Representative elementary volume analysis of polydisperse granular packings using discrete element method

The representative elementary volume (REV) for three-dimensional polydisperse granular packings was determined using discrete element method simulations. Granular mixtures of various sizes and particle size distributions were poured into a cuboid chamber and subjected to uniaxial compression. Findings showed that the minimum REV for porosity was larger compared with the REV for parameters such as coordination number, effective elastic modulus, and pressure ratio. The minimum REV for porosity and other parameters was found to equal 15, 10, and 5 times the average grain diameter, respectively. A study of the influence of sample size on energy dissipation in random packing of spheres has also confirmed that the REV size is about 15 times the average grain diameter. The heterogeneity of systems was found to have no effect on the REV for the parameters of interest for the narrow range of coefficient of uniformity analyzed in this paper. As the REV approach is commonly applied in both experimental and numerical studies, determining minimum REV size for polydisperse granular packings remains a crucial issue.     

基于球形颗粒几何排列的离散元试样高效生成方法

在球体离散元数值模拟中,颗粒的初始排列状态是影响计算效率和计算结果的重要环节。本文采用前进面几何构造算法,提出了一种基于网格搜索的球形颗粒随机排列高效算法。通过求解空间三边方程,满足了粒径设置的任意大小的颗粒依次置入前进面的外侧,并与构成前进面的三个颗粒相互接触。为获得高体积分数的颗粒簇,该算法允许颗粒改变其粒径大小。采用颗粒网格化方法可以简化前进面的搜索,并由此提高排列效率。通过计算平均配位数、体积分数和二阶结构张量的特征值,对不同粒径比下得到的立方体试样进行了分析,得到试样配位数及体积分数均随着粒径比的增大而增大,且得到的试样为各向同性。此外,空间网格的大小和初始颗粒的生成点对随机排列的效率均会产生显著的影响。最后,对非规则铁路道砟进行了精细构造及压碎模拟,发现DEM模拟得到的应力-应变曲线与试验结果基本吻合,验证了该算法得到的颗粒试样在模拟道砟裂纹起裂、扩展等过程的有效性。     

椭球颗粒体系剪切过程中自由体积的分布与演化

颗粒材料是一种复杂的多体相互作用体系, 由大量离散的颗粒和其周围的自由体积组成. 虽然颗粒的自由体积与颗粒材料的力学性能和变形特征的相关性已得到证实, 但是由于表征上的困难, 目前对非球形颗粒体系的局部自由体积的认识还不够充分. 本文采用连续离散耦合分析方法进行了不同主轴长度的椭球颗粒试样的三轴剪切数值模拟, 基于Set Voronoi算法对剪切过程中的颗粒试样进行了Voronoi元胞分割, 分析了颗粒试验在剪切过程中自由体积的统计分布特性和演化规律, 研究了颗粒形态对自由体积的影响. 剪切过程中Voronoi元胞的各向异性逐渐增强, 且各项异性增强程度随颗粒非球度的增加而增大, 表明非球颗粒在剪切过程中经历更加强烈的重排列. 具有不同非球度的椭球颗粒体系的局部孔隙比均服从k?Γ分布, 且这个分布仅与颗粒体系的全局孔隙比相关, 不受颗粒形态和剪切状态的影响. 局部孔隙比的波动呈现非对称拉普拉斯分布, 非对称参数刻画了局部自由体积收缩和膨胀的博弈, 其与全局孔隙比呈线性关系.      

Effect of particle degradation on electrostatic sensor measurements and flow characteristics in dilute pneumatic conveying

Vigorous particle collisions and mechanical processes occurring during high-velocity pneumatic conveying often lead to particle degradation. The resulting particle size reduction and particle number increase will impact on the flow characteristics, and subsequently affect the electrostatic type of flow measurements. This study investigates this phenomenon using both experimental and numerical methods. Particle degradation was induced experimentally by recursively conveying the fillite material within a pneumatic pipeline. The associated particle size reduction was monitored. Three electrostatic sensors were embedded along the pipeline to monitor the flow. The results indicated a decreasing trend in the electrostatic sensor outputs with decreasing particle size, which suggested the attenuation of the flow velocity fluctuation. This trend was more apparent at higher conveying velocities, which suggested that more severe particle degradation occurred under these conditions. Coupled computational fluid dynamics and discrete element methods (CFD–DEM) analysis was used to qualitatively validate these experimental results. The numerical results suggested that smaller particles exhibited lower flow velocity fluctuations, which was consistent with the observed experimental results. These findings provide important information for the accurate application of electrostatic measurement devices in pneumatic conveyors.     

