Practical validation of the two-fluid model applied to dense gas-solid flows in fluidized beds

This paper discusses the simulation of bubbling gas-solid flows by using the Eulerian two-fluid approach. Predictions of particle motion, bed expansion, bubble size and bubble velocity in bubbling beds containing Geldart B particles are compared with experimental results and correlations found in the literature. In addition, gas mixing in a bed of Geldart A particles is investigated.An in-house code has been developed based on the finite-volume method and the time-splitting approach using a staggered grid arrangement. The velocities in both phases are obtained by solving the 2D Reynolds-averaged Navier/Stokes equations using a partial elimination algorithm (PEA) and a coupled solver. The k-ε turbulence model is used to describe the turbulent quantities in the continuous phase.In general, the model predictions are in good agreement with experimental data found in the literature. Most important observations are: the level of the restitution coefficient was found to be crucial in order to obtain successful results from 2D axisymmetric simulations of a system containing Geldart B particles. Bubble size and bubble rise velocities are not as sensitive to the restitution coefficient. The turbulence model is of outmost importance concerning gas mixing in a fluidized bed of Geldart A particles.From these numerical analyzes an optimized granular flow two-fluid model can be designed for the purpose of simulating reactive systems in fluidized bed reactors.     

Particles mixing induced by bubbles in a gas‐solid fluidized bed

The effect of bubble injection characteristics on the mixing behavior of a gas‐solid fluidized bed is investigated using a discrete particle model. The effect of different parameters including gas injection time, velocity, and mode are studied. Simulation results show that injecting gas at a constant gas flow rate in the form of small bubbles results in a better overall particle mixing. It was also found that the injection velocities have limited effect on particle mixing behavior for the same total gas volume injected into the bed. Moreover, the mixing index (MI) of continuous gas jet bubbling regime is compared with the MI obtained in uniform gas injection regime and the results revealed that the MI of continuous jet bubbling regime has a larger value than that of uniform gas injection regime at the fixed total gas flow rate. In both regimes, z‐direction MI is larger than x‐direction index. The differences between two direction indices are more noticeable in continuous jet bubbling in comparison with the uniform gas injection regime. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1430–1438, 2016     

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.     

Numerical study on microscopic mixing characteristics in fluidized beds via DEM

In this paper, discrete element method (DEM), combined with computational fluid dynamics (CFD), is used to investigate the micro-mixing process in fluidized beds (FBs) of uniform particles. With the aid of snapshots and adoption of Lacey and Ashton indexes, mixing evolvement for two cases, fluidized bed using horizontal distributor with even gas supply and fluidized bed using inclined distributor with uneven gas supply, is discussed in detail. Results indicate that the Ashton index appears to be more effective in assessing the mixing dynamics in this work. Further analyses illustrate that in the case of horizontal distributor incorporated with even gas supply, diffusive mixing pattern is predominant, since bubbles lateral motion is reduced in such a bed; whereas, there is a faster convective mixing process in a fluidized bed using inclined distributor with uneven gas feed, followed by shear mixing. Generally, localized air supply induces the density gradient of particle distribution in the bed, which is the basic agent of convective particle stream. The analyses are confirmed by the comparison of solid flux during the simulations of the two cases. In addition, the mixing mechanism and the mixing time scale agree well with published experimental results.     

三维喷动床内异径干湿颗粒混合特性数值模拟

基于计算流体力学-离散单元法,建立了三维喷动床内气固两相流数学模型,采用Fortran语言编制了并行数值模拟程序。对三维喷动床内两种不同直径的干颗粒及湿颗粒的混合特性进行了数值模拟,并从颗粒角度分析了双组分颗粒的运动机制。利用Lacey混合指数对床内整体以及特定区域的混合程度进行了定量分析,并研究了液桥体积、颗粒密度比以及表观气速对异径颗粒混合的影响。结果表明：在单孔射流喷动床内,干湿两种颗粒流动方式相似,湿颗粒无明显的聚团现象;液桥力对小直径的颗粒影响较大,使不同直径湿颗粒速度差减小;环隙区内颗粒的混合是影响整床颗粒混合的关键因素;液桥体积对颗粒混合的影响较大,对颗粒密度比以及表观气速的影响有限。     

