Numerical simulation of breakage of two-dimensional polygon-shaped particles using discrete element method

Using DEM (Discrete Element Method), a model is presented to simulate the breakage of two-dimensional polygon-shaped particles. In this model each uniform (uncracked) particle is replaced with smaller inter-connected sub-particles which are bonded with each other. If the bond between these sub-particles breaks, breakage will happen. With the help of this model, it is possible to study the influence of particle breakage on macro and micro mechanical parameters. In this simulation, the evolution of microstructure in granular assemblies can be seen by tracing of coordination number during the shear process. Also variation of contact normal, normal force and tangential force anisotropy can be tracked. To do so, two series of biaxial test simulations (breakage is enabled and disabled) are conducted on assemblies of two-dimensional polygon-shaped particles and the results are compared. The results are presented in terms of macro and micro mechanical behavior for different confining pressures.     

Discrete element simulation study of a Freeman powder rheometer

The powder rheometer is a commonly used device for assessing the bulk flow performance of pharmaceutical powders. Discrete element simulations were performed to determine the effects of particle properties such as size, shape, size distribution and friction on the force and torque on the impeller blade in a powder rheometer. DEM simulations are well suited for such a study as they can isolate the impact of each particle property on the bulk powder behavior. The results can then be used to guide the ‘particle engineering’ of pharmaceutical powders to meet specific performance targets. The operation of the FT4 Freeman powder rheometer system was simulated using the discrete element method (EDEM? from DEM Solutions). The effects of various particle properties (size, shape, friction, etc.) were examined using the force and torque on the impeller blade as the key performance indicators. The effect of particle size (mean, distribution) on the mixing torque/force was small and the use of a pre-conditioning step also had minimal impact. As the particle aspect ratio was increased from 1.0 (perfect spheres) to 2.0, both the torque and force values also increased (max increase of ～40%). Increasing the rolling friction of spherical particles produced similar results as the large aspect ratio particles. Increased particle–particle friction caused a larger increase in the measurements (max increase of ～60%) in comparison with increased particle–vessel and particle–impeller friction (max increase of ～20%). Experiments with glass beads were also performed and were used to validate the simulations.     

A mechanistic study of agglomeration in fluidised beds at elevated pressures

Effect of operating pressure on the hydrodynamics of agglomerating gas–solid fluidised bed was investigated using a combination of discrete element method (DEM) for describing the movement of particles and computational fluid dynamic (CFD) for describing the flow of the gas phase. The inter‐particle cohesive force was calculated based on a time dependent model developed for solid bridging by the viscous flow. Motion of agglomerates was described by the multi‐sphere method. Fluidisation behaviour of an agglomerating bed was successfully simulated in terms of increasing the size of agglomerates. The results showed that increasing the operating pressure postpones de‐fluidisation of the bed. Since the DEM approach is a particle level simulation and study about particle–particle interactions is possible, a micro‐scale investigation in terms of cohesive force and repulsive force during agglomeration at elevated pressures was done. The micro‐scale results showed that although the number of contacts between particles was decreased by increasing operating pressure, stronger solid bridge formed between colliding particles at higher pressures. © 2012 Canadian Society for Chemical Engineering     

Extended HPM–DEM coupled simulation of drainage of square particles in a 2D hopper flow

An extended hard particle method–discrete element method coupled model (EHPM–DEM) is proposed to simulate the drainage of square particle in 2D hoppers. The EHPM extends the hard sphere model to adapt for non‐spherical shapes. A vertex‐based extension of DEM is developed to solve collisions of square particles. A new coupled method is proposed, using the EHPM to simulate binary collisions and DEM to simulate multiple contacts. The collision between two triangles and the drainage of square particles in hoppers were simulated and compared to theoretical analysis and experiments, respectively, for validation. Moreover, the advantages of EHPM over DEM and the EHPM–DEM coupled solution over the pure soft DEM solution in computational efficiency have been demonstrated. In addition, the effects of restitution coefficient, friction coefficient, and the filled height on the discharge rates are analyzed, and a uniform discharge feature is discovered, which is especially useful for scaling studies. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1863–1876, 2016     

DEM investigation on the breakage of spherical aggregate under multi-contact loadings

Particle crushing is commonly encountered during the storage, transportation, and handling of granular assemblies. This work is aimed at ascertaining the applicability of four particle breakage criteria frequently mentioned in literature. Discrete element method (DEM) simulations were conducted to investigate the crushing of spherical aggregates under multicontact loadings. Mean and major principal stress criteria, octahedral shear stress criterion, and maximal contact force (MCF) criterion were then evaluated based on the obtained DEM results. It is found that the first three parameters all vary with the number of loading contacts, demonstrating they cannot predict the crushing of particles under arbitrary loading configuration. Simulation results indicate that the MCF at crushing is related to the number and the spatial arrangement of loading contacts. Thus, strictly speaking, this parameter cannot uniquely define particle breakage either. The influences of the microstructural heterogeneity on the breakage strength of particle and also on the applicability of MCF criterion are discussed.     

