Large-scale discrete element modeling in pneumatic conveying

Discrete element method (DEM) is an effective approach to evaluate granular flows, whereas it is hardly used in investigating the design and the operational conditions in industries. This is due to the fact that the number of calculated particles is restricted by the limit of computer memories. In this study, a coarse grain model for large-scale DEM simulations is proposed, where a modeled particle whose size is larger than the original particle is used instead of a crowd of original particles. The coarse grain model is applied to a three-dimensional plug flow in a horizontal pipeline. The plug length, the cycle and the stationary layer area occupation are compared between the coarse grain particle system and the original particle one. The results show that the coarse grain model can simulate the original particle behavior adequately.     

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.     

Study of cold powder compaction by using the discrete element method

The discrete element method (DEM), based on a soft-sphere approach, is commonly used to simulate powder compaction. With these simulations a new macroscopic constitutive relation can be formulated. It is able to de-scribe accurately the constitutive material of powders during the cold compaction process. However, the force-law used in the classical DEM formulation does not reproduce correctly the stress evolution during the high density compaction of powder. To overcome this limitation at a relative density of about 0.85, the high density model is used. This contact model can reproduce incompressibility effects in granular media by implementing the local solid fraction into the DEM software, using Voronoi cells. The first DEM simulations using the open-source YADE software show a fairly good agreement with the multi-particle finite element simulations and experimental results.     

Quantitative validation of the discrete element method using an annular shear cell

The discrete element method (DEM) is often used as the “gold standard” for comparison to continuum-level theories and/or coarse-grained models of granular material flows due to its derivation from first-principal constructs, like contact mechanics. Despite its prevalence, the method is most often validated against experiment in only qualitative ways - comparison of mixing rates, gross features of concentration profiles, etc. - for exactly the reason it has found its popularity; detailed experimental measurements are difficult and often expensive. In this paper, we outline work aimed at using detailed, particle-level experimental measurements to quantitatively validate DEM simulations. Specifically, we examine the flow in a horizontally-aligned annular shear cell. Measurements are performed using digital particle tracking velocimetry (DPTV) so that the velocity, granular temperature, and solids fractions profiles may be extracted. Computationally, we attempt to match the experimental measurements as closely as possible and study the impact of a variety of contact mechanics-inspired force laws as well as perform sensitivity analysis on device and particle geometry and material properties employed.     

Impact of Contact Scaling and Drag Calculation on the Accuracy of Coarse-Grained Discrete Element Method

The accuracy of coarse-grained discrete element method (CGDEM) relies on appropriate scaling rules for contact and fluid-particle interaction forces. For fluidized bed applications, different scaling rules are used and compared with DEM results. The results indicated that in terms of averaged values as mean particle position and voidage profile, the coupling of computational fluid dynamics and CGDEM leads to accurate results for low scaling factors. Regarding the particle dynamics, the approach leads to an underestimation of RMS values of particle position indicating a loss of particle dynamics in the system due to coarse graining. The impact of cell cluster size on drag force calculation is studied. The use of energy minimization multiscale drag correction is investigated, and a reduced mesh dependency and good accuracy are observed.     

Three dimensional discrete element modeling of granular media under cyclic constant volume loading: A micromechanical perspective

Discrete element modeling is employed to investigate the micromechanics of two granular assemblies subjected to constant-volume cyclic loading. For this purpose, two assemblies of spherical particles are modeled at the same confining pressure but with two different void ratios. The cyclic behaviors of the assemblies are inspected and the micromechanical parameters and their variations during cyclic loading are carefully observed and analyzed. The evolution of contact force networks with the progression of the loading cycles confirms that the contact force networks are hysteretic and their formation depends on the previous strain conditions of the assemblies. The distributions of the contact normals and their normal forces are also investigated to obtain a quantitative insight of the changes in the contact force networks. The probability distributions of the normal and tangential forces during cyclic loading are similar to the results of previous experimental studies that were conducted on two-dimensional specimens of granular materials. In addition, variations of the fabric tensors, which were calculated for strong contacts, are studied to trace the changes of the structural anisotropy of the specimens. The results suggest that the structural anisotropy of the specimens increases dramatically when they approach the state of liquefaction and that the degree of anisotropy is more profound in the strong contacts. Finally, the displacements of the particles during specific loading cycles are calculated to determine the relation between the movements of the particles and the changes in the macro-scale behavior of the two assemblies. The results of this study elaborate the origin of liquefaction phenomena with respect to the microstructure of the granular soils, showing the role of different mode of contacts failure in micro-scale (sliding and rolling) on the overall observed behavior of granular soils with two different relative densities, moreover the importance of strong and weak contacts in cyclic constant-volume loading of the media. It also emphasizes on the variation of structural anisotropy in undrained cyclic loading of granular media and its relationship with common soil behavior in macro-scale during liquefaction failure.     

