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.     

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.     

Segregation due to particle shape of a granular mixture in a slowly rotating tumbler

Using DEM particle simulations we consider segregation of a binary granular particle mixture in a slowly rotating cylindrical tumbler where the particles differ only in their shape—spherical versus more cubical particles. We find that the more cubical particles segregate to the inner core of the particle bed while the spherical particles segregate to the curved walls of the tumbler. The main mechanism for this segregation is different energy dissipation rates for the different particle shape types when avalanching down along the free surface. The cubical particles, due to their sharper corners, dissipate energy much faster than the spherical particles. This results in spherical particles reaching the bottom end of the sloped, free surface which are then transported around the cylinder adjacent to the cylinder wall, as rigid body motion. In contrast to size or density segregation, the segregation due to shape is much weaker and takes longer to reach its equilibrium or steady state. In addition, the segregation occurs along the top surface rather than through the top surface (as occurs for size and density segregation). In general, in situations where two particles differ in their ease of flow (viz flowability) the more rapidly flowing particle will segregate to the base of the free surface (which in the case of the tumbler results in spherical particles near the periphery) and the more slowly flowing particle will segregate underneath.     

CFD simulation of particle segregation in a rotating drum. Part I: Eulerian solid phase kinetic viscosity

Although the Eulerian approach coupling the kinetic theory of granular flow is usually used to study granular flows with relative lower solid fractions, it can be used to study relative denser granular flows if appropriate solid phase kinetic viscosity values were adopted. A granular bed surface fitting (BSF) method is proposed to determine the appropriate solid phase kinetic viscosities of the granular flows in a rotating drum. The specularity coefficient is also used to address the interaction between particles and the drum wall. The BSF solid phase kinetic viscosity increases with decreasing of particle sizes and drum rotational speeds. The BSF solid phase kinetic viscosity and the specularity coefficient follow a power-law relationship with 0.6–1.1 as the exponent of the specularity coefficient. The BSF solid phase kinetic viscosities for the particles of two different sizes are used to study particle segregation in a rotating drum. The core thickening segregation mechanism and the segregation band formations are well predicted.     

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.     

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.     

Radial segregation of ternary granular mixtures in rotating cylinders

We carry out an experimental study of the equilibrium segregation of ternary granular mixtures in a rotating cylinder. In all the experiments, 50% of the volume of the cylinder is filled with the granular mixture and the rotational speed used ensures operation in the rolling regime of flow. Mixtures of spherical particles differing only in size and of spherical particles differing in size and density are considered, using steel balls and glass beads of different sizes. Volume fractions of the components (f{\phi}) are measured by sampling at different radial positions (r) to yield the radial volume fraction profiles (f(r){\phi(r)}). Results for mixtures differing only in size of the components indicate that the segregation process is nearly independent of the sizes of the large and middle size particles for the same size of small particles. In the case of mixtures with different size and density components, the segregation patterns depend on the direction of the resultant driving force. In many of the mixtures considered, the pattern of segregation can be qualitatively predicted by considering binary interactions between the components. However, in some mixtures, ternary interactions are found to determine the pattern obtained.     

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.     

Dynamics of bi-dispersed settling suspension of non-colloidal particles in rotating cylinder

Non-neutrally buoyant suspension of bi-dispersed non-colloidal particles in viscous fluid rotating in a horizontal cylinder displays in-homogeneities in particle distribution with alternate bands of high and low particle concentrations along the symmetric axis of the cylinder. Experiments were carried out to characterize the axial segregation in bi-dispersed suspension at various filling fraction and rotation speed of cylinder. The mixture of same particles in absence of any suspending fluid did not show any segregation. However, in case of particles suspended in water it was observed that the rate of segregation increases with increase in filling fraction. Once the particles get segregated along the full length of the cylinder, these bands start to migrate along the tube axis finally merging to give wider bands. For a given filling fraction the rate of segregation increases with the angular speed of the rotating cylinder. When the tube is partially filled the particle segregation is observed at higher angular speed, whereas in fully filled case the segregation starts at much lower rotation speed for the same concentration of particles. The segregation pattern changes as the rotation speed is increased. At higher speed the centrifugal force dominates over gravitational and viscous drag forces and this result into completely different segregation patterns. We have also analyzed the evolution of concentration profile from the image analysis of the particles.     

