CFD simulation of particle segregation in a rotating drum. Part II: Effects of specularity coefficient

Segregation of binary particle mixture in a rotating drum is numerically studied using the Eulerian multiphase computational fluid dynamics (CFD) simulations coupling the solid phase kinetic theory of granular flow model. The corresponding solid kinetic viscosities of the two particulate phases are determined by the previous granular bed surface fitting (BSF) method. The effects of the specularity coefficients used in the simulations on the segregation patterns in the rotating drums are systematically studied by using the specularity coefficient values ranging from 0.15 to 1.0. When using a smaller specularity coefficient value in the simulation, the momentum transferring from the drum wall to the particulate phase is poorer, lowering the kinetic energy of the particulate phase. The lower particulate phase kinetic energy causes slower particle motion in the bed and hence delays the segregation core/band formation. At the same simulation time, the concentration of the smaller particles in the segregation core increases with the increasing of the specularity coefficient value used in the simulation. When the specularity coefficient values larger than 0.4 are used in our simulations, the realistic three-dimensional segregation structures are well predicted. A proper specularity coefficient value should be adopted in Eulerian multiphase CFD simulations of granular flows.     

Numerical studies of particle segregation in a rotating drum based on Eulerian continuum approach

Solid–solid–gas three-phase particle segregation in a half-filled rotating drum is simulated using Eulerian continuum approach coupling the kinetic theory of granular flow. A dynamic angle of repose fitting (DARF) method is proposed to determine granular kinetic viscosities of particles of six different sizes moving in the drum rotating at 10 rpm, 20 rpm or 30 rpm. The DARF granular kinetic viscosity increases and decreases with the increasing of particle size and drum rotational speed, respectively. The determined DARF granular viscosity values are used to simulate size-induced particle segregation in a rotating drum. The simulated small-particle-rich segregation structure shows a central small-particle-rich band together with two small-particle-rich side wings. The size of the wings decreases with the increasing of the drum rotational speed. The formation of radial segregation core and axial segregation bands qualitatively agree with the experimental observations.     

Segregation pattern of binary-size mixtures in a double-walled rotating drum

Size-induced granular segregation was performed systematically and experimentally in an almost fully filled double-walled rotating drum at 10 different rotation speeds and two different side wall types. The motion of the granular materials was recorded using a high-speed camera for image analysis of particle segregation development in the drum. With continual tracking of the particle movements, the velocity, fluctuations, and granular temperatures were measured. The experimental results indicate that both rotation speeds and friction coefficient of side walls significantly affect segregation phenomena in binary-size mixture granular flows. The results demonstrate similar situations to the Brazil-nut effect and its reverse in the radial direction at either high or a low rotational speed (where the Froude number (Fr) is far from 1). At these instances, the maximum granular temperature occurs near the side walls. Specifically, a double segregation effect (DSE) is found at Froude number (Fr) close to 1. These results can be used in many industrial processes, for example, size grading of materials, screening of impurities, and different structures of functionally graded materials. Moreover, the maximum granular temperature occurs in the middle of the ring space. It causes small particles to move toward both side walls as it pushes bigger particles to accumulate in the middle of the ring space of rotating drum.     

Segregation behavior of particles with Gaussian distributions in the rotating drum with rolling regime

The mixing and segregation of granular materials are essential to provide valuable insights and references for practical industrial production. In this paper, the segregation behaviors of particles with Gaussian distributions and 40% filling level in the rotating drum with rolling regime were numerically studied by the discrete element method. The effects of rotation speed and particle size parameter λ (size ratio of the largest versus smallest particles) on the segregation behavior (mixing index, segregation rate), flow characteristics (particle velocity and trajectory, gyration degree and radius, particle size distributions) and the microscopic properties (collision, contact force, axial diffusion, and kinetic energy) of granular systems were systematically investigated. The results show that the segregation rate and degree of particles with Gaussian distributions gradually increase with the increase of the rotation speed and particle size parameter λ. The radial and axial segregation patterns become more obvious with the increase of λ. And the variation of the flow characteristics of particles with different sizes in the same system is also inconsistent. The microscopic properties of Gaussian-dispersed particles change with the rotation speed and λ. The rapid radial segregation depends on the larger pores existed in the granular system, which leads to a gradual increase of the axial dispersion coefficient of large particles and a gradual decrease of the axial dispersion coefficient of small particles.     

