基于EMMS模型的气固鼓泡床的模拟及气泡特性的分析

基于EMMS曳力模型,采用双流体的方法对气固鼓泡床内的气固流动特性进行模拟,建立基于图像处理气泡特性的分析方法,重点研究了不同表观气速下气泡在床层内分布特性,包括气泡平均当量直径、气泡速度和气泡球形度的轴向分布,以及气泡的生命周期。研究结果表明,小气泡多集中在床层底部和壁面区域,而大气泡多集中在床层中间区域。随着表观气速的增加,床层高度不断增加,气泡的球形度降低,气泡的大小、出现频率、上升速度以及生命周期均增加;然而,当表观气速增大到一定程度,继续增加气速对气泡的上升速度影响不大。     

A bubble-based EMMS model for gas–solid bubbling fluidization

An EMMS/bubbling model for gas–solid bubbling fluidized bed was proposed based on the energy-minimization multi-scale (EMMS) method (Li and Kwauk, 1994). In this new model, the meso-scale structure was characterized with bubbles in place of clusters of the original EMMS method. Accordingly, the bubbling fluidized bed was resolved into the suspending and the energy-dissipation sub-systems over three sub-phases, i.e., the emulsion phase, the bubble phase and their inter-phase in-between. A stability condition of minimization of the energy consumption for suspending particles (N_s→min) was proposed, to close the hydrodynamic equations on these sub-phases. This bubble-based EMMS model has been validated and found in agreement with experimental data available in literature. Further, the unsteady-state version of the model was used to calculate the drag coefficient for two-fluid model (TFM). It was found that TFM simulation with EMMS/bubbling drag coefficient allows using coarser grid than that with homogeneous drag coefficient, resulting in both good predictability and scalability.     

Numerical simulation and experimental validation of bubble behavior in 2D gas–solid fluidized beds with immersed horizontal tubes

The two-fluid model based on the kinetic theory of granular flow is considered to be a fundamental tool for modeling gas–solid fluidized beds and has been extensively used for the last couple of decades. However its verification and quantitative validation still remain insufficient for a wide range of reactor geometries and operating conditions. In this study simulations were performed using the two-fluid model for two-dimensional (2D) bubbling gas–solid fluidized beds with and without immersed horizontal tubes. The bubble characteristics – aspect ratio, shape factor, diameter and rise velocity – predicted by the simulation were compared and validated with experimental data obtained from pseudo-2D fluidized beds using digital image analysis technique. The predicted bubble shape and diameter were in good agreement with the experimental data for fluidized beds with and without immersed tubes. The simulation predicted higher bubble rise velocity compared to the experimental results obtained. This was due to the wall effect, which was not taken into consideration during the 2D simulation. In addition the influences of different drag laws, friction packing limits and solid-wall boundary conditions on the different bubble properties were investigated. The results showed that the choice of friction packing limits, drag laws and specularity coefficients have little influence on bubble properties.     

Scale effects in fluidized multiphase reactors

It is shown that the two-phase model for bubbling gas—solid fluidized beds can be extended to bubble column slurry reactors operating in the heterogeneous flow regime by proper definition of the ‘dilute’ and ‘dense’ phases. The ‘dilute’ phase in a bubble column slurry reactor is to be identified with the fast-rising ‘large’ bubbles. The ‘dense’ phase consists of the slurry phase in which ‘small’ bubbles are finely dispersed. With the aid of extensive experimental data obtained in columns of 0.1, 0.19 and 0.38 m diameter it is shown that the rise velocity of the ‘dilute’ phase for gas—solid fluid beds and slurry reactors show analogous scale dependencies and can be modelled in a similar manner. It is also demonstrated that fluidized multiphase reactors can be modelled in a common manner using Computational Fluid Dynamics (CFD) within the Eulerian framework. It is concluded that CFD is an invaluable tool for scaling up of fluidized multiphase reactors.     

TRANSITION OF FLOW REGIME IN FLUIDIZED BEDS WITH SLANTING BLADE BAFFLES

A flow model is proposed to investigate the transition of flow regime from bubbling to turbulent fluidization postulating that the flow in the emulsion phase follows the Richardson-Zaki equation.

Void fraction of the whole bed ε_f and the mean velocity of bubbles U_b were measured in fluidized beds of 0.3 and 0.5 m ID, in which slanting blade baffles were positioned. Mo-catalyst, silica gel, sand and glass beads with size between 135-443 μm were fluidized by air.

