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     

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 virtual finite element model for centered and eccentric mixer configurations

An implementation of the virtual finite element method with unstructured grids for the modeling of laminar flow in eccentric mixers is presented. The effect of the meshing strategy on the quality of the computed flow field is first carefully investigated with a centered impeller. It is shown that both the number of elements in the vicinity of the impeller and the number of kinematics constraints imposed in the virtual finite element formulation control the computational accuracy. The method is then applied to the case of an eccentric mixer provided with a Rushton turbine showing the capabilities of the proposed approach.     

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     

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     

Modeling segregation of polydisperse granular materials in developing and transient free-surface flows

Predicting segregation and mixing of polydisperse granular materials in industrial processes remains a challenging problem. Here, we extend the application of a general predictive continuum model that captures the effects of segregation, diffusion, and advection in two ways. First, we consider polydisperse segregating flow in developing steady segregation and in developing unsteady segregation. In both cases, several terms in the model that were zero in the previously examined case of fully developed streamwise-periodic steady segregation in a chute are now non-zero, which makes application of the model substantially more challenging. Second, we apply the polydisperse approach to density polydisperse materials with the same particle size. Predictions of the model agree quantitatively with experimentally validated discrete element method (DEM) simulations of both size polydisperse and density polydisperse mixtures having uniform, triangular, and log-normal distributions. © 2018 American Institute of Chemical Engineers AIChE J, 65: 882–893, 2019     

Mixing processes in the cavity transfer mixer: A thorough study

In many industrial applications, the quality of mixing between different materials is fundamental to guarantee the desired properties of products. However, properly modeling and understanding polymer mixing presents noticeable difficulties, because of the variety and complexity of the phenomena involved. This is also the case with the Cavity Transfer Mixer (CTM), an add‐on to be mounted downstream of existing extruders, to improve distributive mixing. The present work proposes a fully three‐dimensional model of the CTM: a finite element solver provides the transient velocity field, which is used in the mapping method implementation to compute the concentration field evolution and quantify mixing. Several simulations are run assessing the impact on mixing of geometrical and functioning parameters. In general, the number of cavities per row should be limited and the cavity size rather big to guarantee good mixing quality. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1034–1048, 2018     

Modeling segregation of bidisperse granular materials using physical control parameters in the quasi‐2D bounded heap

Quantitatively predicting segregation of size‐disperse granular materials is of potential value in many industrial applications. We consider granular segregation of size‐bidisperse particles in quasi‐2D bounded heaps, a canonical granular flow, using an advection‐diffusion transport equation with an additional term to account for particle segregation. The equation is characterized by two dimensionless parameters that are functions of control parameters (flow rate, system size, and particle sizes) and kinematic parameters (flowing layer depth, diffusion coefficient, and percolation length scale). As the kinematic parameters are usually difficult to measure in practice, their dependence on the control parameters is determined directly from discrete element method simulations. Using these relationships, it is possible to determine which values of the control parameters result in a mixed or segregated heap. The approach used here is broadly applicable to a wide range of other flow geometries and particle systems. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1524–1534, 2015     

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     

Mixing and segregation in a liquid fluidized bed of particles with different size and density

Experimental studies have been carried out on fluidization of irregular particle mixtures of different size and density. The mixing and segregation phenomena could be interpreted on the basis of the diffusion model of Kennedy and Bretton. The dependence of computed particle dispersion coefficient on liquid velocity, particle density and size has been discussed.     

A study of the axial and radial competition segregation in a rotating drum with internal diameter changing

A binary mixture is mixed in a rotating drum composed by 19 rings with different inner diameters. It is found that the larger particles are concentrated in the rings with smaller inner diameters. The collection of the larger particles in these rings is due to the particle dynamic angle of repose. The transition from the particle segregation core pattern at the end wall to the good radial mixing rings is through a transient turning comet segregation pattern. This transition is closely related to the distance from the ring with the smallest inner diameter to the ring with the largest inner diameter. Having a higher fraction of larger particles in a ring requires both the collection ring having a smaller inner diameter and a smoother inner diameter transition to the neighboring rings.     

