supervisor,
S
UMMARY
As of today, various researchers have developed their own DEM contact model in order to cope with the co-hesive behaviour of bulk material. Their focus was primarily to validate their contact model with any real bulk material so they also executed calibration and verification steps which will be outlined in this literature research. The key processes are based on type of industrial application the material is going to be exposed to, in order to determine the relevant flow properties and their corresponding input parameters for DEM. The approach to determine suitable input parameters for a DEM simulation is nowadays rather simplistic and based on numerous simulations while changing a set of parameters to eventually achieve a reasonable match between the real life experiment and the numerical simulation. Logically this process is very time consuming and expensive, therefore methods to efficiently calibrate a cohesive material in DEM with corre-sponding parameters will be presented in this literature research.In order to get a good feeling for the matter described in the researches, the second chapter will describe the difference between free flowing and cohesive bulk materials by means of flowability. Also bulk material characteristics of both cohesionless as cohesive bulk materials, as well as the corresponding (non-contact) forces that act on the particles will be mentioned. After the various experimental setups which are able to measure the bulk material properties are briefly outlined, the Discrete Element Method will be briefly out-lined in the third chapter. Various contact models for and corresponding required input parameters will be discussed, such that in case of the contact models for cohesive materials, additional parameters will be mentioned short. A brief parameter sensitivity analysis is executed with help of literature to obtain the most sensitive input parameters.
While the terms calibration and verification are frequently used in this field of research, it is noted that they are commonly used as synonyms. The fourth chapter will therefore describe the definitions of calibration, verification and validation and clarify the theoretical meanings and the applicability on discrete element modelling. The fifth chapter will describe four researches with regards to the calibration and verification of a cohesive bulk material. Most of the researchers have developed a unique calibration and verification methodology, which seem not always valid according to the definitions described in Chapter 4.
Because every researcher used a different approach with corresponding issues, it is fair to say that as of today there is not a clear view on a justified calibration and verification methodology which is applicable for various cohesive materials and equipment. Also a review of of the described calibration and verification approaches for cohesive DEM models showed that some researchers just assumed parameters such as the interparticle static friction coefficientµs.ppand the interparticle rolling friction coefficientµr.ppor they did not detail fully how parameters were derived. Researchers nowadays work parallel with each other, instead they should com-bine open source knowledge to generate more DEM validations and benchmarks to increase the acceptance by the industry. While DEM is an valuable addition to the toolkit of engineers, it is plausible to assume that the desire for a generalized calibration and verification for cohesive materials with DEM stays a real challenge for the coming years. Only Grima [2011] showed a well designed methodology which could be the basis of fur-ther research into calibration and verification of cohesive bulk material, accompanied by a multifunctional testing device such as the EPT of Morrissey [2013] for example.
C
ONTENTS
Summary i
1 Introduction 1
1.1 Objective . . . 1
1.2 Structure . . . 1
2 Bulk material characteristics 3 2.1 Flowability of bulk material . . . 3
2.2 Non-contact interparticle forces . . . 4
2.3 Bulk material properties . . . 5
2.3.1 Properties at particle level . . . 5
2.3.2 Properties at bulk level . . . 6
2.4 Useful measuring equipment for cohesive materials . . . 8
3 Discrete Element Method 9 3.1 Working principle briefly . . . 9
3.2 DEM contact models for cohesive material . . . 10
3.2.1 Hertz-Mindlin . . . 10
3.2.2 Hertz-Mindlin with linear cohesion . . . 10
3.2.3 Johnson-Kendall-Roberts (JKR) . . . 10
3.2.4 Edingburgh Elasto-Plastic Adhesion (EEPA) . . . 11
3.3 Relevant DEM parameters and methodology . . . 11
3.3.1 Surface energyγ . . . 12
3.3.2 Cohesion energy density Ce . . . 13
3.4 Parameter sensitivity analysis . . . 14
3.4.1 Grima [2011] . . . 14
3.4.2 Morrissey [2013] . . . 14
3.4.3 Willekens [2014] . . . 14
3.4.4 Overview and remarks . . . 15
4 Definitions of calibration, verification and validation 17 4.1 Calibration . . . 17
4.2 Verification . . . 17
4.3 Validation . . . 18
4.4 Remarks. . . 18
5 Calibration and verification experiments 19 5.1 Research of Jensen [2014] . . . 19
5.1.1 Particle density with volume test . . . 19
5.1.2 Wall friction coefficient with surface friction test. . . 19
5.1.3 Inter particle friction coefficient with angle of repose test . . . 20
5.1.4 Conclusions and remarks . . . 20
5.2 Research of Grima [2011] . . . 21
5.2.1 Systematic approach . . . 21
5.2.2 Calibration and verification of dry, cohesionless coal . . . 22
5.2.3 Calibration and verification of moist, cohesive coal . . . 25
5.2.4 Calibration of dry, cohesionless bauxite . . . 26
5.2.5 Calibration and verification of moist, cohesive bauxite . . . 27
5.2.6 Conclusions and remarks . . . 28 iii
5.3 Research of Olukayode [2014] . . . 29
5.3.1 Calibration of cocoa(12% fat) sample . . . 29
5.3.2 Conclusions and remarks . . . 31
5.4 Research of Morrissey [2013] . . . 31
5.4.1 Calibration of KPRS iron ore fines (1% moisture content) . . . 32
5.4.2 Verification of KPRS iron ore fines with EEPA Non-Linear . . . 33
5.4.3 Conclusions and remarks . . . 34
5.5 Overview . . . 35
6 Conclusions and Recommendations 37 6.1 Conclusions. . . 37
6.2 Recommendations . . . 38
1
I
NTRODUCTION
While the Discrete element method (DEM), developed by Cundall and Strack [1979], applied with free flow-ing bulk materials is commonly accepted in the industry the last few years, the use with cohesive bulk ma-terials stays a real challenge. Although there has no standardised calibration and verification methodology been developed the last few years, the calibration of free flowing bulk material is well covered by now with help of rapidly evolving contact models and available experimental setups for DEM. Note that a DEM mate-rial model is just only an approximation of the real bulk matemate-rial and that the model gets more complex by adding a property like cohesion or adhesion for cohesive materials. The accuracy of the DEM model is further dependent on the amount of available computation power and time, which in the end is a valuable property. It is simply not feasible to completely model a material in DEM that includes every single detail of the real material, hence a calibration is desired.
1.1.
OBJECTIVE
This literature research aims to create an overview of known calibration and verification methods for cohe-sive bulk material with Discrete Element Modelling and serves as a prelude to the desire to have one single experimental setup and methodology which provides enough data to calibrate and verify any cohesive bulk material for any (industrial) application. The main research question could thus be formulated as follows:
Which calibration and verification methods for cohesive bulk materials with DEM are cur-rently used and how can these be improved?
1.2.
STRUCTURE
First, Chapter 2 will describe the difference between free flowing and cohesive bulk materials by means of flowability. Thereafter, bulk material characteristics of both free flowing as cohesive bulk materials, as well as the corresponding (non-contact) forces that act on the particles will be mentioned. Also various testing equipment will be outlined which are able to measure the bulk material properties.
