A CFD‐PBM‐PMLM integrated model for the gas–solid flow fields in fluidized bed polymerization reactors

Although the use of computational fluid dynamics (CFD) model coupled with population balance (CFD‐PBM) is becoming a common approach for simulating gas–solid flows in polydisperse fluidized bed polymerization reactors, a number of issues still remain. One major issue is the absence of modeling the growth of a single polymeric particle. In this work a polymeric multilayer model (PMLM) was applied to describe the growth of a single particle under the intraparticle transfer limitations. The PMLM was solved together with a PBM (i.e. PBM‐PMLM) to predict the dynamic evolution of particle size distribution (PSD). In addition, a CFD model based on the Eulerian‐Eulerian two‐fluid model, coupled with PBM‐PMLM (CFD‐PBM‐PMLM), has been implemented to describe the gas–solid flow field in fluidized bed polymerization reactors. The CFD‐PBM‐PMLM model has been validated by comparing simulation results with some classical experimental data. Five cases including fluid dynamics coupled purely continuous PSD, pure particle growth, pure particle aggregation, pure particle breakage, and flow dynamics coupled with all the above factors were carried out to examine the model. The results showed that the CFD‐PBM‐PMLM model describes well the behavior of the gas–solid flow fields in polydisperse fluidized bed polymerization reactors. The results also showed that the intraparticle mass transfer limitation is an important factor in affecting the reactor flow fields. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1717–1732, 2012     

Particle scale study of heat transfer in packed and bubbling fluidized beds

The approach of combined discrete particle simulation (DPS) and computational fluid dynamics (CFD), which has been increasingly applied to the modeling of particle‐fluid flow, is extended to study particle‐particle and particle‐fluid heat transfer in packed and bubbling fluidized beds at an individual particle scale. The development of this model is described first, involving three heat transfer mechanisms: fluid‐particle convection, particle‐particle conduction and particle radiation. The model is then validated by comparing the predicted results with those measured in the literature in terms of bed effective thermal conductivity and individual particle heat transfer characteristics. The contribution of each of the three heat transfer mechanisms is quantified and analyzed. The results confirm that under certain conditions, individual particle heat transfer coefficient (HTC) can be constant in a fluidized bed, independent of gas superficial velocities. However, the relationship between HTC and gas superficial velocity varies with flow conditions and material properties such as thermal conductivities. The effectiveness and possible limitation of the hot sphere approach recently used in the experimental studies of heat transfer in fluidized beds are discussed. The results show that the proposed model offers an effective method to elucidate the mechanisms governing the heat transfer in packed and bubbling fluidized beds at a particle scale. The need for further development in this area is also discussed. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

沉浸管式流化床的颗粒尺度模拟

为模拟具有复杂几何结构的气固流动系统,文中将计算流体力学和离散单元法与边界元方法结合起来,对沉浸管式流化床内颗粒及气泡的运动行为进行了数值模拟。模拟计算得到的瞬态流型图揭示了气泡绕流沉浸管束时出现的合并和破碎状态及颗粒群的详细运动行为,发现床内气固二相的流动受到沉浸管束存在的显著影响。当颗粒及气相的流动受到沉浸管的阻碍而绕管流动过程中气泡会发生变形,变得扭曲狭长且易被撕碎。同时颗粒与管道壁面碰撞会造成气固二相复杂的动态运动形式,床内的管道大部分时间会被气穴包围,将严重阻碍管道与颗粒之间的传热。     

Three‐dimensional CFD‐PBM coupled model of the temperature fields in fluidized‐bed polymerization reactors

A three‐dimensional (3‐D) computational fluid dynamics model, coupled with population balance (CFD‐PBM), was developed to describe the gas–solid two‐phase flow in fluidized‐bed polymerization reactors. The model considered the Eulerian–Eulerian two‐fluid model, the kinetic theory of granular flow, the population balance, and heat exchange equations. First, the model was validated by comparing simulation results with the classical calculated data. The entire temperature fields in the reactor were also obtained numerically. Furthermore, two case studies, involving constant solid particle size and constant polymerization heat or evolving particle‐size distribution, polymerization kinetics, and polymerization heat, were designed to identify the model. The results showed that the calculated results in the second case were in good agreement with the reality. Finally, the model of the second case was used to investigate the influences of operational conditions on the temperature field. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Development and test of CFD–DEM model for complex geometry: A coupling algorithm for Fluent and DEM

