Discrete element method study on hopper discharge behaviors of binary mixtures of nonspherical particles

This study is aimed at unveiling the influence of binary mixtures of nonspherical particles on hopper discharge behavior, which remains poorly understood. The discrete element method (DEM) is employed to simulate seven particle types with aspect ratios between 0 and 2 (namely, a sphere, two ellipsoids, two cylinders, and two cuboids) with the same volume. Seven monodisperse systems and twelve binary-shape mixtures are assessed. For the monodisperse systems, particle shape is the dominant factor dictating discharge rate, compared to other factors like aspect ratio, preferential orientation, and packing. Regarding the binary-shape mixtures, the discharge rates are similar for all twelve mixtures, reflecting a surprising lack of shape effects, which in turn means the negligible impact of solid volume fraction, aspect ratio, and segregation extent. Moreover, collision force is generally negatively correlated with discharge rate.     

Discrete element analysis of experiments on mixing and stoking of monodisperse spheres on a grate

Understanding the details of the mixing and stoking process on grate firing systems is crucial for the optimization of the combustion process in waste or biomass incineration plants. The Discrete Element Method (DEM) can help to obtain further information on the mixing process within a bed of fuel particles. Especially the influence of a change in operational parameters can be examined avoiding large experimental effort. In the current paper five simulations for a generic grate are compared with the corresponding experiments. The experiments were carried out throughout an anterior parameter study on mixing and stoking on a grate [Sudbrock F.; Simsek E.; Wirtz S.; Scherer V.: “An experimental analysis of the influence of operational parameters on mixing and stoking of a monodisperse granulate on a grate”, Powder Technology 198, Issue 1, 29-37, 2010] [19]. The system considered is equipped with vertically moving bars which induce stoking. In a first approach monodisperse plastic spheres are used. The grate is encased by a transparent polycarbonate housing which provides optical access to the movement of the particles in the wall planes. The mixing process is measured and quantified by image analysis of the front wall of the grate. The mixing behaviour of the particle assembly observed in experiments and simulation appears to be very similar indicating that DEM is able to predict the particle mixing in the bed. In order to quantify the visual observations the mixing behaviour has been evaluated by different mixing parameters. They are compared in dependence of the number of strokes of the grate bars. A good agreement between measurements and simulations could be observed.     

三维喷动床内异径干湿颗粒混合特性数值模拟

基于计算流体力学-离散单元法,建立了三维喷动床内气固两相流数学模型,采用Fortran语言编制了并行数值模拟程序。对三维喷动床内两种不同直径的干颗粒及湿颗粒的混合特性进行了数值模拟,并从颗粒角度分析了双组分颗粒的运动机制。利用Lacey混合指数对床内整体以及特定区域的混合程度进行了定量分析,并研究了液桥体积、颗粒密度比以及表观气速对异径颗粒混合的影响。结果表明：在单孔射流喷动床内,干湿两种颗粒流动方式相似,湿颗粒无明显的聚团现象;液桥力对小直径的颗粒影响较大,使不同直径湿颗粒速度差减小;环隙区内颗粒的混合是影响整床颗粒混合的关键因素;液桥体积对颗粒混合的影响较大,对颗粒密度比以及表观气速的影响有限。     

Discrete element simulation of free flowing grains in a four‐bladed mixer

Numerical simulations of granular flow in a cylindrical vessel agitated by a four‐blade impeller were performed using the discrete element method. Velocity, density, and stress profiles within the mixer displayed a periodic behavior with a fluctuation frequency equal to that of the blade rotation. Blade orientation was found to affect flow patterns and mixing kinetics. For an obtuse blade pitch orientation, a three‐dimensional recirculation zone develops in‐front of the blade due to formation of heaps where the blades are present. This flow pattern promotes vertical and radial mixing. No recirculation zone was observed when the blade orientation was changed to an acute blade pitch. The system's frictional characteristics are shown to strongly influence the granular behavior within the mixer. At low friction coefficients, the 3‐D recirculation in front of the obtuse blade is not present reducing convective mixing. Higher friction coefficients lead to an increase in granular temperature which is associated with an increase in diffusive mixing. Normal and shear stresses were found to vary with mixer height with maximum values near the bottom plate. Additionally, a strong dependence between the magnitude of the shear stresses and the friction coefficient of the particles was found. The stress tensor characteristics indicate that the granular flow in our simulations occurs in the quasi‐static regime. At the same time, the averaged pressure was found to vary linearly with bed height and could be predicted by a simple hydrostatic approximation. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Numerical simulation of aggregate dispersion in different flow fields using discrete element method