Void fraction of the emulsion phase ε _e was calculated on the basis of the above model. Correlating ε _e with superficial gas velocity U_ƒ, we found that ε _e was very close to ε _mƒ in the bubbling regime and that e, increased with increasing U_ƒ in the turbulent regime.

Calculated values of the volume fraction of bubble phase δ were correlated with U_ƒ, from which apparent transition point from bubbling to turbulent regime was estimated. Combining information obtained, transition of flow regime in the above type of fluidized beds is discussed     

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。     

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。     

Bubble Splitting in a Pseudo‐2D Gas‐Solid Fluidized Bed for Geldart B‐Type Particles

Bubble splitting in 2D gas‐solid freely bubbling fluidized beds is experimentally investigated using digital image analysis. The quantitative results can be applied for the development of a new breakage model for bubbly fluidized beds, especially discrete bubble models. The variation of splitting frequency with bubble diameter, new resulting bubble volumes, positions, and also the assumptions of mass and momentum conservation for bubbles after breakage are studied in detail. Small bubbles are found to be more stable than large ones and nearly all mother bubbles split into two almost equally sized daughter bubbles. The momentum of gas bubbles in the vertical direction remains approximately constant after breakage, whereas that of bubbles in the horizontal direction changes with no clear trend. The effect of fluidizing gas velocity in breakage frequency is also examined.     

Extending the EMMS/bubbling model to fluidization of binary particle mixture: Formulation and steady-state validation

The EMMS/bubbling model originally proposed for fluidization of monodisperse particles is extended to fluidization of binary particle mixture in this study. The dense and dilute phases are considered to comprise of two types of particles differing in size and/or density. Governing equations and the stability condition are then formulated and solved by using an optimization numerical scheme. The effects of bubble diameter are first investigated and a suitable bubble diameter correlation is chosen. Preliminary validation for steady state behavior shows the extended model can fairly capture the overall hydrodynamic behaviors in terms of volume fraction of bubbles and average bed voidage for both monodisperse and binary particle systems. This encourages us to integrate this model with CFD for more validations in the future.     

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.     

气固流化系统多尺度跨流域EMMS建模

气固流化床反应器是典型的具有多尺度非均匀动态结构的复杂系统。实现对该类反应器定量描述和定向调控的关键是深入了解系统内介尺度结构的形成和演化特征。能量最小多尺度（EMMS）方法为气固非均匀系统的量化表征提供了一种通用的建模思路。首先回顾了EMMS理论在构建曳力本构关系方面的应用,重点介绍了本课题组在EMMS曳力模型普适化方面所做的部分工作;随后对介尺度结构时空动态演化行为的群平衡建模方法进行了论述,并给出了群平衡和结构曳力模型相耦合的连续介质模拟框架;最后讨论了EMMS原理在预测反应器宏尺度动力学方面的应用,包括模型在不同流域的拓展、操作相图的绘制以及循环流化床的全回路稳态建模方法等。     

Novel phenomenological discrete bubble model of freely bubbling dense gas–solid fluidized beds: Application to two‐dimensional beds

A phenomenological discrete bubble model has been developed for freely bubbling dense gas–solid fluidized beds and validated for a pseudo‐two‐dimensional fluidized bed. In this model, bubbles are treated as distinct elements and their trajectories are tracked by integrating Newton's equation of motion. The effect of bubble–bubble interactions was taken into account via a modification of the bubble velocity. The emulsion phase velocity was obtained as a superposition of the motion induced by individual bubbles, taking into account bubble–bubble interaction. This novel model predicts the bubble size evolution and the pattern of emulsion phase circulation satisfactorily. Moreover, the effects of the superficial gas velocity, bubble–bubble interactions, initial bubble diameter, and the bed aspect ratio have been carefully investigated. The simulation results indicate that bubble–bubble interactions have profound influence on both the bubble and emulsion phase characteristics. Furthermore, this novel model may become a valuable tool in the design and optimization of fluidized‐bed reactors. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

A critical comparison of frictional stress models applied to the simulation of bubbling fluidized beds

