Discrete Particle Simulation Research Articles

Steady-state granular flow in a 3D cylindrical hopper with flat bottom: macroscopic analysis

The information of a hopper flow at a particle scale, obtained from discrete particle simulation, is used to investigate the macroscopic dynamic behaviour of granular flow in a cylindrical hopper with flat bottom by means of an averaging technique. The macroscopic properties including velocity, mass density, stress and couple stress are quantified under the cylindrical coordinate framework, and an effort is made to link these variables to the microscopic variables considered. The velocity and density distributions are first illustrated to match qualitatively the experimental and numerical results, confirming the validity of the proposed averaging method. Four components of stress, T zz , T rr , T rz and T zr , and two dominant components of couple stress, M r θ and M z θ , are then investigated in detail. It is shown that large vertical normal stress is mainly observed in the region close to the bottom corner, large radial normal stress is observed within the particle bed as well as the bottom corner, and large shear stresses in the region adjacent to the vertical wall. The four stresses are relatively small in a region close to the orifice. Their magnitudes are mainly contributed by the interaction forces between particles and between particles and walls. However, the transport of particles also plays a significant role at the orifice, especially, in the vertical normal stress. The couple stress can be ignored except for the regions close to the vertical and bottom walls, where the most dominant components are M r θ adjacent to the vertical wall and M z θ close to the bottom wall. The magnitudes of these macroscopic variables depend on the geometric and physical parameters of the hopper and particles such as the orifice size and wall roughness of the hopper, and the friction and damping coefficients between particles although their spatial distributions are similar.

Discrete Particle Simulation of Solid Flow in a Model Blast Furnace

This paper reports a numerical study of solid flow in a model blast furnace under simplified conditions by means of discrete particle simulation (DPS). The applicability of the proposed DPS approach is validated from its good agreement with the experiment in terms of solid flow patterns. It is shown that the DPS is able to generate a stagnant zone without any need for any arbitrary treatment, and capture the main features of solid flow within the furnace at a microscopic level. The results confirm that the solid flow in a blast furnace can be divided into four different flow regions. However, the flow is strongly influenced by the front and rear walls in a 2D slot model furnace whereas the predicted stagnant zone decreases significantly with wall sliding friction. In a 3D model with periodic boundary conditions incorporated, a smaller stagnant zone is obtained. The effects of solid flow rate, particle properties such as sliding and rolling friction coefficients on the solid flow are also investigated. The results are analysed in terms of solid flow patterns, solid velocity field, porosity distribution and normal force structure. The implication to blast furnace operation is discussed.

Discrete-particle simulations of cohesive granular flow using a square-well potential

In the present study, rapid granular flows with attractive inter-particle forces are investigated. In particular, cohesive forces are incorporated into hard-sphere (molecular dynamics) simulations via a square-well potential. The square-well potential treats cohesive forces as both binary and instantaneous. For simple shear flows, an investigation of the input parameter space indicates that two distinct flow regimes are present. For relatively large cohesive forces, the formation of a large, single agglomerate is observed. For moderate cohesive forces, the sheared system is composed of mostly 2-particle, dynamic agglomerates that are fairly evenly distributed throughout the domain. Furthermore, the results for this latter regime indicate that cohesion attenuates the magnitude of the stress components at higher solids fractions (in the collisional regime) as compared to the non-cohesive case. At lower solids fractions (kinetic regime), however the presence of cohesive forces has little impact on the observed stress.

Investigation of solids transport in a single‐screw extruder using a 3‐D discrete particle simulation

AbstractA non‐isothermal, 3‐D discrete particle simulation based on the discrete element method (DEM) was developed to simulate the solids‐conveying zone and feed hopper of a single‐screw extruder. The method considers each particle in a granular assembly as a separate entity that can interact with other particles or boundaries through collisions or lasting contacts. By using DEM to model the extrusion environment, a priori knowledge of the solids flow was not required in order to simulate the motion of a granular assembly with reasonable accuracy, allowing studies to be conducted in the absence of the solid plug assumption typical of classical solids‐conveying models. In this paper, predicted results were limited to low levels of compaction in the solids assembly (i.e., no particle deformation), in order to understand the behavior of the polymer pellets in their most dynamic state. The results of the DEM model showed reasonably good agreement with experimental data, providing comparable bulk values like output rate, yet also demonstrating its ability to capture the dynamics of solids particle conveying. The model captured the inherent variability of extrusion such as the low‐amplitude, high‐frequency fluctuations referred to as “solids pulsing” and the recirculation of pellets in the feed throat. Polym. Eng. Sci. 44:2203–2215, 2004. © 2004 Society of Plastics Engineers.

