Discrete particle simulation of particulate systems: A review of major applications and findings

Understanding and modelling the dynamic behaviour of particulate systems has been a major research focus worldwide for many years. Discrete particle simulation plays an important role in this area. This technique can provide dynamic information, such as the trajectories of and transient forces acting on individual particles, which is difficult to obtain by the conventional experimental techniques. Consequently, it has been increasingly used by various investigators for different particulate processes. In spite of the large bulk volume, little effort has been made to comprehensively review and summarize the progress made in the past. To overcome this gap, we have recently completed a review of the major work in this area in two separate parts. The first part has been published [Zhu, H.P., Zhou, Z.Y., Yang, R.Y., Yu, A.B., 2007. Discrete particle simulation of particulate systems: theoretical developments. Chemical Engineering Science 62, 3378-3392.], which reviews the major theoretical developments. This paper is the second one, aiming to provide a summary of the studies based on discrete particle simulation in the past two decades or so. The studies are categorized into three subject areas: particle packing, particle flow, and particle-fluid flow. The major findings are discussed, with emphasis on the microdynamics including packing/flow structure and particle-particle, particle-fluid and particle-wall interaction forces. It is concluded that discrete particle simulation is an effective method for particle scale research of particulate matter. The needs for future research are also discussed.     

Numerical modeling of particle fluidization behavior in a rotating fluidized bed

In this study, numerical modeling of particle fluidization behaviors in a rotating fluidized bed (RFB) was conducted. The proposed numerical model was based on a DEM (Discrete Element Method)-CFD (Computational Fluid Dynamics) coupling model. Fluid motion was calculated two-dimensionally by solving the local averaged basic equations. Particle motion was calculated two-dimensionally by the DEM. Calculation of fluid motion by the CFD and particle motion by the DEM were simultaneously conducted in the present model. Geldart group B particles (diameter and particle density were 0.5 mm and 918 kg/m³, respectively) were used for both calculation and experiment. First of all, visualization of particle fluidization behaviors in a RFB was conducted. The calculated particle fluidization behaviors by our proposed numerical model, such as the formation, growth and eruption of bubble and particle circulation, showed good agreement with the actual fluidization behaviors, which were observed by a high-speed video camera. The estimated results of the minimum fluidization velocity (U_mf) and the bed pressure drop at fluidization condition (ΔP_f) by our proposed model and other available analytical models in literatures were also compared with the experimental results. It was found that our proposed model based on the DEM-CFD coupling model could predict the U_mf and ΔP_f with a high accuracy because our model precisely considered the local downward gravitational effect, while the other analytical models overpredicted the ΔP_f due to ignoring the gravitational effect.     

Gas-solid flow in an ironmaking blast furnace-II: Discrete particle simulation

This paper presents a numerical study of the gas-solid flow in an ironmaking blast furnace by combining discrete particle simulation (DPS) with computational fluid dynamics (CFD). The conditions considered include different gas and solid flow rates, asymmetric conditions such as non-uniform gas and solid flow rates in blast furnace raceways, and existence of scabs on the side walls. The obtained results show that main gas-solid flow features under different conditions can be captured by this approach. The computed results are consistent with the experimental observations. Microscopic structures including the force structure are examined to analyze the effect of gas flow on the solid flow at a particle scale. Further, macroscopic properties such as solid pressure and porosity are obtained from the corresponding microscopic properties by an averaging method. It is shown that the solid pressure-porosity relationship in a blast furnace is complicated, varying with different flow zones. None of the literature correlations considered can fully describe such a feature. Based on the simulated results, two correlations are formulated to describe the solid pressure-porosity relationship covering different flow regimes. But their general application needs further tests in future work.     

