Numerical study of cluster formation in a gas–particle circulating fluidized bed

Simulations with two-way coupling are performed for two-dimensional gas–solid flow in a circulating fluidized bed with a total solids concentration of 3% in the riser. The motion of particles is treated by a Lagrangian approach, and particles are assumed to interact through binary, instantaneous, non-frontal, and inelastic collisions with friction. The model for the interstitial gas phase is based on the Navier–Stokes equations for two-phase flow with fluid turbulence calculated by using LES. Several porosity functions exist in the literature relating the drag force for a particle in a cloud to the drag force on an isolated particle. We have studied the influences of this porosity function, observing large differences in the local flow structure. The fluctuating gas–solid motion has been investigated showing a strong anisotropic flow behaviour, which is similar to experimental findings. The instabilities in these flows are strongly linked to the non-linear drag function due to the group effect of particles in a cloud. The collision parameters have been found to have an important influence on the cluster structures.     

Modeling and measurement of granule attrition during pneumatic conveying in a laboratory scale system

A methodology combining theoretical and experimental techniques for characterizing and predicting the friability of granules in a laboratory scale pneumatic conveying systems is developed. Models of increasing mathematical complexity are used for analysis of experimental data. Firstly, a two-dimensional (2-D) computational fluid dynamics (CFD) model of the gas-solid flow within the Malvern Mastersizer laser diffraction equipment is developed to simulate impact of different inlet jet pressures on the flow properties and to calculate average velocity and average volume fraction of particles in the equipment. Secondly, a simple maximum-gradient population balance (MG-PB) mathematical model of breakage is developed. The model is solved using the Quadrature Method of Moments (QMOM) and used for evaluation of experimental data from the Malvern equipment. Different semi-empirical expressions for the breakage kernels and for the daughter distribution functions are tested. Multiple breakage distribution functions are needed to get satisfactory agreement with experimental data. Finally, a CFD-PB model combining CFD and QMOM methodologies is developed. The combined model employs different binary fragment distribution functions and a kernel with the breakage rate proportional to the characteristic particle size and to the square of the impact velocity between a particle and the equipment wall. Simulation results are compared with attrition experimental data indicating that the model is able to capture the qualitative trends and quantitatively predict the Sauter mean diameter d₃₂ at the outlet. However, the lower moments, in particular m₀ and m₁ are under predicted by the model. Based also on the MG-PB model results, it is our hypothesis that chipping, or breakage of particles in multiple fragments results in higher m₀ and m₁ than predicted. Further improvements of the model are proposed to incorporate multiple breakage effects. It is assumed that analogous physically based models combining properties of the gas-solid flow with the PB models can be employed to predict attrition and breakage in large-scale pneumatic conveying systems.     

Implementation and analysis of numerical solution of the population balance equation in CFD packages

Simulation of polydisperse flows must include the effects of particle–particle interaction, as breakage and aggregation, coupling the population balance equation (PBE) with the multiphase modelling. In fact, the implementation of efficient and accurate new numerical techniques to solve the PBE is necessary. The direct quadrature method of moments, known as DQMOM, is a moment-based method that uses an optimal adaptive quadrature closure and came into view as a promising choice for this implementation. In the present work, DQMOM was implemented in two CFD packages: the commercial ANSYS CFX, through FORTRAN subroutines, and the open-source OpenFOAM, by directly coding the PBE solution. Transient zero-dimensional and steady one-dimensional simulations were performed in order to explore the PBE solution accuracy using several interpolation schemes. Simulation cases with dominant breakage, dominant aggregation and invariant solution (equivalent breakage and aggregation) were simulated and validated against an analytical solution. The solution of the population balance equation was then coupled to the two-fluid model, considering that all particles classes share the same velocity field. Momentum exchange terms were evaluated using the local instantaneous Sauter mean diameter of the size distribution function. The two-dimensional tests were performed in a backward facing step geometry where the vortex zones traps the particles and provides high rates of breakage and aggregation.     

