Impact breakage of spherical, cuboidal and cylindrical agglomerates

A numerical study of the micro-mechanics of breakage of agglomerates impacting with a target wall has been carried out using discrete element simulations. Three agglomerates of different shapes are examined, namely spherical, cuboidal and cylindrical. Each agglomerate consists of 10,000 polydisperse auto-adhesive elastic spheres with a normal size distribution. The effect of agglomerate shape and impact site on the damage of the agglomerates under an impact velocity of 1.0 m/s for an interface energy of 1.0 J/m² is reported. It is found from the simulations that cuboidal edge, cylindrical rim and cuboidal corner impacts generate less damage than spherical agglomerate impacts. The cuboidal face, cylindrical side and cylindrical end impacts fracture the agglomerates into several fragments. Detailed examinations of the evolutions of damage ratio, number of wall contacts and total wall force indicate that the size of the contact area and the rate of change of the contact area play important roles in agglomerate breakage behaviour. Internal damage to the agglomerate is closely related to the particle deceleration adjacent to the impact site. However, the local microstructure may not be a decisive factor in terms of the breakage mode for non-spherical agglomerates.     

Numerical modelling of the breakage of loose agglomerates of fine particles

This paper presents a numerical study of the breakage of loose agglomerates based on the discrete element method. Agglomerates of fine mannitol particles were impacted with a target wall at different velocities and angles. It was observed that the agglomerates on impact experienced large plastic deformation before disintegrating into small fragments. The velocity field of the agglomerates showed a clear shear zone during the impacts. The final breakage pattern was characterised by the damage ratio of agglomerates and the size distribution of fragments. While increasing impact velocity improves agglomerate breakage, a 45-degree impact angle provides the maximum breakage for a given velocity. The analysis of impact energy exerted from the wall indicated that impact energy in both normal and tangential directions should be considered to characterise the effects of impact velocity and angle.     

Determination of coalescence kernels for high-shear granulation using DEM simulations

Discrete element method (DEM) modeling is used in parallel with a model for coalescence of deformable surface wet granules. This produces a method capable of predicting both collision rates and coalescence efficiencies for use in derivation of an overall coalescence kernel. These coalescence kernels can then be used in computationally efficient meso-scale models such as population balance equation (PBE) models. A soft-sphere DEM model using periodic boundary conditions and a unique boxing scheme was utilized to simulate particle flow inside a high-shear mixer. Analysis of the simulation results provided collision frequency, aggregation frequency, kinetic energy, coalescence efficiency and compaction rates for the granulation process. This information can be used to bridge the gap in multi-scale modeling of granulation processes between the micro-scale DEM/coalescence modeling approach and a meso-scale PBE modeling approach.     

Mechanical behaviour of porous lanthanide oxide microspheres: Experimental investigation and numerical simulations

Actinide oxide microspheres are considered as promising substituents to powder precursors for the production of ceramic pellets of nuclear fuel or targets. Porous microspheres of sub-millimetric size are synthesised using the Weak Acid Resin process. Controlling their microstructure and their mechanical properties is essential to predict the microstructure of green compacts and sintered pellets. Here, cerium and gadolinium are used to mimic actinides as metal cation. Single microspheres are crushed experimentally using a micropress in a Scanning Electron Microscope (SEM) to investigate their mechanical properties and visualise their fracture behaviour. The results are compared to numerical simulations based on the Discrete Element Method (DEM). In DEM, a microsphere is modelled as an assembly of bonded spheres representing aggregates. Bonds may fracture in tension or shear. A limited number of material parameters (aggregate elastic modulus, bond strength) are sufficient for the accurate simulation of the fracture behaviour of a microsphere.     