An attempt was made to study the aggregate dispersion process in three different flow fields namely; steady shear, elongation flow, and combined shear and elongational flows using the discrete element method. The simulation was performed on two aggregate structures characterized by their fractal dimensions. The predicted results showed that the aggregate break‐up process evaluated in terms of weighted average fragment size 〈w〉 follows a power–law type relation as 〈w〉 = kt^?m in all the three flow fields. The dispersion performance of different flow fields evaluated by dispersing rate and a final steady‐state fragment size was found to be dependent upon the extent of applied stress and flow fields such that at low applied stress levels much smaller steady state values of 〈w〉 could be obtained for the elongational flow. The aggregate structure, characterized by its fractal dimension, was found to have different effects on the aggregate dispersion process depending on the flow field and applied stress level. The results predicted from this simulation could be explained in terms of ability of flow fields in rotating the aggregates and fragments in appropriate position to be broken up and the fractal dimensions of aggregates. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

单孔射流流化床内颗粒混合特性的数值模拟

在欧拉-拉格朗日坐标系下,采用离散单元法对单孔射流流化床内颗粒混合特性进行了数值模拟。引入混合指数对床内轴向及径向布置的颗粒混合质量进行定量分析,并研究了不同表观气速、不同弹性系数对颗粒混合特性的影响。模拟得到了颗粒轴向及径向混合序列图、气体和颗粒速度分布、整床颗粒混合指数分布、参量变化时整床颗粒混合指数分布。结果表明：流化床床层内颗粒混合速度受颗粒内循环能力和颗粒扩散能力的综合作用。单口射流喷动流化床颗粒轴向混合速度主要由颗粒内循环速度决定,颗粒径向混合速度主要由颗粒扩散能力决定。表观气速增大时,颗粒内循环速度增加,从而加快了颗粒轴向混合进程,但对颗粒径向混合影响微弱;弹性系数增大时,颗粒混合速度及混合质量均下降,并且弹性系数增大对颗粒径向混合进程影响小于颗粒轴向混合。     

煤浆混合槽混合性能的数值模拟

利用计算流体力学(CFD)方法研究煤浆混合槽的混合性能。采用Fluent 6.2计算软件,选用多重参考系法(MRF)、RNGk-ε湍流模型以及混合物多相流模型,对卧式煤浆混合槽的内部流动情况进行数值模拟,得到了湍流强度、湍动能、压力、速度分布以及出口各相分布等混合性能。模拟结果与实验结果进行了初步比较,吻合较好。研究结果表明,混合时在挡板和搅拌浆叶之间产生漩涡,有利于防止物料堆积,使混合更均匀。     

粉体混合过程及搅拌功率的DEM数值模拟和实验

采用数值模拟与功率测试相结合的方法,研究直叶桨式粉体混合机搅拌过程及搅拌功率、扭矩的变化规律。对粉体混合机内球形颗粒的混合过程进行离散单元法DEM数值模拟,研究直叶桨式粉体混合机内搅拌转速、搅拌桨直径、桨叶数目等特性参数对粉体混合时搅拌功率和扭矩的影响,并拟合得到功率计算公式。搭建粉体搅拌试验台,测试粉体搅拌功率并与模拟结果比较。结果表明,直叶桨式粉体混合机内功率消耗与搅拌桨转速、搅拌桨直径、桨叶数目等特性参数有密切关系。同时,扭矩值和功率值与搅拌桨转速、搅拌桨直径和桨叶数目都呈正相关。实验得到了与模拟类似的扭矩-转速关系以及功率-转速关系,模拟值与测试值具有较好的吻合性,验证了所推导公式的准确性。     

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。     

Discrete element method simulation of three-dimensional conical-base spouted beds

A discrete element method (DEM) simulation of three-dimensional conical-base spouted beds is presented. The overall height and diameter of the vessel are 0.5 and 0.15 m, respectively, and the nozzle diameter is 0.02 m. The inclined angle of the conical section varies from 0 to 60 degrees. The gas flow is described by the continuity and Navier-Stokes equations and solved by a finite difference method of second order accuracy in space and time. For gas-particle interaction, the Ergun equation (for void fraction smaller than 0.8) and the Wen-Yu model (for void fraction of 0.8 and above) are employed. A new method for treatment of the boundary condition for 3-D gas flow along the cone surface is proposed. This boundary condition satisfies both the continuity and momentum-balance requirements for the gas phase. Usefulness of the present simulation for studying gas flow pattern and particle motion in conical-base spouted beds is demonstrated. The effects of the inclined angle and draft tube on gas and particle flow in spouted beds are discussed.     

