Modifying the inter‐phase drag via solid volume fraction gradient for CFD simulation of fast fluidized beds

The conventional drag model in two‐fluid simulation, which assumes uniform particle distribution in a computational grid, overestimates the drag force, thus failed in capturing the subgrid‐scale strands and resolvable‐scale clusters. This work proposed a new modification to the conventional drag model through considering the heterogeneous distribution of solid volume fraction (SVF), especially, in the inter‐phase boundary (i.e., cluster boundary). The resulting drag model is a function of particle Reynolds number, SVF and the gradient of SVF. This straightforward modification is consistent with the elaborately filtered‐approach‐based modification method in nature. A CFD simulation for a two‐dimensional riser was conducted to validate the new drag model. The outlet solid mass flux, axial and radial time‐averaged voidages from the new drag model agreed well with the experimental measurements, and these results were far better than those from the conventional homogeneous drag models. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2588–2598, 2017     

液固散式流态化CFD模拟中曳力模型的影响

基于无黏性双流体简化模型在商业化软件平台上,通过增加用户自定义子程序考察了Gidaspow、Syamlal-O’Brien、Di Felice、Gibilaro、Dallavalle和BVK曳力模型对液固散式流态化CFD模拟结果的影响行为,探讨了相应的影响机制。经与文献中不同颗粒Reynolds数的代表性实验数据对比后发现：BVK和Dallavalle曳力模型对床层膨胀高度和整体固含率的预测精度较高;BVK、Syamlal-O’Brien以及Dallavalle曳力模型给出的床内固含率径向分布较为准确;BVK曳力模型较为准确地再现了颗粒轴向速度的径向分布特征。BVK曳力模型的影响机制与液固散式流态化中颗粒动力学特性相符合,在所考察范围内其预测性能最优;Dallavalle曳力模型在其余5个传统模型中预测性能较优且形式简洁在程序中易于实现。     

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     

Drag models coupled with CFD–PBM method for simulation in bubble columns

In this study, three-dimensional numerical simulation of gas–liquid flow in bubble columns was realized by using the computation fluid dynamics (CFD)–population balance model (PBM). The new drag model improves the stability-constrained multi-fluid (SCMF-C) model because of the consideration of the wake accelerating and the hindering effects for calculating the drag correction factor. The gas holdup, axial liquid velocity, and bubble size distribution (BSD) predicted by four drag models at 0.02 and 0.1 m/s were compared. The results revealed that the proposed drag model can provide excellent predictions for both bubbly and heterogeneous flows. Because the wake accelerating and the hindering effects were considered, reliable predictions were achieved for the gas holdup, and the problem of uniform gas holdup distribution was mitigated. Therefore, the SCMF-C model can be extended for nonuniform BSD. The gas holdup and liquid velocity increased, and the nonuniformity of radial results became pronounced at 0.1 m/s. The profiles of four drag models were similar at a low height, whereas the difference between the simulations of the four models became obvious with the variation of heights. The results of the four models were accurate, and the BSD was wide at 0.1 m/s. Subsequently, the feasibility of the four drag models was evaluated at 0.2 and 0.4 m/s. The results of the comparison revealed that the proposed drag model exhibited excellent feasibility at higher gas velocities and was powerful for the simulation of bubble columns.     

Fluid Dynamic Behavior in a Spouted Bed with Binary Mixtures Differing in Size

In this work, the response surface methodology has been used to quantify the effect of the mixture composition and static bed height on the minimum spouting condition, as well as on the segregation phenomena, for a spouted bed operating with binary mixtures, differing in size. In order to analyze the segregation phenomena, some computational fluid dynamic (CFD) simulations were performed. The CFD simulations, based on a Eulerian granular multiphase model, showed good agreement with experimental characteristic curves of a spouted bed operating with different mixtures compositions. Moreover, the simulated radial and axial profiles of fraction of the largest particles showed a coherent behavior, when compared with literature results.     

Numerical Simulation of Particle Segregation in Bubbling Gas‐Fluidized Beds

A multi‐fluid Eulerian model incorporating the kinetic theory of granular flow is used for the simulation of bubbling fluidized beds containing a binary mixture of Geldart B particles at low gas velocities. The cases of density, size and combined density/size segregation are investigated using computational fluid dynamic simulations. Various expressions for the drag force are evaluated for predicting different segregations. The simulation results show that summation of the particle‐particle drag force, i.e., the “hindrance effect” term, and the Stokes drag of particles, which is modified based on the Wen‐Yu drag model can be used for accurate simulation of a binary mixture of particles differing in size, density, or both. Bed expansion and dimensionless axial segregation profiles of CFD results are compared with the experimental data and good agreement is found.     

