Effect of drum structure on particle mixing behavior based on DEM method

The optimization of the drum structure is beneficial to improve the particle motion and mixing in rotary drums. In this work, two kinds of drum structures, Lacy cylinder drum (LC) and Lacy-lifters cylinder drum (LLC), are developed on the basic of cylinder drum to enhance the heat transfer area. The particle motion and mixing process are simulated by DEM method. Based on the grid independence and model validation, the contact number between particles and wall, particle velocity profile, thickness of active layer, particle exchange coefficient, particle concentration profile and mixing index are demonstrated. The influences of the drum structure and the operation parameters are further evaluated. The results show that the contact number between particles and wall is improved in LC and LLC compared to cylinder drum. The particle velocity in LC is higher than that in cylinder drum at high rotating speed, and the particle velocity of the particle falling region is significantly improved in LLC. Compared to cylinder drum and LC, the thickness of active layer in LLC is smaller, while the local particle mixing quality is proved to be the best in the active region. In addition, the particle exchange coefficients between static region and active region in the three drums are compared and LLC is found tending to weaken the particle flow. Besides, the fluctuations of particle concentration in the active region, static region, and boundary region are weakened in LLC, and the equilibrium state is reached earlier. In addition, the overall particle mixing performance in cylinder drum, LC and LLC is analyzed. The particle mixing performance in cylinder drum is the worst, while the difference in mixing quality of LC and LLC depends on the operation conditions.     

Cataracting-centrifuging transition investigation using nonspherical and spherical particles in a rotary drum through CFD simulations

This paper aims to systematically investigate the cataracting-centrifuging transition in a rotary drum involving spherical and nonspherical particles by using the Multiphase Granular Eulerian Model (MGEM). The effects of drum length and particle shape on the cataracting-centrifuging transition behavior were analyzed. The results showed that drum length plays an important role in the cataracting-centrifuging transition, although most related works in the literature do not consider this. The particle shape also significantly affects the cataracting-centrifuging transition behavior. Nonspherical particles required lower rotation speeds than spherical particles to reach the centrifuging condition. The particle shape was shown to be related to the critical solid fraction (α_sc) from Schaeffer’s model, although further investigations are required to completely correlate particle spherecity with critical solid volume fractions.     

An investigation into flow mode transition and pressure fluctuations for fluidized dense-phase pneumatic conveying of fine powders

This paper presents the results of an ongoing investigation into the fluctuations of pressure signals due to solids–gas flows for dense-phase pneumatic conveying of fine powders. Pressure signals were obtained from pressure transducers installed along different locations of a pipeline for the fluidized dense-phase pneumatic conveying of fly ash (median particle diameter 30 μm; particle density 2300 kg/m³; loose-poured bulk density 700 kg/m³) and white powder (median particle diameter 55 μm; particle density 1600 kg/m³; loose-poured bulk density 620 kg/m³) from dilute to fluidized dense-phase. Standard deviation and Shannon entropy were employed to investigate the pressure signal fluctuations. It was found that there is an increase in the values of Shannon entropy and standard deviation for both of the products along the flow direction through the straight pipe sections. However, both the Shannon entropy and standard deviation values tend to decrease after the flow through bend(s). This result could be attributed to the deceleration of particles while flowing through the bends, resulting in dampened particle fluctuation and turbulence. Lower values of Shannon entropy in the early parts of the pipeline could be due to the non-suspension nature of flow (dense-phase), i.e., there is a higher probability that the particles are concentrated toward the bottom of pipe, compared with dilute-phase or suspension flow (high velocity), where the particles could be expected to be distributed homogenously throughout the pipe bore (as the flow is in suspension). Changes in straight-pipe pneumatic conveying characteristics along the flow direction also indicate a change in the flow regime along the flow.     