Experimental profiles of lateral mixing of feed particles in a three‐dimensional fluidized bed

Solids mixing data of high quality is one of the most crucial steps for quantitative studies, but it is a difficult task to obtain in a fluidized bed especially with a 3D configuration. Therefore a novel sampling technique is developed with bed collapse method, for measuring lateral mixing of feed particles in a 3D fluidized bed. The sampling tool is designed using a “bottom‐to‐top sampling” idea. Its development, configuration and measurement repetition are discussed in detail. The effects of mixing time, fluidizing gas velocity, and particle size of bed material on the tracer distribution are investigated. A quantitative comparison of lateral dispersion coefficient shows that our results agree fairly well with measurements and predictions of correlations for lab‐scale fluidized systems in previous studies. The presented 2D profiles of the lateral mixing can be used to validate fundamental solids mixing models or verifying convenient measurement techniques. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

鼓泡流化床内高灰煤气化过程的颗粒尺度特性研究

基于多相流体质点网格方法(MP-PIC)对高灰煤在三维鼓泡流化床气化过程进行了数值模拟研究。在欧拉-拉格朗日框架下将气相和固相分别视作连续介质和离散相处理。首先,将模拟得到的出口处气体组分结果与实验数据进行对比,实验数据与模拟结果具有良好的一致性。其次,研究了煤颗粒在气化炉内的温度、传热系数、速度和停留时间,从颗粒尺度揭示了鼓泡流化床气化炉内的颗粒分布特性和气固流动特征。结果表明:在气化炉入口附近煤颗粒与床层温差最大,传热系数最大;由于流化床内强非线性的气固流动,床中煤温度和传热系数的空间分布不均匀;煤颗粒和床料的瞬时速度具有稳定的波动幅度,其中垂直方向速度波动最明显,且煤颗粒的瞬时速度比床料的瞬时速度略大;由于颗粒间的剧烈碰撞,延长了煤颗粒停留时间。此外,对鼓泡流化床中煤气化过程颗粒尺度的研究,有助于深入了解固体颗粒的流动行为以及气固相相互作用特性,对鼓泡流化床反应器的设计优化具有重要意义。     

Numerical and experimental investigation of a fluidized bed chamber hydrodynamics with heat transfer

The hydrodynamics and heat transfer of a gas-solid fluidized bed chamber was investigated by computational fluid dynamic (CFD) techniques. A multifluid Eulerian model incorporating the kinetic theory for solid particles was applied to simulate the unsteady state behavior of this chamber. For momentum exchange coefficients, Syamlal-O’Brien drag functions were used. A suitable numerical method that employed finite volume method was applied to discretize the equations. The simulation results also indicated that small bubbles were produced at the bottom of the bed. These bubbles collided with each other as they moved upwards forming larger bubbles. Also, the solid particle temperature effect on heat transfer and hydrodynamics was studied. Simulation results were compared with the experimental data in order to validate the CFD model. Pressure drops and mean gas temperature predicted by the simulations at different positions in the chamber were in good agreement with experimental measurements at gas velocities higher than the minimum fluidization velocity. Furthermore, this comparison showed that the model could predict hydrodynamics and heat transfer behaviors of gas solid fluidized bed reasonably well.     

Discrete element simulation of particle flow in arbitrarily complex geometries

Conventional simulations of dense particle flows in complex geometries usually involve the use of glued particles to approximate geometric surface. This study is concerned with the development of a robust and accurate algorithm for detecting the interaction between a spherical particle and an arbitrarily complex geometric surface in the framework of soft-sphere discrete element model (DEM) without introducing any assumptions. Numerical experiments specially designed to validate the algorithm shows that the new algorithm can accurately predict the contact state of a particle with a complex geometric surface. Based on the proposed algorithm, a new solver for simulation of dense particle flows is developed and implemented into an open source computational fluid dynamics (CFD) software package OpenFOAM. The solver is firstly employed to simulate hydrodynamics in a bubble fluidized bed. Numerical results show that a 3D simulation can predict the bubble size better than a 2D simulation. Subsequently, gas–solid hydrodynamics in an immersed tube fluidized bed is simulated. Results show that bubble coalescence and breakup behavior around the immersed tubes are well captured by the numerical model. In addition, seven different particle flow patterns around the immersed tubes are identified based on the numerical results obtained.     

