Investigating the dynamics of cylindrical particles in a rotating drum using multiple radioactive particle tracking

The behavior of granular flows inside rotating drums is an ongoing area of research. Only a few studies have investigated non‐spherical particles despite the fact that particle shape is known to have a significant impact on flow behavior. In addition, the experimental techniques limit the interpretation of the results of these studies. In this work, we compared the flow behavior of cylindrical and spherical particles using the multiple radioactive particle tracking technique to capture the positions and orientations of cylindrical particles simultaneously. We analyzed two important components of the transverse flow dynamics, that is, the boundary between the active and passive layers, and the velocity profile on the free surface. For the cylindrical particles, two general models are proposed to calculate the velocity profiles on the free surface and the effective particle sizes in the active and passive layers. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2622–2634, 2016     

Segregation behavior of binary mixtures of cylindrical particles with different length ratios in the rotating drum

Particle shape impacts the flow behavior of granular material but this effect is still far from being fully understood. Using discrete element method, the current work explores the segregation phenomena of the binary mixtures of cylindrical particles (differing in length but with the same diameter) in the three-dimensional rotating drum operating in the rolling regime, with each cylindrical particle fully represented by the superquadric equation. The important characteristics and the effect of length ratio on the flow dynamics of the binary mixtures are discussed. Some trends are in sync with those of binary mixtures of spherical particles. Unique to nonspherical particles is the orientation of particles, with results indicating that the cylindrical particles align their major axes perpendicular to the drum axis and this behavior becomes more significant for large particles when the length ratio increases. The length-induced radial segregation causes the orientation of large cylindrical particles to be less uniform.     

DEM study of granular flow characteristics in the active and passive regions of a three‐dimensional rotating drum

Three‐dimensional modeling of the solid motion in a lab‐scale rotating drum has been conducted via the discrete element method. After validating the simulated results with available experimental data, the active‐passive interface was identified, following which particle‐scale information in these two regions, in particular the influences of fill level and rotating velocity, were obtained. The results demonstrate that: (1) the total number of particles in the passive region is three times that in the active, (2) the transverse and axial velocities span a wider range in the active region, with the transverse values being greater, (3) the collision force is much higher in the active region, with the greatest magnitudes in the y direction relative to that in the x and z directions, (4) particle displacements are generally lower and have a narrower distribution in the active region, (5) the local solid residence time (SRT) distribution profiles are similar axially in that the highest SRT magnitudes are at the center region of the bed, while the other parts of the bed have uniform SRT magnitudes. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3874–3888, 2016     

Drag coefficient and settling velocity for particles of cylindrical shape

Solid particles of cylindrical shape play a significant role in many separations processes. Explicit equations for the drag coefficient and the terminal velocity of free-falling cylindrical particles have been developed in this work. The developed equations are based on available experimental data for falling cylindrical particles in all flow regimes. The aspect ratio (i.e., length-over-diameter ratio) has been used to account for the particle shape. Comparisons with correlations proposed by other researchers using different parameters to account for the geometry are presented. Good agreement is found for small aspect ratios, and increasing differences appear when the aspect ratio increases. The aspect ratio of cylindrical particles satisfactorily accounts for the geometrical influence on fluid flow of settling particles.     

Experiments on floating bed rotating drums using magnetic particle tracking

Magnetic particle tracking (MPT) was employed to study a rotating drum filled with cork particles, using both air and water as interstitial medium. This noninvasive monitoring technique allows for the tracking of both particle translation and rotation in dry granular and liquid–solid systems. Measurements on the dry and floating bed rotating drum were compared and detailed analysis of the bed shape and velocity profiles was performed. It was found that the change of particle–wall and particle–particle interaction caused by the presence of water significantly affects the bed behavior. The decreased friction leads to slipping of the particles with respect to the wall, rendering the circulation rate largely insensitive to increased drum speed. It was also found that the liquid–particle interaction is determining for the behavior of the flowing layer. The well-defined experiments and in-depth characterization performed in this study provide an excellent validation case for multiphase flow models.     