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.     

Multi-scale simulation of needle-shaped particle breakage under uniaxial compaction

The breakage of needle-shaped particles within a random packed bed subjected to uni-directional compaction has been simulated using the discrete element method (DEM). Elongated particles with a chosen aspect ratio have been created by linking individual spherical discrete elements by rigid bonds, characterized by a given ultimate bending strength. A randomly packed bed of these elongated particles has been formed and gradually compressed between two infinite parallel solid planes. The particle size distribution as function of the compaction ratio has been studied in dependence on the individual particle strength, the initial particle length, and their distribution. The simulations have shown that the fragmentation generally follows the sequential halving kinetics and that the formation of fines is most profound in systems with a distribution of particle strengths, both within and between individual particles.     

Analysis of particle porosity distribution in fixed beds using the discrete element method

This report discusses the use of the discrete element method (DEM) to the porosity distribution of spherical particles in narrow pipes as a function of the pipe-to-particle diameter ratio. It was found that the packing structure depends mainly on the pipe-to-particle ratio and the particle friction. The numerical results with respect to the radial porosity distribution are in agreement with experimental data from the literature. Radial porosity distributions were calculated using algorithms developed by Mueller. The packing structure of the particles shows channeling for small pipe to particle diameter ratios. The simulated height averaged porosity distribution agrees with models from the literature. Moreover, DEM provides the possibility to include particle properties which reflect on the porosity distribution.     

A proposal for discrete modeling of mechanical effects during drying,combining pore networks with DEM

A discrete modeling approach is introduced to investigate the influence of liquid phase distributions on damage and deformation of particle aggregates during convective drying. The approach is illustrated on a simple 3D aggregate structure, in which monosized spherical particles are arranged in a cubic packing and bonded together at their contacts; the mechanical behavior of this aggregate is simulated by discrete element method (DEM). Liquid phase distributions in the void space are obtained from drying simulations for a pore network. In a one‐way coupling approach, capillary forces are computed over time from the filling state of pores and applied as loads on each particle in DEM. A nonlinear bond model is used to compute interparticular forces. Simulations are conducted for various drying conditions and for aggregates with different mechanical properties. Microcracks induced by bond breakage are observed in stiff material, whereas soft material tends to shrink reversibly without damage. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Breakage probability of irregularly shaped particles

The investigation of breakage probability by compression of single particles was carried out. The spherical glass particles and irregularly shaped particles of NaCl, sugar, basalt and marble were subjected to a breakage test. The breakage test includes the compression up to breakage of 100 particles to obtain the distribution of the breakage probability depending on the breakage force or compression work. The breakage test was conducted for five particle size fractions from each individual material, at two stressing rates. Thus obtained 50 breakage force distributions and corresponding 50 breakage work distributions were fitted with log-normal distribution function.Usually, the breakage probability distribution can be found by means of stress or energy approach. The first one uses the stress to calculate the breakage probability distribution. The second approach uses the mass-related work done to break the particle. We prefer to use the breakage force and energy as essential variables. The correlation between the force and energy at their breakage points is obtained by integrating the characteristic force–displacement curve, i.e. the constitutive function of elastic–plastic mechanical behavior of the particle. The irregularly shaped particle is approximated by comparatively “large” hemispherical asperities. In terms of elastic–plastic deformation of the contacting asperities with the plate, a transition from elastic to inelastic deformation behavior was considered. Thus, one may apply the model of soft contact behavior of comparatively stiff hemispheres. Based on this model a relationship between the breakage force distributions and corresponding energy distributions was analyzed. Every tested material exhibits a linear relationship between average breakage energy and average breakage force calculated for every size fraction.For future consideration both force and energy distributions were normalized by division by average force or energy, consequently. The relationship between the fit parameters of normalized energy distribution and corresponding fit parameters of normalized force distribution was established. The mean value and standard deviation of normalized force distribution can be found from mean value and standard deviation of normalized energy distribution by means of system of two linear equations. The coefficients of those linear equations remain the same for all of the above tested materials; particle size fractions and stressing rates. As a result the simple transformation algorithm of distributions is developed. According to this algorithm the force distribution can be transformed into energy distribution and vice versa.     