DEM simulations of the particle flow on a centrifugal fertilizer spreader

Usually, the performance of centrifugal spreaders must be evaluated in large halls by capturing the fertilizer distribution patterns in standardized tests, often carrying a big cost to the manufacturers. In contrast, this paper proposes a first attempt to model a particle flow subjected to a spinning disc using the Discrete Element Method (DEM) starting from the particle outflow of a bin, using flat as well as inclined discs. The model is validated by experiments in two different ways. The first manner is the measurement of the cylindrical mass distribution along the edge of the disc by a device that collects the fertilizer particles in a tray of baskets around the disc. A second method consists of collecting the particles on the ground after their ballistic flight through the air. Both validation methods are relatively cheap and fit into the present statistical or qualitative interpretation of DEM simulations. Additionally, a number of rotational disc speeds is chosen (300-650 rpm) to incorporate velocity dependent effects of the particle flow. It was found that the DEM simulations show a good qualitative and considerable quantitative agreement with the experiments. The deviations between the simulations and experiments are profound at high disc rotational speeds (500-650 rpm) and can be identified as (1) an underestimation of the simulated particle velocities at the edge of the disc and (2) a too low dispersion on the (vertical) simulated particle velocities at the edge of the disc. A parameter study revealed that (1) can be resolved by introducing a velocity dependent friction coefficient, in agreement with literature. The influence of other model parameters such as particle damping and stiffness appears to be small, while the introduction of a rolling friction coefficient to mimic rolling resistance or particle shape does not provide any answer either, and hence reason (2) at this moment must be addressed to unknown external factors such as disc plane vibrations appearing at higher disc speeds.     

Numerical investigation of particle shape and particle friction on limiting bulk friction in direct shear tests and comparison with experiments

In this study, the discrete element method (DEM) was used to investigate the influence of particle shape and interparticle friction on the bulk friction in a Jenike direct shear test. Spherical particle and non-spherical particles using two overlapping sphere giving particle aspect ratio of up to 2 and a full range of interparticle contact friction coefficient were studied numerically. These were compared with physical Jenike shear tests conducted on single glass beads and paired glass beads. To separate the influence of sample packing density from interparticle contact friction on the bulk shearing response, the same initial packing was used for each particle shape in the simulations. The interplay between contact friction and particle interlocking arising from geometric interaction between particles to produce the bulk granular friction in a direct shear test is explored and several key observations are reported. The results also show that particle interlocking has a greater effect than packing density on the bulk friction and for each particle shape; DEM can produce a good quantitative match of the limiting bulk friction as long as similar initial packing density is achieved.     

Numerical modelling of the quasi-brittle behaviour of refractory ceramics by considering microcracks effect

In the steelmaking industry, the inner lining of ladles is made of refractory ceramics, which are constantly subjected to thermal shocks during their service. Experimentally, it is observed that pre-existing microcracks could significantly increase the thermal shock resistance of these ceramics. The presence of such microcracks network within the refractory microstructure could lead to a non-linear quasi-brittle mechanical behaviour.To model this quasi-brittle behaviour, a suitable numerical approach is the Discrete Element Method (DEM), which can circumvent the limitations of more conventional continuum approaches in capturing microstructural effects required to simulate multi-fracture propagation.Here, it is aimed to simulate such quasi-brittle behaviour by initial well-distributed damages, with a strength dispersion following a Weibull distribution. In this way, the microcracks effect on the quasi-brittle behaviour of a numerical sample under uniaxial and cyclic tensile tests is investigated. Ultimately, a quantitative DEM model to simulate such a complex behaviour is proposed.     

Simulation of entrainment of agglomerates from plate surfaces by shear flows

The entrainment process of agglomerates deposited on plate surfaces by shear flows was simulated using the three-dimensional modified discrete element method (mDEM) and influences of several factors on entrainment process were examined. In the case shear induced force is too weak, deposits are only deformed and particles are barely entrained, however, above some critical value particles are entrained by flows forming agglomerates. It was also clarified that the steric-bulky deposit undergoes the stronger hydrodynamic force and is easy to be entrained. There are two entrainment mechanisms corresponding to the parameter A_s/A which indicates the relative strength of adhesive force between particle and plate surface to that between particles. In case of large A_s/A where the adhesion between particle and plate surface is predominant, the number of entrained particles monotonically decreases as A_s/A increases due to the enhanced binding force. By contrast for small A_s/A, the number of entrained particles is not heavily dependent on A_s/A due to the mechanism in which the upstream side of deposit is lifted and the deposit is deformed extensively then large agglomerates are entrained. The boundary between those two entrainment mechanisms exists at A_s/A=0.5-0.6 which is in good agreement with the theoretical prediction.     