喷射器内湍流混合的多尺度模拟

利用宏观混合分数方差和微观混合分数方差定量表征宏观混合和微观混合状态,对喷射器内的湍流混合进行了多尺度模拟和研究,并计算出了达到完全混合所需要的特征混合时间。对不同操作条件下的多尺度混合情况进行了模拟计算和分析。结果表明：在引射流速度不变的情况下,增加喷嘴速度,可以降低达到完全混合所需要的时间;在喷嘴速度不变的情况下,增加引射流速度,可以增加达到完全混合所需要的时间;在喷嘴和引射流速度比不变的情况下,增加两者绝对速度,可以降低达到完全混合所需要的时间;在本文所研究的情况下,喷射反应器内湍流混合过程由微观混合控制。     

回转干馏炉内颗粒间传热特性的数值模拟

将离散元方法与颗粒热传导模型相结合,研究了页岩灰颗粒与油页岩颗粒在回转干馏炉内的混合传热过程,采用混合指数、颗粒平均温度和温度标准偏差作为评价混合传热效果的指标,分析了填充率、炉体转速、油页岩粒径及抄板形式对颗粒间混合传热特性的影响规律。结果表明,炉体转速和油页岩粒径是影响颗粒混合传热效果的主要因素,而填充率和抄板形式对混合传热效果的影响相对较小。当炉内未设抄板时,随着填充率和油页岩粒径的增大,颗粒间分层现象使混合传热效果变差,而随炉体转速的提高传热效果呈现出先增强后减弱的趋势;设抄板时,抄板形式对炉内颗粒间的混合起到不同程度的扰动作用,从而使传热效果得到显著改善。     

Numerical simulation of breakage of two-dimensional polygon-shaped particles using discrete element method

Using DEM (Discrete Element Method), a model is presented to simulate the breakage of two-dimensional polygon-shaped particles. In this model each uniform (uncracked) particle is replaced with smaller inter-connected sub-particles which are bonded with each other. If the bond between these sub-particles breaks, breakage will happen. With the help of this model, it is possible to study the influence of particle breakage on macro and micro mechanical parameters. In this simulation, the evolution of microstructure in granular assemblies can be seen by tracing of coordination number during the shear process. Also variation of contact normal, normal force and tangential force anisotropy can be tracked. To do so, two series of biaxial test simulations (breakage is enabled and disabled) are conducted on assemblies of two-dimensional polygon-shaped particles and the results are compared. The results are presented in terms of macro and micro mechanical behavior for different confining pressures.     

提升管内气固两相双组分颗粒流动的离散颗粒硬球模型的模拟

基于离散颗粒(DPM)硬球模型,数值模拟提升管内双组分颗粒气固两相湍流流动行为。应用Vreman的亚格子尺度（SGS）模型模拟气体湍流,建立考虑不同颗粒加速度效应的两颗粒碰撞最小时间计算模型。数值模拟预测了大颗粒和小颗粒的速度和浓度分布。研究结果表明小颗粒具有高的轴向速度和脉动速度,而大颗粒具有低的轴向速度和脉动速度。在床中心区域,小颗粒轴向速度分布出现3个峰值,对于大颗粒轴向速度仅出现两个峰值。在壁面区域大颗粒和小颗粒速度均出现两个峰值。沿床径向方向呈现床中心颗粒浓度低、壁面区域颗粒浓度高的环核流动结果。随着表观气速的增大,颗粒浓度沿径向和床高分布趋于均匀。在床中心区域模拟计算轴向颗粒速度、颗粒浓度和RMS速度与文献实验结果相吻合。在提升管内气体湍流对小颗粒流动具有一定的影响,颗粒间碰撞作用对颗粒相流动的影响大于气相湍流的影响。     

Effect of friction coefficient and density on mixing particles in the rolling regime

In this work, optical imaging is used to quantify the mixing dynamics of granular materials. Two different methods (GLCM and Multivariate RGB analysis) are combined to extract surface information and the time to achieve a specific degree of mixing. In particular, the effect of density, friction coefficient, surface quality and particle geometry was studied. The results show that the Froude number alone is not enough to completely characterize the rolling regime. In addition, the filling ratio must be in a specific range which depends on the material properties.     