DEM investigation of mixing indices in a ribbon mixer

Mixing index is an important parameter to understand and assess the mixing state in various mixers including ribbon mixers, the typical food processing devices. Many mixing indices based on either sample variance methods or non-sample variance methods have been proposed and used in the past, however, they were not well compared in the literature to evaluate their accuracy of assessing the final mixing state. In this study, discrete element method (DEM) modelling is used to investigate and compare the accuracy of these mixing indices for mixing of uniform particles in a horizontal cylindrical ribbon mixer. The sample variance methods for mixing indices are first compared both at particle- and macro-scale levels. In addition, non-sample variance methods, namely entropy and non-sampling indices are compared against the results from the sample variance methods. The simulation results indicate that, among the indices considered in this study, Lacey index shows the most accurate results. The Lacey index is regarded to be the most suitable mixing index to evaluate the steady-state mixing state of the ribbon mixer in the real-time (or without stopping the impeller) at both the particle- and macro-scale levels. The study is useful for the selection of a proper mixing index for a specific mixture in a given mixer.     

回转筒内沙石物料混合均匀性的数值模拟

采用离散单元法对回转筒内沙石物料的混合均匀性进行数值模拟研究,并选取回转筒转速、直径、提升条个数和石子填充率作为影响因素,分别设立3个水平,进行回转筒内物料混合的正交模拟,旨在对各因素的敏感性影响程度进行分析。基于试验结果选择物料混合时间和颗粒接触数率作为试验指标,对四个因素进行极差分析和方差分析。结果表明,回转筒转速、直径和石子填充率对物料混合时间的影响显著,提升条个数对混合时间的影响不显著;石子填充率、回转筒转速和提升条个数对物料混合后颗粒接触数率的影响显著,回转筒直径对物料混合后颗粒接触数率的影响不显著。     

Impulsive motion of a suspension: Effect of antisymmetric stresses and particle rotation

A two-phase continuum theory (two-fluid model) for a suspension of rigid spherical particles in a Newtonian fluid is applied to investigate theoretically the flow induced by impulsive motion of an infinite flat plate. Consideration of rotational intertia of the particles gives rise to an antisymmetric part of the volume averaged stress tensor of the continuous phase. The influence of particle rotation and of antisymmetric stresses of the continuous phase, which depend on the relative rotational motion between the particles and the ambient fluid, on the motion of each phase and on the skin friction is examined.Approximate solutions to the equations, corresponding to the physical situation of large and small particle slip, are obtained by power series expansions for small and large times.     

Using the discrete element method to assess the mixing of polydisperse solid particles in a rotary drum

Despite the wide applications of powder and solid mixing in industry, knowledge on the mixing of polydisperse solid particles in rotary drum blenders is lacking. This study investigates the mixing of monodisperse, bidisperse, tridisperse, and polydisperse solid particles in a rotary drum using the discrete element method. To validate the model developed in this study, experimental and simulation results were compared. The validated model was then employed to investigate the effects of the drum rotational speed, particle size, and initial loading method on the mixing quality. The degree of mixing of polydisperse particles was smaller than that for monodisperse particles owing to the segregation phenomenon. The mixing index increased from an initial value to a maximum and decreased slightly before reaching a plateau for bidisperse, tridisperse, and polydisperse particles as a direct result of the segregation of particles of different sizes. Final mixing indices were higher for polydisperse particles than for tridisperse and bidisperse particles. Additionally, segregation was weakened by introducing additional particles of intermediate size. The best mixing of bidisperse and tridisperse particles was achieved for top–bottom smaller-to-larger initial loading, while that of polydisperse systems was achieved using top–bottom smaller-to-larger and top–bottom larger-to-smaller initial loading methods.     

不同形状混合器中二元颗粒的分聚与混合研究

采用实验、模拟及理论的分析方法, 研究了在圆形混合器、椭圆形混合器、正方形混合器中, 不同转速和填充率条件下, 容器形状对二元颗粒体系分聚与混合的影响. 实验中通过改变转速与填充率, 可获得不同的颗粒分聚与混合图样, 对示踪颗粒运动轨迹的分析发现, 在圆形混合器中, 随着混合器转速的增大, 颗粒在径向的随机性减少;在正方形混合器中, 随着混合器转速的增大, 颗粒在径向的随机性增大.模拟结果发现颗粒流动分为两个区域, 在表面的快速流动和在整体的旋转运动. 通过理论分析发现颗粒分聚在圆形混合器中最明显, 在正方形混合器中最弱, 椭圆形混合器介于二者之间.      