Assessment of Model Formulations in the Discrete Particle Simulation of Gas−Solid Flow

Discrete particle simulation has been recognized as a useful numerical technique for elucidating the fundamentals of granular matter. For gas−solid two-phase flow in fluidization, such simulations are achieved by combining the discrete flow of the particle phase with the continuum flow of the gas phase. However, differences exist in the actual implementation of this idea in the literature. This paper attempts to rationalize this matter by discussing important aspects including the governing equations in relation to the so-called models A and B, which use different treatments of pressure drop in the well-established two-fluid model, different coupling schemes between the gas and solid phases, and different equations for quantifying the particle−fluid interaction. For the purpose of quantitative analysis, gas fluidization of binary mixtures of particles is simulated with different model formulations, and a comparison of the results in terms of flow pattern and mixing/segregation kinetics shows a significant...

Impact on Soft Sand: Void Collapse and Jet Formation

Very fine sand is prepared in a well-defined and fully decompactified state by letting gas bubble through it. After turning off the gas stream, a steel ball is dropped on the sand. On impact of the ball, sand is blown away in all directions ("splash") and an impact crater forms. When this cavity collapses, a granular jet emerges and is driven straight into the air. A second jet goes downwards into the air bubble entrained during the process, thus pushing surface material deep into the ground. The air bubble rises slowly towards the surface, causing a granular eruption. In addition to the experiments and the discrete particle simulations we present a simple continuum theory to account for the void collapse leading to the formation of the upward and downward jets.

Comparison of multifluid and discrete particle modelling in numerical predictions of gas particle flow in circulating fluidised beds

From the perspective of wanting to evaluate the modelling of the particulate phase in multifluid computational fluid dynamics simulations, numerical predictions from a multifluid model is compared with predictions from a discrete particle model. Simulations with both one and three representative particle diameters for the particulate phase are performed. The predicted results are compared with experimental findings obtained with Laser Doppler Anemometry. The numerical predictions from the discrete particle code are found to be in better agreement with the experimental findings, but the multifluid code is by far the most efficient. To evaluate the modelling of collisions in the multifluid model, discrete particle simulations which only take into account of energy loss caused by head-on collisions are compared with discrete particle simulations, which take nonfrontal collisions into account.

Micro–macro transition for anisotropic, frictional granular packings

From the structure of a static granular solid, we derive the fabric and the stiffness tensor in average over those pairs of interacting particles with contact within the averaging volume. Starting from a linear expansion of the interaction potential around static equilibrium, stress and elastic strain can be derived from the principles of virtual displacement and virtual stress-change, respectively. Our approach includes both normal and tangential forces separately, in a new modular formulation starting from single contacts. The results are applied to a discrete particle simulation, and the findings include a relation between fabric and coordination number that is almost unaffected by the presence of friction, a different qualitative behavior of fabric and stiffness components, and only three independent entries to the stiffness matrix in its eigen-system. More general, anisotropy evolves directed against the direction of compression, and exponentially fast up to a certain maximal (limit) magnitude––a constitutive model for this behavior is proposed; in the critical state shear regime, the anisotropy is considerably smaller.

The modelling of particle systems with real shapes.

The numerical modelling of particulate processes in environmental science increasingly requires an ability to represent the properties of individual natural particles. Considerable advances have been made in discontinuum modelling using spheres to represent particles. In this paper, we discuss recent developments that illustrate a way forward for tackling the complexity of realistically shaped bodies such as those exhibited by rock fragments. To address the validation of such approaches, we present a comparison of cube-packing experiments and their equivalent numerical simulation. Sensitivity to initial conditions, highlighted for non-spherical bodies, enters the discussion of problems with validation of numerical simulation. The algorithmic details behind these advances in modelling large systems of realistically shaped particles are summarized in our companion paper in this volume.