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.     

Radial segregation of multi-component granular media in a rotating tumbler

Segregation and mixing of granular mixtures are important to the minerals, food processing and pharmaceuticals industry to name just a few. It has recently been demonstrated that a rotating tumbler is a suitable device for separating out binary granular mixtures, i.e. mixtures composed of only two different particle types. However, most practical granular mixtures are composed of multi-component particle types. We therefore study the capability of this rotating tumbler to segregate mixtures composed of more than two components where the particles differ either in size or density. The general pattern of segregation involves the formation of an inner core of smallest or densest particles followed, at larger radii, by the next largest or densest particle type and so-on in an onion-like pattern. In the mixtures where particles differ in size we always get relatively pure inner cores of the smallest particles, while the other regions are less segregated. On the other hand for mixtures whose particles differ in density we get a relatively pure outer region (adjacent to cylinder wall) consisting of the least dense particles while the other regions are less segregated. We attempt to relate the simulation results to phenomenological theory and find that size segregation in a specific multi-component mixture can be suitably described by a recent theoretical model.     

Simulation and verification of particle flow with an elastic collision by the immersed edge-based smoothed finite element method

The immersed edge-based smoothed finite element method (IES-FEM) is proposed for the study of elastic collision particulate flow. Particle collision becomes more realistic by using the penalty function and the hyperelastic constitutive model. The effects of grid resolution and Reynolds numbers on particle terminal velocity and drag coefficient are discussed to verify the calculation accuracy and stability. Single-particle collisions with the bottom and side walls are analyzed and experimentally verified. Results show that the calculation error of IES-FEM is less than 0.6% when the fluid grid size is 0.5 times the particle mesh size and the time step is 10^–4 s. Particle drag coefficient and flow characteristics agree well with the published models and experiment results. To demonstrate the capabilities of IES-FEM in complex elastic particle systems, the collision and rebound of multiple particles are determined, including the drafting–kissing–tumbling of two circular particles; the chase, collision, and deformation of rectangular particles; and the repeated formation and separation of particle clusters. This work extends the application of IES-FEM in particle-resolved direct numerical simulation methods, which will provide an optional tool for future elastic blood cell flow and collision.     

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.     

Constitutive equations for a simple shear flow of a disk shaped granular mixture

Constitutive equations are derived for a granular flow of disk shaped solids in a 2-dimensional, simple shear field. Binary collisions are assumed to be the major mechanism for momentum transfer. Stresses are computed as the average rate of momentum transfer across a surface due to the interparticle collisions. Stresses are formulated explicitly in terms of the shearing rate, concentration of solids, and the physical properties of the solid constituent. The anisotropic collision distribution on the circumference of the disks due to the mean flow gradient is explicitly quantified. The frictional impact during collisions is treated in sufficient detail so that the singularity which existed in previous constitutive equations [1, 2] is removed. This detailed analysis of collision geometry and its effect upon frictional dissipation includes important considerations that have not been included in the numerical simulation models of Campbell and Brennen [3] where particles, after impact, are considered to not have any relative tangential velocity. This assumption by Campbell and Brennen will most likely be the technique by which frictional effects will be commonly handled in the future. Hence the present study will provide an important reference for assessing the effects of using simplifying assumptions when determining frictional effects during particle collisions. The constitutive relationships developed in this investigation are compared to data obtained from computer simulated experiments [3]. The result of the 2-dimensional analysis has practical applications in the study of ice flows on a river surface as reported in [4] and in the conveyance of bulk solids in chutes. Except for geometric complications, the procedure developed in the analysis can be extended to 3-dimensional flows of spherical particles.     

Investigation of spherical and non-spherical binary particles flow characteristics in a discharge hopper

The particulate flow characteristics of granular particles including mung beans, wooden spheres, wooden cylinders, wooden cubic, plastic spheres, plastic cylinders, and their binary mixtures in a flat bottom hopper were studied experimentally using high-speed high-resolution camera recordings. An image processing method based on the color threshold was developed to calculate the area ratio for binary mixtures. The mass discharge rates, the residue inclination angles, and the changes in edge height and center height with time were also investigated. In addition, the effects of different initial packing patterns on the particulate flow, mixing and segregation behaviors were analyzed and compared. It is interesting to find that the shape of particles and the initial binary particle packing patterns have significant effects on the discharging characteristics. The results of this study provide helpful guidance for industrial applications and provide experiment data for computational model validation.     

