DEM simulation of particle percolation in a packed bed

The phenomenon of spontaneous particle percolation under gravity is investigated by means of the discrete element method. Percolation behaviors such as percolation velocity, residence time distribution and radial dispersion are examined under various conditions. It is shown that the vertical velocity of a percolating particle moving down through a packing of larger particles decreases with increasing the restitution coefficient between particles and diameter ratio of the percolating to packing particles. With the increase of the restitution coefficient, the residence time and radial dispersion of the percolating particles increase. The packing height affects the residence time and radial dispersion. But, the effect can be eliminated in the analysis of the residence time and radial dispersion when they are normalized by the average residence time and the product of the packing height and packing particle diameter, respectively. In addition, the percolation velocity is shown to be related to the vertical acceleration of the percolating particle when an extra constant vertical force is applied. Increasing the feeding rate of percolating particles decreases the dispersion coefficient.     

回转窑多粒径颗粒流动与偏析的DEM模拟与实验研究

为明晰回转窑内颗粒的运动行为及偏析机理,以绿豆、黄豆和黑豆为颗粒介质,依次对3种装填顺序下的颗粒流动过程进行离散元模拟与实验研究,以颗粒质量分数和平均粒度为判据,对颗粒偏析进行评价。结果表明,回转窑内颗粒流动区可分为自由滚落区、渗流呆滞区以及窑壁携带区,自由滚落区颗粒流速最大,而渗流呆滞区流速最小。窑内颗粒沿轴向输运过程发生径向偏析,形成夹层结构,小颗粒受渗流作用在渗流呆滞区中心形成内核,大粒径和中等粒径颗粒集中在自由滚落区和窑壁携带区。窑内颗粒力链分布不均匀,强力链分布于近窑壁区,弱力链分布于自由滚落区和渗流呆滞区,且渗流呆滞区力链细而密集。当窑头附近不同粒径颗粒存在轴向速度差时,颗粒在轴向发生掺混,并产生径向偏析。     

颗粒毛细效应影响因素的离散元分析

颗粒毛细效应是指将一根细管插入填充有颗粒物质的容器中并对管施加竖直振动时颗粒在管内上升并最终达到一个稳定的高度的现象,该现象为颗粒物料的逆重力输运提供了一种潜在的技术途径.为探究颗粒毛细效应的影响因素,采用离散元方法,模拟再现了颗粒毛细效应过程,展示了不同管径下颗粒竖直方向速度演变特性,考察了不同容器宽度和振动条件下颗粒最终毛细上升高度随管径的演变规律.结果表明,在容器宽度与粒径比为40、管振幅与粒径比为14.33、管振动频率为12 Hz情况下,管径与粒径比D/d=3.33时,管内颗粒堵塞严重,使得颗粒上升缓慢,并造成颗粒柱中断; D/d=8.33时,起初毛细上升高度增加迅速,随后毛细上升高度的增大逐渐减缓,管内颗粒在管径方向几乎不存在速度梯度; D/d=15时,随着颗粒毛细上升高度的增大,管内颗粒柱分离为速度截然不同的两层,上层颗粒在管径方向几乎不存在速度梯度,而下层颗粒存在明显的速度梯度.研究还发现,在毛细效应能够发生的管径范围内,存在一个对应于颗粒最终毛细上升高度最大值的临界管径,当管径小于临界管径时,颗粒最终毛细上升高度随管径的增大而增大,当管径大于临界管径时,颗粒最终毛细上升...     

Onset velocity of circulating fluidization and particle residence time distribution:A CFD-DEM study

Until now,the onset velocity of circulating fluidization in liquid-solid fluidized beds has been defined by the turning point of the time required to empty a bed of particles as a function of the superficial liquid velocity,and is reported to be only dependent on the liquid and particle properties.This study presents a new approach to calculate the onset velocity using CFD-DEM simulation of the particle residence time distribution(RTD).The onset velocity is identified from the intersection of the fitted lines of the particle mean residence time as a function of superficial liquid velocity.Our results are in reasonable agreement with experimental data.The simulation indicates that the onset velocity is influenced by the density and size of particles and weakly affected by riser height and diameter.A power-law function is proposed to correlate the mean particle residence time with the superficial liquid velocity.The collisional parameters have a minor effect on the mean residence time of particles and the onset velocity,but influence the particle RTD,showing some humps and trailing.The particle RTD is found to be related to the particle trajectories,which may indicate the complex flow structure and underlying mechanisms of the particle RTD.     