Next, the discrete element method will be briefly outlined in Chapter 3 for both free flowing as cohesive bulk materials. Also various contact models and corresponding required input parameters will be discussed. In case of the contact models for cohesive materials, the additional parameters will be mentioned short. At last a parameter sensitivity analysis is done according to the available researches and literature.
Thereafter, Chapter 4 will describe common heard definitions with perspective of calibration, verification and validation which are often not well interpreted. This chapter will clarify the theoretical meanings and the applicability on discrete element modelling.
Afterwards, Chapter 5 will outline four research studies with regards to the calibration and verification of a cohesive bulk material. Some of the researchers have developed a specific calibration methodology which is verified afterwards. At last, an overview of the key points of interests of the researches will be shown, as well as a brief comparison between the different calibration and verification methods.
Finally, the conclusions and recommendations for any future research in this field will be discussed in Chapter 6.
2
B
ULK MATERIAL CHARACTERISTICS
In order to work with DEM, material properties of the bulk solid need to be known to eventually transform into corresponding DEM input parameters. Not all material properties are however relevant for simulation purposes, for example thermal or electrical conductivity. Also the amount of required material properties differ according to free flowing or cohesive bulk material and the type of application the material is intended for. This chapter describes the difference between free flowing and cohesive bulk materials by means of flowability. Also the influence of the corresponding (non-contact) interparticle forces on the flowability of a bulk solid will be mentioned. Thereafter, bulk material characteristics of both free flowing as cohesive bulk materials will be briefly outlined. Also various test equipment will be discussed which are able to measure the required material properties.
2.1.
FLOWABILITY OF BULK MATERIAL
The main difference between free flowing bulk material and cohesive bulk material is the flow and packing behaviour. Flowability is generally defined as the ability of a bulk material to flow, whereas flow means that a bulk solid is plastically deformed due to gravitational and or other loads acting on it (Prescott and Barnum [2000]). The flowability of a bulk material is often described by the unconfined yield strength as function of the consolidation stress and or storage and consolidation time. This relationship is defined as the material flow function F F . In order to compare bulk materials with each other, the flowability of a material is classified by the flow factor f fc, developed by Jenike, which is defined as the ratio between the consolidation stressσ1
and the unconfined yield strengthσc. f fc=σ1
σc
A classification for the flowability of any bulk material is defined by Jenike as follows: • f fc< 1 : not flowing
• 1 < f fc< 2 : very cohesive • 2 < f fc< 4 : cohesive • 4 < f fc< 10 : easy-flowing • 10 < f fc: free-flowing
Other than Jenike’s classification to determine whether a bulk solid is free flowing or cohesive, Castellanos [2005] describes the use of the Cohesive Granular Bond number to calculate the ratio of the interparticle ad-hesion force to the particle’s weight to determine the cohesiveness of a bulk solid. The higher the value for B og, the higher the tendency for the particles to aggregate.
B og= Fa
mg , with Fathe attractive force between two particles.
At last, the flowability of a bulk solid could be characterised by the Hausner Ratio (Grey and Beddow [1969]) and the Carr’s index. The Hausner Ratio is defined as the ratio between the tapped density and the bulk den-sity of a bulk solid, where the tapped denden-sity is defined as the bulk denden-sity after the container, in which the
bulk solid rests, has been mechanically tapped or vibrated until a change of volume has been observed. A Hausner Ratio smaller than 1.25 indicates a free flowing bulk solid while a value greater than 1.25 indicates a cohesive flow behaviour. At last, the Carr’s index is defined as:
Carr’s index = 100ρt apped− ρbul k ρt apped
,
while a value between 5-15 indicates excellent flowability and a value above 23 indicates poor flowability. Note that the Hausner Ratio and Carr’s index are primarily used for powders.
2.2.
N
ON-CONTACT INTERPARTICLE FORCES
The flowability of a bulk solid is also dependent on the particle size. It is commonly known that with increas-ing particle size, the flowability will increase as a result of the presence of non-contact interparticle forces such as van der Waals forces, capillary forces and electrostatic forces, explained by Zhu et al. [2007]. The van der Waals force is shortly described as the force between molecules due to the presence of other molecules nearby and further explained by Israelachvili [2011]. While the van der Waals forces are most present at small interparticle distances, the effects decrease for particle sizes greater than a few 100µm, as Figure 2.1 shows. Although the van der Waals forces increase with increasing diameter for a smooth spherical particle, the ef-fects of the weight of the particle increase more rapidly and cause it to become less dominant (Seville et al. [2000]). Electrostatic forces are present due to different electric potentials of particle surfaces. These forces are however considerably smaller at small distances than the van der Waals forces, but become more signifi-cant when the separation distance between particles is greater.
Figure 2.1: Effects of particle diameter against interparticle force of multiple non-contact forces, Zhu et al. [2007] p3382
Unlike previously described forces at dry granular bulk solids, moist bulk solids bring forward another phe-nomena called liquid bridges, shown in Figure 2.2. The presence of moisture in a granular material induces the forming of liquid bridges between particles. Due to the surface tension of the present liquid, small regions of liquid with a low viscosity are formed between the particles such that they are attracted to each other. The effects of the moisture content in a granular material are schematically shown by Morrissey [2013] in Figure 2.3. According to Parker and Taylor [1966], cohesion is defined as the bonding or joining of two particles of
2.3.BULK MATERIAL PROPERTIES 5
Figure 2.3: Schematic representation of the effects of moisture content for various stages of capillarity, Morrissey [2013] p19
the same material. But a bulk solid itself is considered cohesive when it has a poor flowability, which is due to the relatively high interparticle forces compared to the particle weight.
2.3.
BULK MATERIAL PROPERTIES
The following section will describe the characteristics of a bulk solid at particle level as well as at bulk level. Also the corresponding measuring equipment and methods, regardless of the flowability will be mentioned.
2.3.1.
P
ROPERTIES AT PARTICLE LEVELSOLID DENSITY
The solid densityρs, contrary to the bulk density, is the true density of a particulate solid or powder. The solid density is not dependent whether the sample of particles is compacted or not. A gas pycnometer (Figure 2.4) measures the volume of the bulk material sample which is placed into a chamber after which the density is derived from the known mass and measured volume. Hydrostatic weighing is another method and is mostly used for coarse materials which are placed into a cylinder to determine the displaced volume of a known mass of material.
Figure 2.4: Schematic of a gas pycnometer
POISSON’S RATIO
The Poisson’s ratioν implies the ratio of contraction strain to perpendicular extension strain and is often obtained by literature. The value forν theoretically lies between -1 and 0.5, whereas the value for chalk is approximately 0.35, according to Stanford University [2000].