Numerical Simulation of Particle Segregation in Vibration Fluidized Beds

The influence of vibration parameters on the segregation phenomenon of a binary mixture in a vibration fluidized bed is investigated. Initially, the mixture composed of spherical balls with different densities but same diameter is in a perfect mixing state in the bed. The motion of particles is simulated based on the discrete element method. The effects of friction coefficient, vibration frequency, amplitudes, and gas velocity are analyzed. The coefficient of segregation to the degree of particle segregation is calculated for different operating conditions. The segregation degree in the vibration fluidized bed is found to be higher than that in the bed without vibration. The curve for the segregation degree exhibits a single peak value which represents the optimal segregation result.     

Application of Taguchi methods to DEM calibration of bonded agglomerates

Discrete element modelling (DEM) is commonly used for particle-scale modelling of granular or particulate materials. Creation of a DEM model requires the specification of a number of micro-structural parameters, including the particle contact stiffness and the interparticle friction. These parameters cannot easily be measured in the laboratory or directly related to measurable, physical material parameters. Therefore, a calibration process is typically used to select the values for use in simulations of physical systems. This paper proposes optimising the DEM calibration process by applying the Taguchi method to analyse the influence of the input parameters on the simulated response of powder agglomerates. The agglomerates were generated in both two and three dimensions by bonding disks and spheres together using parallel bonds. The mechanical response of each agglomerate was measured in a uniaxial compression test simulation where the particle was compressed quasi-statically between stiff, horizontal, frictionless platens. Using appropriate experimental designs revealed the most important parameters to consider for successful calibration of the 2D and 3D models. By analysing the interactive effects, it was also shown that the conventional calibration procedure using a “one at a time” analysis of the parameters is fundamentally erroneous. The predictive ability of this approach was confirmed with further simulations in both 2D and 3D. This demonstrates that a judicious strategy for application of Taguchi principles can provide a sound and effective calibration procedure.     

Performance of integration schemes in discrete element simulations of particle systems involving consecutive contacts

In this investigation, which is a follow-up study extending earlier work (Kruggel-Emden, Sturm, Wirtz, & Scherer, 2008), a realistic assessment of the performance of integration schemes in systems of moving particles and consecutive contacts is conducted. Linear contact models are applied throughout this work as they allow for an analytical solution of consecutive oblique impacts. The many-particle systems considered are the discharge of particles from a hopper and particle movement in a shaken container. Results for many-particle systems are robust with respect to the applied integration method and step size once particle interactions are resolved with a sufficient number of steps. The integration schemes are also evaluated based on consecutive particle/wall contacts. Integration of consecutive contacts in a discrete element framework implies repeatedly solving non-continuous systems of differential equations. Various termination conditions for the normal force models and adaptive time stepping for one-step integration methods are investigated. The effect of softened contacts on particle trajectories is discussed. Based on these insights, recommendations for the most accurate integration schemes are made.     

A discrete element model for simulation of a spinning disc fertilizer spreader I. Single particle simulations

Modeling approaches for centrifugal fertilizer spreaders have so far been based on analytical expressions for single particle trajectories derived in the early 60's. However elegant this approach was, it suffers from several disadvantages, the most important of which is failing to incorporate the interaction between the particles in the flow. This paper is the first in a series aiming at simulating the complete spreading process based on the laws of physics and a physically meaningful model for the interactions between the particles, c.q. the contact forces. The result is a model that allows the development of a deeper understanding of the physics underlying the spreading process and provides better predictions. In this paper the model is presented in detail and a series of simple computer experiments are analysed and compared to theoretical predictions. Also, single particle trajectories from DEM simulations are compared to experimental results. Further, some effects of the model parameters are analysed. This paper demonstrates that the model is not only capable of producing realistic simulations, but also provides detailed insight in the physics of the spreading process.     