Advances in micro-mechanical modeling using a bonded-particle model and periodic homogenization within discrete element framework applied to heterogeneous ceramics

The Discrete Element Method (DEM) can account for microcracks initiations and propagations within the microstructure and their impact on the macroscopic properties of ceramics. Combing the DEM with the Periodic Homogenization (PH) allows working with a limited number of elements, thus facilitating the multiscale transition of the elastic properties of ceramics: from the microscale (inclusion/pores scale) to the macroscopic elastic behavior of such continuum media. However, the PH approach for a continuum media is currently less developed in DEM than the FEM. Hence, this study aims to consolidate a DEM framework, using a bonded-particle model and PH to improve the prediction of the elastic properties (Cij tensor) of ceramics. Here, a face-centered cubic unit cell is combining? with periodic boundary conditions to build a 3D representative volume element in DEM to model the macroscopic elastic properties of model materials and is validated by experimental data, analytical and FEM approaches.     

Predicting the flow mode from hoppers using the discrete element method

In this work, the discrete element method (DEM) is used to assess powder flow from hoppers and the results are compared to widely-used hopper design charts. These design charts delineate mass-flow and funnel-flow behavior based on the hopper wall angle and a given set of material properties. The modeled system consists of hoppers with various wall angles and frictional, non-cohesive, spherical particles. The performance is assessed by measuring the particle residence times, particle velocities, and the extent of segregation during discharge. A Mass Flow Index (MFI) based on the velocity profile data is used to quantitatively characterize the nature of the flow pattern as mass-flow, funnel-flow, or some intermediate. The DEM predictions are generally in very good agreement with the Jenike design charts. The level of agreement shown here indicates that DEM cannot only reproduce the current estimates of hopper performance, but also provide additional insight into the flow-such as the internal granular structure-that may be difficult to obtain otherwise.     

Investigation of particle packing in model pharmaceutical powders using X-ray microtomography and discrete element method

This paper outlines a novel technique, based on combination of modern desktop X-ray microtomography, quantitative image processing and computer simulation using the discrete element method (DEM), to investigate randomly packed particles in an attempt to model the process of pharmaceutical tablet manufacture by powder compaction. The systems studied include glass ballotini and spheroidal micronised cellulose (Celphere), all with typical particle sizes between 180 and 300 μm. We demonstrate that X-ray microtomography (XMT) and DEM can reproduce the structure of real packing systems in three-dimensions and have the potential for further investigation of pharmaceutical processes by both modelling and experimental study. This was achieved by generating packing systems using DEM simulations that are consistent with the structural measurements made by XMT on real packed powders via the comparison of their radial distribution functions (RDFs). These results have been validated by direct volume measurements, and scanning electron microscopy (SEM) observations in terms of particle morphologies and size distribution. The result is a significant step forward for the quantitative analysis of model systems for pharmaceutical powders.     

A theoretical analysis of the force models in discrete element method

This paper presents an investigation of the equilibrium, stability and pure rolling problems of a sphere moving on a flat plane with special reference to a few force models which are commonly used in the discrete element method (DEM) and here categorized into two types: with and without rolling friction. It is obtained that according to the models without rolling friction, the set of equilibrium states of the system is not asymptotically stable, which does not agree with the fact that the sphere with small initial tangential velocity, angular velocity and tangential displacement should eventually stop. The models also display that the sphere can roll on the plane without sliding only when both the tangential force and torque acting on the sphere are zero, which is not reasonable for a viscoelastic sphere moving on a hard plane. On the other hand, the models with rolling friction cannot describe the pure rolling motion of the sphere with any material properties. The results highlight the theoretical deficiency associated with the force models in DEM. Based on the findings, modified models are proposed to overcome the above problems.     

Large-scale numerical investigation of solids mixing in a V-blender using the discrete element method

Over the past few years, the discrete element method (DEM) has been used in models for the simulation of granular flows in various mixing applications. If these models have shown rather efficient, they have so far been applied to predict the behavior of small numbers of particles over limited spans of time. The objective of this work is to show that DEM-based models can be used to predict the flow behavior of large numbers of particles over large spans of time and, more particularly, mixing phenomena that take time to manifest in such systems. To this end, several large-scale DEM-based numerical investigations of the flow of monodisperse and bidisperse blends of up to 225 000 particles over a span of 120 s in a V-blender will be discussed using entities such as the particle velocity and granular temperature, the torque of the mixing system, RSD curves and mixing times.     

Modelling of multiple intra-time step collisions in the hard-sphere discrete element method

The Discrete Element Method (DEM) is a commonly used tool for simulating particulate behaviours over time. DEM covers two fundamental bases: the soft-sphere and hard-sphere methods. Existing hard-sphere DEM applies collisions as sequential ordered binary collisions that satisfy momentum conservation and a restitution coefficient; multiple collisions occurring within a single simulation iteration are ordered such that collisions may then be applied in the sequential binary instantaneous manner. It is proposed that multiple intra-time-step collisions be instead applied by averaging the outcomes of all collisions for each particle as detected at the beginning of the iteration, reducing the computational burden of the method.This averaged hard-sphere DEM was compared to soft-sphere DEM with a linear contact-stiffness model yielding an equivalent restitution coefficient for two two-dimensional scenarios, one resulting in transient dilute material behaviour and the other in steady dense material behaviour. The algorithm applying each DEM was written such that direct comparison of the computational time costs of each could be made.The simulation results suggest that significant computational time cost savings are available for simulation of dilute phase materials when applying the averaged hard-sphere DEM, in particular where the physical particle properties require a small time step of soft-sphere DEM.     