Onset velocity of circulating fluidization and particle residence time distribution: A CFD–DEM study

Until now, the onset velocity of circulating fluidization in liquid–solid fluidized beds has been defined by the turning point of the time required to empty a bed of particles as a function of the superficial liquid velocity, and is reported to be only dependent on the liquid and particle properties. This study presents a new approach to calculate the onset velocity using CFD–DEM simulation of the particle residence time distribution (RTD). The onset velocity is identified from the intersection of the fitted lines of the particle mean residence time as a function of superficial liquid velocity. Our results are in reasonable agreement with experimental data. The simulation indicates that the onset velocity is influenced by the density and size of particles and weakly affected by riser height and diameter. A power-law function is proposed to correlate the mean particle residence time with the superficial liquid velocity. The collisional parameters have a minor effect on the mean residence time of particles and the onset velocity, but influence the particle RTD, showing some humps and trailing. The particle RTD is found to be related to the particle trajectories, which may indicate the complex flow structure and underlying mechanisms of the particle RTD.     

竖直振动管中颗粒毛细效应的离散元模拟

将一根细管插入填充有颗粒的静止容器中并对管施加竖直振动,颗粒将在管内发生上升运动,并最终稳定在一定高度,这一现象与液体毛细效应类似,被称为颗粒毛细效应.为探究颗粒毛细效应过程中伴随的颗粒尺度动力学行为及机理,基于离散元方法建立颗粒运动模型,对颗粒毛细效应动力学过程和特性开展数值模拟研究.模拟再现了文献中实验得到的颗粒毛细效应全过程,给出了管内颗粒柱高度随时间的演变规律,结果表明,受到颗粒系统参数的影响,本模拟条件下颗粒毛细效应过程呈现单周期上升、倍周期上升和倍周期稳定三个阶段,在倍周期上升阶段颗粒柱上升速度逐渐减小,平缓过渡到稳定阶段.在此基础上,分析了管内颗粒速度场和填充率分布随时间的演变特性,揭示了颗粒毛细效应过程中由容器传输到管内的颗粒的占比分布.研究发现,管内不同高度位置颗粒的运动并不同步,随着管的振动,管内出现速度波,速度波的传播引起管内颗粒出现膨胀和压缩交替的情况,从而管内颗粒填充率随时间发生周期性波动;在上升阶段,越接近管壁由容器传输到管内的颗粒占比越大,在稳定阶段,管内上层颗粒的对流引起容器传输到管内的颗粒占比发生反转.      

FLOW BEHAVIOR AND MASS TRANSFER IN THREE-PHASE EXTERNAL-LOOP AIRLIFT REACTORS WITH LARGE PARTICLES

The flow behavior and mass transfer in a three-phase external-loop airlift reactor can be improved by adding large particles. The mass transfer and liquid dispersion behavior for a three-phase external-loop reactor with large particles are studied in terms of the effect of the diameter and loading of the large particles on the liquid dispersion coefficient and mass transfer coefficient, The results showed that increasing the diameter or loading of the large particles tend to decrease dispersion and intensify mass transfer, and that an increase in the diameter of the large particles remarkably decreases the particle loop rate, while the effect of fine particles is much less notable.     

FLOW BEHAVIOR AND MASS TRANSFER IN THREE-PHASE EXTERNAL-LOOP AIRLIFT REACTORS WITH LARGE PARTICLES

The flow behavior and mass transfer in a three-phase external-loop airlift reactor can be improved by adding large particles. The mass transfer and liquid dispersion behavior for a three-phase external-loop reactor with large particles are studied in terms of the effect of the diameter and loading of the large particles on the liquid dispersion coefficient and mass transfer coefficient. The results showed that increasing the diameter or loading of the large particles tend to decrease dispersion and intensify mass transfer, and that an increase in the diameter of the large particles remarkably decreases the particle loop rate, while the effect of fine particles is much less notable.     