CFD–Discrete Element Method (DEM) model is an effective approach for studying dense gas–solid flow in fluidized beds. In this study, a CFD–DEM model for complex geometries is developed, where DEM code is coupled with ANSYS/Fluent software through its User Defined Function. The Fluent Eulerian multiphase model is employed to couple with DEM, whose secondary phase acts as a ghost phase but just an image copy of DEM field. The proposed procedure preserves phase conservation and ensures the Fluent phase-coupled SIMPLE solver work stable. The model is used to simulate four typical fluidization cases, respectively, a single pulsed jet fluidized bed, fluidized bed with an immersed tube, fluidization regime transition from bubbling to fast, and a simplified two-dimensional circulating fluidized bed loop. The simulation results are satisfactory. The present approach provides an easily implemented and reliable method for CFD–DEM model on complex geometries.     

Modeling gas‐particle two‐phase flows with complex and moving boundaries using DEM‐CFD with an immersed boundary method

An immersed boundary method (IBM) has been developed and incorporated into the coupled discrete element method and computational fluid dynamics (DEM‐CFD) approach to model particulate systems consisting of a compressible gas and solid particles with complex and/or moving boundaries. The IBM is used to deal with the interaction between gas and complex and moving boundaries by using simple rectangular grids to discretize the fluid field. The developed method has been applied to simulate some typical powder handling processes (e.g., gas fluidization with an immersed tube, segregation in a vertically vibrated bed, and pneumatic conveying). Good agreement is achieved between the present simulation results and the experimental ones reported in the literature. It has been demonstrated that the capacity of DEM‐CFD is enhanced with the incorporation of IBM, which can be used to simulate a wide range of problems that could not be handled with the conventional DEM‐CFD method. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1075–1087, 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     

Experimental and computational study of the bed dynamics of semi‐cylindrical gas–solid fluidized bed

With computational fluid dynamics (CFD) it is possible to get a detailed view of the flow behaviour of the fluidized beds. A profound and fundamental understanding of bed dynamics such as bed pressure drop, bed expansion ratio, bed fluctuation ratio, and minimum fluidization velocity of homogeneous binary mixtures has been made in a semi‐cylindrical fluidized column for gas–solid systems, resulting in a predictive model for fluidized beds. In the present work attempt has been made to study the effect of different system parameters (viz., size and density of the bed materials and initial static bed height) on the bed dynamics. The correlations for the bed expansion and bed fluctuations have been developed on the basis of dimensional analysis using these system parameters. Computational study has also been carried out using a commercial CFD package Fluent (Fluent, Inc.). A multifluid Eulerian model incorporating the kinetic theory for solid particles was applied in order to simulate the gas–solid flow. CFD simulated bed pressure drop has been compared with the experimental bed pressure drops under different conditions for which the results show good agreements.     

基于计算流体力学的气相烯烃聚合反应器模拟综述

气相聚合过程以流化床为核心反应器,其混合、传递和化学反应过程规律对工艺研发具有指导意义。计算流体力学是一种模拟流体流动的方法,可节省大量人力和物力并提供更全面的反应过程信息,在气固流态化领域得到广泛应用。基于计算流体力学的流态化模拟的难点在于如何建立能够恰当描述颗粒团聚过程的曳力模型,关于热量传递甚至聚合反应过程的模拟工作都是基于此发生的。随着计算机运算能力的提高,研究工业尺度的流化床反应器以及由粒径分布而带来的传递过程的影响可能成为模型广度及深度发展的方向。     

Particle‐resolved direct numerical simulation of gas–solid dynamics in experimental fluidized beds

Particle‐resolved direct numerical simulations (PR‐DNS) of a simplified experimental shallow fluidized bed and a laboratory bubbling fluidized bed are performed by using immersed boundary method coupled with a soft‐sphere model. Detailed information on gas flow and individual particles’ motion are obtained and analyzed to study the gas–solid dynamics. For the shallow bed, the successful predictions of particle coherent oscillation and bed expansion and contraction indicate all scales of motion in the flow are well captured by the PD‐DNS. For the bubbling bed, the PR‐DNS predicted time averaged particle velocities show a better agreement with experimental measurements than those of the computational fluid dynamics coupled with discrete element models (CFD‐DEM), which further validates the predictive capability of the developed PR‐DNS. Analysis of the PR‐DNS drag force shows that the prevailing CFD‐DEM drag correlations underestimate the particle drag force in fluidized beds. The particle mobility effect on drag correlation needs further investigation. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1917–1932, 2016     

