The influence of binary drag laws on simulations of species segregation in gas-fluidized beds

Monodisperse drag laws have been traditionally employed in polydisperse systems using ad hoc assumptions due to the lack of adequate drag laws for polydisperse systems. A key component of both continuum and discrete models used to study segregation in gas fluidized beds is the drag law. In this work, both the ad hoc approach and a new drag treatment developed specifically for polydisperse mixtures using lattice-Boltzmann simulations [M.A. Van der Hoef, R. Beetstra, J.A.M. Kuipers, Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force, J. Fluid Mech. 528 (2005) 233–254] are incorporated into a Multi-Phase Particle-in-Cell (MP-PIC) framework to evaluate their impact on simulations of gas-fluidized, binary mixtures. In particular, several systems composed of Geldart group B particles that differ in size and/or density are considered, with special attention paid to axial species segregation at low fluidization velocities. For a system with size difference only, the Van der Hoef et al. [M.A. Van der Hoef, R. Beetstra, J.A.M. Kuipers, Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force, J. Fluid Mech. 528 (2005) 233–254] drag treatment presents a higher degree of mixing than the ad hoc treatment. For a system with size and density differences, where the small particle is the denser and less massive one, the ad hoc treatment predicts a higher degree of mixing than the Van der Hoef et al. [M.A. Van der Hoef, R. Beetstra, J.A.M. Kuipers, Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force, J. Fluid Mech. 528 (2005) 233–254] treatment. For systems with density differences only or both size and density differences where the large particle is the denser one, both drag treatments generate essentially the same segregation profiles. The relative segregation tendencies predicted by each drag treatment is explained through a qualitative analysis of drag force coefficients of each species in the mixture. The simulation results indicate that the drag law treatment plays a crucial role in the qualitative and quantitative nature of segregation predictions at low gas velocities.     

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 parametric study of axial segregation in granular systems

When a cylindrical container, partially filled with a binary granular mixture of particles that differ in size or density, is rotated around its axis, a spontaneous segregation of the two granular components may occur. In order to better understand this phenomenon, we have carried out an experimental study probing the effect of average particle size and relative size difference between particles on the onset of segregation. The experimental study is followed by a novel scaling analysis which relates the deterministic, convective driving force for particle segregation to the randomizing diffusional driving force present in these systems through the definition of an axial granular Péclet number. Values of this granular Péclet number are shown to successfully correlate with segregation behavior in the present study, as well as in comparable results in the literature.     

水力旋流器内非牛顿流体多相流场的数值模拟

利用一种非牛顿流体黏度修正模型描述水力旋流器内高浓度矿浆的非牛顿流动特性,并结合雷诺应力模型(RSM)、混合多相流模型(Mixture)以及拉格朗日颗粒追踪模型(LPT)建立了一种适用于模拟水力旋流器内非牛顿流体多相流场的数学模型。模拟结果与报道的实验值的相对误差均在10%以内,表明了该模型的可靠性。结果表明,非牛顿流体黏度的空间分布与矿浆密度的空间分布类似。沿零轴速包络面(LZVV)的轮廓存在一个高密度环,其原因为某粒径范围内的颗粒受到的径向合力为零,颗粒群沿LZVV做高速旋转运动。分散相的空间分布取决于不同粒径的颗粒受力。对于不同粒径的单位质量颗粒,向外离心力的数值大约为向内压力梯度力的两倍左右,使得大颗粒进入下行流并在底流口收集。随着颗粒粒径的减小,总体向内且具有波动性的流体曳力呈指数增长。向内的流体曳力将部分颗粒推向轴心,经上行流逃逸,同时也增强了颗粒运动的随机性。当颗粒粒径小于一定值后,流体曳力远远大于离心力和压力梯度力,颗粒运动的随机性非常强,宏观表现为均匀分布。     