Discrete particle simulation of gas fluidization of particle mixtures

AbstractThis report presents a numerical study of segregation and mixing of binary mixtures of particles in a gas‐fluidized bed by means of discrete particle simulation, where the motion of individual particles is 3‐D and the flow of continuous gas is 2‐D. Periodic boundary conditions are applied to the front and rear walls to represent a bed of large thickness with a relatively small number of particles. Two initial packing conditions are used in this simulation: completely separated, with the flotsam (1 × 10−3 m in diameter) on the top of the jetsam (2 × 10−3 m in diameter), and well mixed. The flotsam and jetsam are of the same density, with each counting 50% in weight. Gas is injected uniformly at the bottom. Two superficial gas velocities, 1.0 and 1.4 m/s, are used in the simulation, producing significant segregation and good mixing, respectively. The results show that the degree and rate of segregation or mixing are significantly affected by gas velocity and the final equilibrium states are not affected by the initial packing states for a given gas velocity. Significant segregation occurs at a gas velocity of 1.0 m/s, with the top fluidized layer rich in flotsam and the bottom defluidized layer rich in jetsam, whereas there was less segregation at 1.4 m/s with most of the bed fluidized. The simulated results are qualitatively comparable with those observed in the physical experiments conducted under similar conditions. On this basis, the mixing kinetics obtained from the numerical simulation is quantified with a weighted Lacey mixing index and explained in terms of microdynamic results in relation to particle–particle and particle–fluid interactions. It is proposed that an appropriate sampling size should be able to describe properly the two extremes: well mixed and fully segregated. The results also demonstrate that size segregation occurs as a result of the strong fluid drag force lifting the flotsam before a dynamical equilibrium is reached, and the particle–particle interaction, like the particle–fluid interaction, plays an important role in achieving uniform fluidization. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1713–1728, 2004

Discrete element method

Discrete element method (DEM) has been extensively used in the laboratory of particulate and multiphase processing at the University of New South Wales (UNSW) to study the fundamentals of particulate matter at a particle scale. This paper briefly reviews the work in the laboratory, which covers the development of simulation techniques and their application to the study of particle packing and flow, transport properties and constitutive relationships of typical static or dynamic particulate systems. It is concluded, through representative comparison between simulated and measured results under different conditions, that DEM, as a major technique for discrete particle simulation, is an effective method for particle scale research of particulate matter.

On dense granular flows.

The behaviour of dense assemblies of dry grains submitted to continuous shear deformation has been the subject of many experiments and discrete particle simulations. This paper is a collective work carried out among the French research group Groupement de Recherche Milieux Divisés (GDR MiDi). It proceeds from the collection of results on steady uniform granular flows obtained by different groups in six different geometries both in experiments and numerical works. The goal is to achieve a coherent presentation of the relevant quantities to be measured i.e. flowing thresholds, kinematic profiles, effective friction, etc. First, a quantitative comparison between data coming from different experiments in the same geometry identifies the robust features in each case. Second, a transverse analysis of the data across the different configurations, allows us to identify the relevant dimensionless parameters, the different flow regimes and to propose simple interpretations. The present work, more than a simple juxtaposition of results, demonstrates the richness of granular flows and underlines the open problem of defining a single rheology.

Three-dimensional, rapid shear flow of particles with continuous size distributions

Rapid granular flows occur in nature and industry and often contain particles of many sizes. Over the last two decades, significant theoretical and experimental effort has been directed at rapid granular flows with monodisperse or binary particle-size distributions. In contrast, the behavior of rapid granular flows with more than two particle sizes has received only limited attention. The particle-size distributions in many natural and industrial granular flows may be represented as continuous distributions (e.g., Gaussian or lognormal distributions), providing incentive for the investigation of rapid granular flows with these particle-size distributions. As an extension of previous work for two-dimensional simulations of rapid shear flows with Gaussian and lognormal particle-size distributions, this work is directed at three-dimensional flows with continuous size distributions. Event-driven, discrete-particle (“molecular dynamic”) simulations are employed for the three-dimensional simple shear flow of smooth, spherical particles with Gaussian and lognormal particle-size distributions. The results parallel those found previously in two dimensions and demonstrate the effect of distribution width on the stress tensor and granular energy.

