Validating granular segregation rate models

One significant hindrance to the development of granular segregation rate models is the inherent difficulty of performing the dynamic experiments required for validation. Here, we seek to overcome this experimental hurdle by establishing an “equilibrium” between segregation and flow perturbation in free surface granular flows and use steady‐state—rather than dynamic—measurements for validation. That is, we combine the segregation rate expressions to be tested with a segregation control framework such that the perturbation rate enables us to infer the segregation rate by measuring simply the steady state extent of segregation. We use periodic flow inversions via an axially located baffle in a tumbler‐type mixer to provide the perturbations that ultimately alter the steady‐state distribution of particles. This work examines the efficacy of existing models for binary segregation driven by either size or density differences. For completeness, we test our model validation framework both computationally and experimentally. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3756–3763, 2017     

Simulation and modeling of segregating rods in quasi‐2D bounded heap flow

Many products in the chemical and agricultural industries are pelletized in the form of rod‐like particles that often have different aspect ratios. However, the flow, mixing, and segregation of non‐spherical particles such as rod‐like particles are poorly understood. Here, we use the discrete element method (DEM) utilizing super‐ellipsoid particles to simulate the flow and segregation of rod‐like particles differing in length but with the same diameter in a quasi‐2D one‐sided bounded heap. The DEM simulations accurately reproduce the segregation of size bidisperse rod‐like particles in a bounded heap based on comparison with experiments. Rod‐like particles orient themselves along the direction of flow, although bounding walls influence the orientation of the smaller aspect ratio particles. The flow kinematics and segregation of bidisperse rods having identical diameters but different lengths are similar to spherical particles. The segregation velocity of one rod species relative to the mean velocity depends linearly on the concentration of the other species, the shear rate, and a parameter based on the relative lengths of the rods. A continuum model developed for spherical particles that includes advection, diffusion, and segregation effects accurately predicts the segregation of rods in the flowing layer for a range of physical control parameters and particle species concentrations. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1550–1563, 2018     

Density segregation of dry and wet granular mixtures in gas fluidized beds

The Discrete Element Method combined with Computational Fluid Dynamics was coupled to a capillary liquid bridge force model for computational studies of mixing and segregation behaviors in gas fluidized beds containing dry or wet mixtures of granular materials with different densities. The tendency for density segregation decreased with increasing fluidizing velocity, coefficient of restitution, and amount of liquid present. Due to the presence of strong capillary forces between wet particles, there was a high tendency for particles to form agglomerates during the fluidization process, resulting in lower segregation efficiency in comparison with fluidization of dry particles. Particle‐particle collision forces were on average stronger than both fluid drag forces and capillary forces. The magnitudes of drag forces and particle‐particle collision forces increased with increasing fluidizing velocity and this led to higher mixing or segregation efficiencies observed in dry particles as well as in wet particles at higher fluidizing velocities. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4069–4086, 2015     

An arrangement of ideal reactors as a way to model homogenizing processes with a planetary mixer

This article investigates ways of modeling the homogenization mechanism occurring when mixing highly viscous Newtonian fluids with a planetary mixer. In particular, an arrangement of ideal reactors containing a perfect‐mixed zone sweeping out a torus reactor is proposed to represent the dynamics of the mixing process. The originality of the arrangement of ideal reactors developed is due to the time–dependent location of the perfect‐mixed zone in the torus which mimics the periodic revolution motion of the agitator around the vertical and central axis in the vessel. To ascertain the reliability of the method proposed, tracer injections were carried out with a planetary mixer named TRIAXE® system. It is shown that modeling results are in close agreement with experimental ones on the whole range of impeller revolution speeds tested. The model proposed captures well the physical mixing phenomena. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

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     

On the performance of static mixers: A quantitative comparison

The performance of industrially relevant static mixers that work via chaotic advection in the Stokes regime for highly viscous fluids, flowing at low Reynolds numbers, like the Kenics, the Ross Low-Pressure Drop (LPD) and Low-Low-Pressure Drop (LLPD), the standard Sulzer SMX, and the recently developed new design series of the SMX, denoted as SMX(n) (n, N_p, N_x) = (n, 2n − 1, 3n), is compared using as criteria both energy consumption, measured in terms of the dimensionless pressure drop, and compactness, measured as the dimensionless length. Results are generally according to expectations: open mixers are most energy efficient, giving the lowest pressure drop, but this goes at the cost of length, while the most compact mixers require large pressure gradients to drive the flow. In compactness, the new series SMX(n), like the SMX(n = 3) (3, 5, 9) design, outperform all other devices with at least a factor 2. An interesting result is that in terms of energy efficiency the simple SMX (1, 1, 4, θ = 135°) outperforms the Kenics RL 180°, which was the standard in low pressure drop mixing, and gives results identical to the optimized Kenics RL 140°. This makes the versatile “X”-designs, based on crossing bars, superior in all respects.     