COEFFICIENT OF RESTITUTION
The coefficient of restitution epis commonly defined as the ratio of relative speed of the particle after collision to relative speed of the particle before collision. The value is equal to 1 when the collision is fully elastic and 0 for an inelastic collision. The relevance for this property is that, the higher the coefficient of restitution, the greater the amount of particles will separate after collision with each other due to the fact that the damped normal force is higher than the adhesive forces present Morrissey [2013]. The coefficient of restitution of a particle can be determined with a high speed camera while a particle is dropped from a given height onto another particle or surface and the rebound height is measured.
STATIC FRICTION
The interparticle static friction coefficient, denoted asµs.pp, indicates the resistance a particle experiences when it is in contact with another particle while being sheared. The approximation of the static friction
coefficient can be done by a inclination test where two particles of the bulk solid sample are are placed onto each other while the mechanism is slowly inclined to the angle where slip occurs. A more accurate but time consuming method is by using the Jenike shear tester. With the Jenike shear tester, a linearised yield locus of the material can be obtained from which the angle of internal frictionϕ can be determined. From the angle of internal friction, the coefficient of friction can be calculated by:
µs.p p= tanϕ ROLLING FRICTION
The rolling friction coefficient, denoted asµr.pp, characterizes the rolling resistance of a particle in contact with another particle. Rolling resistance is considered to be less dominant above static friction with spherical particles as the contact area is smaller, according to Persson [2013]. A sample of particles of the bulk solid can be placed on a plate mechanism which is slowly inclined after which the particles will start to slide and roll down. The moment the particles are starting to move downwards, the angle of the plate is measured and the rolling friction coefficient is calculated the same way as mentioned above.
2.3.2.
P
ROPERTIES AT BULK LEVEL BULK DENSITYThe bulk densityρbis defined as the ratio of the mass m of the sample divided by the amount of volume V the sample occupies. Because the bulk density is in fact the average density of the sample over a certain volume, it is always lower than the solid density due to voids between individual particles.
YOUNG’S MODULUS
The Young’s modulus E is known for the characterization of the amount of stiffness of an elastic material and can be determined by dividing the tensile stressσ of the material by the elastic strain ². The higher the value, the stiffer the material. Typical values for a granular material like sand lie between 10 MPa and 80 MPa. The Young’s modulus can be obtained by a confined compression test(Coetzee and Els [2009]) or by literature. ANGLE OF REPOSE
The angle of repose, denoted withαm, is defined as the slope of a poured or drained conical pile of loose uncompacted bulk solid. The most common method is shown in Figure 2.5a where a bulk solid is poured via a funnel into a pile of which the slope is measured. Figure 2.5b shows the drained angle of repose while Figure 2.5c shows the dynamic angle of repose. The dynamic angle of repose is created and measured by slowly rotating a drum with bulk solid, however in case of cohesive material, avalanches are unavoidable which makes the determination of the angle of repose quite difficult. When a cohesive bulk solid is used with the poured angle of repose test, quite often steep inconsistent piles are formed which makes it impossible to measure an accurate angle of repose, as can be seen in Figure 2.6. Although the results of the angle of repose test could not give a distinct judgement about the flowability of the bulk solid in applications as silo’s, hoppers and feeders, an overview (Figure 2.7) of the flowability of a bulk solid with help of the poured angle of repose test is developed by Woodcock and Mason [1988].
Figure 2.5: Angle of repose test methods, Schulze [2008] p172
PARTICLE SHAPES
The particle’s shape also plays a role with regards to flowability of the bulk material. Dry, coarse, smooth, spherical particles flow better than than shaped, non-spherical particles because of the reduced effect of interparticle friction. Cohesive bulk solids however, endure interparticle adhesive forces which generally
2.3.BULK MATERIAL PROPERTIES 7
Figure 2.6: Possible result of a poured angle of repose test with a cohesive bulk solid, Schulze [2008] p173
Figure 2.7: Overview of the flowability of bulk solids based on the poured angle of repose test, Woodcock and Mason [1988]
reduce the ability to flow, but roughly shaped particles are less able to approach each other which in term stimulates flow. It is often seen that for shaped particles, the rolling friction between particles plays a more dominant role than the static friction, which will be clarified through research in section 5.
PARTICLE SIZE DISTRIBUTION
The particle size distribution (PSD) is obtained by sieving a representative bulk solid sample such that discrete size ranges of particle sizes are obtained. The PSD describes the entire range of particle diameters, which is useful to determine the average particle diameter that is required in DEM later on.
OVERVIEW OF RELEVANT BULK MATERIAL PROPERTIES
An overview of all relevant bulk material properties is shown in Table 2.1. At last, for a more detailed and extensive overview of various measuring devices to characterize material- and flow properties of bulk solids, it is recommended to read section 6.3 from Schulze [2008].
Property Symbol Unit Comment
Particle level
Solid density ρs kg m−3
Shear modulus G Pa
Poisson’s ratio ν
Coefficient of restitution ep
Particle-particle static friction coefficient µs.pp Particle-particle rolling friction coefficient µr.pp
Particle-wall static friction coefficient µs.pw Neglected in this study Particle-wall rolling friction coefficient µr.pw Neglected in this study
Bulk level
Bulk density ρb kg m−3
Young’s modulus E Pa
Angle of repose αm ◦ Depends on the testing equipment
Particle shape
Particle size distribution x50 Mean particle radius
Table 2.1: Overview of relevant bulk material properties
2.4.
USEFUL MEASURING EQUIPMENT FOR COHESIVE MATERIALS
As the previously described measuring equipment and material properties are applicable in general, some equipment is primarily developed for use with cohesive bulk material. While this literature research is fo-cused on the calibration and verification methods for cohesive material, some of these devices are briefly mentioned in the following section.
TENSILE STRESS TEST
The AJAX tensile tester is designed to directly measure the tensile strength of samples of bulk powders at dif-ferent consolidation pressures. It is not restricted for use with powders as Grima [2011] shows in his research. The principle is that a bulk solid is placed and consolidated in a diametrically split cell, thereafter a force is applied to split the cell until a crack appears in the consolidated sample such that the stress at tensile failure can be obtained and the test is repeated several times for various consolidation pressures. Results of this test are useful to approximate the required cohesion energy with the linear cohesion model in DEM, which will be outlined in section 5.2.
EDINBURGHPOWDERTESTER
Morrissey [2013] developed the Edinburgh Powder Tester (EPT), a semi-automated uniaxial tester which is able to measure the cohesive strength of a bulk solid with help of various tests.A confined compression test as well as a unconfined compression test can be executed with the EPT. Consider the research of Morris-sey [2013] for a complete detailed description of the working principles of the EPT, while section ?? briefly describes the calibration and verification procedures withdrawn from his research.