2D DEM simulation of particle mixing in rotating drum:A parametric study

Mixing behaviors of equal-sized glass beads in a rotating drum were investigated by both DEM simulations and experiments. The experiments indicated that higher rotation speed can significantly enhance mixing. The particle profiles predicted by 2D DEM simulation were compared with the experimental results from a quasi-2D drum, showing inconsistency due to reduction of contacts in the single-layer 2D simulation which makes the driving friction weaker than that in the quasi-2D test, better results could be rea...     

The effect of side walls on particles mixing in rotating drums

In this paper, we study the effects of the presence and shape of side walls and of the overall length of rotating cylindrical drums on the mixing of particles with differing sizes by application of the discrete element method (DEM). By varying the semi-axis of the spheroidally shaped side walls and the length of the overall drum, we observe the formation of circulation patterns near the side walls. Although there is a vast amount of literature studying mixing regimes in rotating drums, little is known about the effect of the side walls of the drum on particle mixing. The results of our study demonstrate that introducing curved side walls induces a strong circulation pattern near these side walls, but has, paradoxically, a negative impact on mixing and actually promotes segregation. The cause for this segregation is the difference in velocity of differently sized particles near the curved side walls. Large particles accumulate at the curved side walls, whereas small particles move away from the curved side walls. When the length of the drum is increased, the overall effect of the side walls is decreased, although it does remain observable, even in very large drums.     

基于离散单元法和人工神经网络的近壁颗粒动力学特征研究

颗粒与壁面的相互作用往往对颗粒流动具有显著影响. 为研究颗粒与壁面作用机理, 对滚筒内颗粒流动过程进行离散单元法(DEM)数值模拟. 基于模拟结果统计分析靠近壁面处颗粒的运动特征, 结果表明, 小摩擦系数时颗粒平动和旋转速度均近似满足正态分布, 但由于壁面影响, 摩擦系数增大时颗粒沿滚筒轴向的旋转速度偏离正态分布, 颗粒动力学理论推导壁面边界条件时应考虑速度正态分布的修正及速度脉动的各向异性. 采用人工神经网络(ANN)构建了颗粒无因次旋转温度、滑移速度和平动温度之间的函数模型, 进而可以在常规双流模型壁面边界条件中考虑颗粒旋转的影响. 基于DEM模拟及结果分析可以为壁面边界条件的理论构造和半经验修正提供基础数据和封闭模型.      

Computational fluid dynamics simulations of aerosol behavior in a high-speed (Heubach) rotating drum dustiness tester

Potential exposure from hazardous dust may be assessed by evaluating the dustiness of the powders being handled. Dustiness is the tendency of a powder to aerosolize with a given input of energy. Previously we used computational fluid dynamics (CFD) to numerically investigate the flow inside the European Standard (EN15051) rotating drum dustiness tester during its operation. The present work extends those CFD studies to the widely used Heubach rotating drum. Air flow characteristics are investigated within the Abe-Kondoh-Nagano k-epsilon turbulence model; the aerosol is incorporated via a Euler-Lagrangian multiphase approach. The air flow inside these drums consists of a well-defined axial jet penetrating relatively quiescent air. The spreading of the Heubach jet results in a fraction of the jet recirculating as back-flow along the drum walls; at high rotation rates, the axial jet becomes unstable. This flow behavior qualitatively differs from the stable EN15051 flow pattern. The aerodynamic instability promotes efficient mixing within the Heubach drum, resulting in higher particle capture efficiencies for particle sizes d < 80 μm.     

