Numerical study of size-driven segregation of binary particles in a rotary drum with lower filling level

Discrete element method (DEM) simulations of size-driven segregation of binary particles in a rotary drum were conducted to investigate the influence of filling level, size ratio, and rotation speed on the segregation performance. Segregation experiments with different filling levels were used to verify the DEM model and analyze the influence of filling levels on segregation. The granular bed was divided into five layers to study the axial segregation in the rotary drum. The total velocity fluctuation was used to discuss the granular behavior from a mesoscopic perspective. A segregation index was adopted to quantify the segregation performance with different parameters. It was found that binary particles in the drum with different filling levels have different segregation patterns. A core of small particles was formed in the middle of granular bed for the case with a higher filling level, while there is no core formed for the case with a lower filling level. Results obtained indicate that the size-driven segregation in the drum with lower filling level increases with the increase of size ratio. Within the rolling regime, the rotation speed has little influence on the final segregation index of particles.     

Effect of size distribution on mixing of a polydisperse wet granular material in a belt-driven enclosure

We use a recently developed coupled fluid–particle discrete element model to study mixing of a wet granular material in a two dimensional setting. The particles are modeled as linearly elastic disks and are considered to be immersed in a Newtonian fluid. The fluid–particle interaction is modeled using a linear drag model under the assumption that the fluid inertia is small compared to particle inertia. The granular slurry is driven by a belt moving at constant velocity in a square cavity. In the simulations, we consider three types of size distributions: monodisperse, bidisperse with several particle size ratios, and polydisperse Gaussian distributions with several different standard deviations. Mixing is characterized using both strong and weak measures. Size segregation is observed only in the bidisperse simulations. The energy required for mixing polydisperse slurries decreases with increasing standard deviation of the particle sizes. Finally, we show the benefits of engineering certain polydisperse particle size distributions towards minimizing energy consumption.     

鼓泡床内双组分颗粒流动行为的数值模拟

为了模拟预测粒径和密度同时存在差异的双组分颗粒体系的分级混合行为,基于欧拉-欧拉方法建立多流体模型,采用颗粒动力学理论描述颗粒相性质,分别通过Gidaspow和Syamlal曳力模型描述气-固相曳力和固-固相作用力。结果表明,模拟得到的轴向和径向颗粒浓度分布与实验数据吻合较好;当在较小气流速度下出现分级行为时,床层底部富沉积组分层中沉积组分的运动十分有限,而在较大气流速度下处于完全混合状态时,床层内部颗粒运动较为剧烈。     

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.     

Simulation of granular packing of particles with different size distributions

The study of granular matter composed of spherical particles is of interest in manufacturing, material, and metallurgy. The viscoelastic and frictional contacts between the particles are the cause of forming the agglomeration. We present a numerical simulation for particles packing with three different kinds of size distributions: monosize, bimodal, and Gaussian, using distinct element method (DEM). The particles are initially put randomly but without any overlap, and then fall down due to the gravity force and collide with neighbor particles. Because of the dissipative factors of viscoelastic collision and frictional force, all the particles finally come together to form an agglomeration. Coordination number, porosity, radial distribution function, and force distribution are calculated for different size distributions. It is demonstrated that particle size distribution does affect the granular packing structure.     

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.     

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.     

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.     

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.     

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.     

Study on hydrodynamic characteristics of the liquid-solid circulating fluidized bed with a central pulsating nozzle by numerical approach

Pulsating fluidization is gaining increasing attention due to its superiority in efficiency improvement. A novel type of liquid–solid circulating fluidized bed with a central pulsating nozzle was proposed to improve the reaction efficiency in this work. Based on Eulerian-Eulerian two-fluid model and the kinetic theory of granular flow, the hydrodynamic characteristics in the riser was investigated by three-dimensional numerical simulation. The effects of pulsating liquid flow and particle properties on the distributions of solids holdup, the radial velocity of the particles, the slip velocity and the radial mixing degree were studied. The simulation results showed that with the addition of the central pulsating liquid flow, the particles displayed apparent radial motion, and the interphase mixing degree as well as the interphase mass transfer efficiency were enhanced. Based on the numerical results, the regression formulas of the axial and radial slip velocities were obtained respectively.     