基于离散元方法的RDX-Al颗粒混合数值模拟分析

基于离散元方法,以旋转筒内RDX-Al二元颗粒体系的搅拌过程为研究对象进行模拟。采用离散元软件(EDEM),首先研究RDX-Al二元颗粒各自随转速的变化趋势,并进一步得出二元颗粒变化率的特点,做出分布上的拟合,得出最吻合模拟试验的函数为指数函数。然后,将旋转筒细分为多个单元空间,考察旋转轴与单元空间之间的距离对二元颗粒混合效果的影响。结果表明:单元空间离旋转轴越远,即旋转半径越大,颗粒之间的变化率也就越快,越容易达到均匀状态。最后,考察加入抄板的影响,结果表明:RDX-Al二元颗粒趋于的稳定值分别发生了改变。     

Tracking particles in sands based on particle shape parameters

The acquisition of particle kinematics of deforming sands generally requires tracking the particles within the specimen. For this purpose, one particle tracking method based on particle polar radius functions (PR-Track) and a second method based on the SH spectrum of particle spherical harmonics (SH-Track) are presented. Both methods are applied to the acquisition of particle kinematics of a Leighton Buzzard sand sample undergoing shearing in a miniature loading apparatus using X-ray micro-tomography. The results are compared to those from a particle volume-based particle tracking method (PV-Track). It is found that PR-Track and SH-Track return particle tracking results with a high precision which is comparable to PV-Track. For the tested sample, PR-Track is about 0.4 times faster than SH-Track. Furthermore, PR-Track and SH-Track have a much lower computational efficiency than PV-Track. However, PR-Track and SH-Track do not require particles to be displaced in a similar manner to their neighbours, which is assumed by PV-Track. Particle tracking results from PR-Track and SH-Track are not sensitive to search region sizes. These features imply that PR-Track and SH-Track are capable of tracking particles of granular media undergoing a large and complicated deformation. This capability is verified in a simple case study by applying the methods to track particles undergoing particle column collapse.     

Insights from simulations into mechanisms for density segregation of granular mixtures in rotating cylinders

The Discrete Element Method (DEM) is used to study the segregation of a binary mixture of differing density (but same size) granular material in an axially rotating cylinder. The rotation rates used produce a flow that is on the borderline between the avalanching and rolling regimes. The simulations replicate the experimental data well at both qualitative and quantitative levels. Both wall-induced and radial segregation are observed. The simulations show segregation is delineated into two main time regimes. At early times segregation is rapid (when the dense core is being established) and slows down appreciably thereafter. The final asymptotic state is found to be independent of the initial segregation state of the particles. We compare these results with previous theoretical models and relate these two distinct time regimes to the underlying segregation mechanisms. These comparisons suggest segregation varies as a function of two fundamental quantities (a) density ratio of particles and (b) angular speed of the rotating cylinder. It is shown that maximal segregation occurs for specific ranges of these quantities.     

Rapid couette flow of cohesionless granular materials

Summary Presented is an analysis on the Couette flow of cohesionless granular materials between two co-axial rotating cylinders. The constitutive equations employed have been postulated on the basis of available experimental and theoretical results which take into account the particle collisions as well as dynamic pressures induced by the trace of the unsemble phase average of the square of flow fluctuations. These constitutive equations loosely resemble the Reiner-Rivlin fluid behavior, and predict normal stress effects.New non-Newtonian effects in striking manners have been predicted in the cases of outer cylinder rotating-inner cylinder fixed as well as outer cylinder fixed-inner cylinder rotating. The theoretical predictions for the free surface profile for these two cases agree with our experimental observations and point to the validity of the proposed constitutive equations. All our results are based on no-slip conditions on the boundary surfaces. Furthermore, the results obtained are different from the classical results obtained for the Couette flow of simple non-Newtonian fluids.With 4 Figures