Reliability study of super-ellipsoid DEM in representing the packing structure of blast furnace

In industrial blast furnaces (BFs), the investigations involving the flow behaviors of particles and the resultant burden structure are essential to optimize its operation stability and energy consumption. With the advance of computing capability and mathematical model, the discrete element method (DEM) specialized in characterizing particle behavior has manifested its power in the investigation of BFs. In the framework of DEM, many particle models have been developed, but which model is more suitable for simulating the particle behaviors of BFs remains a question because real particles in BFs have large shape and size dispersity. Among these particle models, the super-ellipsoid model possesses the ability to change shape flexibly. Therefore, the focus of this study is to investigate whether the super-ellipsoid model can meet the requirement of authenticity and accuracy in simulating the behaviors of particles with large shape and size dispersity. To answer this question, a simplified BF charging system composed of a hopper and a storage bin is established. The charging process and the final packing structure are analyzed and compared between experiments and simulations with different shape indexes. The results show that super-ellipsoid particles have prominent advantages over spherical particles in terms of representing the real BF particles, and it can more reasonably reproduce the flow behaviors and packing structure of experimental particles. The computation cost of super-ellipsoid particles is also acceptable for engineering applications. Finally, the micro-scale characteristics of packing structure is analyzed and the single-ring charging process in industry-scale BF using super-ellipsoid particles is conducted.     

点载荷作用下密集颗粒物质的传力特性分析

利用颗粒离散元商业软件PFC3D, 模拟了在2m*1m*0.01m容器中直径分别为0.01m, 0.008m和0.006m的颗粒各1*10$^4$个, 受重力作用下的静态密集堆积; 以此为初始条件, 在表层随机选择7个颗粒分别施加5.2*10$^{ - 2}$N(100倍最大颗粒重量)的点载荷, 进行应力传播特点研究. 结果表明: 力的传递在局部范围内呈现很强的各向异性; 应力涨落随着距离的增加呈指数下降; 在大于5倍最大颗粒粒径时, 其分布可以使用弹性力学理论来计算. 探讨了摩擦系数$\mu =0$, 0.2, 1对应力传递的影响, 随着摩擦系数的增加, 各向异性范围减小.     

石英砂粒径对水合物沉积物力学性质的影响

利用自主研发的水合物沉积物原位合成与力学性质测试的高压低温三轴仪,通过多级加荷的试验方法,以不同粒径的砂粒作为沉积物骨架进行三轴压缩试验,得到了剪切过程的应力-应变关系曲线,以及不同粒径尺寸沉积物的强度,还有剪切过程中的体积变化关系。结果表明:含水合物沉积物强度随着沉积物粒径尺寸的增大而增强;在降压剪切过程中,所有粒径的水合物沉积物式样均有明显的剪缩现象。     

An empirical model predicting the viscosity of highly concentrated, bimodal dispersions with colloidal interactions

The relationship between particle size distribution and viscosity of concentrated dispersions is of great industrial importance, since it is the key to get high solids dispersions or suspensions. The problem is treated here experimentally as well as theoretically for the special case of strongly interacting colloidal particles. An empirical model based on a generalized Quemada equation is used to describe η as a function of volume fraction for mono- as well as multimodal dispersions. The pre-factor η˜ accounts for the shear rate dependence of η and does not affect the shape of the η vs φ curves. It is shown here for the first time that colloidal interactions do not show up in the maximum packing parameter and φ_max can be calculated from the particle size distribution without further knowledge of the interactions among the suspended particles. On the other hand, the exponent ɛ is controlled by the interactions among the particles. Starting from a limiting value of 2 for non-interacting either colloidal or non-colloidal particles, ɛ generally increases strongly with decreasing particle size. For a given particle system it then can be expressed as a function of the number average particle diameter. As a consequence, the viscosity of bimodal dispersions varies not only with the size ratio of large to small particles, but also depends on the absolute particle size going through a minimum as the size ratio increases. Furthermore, the well-known viscosity minimum for bimodal dispersions with volumetric mixing ratios of around 30/70 of small to large particles is shown to vanish if colloidal interactions contribute significantly. Received: 7 June 2000/Accepted: 12 February 2001     

