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。     

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.     

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.     

Acceleration of CFD simulation of gas-solid flow by coupling macro-/meso-scale EMMS model

Gas-solid flow features significant dynamic multi-scale structure; multi-scale modeling is therefore in order. In this article, the macro-scale EMMS model was coupled with a two-fluid method (TFM) elaborated by the meso-scale EMMS model resolving sub-grid scale heterogeneity to simulate the hydrodynamics of circulating fluidized bed (CFB) risers. The overall flow distribution under the steady state was approximately predicted by the macro-scale EMMS model, which serves as the initial condition for meso-scale TFM simulations reproducing the dynamic behavior of heterogeneous gas-solid flows. Using the solid circulation flux as criterion, it was shown that this coupling approach can significantly reduce the time required to reach the statistically steady state, as compared to the packed bed or homogeneously dispersed initial condition. It also suggests a general approach to speedup dynamic simulation in the multi-scale paradigm of computation.     

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...     

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.     

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.     

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.     

Simulation of particles and gas flow behavior in a riser using a filtered two-fluid model

Flow behavior of gas and particles is predicted by a filtered two-fluid model by taking into the effect of particle clustering on the interphase momentum-transfer account. The filtered gas–solid two-fluid model is proposed on the basis of the kinetic theory of granular flow. The subgrid closures for the solid pressure and drag coefficient (Andrews et al., 2005) and the solid viscosity (Riber et al., 2009) are used in the filtered two-fluid model. The model predicts the heterogeneous particle flow structure, and the distributions of gas and particle velocities and turbulent intensities. Simulated solids concentration and mass fluxes are in agreement with experimental data. Predicted effective solid phase viscosity and pressure increase with the increase of model constant c_g and c_s. At the low concentration of particles, simulations indicate that the anisotropy is obvious in the riser. Simulations show the subgrid closures for viscosity of gas phase and solid phase led to a qualitative change in the simulation results.     

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.     

The impacts of standard wall function and drag model on the turbulent modelling of gas–particle flow in a circulating fluidised bed riser

A transient turbulence model was applied to simulate the gas–particle system in a circulating fluidised bed riser. The k–epsilon turbulent equations coupled with the fluctuating energy equation were used to simulate the gas–particle system in a riser. The simulation results were validated by the experimental data of a CFB system. A grid study was implemented to examine the impact of grid discretisation. A comparison between the conventional drag models and the EMMS model was also conducted. Other factors, like the restitution coefficient particle to particle, was also found to have a significant impact on the turbulence model. © 2013 Canadian Society for Chemical Engineering     

亚格子过滤双流体模型的网格依赖性

基于双流体方程和颗粒动力学理论的计算模型被广泛应用于流化床的气固两相流数值计算,高精度网格是其准确计算流动的必要条件。一些经典的微尺度阻力模型,其网格尺度决定其模拟结果的精度。亚格子过滤双流体模型是一种有效的适用于粗糙网格的计算模型,其包含的气固相间作用力和颗粒相应力本构方程是在高精度网格条件下,以微尺度双流体方程和颗粒动力学理论计算得到的气固流场为基础,对计算结果进行小尺度过滤后得出。使用亚格子过滤双流体模型替换基于颗粒动力学理论的双流体模型,针对同一物理问题,在不同网格尺度下进行了数值计算,结果表明此计算模型相比经典阻力模型具有较好的网格无关特性,并且和实验结果较为一致。同时也对颗粒动力学理论与之相结合进行了尝试,即仅使用亚格子过滤阻力模型,颗粒相应力仍然使用颗粒动力学模型,其计算结果的网格无关性及与实验值的吻合程度优于经典模型。     

Numerical predictions of flow behavior and cluster size of particles in riser with particle rotation model and cluster-based approach

