Rapid Gravity Flow of a Granular Medium

An experimental study is performed to analyze the equation of state of a granular medium, which relates its dilatancy, shear rate, and pressure by an analogy between a granular medium under rapid shear and a dense gas. A method is developed for the contactless determination of the solid-phase concentration distribution in the two-dimensional flow of a granular medium using x-ray analysis. The method is used to explore the concentration profiles in rapid gravity flows of ceramic particles down a rough incline. The adequacy of the equation of state of a granular medium under rapid shear and for unordinary properties of the gravity flow down a rough incline is directly confirmed.     

Segregation kinetics in the rapid gravity flow of granular materials

An experimental analytical method for determining the kinetic segregation coefficient in the rapid gravity flow of a granular material down a rough incline is proposed. It is found that it is possible to predict the velocity of transverse displacement of individual large and small particles in the rapid gravity flow using a single kinetic segregation coefficient for different particle sizes and structural and kinematic characteristics of the flow. A previously proposed equation of segregation kinetics is refined, and its predictive power is analyzed.     

Three-dimensional, rapid shear flow of particles with continuous size distributions

Rapid granular flows occur in nature and industry and often contain particles of many sizes. Over the last two decades, significant theoretical and experimental effort has been directed at rapid granular flows with monodisperse or binary particle-size distributions. In contrast, the behavior of rapid granular flows with more than two particle sizes has received only limited attention. The particle-size distributions in many natural and industrial granular flows may be represented as continuous distributions (e.g., Gaussian or lognormal distributions), providing incentive for the investigation of rapid granular flows with these particle-size distributions. As an extension of previous work for two-dimensional simulations of rapid shear flows with Gaussian and lognormal particle-size distributions, this work is directed at three-dimensional flows with continuous size distributions. Event-driven, discrete-particle (“molecular dynamic”) simulations are employed for the three-dimensional simple shear flow of smooth, spherical particles with Gaussian and lognormal particle-size distributions. The results parallel those found previously in two dimensions and demonstrate the effect of distribution width on the stress tensor and granular energy.     

颗粒斜槽流的实验研究与数值模拟

从实验和理论两个方面对颗粒慢速斜槽流进行了研究。建立颗粒慢速斜槽流的实验装置 ,采用示踪颗粒法测定表面速度 ;通过测量表面速度和流层厚度 ,初步分析了流率及壁面状况对流动的影响。用有限元法对粗糙表面上的慢速斜槽流进行了数值模拟     

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.     

A continuum constitutive model for cohesionless granular flows

A constitutive model is developed to represent shear granular flows of cohesionless solids. The model is based on the postulate that the friction coefficient and the solids fraction in a moving granular material are exclusive functions of the inertial number, which represents the ratio of inertial to normal stress forces. The constitutive equation obtained has the same form as a multidimensional Bingham fluid model, albeit with apparent viscosity and yield stress that depend on the vertical normal stress. The model is applied to previously published experimental results dealing with shear flows of granular beds made up of cohesionless spherical particles. The first case analyzed corresponds to a granular bed moving on top of a rotating disk. The model captures the main trends of the velocity profiles with a single adjustable parameter. The second case is a conventional Couette flow, for which the model is capable of representing the velocity and solids fraction profiles measured experimentally.     

多层流态化床的研究Ⅰ 液-固系

本文研究了液-固系多层流态化床（溢流管式）中两相流动的特性,其内容包括液相的纵向混合,液体通过多孔分布板的压降,颗粒物料通过溢流管孔口的自由流落,溢流管在流化床中工作的性能及多层床的操作特性。提出了可供设计参考的关联式。     