Experimental and numerical investigations of the shear behavior of binary particle blends

In this study, a Schulze ring shear tester and the discrete element method (DEM) are employed to investigate the effect of polydispersity on the binary shear flows. Both experimental results and DEM simulations show that the preshear stresses are greater for binary blends than for monodispersed particles. The flowability of these mixtures is strongly affected by the solid fraction, with minimal flow function values correlating to maximum packing fraction. However, minimum flow function values are not observed at the same packing fractions where the maximum preshear stress occurs. Using DEM, it is demonstrated that the decrease of angular velocity of larger particles due to the addition of small adhesive particles reduces and the fraction of large-small particle contact both make contributions to shear stress difference. A mechanism is proposed to quantify the effects of these two factors.     

Numerical simulation of particle breakage in dry impact pulverizer

A novel method to simultaneously simulate particle motion and its breakage in a dry impact pulverizer was developed. The motion of particles in the pulverizer was calculated using a discrete phase model (DPM)‐computational fluid dynamics (CFD) coupling model. When the particle impacts against a vessel wall, impact stress acting on the particle is calculated from Hertz's theory as a function of the impact velocity. At the same time, the particle strength as a function of the particle size is calculated from Griffith's theory. If the impact stress is larger than the particle strength, the particle is broken and replaced with smaller fragments. The size distribution of the fragments is obtained from a breakage function proposed. The motion of the fragments is calculated again by using the DPM‐CFD coupling model. By repeating the above calculations over the whole particles, the grinding phenomenon can be simulated. The calculated results showed good agreement with the experimental one, and validity of the proposed method was confirmed. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3601–3611, 2013     

Analysis of granule breakage in a rotary mixing drum: Experimental study and distinct element analysis

Rotary drums are commonly used in particulate solid industries for mixing, coating and reactions. The process is often accompanied by undesirable breakage of granules. For this reason, a scaled-down version is sometimes used as an attrition testing device. In this work, the attrition of granules inside a rotary drum at 18, 35 and 52 rpm drum rotation speeds for 4000 cycles is studied. The granules used in this study have been produced by extrusion and spheronisation with a size range of 500 to 1000 μm. The rotary drum has an internal diameter of 0.39 m, axial length of 0.3 m and a single baffle. The extent of breakage is quantified by sieving out fine debris which is two sieve sizes smaller than the feed particles. To relate the extent of breakage in the drum to granule characteristics, single granule impact tests have been performed on one type of granule at several velocities. The effects of particle size and impact velocity are analysed and a power-law relationship is fitted between impact velocity and single granule breakage. This information is then used to simulate granule breakage in a rotary drum by Distinct Element Method (DEM). The drum is simulated for 5 rotations at the rotational speeds stated above and the breakage rate is extrapolated to 4000 cycles where it is compared to experimental results obtained. The trends for particle breakage in both experiments (determined by sieving) and extrapolated DEM simulations are in agreement however the orders of magnitudes are different. The comparison shows that the extent of breakage obtained from extrapolated simulations is overestimated at drum speed of 35 and 52 rpm and underestimated at 18 rpm. There is close agreement between experiments and extrapolated DEM simulations for particle breakage at 18 rpm only after 4000. Furthermore, the effect of air drag on the attrition of granules by impact at a drum rotation speed of 52 rpm is investigated, where it is found to significantly reduce the breakage results.     

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 simulations of flow behavior of gas and particles in spouted beds using frictional-kinetic stresses model

Flow behavior of gas and particles is simulated in the spouted beds using a Eulerian-Eulerian two-fluid model on the basis of kinetic theory of granular flow. The kinetic-frictional constitutive model for dense assemblies of solids is incorporated. The kinetic stress is modeled using the kinetic theory of granular flow, while the friction stress is from the combination of the normal frictional stress model proposed by Johnson and Jackson (1987) and the frictional shear viscosity model proposed by Schaeffer (1987) to account for strain rate fluctuations and slow relaxation of the assembly to the yield surface. An inverse tangent function is used to provide a smooth transitioning from the plastic and viscous regimes. The distributions of concentration, velocity and granular temperature of particles are obtained in the spouted bed. Calculated particle velocities and concentrations in spouted beds are in agreement with the experimental data obtained by He et al. (1994a, b). Simulated results indicate that flow behavior of particles is affected by the concentration of the transition point in spouted beds.     