An experimental study of the flow of nonspherical grains in a rotating cylinder

The effect of particle aspect ratio on the rheology of the flow of granular materials is studied experimentally in a quasi–two‐dimensional rotating cylinder, using two varieties of prolate spheroidal grains with different aspect ratios. Image analysis of high speed videos is used to obtain the flow profiles near the centre of the cylinder. The dynamic angle of repose and apparent viscosity in the medium show significant increase with increasing aspect ratio. The mean velocity, root mean square velocity and shear rate profiles are qualitatively similar for nonspherical and spherical particles, however, their magnitudes increase with increasing aspect ratio. A simple scaling is shown to predict the maximum thickness of the flowing layer for all the particles. The predictions of a model for the flow match with the measured mean velocity profiles and layer thickness. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4307–4315, 2017     

The effect of particle rotation on the motion and rejection of capsular particles in slit pores

The results from a two‐dimensional computational model describing the motion of capsule‐shaped particles in a slit pore under small Re conditions are reported. Average particle velocities and particle rejection coefficients were determined for capsules with aspect ratios of 2 and 4. Two different approaches were used to characterize particle rotation and hydrodynamic particle‐pore wall interactions. In one approach, all sterically allowed particle orientation angles had equal probability, i.e., infinite rotational diffusion was assumed. In the second approach, particles were allowed to freely rotate in the pore; particle orientations were dictated by hydrodynamic forces acting on the particle surface and rotational particle diffusion was neglected. Minimal lateral migration across the pore was observed for the freely rotating particles. Although particle alignment was observed for the freely rotating particles, rejections predicted from the two approaches were found to be in close agreement. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2828–2836, 2018     

滚筒端面对颗粒物料轴向流动特性影响的离散模拟研究

针对碎渣工艺中仅一个端面可随侧壁转动的短滚筒体系，采用离散单元法模拟研究了滚筒轴径比和转动速度对颗粒物料轴向流动特性的影响。模拟结果表明，系统内形成了显著的轴向对流结构：物料层顶部处颗粒物料会朝向滚筒固定端面一侧运动，而物料层趾部区域颗粒则朝向滚筒转动端面一侧运动。低转速条件下，沿物料自由表面由顶部到趾部，颗粒轴向速度呈非对称分布，顶部区域颗粒轴向速度绝对值显著小于趾部区域颗粒轴向速度绝对值；两部分区域颗粒轴向速度绝对值分别在y/R=±0.725处达到极大值，且轴向速度为0的位置并不出现在切向的中间位置。改变滚筒的轴长对这种非对称分布的影响近似可忽略，但是增大滚筒转速会增大颗粒轴向运动速度并逐步减弱这种非对称性。改变滚筒转速，对物料顶部区域颗粒的轴向流动的影响要大于对趾部区域颗粒轴向流动的影响。当滚筒轴径比达到1.2后，滚筒转动端面对物料轴向流动的影响区域不会随滚筒转速的增大而呈现显著变化。这些结果为实际滚筒碎渣工艺的结构优化提供了理论指导。     

Granular flow in a rotating drum with gaps in the side wall

This paper presents a numerical investigation of the motion of bi-sized particles in a short rotating drum by using Discrete Element Method (DEM). The side wall of the drum has equally spaced gaps whose width is just between the two particle diameters. One end wall of the drum is fixed while the other rotates with the side wall. Small particles are fed into the drum continuously at the center region in the axial direction. The effect of rotating speed on the volumetric holdup and residence time of small particle is investigated. A critical rotating speed is found, below which the decrease of rotating speed will increase the volumetric holdup and the residence time of the small particles sharply. A jump in the axial distribution of the outflow rate of the small particles is observed at the region adjacent to the fixed end wall. The flow pattern inside the drum is analyzed. In the region between the fixed end wall and the feeding point, all small particles, on average, move towards the fixed end wall. While in the region between the rotating end wall and the feeding point, the small particles curve away the rotating end wall in the upper part of the charge and return to this wall in the lower part. The particle temperature distributions at different rotating speeds are explored to understand the flow behavior observed in these simulations.     

Using the discrete element method to develop collisional dissipation rate models that incorporate particle shape

Discrete Element Method simulations of Homogeneous Cooling Systems (HCS) are used to develop a collisional dissipation rate model for non‐spherical particle systems that can be incorporated in a two‐fluid multiphase flow framework. Two types of frictionless, elongated particle models are compared in the HCS simulations: glued‐sphere and true cylinder. Simulation results show that the ratio of translational to rotational granular temperatures is equal to one for the true cylindrical particles with particle aspect ratios (AR) greater than one and glued‐sphere particles with AR >1.5, while the temperature ratio is less than one for glued‐sphere particles with 1 < AR <1.5. The total collisional dissipation rate, which is associated with both translational and rotational granular temperature change rates, increases linearly with the particle aspect ratio. Thus, a collisional dissipation rate model for the elongated cylinders is developed by a simple modification of the existing spherical particle model. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5384–5395, 2017     