EFFECTS OF PARTICLE CHARACTERISTICS ON THE PERFORMANCE OF A FAST FLUIDIZED BED REACTOR

A heterogeneous model for the fast fluidized bed reactor which carries out a gas-solid non catalytic reaction is presented. The hydrodynamics of the fast fluidized bed is characterized by the model of Kwauk et al. (1985) which assumes the existence of two phases; a dense phase and a dilute pneumatic transport phase. For a given solid flowrate, the length of the reactor occupied by each phase depends on gas velocity, particle diameter and density and average voidage within the reactor. The gas-solid reaction is assumed to follow the shrinking core model. The solids are assumed to be completely backmixed in the dense phase and move in plug How in the dilute pneumatic transport phase. The gas phase is assumed to be in plug flow in both phases

For given gas and solid flowrates, the transition from the dense phase flow to the fast fluidized bed (containing two regions) as functions of particle size and density is determined using the model of Kwauk et al. (1985). The numerical solution of the governing mass balance equations show that for given solid and gas flowrates, (and average voidage) the gas phase conversion shows an unusual behavior with respect to particle diameter and density. Such behavior is resulted from the effects of particle diameter and density on the reactor volume occupied by each phase and the effect of particle diameter on the apparent reaction rate. The numerical results show that a fast fluidized bed gives the best conversion at large particle density and for the particle diameter which results the fast fluidized bed to be operated near the pure dense phase flow.     

Effects of using two- versus three-dimensional computational modeling of fluidized beds: Part II, budget analysis

The partial differential equations for modeling gas-solid flows using computational fluid dynamics are compared for different coordinate systems. The numerical results of 2D and 3D simulations for both cylindrical and rectangular domains are presented in Part I (N. Xie, F. Battaglia, S. Pannala, Effects of using two- versus three-dimensional computational modeling of fluidized beds: Part I, Hydrodynamics (2007-this volume), doi:10.1016/j.powtec.2007.07.005), comparing the hydrodynamic features of a fluidized bed. The individual terms of the governing equations in 2D and 3D simulations with the cylindrical and Cartesian coordinate systems are evaluated in this study through a budget analysis. The additional terms appearing in the 3D equations can be used to explain the discrepancies between 2D and 3D simulations. The values of the additional terms is shown to increase as inlet gas velocity increases. This explains the good agreement between 2D and 3D simulations that is observed for bubbling regimes with low gas velocity, and why the differences between 2D and 3D simulations increases for slugging and turbulent regimes.     

CFD simulations of bubbling beds of rough spheres

Hydrodynamics of three-dimensional gas-solid bubbling fluidized beds are numerically analyzed. The particle-particle interactions are simulated from the kinetic theory for flow of dense, slightly inelastic, slightly rough sphere proposed by Lun [1991. Kinetic theory for granular flow of dense, slightly inelastic, slightly rough sphere. Journal of Fluid Mechanics 233, 539-559] to account for rough sphere binary collisions and the frictional stress model proposed by Johnson et al. [1990. Frictional-collisional equations of motion for particulate flows and their application to chutes. Journal of Fluid Mechanics 210, 501-535] to consider the frictional contact forces between particles. The present model is evaluated by measured particle distributions and velocities of Yuu et al. [2001. Numerical simulation of air and particle motions in group-B particle turbulent fluidized bed. Powder Technology 118, 32-44] and experimental bed expansion of Taghipour et al. [2005. Experimental and computational study of gas-solid fluidized bed hydrodynamics. Chemical Engineering Science 60, 6857-6867]. Our computed results indicated that the present model gives better agreement with experimental data than the results from original kinetic theory for frictionless slightly inelastic sphere of Ding and Gidaspow [1990. A bubbling fluidization model using kinetic theory of granular flow. A.I.Ch.E. Journal 36, 523-538] with and without solid friction stress model.     

