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     

Hydrodynamic modelling of binary mixture in a gas bubbling fluidized bed using the kinetic theory of granular flow

A multi-fluid Eularian CFD model with closure relationships according to the kinetic theory of granular flow has been applied to study the motions of particles in the gas bubbling fluidized bed with the binary mixtures. The mutual interactions between the gas and particles and the collisions among particles were taken into account. Simulated results shown that the hydrodynamics of gas bubbling fluidized bed related with the distribution of particle sizes and the amount of energy dissipated in particle-particle interaction. In order to obtain realistic bed dynamics from fundamental hydrodynamic models, it is important to correctly take the effect of particle size distribution and energy dissipation due to non-ideal particle-particle interactions into account.     

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     

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     

Evaluation of wall boundary condition parameters for gas–solids fluidized bed simulations

Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas–solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas–solids flow. A model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (Li and Benyahia, AIChE J. 2012;58:2058–2068) is implemented in the open‐source CFD code‐MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial‐slip boundary conditions for the solids phase. Through a series of two‐dimensional numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient. Published 2013 American Institute of Chemical Engineers AIChE J, 59: 3624–3632, 2013     

流化床法制备粒状多晶硅研究进展

综述流化床法制备粒状多晶硅的技术概况及生产技术问题的研究情况。     

Hydrodynamics of binary fluidization in a riser: CFD simulation using two granular temperatures

A new computational fluid-dynamic (CFD) model with a separate granular temperature (2/3 random particle kinetic energy per unit of mass) equation for each phase or particle size was developed using constitutive equations derived earlier by Huilin, Gidaspow and Manger. In agreement with the experiment and model of Mathiesen, Solberg and Hjertager the new model computes the observed core-annular flow regime. It predicts the trends of the observed radial and axial particle diameter distributions. For elastic particles the computed particle velocity distributions are parabolic. They are close to the laminar type approximate analytical solution for flow in a pipe, where the mean velocity equals the inlet flux divided by the particle density and volume fraction. The computed turbulent intensity is lower for large particles than for small particles, as measured. This is in agreement with an approximate analytical solution for the granular temperature in the developed flow region of a riser for elastic particles. Computations show that for sufficiently inelastic particles the granular temperature in the center can be lower than near the wall resembling the measured particle fluctuating velocity distribution.     

Studies on segregation of binary mixture of solids in continuous fast fluidized bed: Part II. Effect of particle size

Experimental investigations on the continuous fast fluidized bed were extended for size segregation of binary mixture of solids in the column with air as the separation medium [1]. The feed is either jetsam-rich or flotsam-rich binary mixture of particles of different size, but same density. The variables tested were superficial gas velocity, solids feed rate and feed characteristics. At steady state, there exists physical equilibrium between the evolved flotsam and the residual jetsam when the granular solids are in fluid-like state as in the case of density segregation of solids [1]. Using the analogy of the binary liquid mixtures separation by distillation, the phase diagram was constructed from the experimental observations. The effect of solids feed rate, feed composition, particle size ratio and particle size on equilibrium distribution of the flotsam and jetsam were presented.     

模拟颗粒流动的离散元方法及其应用

介绍了离散元 (DEM)方法的基本原理、颗粒运动控制方程和颗粒相互作用力的数学模型。综述了DEM在流化床和固定床反应器 ,以及一些单元操作如料仓卸料过程、混合过程等中的最新应用和研究结果 ,表明DEM能够反映过程的本质机理 ,可以利用基本的数据模拟复杂的颗粒流动系统。最后指出了DEM发展中亟待解决的问题     

流化床技术制备粒状多晶硅的研究进展

概述流化床技术制备粒状多晶硅的研究进展,简介粒状多晶硅的生长机制和物理性能,阐述流化床技术在多晶硅生产领域的发展方向。     

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。     

Vaporization model of MgCl2-CaCl2 binary melts in fluidized bed

The present study investigated the vaporization kinetics of MgCl2,CaCl2 and their binary melts in a fluidized bed at 1073-1273 K,and developed a vaporization model for the binary melts to explore the possibility of achieving enhanced vaporization rate for the feedstock containing CaO greater than 0.2 wt％.The vaporization rate constant of MgCl2 is more than seven times than that of CaCl2 at 1273 K.The vaporization rate of the binary melt was significantly affected by the composition,a small quantity of CaCl2 can remarkably deteriorate the overall vaporization rate,Experimental results coincide well with the numerical simulation by the vaporization model which regards the evolution of vaporization rate with melts composition.A correlation between the necessary operation temperature and the CaO/(CaO + MgO) of the feedstock was proposed.Predictions reveal that a similar vaporization rate for 0.2 wt％-0.4 wt％ CaO content feedstock with 0.2 wt％ could be achieved at lower than 1365 K.     