The effects of particle and gas properties on the fluidization of Geldart A particles

We report on 3D computer simulations based on the soft-sphere discrete particle model (DPM) of Geldart A particles in a 3D gas-fluidized bed. The effects of particle and gas properties on the fluidization behavior of Geldart A particles are studied, with focus on the predictions of U_mf and U_mb, which are compared with the classical empirical correlations due to Abrahamsen and Geldart [1980. Powder Technology 26, 35-46]. It is found that the predicted minimum fluidization velocities are consistent with the correlation given by Abrahamsen and Geldart for all cases that we studied. The overshoot of the pressure drop near the minimum fluidization point is shown to be influenced by both particle-wall friction and the interparticle van der Waals forces. A qualitative agreement between the correlation and the simulation data for U_mb has been found for different particle-wall friction coefficients, interparticle van der Waals forces, particle densities, particle sizes, and gas densities. For fine particles with a diameter , a deviation has been found between the U_mb from simulation and the correlation. This may be due to the fact that the interparticle van der Waals forces are not incorporated in the simulations, where it is expected that they play an important role in this size range. The simulation results obtained for different gas viscosities, however, display a different trend when compared with the correlation. We found that with an increasing gas shear viscosity the U_mb experiences a minimum point near , while in the correlation the minimum bubbling velocity decreases monotonously for increasing μ_g.     

A CFD-DEM study of the cluster behavior in riser and downer reactors

This paper presents a numerical study of the particle cluster behavior in a riser/downer reactor by means of combined computational fluid dynamics (CFD) and discrete element method (DEM), in which the motion of discrete particles is obtained by solving Newton's equations of motion and the flow of continuum gas by the Navier-Stokes equations. It is shown that the existence of particle clusters, unique to the solid flow behavior in such a reactor, can be predicted from this first principle approach. The results demonstrate that there are two types of clusters in a riser and downer: one is in the near wall region where the velocities of particles are low; the other is in the center region where the velocities of particles are high. While the extent of particle aggregation appears to be similar, the duration time for the first type in a downer is shorter than in a riser. Furthermore, it is demonstrated that the formation of clusters is affected by a range of variables related to operational conditions, particle properties, and bed properties and geometry. The increase of solid volume fraction, sliding and rolling friction between particles or between particles and wall, or damping coefficient can enhance the formation of clusters. The use of multi-sized particles can also promote the formation of clusters. But the increase of gas velocity or use of a wider bed can suppress the formation of clusters. The van der Waals force may enhance the formation of clusters when solid concentration is high but suppress the formation of clusters near the wall region when solid concentration is low.     

Discrete particle simulations for flow of binary particle mixture in a bubbling fluidized bed with a transport energy weighted averaging scheme

Flow behavior of small and big particles with the same particle density in a bubbling fluidized bed is modeled by a combined approach of discrete particle method and computational fluid dynamics (CFD-DPM). The collision time of a collision pair is computed by a quartic equation in which the effect of acceleration due to the different diameters is considered. A transport energy weighted averaging approach is proposed to determine the local gas velocity at a particle. The fluidization behavior of binary mixture differing in size is experimentally and numerically studied in the gas bubbling fluidized bed. The distributions of mass fraction of small and big particles along the bed height are simulated, and the profiles of the mean particle diameters of binary mixture are determined. The numerical results are in agreement with experimental data. The distributions of granular temperature, stresses, and shear viscosities of small and big particles are compared.     

CFD–DEM modeling of gas fluidization of fine ellipsoidal particles

Particle characteristics are important factors affecting gas fluidization. In this work, the effects of both particle size and shape on fluidization in different flow regimes are studied using the combined computational fluid dynamic–discrete element method approach. The results are first analyzed in terms of flow patterns and fluidization parameters such as pressure drop, minimum fluidization, and bubbling velocities. The results show that with particle size decreasing, agglomerates can be formed for fine ellipsoidal particles. In particular, “chain phenomenon,” a special agglomerate phenomenon exists in expanded and fluidized beds for fine prolate particles, which is caused by the van der Waals force. The minimum fluidization velocity increases exponentially with the increase of particle size, and for a given size, it shows a “W” shape with aspect ratio. A correlation is established to describe the dependence of minimum fluidization velocity on particle size and shape. Ellipsoids have much higher minimum bubbling velocities and fluidization index than spheres. © 2015 American Institute of Chemical Engineers AIChE J, 62: 62–77, 2016     