Simulation of gas–solid flows in riser using energy minimization multiscale model: Effect of cluster diameter correlation

Reduced effective drag is observed in gas–solid riser flows due to formation of clusters. Thus cluster diameter correlation has direct impact on the calculated drag and the hydrodynamics predictions. However, its effect has not been studied. Therefore in this study, the effect of cluster diameter correlations on the drag coefficient and simulation predictions is evaluated. A structure-based drag is derived using the EMMS model, and is used to carry out computational fluid dynamics (CFD) simulations for low solid flux fluid catalytic cracking (FCC) risers. The results are compared with those using the Gidaspow drag model, as well as experimental data and previous simulation results. The time-averaged axial and radial profiles of voidages are compared with the experimental data. The comparison shows that only EMMS model is able to capture the axial heterogeneity with the dense bottom and dilute top sections. The radial profiles using both drag models shows only qualitative agreement with the experimental data. The results using the EMMS and Gidaspow drag model show a reasonable agreement near the wall and the centre, respectively. In order to improve the quality of the results obtained by the EMMS model, simulations are conducted using calculated drag coefficients from different cluster diameter correlations. The cluster diameter correlation proposed by Harris et al. (2002) gives reasonable qualitative and quantitative agreement with the experimental data for axial voidage profile, particularly in the dense bottom section; however, the quantitative disagreements in the radial profiles persists.     

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.     

3‐D full‐loop simulation of an industrial‐scale circulating fluidized‐bed boiler

Three‐dimensional (3‐D) simulations using an Eulerian multiphase model were employed to explore flow behaviors in a full‐loop industrial‐scale CFB boiler with and without fluidized‐bed heat exchanger (FBHE), where three solids phases were employed to roughly represent the polydisperse behavior of particles. First, a simulation of the boiler without FBHE is implemented to evaluate drag models, in terms of pressure profiles, mixing behaviors, radial velocity profiles, etc. Compared to the conventional model, the simulation using the energy‐minimization multiscale (EMMS) model successfully predicts the pressure profile of the furnace. Then, such method is used to simulate the boiler with FBHE. The simulation shows that solid inventory in the furnace is underpredicted and reduced with an increase of the valve opening, probably due to the underevaluated drag for FBHE flows. It is suggested to improve EMMS model which is now based on a single set of operating parameters to match with the full‐loop system. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1108–1117, 2013     

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。     

Comparison and evaluation of interphase momentum exchange models for simulation of the solids volume fraction in tapered fluidised beds

An Eulerian computational fluid dynamics (CFD) model with granular flow extension was used to simulate a gas–solid fluidised bed in a tapered reactor. Various drag coefficient models were evaluated, which are used to calculate the drag force, describing the momentum transfer between the gas and solid phases. Comparison and evaluation between time-averaged solids volume fractions obtained from experiments and from simulations with several drag coefficient models were made. The predicted results obtained by the different drag models were verified using experimental data of Depypere et al. (2009). Initial results using a 2-phase Eulerian model showed poor agreement with experimental results. However, extending the Eulerian model to include 3 solid phases—with different mean particle diameter per phase in order to account for the particle size distribution of the fluidised solid material—yielded good agreement with experimental results. Furthermore, quantitative analyses showed that the modified Gidaspow drag model gave the best agreement between CFD simulations and experimental data.     

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     

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。     

基于EMMS模型的搅拌釜内气液两相流数值模拟

采用欧拉-欧拉模型对搅拌釜内气液两相流进行了三维CFD模拟,重点研究了采用不同曳力模型时CFD模拟对搅拌桨附近排出流区两相流动的预测能力。模拟结果表明CFD能准确地预测排出流区的液相速度分布,但采用传统的Schiller-Naumann曳力一定程度上低估了排出流区的气液相间曳力,导致在完全扩散区CFD预测的分布器和桨叶下方区域气含率偏小,而基于气液非均匀结构和能量最小多尺度（EMMS）方法得到的DBS-Global曳力模型能更准确地描述完全扩散区气液搅拌釜内流动情况。与传统曳力模型相比,采用DBS-Global曳力模型能显著提高对气含率的预测。     

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     

浆态床内固含率轴向分布的数值模拟

采用DBS曳力模型计算气液相间作用,分别采用Gidaspow曳力模型、经Brucato修正的Gidaspow曳力模型和Schiller?Naumann曳力模型计算液固相间作用,忽略气固间的直接作用,对比了浆态床内不同颗粒粒径体系轴向固含率的模拟和实验结果. 结果表明,不同液固相间曳力模型对气含率的预测影响不大;在颗粒粒径较大(140 ?m)的体系中,较低表观气速下气液DBS与液固Schiller?Naumann曳力模型组合模拟的固含率随床高度增加而减小,与实验结果吻合,而其它曳力模型组合的模拟结果较差,轴向分布较均匀;在颗粒粒径较小(35 ?m)的体系中,几种曳力模型组合的模拟结果均与实验结果吻合较好,轴向分布较均匀.     