A particle‐scale index in the quantification of mixing of particles

Discrete element method (DEM) is a useful tool for obtaining details of mixing processes at a particle scale. It has been shown to satisfactorily describe the flow structure developed in bladed mixers. Here, the advantage is taken of the microstructure gained from DEM to evaluate how best to quantify the microstructure created by mixing. A particle‐scale mixing index (PSMI) is defined based on coordination numbers to represent the structure of a particle mixture. The mixture quality is then analyzed qualitatively and quantitatively in three different ways: a macroscopic mixing index based on the conventional approach, coordination number, and PSMI. Their effectiveness is examined based on DEM data generated for different particle loading arrangements and binary mixtures of particles with various volume fractions, size ratios, and density ratios. Unlike the two other methods, PSMI reveals in a straightforward manner whether a binary mixture of different particles is mixing or segregating over time, while being able to detect particle‐scale structural changes accompanying the mixing or segregation processes in all the mixtures investigated. Moreover, PSMI is promising in that it is not influenced by the size and number of samples, which afflict conventional mixing indexes. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

复合移动床电石反应器中颗粒运动的离散单元法模拟

针对复合移动床反应器内固体颗粒运动,采用离散单元法模型（DEM）考察布料器分别为扇形开口和矩形开口时,布料器转速和开口对颗粒运动的影响,并基于文献结果论证了本文模型的准确性。模拟结果表明：①对于不同布料器,颗粒在移动床中呈现平推流和汇聚流两种流动形态。②随布料器转速及开口的增加,颗粒质量通量非线性增加。③随布料器转速的增加,下落床径向上颗粒分布更均匀;随布料器开口的增大,下落床径向上颗粒分布范围变大,颗粒分布更均匀;对下落床径向上颗粒分布,布料器扇形开口时分布呈U形、矩形开口时分布呈M形。④沿反应器轴向向下,颗粒分布有均匀化趋势;扇形开口布料器对颗粒分布的离散系数大于1,矩形开口布料器对颗粒分布的离散系数约为0.5。     

Adding active particles for overall aggregation in a mixing tank: A computational study

In order to achieve flocculation in a dense agitated solid-liquid suspension of nonaggregating particles, we explore scenarios where we add a limited amount of aggregative (ie, active) particles that can bind the nonaggregative particles. The performance of this process hinges on the competition between mixing (spreading the active particles over the flow volume) and aggregation among the active particles, with the latter reducing their effectiveness. The research has been conducted in a computational manner: direct simulations of transitional flow in a mixing tank (at an impeller-based Reynolds number of 4000) are two-way coupled with the dynamics of a collection of spherical, equally sized particles that are given specific aggregative properties. The overall solids volume fraction is 10%. A small fraction of all solid particles (5.8%) is active. Aggregation is quantified by means of the average coordination number as well as the aggregate size distribution. The way the active particles are released in the tank volume has a significant effect on the overall levels of aggregation, specifically for active particles with a strong aggregative force.     

卧式单轴捏合反应器流动与混合特性的数值模拟

选取卧式单轴捏合反应器为研究对象,搭建了一个可视化实验装置来研究其分布混合过程,并且通过三维有限元数值模拟方法和网格重叠技术获取了高黏牛顿流体在反应器中的流速分布、剪切速率分布与混合指数分布,进一步采用粒子示踪技术分析了全局与局部分布混合过程,对示踪粒子的运动轨迹进行统计分析得到了拉伸率与混合效率,并且考察了搅拌结构对流动与混合过程的影响。结果表明,实验与数值模拟结果吻合较好。捏合反应器中几乎不存在流动死区,搅拌轴上的动态捏合杆与搅拌槽壁面上的静态捏合杆之间存在周期性的捏合作用,可以强化自清洁性能、剪切作用、整体与局部分布混合过程、分散混合性能以及混合效率。拉伸率随着混合时间以指数形式增加,时均混合效率大于零。