Numerical investigation of reverse segregation in debris flows by DEM

Studies of the mechanisms and the effects on the flowing mobility for hazardous geophysical flows (e.g., debris flows) is crucial for hazard mitigation and prediction. Granular flows with grains of mixed sizes are numerically modeled and the contact behavior of solid particles is fundamentally studied using the discrete element method. The mechanical effects of particle contacts (shearing and collision) are contrasted with geometrical effects (kinetic sieving) to explain the mechanism of reverse segregation. Compared to granular flows with uniform solid particles, the effect of segregation on granular flowing mobility is investigated. It is found that reverse segregation can significantly influence the flowing mobility and the flowing regimes in the front head of the granular body. A mechanical explanation of the segregation mechanism can be presented by a new dimensionless number, which is correlated with the contact force.     

Cross-sectional and axial flow characteristics of dry granular material in rotating drums

Cross-sectional and axial flow behaviors of dry granular material in rotating drums are closely related to the dynamic characteristics and velocity distributions between the surface layer and bed material. In this study, both 2D and 3D dry granular flow patterns in horizontal rotating drums are experimentally investigated with flow imaging analysis. A dimensionless flow parameter combining the effects of Froude number, relative particle size and volume filling is proposed in this study, which controls the flow characteristics in a rational drum such as dynamic angle of repose, thickness of the flowing layer, relative free surface velocity, and the shear rates in the flowing layer. The dimensionless granular temperature exhibits linear distribution in the flowing layer, being maximum at the free surface and being negligible at the interface in the rolling regime. The measured shear rate of the plug flow departs from drum angular velocity under the wall slip conditions when the drum surface is smooth. Due to the existence of axial convection and lateral surface profile, the mass flux in the flowing layer is always less than that of the plug flow in the 3D granular flows based on sidewall particle images. One the other hand, the mass flux in the flowing layer is always equal or greater than that of the plug flow in the 2D granular flows. 2D granular flows exhibit higher angles of repose and surface velocities than those of the 3D granular flows at the same volume fillings.     

Comparative study of the single and double specularity coefficients on two-fluid modeling of a pseudo-2D gas–solid fluidized bed

The specularity coefficient is an unmeasurable parameter in the most popular wall boundary model during the two-fluid modeling of dense gas–solid flows. Using multiphaseEulerFoam solver, the influence of different specularity coefficient setting strategies on the gas–solid flow inside a pseudo-2D fluidized bed has been explored. It is found that the single specularity coefficient plays a regulatory role in the quantitative prediction. Increasing the specularity coefficient would cause a fluidization transition from freely bubbling to slugging, and the bed characteristics such as pressure drop and bed expansion present monotonic nonlinear changes. The double specularity coefficients approach is shown to significantly improve the predictive accuracy through verifying with the measured particle velocities, bubble diameter and rise velocity. In addition, the lognormal bubble size distribution and Gaussian bubble rise velocity distribution are observed. The specularity coefficient for walls in thickness direction is crucial and its different effects are unignorable. Overall, the present study provides a practical strategy of double specularity coefficients for the solid wall boundary conditions during two-fluid modeling.     

MRI measurement of granular flows and fluid-particle flows

It is difficult to observe directly the particle motion inside a dense granular flow or a fluid-particle flow because of the existence of surrounding particles. MRI (Magnetic Resonance Imaging) is one of the non-invasive and non-destructive measurement techniques for such flows. MRI can measure the velocity distribution (tagging method and phase method), which is an outstanding advantage of the MRI measurement. This paper briefly explains the principle of the MRI measurement. Then MRI is applied to some dense granular flows or fluid-particle flows, such as the rotating drum, vibrated granular bed, hopper flow and spouted bed.     