The influence of gravity on dynamic properties in sheared granular flows

The influences of gravity on the granular flow behavior and dynamic properties were experimentally studied in a vertical shear cell device where the shear dilation direction of granular materials was perpendicular to the gravity direction. The particle motions were recorded by a high-speed camera from three different observational views. By using image processing technology and the particle tracking method, the average velocities and granular temperatures in the streamwise and the transverse directions were successfully measured and analyzed. The results show that the anisotropic motions exist in sheared granular flows. The dynamic properties in the streamwise direction are larger than those in the transverse direction. Due to the gravity effect and bulk flow of granular materials, the local packing structure is not homogenous in the vertical shear cell. By comparing the three different observational views in the vertical shear cell, we find that the spatial average velocity and self-diffusion coefficient are the greatest but the shear rate and granular temperature are the smallest when the particles are co-flowing with gravity causing the most dilute packing structure due to the gravity effect. Similar experiments were also performed in a horizontal shear cell where the shear dilation direction of granular materials was against the gravity direction. The dynamic properties are smaller in the horizontal shear cell than those in the vertical shear cell. It is because the horizontal shear cell has the smaller shear rate with the shear dilation direction against the gravity direction.     

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.     

Testing the validity of the spherical DEM model in simulating real granular screening processes

We investigate the flow of a granular material over a vibrated horizontal screen. We perform a direct quantitative comparison, across a range of operating conditions, between laboratory scale experiments and simulations using the discrete element method (DEM). We test the extent to which the commonly employed DEM approximation of particles being spherical affects the ability of the model to realistically reproduce the behaviour of industrial screening systems where the particles are generally non-spherical in shape.The simulation geometry and input particle size distribution are set up to exactly match the experimental system, which consists of a horizontal screen with a wire mesh cloth onto which quarry rock is fed at a series of input flow rates. The screen is vibrated, causing the granular bed to flow over the deck and vertically stratify with finer material passing through the screen, where it is collected in a series of bins located along the length of the screen. The size distribution of the material flowing through each section of the screen is found by analyzing the contents of each collection bin.The best agreement is found for very low flow rates, where the vast majority of the below aperture size material is rapidly captured just after it enters the screen in both the simulation and experiment. At higher flow rates, significant quantitative errors are found with the over-prediction of the flow rate through the screen for near grate sized particles. This is attributed to the higher rate of percolation through the bed and the easier capture by the screen surface of the spherical shaped material. The near aperture sized spherical particles also show a very strong tendency to peg the screen, becoming trapped in the screen openings and limiting further flow through those parts the screen. The use of spherical particles in the DEM simulation of vibrating screens is therefore found to be inadequate for modelling realistic flow and separation of particles that are not actually spherical.     

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     

散斑能见度光谱法测量筒仓内颗粒流的颗粒温度

筒仓内颗粒流在化工生产中广泛应用,准确描述颗粒流的动力学规律对于调控化工反应过程中的混合和传输效率极为重要。颗粒温度是影响颗粒流的重要参数之一,为此搭建了基于线阵CCD相机的散斑能见度光谱测量装置,选取均值粒径分别为0.94和1.55 mm的球形颗粒进行实验。通过测量卸料过程中筒仓内颗粒流的时变颗粒温度,发现了离散颗粒运动在介尺度条件下具有稳定性。进一步,对比两种粒径颗粒的颗粒温度值,观察到稳态流动中大粒径颗粒具有更高的能量耗散,从而建立了宏观质量流率与介观颗粒温度之间的联系。通过分析筒仓内颗粒温度场的分布特征,发现了孔口附近的离散颗粒存在定向有序的运动。最后,根据筒仓内颗粒流堵塞过程中的颗粒温度变化曲线,揭示了颗粒流堵塞的弛豫变化规律。实验结果揭示的筒仓内颗粒流的运动规律,为完善化工生产中颗粒材料的存储与运输提供了参考数据。     

粗糙颗粒动理学及流化床内气固流动的数值模拟

基于气体分子动理学和颗粒动理学理论,考虑颗粒旋转流动对颗粒碰撞能量交换和耗散的影响,建立粗糙颗粒动理学。采用Chapman-Enskog颗粒速度分布函数,提出了颗粒相应力、热通量和颗粒碰撞能量耗散计算模型。采用欧拉-欧拉气固双相流模型,数值模拟鼓泡流化床内气体-颗粒两相流动特性。模拟结果得到了床内颗粒相速度和脉动速度分布,与Yuu等实验结果相吻合。分析不同的切向弹性恢复系数对颗粒相拟总温的变化规律,结果表明在低颗粒浓度时颗粒拟总温随切向弹性恢复系数而增加。     