Segregation in polydisperse fluidized beds: Validation of a multi-fluid model

In many industrial-scale fluidized-bed reactors, particle mixing and segregation play an important role in determining reactor performance. Detailed information about the particle size distribution (PSD) throughout the bed at different operating conditions is crucial for design and scale up of practical systems. In this work, a multi-fluid model based on the Euler-Euler approach and the direct quadrature method of moments (DQMOM) is used to describe particle segregation, and the model predictions are validated with available experimental and simulation data. For binary mixtures, multi-fluid simulations are compared with digital image analysis experiments for beds of glass beads. By properly defining the solid-solid drag force, the multi-fluid model can reproduce the segregation rate found experimentally for different flow conditions with binary mixtures. Segregation phenomena in gas-solid fluidized beds with a continuous PSD are also investigated. Here, the multi-fluid simulations are compared with discrete particle simulations (DPS). Using the moments of the PSD from DPS, the weights and abscissas used in DQMOM are initialized in the multi-fluid model. The segregation rate and the local moments of the PSD predicted by the multi-fluid model are compared to the DPS results. The dependence of the results on the number of DQMOM nodes is also investigated.     

Direct numerical simulations of dynamic gas‐solid suspensions

Direct numerical simulation results for gas flow through dynamic suspensions of spherical particles is reported. The simulations are performed using an immersed boundary method, with careful correction for the grid resolution effect. The flow systems we have studied vary with mean flow Reynolds number, solids volume fraction, as well as particle/gas density ratio. On the basis of the simulation results, the effect of particle mobility on the gas‐solid drag force is analyzed and introduced into the existing drag correlation that was derived from simulations of stationary particles. This mobility effect is characterized by the granular temperature, which is a result of the particle velocity fluctuation. The modified drag correlation is considered so‐far the most accurate expression for the interphase momentum exchange in computational fluid dynamics models, in which the gas‐solid interactions are not directly resolved. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1958–1969, 2016     

Computational investigation of the mechanisms of particle separation and “fish‐hook” phenomenon in hydrocyclones

The motion of solid particles and the “fish‐hook” phenomenon in an industrial classifying hydrocyclone of body diameter 355 mm is studied by a computational fluid dynamics model. In the model, the turbulent flow of gas and liquid is modeled using the Reynolds Stress Model, and the interface between the liquid and air core is modeled using the volume of fluid multiphase model. The outcomes are then applied in the simulation of particle flow described by the stochastic Lagrangian model. The results are analyzed in terms of velocity and force field in the cyclone. It is shown that the pressure gradient force plays an important role in particle separation, and it balances the centrifugal force on particles in the radial direction in hydrocyclones. As particle size decreases, the effect of drag force whose direction varies increases sharply. As a result, particles have an apparent fluctuating velocity. Some particles pass the locus of zero vertical velocity (LZVV) and join the upward flow and have a certain moving orbit. The moving orbit of particles in the upward flow becomes wider as their size decreases. When the size is below a critical value, the moving orbit is even beyond the LZVV. Some fine particles would recircuit between the downward and upward flows, resulting in a relatively high separation efficiency and the “fish‐hook” effect. Numerical experiments were also extended to study the effects of cyclone size and liquid viscosity. The results suggest that the mechanisms identified are valid, although they are quantitatively different. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Passive rate‐based separation in collisional flows

The passive separation of a binary mixture of spherical particles is accomplished using a laboratory scale quasi‐two‐dimensional inclined board such that gravity alone drives the flow of the mixture through a static array of obstacles. Experimental results compare well with simulations both qualitatively and quantitatively. An increase in separation is observed for increasing board length, whereas a decrease in separation is observed as the solid fraction (area coverage) of particles increases. The possibility of designing green technology for solid‐solid separations by taking advantage of particle properties that aid naturally occurring segregation is demonstrated. A probability‐based model is suggested as a way to predict the viability of separation between particle types as a function of particle size and coefficient of restitution. It should be noted that size separation is achieved despite peg spacings that are larger than both particles in a mixture. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3717–3727, 2017     