飞行加速度对发动机内粒子轨迹影响研究

利用Euler-Lagrange模型方程，对发动机内的三维两相流动进行了数值模拟，分析了不同过载组合、不同粒子直径、不同壁面恢复系数对发动机燃烧室内粒子的聚集部位、浓度分布、冲刷速度、冲刷角度等的影响。计算结果表明：在纵向和横向过载相等的情形下，粒子的最大聚集密度随过载量的增加，呈先减小后增加的趋势，最大聚集点随过载量的增加向流动方向移动，过载量的大小对粒子的冲刷角度、冲刷速度影响较大；在相同工况下，随粒子直径的增加，最大聚集部位向流动方向移动，最大聚集密度增加；随粒子壁面恢复系数恢复得减小，最大聚集部位向发动机头部移动，最大聚集密度增加。     

Characterization of particle-laden, confined swirling flows by phase-doppler anemometry and numerical calculation

The particle dispersion characteristics in a confined swirling flow with a swirl number of approx. 0.5 were studied in detail by performing measurements using phase-Doppler anemometry (PDA) and numerical predictions. A mixture of gas and particles was injected without swirl into the test section, while the swirling airstream was provided through a co-flowing annular inlet. Two cases with different primary jet exit velocities were considered. For these flow conditions, a closed central recirculation bubble was established just downstream of the inlet.

The PDA measurements allowed the correlation between particle size and velocity to be obtained and also the spatial change in the particle size distribution throughout the flow field. For these results, the behaviour of different size classes in the entire particle size spectrum, ranging from about 15 to 80 μm, could be studied, and the response of the particles to the mean flow and the gas turbulence could be characterized. Due to the response characteristics of particles with different diameters to the mean flow and the flow turbulence, a considerable separation of the particles was observed which resulted in a streamwise increase in the particle mean number diameter in the core region of the central recirculation bubble. For the lower particle inlet velocity (i.e. low primary jet exit velocity), this effect is more pronounced, since here the particles have more time to respond to the flow reversal and the swirl velocity component. This also gave a higher mass of recirculating particle material.

The numerical predictions of the gas flow were performed by solving the time-averaged Navier-Stokes equations in connection with the well known kε turbulence model. Although this turbulence model is based on the assumption of isotropic turbulence, the agreement of the calculated mean velocity profiles compared to the measured gas velocities is very good. The gas-phase turbulent kinetic energy, however, is considerably underpredicted in the initial mixing region. The particle dispersion characteristics were calculated by using the Lagrangian approach, where the influence of the particulate phase on the gas flow could be neglected, since only very low mass loadings were considered. The calculated results for the particle mean velocity and the mass flux are also in good agreement with the experiments. Furthermore, the change in the particle mean diameter throughout the flow field was predicted approximately, which shows that the applied simple stochastic dispersion model also gives good results for such very complex flows. The variation of the gas and particle velocity in the primary inlet had a considerable impact on the particle dispersion behaviour in the swirling flow and the particle residence time in the central recirculation bubble, which could be determined from the numerical calculations. For the lower particle inlet velocity, the maximum particle size-dependence residence time within the recirculation region was considerably shifted towards larger particles.     

Particle dynamics calculations of wall stresses and slip velocities for couette flow of smooth inelastic spheres

The objective of this work is to characterize the effects of boundary geometry on the flow of dry granular materials composed of smooth, inelastic spheres between parallel, bumpy walls in the absence of gravity. Particle dynamic simulations are done in which wall stresses and slip velocities are computed over a wide range of parameters, including shear gap height, geometry of the wall particles, wall to free particle diameter ratio, and normal restitution coefficient. Calculated wall stresses and slip velocities are found to be highly sensitive to boundary roughness, which is characterized in terms of the mean spacing value for the wall particles. Most noticeable is a pronounced stress drop for dense flows with an associated large slip velocity in a system having a narrow shear gap height.     

Shear wave velocity in sand considering the effects of frequency based on particle contact theory

Since the shear waves involved in in-situ and laboratory measurement methods vary significantly in terms of the frequency range, it is necessary to consider the effects of frequency on the shear wave velocity. In this study, sand particles are assumed to be spherical solid particles with an equal radius and identical material properties, and sand skeletons are regarded as granular aggregations generated through the random packing of sand particles. It is also assumed that the sand particles only undergo elastic deformation during shear wave propagation. Based on a spherical particle model, a formula is obtained for calculating the shear wave velocity in sand, with the shear wave frequency as an extra influencing parameter. The quantitative calculations demonstrate that the shear wave velocity decreases with an increase of sand porosity, and accelerates with increases of vertical effective stress and elastic modulus of the sand particles. It is also indicated that both the particle density and Poisson’s ratio of the sand particles have negligible effects on the shear wave propagation. The frequency dispersion characteristics of shear wave propagating in sand are also discussed. Moreover, the critical frequency is defined and its analytical expression is derived. The calculation results obtained using the proposed equations agree well with the in-situ measurement results and bender element test data.     