A solids mixing rate correlation for small scale fluidized beds

A new first degree solids mixing rate is proposed to evaluate the mixing of solids in small scale fluidized beds. Particle mixing experiments were carried out in a 2D fluidized bed with a cross-section of 0.02 m × 0.2 m and a height of 1 m. White and black particles with average diameters of 850 and 450 μm were used in our experiments. Image processing was used to measure the concentration of the tracers at different times. The effects of four representative operating parameters (superficial gas velocity, ratio of tracer particles to bed particles, tracer particle position, and particle size) on mixing are discussed with reference to the mixing index. We found that the Lacey index depends on the concentration of the tracers. The position of the tracers affects the initial mixing rate but not the final degree of mixing. However, the new mixing rate equation does not depend on the initial configuration of the particles because this situation is considered to be the initial condition. Using the data obtained in this work and that found in literature, an empirical correlation is proposed to evaluate the mixing rate constant as a function of dimensionless numbers (Archimedes, Reynolds, and Froude) in small scale fluidized beds. This correlation allows for an estimation of the mixing rate under different operating conditions and for the detection of the end point and/or the time of mixing.     

Modelling of gas–solid turbulent channel flow with non-spherical particles with large Stokes numbers

This paper describes a complete framework to predict the behaviour of interacting non-spherical particles with large Stokes numbers in a turbulent flow. A summary of the rigid body dynamics of particles and particle collisions is presented in the framework of Quaternions. A particle-rough wall interaction model to describe the collisions between non-spherical particles and a rough wall is put forward as well. The framework is coupled with a DNS-LES approach to simulate the behaviour of horizontal turbulent channel flow with 5 differently shaped particles: a sphere, two types of ellipsoids, a disc, and a fibre. The drag and lift forces and the torque on the particles are computed from correlations which are derived using true DNS.The simulation results show that non-spherical particles tend to locally maximise the drag force, by aligning their longest axis perpendicular to the local flow direction. This phenomenon is further explained by performing resolved direct numerical simulations of an ellipsoid in a flow. These simulations show that the high pressure region on the acute sides of a non-spherical particle result in a torque if an axis of the non-spherical particle is not aligned with the flow. This torque is only zero if the axis of the particle is perpendicular to the local direction of the flow. Moreover, the particle is most stable when the longest axis is aligned perpendicular to the flow.The alignment of the longest axis of a non-spherical particle perpendicular to the local flow leads to non-spherical particles having a larger average velocity compared to spherical particles with the same equivalent diameter. It is also shown that disc-shaped particles flow in a more steady trajectory compared to elongated particles, such as elongated ellipsoids and fibres. This is related to the magnitude of the pressure gradient on the acute side of the non-spherical particles. Finally, it is shown that the effect of wall roughness affects non-spherical particles differently than spherical particles. Particularly, a collision of a non-spherical particle with a rough wall induces a significant amount of rotational energy, whereas a corresponding collision with a spherical particle results in mostly a change in translational motion.     

Two-dimensional motion of a set of particles in a free surface flow with image processing

A method to analyze bed load with image processing was developed. The motion of coarse spherical particles on a mobile bed entrained by a shallow turbulent flow down a steep channel was filmed with a high-speed camera. The water free surface and the particle positions were detected combining classical image processing algorithms. We developed a particle-tracking algorithm to calculate all particle trajectories and motion regimes, rolling or saltation. At constant slope, the contribution of the rolling particles to the solid discharge only slightly differed when the particle supply was increased. At a slope of 10%, it represented about 40%. In contrast, rolling became the major regime when the slope increased, at a slope of 15% it represented up to 80% of the total solid discharge.Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

GPU-enhanced DEM analysis of flow behaviour of irregularly shaped particles in a full-scale twin screw granulator

During twin screw granulation (TSG), small particles, which generally have irregular shapes, agglomerate together to form larger granules with improved properties. However, how particle shape impacts the conveying characteristics during TSG is not explored nor well understood. In this study, a graphic processor units (GPUs) enhanced discrete element method (DEM) is adopted to examine the effect of particle shape on the conveying characteristics in a full scale twin screw granulator for the first time. It is found that TSG with spherical particles has the smallest particle retention number, mean residence time, and power consumption; while for TSG with hexagonal prism (Hexp) shaped particles the largest particle retention number is obtained, and TSG with cubic particles requires the highest power consumption. Furthermore, spherical particles exhibit a flow pattern closer to an ideal plug flow, while cubic particles present a flow pattern approaching a perfect mixing. It is demonstrated that the GPU-enhanced DEM is capable of simulating the complex TSG process in a full-scale twin screw granulator with non-spherical particles.     