Effect of particle shape on micro- and mesostructure evolution of granular assemblies under biaxial loading conditions

Discrete element method (DEM) numerical biaxial tests on samples with different particle shapes are performed to investigate how the multiscale evolves with varying particle shape. The samples used in such simulations are composed of circular, square, and elongated particles, respectively. For the numerical results, analyses are conducted in terms of microscopic evolution, i.e. particle rotation and evolution of fabric, and mesoscopic evolution, i.e. the evolution of loops and improved clustering coefficient. At the microscale, the mean particle rotation of circular particles is remarkably larger than those of square and elongated particles, and the shear band localization phenomenon is more obvious when the aspect ratio (AR) decreases. Considering the fabric evolving with particle shape, the value of anisotropy gradually increases when particle shape becomes irregular, and contacts of circular particles are pronouncedly less than those of irregular particles from the coordination number and curves of degree distribution. At the mesoscale, when the particle relationship is considered, the isotropic particles (i.e. circular and square particles) have similar evolutions of loops and modified clustering coefficient, whereas the elongated particles have remarkable three loops and modified clustering coefficient, which are both larger than those of isotropic particles.     

离散元法铁粉末压制中粒径分布对力链演化机制的影响

为阐明粒径分布对铁粉压制中体系内部细观力学行为的影响, 基于离散元理论, 通过改变铁粉颗粒粒径分布建立压制模型, 结合力链提取方法, 通过对力链空间分布、力链数目、力链长度和力链方向性的分析, 探究粒径分布对力链演化的影响机理. 研究结果表明: 不同粒径分布的粉体压制时形成的力链空间分布具有差异, 粒径分布范围越小, 形成的力链分布越集中, 反之, 粒径分布范围越大, 形成的力链分布越松散且均匀; 在粉末压制时, 粒径分布对力链数目也有影响, 具体表现为随着粉体的粒径分布范围变大, 力链总数逐渐减少; 粉体的粒径分布对颗粒形成短力链的数目起着显著影响, 而对力链长度的影响较为有限; 随着粒径分布范围的增大, 力链的方向由均匀分布逐渐集中在特定角度方向, 表现出一定各向异性, 形成的交叉力链网络结构有利于提高粉体致密化程度. 本文为从粉体粒径分布影响层面拓展粉末压制细观力学理论提供基础, 亦为进一步结合粉体粒径分布及体系内力链演变过程改善粉末致密化行为提供指导.      

转动驱动圆角立方体颗粒有序堆积的离散元模拟

宏观颗粒体系的有序堆积研究可以为热系统中微观粒子的自组装提供研究模型,也有助于工业生产中提高颗粒材料的填充率.实验发现圆筒中的圆角立方体颗粒受容器往复旋转剪切作用会实现有序堆积.为探究旋转圆筒中立方体颗粒有序堆积过程的内部结构演化过程和动力学机理,采用超二次曲面方程构造了圆角立方体颗粒,基于离散元方法对旋转剪切作用下圆...     

Microstructural investigations of the yielding behaviour of bidisperse magnetorheological fluids

Particle level simulations were used to investigate the effects of size bidispersity and particle size ratios on the static and yielding behaviour of magnetorheological fluids (MRF). The MRF were treated as linearly magnetisable, neutrally buoyant particles dispersed in a viscous carrier liquid. In the quiescent mode (static structures), the bidisperse suspensions were found to have a higher tendency to form straight chains than the monodisperse suspensions; this is consistent with previous findings. Under steady shearing, the bidisperse suspensions exhibited higher stress enhancement than the monodisperse systems. The stress enhancement in bidisperse suspensions is likely to be due to the population and orientation of interacting large particles in the bidisperse suspensions.     