SEVILLAPOWDERTESTER
The Sevilla Powder Tester (SPT), developed by Castellanos [2005], is an automated device which is able to characterize fine powders with a particle diameter less than 100µm. It utilizes dry nitrogen gas which is pumped up- or downward through a porous plate at which the powder sample is resting. Afterwards the fol-lowing pressure drop over the porous plate is measured while the plate is being vibrated by a electromagnetic shaker. Various tests can be executed, which are fully described in the research of Castellanos [2005]. SWING-ARM SLUMP TESTER
Grima [2011] uses a swing-arm slump tester in his research, which is a testing device to study the influence of particle friction and rolling resistance on the formation of granular piles. It is mainly focused at the particle-particle interactions while the particle-particle-boundary interactions are found negligible. The experimental setup is shown in Figure 2.8 and consists of an acrylic split tube connected to a swinging arm mechanism. Note that the acrylic split tube comes in two versions, a 60 mm Inner Diameter version and a 100 mm I.D. version. One of the reasons why a split tube is used, is because the retracting of both half cylinders due to the pulling of the swing arms will minimise the interaction between particles and boundary. To further reduce the interaction between particles and boundaries, a 150 mm I.D. ring is placed beneath the split tube and filled with particles to form a bed of particles below the tube. It is necessary that the material is poured loosely into the split
Figure 2.8: Schematic of the swing arm slump tester to calibrate particle-particle interactions, Grima [2011]
cylinder after which the mechanism will retract the swing arms to remove the cylinder walls from the material. This allows to examine the angle of repose as well as the pile height of the bulk material. Results of the executed tests are fully described in Grima [2011] and briefly outlined in section 5.2.
3
D
ISCRETE
E
LEMENT
M
ETHOD
The discrete element method (DEM) will be briefly outlined in this chapter for both free flowing as cohesive bulk material. While DEM applied with free flowing bulk materials is commonly accepted in the industry the last few years, the use with cohesive bulk materials stays a real challenge (Grima et al. [2011]). The challenge originates from the fact that the behaviour of cohesive material is quite well understood, but hard to predict with DEM. Many factors affect the flow behaviour of a cohesive bulk solid, such that the input parameters required for DEM are often chosen iteratively to approximate the real flow behaviour. As of today, DEM has proven to be an effective tool to simulate the granular flow behaviour of bulk materials. Some researchers have developed a custom DEM contact model, often as a customization based on a traditional contact model. Some of these contact models are described in this chapter, also the corresponding required input parameters will be outlined.
3.1.
WORKING PRINCIPLE BRIEFLY
The most often used approach with discrete element modelling was developed by Cundall and Strack [1979] and is suitable to simulate multiple particle contacts while applying interparticle contact forces. As the name suggests, the method uses a specified discrete timestep and generates a finite number of particles which interact with each other due to contact and non-contact forces. With help of Newton’s law of motion, every particle’s position and velocity is individually updated every timestep. The method can be divided in several steps:
1. Initialize: Transform the specified input parameters into actual particles with corresponding material properties, system environment and miscellaneous properties such as the timestep.
2. Detect: Search within the boundaries of the system to particles and determine whether each particle is in contact with another particle.
3. Calculate: Calculate the contact(normal and shear forces) and non-contact forces at all particle-particle and particle-boundary contacts.
4. Apply: Based on the forces and moments, integrate the equations of motion to generate a new value for the acceleration and velocity of each particle.
5. Update: Compute new particle positions according to the recently obtained acceleration and velocity. For a more detailed description it is recommended to read Asmar et al. [2002] and Toetenel [2014].
The main benefit with DEM is the fact that it has become relatively cheap and easy to obtain information about the static and dynamic behaviour of particles in a system compared to the method where physical ex-periments are necessary to obtain this information (Zhu et al. [2008]). One of the most often used software package that utilizes the DEM principle is EDEM by DEM Solutions Solutions [2014].
3.2.
DEM
CONTACT MODELS FOR COHESIVE MATERIAL
In order to get a DEM simulation started, a contact model has to be selected with corresponding input pa-rameters. The last couple of years many researches have developed their own contact model, mostly based on traditional contact models such as the Hertz-Mindlin Mindlin and Deresiewicz [1953] and Linear Spring Dashpot contact model Cundall and Strack [1979]. While these traditional examples are validated for free flowing material in the meantime, they cannot be used with cohesive material successfully. The additional non-contact forces which are present at moist bulk solids or fine powders need to be implemented correctly by an extra input parameter. The developed contact models for cohesive material have their own method of calculating the effects of these non-contact forces, hence every contact model requires a unique input parameter to simulate the cohesive behaviour (Toetenel [2014]). This section will briefly describe the most interesting contact models developed for cohesive material together with their required input parameters. Also the Hertz-Mindlin contact model for free flowing bulk solids will be described, as 5.1 and 5.2 have used this contact model as basis of their calibration and verification methodology in their research.
3.2.1.
H
ERTZ-M
INDLINThe non-linear Hertz-Mindlin contact model is a normal force contact model which involves the theory of Hertz [1882] that accounts for the effects of contact of two elastic spheres. The theory implies a normal force-displacement relationship which yields a non-linear correlation between the two spheres. Decades later it were Mindlin and Deresiewicz [1953] who developed the actual contact model by adding the effects of a tangential force-displacement for elastic spheres under frictional contact. As of today, the Hertz-Mindlin contact model, shown in Figure 3.1, is one of the most used contact models for free flowing materials with DEM. For a more detailed description of the development and mathematics it is recommended to also read Di Renzo and Di Maio [2005] and Vu-Quoc et al. [2001].
Figure 3.1: Schematic representation of a simplified Hertz-Mindlin contact model, Solutions [2014]
3.2.2.
H
ERTZ-M
INDLIN WITH LINEAR COHESIONThe Hertz-Mindlin linear cohesion contact model is implemented in the EDEM code (Solutions [2014]) and adds an additional normal cohesive force which is proportional to the contact area of the particle Ac. The theory behind the normal cohesive force is based on the following equation:
Fncoh= −KcohAc= −πrt2Ce
where rtis the tangential radius of overlap and Ceis the cohesion energy density per unit of volume (J m−3). The Hertz-Mindlin linear cohesion contact model is used to calibrate and verify bulk solid material in the research of Grima [2011] and is described in section 5.2.
3.2.3.
J
OHNSON-K
ENDALL-R
OBERTS( JKR)
The Johnson-Kendall-Roberts (JKR) contact model, developed and described by Johnson et al. [1971], is an-other extension of the theory of Hertz [1882] by implementing the effects of adhesion and surface energyγ per unit of contact area (J m−2). The principle behind this contact model is based on the fact that the ad-hesion force between two spherical surfaces is not reliant on the elastic modulus of the materials in contact. The equation behind this contact model is given by:
3.3.RELEVANTDEMPARAMETERS AND METHODOLOGY 11 FJ K R= 4E∗a3 3R∗ − 4 q π∆γE∗a3
where a is the contact radius, R∗is the equivalent radius and E∗is the equivalent Young’s modulus.