基于EMMS介尺度模型的双分散鼓泡流化床的模拟

双分散气固鼓泡流化床中颗粒通常具有不同粒径或密度,导致产生颗粒偏析等现象,影响传递和反应行为。颗粒分离和混合与气泡运动密不可分,其中相间曳力起关键作用。最近Ahmad等提出了一种基于气泡结构的双分散介尺度曳力模型,能成功预测双分散鼓泡流化床的床层膨胀系数。本研究耦合该曳力模型与连续介质方法,模拟了两种不同的双分散鼓泡流化床,通过分析不同流化状态下的气泡运动、颗粒浓度比的轴向分布等参数,进一步检验模型的适用性。研究表明,当双分散颗粒处于完全流化状态时,耦合双分散介尺度曳力模型可合理预测不同颗粒的分离现象;而其处于过渡流化状态时,新曳力模型和传统模型均无法获得合理结果,此时调节固固曳力可改进模拟结果。     

Discrete particle simulation of solids motion in a gas–solid fluidized bed

The solids motion in a gas–solid fluidized bed was investigated via discrete particle simulation. The motion of individual particles in a uniform particle system and a binary particle system was monitored by the solution of the Newton's second law of motion. The force acting on each particle consists of the contact force between particles and the force exerted by the surrounding fluid. The contact force is modeled by using the analogy of spring, dash-pot and friction slider. The flow field of gas was predicted by the Navier–Stokes equation. The solids distribution is non-uniform in the bed, which is very diluted near the center but high near the wall. It was also found that there is a single solids circulation cell in the fluidized bed with ascending at the center and descending near the wall. This finding agrees with the experimental results obtained by Moslemian. The effects of the operating conditions, such as superficial gas velocity, particle size, and column size on the solids movement, were investigated. In the fluidized bed containing uniform particles better solids mixing was found in the larger bed containing smaller size particles and operated at higher superficial gas velocity. In the system containing binary particles, it was shown that under suitable conditions the particles in a fluidized bed could be made mixable or non-mixable depending on the ratios of particle sizes and densities. Better mixing of binary particles was found in the system containing particles with less different densities and closer sizes. These results were found to follow the mixing and segregation criteria obtained experimentally by Tanaka et al.     

MIXING/SEGREGATION POTENTIAL IN BINARY LIQUID FLUIDIZED BEDS

The mechanism underlying mixing/segregation of binary particles in liquid fluidized beds is reviewed and investigated in this paper. Binary mixtures of particles, when fluidized, sometimes segregate and display a behaviour called layer inversion, At low fluid velocities, one of the components is primarily found in a discrete layer at the bottom of the bed, while the other is predominantly at the top. At higher fluid velocities, the order of arrangement is reversed. The literature provides a variety of explanations for this phenomenon, derived from quite different theoretical bases. A comparative analysis of these different approaches is presented here together with the experimental results available in the literature. Based on the best model, further experimental investigation is carried out to provide; (i) comprehensive criteria to predict whether a given binary mixture of any type (both size and density variant, size variant only, density variant only) will mix/segregate or show layer inversion, and (ii) mixing/segregation regime map in terms of size ratio and density ratio of the particles for a given fluidizing medium. Therefore, knowing the properties of given particles, a second type of particles can be chosen in order to avoid or to promote segregation according to the particular process requirement.     

The Segregation in the Binary‐Solid Liquid Fluidized Bed

A new mechanism is proposed to interpret the phenomena observed in the liquid fluidization of the binary particle mixture. Two main factors, the bulk density and voidage fluctuation, are considered to determine the position of the layer of particles in the bed. The new model successfully explains the layer inversion phenomenon and mixing‐segregation equilibrium, which is the result of the above two factors acting together. The model also proves that bulk density is a simple and reliable method to predict the inversion velocity by comparison with the experimental results reported in the literature.     