Characterization of particle-laden, confined swirling flows by phase-doppler anemometry and numerical calculation

The particle dispersion characteristics in a confined swirling flow with a swirl number of approx. 0.5 were studied in detail by performing measurements using phase-Doppler anemometry (PDA) and numerical predictions. A mixture of gas and particles was injected without swirl into the test section, while the swirling airstream was provided through a co-flowing annular inlet. Two cases with different primary jet exit velocities were considered. For these flow conditions, a closed central recirculation bubble was established just downstream of the inlet.

The PDA measurements allowed the correlation between particle size and velocity to be obtained and also the spatial change in the particle size distribution throughout the flow field. For these results, the behaviour of different size classes in the entire particle size spectrum, ranging from about 15 to 80 μm, could be studied, and the response of the particles to the mean flow and the gas turbulence could be characterized. Due to the response characteristics of particles with different diameters to the mean flow and the flow turbulence, a considerable separation of the particles was observed which resulted in a streamwise increase in the particle mean number diameter in the core region of the central recirculation bubble. For the lower particle inlet velocity (i.e. low primary jet exit velocity), this effect is more pronounced, since here the particles have more time to respond to the flow reversal and the swirl velocity component. This also gave a higher mass of recirculating particle material.

The numerical predictions of the gas flow were performed by solving the time-averaged Navier-Stokes equations in connection with the well known kε turbulence model. Although this turbulence model is based on the assumption of isotropic turbulence, the agreement of the calculated mean velocity profiles compared to the measured gas velocities is very good. The gas-phase turbulent kinetic energy, however, is considerably underpredicted in the initial mixing region. The particle dispersion characteristics were calculated by using the Lagrangian approach, where the influence of the particulate phase on the gas flow could be neglected, since only very low mass loadings were considered. The calculated results for the particle mean velocity and the mass flux are also in good agreement with the experiments. Furthermore, the change in the particle mean diameter throughout the flow field was predicted approximately, which shows that the applied simple stochastic dispersion model also gives good results for such very complex flows. The variation of the gas and particle velocity in the primary inlet had a considerable impact on the particle dispersion behaviour in the swirling flow and the particle residence time in the central recirculation bubble, which could be determined from the numerical calculations. For the lower particle inlet velocity, the maximum particle size-dependence residence time within the recirculation region was considerably shifted towards larger particles.     

DEM simulation of particle percolation in a packed bed

The phenomenon of spontaneous particle percolation under gravity is investigated by means of the discrete element method. Percolation behaviors such as percolation velocity, residence time distribution and radial dispersion are examined under various conditions. It is shown that the vertical velocity of a percolating particle moving down through a packing of larger particles decreases with increasing the restitution coefficient between particles and diameter ratio of the percolating to packing particles. With the increase of the restitution coefficient, the residence time and radial dispersion of the percolating particles increase. The packing height affects the residence time and radial dispersion. But, the effect can be eliminated in the analysis of the residence time and radial dispersion when they are normalized by the average residence time and the product of the packing height and packing particle diameter, respectively. In addition, the percolation velocity is shown to be related to the vertical acceleration of the percolating particle when an extra constant vertical force is applied. Increasing the feeding rate of percolating particles decreases the dispersion coefficient.     

DEM simulation of particle percolation in a packed bed

The phenomenon of spontaneous particle percolation under gravity is investigated by means of the discrete element method. Percolation behaviors such as percolation velocity,residence time distribution and radial dispersion are examined under various conditions. It is shown that the vertical velocity of a percolating particle moving down through a packing of larger particles decreases with increasing the restitution coefficient between particles and diameter ratio of the percolating to packing particles. With the increase of the restitution coefficient,the residence time and radial dispersion of the percolating particles increase. The packing height affects the residence time and radial dispersion. But,the effect can be eliminated in the analysis of the residence time and radial dispersion when they are normalized by the average residence time and the product of the packing height and packing particle diameter,respectively.In addition,the percolation velocity is shown to be related to the vertical acceleration of the percolating particle when an extra constant vertical force is applied. Increasing the feeding rate of percolating particles decreases the dispersion coefficient.     