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.     

EXPERIMENTAL AND NUMERICAL INVESTIGATIONS OF SOLIDS MIXING IN A GAS FLUIDIZED BED

Solids mixing in a bubbling gas-fluidized bed was Investigated using two Independent methods. In the first method, distributions of solids mean velocity and bulk density, and dispersion coefficients were measured, employing the single particle mode of the particle tracking technique. This technique tracks the position of a single radioactive particle, dynamically identical to bed particles, by using a bank of scintillation detectors around the bed. Time-differentiation of the instantaneous tracer positions then yields the local velocities which were ensemble-averaged locally after long experimental runs to yield the mean velocity distribution. Lagrangian autocorrelation functions were obtained to determine the radial and axial dispersion coefficients, which were found to differ by an order of magnitude. These experimental data formed the basis of a numerical model of convective-diffusive mixing, formulated to predict the time-dependent concentration distribution for a given set of initial conditions. The second method employed the multiparticle tracking mode in which the downward migration and mixing of a quantity of radioactive particles Introduced at the top of the bed was monitored by the radiation detectors. The variation of the detector outputs with time served as an Indicator of the distribution of the radioactive swarm. When the results were compared with the predicted detector outputs using the model with independently obtained velocity and dispersion coefficient distributions, good agreement was found, especially at higher fluidization velocities.     

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.     

Experimental investigation of axial dispersion in a horizontal rotating cylinder

This work reports experimental measurements of the dispersion of particles during rotation in a horizontal cylinder. The axial dispersion of a pulse of approximately monodisperse black glass ballotini into a bed of clear glass ballotini of the same size is analysed. This is done using a sectioning technique, where the concentration is determined throughout the cylinder for a given rotation time and speed. The concentration profile is fitted to an appropriate solution of Fick’s second law to determine the dispersion coefficient. The dispersion coefficient is compared for various drum rotation rates and glass ballotini sizes. The cylinder was filled to 35 % by volume and rotated at a range of speeds between 5 and 20 rpm. The particle sizes vary from 1.14 to 3.15 mm. The dispersion coefficient was found to be dependent on both particle size and rotation speed. As the rotation speed, \(\omega \), was increased the dispersion coefficient increased proportionally to \(\omega ^{0.8}\). As the particle diameter, \(d_p\), was increased the dispersion coefficient increased proportionally to \(d_p^{1.84}\). These results are compared with previous experimental and simulation data, in particular the simulations of Third et al. (Powder Technol 203:510, 2010). Strong agreement was found between the simulations of Third et al. and the experimental results.

     

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.     

Primary particle movement and change of property of cast iron by centrifugal effect in semi-solid processing

The particle distribution in semi-solid slurry under centrifugal field was simulated and the main factors such as fraction of solid, rotation speed, and holding time effecting the particle distributions are discussed. The simulation results showed that primary particles rich zone is produced in radially outer area and these results are in good agreement with the experiment. The centrifugal effect produces the primary particles distribution along the radial direction. Denser particles are concentrated in outside than inner side. For high fraction of solid samples, ‘wall’ appear in the middle of samples because of high viscosity region making particle difficult to move. Longer holding time gives denser primary particles concentrated more in outside than inner side. Higher rotation speed gives increased gradient of hardness in the radial direction. It is due to that number of primary austenite at inner side at higher rotation speed is less than that at lower rotation one. At higher rotation speed, ledeburite forms more at inner side of specimen than at the other one. It is also shown that semi-solid processing at lower fraction of solid gives higher hardness because smaller number of primary austenite, namely more ledeburite forms in microstructure. The present study gives useful information on producing material with locally changing property by semi-solid processing.     

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.     

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.