Discrete element-embedded finite element model for simulation of soft particle motion and deformation

The motion and deformation of soft particles are commonly encountered and important in many applications. A discrete element-embedded finite element model (DEFEM) is proposed to solve soft particle motion and deformation, which combines discrete element and finite element methods. The collisional surface of soft particles is covered by several dynamical embedded discrete elements (EDEs) to model the collisional external forces of the particles. The particle deformation, motion, and rotation are independent of each other in the DEFEM. The deformation and internal forces are simulated using the finite element model, whereas the particle rotation and motion calculations are based on the discrete element model. By inheriting the advantages of existing coupling methods, the contact force and contact search between soft particles are improved with the aid of the EDE. Soft particle packing is simulated using the DEFEM for two cases: particle accumulation along a rectangular straight wall and a wall with an inclined angle. The large particle deformation in the lower layers can be simulated using current methods, where the deformed particle shape is either irregular in the marginal region or nearly hexagonal in the tightly packed central region. This method can also be used to simulate the deformation, motion, and heat transfer of non-spherical soft particles.     

Steady rotation of a composite sphere in a concentric spherical cavity

The problem of steady rotation of a compositesphere located at the centre of a spherical container has beeninvestigated.A composite particle referred to in this paperis a spherical solid core covered with a permeable sphericalshell.The Brinkman’s model for the flow inside the composite sphere and the Stokes equation for the flow in the spherical container were used to study the motion.The torque experienced by the porous spherical particle in the presence ofcavity is obtained.The wall correction factor is calculated.In the limiting cases,the analytical solution describing thetorque for a porous sphere and for a solid sphere in an unbounded medium are obtained from the present analysis.     

An analysis of the chaotic motion of particles of different sizes in a gas fluidized bed

The dynamic behavior of individual particles during the mixing/segregation process of particle mixtures in a gas fluidized bed is analyzed. The analysis is based on the results generated from discrete particle simulation, with the focus on the trajectory of and forces acting on individual particles.Typical particles are selected representing three kinds of particle motion:a flotsam particle which is initially at the bottom part of the bed and finally fluidized at the top part of the bed; a jetsam particle which is initially at the top part of the bed and finally stays in the bottom de-fluidized layer of the bed; and a jetsam particle which is intermittently joining the top fluidized and bottom de-fluidized layers. The results show that the motion of a particle is chaotic at macroscopic or global scale, but can be well explained at a microscopic scale in terms of its interaction forces and contact conditions with other particles, particle-fluid interaction force, and local flow structure. They also highlight the need for establishing a suitable method to link the information generated and modeled at different time and length scales.     

Slow Motion of an Assemblage of Porous Spherical Shells Relative to a Fluid

The body-force-driven motion of a homogeneous distribution of spherically symmetric porous shells in an incompressible Newtonian fluid and the fluid flow through a bed of these shell particles are investigated analytically. The effect of the hydrodynamic interaction among the porous shell particles is taken into account by employing a cell-model representation. In the limit of small Reynolds number, the Stokes and Brinkman equations are solved for the flow field around a single particle in a unit cell, and the drag force acting on the particle by the fluid is obtained in closed forms. For a suspension of porous spherical shells, the mobility of the particles decreases or the hydrodynamic interaction among the particles increases monotonically with a decrease in the permeability of the porous shells. The effect of particle interactions on the creeping motion of porous spherical shells relative to a fluid can be quite significant in some situations. In the limiting cases, the analytical solution describing the drag force or mobility for a suspension of porous spherical shells reduces to those for suspensions of impermeable solid spheres and of porous spheres. The particle-interaction behavior for a suspension of porous spherical shells with a relatively low permeability may be approximated by that of permeable spheres when the porous shells are sufficiently thick.