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     

Density segregation in vibrated granular beds with bumpy surfaces

Segregation of granular materials by virtue of density or size is a commonly encountered phenomenon in nature. Despite its widespread interest among many researchers in recent years, a complete and unified understanding of granular segregation remains elusive to date. Using molecular dynamics simulations, we report a novel technique of inducing density segregation in a binary mixture of granular materials subjected to vibrations by the use of a bumpy vibrating base. Density segregation in the vertical directions may be induced by oscillating the bumpy base composed of discrete solid particles vertically or horizontally. In both cases, lighter particles tended to rise to the top of the granular bed and form a layer above the heavier particles. We suggest that differences in granular temperature profiles arising from the two different modes of vibrations may play an important role in determining the extent of density segregation occurring in binary granular mixtures. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

颗粒物料在半封闭式回转鼓内的混合特性

采用DEM离散单元法,对不同转速与倾角下半封闭式回转鼓内颗粒物料的混合过程进行了模拟。通过“颗粒接触数”定义的分离指数S,分析了不同转速和倾角对回转鼓内颗粒物料径向与轴向混合特性的影响。结果表明：转速与倾角对回转鼓内颗粒物料径向与轴向混合特性有显著的影响;倾角不变,转速分别为15r/min、30r/min、45r/min时,颗粒物料的径向与轴向混合速度随转速的增加而增加,当转速超过30r/min后,增加转速对径向与轴向混合速度的影响越来越小;转速不变,倾角分别为0°、17°、34°时,增大倾角能有效的增加轴向混合速度,但对径向混合速度没有促进作用,当倾角超过17°后,轴向混合速度的增幅随着倾角的增加而逐渐变小,而径向混合速度随着倾角的增大而减小,但增加转速可以减小径向混合速度下降幅度。     

Fluidization of mixtures of two solids: A unified model of the transition to the fluidized state

Fluidization of binary beds of dissimilar solids has place along a fluidization velocity interval bounded by the “initial” and the “final fluidization velocity” of the mixture, with segregation phenomena that continuosly change the internal distribution of its components. Varying with the relative importance of size and density differences between components, the fluidization process may follow more than one mechanism, depending on whether the process of fluidization starts from bed top or bottom. It is shown how, irrespective of the fluidization pattern exhibited by the two‐solid system, the limiting velocities of its fluidization interval can be calculated with good accuracy by the same relationships, derived from the analysis of the fluidization force equilibrium. The model proposed provides a unique theoretical frame for the analysis of the fluidization behavior of any two‐solid system and encompasses as a particular case the behavior of simpler mixtures, whose components differ only in density or size. © 2012 American Institute of Chemical Engineers AIChE J, 59: 729–735, 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。     

从质量流向漏斗流转变过程中的动力学分析

球床模块式高温气冷堆的堆芯是全陶瓷型包覆铀燃料制成的球形颗粒,与石墨颗粒混合堆积而成,堆芯颗粒流的流态取决于颗粒尺度的平移、旋转等动力学量,以及力链、涡旋等介尺度物理量。为了分析颗粒的平移、旋转等动力学量对颗粒流流态的影响。基于筒仓颗粒流的物理模型,首先开展了筒仓颗粒流流变过程的实验测量,并使用基于 Hertz-Mindlin和 RVD （relative velocity dependent）滚动摩擦接触模型的离散单元法 （distinct element method, DEM）,研究了锥形筒仓颗粒流流变过程中球形颗粒的动力学量。进一步,基于DEM计算结果进行分析,发现筒仓自上而下呈现出质量流向漏斗流过渡的混合流状态。在筒仓混合流的不同流型区域中,平移速度和旋转速度之间的相关性是相反的;颗粒间的相对切向运动较大的区域集中在漏斗流区域与边壁区域。了解筒仓流变过程中颗粒的动力学特征,有助于优化筒仓颗粒流动,并减少颗粒表面的磨损。     

Mixing behaviors of wet granular materials in gas fluidized bed systems

The discrete element method combined with computational fluid dynamics was coupled with a capillary liquid bridge force model for computational studies of mixing behaviors in gas fluidized bed systems containing wet granular materials. Due to the presence of strong capillary liquid bridge forces between wet particles, relative motions between adjacent particles were hindered. There was a high tendency for wet particles to form large aggregates within which independent motions of individual particles were limited. This resulted in much lower mixing efficiencies in comparison with fluidization of dry particles. Capillary liquid bridge forces were on average stronger than both fluid drag forces and particle–particle collision forces and this accounted for the difficulty with which individual particles could be removed and transferred between aggregates. Such exchange of particles between aggregates was necessary for mixing to occur during fluidization of wet granular materials but required strong capillary liquid bridge forces to be overcome. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4058–4067, 2013     

颗粒外掠含不同掺混单元平板的流动换热特性

为了提高板壳式换热器的换热性能,通过离散元法研究了平面、梯形、椭圆形、梯形+椭圆形和三角形掺混单元对颗粒流动和换热的影响。研究表明:平面的掺混率几乎为零,梯形掺混单元的掺混率最高。颗粒在绕过除平面外的掺混单元时,温度边界层被破坏,并在掺混单元下游区域重新发展。在掺混单元上游区域,掺混单元对颗粒运动有阻碍作用,阻碍作用越大接触热阻越小。颗粒在梯形掺混单元下游的特征速度最大,入口平均温度最高。梯形掺混单元的掺混效率最高。在掺混单元下游区域,梯形、椭圆形、梯形+椭圆形和三角形掺混单元的传热系数显著大于平面(平均增加41.5%、31.5%、28.9%和25.3%)。相比其他掺混单元,颗粒外掠梯形掺混单元的流动换热特性最好。     

水平轴风力机叶片自振频率计算方法研究

本文应用商业有限元软件,通过选取不同的单元类型(梁单元和壳体单元)对国内200kW风力机叶片进行模态分析。结果表明,两种方法精确相符,从而证明在计算叶片自振基频时可把复杂叶片结构简化为一悬臂梁来进行分析。鉴于把叶片简化为一悬臂梁进行结构动力有限元计算易于实现计算的程序化,基频计算具有足够的精度且计算效率高,因此其对于叶片的初步结构设计具有一定意义,在分析叶片基频时不必建立复杂的三维叶片有限元模型。     

风机叶片根端连接的有限元分析

本文基于ANSYS软件建立风机叶片根端连接部分的有限元模型,并对叶根玻璃钢部分及T型连接螺栓进行应力分析和强度校核,为叶片根端连接的设计、优化及材料的选用提供可靠的依据和指导。