Stochastic simulations of particle-laden isotropic turbulent flow

Numerical simulations are performed of dispersion and polydispersity of particles in isotropic incompressible turbulence. The mass loading of the particles is assumed to be small; thus the effects of particles on turbulence is neglected (one-way coupling). A stochastic model is employed to simulate the carrier phase. The results of the simulations are compared with direct numerical simulation (DNS) data and theoretical results. The stochastic model predicts most of the trends as portrayed by DNS and theory. However, the continuity effect associated with the crossing trajectories effect is not captured. Also, the peaking in the variation of the particle asymptotic diffusivity coefficient with the particle time constant is not observed. For evaporating particles, the stochastic model predicts thinner probability density functions (pdfs) for the particle diameter as compared with DNS generated pdfs. The model is implemented to investigate the effects of gravity on evaporation. It is shown that the depletion rate increases with increase of the drift velocity at short and intermediate times, but an opposite trend is observed at long times. The standard deviation and skewness of the particle diameter indicate peak values in their variations with the drift velocity. Dispersion of evaporating particles decreases with respect to that of non-evaporating particles at small drift velocities; an opposite trend is observed at large drift velocities. The effects of the initial evaporation rate and the particle Schmidt number on the evaporation in the gravity environment are also studied.     

Evaluation of stochastic particle dispersion modeling in turbulent round jets

ODT (one-dimensional turbulence) simulations of particle-carrier gas interactions are performed in the jet flow configuration. Particles with different diameters are injected onto the centerline of a turbulent air jet. The particles are passive and do not impact the fluid phase. Their radial dispersion and axial velocities are obtained as functions of axial position. The time and length scales of the jet are varied through control of the jet exit velocity and nozzle diameter. Dispersion data at long times of flight for the nozzle diameter (7 mm), particle diameters (60 and 90 µm), and Reynolds numbers (10, 000–30, 000) are analyzed to obtain the Lagrangian particle dispersivity. Flow statistics of the ODT particle model are compared to experimental measurements. It is shown that the particle tracking method is capable of yielding Lagrangian prediction of the dispersive transport of particles in a round jet. In this paper, three particle-eddy interaction models (Type-I, -C, and -IC) are presented to examine the details of particle dispersion and particle-eddy interaction in jet flow.     

Application of DEM modified with enlarged particle model to simulation of bead motion in a bead mill

We applied the discrete element method （DEM） of simulation modified by an enlarged particle model to simulate bead motion in a large bead mill. The stainless-steel bead mill has inner diameter of 102 mm and mill length of 198 mm. The bead diameter and filling ratio were fixed respectively at 0.5 mm and 85%. The agitator rotational speed was changed from 1863 to 3261 rpm. The bead motion was monitored experimentally using a high-speed video camera through a transparent mill body. For the simulation, enlarged particle sizes were set as 3-6 mm in diameter. With the DEM modified by the enlarged particle model, the motion of enlarged particles in a mill was simulated.The velocity data of the simulated enlarged particles were compared with those obtained in the experiment. The simulated velocity of the enlarged particles depends on the virtual frictional coefficient in the DEM model. The optimized value of the virtual frictional coefficient can be determined by considering the accumulated mean value. Results show that the velocity of the enlarged particles simulated increases with an increase in the optimum virtual frictional coefficient, but the simulated velocity agrees well with that determined experimentally by optimizing the virtual frictional coefficient in the simulation. The computing time in the simulation decreases with increased particle size.     