Influence of random pore defects on failure mode and mechanical properties of SiC ceramics under uniaxial compression using discrete element method

To investigate the relationship between micro-defects in ceramic materials and macro mechanical properties and behaviours, a computational model of SiC ceramics with randomly oriented elliptical pores was established using the discrete element method (DEM). The effects of pore defect content and its aspect ratio on the failure mode, stress-strain curve and mechanical properties of specimen were investigated under uniaxial compression. The effective Young's modulus which was obtained from DEM simulations was compared with the predictions of Mori-Tanaka scheme (MTS) and Self-Consistent scheme (SCS) at various pore defect densities. The results showed that the compressive strength and crack initiation stress decrease nonlinearly as the pore defect content increases. Furthermore, the smaller the aspect ratio of the elliptical pore defects was, the more obvious the weakening trend was. As the pore defect content increases, the failure mode of the specimen changed from brittle fracture to tensile-shear mixing and then to axial splitting. The stress-strain curves showed a certain “softening” period during the loading process. The effective Young's modulus obtained from the DEM simulations coincides with the approximations of MTS and SCS at low pore densities. However, when the pore defect density became larger, the DEM simulation results were slightly lower than the theoretical results of the Mori-Tanaka scheme, which only considers the weak interaction between defects.     

Numerical study on microscopic mixing characteristics in fluidized beds via DEM

In this paper, discrete element method (DEM), combined with computational fluid dynamics (CFD), is used to investigate the micro-mixing process in fluidized beds (FBs) of uniform particles. With the aid of snapshots and adoption of Lacey and Ashton indexes, mixing evolvement for two cases, fluidized bed using horizontal distributor with even gas supply and fluidized bed using inclined distributor with uneven gas supply, is discussed in detail. Results indicate that the Ashton index appears to be more effective in assessing the mixing dynamics in this work. Further analyses illustrate that in the case of horizontal distributor incorporated with even gas supply, diffusive mixing pattern is predominant, since bubbles lateral motion is reduced in such a bed; whereas, there is a faster convective mixing process in a fluidized bed using inclined distributor with uneven gas feed, followed by shear mixing. Generally, localized air supply induces the density gradient of particle distribution in the bed, which is the basic agent of convective particle stream. The analyses are confirmed by the comparison of solid flux during the simulations of the two cases. In addition, the mixing mechanism and the mixing time scale agree well with published experimental results.     

Breakage behaviour of spherical granulates by compression

This paper describes the deformation and breakage behaviour of granulates in single particle compression test. Three industrial spherical granulates—γ-Al₂O₃, the synthetic zeolite Köstrolith^® and sodium benzoate (C₆H₅COONa) were used as model materials to study the mechanical behaviour from elastic to plastic range. The elastic compression behaviour of granulates is described by means of force-displacement curves, by application of Hertz-Huber contact theory and continuum mechanics. An elastic-plastic contact model was proposed to describe the deformation behaviour of elastic-plastic granules. The effects of granulate size and stressing velocity on the breakage force and contact stiffness during elastic and elastic-plastic displacement are examined. It is shown that the zeolite granulates with elastic-plastic behaviour have viscous properties as well. Breakage mechanisms of granulates during elastic, elastic-plastic and plastic deformation are also explained. The breakage probability is approximated by Weibull distribution function. The behaviour of the granulate during compression under the repeated loading-unloading conditions was investigated.     

Numerical investigation of steady and unsteady state hopper flows

This paper presents a numerical study of the steady and unsteady state granular flows in a cylindrical hopper with flat bottom by means of the discrete element method (DEM). For both flows, the simulations were conducted under comparable conditions so that the similarity and difference between them can be examined. The distributions of the physical properties including velocity, force structure, stress and couple stress for the two hopper flows are investigated. The results suggest that the trends of these distributions for the two hopper flows are similar. In particular, for both cases, the distributions of the normal stresses are related to the normal force structures. Thus, corresponding to the large interaction forces between particles near the bottom corner and in the transitional zone, all the normal stresses are large near the bottom corner, and the radial and circumferential normal stresses are relatively large in the transitional zone. However, there are differences in the magnitudes of some physical properties for the unsteady and steady state flows. Compared with the steady state flow, the unsteady state flow has a narrower velocity distribution, and more particles experience large contact forces. Its radial and circumferential normal stresses in the plug flow and transitional zones are larger. With the decrease of the number of particles or with discharging time, the plug flow and transitional zones reduce, and the differences in the considered properties except wall shear stress and couple stress between the two flows decrease.     