气固流化床介尺度结构形成机制及过滤曳力模型研究进展

气固流化床中,介于颗粒与宏观尺度间的复杂的时空多尺度结构（介尺度结构）将完全改变气固相间作用规律,加大了流态化系统调控及预测的难度。为此,需要构建考虑结构影响的相间本构关系。其中,曳力作为影响流态化动力学特征的主导因素,对其研究尤为重要。从结构产生演化的机制出发,概述结构影响曳力的机理,以模型构建流程的角度对结构和过滤两类模型进行总结,并重点综述过滤模型构建在提升准确性、有效性、通用性和考虑更多物理机制方面的最新进展。研究表明：提升模型通用性和考虑真实系统中更丰富的物理机制仍是建模中亟待解决的问题,结合结构演化机制理性建模和充分发挥机器学习数据分析处理优势或是曳力建模进一步发展的关键。     

Simulation study of the effect of wall roughness on the dynamics of granular flows in rotating semicylindrical chutes

A discrete element model (DEM) is used to investigate the behavior of spherical particles flowing down a semicylindrical rotating chute. The DEM simulations are validated by comparing with particle tracking velocimetry results of spherical glass particles flowing through a smooth semicylindrical chute at different rotation rates of the chute. The DEM model predictions agree well with experimental results of surface velocity and particle bed height evolution. The validated DEM model is used to investigate the influence of chute roughness on the flow behavior of monodisperse granular particles in rotating chutes. To emulate different base roughnesses, a rough base is constructed out of a square close packing of fixed spherical particles with a diameter equal to, smaller, or larger than the flowing particles. Finally, the DEM model is used to study segregation in a binary density mixture for different degrees of roughness of the chute. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2117–2135, 2015     

Modeling of cluster structure-dependent drag with Eulerian approach for circulating fluidized beds

Flow behavior of gas and solids is simulated in combination the gas-solid two-fluid model with a cluster structure-dependent (CSD) drag coefficient model. The dispersed phase is modeled by a Eulerian approach based upon the kinetic theory of granular flow (KTGF) including models for describing the dispersed phase interactions with the continuous phase. The drag forces of gas-solid phases are predicted from the local structure parameters of the dense and dilute phases based on the minimization of the energy consumed by heterogeneous drag. The cluster structure-dependent (CSD) drag coefficients are incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. Simulation results indicate that the dynamic formation and dissolution of clusters can be captured with the cluster structure-dependent drag coefficient model. Simulated solid velocity and concentration of particles profiles are in reasonable agreement with experimental results.     

宽Re范围内气泡和液滴曳力系数的关联模型

流粒(气泡或液滴)的曳力系数CD和上升/终端速度因有助于准确预测反应器内相含率分布、液相速度分布、流粒停留时间和传质速率而具有重要意义.但现有用于估算流粒CD的关联式大多分段且只在低雷诺数Re区间内有效,并难以同时准确预测不同实验体系和操作条件下的实验结果.针对这些不足,基于实验测量和理论分析,本工作提出了一个能够在整...     

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。     

Shape dependence of resistance force exerted on an obstacle placed in a gravity‐driven granular silo flow

Resistance force exerted on an obstacle in a gravity‐driven slow granular silo flow is studied by experiments and numerical simulations. In a two‐dimensional granular silo, an obstacle is placed just above the exit. Then, steady discharge flow is made and its flow rate can be controlled by the width of exit and the position of obstacle. During the discharge of particles, flow rate and resistance force exerting on the obstacle are measured. Using the obtained data, a dimensionless number characterizing the force balance in granular flow is defined by the relation between the discharge flow rate and resistance‐force decreasing rate. The dimensionless number is independent of flow rate. Rather, we find the weak shape dependence of the dimensionless number. This tendency is a unique feature for the resistance force in granular silo flow. It characterizes the effective flow width interacting with the obstacle in granular silo flow. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3849–3856, 2018     

Layer inversion and mixing of binary solids in two- and three-phase fluidized beds

Water fluidization in a 210 mm diameter semi-cylindrical acrylic column of a binary solids mixture of 3.2 mm polymer beads (ρ_s=1280 kg/m³) and 0.385 mm glass beads (ρ_s=2500 kg/m³) at superficial liquid velocities from 18.1 to 43.1 mm/s is shown to generate layer inversion at a superficial liquid velocity, U_L, of 33.1 mm/s. Introduction of air with a superficial velocity, U_g, of 1.92 mm/s yielded a layer inversion velocity at U_L=30.4 mm/s. The latter is explainable if it is assumed that the determinant of layer inversion is the interstitial liquid velocity and that therefore the main function of the gas in this respect is to occupy space.Mixing of the binary solids, as quantified by a mixing index applied to measured particle compositions at different levels of the fluidized bed, is shown to be greatest at the layer inversion velocity for liquid fluidization and, in general, to increase as co-current gas flow increases at a fixed value of U_L.     

Derivation and validation of a binary multi-fluid Eulerian model for fluidized beds

The paper presents a multi-fluid Eulerian model derived from binary kinetic theory of granular flows, free path theory and an empirical friction theory. The effects of the inter- and inner-particle collisions, particle translational motions and particle–particle friction are included. As the effects due to fluiddynamic particle velocity differences and particle–particle friction are considered, some unconventional terms are produced compared with the previous models. Model validation using the data from Mathiesen et al. (2000) shows that the coupling terms give a stronger and more realistic particle–particle coupling because the effects due to the fluiddynamic velocity differences are considered. The model gives reasonable predictions of the particle volume fraction, particle velocities and velocity fluctuations. The model analysis reveals that the basic particle velocity fluctuations constitute 2 terms: the velocity fluctuations of the discrete particles, and the velocity fluctuations of the continuous fluid flow. Furthermore, the simulation results show that the velocity fluctuations of the continuous fluid flow are dominant in a binary riser flow.