Flow behavior of particles in a circulating fluidized bed (CFB) riser is numerically simulated using a two-fluid model incorporating with the kinetic theory for particle rotation and friction stress models. The particle rotations resulting from slightly friction particle-particle collisions was considered by introducing an effective coefficient of restitution based on the kinetic theory for granular flow derived by Jenkins and Zhang [2002. Kinetic theory for identical, frictional, nearly elastic spheres. Physics of Fluids 14, 1228-1235]. The normal friction stress model proposed by Johnson et al. [1990. Frictional-collisional equations of motion for particles flows and their application to chutes. Journal of Fluid Mechanics 210, 501-535] and a modified frictional shear viscosity model proposed by Syamlal et al. [1993. MFIX Documentation and Theory Guide, DOE/METC94/1004, NTIS/DE94000087] were used as the particle frictional stress model. The drag force between gas and particle phases was modified with cluster-based approach (CBA). The flow behavior of particles and the cluster size in a riser of Wei et al. [1998. Profiles of particle velocity and solids fraction in a high-density riser. Powder Technology 100, 183-189] and Issangya et al. [2000. Further measurements of flow dynamics in a high-density circulating fluidized bed riser. Powder Technology 111, 104-113] experiments are predicted. Effects of the rotation and friction stress models on the computed results are analyzed. It is concluded that particle rotations reduce the cluster size and alter the particle flows and distributions through more particle fluctuation energy dissipations. Effects of frictional stress on flow behavior and cluster size are not significant because the particle phase in the CFB riser is not dense enough to take into account for the particle-particle contact interactions.     

流态化模拟:基于介尺度结构的多尺度CFD

介尺度结构是研究气固流态化多尺度行为的关键。传统的基于平均化处理方式的双流体模拟不能准确描述流化床中的多尺度流动和传递行为。相较而言,基于能量最小多尺度(EMMS)方法的结构多流体模型(SFM)基于局部空间(网格)内的非均匀介尺度结构流动特征,其宏观预测结果与网格分辨率基本无关,因而可以大幅降低模拟计算量。基于SFM模拟得到的流动结构,EMMS多尺度传质模型进一步成功解释了传统传质文献中的数据差异。集成上述模型,形成了一整套模拟流化床流动-传递-反应耦合过程的多尺度计算流体力学(CFD)方法,并将其应用于预测循环流化床中典型的S型轴向分布、揭示噎塞转变的机理以及流化床放大困难的原因。多尺度CFD使工业规模循环床的三维、全系统、动态流动-反应耦合过程的准确模拟成为可能,并为实现从模拟向实时虚拟过程转变的目标打下基础。     

Experimental validation of the gas-solid flow in the CFB riser

In this paper, an experimental study is performed to investigate the flow structure in a circulating fluidized bed (CFB). The typical core-annulus structure and small amount of back-mixing of particles near the wall of the riser were observed. The axial solid concentration distributions contain a dilute region towards the up-middle zone and a dense region near the bottom and the top exit zones. Furthermore, the solid concentration decreases with the increase of the superficial gas velocity, and increases with the increment of the circulation rate at the same height position. The total pressure drop of the main bed represents a linear relationship with the solid flux rate. In the dense phase zone, the solid concentration increases linearly with the augmentation of the solid flux, however, the change of the solid concentration is slight, even unchangeable at the up zones. In addition, based on the Energy-Minimization Multi-Scale (EMMS) method, a revised drag force model is proposed, which is coupled in the Eulerian two-fluid model for simulating the flow structure in the riser. Numerical results are consistent with the experimental data, which indicate the revised drag force model is very successful in simulating flow structure of the dense gas-solid two-phase flow.     

Modeling of drag with the Eulerian approach and EMMS theory for heterogeneous dense gas-solid two-phase flow

Combined with the Eulerian approach, energy minimization multi-scale (EMMS) theory was used to develop a new theoretical model for the drag between the gas and solid phases in dense fluidized systems. The energy minimization was used in the solution procedure as an additional stability condition to close the conservation equations. The model was derived without introducing any empirical factors, so it can be used for more flow conditions in circulating fluidized beds (CFBs) than empirical models, especially for heterogeneous gas-solid two-phase flows that include cluster formation. Non-uniform particle distribution in computational cells, which is usually not described by the differential equations, is also considered in the new drag model. Both the drag values given by the model and simulation results for real systems agree well with experimental data. The results show that the model reasonably describes the interactions between the gas and particle phases in dense flows.     

Modeling of cluster structure-dependent drag with Eulerian approach for circulating fluidized beds

Flow behavior of gas and solids is simulated in combination the gas-solid two-fluid model with a cluster structure-dependent (CSD) drag coefficient model. The dispersed phase is modeled by a Eulerian approach based upon the kinetic theory of granular flow (KTGF) including models for describing the dispersed phase interactions with the continuous phase. The drag forces of gas-solid phases are predicted from the local structure parameters of the dense and dilute phases based on the minimization of the energy consumed by heterogeneous drag. The cluster structure-dependent (CSD) drag coefficients are incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. Simulation results indicate that the dynamic formation and dissolution of clusters can be captured with the cluster structure-dependent drag coefficient model. Simulated solid velocity and concentration of particles profiles are in reasonable agreement with experimental results.