Numerical study of forced axial segregation of binary density granular system in a split rotary drum

Driving and controlling the segregation in a rotary drum is both a theoretical and a practical challenge in powder technology. A novel horizontal split drum design composed of two reverse rotating sub-drums was explored to drive axial segregation of granular matter. DEM (Discrete Element Method) simulations were performed to study the particle dynamics and segregation performance of binary density particles in the split drum. Then, the effects of drum speed, the speed ratio of the two sub-drums, and the split position on the axial segregation were analyzed. It was found that true axial segregation occurred in the split drum and heavier particles tend to accumulate in the region near the split. An increase in drum speed can accelerate the segregation but it has no obvious influence on the final axial distribution of particles. The results obtained indicate when two sub-drums rotate at different speeds, the concentrated region of heavier particles moves towards the low-speed sub-drum. These findings could lead to new designs for a broad range of particle processing industries.     

Numerical analysis of restitution coefficient,rotational speed and particle size effects on the hydrodynamics of particles in a rotating drum

Hydrodynamic behavior of two dimensional horizontal rotating drum was studied by using finite volume method and granular kinetic theory. In this work, the effects of the different parameters such as rotation speed, restitution coefficient and particle size on the hydrodynamic and especially on the granular temperature of particles were investigated. At first, the results of present work were verified with previous experimental results. Packing limit of 0.6 and restitution coefficient of 0.95 with Gidaspow inter-phase momentum coefficient showed the good agreement with experimental works. It is found that by increasing the restitution coefficient, the granular temperature at different depth of bed increased and affected the hydrodynamic behavior of the bed. Also, particle size and rotation speed directly changed the granular temperature. Moreover, augmentation of the rotation speed leads to increasing the repose angle which caused better mixing of bed, granular temperature rising and consequently particle velocity alteration in the bed.     

Influences of fine powder on dynamic properties and density segregation in a rotating drum

In this paper, the influences of the addition of a small amount of fine powder and rotation speed on the dynamic properties and density-induced segregation behavior of granular matter in a quasi-two-dimensional rotating drum were experimentally investigated. An optical camera was applied to capture the motion of the particles in the drum. Image-processing technology and a particle tracking method were applied for determining the velocity, granular temperature and segregation index of granular materials. The results indicate that the addition of a small amount of fine powder has a significant effect on dynamic properties and density-induced segregation behavior. The average velocity and the average granular temperature are enhanced with the increase of the fine powder content because of the lubrication effect between particles. Additionally, the results indicate that density segregation is strengthened with the increase of fine powder.     

A cellular automaton for segregation during granular avalanches

Segregation is a complex and poorly understood phenomenon that is prevalent in many industrial and natural granular flows. When grains flow down a slope [1–5], are spun in a rotating drum [6–8] or shaken in a box [9], we observe those grains organising into intriguing patterns. Kinetic sieving is the dominant mode of segregation in granular avalanches, where separation of particles occurs according to size. Using a cellular automaton we have modelled kinetic sieving as the swapping of particles in a one-dimensional system. From the cellular automaton we have deduced a continuum model to describe the segregation.     

Effect of base roughness on size segregation in dry granular flows

This paper presents simulations of dry granular flows along a sloping channel using the discrete element method. The kinetic sieving and squeeze expulsion theories are utilized to study the effects of base roughness on size segregation and the underlying mechanisms. Basal friction has a significant influence on flowing regimes inside the granular body, and a larger base friction accelerates the size segregation process. The front zone of the granular body is more likely to be collision dominated with increasing base friction; as a result, the energy dissipated by frictional shearing decreases, and damping energy due to particles collisions is enhanced. Meanwhile, granular flows become much looser, and collisions between particles increase rapidly. It is shown that the differences in the kinetics among grains of mixed sizes and the mechanical effects of particle contacts can explain the mechanism of size segregation. The parameter representing the intensity of particles exchange also increases as base friction increases. The forces acting on particles are also affected by base friction. The dimensionless contact force describing the contribution of contact channel-normal stress increases as base friction increases, which indicates that a higher dispersive trend has developed inside the granular body.     