Application of CFD and breakage modelling for predicting the size reduction of protein precipitates during transport

Particle breakage due to fluid flow through various geometries can have a major influence on the performance of particle/fluid transport and separation processes. Whey protein precipitate dispersions were used as a case study to investigate the effect of flow intensity and exposure time on the breakage of precipitates during transport. Computational fluid dynamic (CFD) simulations were performed to evaluate the turbulent energy dissipation rate (?) and associated exposure time along various flow geometries. A breakage model, incorporating the CFD output and experimentally determined parameter values, was found to provide a satisfactory capability for predicting the breakage of the protein precipitate particles. The breakage modelling approach was then applied to particles formed under different agitation intensities during the precipitation process. The formation history of the precipitates had a significant effect on their structure and strength and hence different breakage rates were observed. The precipitate dispersions were propelled through a number of different geometries such as bends, tees and elbows. The shape of the flow geometry was found to have an important effect on particle size reduction. This predictive particle breakage modelling approach was then applied to larger-scale flow geometries with cross-sectional area of 150 times greater than the experimental.     

新型旋流器分离重质和轻质颗粒的数值模拟

采用颗粒随机轨道模型(DPM)并利用计算流体动力学(CFD)软件对宽域旋流器内低浓度的重质颗粒和轻质颗粒的运动状态进行模拟.结果表明:用颗粒随机轨道模型(DPM)计算颗粒轨道模拟结果与实验结果基本相符;重质颗粒主要运动在外旋流,并很快被分离捕集;轻质和小粒径重质颗粒与液流有很好的跟随性,主要运动在内旋流.颗粒分离有一定的随机性;顶部短路流颗粒从侧向排轻口排出;增长圆锥段有助于颗粒从液相分离.     

导叶式旋风管排尘口处颗粒返混夹带现象

通过数值模拟的方法,研究导叶式旋风管内颗粒返混夹带现象。研究表明,排尘口下方存在明显的灰斗返混现象,颗粒返混质量流率占入口颗粒质量流率的38%,排尘锥内部颗粒返混夹带量占入口颗粒流率的47%;排尘口上方1.1D(D为旋风管直径)范围是主要的二次分离空间,最终影响分离效率的返混颗粒仅占入口颗粒质量流率的2.5%;13 μm以下的返混颗粒会对分离器总效率产生影响,粒径越小,影响作用越明显。     

Toughening of unmodified polyvinylchloride through the addition of nanoparticulate calcium carbonate and titanate coupling agent

PVC/CaCO₃ polymer nanocomposites of differing compositions were produced using a two‐roll mill and compression molding. In all formulations, 0.6 phr of titanate was incorporated to assist dispersion during processing. The morphology was observed using transmission electron microscopy, and the static and dynamic mechanical and fracture properties were determined. Fracture toughness examination was performed according to strain energy release test method. The presence of nanometer‐sized CaCO₃ particles led to a slight decrease in the tensile strength but improved the impact energy absorption, storage modulus, and fracture toughness. The use of titanate coupling agent softened the polymer matrix and reduced the matrix's modulus. Fracture surface examinations by scanning electron microscopy showed that the coupling agent improved particle–matrix bonding and inhibited void formation around the particles. Finite element analysis suggested that the improved particle–matrix bonding reduced the matrix's plasticity around the particles, which decreased the toughening efficiency of the composites. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

CFD–DEM simulation of tube erosion in a fluidized bed

The erosion of the immersed tubes in a bubbling‐fluidized bed is studied numerically using an Eulerian–Lagrangian approach coupling with a particle‐scale erosion model. In this approach, the motion of gas and particles is simulated by the CFD–DEM method, and an erosion model SIEM (shear impact energy model) is proposed to predict the erosion of the tubes. The model is validated by the good agreement of the simulation results and previous experimental data. By analyzing the simulation results, some characteristics of the tube erosion in the fluidized bed are obtained, such as the distribution of the erosion rate around the tube, the variation of the erosion rate with the position of the tube, the effect of the friction coefficient of particles on the erosion, the relationship between the maximum and the average erosion rate, etc. The microscale behavior of particles around the tubes is also revealed and the linear relationship between the erosion and the shear impact energy is confirmed by the simulation results and experiment. The agreement between simulation and experiment proves that the microscale approach proposed in this article has high accuracy for predicting erosion of the tubes in the fluidized bed, and has potential to be applied to modeling the process in other chemical equipment facing solid particle erosion. © 2016 American Institute of Chemical Engineers AIChE J, 63: 418–437, 2017     