Predicting discharge dynamics from a rectangular hopper using the discrete element method (DEM)

Accurate prediction of the discharge rate from hoppers is important in many industrial processes involving the handling of granular materials. The present work investigates the parameters affecting the discharge rate using the discrete element method (DEM). The effects of particle properties (particle size and size distribution) and hopper geometry (hopper width, outlet width, angle and fill height) are studied and compared to previously published experimental correlations. The results indicate that DEM simulations are fully capable of reproducing trends in the discharge rate that are well-known experimentally. For example, particle size and hopper width are shown to have a minimal influence on the discharge rate. In addition, for rectangular hoppers, the discharge rate is shown to vary with the outlet width raised to the power as given by the modified Beverloo correlation. The DEM simulations are also used to explore a wider range of parameters that have not been or are not easily explored experimentally. For example, the effects of hopper friction, particle friction, coefficient of restitution are investigated, and particle friction is shown to have a significant influence on the hopper discharge behavior.     

A comparison of discrete element simulations and experiments for ‘sandpiles’ composed of spherical particles

Discrete element simulations, with the particle–particle interaction model based on classical contact mechanics theory between two non-adhesive spheres, were carried out and compared with ‘sandpile’ experiments using spherical particles in order to assess the validation of the simulation data. The contact interaction model is a combination of Hertzian theory for the normal interaction and Mindlin–Deresiewicz theory for the tangential interaction. To ensure the consistency of the simulations with the experiments, the measurement of sliding friction, a key parameter in DEM simulations, was highlighted. A simple experimental method for establishing the value of the friction coefficient was proposed and used in measuring the friction of the rough glass beads and steel balls to be modelled in the simulations. The simulations were carried out for two cases according to particle arrangements: the first is quasi-two-dimensional (Q2D), with a smaller flat cuboidal box containing the spherical particles inside another box for discharge, and the second case is axisymmetric (3D). For both cases, simulations and experiments were carried out for assemblies of polydisperse rough glass beads under the same conditions. Comparisons were made that showed that the profiles and hence the measured angles of repose, in each case, were in good agreement, thus supporting the validity of the discrete element model used. Further numerical–experimental comparisons were carried out for 3D conical piles using smooth monodisperse steel balls and the same conclusions were obtained.     

Speed-up of computing time for numerical analysis of particle charging process by using discrete element method

The objective of this paper is to improve the computing time for numerical analysis of particle charging process by using discrete element method. The rule for ignoring the calculations of contact forces and updating trajectories of unmoved particles were discussed. When the relative displacement of a particle within certain calculation steps became less than 0.1% of particle radius, this particle was determined to be unmoved and the calculations of this particle were ignored. The computing time was improved significantly when this new method was used, and its calculation speed was more than two times faster than that of original. It was found that this speed-up method is more useful for the cases that the particle becomes unmoved in short time or the height of charged bed is large. The simulation of charging process in an industrial-scale surge hopper was studied by using new method, the calculation speed became 2.88 times faster than that of original, and the quite similar particle size segregation between original and new methods was given. This new method for speed-up of the charging process in DEM is very useful, and the charging processes of the industrial scale storages can be simulated by using this method.     

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.     

Two-dimensional discrete element modeling of a spherical steel media in a vibrating bed

A discrete element model was developed to model granular flow in different vibratory beds and the results are compared with experimental measurements of bulk flow velocity and bed expansion. The sensitivity of the model predictions to the contact parameters was considered and the parameters were optimized with respect to the experimental results. The difference between the model predictions of the bulk flow velocity and the measurements was less than 10% at four locations in media beds of two depths. The average bulk density of the vibrating beds was also predicted to be within 10% of the measured values.     

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.     

Discrete element method simulation of three-dimensional conical-base spouted beds

A discrete element method (DEM) simulation of three-dimensional conical-base spouted beds is presented. The overall height and diameter of the vessel are 0.5 and 0.15 m, respectively, and the nozzle diameter is 0.02 m. The inclined angle of the conical section varies from 0 to 60 degrees. The gas flow is described by the continuity and Navier-Stokes equations and solved by a finite difference method of second order accuracy in space and time. For gas-particle interaction, the Ergun equation (for void fraction smaller than 0.8) and the Wen-Yu model (for void fraction of 0.8 and above) are employed. A new method for treatment of the boundary condition for 3-D gas flow along the cone surface is proposed. This boundary condition satisfies both the continuity and momentum-balance requirements for the gas phase. Usefulness of the present simulation for studying gas flow pattern and particle motion in conical-base spouted beds is demonstrated. The effects of the inclined angle and draft tube on gas and particle flow in spouted beds are discussed.