The effect of liquids on radial segregation of granular mixtures in rotating drums

The presence of liquids can significantly affect the dynamics of granular flow. This paper investigates the effect of liquids on radial segregation of granular mixture in a rotating drum using the discrete element method. The wet granular mixture, due to differences in particle size and density, segregates in a similar way to that of dry particles: lighter/larger particles move to the periphery of the bed while heavier/smaller particles stay in the centre. An index based on the variance of local concentration of one type of particles was proposed to measure the degree of segregation. While the liquid induced capillary force slows down the segregation process, its effect on the final state is more complicated: small cohesion shows no or even positive effect on segregation while high cohesion significantly reduces particle segregation. The effect can be explained by the change of flow regimes and the competing effects of mixing and segregation (un-mixing) in particle flow which are both reduced by the interparticle cohesion. A diagram is generated to describe the combined effect of particle size and density on segregation of wet particles. A theory is adopted to predict the segregation of particles under different density/size ratios.     

Influence of particle shape on mixing rate in rotating drums based on super-quadric DEM simulations

Fundamental research on the flow and mixing of non-spherical particles is critical for industrial production and design. In this paper, the Discrete Element Method (DEM) is used to study the flow and mixing of granular materials in the horizontal rotating drum, and the periodic boundary condition is employed to eliminate end wall effect. Super-quadric elements are adopted to describe spherical and non-spherical particles. The influences of rotating speed, blockiness, and aspect ratio on the mixing rate are investigated by the Lacey mixing index. The results show that the rotating speed has a primary effect on the mixing rate, whereas the effect of the particle shape on the mixing rate is a secondary factor for non-spherical granular systems. Moreover, the mixing rate of spherical and non-spherical particle systems is significantly different. The mixing rate of spheres is the lowest, and the cubes have a higher mixing rate than the cylinders. As the blockiness decreases or aspect ratio deviates from 1.0, the mixing rate decreases. Ordered face-to-face contacts and dense packing structures result in a higher mixing rate. The analysis of kinetic energy shows that particle shape affects the transfer efficiency of external energy to the granular systems. The translational kinetic energy of non-spherical particles is higher than that of spherical particles, and their rotational kinetic energy is lower than that of spheres. Meanwhile, the blockiness enhances the transfer efficiency of external energy to the non-spherical systems; in contrast, the aspect ratio reduces the energy conversion efficiency.     

Texture of granular surface flows: experimental investigation and biphasic non-local model

We investigate here the rheology of dense granular surface flow. First, steady surface flows in a rotating drum are studied experimentally and a large number of clusters of `jammed' grains embedded in the flowing layer is evidenced. The clusters size is power-law distributed, from the grain size scale up to the thickness of the flowing layer. Theoretical implications are then discussed and a non-local biphasic rheological law is proposed. The resulting model succeeds quantitatively to account for the unusual shape of the velocity profile within granular surface flows as well as for the different scalings observed in rotating drum experiments.     

Experimental study of density segregation at end walls in a horizontal rotating cylinder saturated with fluid: friction to lubrication transition

What is the effect of interstitial fluid viscosity on granular density segregation in a horizontal rotating cylinder? We conducted experiments in the rolling regime with equal amounts of equal sized high and low density, nearly spherical granular particles saturated with air, water, and water-glycerin mixtures. We held particle density, rotation rate and characteristic length scale constant to highlight differences due purely to the interstitial fluid. Images of the granular flow at an end wall were used to determine radial and axial density segregation rates and patterns. Over a four decade change in viscosity, segregation rates varied by only a factor of two. However, for ratios of lubrication to frictional stresses above one, segregation rates decreased by about 30%, and we observed several notable phenomena in the segregation pattern formation. These were a creeping mode of radial density segregation, a change in shape of the granular bed to kidney shaped from flat, and for cylinders more than half full the typically reported unsheared central portion of the granular bed (often referred to in the literature as a core region) was disrupted by a wavy instability where the rate of disappearance of the core region decreased as the fill level increased.     