The behaviour of a gas-solid flow in a bubbling fluidized bed operated near the minimum fluidization condition is strongly influenced by the frictional stresses between the particles, these being highly concentrated and their motion dominated by enduring contact among them and with the walls.The effect of the introduction of frictional stresses in a Eulerian-Eulerian two fluid model based on the kinetic theory of the granular flow is evaluated. The models of Johnson and Jackson [1987. Frictional-collisional constitutive relations for granular materials, with application to plane shearing. Journal of Fluid Mechanics 176, 67-93], Syamlal et al. [1993. Mfix documentation: volume I, theory guide. Technical Report DOE/METC-9411004, NTIS/DE9400087, National Technical Information Service, Springfield, VA], and Srivastava and Sundaresan [2003. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129, 72-85] are compared with the kinetic theory of the granular flow and with experimental data both in a bubbling fluidized bed with a central jet and in a bubbling fluidized bed with a porous distributor. The predicted evolution of the bubble diameter along the height of the fluidized beds is examined, the shapes of the bubbles predicted by the models are compared and the evolution in time of the bubbles is shown. In the case of the bed with a central jet, the bubble detachment time is also calculated. The results show that the introduction of a frictional stress model improves the prediction of the bubbles diameter in a bubbling fluidized bed with a central jet and positively affects the bubbles diameter distribution in a uniformly fed bubbling fluidized bed. The high sensitivity of the model to the value of the particulate phase fraction at which frictional stresses start to be accounted for is pointed out through a sensitivity analysis performed on the Srivastava and Sundaresan [2003. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129, 72-85] model.     

Euler multiphase-CFD simulation on a bubble-driven gas–liquid–solid fluidized bed

An integrated flow model was developed to simulate the fluidization hydrodynamics in a new bubble-driven gas–liquid–solid fluidized bed using the computational fluid dynamic (CFD) method. The results showed that axial solids holdup is affected by grid size, bubble diameter, and the interphase drag models used in the simulation. Good agreements with experimental data could be obtained by adopting the following parameters: 5 mm grid, 1.2 mm bubble diameter, the Tomiyama gas–liquid model, the Schiller–Naumann liquid–solid model, and the Gidaspow gas–solid model. At full fluidization state, an internal circulation of particles flowing upward near the wall and downward in the centre is observed, which is in the opposite direction compared with the traditional core-annular flow structure in a gas–solid fluidized bed. The simulated results are very sensitive to bubble diameters. Using smaller bubble diameters would lead to excessive liquid bed expansions and more solid accumulated at the bottom due to a bigger gas–liquid drag force, while bigger bubble diameters would result in a higher solid bed height caused by a smaller gas–solid drag force. Considering the actual bubble distribution, population balance model (PBM) is employed to characterize the coalescence and break up of bubbles. The calculated bubble diameters grow up from 2–4 mm at the bottom to 5–10 mm at the upper section of the bed, which are comparable to those observed in experiments. The simulation results could provide valuable information for the design and optimization of this new type of fluidized system.     

EMMS-based Eulerian simulation on the hydrodynamics of a bubbling fluidized bed with FCC particles

Although great progress has been made in modeling the bubbling fluidization of Geldart B and D particles using standard Eulerian approach, recent studies have shown that suitable sub-grid scale models should be introduced to improve the simulation on the hydrodynamics of Geldart A particles. In this study, the flow structures inside a bubbling fluidized bed of FCC particles are simulated in an Eulerian approach employing the energy minimization multi-scale (EMMS) model (Chemical Engineering Science, 2008, 63: 1553-1571) as the sub-grid scale model for effective inter-phase drag force, using an implicit cluster diameter expression. It was shown that the experimentally found axial and radial solid concentration profiles and radial particle velocity profiles can be well reproduced.     

Coarse grid simulation of bed expansion characteristics of industrial-scale gas–solid bubbling fluidized beds

Two-fluid modeling of the hydrodynamics of industrial-scale gas-fluidized beds proves a long-standing challenge for both engineers and scientists. In this study, we suggest a simple method to modify currently available drag correlations to allow for the effect of unresolved sub-grid scale structures, by assuming that the particles inside each computational cell are presented in the form of a two-phase structure. This method would thus make it possible to simulate the hydrodynamics of industrial-scale bubbling fluidized beds of Geldart B and D particles with a coarse computational mesh. It is shown that with the proposed modification of the drag force correlation, the experimentally measured bed expansion characteristics of industrial-scale bubbling fluidized beds can be reasonably predicted at acceptable computational cost. Also the simulation result for the macroscopic solid circulation pattern is in qualitative agreement with the 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     

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