Note that when the surface energy is 0, the JKR theory is equivalent to the Hertz-Mindlin theory. The JKR contact model is implemented in the latest version of EDEM and is suitable to simulate material behaviour for cohesive materials with a relatively low Young’s Modulus and or fine cohesive powders (Solutions [2014]). The JKR contact model was evaluated extensively by Morrissey [2013] with numerous simulations. Each sim-ulation was based on the Edinburgh Powder Tester and the surface energyγ was varied between 0.1 J m−2 and 25 J m−2. The results have shown that the JKR contact model is able to accurately simulate a powder packing process, but it fails to capture the stress history dependent behaviour which is found to be important for storage and handling purposes with regards to cohesive granular material.
3.2.4.
E
DINGBURGHE
LASTO-P
LASTICA
DHESION(EEPA)
The Edinburgh Elasto-Plastic Adhesion (EEPA) contact model was developed by Morrissey [2013] because he figured out that the flow behaviour and handling characteristics of cohesive granular solids are strongly reliant on the consolidation stress which the material has experienced initially. He found out that the stress history of the material was required to represent the cohesive behaviour appropriately. In order to capture the stress history it was necessary to include some contact plasticity while the JKR contact model and many other contact models solely rely on elasticity. While real life particles vary much at size, shape and surface roughness, Morrissey [2013] considers the behaviour of cohesive bulk solids on a meso-scale instead of the usual micro-scale. That means that each DEM particle is part of a agglomerate of a significant amount of particles which are in contact and have interaction. As a consequence, the measuring of particle friction or surface energy to calibrate the material does not require any kind of microscope any more but can be exe-cuted with help of bulk scaled experiments. The benefit of this is the huge reduction of required computation time because not every individual particle has to be calculated any more. In the meantime, the EEPA contact model has been implemented in the latest version of EDEM Solutions [2014] and it is expected that the use of this contact model will increase the coming years. Section ?? will describe the calibration and verifica-tion methods which are extensively described along with more details about the EEPA contact model in his research.
3.3.
RELEVANT
DEM
PARAMETERS AND METHODOLOGY
Various corresponding input parameters are required after a contact model has been selected in order to suc-cessfully execute a DEM simulation. Apart from the parameters that only belong to the material, also general simulation settings such as a timestep are required. In case of cohesive material, the chosen contact model often requires additional input parameters to account for the present non-contact forces. This section will therefore outline the required input parameters as well as the differences between the contact models men-tioned in section 3.2.
First the desired contact model has to be selected within the DEM software. According to the chosen con-tact model, some unique parameters appear which require an input value. While the JKR and EEPA concon-tact models require a value for the surface energyγ, the Hertz-Mindlin linear cohesion contact model requires a value for the cohesion energy density Ce instead. Because the theory behind the EEPA contact model is slightly different than the other two contact models, as described in section 3.2.4, more input parameters are required to successfully run a DEM simulation with the EEPA contact model. Subsequently the simulation parameters need to be properly configured in order to get the accuracy and computation time according to desired. Then the measured material properties, described in section 2.3, need to be transformed into useful DEM parameters for the material configuration. Note that the required particle density in DEM is different from the measured bulk density, however section 2.3.2 does describe the measuring of the actual particle density. Another way to determine the particle density when only the bulk density is known or measured is described in section 5.1. An overview of all the relevant input parameters for the simulation settings of the previously described contact models is shown in Table 3.1.
Input parameter Symbol Unit Comment
Simulation
Timestep t s
Simulation time T s
Number of particles
Gravity g m s−2 X,Y,Z direction
Material Particle density ρs kg m−3 Poisson’s ratio ν Young’s modulus E Pa Shear modulus G Pa Coefficient of restitution e
Particle shape Shaped or spherical (Not actually a parameter)
Average particle diameter r mm According to the PSD
Contact model
Particle-particle static friction coefficient µs.pp Particle-particle rolling friction coefficient µr.pp
Particle-wall static friction coefficient µs.pw Adopted, not calibrated Particle-wall rolling friction coefficient µr.pw Adopted, not calibrated
Surface energy γ J m−2 Used with JKR and EEPA
Cohesion energy density Ce J m−3 Used with H-M linear cohesion
Constant pull-off force f0 N Used with EEPA (Morrissey [2013] section 6.3.1)
Loading spring stiffness k1 N m−1 Used with EEPA (Morrissey [2013] section 6.2.1)
Unloading spring stiffness k2 N m−1 Used with EEPA (Morrissey [2013] section 6.2.2)
Power value for adhesion branch X Used with EEPA (Morrissey [2013] section 6.3.3) Tangential Stiffness multiplier Kt m Used with EEPA (Morrissey [2013] section 6.2.3)
Table 3.1: Overview of relevant DEM input parameters
3.3.1.
S
URFACE ENERGYγ
The influence of the surface energy on the contact between elastic solids was described by Johnson et al. [1971]. It is stated that the surface energy and strength of adhesion between elastic bodies are definitely linked by actions of surface forces. The surface energy is defined as the amount of mechanical work that is needed to separate two elastic bodies from the adhesive bond and to create new surfaces. While this state-ment is quite on its own, no explicit experistate-mental evidence has been found yet (Bikerman [1965]). Johnson et al. [1971] mentions that under conditions of light loading between elastic solids, surface forces could make a serious contribution to the contact equilibrium between the bodies.
While it is theoretically possible to measure the surface energy, the experiment preconditions and sample particle properties have to be very secure to obtain the right accuracy. Therefore it is more efficient to apply the mathematics given in Johnson et al. [1971], because the verified equation on rubber and gelatine spheri-cal, flat particles is proven to be sufficient to approximate the interfacial surface energy of solids.
3.3.RELEVANTDEMPARAMETERS AND METHODOLOGY 13
3.3.2.
C
OHESION ENERGY DENSITYC
eThe cohesive energy of a material is not a measurable property and therefore two methods are shown to ob-tain a good approximation of the correct value in DEM (Grima [2011]). The first method involves an equation derived by Rumpf [1962] to establish a correlation between the isostatic tensile strengthσtand the cohesive energy of a material: σt=1 − ² ² Fncoh d2 p
where² is the porosity and dpis the particle diameter.
While Rumpf’s equation is not directly applicable to scaled non-spherical particles, in combination with the normal overlapδnestimated from a physical experiment, a rough estimation of the cohesive energy is made by (Grima [2011] section 4.8) and is shown in Figure 3.2.
Figure 3.2: Cohesion energy vs. major consolidation stress for moist coal - method 1, Grima [2011] p124
The second approach was developed by DEM Solutions and utilizes several properties such as the gravita-tional forces between two spheres, the Hertz-Mindlin non-linear normal contact stiffness and the mass of a sphere (d = 4.5 mm) to calculate the normal overlap and contact area (Grima [2011]). The results lead to an approximation of the cohesive energy based on the contact pressure, shown in Figure 3.3.
Figure 3.3: Approximation of cohesion energy - method 2, Grima [2011] p125
3.4.
PARAMETER SENSITIVITY ANALYSIS
This section will provide a summary and an overview of the sensitivity of the input DEM parameters according to various researches and literature.
3.4.1.