MIXING/SEGREGATION POTENTIAL IN BINARY LIQUID FLUIDIZED BEDS

The mechanism underlying mixing/segregation of binary particles in liquid fluidized beds is reviewed and investigated in this paper. Binary mixtures of particles, when fluidized, sometimes segregate and display a behaviour called layer inversion, At low fluid velocities, one of the components is primarily found in a discrete layer at the bottom of the bed, while the other is predominantly at the top. At higher fluid velocities, the order of arrangement is reversed. The literature provides a variety of explanations for this phenomenon, derived from quite different theoretical bases. A comparative analysis of these different approaches is presented here together with the experimental results available in the literature. Based on the best model, further experimental investigation is carried out to provide; (i) comprehensive criteria to predict whether a given binary mixture of any type (both size and density variant, size variant only, density variant only) will mix/segregate or show layer inversion, and (ii) mixing/segregation regime map in terms of size ratio and density ratio of the particles for a given fluidizing medium. Therefore, knowing the properties of given particles, a second type of particles can be chosen in order to avoid or to promote segregation according to the particular process requirement.     

A 3D semi-digital model for the placing of granular materials

A 3D semi-digital model has been developed in order to simulate the gravitational placing of granular mixtures composed of spherical particles of different sizes allowing the optimization of mixtures proportions. The aim is to control concrete placing in formworks particularly in the presence of reinforcement bars. In this case, the representation of a large number of particles is necessary and segregation or wall effects have to be taken into account. Moreover, an easy representation of complex geometries and obstacles of arbitrary shapes should be possible. In order to respect these conditions, the used 3D semi-digital model is based on the digitization of a calculation volume and on the representation of spherical particles with real numbers. The model takes into account only steric repulsion between particles and simulates their collisions during placing by random displacements. The simplicity of the model allows the simulation of up to 2 million spherical particles without spending too much computational time. The model can therefore be used for the simulation of granular materials having a spread granulometry-like concrete.The packing density of binary mixtures of spherical particles with different size ratios and varying proportions of small and big particles is first studied. The results are compared successfully with theoretical packing density of binary mixtures without interactions. It is therefore demonstrated that the semi-digital model can be used for the simulation of binary mixtures having low size ratios (0.1), which corresponds approximately to the size ratio of fine and coarse aggregates in concrete.Secondly, digitized cylindrical obstacles are added in the systems with the aim to represent reinforcement bars in a formwork. The influence of small and big particles proportioning on the local packing density and the homogeneity of the mixture is studied. The results show that in the presence of obstacles, the optimum placing is obtained when the proportion of small particles in the mixture is higher than that without obstacles. This is due principally to the looser packing of big particles around obstacles.     

Discrete particle simulation of gas fluidization of ellipsoidal particles

Fluidization is widely used in industries and has been extensively studied, either experimentally or theoretically, in the past decades. In recent years, a coupled simulation approach of discrete element method (DEM) and computational fluid dynamics (CFD) has been successfully developed to study the gas–solid flow and heat transfer in fluidization at a particle scale. However, to date, such studies mainly deal with spherical particles. The effect of particle shape on fluidization is recognized but not properly quantified. In this paper, the CFD–DEM approach is extended to consider the fluidization of ellipsoidal particles. In the simulation, particles used are either oblate or prolate, with aspect ratios varying from very flat (aspect ratio=0.25) to elongated (aspect ratio=3.5), representing cylinder-type and disk-type shaped particles, respectively. The commonly used correlations to determine the fluid drag force acting on a non-spherical particle are compared first. Then the model is verified in terms of solid flow patterns. The effect of aspect ratio on the flow pattern, the relationship between pressure drop and gas superficial velocity, and microscopic parameters such as coordination number, particle orientation and force structure are investigated. It is shown that particle shape affects bed permeability and the minimum fluidization velocity significantly. The coordination number generally increases with aspect ratio deviating from 1.0. The analysis of particle orientations shows that the bed structures for ellipsoids are not random as that for spheres. Oblate particles prefer facing upward or downward while prolate particles prefer horizontal orientation. Spheres have the largest particle–particle contact force and fluid drag force under the comparable conditions. With aspect ratio deviating from 1.0, particle–particle interaction and fluid drag become relatively weak. The proposed model shows a promising method in examining the effect of particle shape on different flow behaviour in gas fluidization.     