单孔射流流化床内颗粒混合特性的数值模拟

在欧拉-拉格朗日坐标系下,采用离散单元法对单孔射流流化床内颗粒混合特性进行了数值模拟。引入混合指数对床内轴向及径向布置的颗粒混合质量进行定量分析,并研究了不同表观气速、不同弹性系数对颗粒混合特性的影响。模拟得到了颗粒轴向及径向混合序列图、气体和颗粒速度分布、整床颗粒混合指数分布、参量变化时整床颗粒混合指数分布。结果表明：流化床床层内颗粒混合速度受颗粒内循环能力和颗粒扩散能力的综合作用。单口射流喷动流化床颗粒轴向混合速度主要由颗粒内循环速度决定,颗粒径向混合速度主要由颗粒扩散能力决定。表观气速增大时,颗粒内循环速度增加,从而加快了颗粒轴向混合进程,但对颗粒径向混合影响微弱;弹性系数增大时,颗粒混合速度及混合质量均下降,并且弹性系数增大对颗粒径向混合进程影响小于颗粒轴向混合。     

灰熔聚气化炉内气体与固体混合特性的研究

气化炉内的气化剂与煤粉的混合特性直接影响着气化炉内的碳转化率和灰熔聚流化床气化炉的热效率。研究气化炉内气体和固体颗粒的混合特性,掌握炉内气体和固体颗粒的轴向和径向的运动规律,对认识床内传热和传质机理具有重要的意义。基于欧拉双流体模型,结合颗粒动力学理论,应用商用FLUENT软件,对太原化学工业集团有限公司运行的灰熔聚流化床气化炉内的气体与固体的混合特性进行了数值模拟。     

基于连续方法的气固循环流化床全回路模拟及稳定性分析

相比对单个操作单元的模拟，气固循环流化床的全回路模拟能全面揭示各单元之间的联系、诊断操作突变等现象，对实际工业生产更具指导意义。本研究在连续介质模型结合颗粒动理论的框架下，对一套虚拟过程工程(VPE)的气固循环流化床装置进行了全回路模拟和稳定性分析。模拟发现了提升管中的颗粒浓度及压降发生大幅度的周期性震荡现象，两种完全不同的操作状态，即稀相输送和浓相输送，交替式地出现。为分析该现象产生的原因，考察了模型因素(主要是气固相间曳力)和操作因素(颗粒藏料量和提升管表观气速)对周期性震荡现象的影响。研究发现，将考虑非均匀结构影响的曳力替换成均匀曳力，仍不能消除周期震荡现象，其颗粒输送返回装置(Loop-seal)压头不足以保证颗粒从下降管平稳输送到提升管，而降低气速和增大藏料量都有利于颗粒循环输送的稳定性，防止“窜气”现象的发生。结合上述现象，进一步聚焦影响颗粒输送的关键点，即Loop-seal气动阀，采用引入虚拟阀门的方式提高Loop-seal输送管中的输送阻力，从而有效改进了全回路模拟的稳定性，其预测得到的提升管轴向压降分布与实验值基本吻合。     

DSMC-LES方法数值模拟鼓泡流化床内气泡和颗粒流动行为

基于稠密气体分子动力学和气固两相流体动力学,建立流化床稠密气固两相离散颗粒运动-碰撞解耦模型,采用直接模拟蒙特卡罗方法(DSMC)模拟颗粒间的碰撞,采用考虑颗粒脉动流动对气相湍流流动影响的大涡模拟(LES)研究气相湍流,单颗粒运动满足牛顿第二定律,颗粒相和气相相间作用的双向耦合由牛顿第三定律确定.数值模拟流化床中颗粒流动以及气泡的生成、长大和破碎过程,获得颗粒轴向和径向速度的概率密度分布,及颗粒浓度分布.计算结果表明床内气泡的形成造成床内颗粒的循环,使得流化床内颗粒具有不同的轴向和径向脉动速度,颗粒分速度分布近似服从高斯分布.颗粒温度随颗粒浓度增加,达到最大值后,随颗粒浓度增大而下降.流化床颗粒浓度脉动主要是低频部分,高频分量较低,表明在流化床内颗粒浓度脉动频率低,能量高,颗粒浓度脉动主频率为0.4～1.0Hz,其值与Pain et al.获得的颗粒浓度脉动主频率基本吻合.     