G
RIMA[2011]
Grima [2011] reasons very clearly which DEM input parameters he had varied. He found that trying to opti-mise too many input parameters would lead to a huge amount of iterations which is equal to computation time. Therefore he suggested a methodology where the static interparticle friction coefficientµswas obtained by a physical measurement while the interparticle rolling friction coefficientµrand the cohesion energy den-sity Cewere obtained by approximation and trial and error. The influence ofµs,µr, G and Cewere examined with DEM simulations by varying these the input parameters several times. Detailed results are described in Grima [2011] and section 5.2. It seems that there is a generally greater sensitivity to the rolling friction coefficient than to the static friction coefficient. The rolling friction is crucial to obtain a realistic rapid flow behaviour of spherical bulk solids in unconfined applications. Alsoµr affects the bulk density, because the increase of the rolling friction coefficient increases the amount of voids between particles, hence the bulk density decreases. Also the sensitivity of the shear modulus G was examined and it turned out that scaling down the value for the shear modulus is an effective method to reduce the computation time. In case of modelling the flow behaviour of a cohesionless bulk solid, it was observed that the shear modulus G and the interparticle static friction coefficientµswere not sensitive. In case of modelling a bulk flow of cohesive material with the Hertz-Mindlin linear cohesion model, it turned out that G is actually sensitive because the cohesion energy density Ceis dependent on G.
3.4.2.
M
ORRISSEY[2013]
Morrissey [2013] found out after several DEM simulations with iron ore fines and various input parameter configurations, which input parameters were more sensitive than others to the resulting particle behaviour. As previously mentioned in section 3.2.4, the self developed EEPA contact model was used. He concludes that a lower value for the loading stiffness k1 could lead to a larger contact overlap, thus potentially greater adhe-sion forces. A higher value for the unloading stiffness k2 leads directly to potentially large adheadhe-sion values, which is responsible for the flowability. However, the varying of k2 had little influence on the unconfined bulk stiffness because the packing porosity and the tangential stiffness Ktseem to be more import. Especially the tangential stiffness was found to be decisive in the controlling of the unconfined bulk stiffness until the yield point of the material was reached while the sample of particles is undergoing shear. However, the tangen-tial stiffness has not been studied in detail for cohesive, non-spherical particles and further research at this topic is recommended. Also the interparticle friction and the particle shape turned out to have a significant share on the unconfined strength of the sample of particles. Generally a higher interparticle friction coeffi-cient leads to a stronger agglomerate on macroscopic level. This phenomenon often leads to a more obvious peak strength after which a noticeable drop of strength is detected. At last, the coefficient of restitution e was observed to have little influence on both the compression process and and the generation of the resulting unconfined strength.
3.4.3.
W
ILLEKENS[2014]
Willekens [2014] has done a literature research on the calibration and verification methods for DEM on free flowing materials and also included a sensitivity analysis of the various researches he examined. Although the difference between cohesive and free flowing material models is considerable, it is useful to gain an insight in the sensitivity of the DEM parameters for free flowing material as that could be a good basis to a reasonable cohesive model (Grima [2011], Jensen et al. [2014]). Willekens [2014] states that the use of spherical versus shaped particles is quite arbitrary. Some researches show that the use of a shaped particle delivers a better result than with a spherical particle shape (Barrios et al. [2013]), while other researches demonstrate that both type of particle shapes show satisfying results ((Grima [2011], Härtl and Ooi [2011], Wensrich and Katterfeld [2012]).
3.4.PARAMETER SENSITIVITY ANALYSIS 15
3.4.4.
O
VERVIEW AND REMARKSAlthough many researchers often have their own methodology to model a material with DEM, every re-searcher must cope with the different influences that a specific input parameter has on the results in combi-nation with the other parameters. While there is no generalized approach to calibrate and verify a cohesive material in DEM yet, every research is often preceded with a brief literature research into the sensitivity of relevant DEM parameters. This procedure should minimize the risk of inefficient modelling, however it is shown that there is no firm conception on the right way to go. An overview of the sensitivity from previous research and the literature research of Willekens [2014] is shown in Table 3.2.
Parameter Sensitive Insensitive
ρs - Grima, Morrissey, Willekens
ν - Grima, Morrissey, Willekens
E - Grima, Morrissey, Willekens
G Grima, Morrissey Willekens
e - Grima, Morrissey, Willekens
µs.pp Grima, Morrissey, Willekens -µr.pp Grima, Morrissey, Willekens
-µs.pw - Grima, Morrissey, Willekens
µr.pw - Grima, Morrissey, Willekens
γ Grima, Morrissey
-Ce Grima
-k1 Morrissey
-k2 Morrissey
-Table 3.2: Overview of sensitivity of DEM input parameters
From Table 3.2 it becomes clear that both interparticle friction coefficientsµs.ppandµr.ppare considered sensitive by multiple researches. It must be mentioned that, although the interparticle static friction coeffi-cient is considered sensitive, the interparticle rolling friction coefficoeffi-cient is more dominant. While Willekens [2014] primarily studied cohesionless bulk material researches, the Shear modulus G turned out to only have an influence on calibration with cohesive materials. Obviously, the corresponding key parameters for each specific contact model such as the cohesive energy Ce, surface energyγ and stiffness k1and k2are sensitive
for cohesive material calibration. Note that the particle-wall friction coefficients are found to have a negli-gible influence on calibration due to the experimental setups which were designed to avoid wall friction. All other parameters are either obtained from literature or measured and kept constant thereafter. At last, un-fortunately none of the researches actually mentioned the required amount of simulation runs to obtain a reliable calibration.
4
D
EFINITIONS OF CALIBRATION
,
VERIFICATION AND VALIDATION
Calibration, verification and validation are crucial processes in creating a reliable DEM simulation whilst providing confidence to the end user. In order to create a reliable DEM model, the three processes have to be executed accurately. Since there is not a generalised methodology for all computer simulation models, the root definitions of the processes will be described in this section together with the perspective of the discrete element method. Although the literature on the verification and validation of simulation models is extensive, it is often noticed that some of the definitions are confused with one and other. The confusion over the terminology that used to describe the testing of models comes from the fact that the terms verification and validation are often used as synonyms in ordinary language, according to Mazzotti and Vinci [2007].4.1.
C
ALIBRATION
Generally speaking, all models require input parameters and constants to produce numerical results. The process of determining the required values is often called the parameter estimation. Hence, the definition of calibration is given by Rykiel [1996] as:
Calibration is the estimation and adjustment of model parameters and constants to improve the agreement between model output and a data set.
This means in short that the calibration procedures are used to estimate the required input parameters that are otherwise unknown. In the specific case for discrete element modelling, calibration is defined as the pro-cess to find a set of DEM input parameters by comparing bulk behaviour from physical experiments with the results of the simulations. It is recommended to perform at least two types of experiments and simulations multiple times, such that the interdependency between the parameters is minimized and the accuracy of the calibration is increased. Ideally it should be possible to select an optimized set of input parameters after the multiple tests and simulations have been carried out.
4.2.