Wave propagation in a dynamic system of soft granular materials

The wave propagation in a dynamic system of soft elastic granules is investigated theoretically and numerically. The perturbation theory for simple fluids is applied to the elastic granular system in order to relate the elastic properties of individual particles with the "thermodynamic" quantities of the system. The properties of a piston-driven shock are derived from the obtained thermodynamic relations and the Rankine-Hugoniot relations. The discrete particle simulation of a piston-driven shock wave in a granular system is performed by the discrete element method. From theoretical and numerical results, the effect of the elastic properties of a particle on shock properties is shown quantitatively. Owing to the finite duration of the interparticle contact, the compressibility factor of the elastic granular system decreases in comparison with that of the hard-sphere system. In addition, the relation between the internal energy and the granular temperature changes due to the energy preserved with the elastic deformation of the particle. Consequently, the shock properties in soft particles are considerably different from those in the hard-sphere system. We also show the theoretical prediction of the speed of sound in soft particles and discuss the effect of the elasticity on an acoustic wave.

The drag force in two-fluid models of gas–solid flows

Currently, the two most widespread methods for modelling the particulate phase in numerical simulations of gas-solid flows are discrete particle simulation (see, e.g., Mikami, Kamiya, & Horio, 1998), and the two-fluid approach, e.g., kinetic theory models (see, e.g., Louge, Mastorakos, & Jenkins, 1991). In both approaches the gas phase is described by a locally averaged Navier-Stokes equation and the two phases are usually coupled by a drag force. Due to the large density difference between the particles and the gas, inter-phase forces other than the drag force are usually neglected, so it plays a significant role in characterising the gas-solid flow. Yasuna, Moyer, Elliott, and Sinclair (1995) have shown that the solution of their model is sensitive to the drag coefficient. In general, the performance of most current models depends critically on the accuracy of the drag force formulation.

Discrete particle simulation of solids motion in a gas–solid fluidized bed

The solids motion in a gas–solid fluidized bed was investigated via discrete particle simulation. The motion of individual particles in a uniform particle system and a binary particle system was monitored by the solution of the Newton's second law of motion. The force acting on each particle consists of the contact force between particles and the force exerted by the surrounding fluid. The contact force is modeled by using the analogy of spring, dash-pot and friction slider. The flow field of gas was predicted by the Navier–Stokes equation. The solids distribution is non-uniform in the bed, which is very diluted near the center but high near the wall. It was also found that there is a single solids circulation cell in the fluidized bed with ascending at the center and descending near the wall. This finding agrees with the experimental results obtained by Moslemian. The effects of the operating conditions, such as superficial gas velocity, particle size, and column size on the solids movement, were investigated. In the fluidized bed containing uniform particles better solids mixing was found in the larger bed containing smaller size particles and operated at higher superficial gas velocity. In the system containing binary particles, it was shown that under suitable conditions the particles in a fluidized bed could be made mixable or non-mixable depending on the ratios of particle sizes and densities. Better mixing of binary particles was found in the system containing particles with less different densities and closer sizes. These results were found to follow the mixing and segregation criteria obtained experimentally by Tanaka et al.

Dynamical clustering of red blood cells in capillary vessels.

We have modeled the dynamics of a 3-D system consisting of red blood cells (RBCs), plasma and capillary walls using a discrete-particle approach. The blood cells and capillary walls are composed of a mesh of particles interacting with harmonic forces between nearest neighbors. We employ classical mechanics to mimic the elastic properties of RBCs with a biconcave disk composed of a mesh of spring-like particles. The fluid particle method allows for modeling the plasma as a particle ensemble, where each particle represents a collective unit of fluid, which is defined by its mass, moment of inertia, translational and angular momenta. Realistic behavior of blood cells is modeled by considering RBCs and plasma flowing through capillaries of various shapes. Three types of vessels are employed: a pipe with a choking point, a curved vessel and bifurcating capillaries. There is a strong tendency to produce RBC clusters in capillaries. The choking points and other irregularities in geometry influence both the flow and RBC shapes, considerably increasing the clotting effect. We also discuss other clotting factors coming from the physical properties of blood, such as the viscosity of the plasma and the elasticity of the RBCs. Modeling has been carried out with adequate resolution by using 1 to 10 million particles. Discrete particle simulations open a new pathway for modeling the dynamics of complex, viscoelastic fluids at the microscale, where both liquid and solid phases are treated with discrete particles. Figure A snapshot from fluid particle simulation of RBCs flowing along a curved capillary. The red color corresponds to the highest velocity. We can observe aggregation of RBCs at places with the most stagnant plasma flow.