CFD‐DEM Model for Simulating Solid Exchange in a Dual‐Leg Fluidized Bed

The domain coverage method (DCM) is proposed to establish a computational fluid dynamics‐discrete element method (CFD‐DEM) model based on irregular mesh. The gas field was solved by Fluent software and the DEM model was coupled with Fluent software by user‐defined functions. Gas turbulent viscosity was calculated by the coupled k‐? two‐equation model and the soft‐sphere collision model was used to get particle contact force. The CFD‐DEM model based on irregular mesh was firstly verified to be reasonable by comparing the simulated injected bubble with that simulated by Bokkers et al. The solid exchange behavior was studied numerically in a 2D dual‐leg fluidized bed (DL‐FB). The simulation results were compared with experimental results and proved that the CFD‐DEM model is established successfully based on the efficient DCM. The DEM model is expanded to be used on irregular mesh in fluidized beds with complex geometries.     

An extended DEM–CFD model for char combustion in a bubbling fluidized bed combustor of inert sand

This paper proposes a transient three-phase numerical model for the simulation of multiphase flow, heat and mass transfer and combustion in a bubbling fluidized bed of inert sand. The gas phase is treated as a continuum and solved using the computational fluid dynamics (CFD) approach; the solid particles are treated as two discrete phases with different reactivity characteristics and solved on the individual particle scale using an extended discrete element model (DEM). A new char combustion submodel considering sand inhibitory effects is also developed to describe char particle combustion behavior in the fluidized bed. Two conditions, i.e. a single larger graphite particle and a batch of smaller graphite particles, are used to test the prediction capability of the model. The model is validated by comparing the predicted results with the previous measured results and conclusions in the literature in terms of bed hydrodynamics, individual particle temperature, char residence time and concentrations of the products. The effects of bed temperature, oxygen concentration and superficial velocity on char combustion behavior are also examined through model simulation. The results indicate that the proposed model provides a proximal approach to elucidate multiphase flow and combustion mechanisms in fluidized bed combustors.     

Experimental and numerical research for fluidization behaviors in a gas–solid acoustic fluidized bed

The effects of sound assistance on fluidization behaviors were systematically investigated in a gas–solid acoustic fluidized bed. A model modified from Syamlal–O'Brien drag model was established. The original solid momentum equation was developed and an acoustic model was also proposed. The radial particle volume fraction, axial root‐mean‐square of bed pressure drop, granular temperature, and particle velocity in gas–solid acoustic fluidized bed were simulated using computational fluid dynamics (CFD) code Fluent 6.2. The results showed that radial particle volume fraction increased using modified drag model compared with that using the original one. Radial particle volume fraction was revealed as a parabolic concentration profile. Axial particle volume fraction decreased with the increasing bed height. The granular temperature increased with increasing sound pressure level. It showed that simulation values using CFD code Fluent 6.2 were in agreement with the experimental data. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Fictitious particle method: A numerical model for flows including dense solids with large size difference

Large solids coexist with small solids in a number of dense gas‐solid flow applications such as fluidized beds and pneumatic conveyers. A new numerical model that is based on the discrete element method–computational fluid dynamics mesoscopic model and extended by introducing an idea appearing in volume penalization method is presented. In computational cells including large and small solids, the amount of momentum exchange between the fluid and the solids is estimated by assuming that a large solid consist of small, dense fictitious particles. We describe the proposed model in detail and show the optimal model parameters found through a number of parameter‐dependency studies. Validation study is performed for the motion of a large sphere in a bubbling fluidized bed and good agreements are confirmed for floating and sinking motions of the sphere between the present model and the experiment. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1606–1620, 2014     

CFD modeling and validation of the turbulent fluidized bed of FCC particles

An experimental and computational study is presented on the hydrodynamic characteristics of FCC particles in a turbulent fluidized bed. Based on the Eulerian/Eulerian model, a computational fluid dynamics (CFD) model incorporating a modified gas‐solid drag model has been presented, and the model parameters are examined by using a commercial CFD software package (FLUENT 6.2.16). Relative to other drag models, the modified one gives a reasonable hydrodynamic prediction in comparison with experimental data. The hydrodynamics show more sensitive to the coefficient of restitution than to the flow models and kinetics theories. Experimental and numerical results indicate that there exist two different coexisting regions in the turbulent fluidized bed: a bottom dense, bubbling region and a dilute, dispersed flow region. At low‐gas velocity, solid‐volume fractions show high near the wall region, and low in the center of the bed. Increasing gas velocity aggravates the turbulent disorder in the turbulent fluidized bed, resulting in an irregularity of the radial particle concentration profile. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

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.     