VERIFICATION
Theoretically speaking, Fishman and Kiviat [1967] define verification in the context of simulation modelling as:
Verification is a demonstration that the modelling formalism is correct. Whereas Shugart [1984] defines verification as:
Verification implies the procedures in which a model is tested to determine whether it can be made consistent with some set of observations.
When these definitions are diverted to the case of the verification process with discrete element modelling, it means that after at least two calibration experiments have led to an optimised set of input parameters, an-other different experiment is being executed with the same material while the input parameters in the DEM
simulation are defined by the optimised set of parameters obtained from calibration. The material is consid-ered verified if the physical experiment results are within a specified tolerance of the DEM simulation results. If the results from the physical experiment and the DEM simulation are too far off, the input parameters should be adjusted according to the previous calibration method and the verification step has to be redone.
4.3.
VALIDATION
After a model has been verified, it should be validated to ensure that the model is acceptable for use for the purpose it was designed for. Note that a validated model does not represent any absolute truth and it is not the best model theoretically thinkable. The validation step compares simulated system output with real system observations using data not used in model development (Schott [2014]). Theoretically, validation is defined by Shugart [1984] as:
Validation implies the procedures in which a model is tested on its agreement with a set of obser-vations that are independent of those obserobser-vations used to structure the model and estimate its parameters.
While Rykiel [1996] describes validation as:
A demonstration that a model within its domain of applicability possesses a satisfactory range of accuracy consistent with the intended application of the model. Also validation is not a procedure for testing scientific theory or for certifying the ‘truth’ of current scientific understanding, nor is it a required activity of every modelling project. Validation means that a model is acceptable for its intended use because it meets specified performance requirements.legit
In case of discrete element modelling, validation can be seen as the prediction of the response of the bulk material in a more complex application than the experimental environment. Validation ensures that the DEM model behaves like it should and it esstablishes confidence in the usefulness of the model output towards the user or customer.
4.4.
REMARKS
With previously described definitions in mind, the applicability on Discrete Element Modelling is considered to be legit. The most difficult part of model validation is the process of convincing the end user that the model actually simulates the behaviour similar to the real world. While the validation step with DEM models cur-rently seem fine to the model builders, it must be seen from multiple perspectives. The end user for example, rarely has the technological background to be able to understand all verification tests that are executed. It is therefore recommended to spend more energy in the validation part by means of validation tests. Shannon [1981] describes possible quantitative and qualitative tests in order to try to convince the user that the model is valid. For example, when a model appears to be plausible, it should demonstrate behaviour similar to the real world. This behaviour comes with some aspects like continuity, consistency and response to degeneracy and absurd conditions.
5
C
ALIBRATION AND VERIFICATION
EXPERIMENTS
In this Chapter, four different researches are described. While Grima [2011], Morrissey [2013], Olukayode Isaiah [2014] are focused on cohesive bulk materials, Jensen et al. [2014] is focused on free flowing DEM calibration which could be a basis for a cohesive DEM calibration.5.1.
RESEARCH OF
JENSEN
[2014]
Jensen et al. [2014] present three simple calibration modelling steps for dry and semi-dry granular material, which should result in a reduction of the amount of necessary iterations. The three tests included in the steps are designed to be as simple as possible to generate a solid starting point for every DEM simulation. The three steps are designed to be run in a specific order in order to enhance the accuracy of the calibration by isolating a single physical characteristic in each test. The paper states that the methods described were designed specifically for dry material, however the three tests should be a good starting point for calibration of moist materials when more calibration tests are included to fully capture the adhesive forces that exist between moist or fine particles. The parameters that define the behaviour of wet material can be found from the equations developed by Rabinovich et al. [2005]. In order to calibrate the dry material, the following material properties and corresponding calibration tests are necessary:
5.1.1.
P
ARTICLE DENSITY WITH VOLUME TESTAs mentioned in section 3.3, DEM software requires the particle density instead of the bulk density of a ma-terial. While the particle density is often not known, the bulk density needs to be used. The bulk density however, can be easily determined by a physical experiment called the volume test(section ??). Given the bulk density of the material, the particle density could be determined with help of a DEM simulation of the volume test. The simulation requires a container with a known volume, able to hold the DEM particles and an initial value for the particle density has to be estimated. After the DEM particles are generated and dropped into the container, a settling time is maintained to make sure that each DEM particle has reached its static equilibrium. After that, the top of the container is levelled such that all DEM particles lay inside the volume of the container. Next, the total mass of the elements within the container must be divided by the volume to gather the DEM bulk density. Finally the particle density needs to be scaled by the ratio of DEM bulk density and physical bulk density.
5.1.2.
W
ALL FRICTION COEFFICIENT WITH SURFACE FRICTION TESTThe purpose of this test is to obtain the coefficient of friction between the DEM particles and the surface ma-terial of the equipment they will come in contact with. The simulation requires a long narrow flat chute with side walls to guide the DEM particles and an estimated value of the friction coefficient. The DEM particles are loaded at the closed side of the chute and kept fixed by a gate to guarantee a static equilibrium. Hereafter the gate will be pulled away and the chute will rotate until the angle is high enough to let the DEM particles slide down. The obtained angle is then compared with the angle gained from the physical experiment. Since this material property is not linear, a gradient between the two values has to be determined and applied to the
Figure 5.1: DEM simulation of volume test, Jensen et al. [2014] p7
initial friction value in order to repeat the process a several times until the gradient falls within a reasonable tolerance.
Figure 5.2: DEM simulation of surface friction test, Jensen et al. [2014] p8
5.1.3.
I
NTER PARTICLE FRICTION COEFFICIENT WITH ANGLE OF REPOSE TESTThe last test focuses on the inter particle friction with help of the angle of repose test. A cone is created above a horizontal plate with the DEM software and the DEM particles are generated above the cone. Again an estimation has to be made for the initial friction coefficient and the simulation is started. The DEM particles will fall through the cone, creating a pile at the horizontal plate. The angle of repose of the DEM simulation is then compared with the angle of repose of the physical test and once again a gradient has to be determined between these two values. The gradient must then be applied to the initial value of the friction coefficient until the gradient falls within a reasonable tolerance.
Figure 5.3: DEM simulation of angle of repose test, Jensen et al. [2014] p9
5.1.4.
C
ONCLUSIONS AND REMARKSThe objective of Jensen et al. [2014] was to present a calibration methodology for free flowing materials with DEM and improve the precision of the corresponding DEM simulations. Jensen et al. [2014] have presented a simple and quick calibration method for free flowing material to improve the accuracy and computation time of DEM simulations. The author further states that the provided steps for free flowing material could
5.2.RESEARCH OFGRIMA[2011] 21
be expanded to cope with cohesive material in a similar way. He also proposed other calibration tests such as the rotating drum and jenike shear cell briefly. Although Jensen et al. [2014] concludes that the described methods are quick and efficient, it is also noted that as with all simulations accuracy is lost in idealization. It can be questioned whether these apparent simple tests are actually useful as basis for cohesive material. However, in theory it should be possible to extent this method to cohesive bulk material, as Grima in section 5.2 mentions.