Clustering revealed in high‐resolution simulations and visualization of multi‐resolution features in fluid–particle models

AbstractSimulating natural phenomena at greater accuracy results in an explosive growth of data. Large‐scale simulations with particles currently involve ensembles consisting of between 106 and 109 particles, which cover 105–106 time steps. Thus, the data files produced in a single run can reach from tens of gigabytes to hundreds of terabytes. This data bank allows one to reconstruct the spatio‐temporal evolution of both the particle system as a whole and each particle separately. Realistically, for one to look at a large data set at full resolution at all times is not possible and, in fact, not necessary. We have developed an agglomerative clustering technique, based on the concept of a mutual nearest neighbor (MNN). This procedure can be easily adapted for efficient visualization of extremely large data sets from simulations with particles at various resolution levels. We present the parallel algorithm for MNN clustering and its timings on the IBM SP and SGI/Origin 3800 multiprocessor systems for up to 16 million fluid particles. The high efficiency obtained is mainly due to the similarity in the algorithmic structure of MNN clustering and particle methods. We show various examples drawn from MNN applications in visualization and analysis of the order of a few hundred gigabytes of data from discrete particle simulations, using dissipative particle dynamics and fluid particle models. Because data clustering is the first step in this concept extraction procedure, we may employ this clustering procedure to many other fields such as data mining, earthquake events and stellar populations in nebula clusters. Copyright © 2003 John Wiley & Sons, Ltd.

Discrete Particle Simulation and Visualized Research of the Gas−Solid Flow in an Internally Circulating Fluidized Bed

In this paper, the DEM (discrete element method) is used to simulate the gas−solid flow of a two-dimensional internally circulating fluidized bed. Eulerian and Lagrangian methods are used to deal with gas-field and discrete particles, respectively. The gas flow is determined by the local average Navier−Stokes equation, the motion of individual particle is obtained by solving Newton's second law of motion, and particle collisions are taken into account. The simulated results indicate that there is particle circulation from the high-velocity region to the low-velocity region in internally circulating fluidized beds with uneven air distributions; therefore, the mixing characteristics of the bed material are good. Through visualization experiments, we confirm that there is transverse movement of bubbles from the high-velocity side to the low-velocity side in internally circulating fluidized beds. Thus, particles in the trailing vortex of bubbles also move transversely. This is an important factor that results in particle circulation in internally circulating fluidized beds.

Effect of pressure on gas–solid flow behavior in dense gas-fluidized beds: a discrete particle simulation study

A computational study has been carried out to assess the influence of pressure on the flow structures and regime transitions in dense gas-fluidized beds using the discrete particle simulation (DPS) approach. By employing particle level simulation, the particle–particle–fluid interactions were analyzed to highlight the intrinsic mechanisms underlying the gas–solid flow patterns and to elucidate elevated pressure-induced improvement of fluidization quality. Our results show that the bed pressure drop could be predicted satisfactorily with the discrete particle model. Furthermore, an elevated pressure reduces the incipient fluidization velocity, widens the uniform fluidization regime, shortens the bubbling regime and leads to a quick transition to the turbulent regime. Spanning from the incipient fluidization to the turbulent regime, an elevated pressure efficiently depresses the bubble growth and therefore produces more uniform gas–solid flow structures. In particular, it is found that an elevated pressure changes the roles of particle–particle collision and particle–fluid interaction in their competition. An elevated pressure through enhancing gas–solid interaction and reducing the particle collision frequency, effectively suppresses the formation of large bubbles. As a consequence, a more uniform gas–solid flow structure with a higher bed height is produced, leading to the particulate fluidization.