Estimation of structural element sizes in sand and compacted blocks of ground calcium carbonate using a void network model

An algorithm has been developed for the calculation of the size of the effective structural or skeletal elements which make up the solid phase of an unconsolidated or consolidated porous block. It is based on a previously presented algorithm, but it has now been validated on unconsolidated samples and tested on consolidated samples. It also includes a virtual reality representation of the structures. First, a network model named Pore-Cor is made to reproduce the percolation behaviour of the experimental sample, by matching its simulated percolation characteristics to an experimental mercury intrusion curve. The algorithm then grows skeletal elements between the cubic pores and cylindrical throats of the void network model until they touch up to four of the adjacent void features. The size distributions of the simulated solid elements are compared with each other and with experimentally determined particle size distributions, using a Mann–Whitney test. The algorithm was shown to simulate skeletal elements with the correct trends in size distribution for two different sand samples, provided the sand packed itself optimally under the applied mercury pressure. It was also applied to two samples of variously compressed calcium carbonate powder, having fine and coarse particle size distributions respectively. The simulation demonstrated that on compressing the powder at the minimum force, the skeletal elements differed from the constituent particle sizes, as expected. The average size of the skeletal elements increased as the compression force was increased on the calcium carbonate powders. The results suggest that the method could be useful as a tool for probing the effect of compaction on aggregation or sintering, and for studying other effects such as cementation in geological samples, where other more direct techniques cannot be applied.     

粗粒土离散元非球趋真颗粒模型

颗粒形状对粗粒土的物理力学特性有着显著的影响。离散元法广泛应用于粗粒土宏观物理力学特性的细观机理研究。为了考虑颗粒形状的影响,亟待发展计算高效的离散元非球趋真颗粒模型。本文基于X射线CT扫描技术并结合数字图像处理技术,对光滑和棱角性两类典型粗粒土(鹅卵石与碎石)进行三维重构,并提出了两类趋真颗粒模型,分别采用扩展超椭球模型和球多面体模型进行趋真逼近;开展了两类颗粒试样的3D打印和单轴压缩试验,分析了配位数和局部孔隙率分布等细观特性;基于离散元开源程序SudoDEM开展了两类试样的离散元模拟,并将模拟细观分析结果与物理试验进行了对比。结果表明,提出的两类趋真颗粒模型能够较好地对粗粒土颗粒进行离散元建模。     

THE VARIATIONS OF PHYSICAL AND MECHANICAL PROPERTIES OF REMODELING AND UNDISTURBED EXPANSIVE ROCKS OF DIFFERENT PARTICLE SIZES 1)

以南宁盆地膨胀岩为研究对象,通过室内试验测定原状样与不同颗粒粒径重塑样的膨胀力、抗剪强度及热特性,研究其性质差异。结果表明：重塑后不同粒径范围膨胀岩土样的无荷膨胀率较原状样明显升高,而主应力差峰值、抗剪强度和热物理指标较原状样均有降低。因此,应选择合适粒径范围的土颗粒重塑代替原状样进行室内试验：无荷膨胀率和膨胀力试验应选择粒径范围1 mm≤d<2 mm的土颗粒;三轴试验和热物理指标测试应尽量选择粒径较小的土颗粒。     

Hydrodynamic and thermal interactions of a cluster of solid particles in a pool of liquid of different Prandtl numbers using two-fluid model

The knowledge of thermal interaction between hot particles and liquid is essential for many engineering applications. The main focus of the present study is to understand the underlying phenomena of transient interaction between the hot particles and the liquid of varying Prandtl number under different parametric conditions. Analysis is carried out numerically using in-house multiphase code based on Eulerian two-fluid laminar model. The code is validated against existing results. The dispersion and penetration characteristics of the particles are observed to be a strong function of Prandtl number as well as volume fraction and particle diameter, with a stronger mushrooming observed for lower particle size or high Prandtl number liquid. The thermal interaction is observed to be between the particles and the narrow thermal envelope surrounding the particles. The particles cooling rate are observed to be several orders faster in a liquid with lower Prandtl number.