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     

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     

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     

旋流静态混合器内瞬态流动特性研究进展

首先概括了静态混合的技术特色;其次,重点综述了近年来旋流静态混合器内脉动压力与速度波动的统计特征、多尺度分形和混沌混合特性等方面的研究进展;实验研究发现Kenics静态混合器各点压力最大波动幅值与进口流量呈二次函数关系,脉动功率谱随着频率的增加呈幂函数关系衰减;轴截面内壁面自由涡和主体区强制涡相互耦合诱导混沌流的产生,同时提高速度与温度梯度的场协同程度。最后,总结了静态混合器内螺旋元件的切割分流、改变流向和径向混合等功能在强化CO2水合物形成过程中的作用。指出将计算流体力学、映射法等方法同LIF、PIV、PFS有机结合可有效地分析静态混合器内多相流动混合机理。     

The effect of mixer properties and fill level on granular flow in a bladed mixer

The discrete element method was used to study the effect of mixer properties and fill level on the granular flow of monodisperse, cohesionless spheres in a bladed mixer. For fill levels just covering the span of the blades, a three‐dimensional (3‐D) recirculation zone develops in front of the blades, which promotes vertical and radial mixing. Increasing fill level reduces the size of the recirculation zone, decreases bed dilation and hinders particle diffusivities. However, above a critical fill level, the behavior of the particles within the span of the blade is found to be invariant of fill level. At low‐fill levels, the pressure within the particle bed varies linearly with bed height and can be approximated by hydrostatics. At higher fill levels, a constant pressure region develops within the span of the blades due to the angled pitch of the blades. Cylinder wall friction is shown to significantly influence granular behavior in bladed mixers. At low‐wall friction, the 3‐D recirculation zone observed for high‐wall friction conditions does not develop. High‐wall friction leads to an increase in convective and diffusive particle mixing. Shear stresses are shown to be a function of wall friction. Blade position along the vertical axis is shown to influence flow patterns, granular temperature and stress. The effect of increasing the mixer diameter at a constant particle diameter was also studied. When the mixer diameter is larger than a critical size such that wall effects are minimized, the observed granular behavior follows simple scaling relations. Particle velocities and diffusivities scale linearly with mixer size and blade speed. Normal and shear stress profiles are found to scale linearly with the total weight of the particle bed. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Quantification of laminar mixing in the kenics static mixer: An experimental study

The laminar flow field in a Kenics KM static mixer has been studied using laser induced fluorescence and digital image analysis. Mixing was quantified by measurement of the number average striation thickness, variance of striation widths and interfacial area, for elements of length to diameter (L/D) ratios of 0.8, 1.0, 1.5 with 90° twist per element. From flow visualisations, transitions were observed in the flow where vortices developed above the first and second elements at Reynolds numbers of 43 and 90 for L/D = 0.8 and Reynolds numbers of 55 and 105 for L/D = 1.0. It was found that these vortices did not appreciably enhance mixing based on striation thickness and variance of striation widths measurements after 4 to 5 elements. The influence of viscosity ratio showed a viscosity ratio (dyed stream/bulk stream) of I had faster interfacial area growth and created more uniform mixtures compared to a viscosity ratio of 0.2 for flow rate ratio of 0.2.     

Mixing analysis in a coaxial mixer

The performance of a coaxial mixer in the laminar-transitional flow regime was numerically investigated with Newtonian and non-Newtonian fluids. These mixers comprised two shafts: a central fast speed shaft mounted with an open turbine, and a slow speed shaft fitted with a wall scraping anchor arm. To model the complex hydrodynamics inside the vessel, the virtual finite element method (POLY3D^TM software) coupled with a Lagrange multiplier approach to cope with the non-linearity coming from the rheological model was employed. Co-rotation and counter-rotation mode were compared, based on several numerical criteria, namely, mixing time, power consumption and pumping rate. It was found that co-rotating mode is more efficient than counter-rotating mode in terms of energy, pumping rate and homogenization time.     

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。     

螺带式混凝土搅拌机混合特性及DEM模拟

采用离散单元法模拟新拌混凝土于搅拌机中的混合过程,研究了双筒螺带式混凝土搅拌机的混合效率。 用Hertz-Mindlin with JKR接触方法建立新拌混凝土离散元模型,模拟了坍落度实验、L箱实验和流变仪实验,将模拟结果与实验结果进行对比,校准模型参数,采用混合系数定量研究了不同初始装填方式下搅拌机的混合效率。结果表明,采用上下装填方式时搅拌机混合效率较高;对任一初始装填方式,左部区域与右部区域、前部区域与后部区域间混合效率无明显差别,而上部区域混合效率比底部区域高,底部出料口处存在搅拌盲区,采用舍弃初始出料的方法可提高新拌混凝土性能。转速较高时混合效率较高,相同旋转圈数时,混合效率基本相同。