Experimental and numerical investigation of sands and Geldart A biomass co-fluidization

This article investigated the fluidization of sands and small Geldart A biomass mixtures. The mixture fluidized like Geldart A type particles with a uniform bed expansion regime before bubbling. The video recorded color distance between pure sands and sands–biomass mixtures was used to estimate the sands–biomass mixing. The coarse-grained computational fluid dynamics–discrete element method with a hybrid drag model which couples the Syamlal–O'Brien drag and a filtered drag can capture the mixing while the simulation with Gidaspow drag predicted a segregated bed. The simulations were further validated with experimental measured pressure drops. The time averaged pressure drop equals the weight of the bed material, however, its fluctuation is about three times of the bed material fluctuation.     

Coarse grained computational fluid dynamic simulation of sands and biomass fluidization with a hybrid drag

The bubbling fluidized bed reactor is widely used in fast pyrolysis of biomass. Discrete simulation of this reactor is challenging due to many sand particles and lack of accurate drag corrections accounting for the interaction of two different solid particles with different properties. In this research, the computational cost is reduced by using the coarse-grained computational fluid dynamic-discrete element method, where many sand particles are lumped into a larger numerical parcel. The Syamlal–O'Brien drag model is used for sand, while Ganser correction coupled with Gidaspow model is used for the nonspherical biomass particles. This hybrid approach shows superior behavior over other drag models using pressure drops as a benchmark. The predicted bed height and pressure fluctuating frequencies compare well with experiment. The mixing of biomass is close to perfect if the superficial velocity is larger than four times the minimum fluidization velocity.     

侧进式搅拌釜内气液两相流的数值模拟

采用计算流体力学(CFD)技术对φ1.5 m×1.2 m侧进式气液搅拌釜内气液两相流场进行数值模拟,检验了3种气液分界面边界条件和两种相间曳力模型。通过UDF程序将上述模型分别与欧拉双流体模型和 dispersed k-ε 两相湍流模型进行耦合计算,得到搅拌功率准数、总体气含率和气相分布,并与冷模实验结果进行对比,得到能准确预测的CFD模型。研究结果表明,3种气液界面边界条件下采用标准S-N模型计算所得的功率准数和气体分布误差均较大,而Brucato-Tsuchiya模型的预测结果更接近实验结果;气液界面边界条件对总体气含率的预测影响较大,采用速度进口或脱气边界和Brucato-Tsuchiya模型耦合计算所得的结果误差比压力出口边界明显要小。     

Simulation of the layer inversion phenomenon in binary liquid--fluidized beds by DEM–CFD with a drag law for polydisperse systems

Liquid-fluidized beds of particular binary mixtures exhibit the layer inversion phenomenon, a peculiar result of the mechanical equilibrium developing in such multiphase systems. Because of the crucial role of the hydrodynamic interaction, these are ideal test cases for assessing fluid-particle models in multi-particle CFD simulations. In the present work the layer inversion phenomenon is reproduced via Discrete Element Method (DEM) simulations, in which the drag force model for polydisperse systems described in Cello et al. (2010) is used. The simulations serve primarily to assess the suitability of the DEM–CFD approach and particularly the validity of the above drag model, although the results available may also prove very useful to investigate the prevailing mechanisms. To analyze a sufficiently broad variety of cases, involving different solid species, size ratios and operating conditions, three systems selected amongst the published literature are considered. The comparison of simulation and experimental observation is carried out in terms of overall bed and mixed layer interface heights, voidage and component distributions along bed height and time evolution of the species centers of mass. Simulations with liquid velocities below, above and at the critical inversion conditions are carried out. Additionally, simulations using a drag force model traditionally used for monodisperse beds are reported for comparison. The results not only demonstrate the importance of correctly accounting for the local size distribution in the bed, but also prove the validity of the overall computational approach. The predictions of the simulations are in good to excellent agreement with experiments, depending on the system considered, both in terms of critical velocity and, most notably, expansion of the individual components in the bed. The analysis of the hydrodynamics in the bed allows to investigate the local particle flow field, highlighting the presence of a steady irregular motion of the solids in apparently chaotic vortices continuously forming and disappearing, which is thought to be the mechanism responsible for mixing. The fluid–particle interaction forces exhibit a constant profile along bed height, even in the presence of a strongly non-uniform concentration profile.