Experimental and numerical simulation of lignite chemical looping gasification with phosphogypsum as oxygen carrier in a fluidized bed

Phosphogypsum (PG) is a solid waste produced in the wet process of producing phosphoric acid.Lignite is a kind of promising chemical raw material.However,the high sulfur of lignite limits the utilization of lig-nite as a resource.Based on fluidized bed experiments,the optimal reaction conditions for the production syngas by lignite chemical looping gasification (CLG) with PG as oxygen carrier were studied.The study found that the optimal reaction temperature should not exceed 1123 K;the mole ratio of water vapor to lignite should be about 0.2;the mole ratio of PG oxygen carrier to lignite should be about 0.6.Meanwhile,commercial software Comsol was used to establish a fuel reaction kinetics model.Through computational fluid dynamics (CFD) numerical simulation,the process of reaction in fluidized bed were well captured.The model was based on a two-fluid model and coupled mass transfer,heat transfer and chemical reac-tions.This study showed that the fluidized bed presents a flow structure in which gas and solid coexist.There was a high temperature zone in the middle and lower parts of the fluidized bed.It could be seen from the results of the flow field simulated that the fluidized bed was beneficial to the progress of the gasification reaction.     

A mechanistic study of agglomeration in fluidised beds at elevated pressures

Effect of operating pressure on the hydrodynamics of agglomerating gas–solid fluidised bed was investigated using a combination of discrete element method (DEM) for describing the movement of particles and computational fluid dynamic (CFD) for describing the flow of the gas phase. The inter‐particle cohesive force was calculated based on a time dependent model developed for solid bridging by the viscous flow. Motion of agglomerates was described by the multi‐sphere method. Fluidisation behaviour of an agglomerating bed was successfully simulated in terms of increasing the size of agglomerates. The results showed that increasing the operating pressure postpones de‐fluidisation of the bed. Since the DEM approach is a particle level simulation and study about particle–particle interactions is possible, a micro‐scale investigation in terms of cohesive force and repulsive force during agglomeration at elevated pressures was done. The micro‐scale results showed that although the number of contacts between particles was decreased by increasing operating pressure, stronger solid bridge formed between colliding particles at higher pressures. © 2012 Canadian Society for Chemical Engineering     

Effect of Operating Parameters on Gas‐Solid Hydrodynamics and Heat Transfer in a Spouted Bed

Through a combined computational fluid dynamics and discrete element method approach, the effect of the operating parameters on the hydrodynamics and heat‐transfer properties of gas‐solid two‐phase flows in a spouted bed are extensively investigated. Considering the high velocity in the fountain region, gas turbulence is resolved by employing the large‐eddy simulation. The rolling friction model is adopted for more precise predictions of solid behavior near the wall. Subsequently, the gas‐solid flow patterns, gas‐solid velocities, and temperature evolution are investigated. Moreover, different operating conditions and geometry configurations are evaluated with respect to heat‐transfer performance. The results provide a fundamental understanding of heat‐transfer mechanisms in spouted beds.     

竖直管气固鼓泡流化床传热机理的CPFD模拟

针对细颗粒气固鼓泡流化床中床料与竖直传热管壁面间的传热行为,在前期实验的基础上,采用计算颗粒流体力学(CPFD)方法从颗粒在传热壁面更新的角度,深入分析了传热特性与壁面气固流动行为之间的关联性。结果表明,模拟得到的传热管壁面颗粒更新通量和基于颗粒团更新模型的颗粒团平均停留时间均能很好解释实验测得的传热系数变化规律,这证实颗粒团更新是影响传热过程的控制性因素。模拟还发现随加热管从床层中心向边壁的移动,加热管周向方向上颗粒更新通量和传热系数的不均匀性都呈增大趋势。随着表观气速的增大,气泡行为导致床层颗粒内循环流率增大,这是导致颗粒团在加热管壁面上的更新频率增大以及床层与壁面间传热系数增大的根源。