CFD–DEM simulation of the gas–solid flow in a cyclone separator

In this work, a numerical study of the gas–solid flow in a gas cyclone is carried out by use of the combined discrete element method (DEM) and computational fluid dynamics (CFD) model where the motion of discrete particles phase is obtained by DEM which applies Newton’s equations of motion to every individual particle and the flow of continuum fluid by the traditional CFD which solves the Navier–Stokes equations at a computational cell scale. The model successfully captures the key flow features in a gas cyclone, such as the strands flow pattern of particles, and the decrease of pressure drop and tangential velocity after loading solids. The effect of solid loading ratio is studied and analysed in terms of gas and solid flow structures, and the particle–gas, particle–particle and particle–wall interaction forces. It is found that the gas pressure drop increases first and then decreases when solids are loaded. The reaction force of particles on gas flow is mainly in the tangential direction and directs mainly upward in the axial direction. The reaction force in the tangential direction will decelerate gas phase and the upward axial force will prevent gas phase from flowing downward in the near wall region. The intensive particle–wall collision regions mainly locate in the wall opposite to the cyclone inlet and the cone wall. Moreover, as the solid loading ratio increases, number of turns travelled by solids in a cyclone decreases especially in the apex region of the cyclone while the width of solid strands increases, the pressure drop and tangential velocity decrease, the high axial velocity region moves upwards, and the radial flow of gas phase is significantly dampened.     

Discrete element simulation of a flat-bottomed spouted bed in the 3-D cylindrical coordinate system

A spouted bed is simulated in three dimensions by a discrete element method (DEM) in a cylindrical coordinate system. The numerical scheme is based on a second order finite difference method in space and a second order Adams-Bashforth method for time advancement. Gas-particle interaction is assumed to obey the Ergun equation (for void fraction less than 0.8) and its corrected model by Wen and Yu (for void fraction greater than 0.8). The spouted bed vessel is a flat-bottomed cylinder in height and in diameter. The gas inlet diameter is . Three hundred thousand monosized spheres of diameter are used in the simulation. The typical characteristics of spouted beds, such as spout, annulus and fountain, are reproduced. Particle velocity profiles show good agreement with experimental results and self-similarity of the radial distribution of axial particle velocities is reported. Gas flow patterns are also studied and the effect a vortex ring fixed at the bottom of the vessel is investigated. The simulation is validated through comparisons with results reported in the literature.     

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.     

离散单元法及其在流态化领域的应用

经过三十余年的发展,离散单元法（discrete element method,DEM）已经发展成为一种广泛应用于过程工程领域中颗粒体系研究的数值方法,特别是将DEM与计算流体力学（computational fluid dynamics,CFD）相结合形成的CFD-DEM耦合方法,已经在流态化研究领域得到广泛应用。首先对DEM模型进行了综述,包括DEM模型的基本原理、颗粒形状模型、接触力模型、非接触力模型、流体作用力模型等;然后对CFD-DEM耦合方法及其在流态化领域的一些主要应用进行了介绍,包括在流化床、气力输送以及过程工程领域里的一些其他应用。最后对DEM模型以及CFD-DEM耦合方法的发展趋势进行了预测,希望能促进DEM方法的发展,并推动其在过程工程领域中的应用。     

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.     

Numerical simulation of reacting plane mixing layer by particle method

This paper proposes a two-dimensional particle method for a plane mixing layer with a single-step and irreversible chemical reaction. The vorticity and concentration fields are discretized into the vortex and concentration elements, respectively, and the behavior of the elements is calculated with the Lagrangian method. The reaction is estimated through the calculation for the time rate of change in the strength for concentration element. The method is applied to simulate the reactive plane mixing layer. The simulation demonstrates that the mixing and reaction phenomena caused by the large-scale eddies are successfully captured. It is also confirmed that the effects of the Damköhler number and stoichiometric ratio on the reaction are favorably analyzed by the method.     