粗糙颗粒动理学及稠密气固两相流动的数值模拟

考虑颗粒碰撞过程中摩擦作用,给出了粗糙颗粒碰撞动力学.引入颗粒相拟总温来表征颗粒平动和转动脉动能量的特征.基于气体分子运动论,建立颗粒碰撞中平动和旋转共同作用的粗糙颗粒动理学,给出了颗粒相压力和黏度等输运参数计算模型.运用基于颗粒动理学的欧拉-欧拉气固两相流模型,数值模拟了流化床内气体颗粒两相流动特性,分析了颗粒旋转流动对颗粒碰撞能量交换和耗散的影响.模拟得到的流化床内径向颗粒浓度和提升管内颗粒轴向速度与他人实验结果相吻合.模拟结果表明随着颗粒浓度的增加,颗粒相压力和能量耗散逐渐增加,而颗粒拟总温先增加后下降.随着颗粒粗糙度系数的增加,床内平均颗粒相拟总温和能量耗散增加,表明颗粒旋转产生的摩擦将导致颗粒旋转脉动能量的改变,影响床内气体-颗粒两相宏观流动特性.      

离散颗粒流动堆积行为离散元模拟及实验研究

工程应用中存在许多颗粒流动堆积问题.首先设计了一系列测量方法,通过大量的实验和统计分析,得到了颗粒的多种物理参数.并以工程中高炉炉顶称量料罐为背景,采用离散元方法模拟不同物理条件下离散颗粒的流动堆积行为,得出料罐内颗粒系统中颗粒之间力的分布不均匀,而且强力链分布主要与料罐的左下壁方向平行.同时,设计并制作了具有多参数调节的离散颗粒料罐实验模型,进行了相应的物理实验,实测结果与数值模拟吻合良好.     

Application of DEM modified with enlarged particle model to simulation of bead motion in a bead mill

We applied the discrete element method (DEM) of simulation modified by an enlarged particle model to simulate bead motion in a large bead mill. The stainless-steel bead mill has inner diameter of 102 mm and mill length of 198 mm. The bead diameter and filling ratio were fixed respectively at 0.5 mm and 85%. The agitator rotational speed was changed from 1863 to 3261 rpm. The bead motion was monitored experimentally using a high-speed video camera through a transparent mill body. For the simulation, enlarged particle sizes were set as 3–6 mm in diameter. With the DEM modified by the enlarged particle model, the motion of enlarged particles in a mill was simulated. The velocity data of the simulated enlarged particles were compared with those obtained in the experiment. The simulated velocity of the enlarged particles depends on the virtual frictional coefficient in the DEM model. The optimized value of the virtual frictional coefficient can be determined by considering the accumulated mean value. Results show that the velocity of the enlarged particles simulated increases with an increase in the optimum virtual frictional coefficient, but the simulated velocity agrees well with that determined experimentally by optimizing the virtual frictional coefficient in the simulation. The computing time in the simulation decreases with increased particle size.     

颗粒物质在竖直管中下行蠕动流动的实验测量

颗粒流蠕动行为是颗粒物质在竖直管中流动时常见的一种流动现象,其产生机理较复杂。为此,本文在在内径为150mm、高为5000mm的竖直管实验装置上,以FCC催化剂为固体颗粒物料,采用PV6型颗粒速度测量仪,测量不同颗粒流率下竖直管中的颗粒下行蠕动流动速度以及颗粒固含率,系统地考察了颗粒物质在竖直管中下行流动时的蠕动流动特性及产生机理。实验结果表明,颗粒物质在竖直管中下行流动时的流动行为可划分为两种形式。在颗粒流率较小时,颗粒物质下行速度呈现脉冲式变化,有速度停滞,可称之为蠕动I型流动。随着颗粒流率的增加,颗粒下行速度停顿消失,但仍是起伏变化,为蠕动II型流动。当颗粒流率增大到一定值后,颗粒物质下行蠕动行为消失,转变为流化流动。颗粒物质下行的蠕动行为是出口区颗粒成拱与崩塌、颗粒与器壁滑动摩擦和颗粒力链作用的综合反映。     

Impact of a bead on a rotating wall

We study experimentally the impact of a plastic bead on a rotating wall made of steel (velocity Ω; radial position x₀). The results show that the restitution coefficient is directly function of the impact velocity x₀Ω and is invariant by changing frame reference. The influence of the height of release of the particle on its angular velocity after impact is also studied. We observe an increase of the angular velocity with height followed by a saturation. We propose an interpretation for this evolution considering that the particle may roll without sliding during all the impact. This physical feature is not always taken into account in existing models of impact between rigid bodies. To cite this article: F. Rioual et al., C. R. Mecanique 336 (2008).