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.     

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。     

Numerical investigation for the suitable choice of bubble diameter correlation for EMMS/bubbling drag model

Mesoscale bubbles exist inherently in bubbling fluidized beds and hence should be considered in the constitutive modeling of the drag force. The energy minimization multiscale bubbling(EMMS/bubbling) drag model takes the effects of mesoscale structures(i.e., bubbles) into the modeling of drag coefficient and thus improves the coarse-grid simulation of bubbling and turbulent fluidized beds. However, its dependence on the bubble diameter correlation has not been thoroughly investigated. The hydrod...     

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.     

Sensitivity Study on Modeling an Internal Airlift Loop Reactor Using a Steady 2D Two‐Fluid Model

The sensitivity study of bubbly flow in an internal airlift loop reactor is presented using a steady Reynolds averaging two‐fluid model. Comparative evaluation of different drag formulations, drag coefficient correlations, turbulence effect on the drag coefficient, outlet slip velocity, and bubble size is performed and the respective influence to the simulation results is highlighted. It is found that a complicated drag formulation may not result in reliable predictions. All the drag coefficient correlations underpredict the gas holdup if the influence of turbulence on the drag coefficient is not well incorporated. Fortunately, the global hydrodynamics is not sensitive to the outflow slip velocity for a wide range, so a steady two‐fluid model can be used to simulate the bubbly flow when the flow field is fully developed. The correct estimation of bubble size with properly selected correlations play an important role in successful simulation of gas‐liquid bubbly flow in airlift loop reactors.     

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.     

An advanced EMMS scheme for the prediction of drag coefficient under a 1.2 MWth CFBC isothermal flow—Part II: Numerical implementation

The arithmetic results from the formulation of an EMMS analysis for the calculation of drag coefficient between the co-existing phases in a CFB riser were implemented in a CFD code and three dimensional simulations of the isothermal flow of a 1.2 MW_th CFBC unit were performed. Gas and inert material were modeled in an Eulerian fashion. Except from EMMS scheme, Gidaspow's correlation was also tested for reasons of comparison. Gidaspow's drag model is based on the assumption of homogeneous conditions inside a control volume, whilst the EMMS analysis encounters the effect of spatiotemporal multi-scale gas–particle structures on the induced drag force. Moreover, regarding the grid density, smaller control volumes enhance the validity of the homogeneous assumption. Thus, the effect of the grid density on the numerical results was also examined, using two uniform computational grids, consisting of hexahedral computational cells. Numerical results were compared with available experimental data, as far as the pressure drop along the bed is concerned. A good agreement with the experimental data was achieved in the case of the dense grid (43 mm/cell) using both approaches. In the case of the coarse grid (86 mm/cell), Gidaspow's correlation clearly under-predicted the experimentally measured pressure drop along the bed. This under-prediction was more significant in the lower part of the bed. On the other hand, the implementation of the EMMS scheme increased the accuracy of the model, mainly in the bottom region, since particles clustering was taken into account, a phenomenon which is more evident in latter region. In this area the drag force calculated via EMMS method is considerably less than the drag force calculated by Gidaspow's correlation. Overall, it is proven that the EMMS model is a very promising numerical tool for the more accurate drag force calculation since it reproduces numerically the effect of clustering mechanism on the time evolution of this complicated phenomenon, increasing the accuracy of the predictions without the need of denser numerical grids.     

垂直并流向上气固两相流中流动结构的分析及曳力系数的计算

This study investigates the heterogeneous structure and its influence on drag coefficient for concurrent up gas-solid flow.The energy-minimization multi-scale (EMMS) model is modified to simulate the variation of structure parameters with solids concentration,showing the tendency for particles to aggregated to form clusters and for fluid to pass around clusters.The global drag coefficient is resolved into that for the dense phase,for the dilutephase and for the so-called inter-phase,all of which can be obtained from their respective phase-specific structure parameters.The computational results show that the drag coefficients of the different phases are quite different,and the global drag coefficient calculated from the EMMS approach is much lower than that from the correlation of Wen and Yu.The simulation results demonstrate that the EMMS approach can well describe the heterogeneous flow structure,and is very promising for incorporation into the two-fluid model or the discrete particle model as the closure law for drag coefficient.     

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.     

Searching for a mesh-independent sub-grid model for CFD simulation of gas-solid riser flows

This work aims to examine the effects of grid size in applying the two-fluid model (TFM), and thereby attempts to search for a mesh-independent sub-grid model for simulating gas-solid riser flows. To this end, we performed a series of TFM simulations over a periodic domain with various grid resolutions and drag closures. Of these drag models, EMMS/matrix model in its simplified version was chosen to be the focus of discussion. It was found that TFM simulation with a homogeneous drag model reaches its numerically asymptotic solution when the grid scale is as small as 10 times the particle diameter, but it still fails to capture the characteristic S-shaped axial voidage profile and highly over-predicts the solids flux. By comparison, EMMS/matrix model seems to reach a mesh-independent solution of the effect of sub-grid structures on the drag force, and predict successfully the axial voidage profile and the solids flux with even coarse grid. Therefore, the fine-grid TFM simulation is inadequate for gas-solid riser flows. We need sub-grid modeling of the heterogeneous structure.     