5.2.
RESEARCH OF
GRIMA
[2011]
Grima [2011] has developed techniques to calibrate DEM models based on physical bench scale tests which reproduced the bulk flow behaviour to be modelled on a larger industrial scale where slow or rapid flow occurs. Grima discovered that most of the DEM studies done on granular material mainly focus on dry non-cohesive materials. The lack of understanding the flow behaviour of non-cohesive materials in industrial applica-tions raise a lot of potential problems such as material hold-ups and material sticking to surfaces. So in his research he included both free flowing and cohesive bulk materials, such as polyethylene pellets, coal and bauxite. For each type of material a set of interaction parameters for DEM simulations were determined and verified according to a systematic methodology. He also found that some DEM parameters are more sensitive than others, especially when modelling cohesive materials with use of the simple linear cohesion model as well as with the JKR contact model. The following sections cover the systematic approach and execution of the calibration of dry coal, moist coal and cohesive bauxite. First the systematic approach to calibrate a dry bulk material, and later on a cohesive bulk material is described. Also the custom made experimental setup, a swing-arm slump tester, is briefly outlined at which the calibration of dry and moist black washed coal is executed. A couple of tuning techniques are utilised regarding the particle size distribution and computa-tion time of DEM simulacomputa-tions. In order to calibrate a cohesive bulk material, a decision on the desired DEM contact model is required.
5.2.1.
S
YSTEMATIC APPROACHGrima provided a clear overview of the various methods to determine the parameters and properties which he found relevant for calibration of a particle-particle interaction material model, Figure 5.4. While the re-search is focused at modelling particle flow behaviour under dynamic circumstances like rapid or slow flow of bulk material through transfer systems, the described parameters and properties are therefore only relevant in the dynamic regime rather than in the quasi-static regime. With numerous methods available to measure relevant material properties (section 2.3), a structured methodology is developed to eliminate redundant pa-rameter iterations in the DEM simulations in order to keep the computation time as low as possible while achieving an accurate material model. The basis of the developed methodology, Figure 5.5, concerns the
de-Figure 5.4: Method to measure and calibrate particle-particle properties, Grima [2011] p83
termination of several measurable parameters like Ep,µs.pp, ep,ρsand the psd of free flowing material. These material properties can be easily obtained by the bench scale tests described in section 2.3. After this, other key parameters likeνp, Ep, PSD, shape for DEM are approximated with use of documentation and scaling.
Next, in DEM only two parameters(µs.ppandµr.pp) are kept variable to decrease the amount of necessary iterations in order to calibrate and verify the material model for free flowing material against the physical experiments. Onceµs.ppandµr.ppare determined and verification is done, a cohesive material model could be achieved by adding a new parameter for cohesion while keeping the other parameters unchanged. In case of using the linear cohesion model, the cohesion energy density Ceparameter is needed and varied to cali-brate and verify the cohesive material model against physical experiments. When the JKR model is used, the surface energyγ is needed. In order to actually calibrate and verify the material model, an experimental set
Figure 5.5: Flow chart of methodology to measure and calibrate particle-particle interactions of material model, Grima [2011] p85
up must be used. The setup used in this research is called a swing-arm slump tester and is already mentioned in section 2.4.
5.2.2.
C
ALIBRATION AND VERIFICATION OF DRY,
COHESIONLESS COALThis section will cover the DEM calibration and verification of dry cohesionless coal with the help of several contact models. The material consists of fine particles with a particle diameter of less than 4 mm, referred to as PSD 1, shown in Figure 5.6. The material was split into three categories based on the moisture content: dry, 7.5 and 15 percent wet basis. The flowability of the coal is characterized by evaluating the flowability classification by Jenike expressed in Schulze [2008] and previously described in section 2.3. The 7.5 percent moisture content coal sample turned out to have a flowability of f fc= 2.91 atσ1= 10 kPa and the 15 percent
moisture content coal sample has a flowability of f fc= 3.13. According to Jenike’s classification, both moist coal samples are acclaimed to be cohesive.
Also coal commonly consists of a wide spectrum of particle sizes, thus a particle size distribution is obtained by sieving the coal sample. Because fine coal particles smaller than 1 mm are hard to model with DEM due to the large number of particles and the required amount of computation time, the original particle size distri-bution has therefore been truncated and multiplied by a factor 4. This is a common method in the industry to decrease the amount of DEM particles and computation time, according to Favier [2007]. The shape of the coal particles is obviously not a sphere, as shown in Figure 5.7. In order to model the characteristics of the material as realistic as necessary, complete spherical elements are avoided. Instead, particles of 4 diameter spheres (Particle A) and particles of 3 diameter spheres (Particle B) are modelled with EDEM to achieve the desired minor particle diameter obtained from the experimental particle size distribution, Figure 5.8. CALIBRATION: SWING-ARM SLUMP TEST OF DRY COAL
The obtained results from the swing-arm slump DEM tests with the 60 mm and 100 mm I.D. split tubes are listed in Figure 5.9 and Figure 5.10 respectively. The properties which were experimentally found were com-pared with the properties found with the numerous DEM simulations with varying input parameters such as
5.2.RESEARCH OFGRIMA[2011] 23
Figure 5.6: Sample of black washed coal - PSD 1: d < 4 mm, Grima [2011] p105
Figure 5.7: Sample of particle shape of black washed coal - PSD 1: d < 4mm, Grima [2011] p107
Figure 5.8: DEM modelled particles of washed coal - (a) Particle A, (b) Particle B, Grima [2011] p109
Property Value Unit Comment
ρs 1455-1489 kg m−3 Gas pycnometer 1385-1442 Water displacement ρb 773-800 kg m−3 d < 4 mm, dry 616-696 d < 4 mm, 7.5% mc 618-666 d < 4 mm, 15% mc µs.pp 0.58 - dry ep 0.55 -Table 5.1: Summary of material properties
Parameter Value Unit Comment
ρsp 1430 kg m−3 Coal, average of measurements
Ep 2.43 GPa Coal, approximated from Greenhalgh and Emerson 1986 νp 0.35 - Coal(Greenhalgh and Emerson 1986; Wang et al. 2009a)
µs.p p 0.6 - Coal-to-Coal
ep 0.55 - Coal-to-Coal
∆t 1.48 µs PSD 1
Table 5.2: Summary of DEM parameters
µs.p pandµr.p p. During the tests with the 60 mm I.D. split tube, theµs.ppis kept constant at 0.6 while varying theµr.p pbetween 0.01 and 0.02. Results show that aµs.ppof 0.6 and aµr.ppof 0.1 deliver the best agreement with the results from the bench scale model. Note that the sensitivity ofµs.pphas been examined and found to be weak compared to the sensitivity ofµr.pp, regarding the values ofθr and hp. When considering the DEM results of the swing-arm slump test with the 100 mm I.D. split tube, multiple reasonable matches with the bench scale model are obtained while theµs.ppwas varied between 0.5 and 0.7 and theµr.p pwas varied