图像法用于流化床颗粒混合特性的研究

利用基于相关的图像法速度测量技术,测量了小型二维气固流化床密相区颗粒运动速度分布.并提出了用颗粒速度不均匀指数来衡量流化床内颗粒的速度波动与混合.速度波动对于物料扩散与对流混合均十分重要.在流化床下部,颗粒运动速度往往低于床层表面,但速度不均匀指数则高于床层表面.在床层底部颗粒速度不均匀指数随流化床气泡产生而变化.床层内部混合以对流及扩散为主,而在床层表面,混合以对流为主.床层下部速度波动有利于颗粒在床内的扩散及对流混合.流化风量的增加可以增强颗粒的混合.针对这些结论,在流化床垃圾焚烧炉的设计中,对不同的组分选用不同的给料方式,可以促进物料在床内的混合.     

耦合EMMS曳力与简化双流体模型的气固流动模拟

提出了一种耦合EMMS曳力的简化双流体模型,该模型忽略固相黏度,用简单的经验关联式来计算固相压力,并且耦合考虑了介尺度结构的EMMS曳力模型来计算气固相间作用力。采用简化双流体模型成功模拟一个三维实验室尺度鼓泡流化床,数值模拟结果与完整双流体模型以及实验测量结果进行了比较,结果表明耦合EMMS曳力的简化双流体模型模拟结果与完整双流体模型耦合EMMS曳力的模拟结果基本相当,并且都与实验结果吻合良好,然而简化双流体模型的计算速度是完整双流体模型的两倍以上。这表明曳力模型在气固模拟中起着主导作用,而固相应力的作用是其次的,耦合EMMS曳力的简化双流体模型在实现工业规模气固反应器快速模拟中具有巨大潜力。     

流化床内颗粒流体两相流的CFD模拟

采用先进的CFD模拟技术分析流化床内两相复杂体系的非线性流体动力学特征已得到普遍认同,但是由于不同研究者对颗粒与颗粒以及颗粒与流体之间相互作用力认识的差异,导致欧拉-欧拉框架下动量守恒方程的不同表达形式。本文在总结文献中有关颗粒黏性力、固相压力和两相间作用力的基础上,从双流体理论出发,提出了一个考虑拟平衡态下固体颗粒对流体相和固相动量守恒方程均有影响的简捷流体动力学模型。该模型的主要特点是表征颗粒离散属性的特征长度视为颗粒直径的同一数量级。随后在CFX4.4商业化软件平台上通过增加用户自定义子程序,对网格尺度、时间步长和最大颗粒堆积率的无关性进行检验,介绍了作者近年来采用该模型模拟二维/三维流化床内液固体系的散式流态化、气固Geldart A类物料的散式/聚式流态化和床层塌落特性以及Geldart B/D类物料的鼓泡/射流流态化和床层塌落的研究进展。模拟的主要结果与经典理论、本研究实验和文献报道数据相一致,说明该模型可以用来预测流化床内密相颗粒流体体系的动力学特性。     

布风方式对流化床混合特性的影响

通过将离散单元法同计算流体力学相结合,对流化床内物料混合过程进行了研究。给出了水平布风板均匀布风、倾斜布风板非均匀布风2种情况下的示踪颗粒场历变过程。模拟结果表明:瞬时颗粒场组图能够较为直观表征床内混合现象;其中,在均匀布风情况下,床内气泡横向运动受到限制,颗粒整体横向运动能力较弱,混合方式以扩散混合为主;而对于非均匀布风流化床,床内存在较大的横向颗粒浓度梯度,对流混和起主要作用,且混合速度较为迅速。