Jamming in granular shear flows of frictional,polydisperse cylindrical particles

In this work, frictional, cylindrical particle shear flows with different size distributions (monodisperse, binary, Gaussian, uniform) are simulated using the Discrete Element Method (DEM). The influences of particle size distribution and interparticle friction coefficient on the solid phase stresses, bulk friction coefficient, and jamming transition are investigated. In frictional dense flows, shear stresses rise rapidly with the increasing solid volume fraction when jamming occurs. The results suggest that at the jamming volume fraction, stress fluctuation and granular temperature achieve the maximum values, and the rate of the stress increase with increasing solid volume fraction approaches the peak value. Meanwhile, the degree of cylindrical particle alignment approaches a valley value. In the polydisperse flows, the jamming volume fraction exhibits significant dependences on the fraction of the longer particles and the particle size distribution. Two models considering the effect of particle size distribution are discussed for predicting the jamming volume fractions of polydisperse flows with frictional, cylindrical particles.     

Particle screening phenomena in an oblique multi-level tumbling reservoir: a numerical study using discrete element simulation

Due to their wide usage in industrial and technological processes, granular materials have captured great interest in recent research. The related studies are often based on numerical simulations and it is challenging to investigate computational phenomena of granular systems. Particle screening is an essential technology of particle separation in many industrial fields. This paper presents a numerical model for studying the particle screening process using the discrete element method that considers the motion of each particle individually. Dynamical quantities like particle positions, velocities and orientations are tracked at each time step of the simulation. The particular problem of interest is the separation of round shape particles of different sizes using a rotating tumbling vertical cylinder while the particulate material is continuously fed into its interior. This rotating cylinder can be designed as a uniform or stepped multi level obliqued vertical vessel and is considered as a big reservoir for the mixture of particulate material. The finer particles usually fall through the sieve openings while the oversized particles are rebounded and ejected through outlets located around the machine body. Particle–particle and particle–boundary collisions will appear under the tumbling motion of the rotating structure. A penalty method, which employs spring-damper models, will be applied to calculate the normal and frictional forces. As a result of collisions, the particles will dissipate kinetic energy due to the normal and frictional contact losses. The particle distribution, sifting rate of the separated particles and the efficiency of the segregation process have been studied. It is recognized that the screening phenomenon is very sensitive to the machines geometrical parameters, i.e. plate inclinations, shaft eccentricities and aperture sizes in the sieving plates at different levels of the structure. The rotational speed of the machine and the feeding rate of the particles flow have also a great influence on the transportation and segregation rates of the particles. In an attempt to better understand the mechanism of the particle transport between the different layers of the sifting system, different computational studies for achieving optimal operation have been performed.     

Application of magnetic resonance imaging techniques to particulate systems

Magnetic resonance imaging (MRI) is a well-established technique in the medical field, typically for imaging liquid water in the human body, but it is increasingly being used in the field of engineering and materials science. A particular section of this is in the area of particulate systems and granular material flows. MRI is being used to provide a unique insight into particle distribution and motion with in situ measurements. In this paper we discuss how judicious choice and development of imaging technique applied to various different granular systems can provide us with valuable new data on the processes occurring in granular flows. Experimental results focus on rotating bed segregation, velocity imaging in vertical fluidized beds and phase-resolved velocity distributions within vertical vibro-fluidized beds. A discussion of the various imaging techniques used to acquire these data is also given.