Kinetic theory based CFD simulation of turbulent fluidization of FCC particles in a riser

The turbulent fluidization regime is characterized by the co-existence of a dense, bottom region and a dilute, top bed. A kinetic theory based CFD code with a drag corrected for clusters captured the basic features of this flow regime: the dilute and dense regions, high dispersion coefficients and a strong anisotropy. The computed energy spectrum captures the observed gravity wave and the Kolmogorov -5/3 law at high frequencies. The computed turbulent kinetic energy is close to the measurements for FCC particles. The CFD simulations compared reasonably well with the measured core-annular flow experiments at very high solid fluxes. The computed granular temperatures, solids pressures, FCC viscosities and frequencies of oscillations were close to measurements reported in the literature. The computations suggest that unlike for the flow of group B particles, the oscillations for the FCC particles in the center of the riser are primarily due to the oscillations of clusters and not due to oscillations of individual particles. Hence mixing is not on the level of individual particles.     

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.     

Numerical simulation of liquid transfer between particles

Liquid transfer between particles plays a central role in the operation of a variety of particle processing equipment, including flotation, spray-coating, flocculation, granulation, and drying. In each of these applications, the local liquid concentration within the bed dramatically affects the flow behavior of the system and can strongly impact performance. In this work, we introduce a dynamic liquid transfer model for use in discrete element modeling (DEM) of heterogeneous particle systems. We explicitly track moisture levels on individual particles and utilize an experimentally validated rule-set for liquid transfer upon forming/breaking contacts. As a test of this new model we present results from the simulation of a rotary drum spray-coating system, but expect that this liquid transfer-modified DEM is general and would be applicable to wide range of processing operations.     

Coupled CFD–DEM of particle-laden flows in a turning flow with a moving wall

The nature of the particle–solid interactions and particle–fluid interactions in rectangular duct bend geometry with/without a moving wall is studied, taking into account particle collision, colloidal, and hydrodynamic forces, and four way coupling between the fluid flow and particles. The focus is on systems where particles and fluid phase have similar length scales, fluid Reynolds number (Re_f) ∼ 1, and particle's Stokes number (St) ∼ 1. Particles move toward the walls of the channel near the bend, and have long residence times in these regions. Buoyancy force has negligible effect on particle motion, where adhesion and drag forces lead to particle motion and agglomeration patterns. The effect of a free surface on agglomeration sites in the turning flow is elucidated.     

Discrete element simulation of particle flow in arbitrarily complex geometries

Conventional simulations of dense particle flows in complex geometries usually involve the use of glued particles to approximate geometric surface. This study is concerned with the development of a robust and accurate algorithm for detecting the interaction between a spherical particle and an arbitrarily complex geometric surface in the framework of soft-sphere discrete element model (DEM) without introducing any assumptions. Numerical experiments specially designed to validate the algorithm shows that the new algorithm can accurately predict the contact state of a particle with a complex geometric surface. Based on the proposed algorithm, a new solver for simulation of dense particle flows is developed and implemented into an open source computational fluid dynamics (CFD) software package OpenFOAM. The solver is firstly employed to simulate hydrodynamics in a bubble fluidized bed. Numerical results show that a 3D simulation can predict the bubble size better than a 2D simulation. Subsequently, gas–solid hydrodynamics in an immersed tube fluidized bed is simulated. Results show that bubble coalescence and breakup behavior around the immersed tubes are well captured by the numerical model. In addition, seven different particle flow patterns around the immersed tubes are identified based on the numerical results obtained.     

Computation of gas and solid dispersion coefficients in turbulent risers and bubbling beds

A literature review shows that dispersion coefficients in fluidized beds differ by more than five orders of magnitude. To understand the phenomena, two types of hydrodynamics models that compute turbulent and bubbling behavior were used to estimate radial and axial gas and solid dispersion coefficients. The autocorrelation technique was used to compute the dispersion coefficients from the respective computed turbulent gas and particle velocities.The computations show that the gas and the solid dispersion coefficients are close to each other in agreement with measurements. The simulations show that the radial dispersion coefficients in the riser are two to three orders of magnitude lower than the axial dispersion coefficients, but less than an order of magnitude lower for the bubbling bed at atmospheric pressure. The dispersion coefficients for the bubbling bed at 25 atm are much higher than at atmospheric pressure due to the high bed expansion with smaller bubbles.The computed dispersion coefficients are in reasonable agreement with the experimental measurements reported over the last half century.