Breakage probability of irregularly shaped particles

The investigation of breakage probability by compression of single particles was carried out. The spherical glass particles and irregularly shaped particles of NaCl, sugar, basalt and marble were subjected to a breakage test. The breakage test includes the compression up to breakage of 100 particles to obtain the distribution of the breakage probability depending on the breakage force or compression work. The breakage test was conducted for five particle size fractions from each individual material, at two stressing rates. Thus obtained 50 breakage force distributions and corresponding 50 breakage work distributions were fitted with log-normal distribution function.Usually, the breakage probability distribution can be found by means of stress or energy approach. The first one uses the stress to calculate the breakage probability distribution. The second approach uses the mass-related work done to break the particle. We prefer to use the breakage force and energy as essential variables. The correlation between the force and energy at their breakage points is obtained by integrating the characteristic force–displacement curve, i.e. the constitutive function of elastic–plastic mechanical behavior of the particle. The irregularly shaped particle is approximated by comparatively “large” hemispherical asperities. In terms of elastic–plastic deformation of the contacting asperities with the plate, a transition from elastic to inelastic deformation behavior was considered. Thus, one may apply the model of soft contact behavior of comparatively stiff hemispheres. Based on this model a relationship between the breakage force distributions and corresponding energy distributions was analyzed. Every tested material exhibits a linear relationship between average breakage energy and average breakage force calculated for every size fraction.For future consideration both force and energy distributions were normalized by division by average force or energy, consequently. The relationship between the fit parameters of normalized energy distribution and corresponding fit parameters of normalized force distribution was established. The mean value and standard deviation of normalized force distribution can be found from mean value and standard deviation of normalized energy distribution by means of system of two linear equations. The coefficients of those linear equations remain the same for all of the above tested materials; particle size fractions and stressing rates. As a result the simple transformation algorithm of distributions is developed. According to this algorithm the force distribution can be transformed into energy distribution and vice versa.     

新型入口对石膏旋流器工作性能的影响

针对火电厂石膏旋流器分级效果不理想的问题,设计具有分离块和隔板的新型入口,以改善石膏旋流器的工作性能。采用Fluent软件,应用Reynolds应力模型(RSM)与离散相模型(DPM)模拟新型入口中不同粒度颗粒的运动情况,模拟结果表明:随颗粒粒径增大,颗粒的运动半径与运动距离均增大,不同粒径颗粒在新型入口内能实现初步分级。对普通入口与新型入口石膏旋流器分别进行性能实验,获得不同工况下生产能力、出流浆液密度以及旋流器分级效率等指标参数,经比较可知,采用新型入口后,石膏旋流器底流质量浓度明显增大,10～30 μm石膏颗粒的分级效率有显著提高,最大增幅可达15%,同时,6 μm以下石膏颗粒的底流夹细现象也有一定程度的改善,但由于入口段流动阻力增大,生产能力略有下降。     

Breakage model development and application with CFD for predicting breakage of whey protein precipitate particles

Particle breakage due to fluid flow through various geometries can have a major influence on the performance of particle/fluid processes and on the product quality characteristics of particle/fluid products. In this study, whey protein precipitate dispersions were used as a case study to investigate the effect of flow intensity and exposure time on the breakage of these precipitate particles. Computational fluid dynamic (CFD) simulations were performed to evaluate the turbulent eddy dissipation rate (TED) and associated exposure time along various flow geometries. The focus of this work is on the predictive modelling of particle breakage in particle/fluid systems. A number of breakage models were developed to relate TED and exposure time to particle breakage. The suitability of these breakage models was evaluated for their ability to predict the experimentally determined breakage of the whey protein precipitate particles. A “power-law threshold” breakage model was found to provide a satisfactory capability for predicting the breakage of the whey protein precipitate particles. The whey protein precipitate dispersions were propelled through a number of different geometries such as bends, tees and elbows, and the model accurately predicted the mean particle size attained after flow through these geometries.     