Self-fluidization of subaerial rapid granular flows

The fast motion of gravity currents of granular solids is studied with a focus on the dynamical structure of the frontal zone. The front of the current is “immobilized” and observed in a fixed frame of reference by letting the current flow inside a rotary drum, big enough to make curvature effects negligible. The study addresses the motion of beds made of particles of different size and density, corresponding to different values of the incipient fluidization velocity. The establishment of a variety of flow regimes, including intermittent avalanching, periodic “plunging breaking” and permanent fluidization of the granular solids in the frontal zone has been recorded. Flow regimes have been related to flow conditions and to the nature of the granular solids with an attempt to define a criterion for the self-fluidization of the current. Results suggest that such a criterion should include the canonical Froude number, determining the onset of front instabilities, and the ratio of the incipient fluidization velocity of the bed solids to the velocity of the current. The relative importance of the establishment of a purely “granular liquid” state versus fluidization due to gas entrainment is addressed and discussed with a focus on the effects on solids flowability.     

Shape dependence of resistance force exerted on an obstacle placed in a gravity‐driven granular silo flow

Resistance force exerted on an obstacle in a gravity‐driven slow granular silo flow is studied by experiments and numerical simulations. In a two‐dimensional granular silo, an obstacle is placed just above the exit. Then, steady discharge flow is made and its flow rate can be controlled by the width of exit and the position of obstacle. During the discharge of particles, flow rate and resistance force exerting on the obstacle are measured. Using the obtained data, a dimensionless number characterizing the force balance in granular flow is defined by the relation between the discharge flow rate and resistance‐force decreasing rate. The dimensionless number is independent of flow rate. Rather, we find the weak shape dependence of the dimensionless number. This tendency is a unique feature for the resistance force in granular silo flow. It characterizes the effective flow width interacting with the obstacle in granular silo flow. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3849–3856, 2018     

An approximate consideration on the mechanism of gravity flow of particles through an aperture of a storage vessel on the basis of a block-flow model

A model is proposed for the gravity flow of particles that is particularly applicable to cohesive powders. The flow criterion is first estimated by describing the distribution of solids pressure within a vessel and by calculating the ‘flowability’ of a cylindrical block above the aperture. A flow rate equation is derived from a dynamic force balance on the block which gives an acceleration and a velocity profile in the discharging block. The seemingly steady flow is in fact a rapidly fluctuating one as the loading switches from one state to another. Computed results from the model explain several well known phenomena in particle discharge from hoppers and the method described gives a clear basis for design.     

Measurement of the Aerodynamic Drag Force on Single Aerosol Particles

The “picobalance” (quadrupole) was used to measure the aerodynamic drag force on individual solid particles and droplets by suspending the object in a laminar jet of gas introduced through the bottom electrode. Particles ranging in diameters from about 1 to 150 μm can be studied in this manner. The DC voltage required to maintain the particle position against the opposing forces of aerodynamic drag and gravity was measured to determine the drag force. The flow velocity at which the aerodynamic drag force balances the gravitational force yields information on the aerodynamic size, and the DC voltage required to suspend the particle against gravity with no flow provides a measure of the particle mass. Particle mobilities for spherical and irregularly shaped solids are presented. Light-scattering measurements for spherical particles provide an independent determination of size; the results are generally in good agreement with the aerodynamic size. It is shown that the electrodynamic balance can be used to measure drag forces much larger than the particle weight.     

An effective-medium analysis of confined compression of granular materials

A simplified model for confined compression of granular materials is considered, which idealizes the collection of particles as a (central) force network. Applying an effective-medium procedure, an equation with micromechanically well-defined parameters is derived, which relates the applied pressure to the engineering strain of the powder during uniaxial compression. Despite the simplicity of the model, comparison with experimental data for mm-sized spherical granules indicates that this equation is able to satisfactorily predict the overall compression profile from single-particle data.