The influence of DEM simulation parameters on the particle behaviour in a V-mixer

Results are described of simulations based on the discrete element method (DEM) using a code developed by Tsuji, Kawaguchi, and Tanaka (Discrete particles simulation of 2-dimensional fluidized bed. Powder Technology 77 (1993) 79-87). The mechanical interactions between particles and also between particles and the walls in granular flows are modelled by linear springs, dash-pots and friction sliders. The simulation parameters are the restitution coefficient, normal stiffness, friction coefficient between particles and between particles and the walls, and two ratios which relate the normal and tangential stiffness and damping coefficients. Their influence on particle motion in a V-mixer has been evaluated and compared with radioactive tracer measurements of particle motion. A number of quantitative methods for comparing DEM and experimental data were developed. Given the simplified nature of the modelled interactions, the agreement between the predicted and measured data is remarkably close for restitution coefficient values of 0.7 and 0.9, internal friction coefficient values of 0.3 and 0.6 and wall friction coefficient values of 0 and 0.3. The internal and wall friction coefficients are important in determining the initiation of particle movement, while the value of the restitution coefficient has a larger influence on particles in a dynamic state. The simulation of the fully elastic case (coefficient of restitution =1.0) with zero internal and wall friction, gives results that are very different from the experiment data.     

颗粒移动床内不稳定运动的计算颗粒动力学模拟

采用考虑滚动摩擦的三方程离散单元法（DEM）模型对侧开孔的移动床中的颗粒流动进行了数值研究。结果表明,计算颗粒动力学(CGD)方法可对复杂颗粒系统内颗粒的运动行为进行准确的预测,包括时均速度场和脉动速度场。讨论了模型中颗粒摩擦参数的重要影响,并对颗粒流动表现出的间歇现象进行了分析。颗粒流动与流体流动有相似之处,都存在随机的脉动,但颗粒流的随机脉动机理与流体中的湍流机理有很大不同,颗粒流动会表现出很强的不连续性。     

Distinct element analysis of attrition of granular solids under shear deformation

The attrition of spherical particles in a periodic cell under shear straining is analysed by distinct element method (DEM). The damage mechanisms of surface wear and fragmentation are under consideration. The side crushing strength (SCS) of single particles is used as the criterion for fragmentation. For surface damage, the abrasive wear by the formation of lateral cracks during shearing is calculated using a model of chipping for the semi-brittle failure mode. The contributions to attrition by surface wear and particle fragmentation are therefore decoupled and quantified. The simulation results are then compared with the experimental data reported previously.The contribution of fragmentation to the overall attrition is found to be dominant over the full range of strains tested in this work in agreement with the experimental data. The extent of attrition predicted by the simulations compares generally well with the experimental data except at the lowest normal stress and at high shear strains. For the former, the reason for the poor agreement is unclear. For the latter, the difference is attributed to the presence of fragments and debris as they affect the contact force distribution and this feature has not been simulated. The parametric sensitivity analyses indicate that the simulation results are sensitive to particle properties such as Young's modulus and the coefficient of friction. Therefore, careful material characterisation is necessary in order to get reliable predictions. The effect of the shear strain rate on particle breakage has also been examined by simulation. The results indicate that the rate of attrition is not sensitive to strain rates normally used for shear cell tests, i.e., of order of .     

Particle grinding by high‐intensity ultrasound: Kinetic modeling and identification of breakage mechanisms

High‐intensity ultrasound, is sought as a means to break particles. A horn‐type ultrasonic transducer is used to apply HIU into a suspension of alumina particles causing breakage to occur. The rate of particle breakage is monitored continuously via in‐line laser‐based particle chord length measurement. Kapur function analysis is used to arrive at the grinding kinetics under variations of ultrasonic power, particle loading, temperature of the suspension and particle size. The first Kapur function increases monotonically with increase in input ultrasonic power. Increasing temperature also increases the first Kapur function but an optimum in the range investigated (10–50°C) is observed near 25°C. An exponential relation is found for the variation of first Kapur function with particle size, this being unique to ultrasound‐mediated particle breakage. The breakage mechanism is attributed mainly to particle abrasion. Different breakage mechanisms are observed at different temperatures. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

岩石爆破中塑性压剪损伤的数值模拟

为计算爆破导致的塑性压剪损伤,基于岩石微元强度分布的随机性,采用连续介质力学与损伤力学理论,建立一种岩石损伤软化统计本构模型,并将此模型合理地嵌入到大型有限元软件LS-DYNA中,对无限岩体中的球形和柱形药包爆破压剪损伤问题进行了数值模拟,获得了不同围压下的应力-应变关系数据和不同时刻损伤分布的资料。该模型本构参数少,能够较好地反映出介质的损伤与软化等特征。