Particle grinding by high‐intensity ultrasound: Kinetic modeling and identification of breakage mechanisms

High‐intensity ultrasound, is sought as a means to break particles. A horn‐type ultrasonic transducer is used to apply HIU into a suspension of alumina particles causing breakage to occur. The rate of particle breakage is monitored continuously via in‐line laser‐based particle chord length measurement. Kapur function analysis is used to arrive at the grinding kinetics under variations of ultrasonic power, particle loading, temperature of the suspension and particle size. The first Kapur function increases monotonically with increase in input ultrasonic power. Increasing temperature also increases the first Kapur function but an optimum in the range investigated (10–50°C) is observed near 25°C. An exponential relation is found for the variation of first Kapur function with particle size, this being unique to ultrasound‐mediated particle breakage. The breakage mechanism is attributed mainly to particle abrasion. Different breakage mechanisms are observed at different temperatures. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Analysis of catalyst particle strength by impact testing: The effect of manufacturing process parameters on the particle strength

The mechanical strength of porous alumina catalyst carrier beads, used in the reforming units with continuous catalytic regeneration, was measured by impact testing. With this testing method particle strength can be measured at higher strain rates than the traditional crushing test method, hence providing a better simulation of pneumatic conveying and chute flow conditions, and also a large number of particles can be tested quickly. This is important for particles with a brittle failure mode such as the alumina particles used in this work as a wide distribution of mechanical strength usually prevails. Extensive impact testing was carried out first with an industrial sample, in order to understand the failure mechanism of this type of particles and to develop a methodology for analysing the extent of breakage by impact. Then the method was used to analyse the effect of a number of process parameters, such as filler, macroporosity and drying procedure on the particle strength with the aim of optimising the manufacturing process. The impact test results were then used to test the model of breakage behaviour of particulate solids proposed by Vogel and Peukert [Vogel and Peukert, Breakage behaviour of different materials—construction of a mastercurve for the breakage probability. Powder Technol., 129 (2003) pp. 101-110].     

DEM simulations of spherical particle–particle collisions

The randomness, diversity, and complexity of the high-speed particle crushing process bring great difficulties to the theoretical analysis of powder engineering. In this paper, the discrete element method is used to simulate the collision of spherical particles, which provides a reference for studying the process and mechanism of crushing between particles under impact load. The Hertz–Mindlin with bonded contact model is used as the particle–particle contact model. The central collisions of particles with different diameter ratios under different high-speed motions and the eccentric collisions with different eccentricities are discussed. The results show that the bond damage increases with the increase of relative velocity in both centre impact and eccentric impact. In centre collisions, particles of smaller objects are more fragmented than particles of larger objects. For smaller target particles, the larger the diameter ratio is, the more particle elements are detached from the target particles, and the greater the bond breakage rate. For larger target particles, the larger the diameter ratio is, the less the particle element falls off and the smaller the bond breakage rate. This provides guidance for the collision and crushing of particles with different particle size ratios and different eccentricities during high-speed motion in engineering applications in the future.     

Numerical modeling of particle fluidization behavior in a rotating fluidized bed

In this study, numerical modeling of particle fluidization behaviors in a rotating fluidized bed (RFB) was conducted. The proposed numerical model was based on a DEM (Discrete Element Method)-CFD (Computational Fluid Dynamics) coupling model. Fluid motion was calculated two-dimensionally by solving the local averaged basic equations. Particle motion was calculated two-dimensionally by the DEM. Calculation of fluid motion by the CFD and particle motion by the DEM were simultaneously conducted in the present model. Geldart group B particles (diameter and particle density were 0.5 mm and 918 kg/m³, respectively) were used for both calculation and experiment. First of all, visualization of particle fluidization behaviors in a RFB was conducted. The calculated particle fluidization behaviors by our proposed numerical model, such as the formation, growth and eruption of bubble and particle circulation, showed good agreement with the actual fluidization behaviors, which were observed by a high-speed video camera. The estimated results of the minimum fluidization velocity (U_mf) and the bed pressure drop at fluidization condition (ΔP_f) by our proposed model and other available analytical models in literatures were also compared with the experimental results. It was found that our proposed model based on the DEM-CFD coupling model could predict the U_mf and ΔP_f with a high accuracy because our model precisely considered the local downward gravitational effect, while the other analytical models overpredicted the ΔP_f due to ignoring the gravitational effect.     