回转干馏炉内二组元颗粒混合机理及混合度分析

采用非等径二组元颗粒,用圆形滚筒模拟回转干馏炉,研究回转干馏炉转速对颗粒径向混合的影响。以滚筒径向颗粒Lacey指数作为混合指数,对5种不同转速下滚筒侧表面颗粒的混合指数与混合机理进行研究,对比分析了混合指数的变化趋势。结果表明：在圆形滚筒混合器内1/6填充率、倾角为0°的情况下,在转速为13.3 r/min时混合度优于其它转速,以对流混合与扩散混合为主;通过对混合质量与混合机理综合分析,得颗粒混合呈现“双振荡趋势”。     

The effect of particle shape on simple shear flows

Simple shear flows, (without gravity force and implemented using periodic boundary conditions or in Couette flow configurations with gravity) have been the subject of study using DEM simulation for more than two decades. Earlier studies explored the effect of attributes such as shear rate, particle size and domain scale on the distribution of the particles in the flow, velocity profiles and the stress distributions. These studies were conducted using simple shapes for the particles such as spheres. In recent years, the importance of particle shape on flow has been recognized in a range of industrial application including mixing, comminution, hopper discharge and chute flows. In this paper, we return to the simple shear flows and quantitatively explore the effect of particle shape on velocity, volume fraction, granular temperature and stress distributions across the channel. Particle shape is found to sharply increase the strength of the material making it stronger and harder to shear. The generation of particle spin throughout the flow of non-circular particles leads to high granular temperatures, dilative pressures and lower solid fractions in the core of the flow. For aspect ratios between 0.6 and 0.5, a transition in the effective behaviour of the wall boundary conditions is identified. The connections of shape to spin, to granular temperature, to bulk flow changes are elaborated.     

A study of the three‐dimensional particle size segregation structure in a rotating drum

Three‐dimensional particle size segregation structures of binary mixtures of six different size ratios (SR = 1.42–3.37) in a rotating drum are studied. The formation of two smaller particle satellites around the central smaller‐particle rich band after the band formation core‐thickening mechanism is reported for the first time. The binary mixtures of six SRs show three satellite shapes, including the small bump shape, the axe shape, and the hemisphere shape. Except for the binary mixture of SR = 2.01 with the axe satellite shape, the satellite size increases with the increasing of the SR value at the same bed depth. The degrees of mixing of binary mixtures of six different SRs at different bed depths are analyzed using the Lacey mixing index. The degree of mixing at the bed surface and close to the drum cylindrical wall can be explained by the drift‐diffusional model of Savage (1993). © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Modeling granular material blending in a rotating drum using a finite element method and advection‐diffusion equation multiscale model

A multiscale model is presented for predicting the magnitude and rate of powder blending in a rotating drum blender. The model combines particle diffusion coefficient correlations from the literature with advective flow field information from blender finite element method simulations. The multiscale model predictions for overall mixing and local concentration variance closely match results from discrete element method (DEM) simulations for a rotating drum, but take only hours to compute as opposed to taking days of computation time for the DEM simulations. Parametric studies were performed using the multiscale model to investigate the influence of various parameters on mixing behavior. The multiscale model is expected to be more amenable to predicting mixing in complex geometries and scale more efficiently to industrial‐scale blenders than DEM simulations or analytical solutions. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3277–3292, 2018     

Characterization of Mixing and Size Segregation in a Rotating Drum by a Particle Tracking Method

The mechanisms of segregation in solids mixing, even in simple rotating drums, are not clearly understood. Although most past studies have focused on binary mixtures, this work investigates the effect of polydispersity on granular flow, mixing, and segregation in a rotating drum operated in rolling regime through particle trajectories obtained from the radioactive particle tracking technique. Velocity profiles, radial segregation, and axial dispersion coefficients for monodisperse and polydisperse systems of glass beads are analyzed with respect to rotational speed and particle size. A model is introduced to predict the residence times along streamlines and evaluate the rate at which the material renews at the free surface and within the inner layers of the bed. Our results reveal similar velocity profiles and residence times for monodisperse and polydisperse systems. They also indicate that the particles distribute along the radial direction of the drum, although not necessarily in a core/shell configuration. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1894–1905, 2013     

滚筒端面对颗粒物料轴向混合过程影响的离散模拟

基于离散单元法模拟了仅颜色存在差异的两组分颗粒物料在轴径比0.3的窄滚筒中的轴向混合过程,滚筒的左侧端面固定,右侧端面可随侧壁旋转。结果表明,不同物料装载量和滚筒转速下,在达到完全混合状态前,黄红颗粒物料初始轴向界面处可能出现3种不同的径向结构：黄?红结构、红?黄?红结构和红?黄结构。红?黄?红结构和红?黄结构工况下,固定端面一侧还可出现更复杂的多层三明治结构。径向结构源自滚筒端面效应导致的颗粒轴向对流,颗粒轴向速度在切向截面上的分布决定了径向结构的类型。     