The effects of air and particle density difference on segregation of powder mixtures during die filling

Segregation of mono-disperse binary mixtures with different particle densities during die filling in the presence of air was numerically analysed using a coupled discrete element method (DEM) and computational fluid dynamics (CFD) approach. Die filling with powders of different particle density ratios (i.e. the ratio of the heavy particles to the light particles) at various shoe speeds was simulated, in order to explore the effects of air and particle density difference on segregation. For die filling from a stationary shoe, the air can induce significant segregation by hindering the deposition of light particles (i.e., air-sensitive particles). As the particle density ratio increases, the light particles are deposited into the die at even lower speeds compared with the heavy ones due to the effect of air drag, resulting in an increase in the degree of segregation. For die filling with a moving shoe, segregation occurs due to different post-collisional velocities resulting from different particle inertia; and the degree of segregation increases as the particle density ratio increases due to the increasing difference in particle inertia. It is found that, as the shoe velocity increases, the powder flow pattern changes from nose flow dominated to bulk flow dominated and the degree of segregation generally decreases. The effect of air is limited for nose flow dominated die filling because the air can easily evacuate through the gap between the die walls and flowing powder stream. When bulk flow dominates in die filling, the air can be entrapped in the die, which has a significant impact on the powder flow and segregation behaviours. Finally, the effect of interparticle friction on segregation was investigated.     

Experimental and numerical investigation of the hydroerosive grinding

This paper presents an Euler-Euler approach for the numerical simulation of the hydroerosive grinding (HE) process. It describes a two-phase slurry flow consisting of a liquid and a dispersed solid phase which causes wear at walls of devices. The continuous fluid phase is solved using a finite volume scheme in which the Large Eddy Simulation (LES) [1] model is applied to resolve large-scale turbulent structures. The solid phase is dispersed and treated as a second continuum in which drag and lift forces as well as added mass, pressure and history force are taken into account. Considering particle-particle interactions, the granular model from Gidaspow [2] is used for particle volume concentrations over 1%. Investigations of erosion processes proofed that non-spherically shaped particles as well as harder particles increase the wear on devices significantly. Consequently, non-spherical particles are utilised for the hydroerosive grinding. Their steady drag, unsteady drag and lift coefficients, depending on the particle Reynolds number, are determined by a direct numerical simulation via an in-house LES Lattice-Boltzmann solver. This Lattice-Boltzmann method was presented for laminar flows by Hölzer and Sommerfeld [3]. In this work, interpolating functions of these coefficients are implemented in the Euler-Euler approach which enables the simulation of non-spherical particle transport. Hydroerosive grinding experiments in 3D throttles and 3D planar geometries are carried out to determine an erosion model depending on particle impact velocity, particle size, particle concentration and wall hardness. Implementation of a mesh-morphing algorithm combined with the Euler-Euler scheme of the commercial solver ANSYS CFX11 [4] enables an online simulation of the hydroerosive grinding process. Additionally, the online simulation is used to validate the applied numerical methods. Very good agreements are achieved and will be presented in this paper.     

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     

Numerical Simulation for Particle Penetration Depth Distribution in Deep Bed Filtration

A two‐dimensional model has been developed to simulate particle penetration through porous media. The particle penetration depends on many parameters including the Reynolds number, particle drag coefficient, the ratio of the diameter of injected to filtered particles, fluid velocity, and pore size, etc. The numerical model for separation efficiency in periodic porous media was studied. Previous work has described the effects of injected particle size, Reynolds number and particle drag coefficient. In this study, the porous media flow is modeled (solution of the Navier‐Stokes equations) by using the finite element method, and the analysis is restricted to the case of two‐dimensional periodic porous media. The effects of these factors and particle depth distribution in porous media are investigated. It is noted that the results for the three Reynolds numbers 1, 16.56, and 100, are qualitatively similar, and about 40 % of particles are trapped in the top part of the filter.