Formulation of a physically motivated specific breakage rate parameter for ball milling via the discrete element method

A physically based specific breakage rate parameter of the population balance model for batch dry‐milling is formulated, which explicitly accounts for the impact energy distribution calculated by the discrete element method (DEM). Preliminary DEM simulations of particle impact tests were first performed, which concluded that dissipation energy should be used in contrast to collision energy to accurately define the impact energy distribution. Subsequently, DEM simulations of the motion of spheres representing silica glass beads in a ball mill were performed to determine the specific breakage rate parameter, which was in good agreement with those found experimentally. An analysis of the impact energy distribution, which was only possible within context of the physically motivated specific breakage rate parameter, emphasized the importance of accounting for a threshold impact energy. Without proper assessment of the impact energy distribution, DEM simulations may lead to an erroneous evaluation of milling experiments. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2404–2415, 2014     

Numerical simulation of particle breakage of angular particles using combined DEM and FEM

One of the effective parameters of the behavior of rockfill materials is particle breakage. As a result of particle breakage, both the stress–strain and deformability of materials change significantly. In this article, a novel approach for the two-dimensional numerical simulation of the phenomenon in rockfill (sharp-edge particles) has been developed using combined DEM and FEM. All particles are simulated by the discrete element method (DEM) as an assembly and after each step of DEM analysis, each particle is separately modeled by FEM to determine its possible breakage. If the particle fulfilled the proposed breakage criteria, the breakage path is assumed to be a straight line and is determined by a full finite element stress–strain analysis within that particle and two new particles are generated, replacing the original particle. These procedures are carried out on all particles in each time step of the DEM analysis. Novel approach for the numeric of breakage appears to produce reassuring physically consistent results that improve earlier made unnecessary simplistic assumptions about breakage. To evaluate the effect of particle breakage on rockfill's behavior, two test series with and without breakable particles have been simulated under a biaxial test with different confining pressures. Results indicate that particle breakage reduces the internal friction but increases the deformability of rockfill. Review of the v–p variation of the simulated samples shows that the specific volume has initially been reduced with the increase of mean pressures and then followed by an increase. Also, the increase of stress level reduces the growing length of the v–p path and it means that the dilation is reduced. Generally, any increase of confining stress decreases the internal friction angle of the assembly and the sample fail at higher values of axial stresses and promotes an increase in the deformability. The comparison between the simulations and the reported experimental data shows that the numerical simulation and experimental results are qualitatively in agreement. Overall the presented results show that the proposed model is capable with more accuracy to simulate the particle breakage in rockfill.     

An adhesive CFD‐DEM model for simulating nanoparticle agglomerate fluidization

Nanoparticles are fluidized as agglomerates with hierarchical fractal structures. In this study, we model nanoparticle fluidization by assuming the simple agglomerates as the discrete element in an adhesive (Computational Fluid Dynamics—Discrete Element Modelling) CFD‐DEM model. The simple agglomerates, which are the building blocks of the larger complex agglomerates, are represented by cohesive and plastic particles. It is shown that both the particle contact model and drag force interaction in the conventional CFD‐DEM model need modification for properly simulating a fluidized bed of nanoparticle agglomerates. The model is tested for different cases, including the normal impact, angle of repose (AOR), and fluidization of nanoparticle agglomerates, represented by the particles with the equivalent material properties. It shows that increasing the particle adhesion increases the critical stick velocity, angle of repose, and leads from uniform fluidization to defluidization. The particle adhesion, bulk properties, and fluidization can be linked to each other by the current adhesive CFD‐DEM model. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2259–2270, 2016