Using stereo XPTV to determine cylindrical particle distribution and velocity in a binary fluidized bed

Nonspherical particles are commonly found when processing biomass or municipal solid waste. In this study, cylindrical particles are used as generic nonspherical particles and are co-fluidized with small spherical particles. X-ray particle tracking velocimetry is used to track the three-dimensional particle position and velocity of a single tagged cylindrical particle over a long time period in the binary fluidized bed. The effects of superficial gas velocity (u _f), cylindrical particle mass fraction (α), particle sphericity (Φ), and bed material size on the cylindrical tracer particle location and velocity are investigated. Overall, the cylindrical particles are found in the near-wall region more often than in the bed center region. Increasing the superficial gas velocity u _f provide a slight improvement in the uniformity of the vertical and horizontal distributions. Increasing the cylindrical particle mass fraction α causes the bed mixing conditions to transition from complete mixing into partial mixing. © 2018 American Institute of Chemical Engineers AIChE J, 65: 520–535, 2019     

Numerical investigation of monodisperse granular flow through an inclined rotating chute

A discrete element model of spherical glass particles flowing down a rotating chute is validated against high quality experimental data. The simulations are performed in a corotating frame of reference, taking into account Coriolis and centrifugal forces. In view of future extensions aimed at segregation studies of polydisperse granular flows, several validation steps are required. In particular, the influence of the interstitial gas, a sensitivity study of the collision parameters, and the effect of system rotation on particle flow is investigated. Shirsath et al. have provided the benchmark laboratory measurements of bed height and surface velocities of monodisperse granular flow down an inclined rotating chute. With a proper choice of the friction coefficients, the simulations show very good agreement with our experimental results. The effect of interstitial gas on the flow behavior is found to be relatively small for 3‐mm granular particles. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3424–3441, 2014     

Numerical simulation of the transient temperature distribution inside moving particles

This work is devoted to the two‐dimensional (2D) numerical simulation of heat and fluid flow by granular mixing in a horizontally rotating kiln. The heat and fluid flow in the gas phase are solved directly using a fixed Eulerian grid. At the same time, the particle dynamics and their collisions are solved on a Lagrangian grid. The no‐slip boundary condition on the particle surface is implemented using the fictitious boundary method. The heat transfer inside the particles is calculated utilising two models: the first is the direct solution of the energy conservation equation in Lagrangian and Eulerian space and the second is the so‐called linear model, which assumes a homogeneous distribution of the temperature inside each particle. Numerical simulations showed that if the thermal diffusivity of the gas phase significantly exceeds the same parameter of the particles, the linear model over‐predicts the heating rate of the particles. The analysis of the time‐averaged flow field inside the kiln showed that in the gas phase a double vortex structure is formed which increases the convective heat transfer in the upper part of the particulate bed. The influence of the particle size, the angular velocity of the drum and the fluid on the heating rates of particles is studied and discussed.     

Nonspherical particles in a pseudo‐2D fluidized bed: Experimental study

Fluidization is widely used in industries and has been extensively studied, both experimentally and theoretically, in the past. However, most of these studies focus on spherical particles while in practice granules are rarely spherical. Particle shape can have a significant effect on fluidization characteristics. It is therefore important to study the effect of particle shape on fluidization behavior in detail. In this study, experiments in pseudo‐2D fluidized beds are used to characterize the fluidization of spherocylindrical (rod‐like) Geldart D particles of aspect ratio 4. Pressure drop and optical measurement methods (Digital Image Analysis, Particle Image Velocimetry, Particle Tracking Velocimetry) are employed to measure bed height, particle orientation, particle circulation, stacking, and coordination number. The commonly used correlations to determine the pressure drop across a bed of nonspherical particles are compared to experiments. Experimental observations and measurements have shown that rod‐like particles are prone to interlocking and channeling behavior. Well above the minimum fluidization velocity, vigorous bubbling fluidization is observed, with groups of interlocked particles moving upwards, breaking up, being thrown high in the freeboard region and slowly raining down as dispersed phase. At high flowrates, a circulation pattern develops with particles moving up through the center and down at the walls. Particles tend to orient themselves along the flow direction. © 2018 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 64: 1573–1590, 2018