Full‐Loop Simulation of Gas‐Solids Flow in a Pilot‐Scale Circulating Fluidized Bed

In order to study the system hydrodynamics in a circulating fluidized bed (CFB), a 3D full‐loop simulation was conducted for a pilot‐scale CFB. The Eulerian‐Eulerian two‐fluid model with the kinetic theory of granular theory helped to simulate the gas‐solids flow in the CFB. The system hydrodynamics including pressure balance, vectors of gas and solids, distribution of solids holdup, and instantaneous circulating rates were obtained to get a comprehensive understanding of the system. It was predicted that the main driving force was the pressure drop of the storage tank. The storage height and valve opening were critical operating factors to control the riser operation. The effects of operating conditions including solids circulating rates and superficial gas velocity on the hydrodynamics were investigated to provide guidance for the stable operation of the CFB system.     

基于MP-PIC方法改进EMMS/DP曳力模型

改进了面向离散粒子法的能量最小多尺度曳力模型(EMMS/DP)的颗粒参数生成方式,并将非均匀因子(HD)与固相浓度和滑移速度关联以考虑介尺度结构动态效应的影响,用改进的EMMS/DP模型与多相流质点网格模型(MP-PIC)耦合模拟气固两相流提升管系统,模拟结果与实验值吻合很好,考察了MP-PIC方法的网格无关性和粗粒化模型参数.     

CFD Simulation of Mixing and Segregation of Binary Solid Mixtures in a Dense Fluidized Bed

The mixing and segregation behaviour of binary solid mixtures has been extensively studied through various experiments, while accurate CFD simulations are difficult to achieve due to process complexity and a lack of reliable constitutive relations. In this study, CFD simulations of a dense fluidized bed with glass and polystyrene particles were performed in order to identify a universal set of simulation parameters and models for simulating binary mixtures with different mixed and segregation behaviour. Through a comparison to experimental data, it was found that the EMMS drag model coupled with the Ma-Ahmadi solid pressure and radial distribution models predicted more a reasonable axial distribution of solid phases than the Syamlal O'Brien drag model coupled with the Lun et al. solid pressure and radial distribution models. The increase in the solid-solid drag further improved the simulation results.     

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     

Comparative analysis of subgrid drag modifications for dense gas‐particle flows in bubbling fluidized beds

Many subgrid drag modifications have been put forth to account for the effect of small unresolved scales on the resolved mesoscales in dense gas‐particle flows. These subgrid drag modifications significantly differ in terms of their dependencies on the void fraction and the particle slip velocity. We, therefore, compare the hydrodynamics of a three‐dimensional bubbling fluidized bed computed on a coarse grid using the drag correlations of the groups of (i) EMMS, (ii) Kuipers, (iii) Sundaresan, (iv) Simonin, and the homogenous drag law of (v) Wen and Yu with fine grid simulations for two different superficial gas velocities. Furthermore, we present an (vi) alternative approach, which distinguishes between resolved and unresolved particle clusters revealing a grid and slip velocity dependent heterogeneity index. Numerical results are analyzed with respect to the time‐averaged solids volume fraction and its standard deviation, gas and solid flow patterns, bubble size, number density, and rise velocities. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4077–4099, 2013     

Eulerian simulation of gas–solid flows with particles of Geldart groups A, B and D using EMMS-based meso-scale model

In gas–solid riser flows, meso-scale structures affect the overall performance significantly. The two-fluid model (TFM) with structure-dependent EMMS (energy-minimization multi-scale) drag coefficient has proved to allow grid-independent solutions of the effect of meso-scale structures, and succeeded in predicting riser flows with the Geldart A particles (Lu et al., 2009, Chem. Eng. Sci., 64: 3427–3447). In this paper, to investigate the effects of particle properties on these meso-scale structures, for all particle types, two-fluid modeling with and without consideration of meso-scale structures were performed and compared. Generally, the modeling with EMMS drag coefficient shows better results than without considering meso-scale structures, but their discrepancy decays with the Archimedes number.     

Toward a mesoscale‐structure‐based kinetic theory for heterogeneous gas‐solid flow: Particle velocity distribution function

Mesoscience has recently been proposed as a possible general concept for describing complex systems far from equilibrium, however, concrete formulations are needed, and particularly, a statistical mechanics foundation of mesoscience remains to be explored. To this end, the mathematical theory of stochastic geometry is combined with the energy minimization multi‐scale (EMMS) principle under the concept of mesoscience to propose a statistical mechanics framework. An EMMS‐based particle velocity distribution function is then derived as an example to show how the proposed framework works, and more importantly, as a first key step toward a generalized kinetic theory for heterogeneous gas‐solid flow. It was shown that the resultant EMMS‐based distribution is bimodal, instead of the widely‐used Maxwellian distribution, but it reduces to the Maxwellian distribution when the gas‐solid system is homogeneous. The EMMS‐based distribution is finally validated by comparing its prediction of the variance of solid concentration fluctuation and granular temperature with experimental data available in literature. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2649–2657, 2016     

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。