Size segregation of spherical nickel pellets in the surface flow of a packed bed: Experiments and Discrete Element Method simulations

The size segregation of binary mixtures of spherical nickel pellets flowing into a packed bed was investigated with Discrete Element Method (DEM) simulations and physical experiments in 30 cm and 60 cm wide rectangular test cells. Each test cell approximates a vertical slice of a cylindrical packed bed, with a rising feed tube on one side of the cell representing the stationary frame of reference in the packed bed. As the feed tube is raised, the pellets flow laterally into the test cell to form a sloping surface inclined to the horizontal by the angle of repose. The lateral flow of pellets is confined near the surface of the packed bed, and was intermittent in character (i.e. surging). Velocity vectors show the detailed flow field in the simulated test cells. The smaller pellets were found to be concentrated near the core of the granular assembly, and the larger pellets segregate to the outer wall farthest from the feed tube. The degree of segregation, or coefficient of variation (variance/mean), is proportional to the diameter ratio α of the pellets and the length of the surface, and inversely proportional to the mass fraction of the smaller pellets within the range of parameters studied. The DEM simulations had an average deviation in mass fraction of 0.07 and maximum deviation of 0.22 from the experimental data.     

Numerical simulation of particle motion in a gradient magnetically assisted fluidized bed

Flow behavior of magnetizable particles is simulated in a two-dimensional gradient magnetically assisted bubbling fluidized bed. The motion of particles is simulated by discrete element method (DEM) with the consideration of external magnetic forces at a constant gradient magnetic field along bed height. The distributions of velocity and concentration of magnetizable particles are analyzed at the different magnetic field intensities. The simulations show a significant effect on the motion of particles with vertical magnetic-fields applied. When the magnetic field strength is increased to a value at which the fluidization of strings starts, the particles are found to form straight-chain aggregates in the direction of the magnetic field. At very high magnetic field strengths, defluidization is observed. Gas pressure drop of bed decreases with the increase of magnetic-flux densities. The granular temperature of particles increases, reaches a maximum, and then decreases with the increase of magnetic-flux density. Through the analysis of the motion of particles, it is concluded that the moderate strength magnetic field gives a high fluctuation of particles and distribute gas more evenly in the bed.     

Discrete element simulation of SiC ceramic containing a single pre-existing flaw under uniaxial compression

A model of a SiC ceramic containing a single pre-existing flaw was established based on the discrete element method. The effects of the flaw inclination angles, which ranged from 0° to 75°, on the mechanical properties of the specimen under uniaxial compression were studied. The evolution of the force-chain field, displacement field and stress field around the pre-existing flaw in the process from the load to failure was also analysed. The results showed that the flaw inclination angle affected the mechanical properties of the specimen as well as the initiation and propagation of the first crack. Based on the investigation of the force chain field, it was found that the distribution curve of the normal force carried by the parallel bond in the specimen with the corresponding angles under compression is similar to the “peanut” rose diagram, while the shear force distribution curve is similar to the "butterfly wings" rose diagram. In addition, in the analysis of the displacement field and the stress field, the displacement field around the flaw can be divided into four types in the process from specimen loading to its failure. Meanwhile, it was found that initiation of the first crack was affected by tensile stress. With the propagation of the first crack, the tensile stress concentration region at the flaw tip moved and dissipated correspondingly.     

Numerical simulation of particle dynamics in different flow regimes in a rotating drum

Flow regimes in a horizontal rotating drum are important to industrial applications but the underlying mechanisms are not clear. This paper investigated the granular flow dynamics in different regimes using the discrete element method. By varying the rotation speed and particle-wall sliding friction over a wide range, six flow regimes were produced. The macroscopic and microscopic behaviour of the particle flow were systematically analysed. The results showed that the angle of repose of the moving particle bed had a weak dependence on the rotation speed in the slumping and rolling regimes, and increased significantly as the flow transited to the cascading and cataracting regimes. The mean flow velocity increased with the rotation speed, but the normalised velocity against the drum speed in the continuous regimes collapsed into a single curve, which can be well described by a log-normal distribution. The particle bed at low rotation speed had a similar density to those of the random loose packing, and became more dilated with the increase of the rotation speed. Similarly, the mean coordination number showed linear dependence on the drum speed. Both the collision energy and collision frequency increased with the rotation speed. However, the normalised collision energy in different regimes can be fitted with a simple scaling law.