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...     

Kinetic theory based computation of PSRI riser: Part I—Estimate of mass transfer coefficient

The PSRI benchmark challenge problem one is modeled using kinetic theory based CFD with the energy minimization multi-scale (EMMS) drag law. These computations give a better comparison than the previous models to measured solids mass flux, solids density and pressure drop.The computer model was also used to calculate axial and radial normal Reynolds stresses, energy spectra, power spectra, granular temperatures, the FCC viscosity and axial and radial dispersion coefficients. The computed cluster sizes agreed with the published empirical correlations. Then, the mass transfer coefficients and the Sherwood numbers are estimated based on particle cluster sizes. The conventional Sherwood number is scaled with the particle cluster diameter. The Sherwood number is the order of 10^-2 and the mass transfer coefficient is the order of . This Sherwood number is two orders of magnitude smaller than the diffusion controlled limit of two based on particle diameter, in agreement with the experimental data for fluidization of fine particles.     

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.     

Profiling solid volume fraction in a conical bed of dry micrometric particles: Measurements and numerical implementations

In order to develop predictive process models in conical fluidized beds, there is an ongoing search for experimental methods and simulation tools to measure and model hydrodynamics parameters. Accordingly, experiments carried out in a conical fluidized bed containing micrometric TiO₂ particles with a wide particle size distribution. An optical fiber technique was employed to determine the effect of particles loading on the solid volume fraction. The axial and radial profiles of solid volume fraction have then been determined to evaluate the sensitivity of different models, including Syamlal-O?Brien (1988), Arastoopour et al., (1990) and Gidaspow (1994) drag models. The Eulerian-Eulerian model with frictional stress models and three different boundary conditions (BCs), consisting of no-slip, partial-slip and free-slip have been used in the numerical simulations. The Gidaspow model with the partial-slip BC gives the best agreement with experimental data for different particle loadings.     

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.     

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.     

Computational fluid dynamics (CFD) modeling of spouted bed: Assessment of drag coefficient correlations

In the computational fluid dynamics (CFD) modeling of gas-solids two-phase flows, drag force is the only accelerating force acting on particles and thus plays an important role in coupling two phases. To understand the influence of drag models on the CFD modeling of spouted beds, several widely used drag models available in literature were reviewed and the resulting hydrodynamics by incorporating some of them into the CFD simulations of spouted beds were compared. The results obtained by the different drag models were verified using experimental data of He et al. [He, Y.L., Lim, C.J., Grace, J.R., Zhu, J.X., Qin, S.Z., 1994a. Measurements of voidage profiles in spouted beds. Canadian Journal of Chemical Engineering 72 (4), 229-234; He, Y.L., Qin, S.Z., Lim, C.J., Grace, J.R., 1994b. Particle velocity profiles and solid flow patterns in spouted beds. Canadian Journal of Chemical Engineering 72 (8), 561-568.] The quantitative analyses showed that the different drag models led to significant differences in dense phase simulations. Among the different drag models discussed, the Gidaspow (1994. Multiphase Flow and Fluidization, Academic Press, San Diego.) model gave the best agreement with experimental observation both qualitatively and quantitatively. The present investigation showed that drag models had critical and subtle impacts on the CFD predictions of dense gas-solids two-phase systems such as encountered in spouted beds.     

Effect of slip boundary conditions on the simulation of microparticle velocity fields in a conical fluidized bed

The hydrodynamic performance of micrometric TiO₂ particles has been experimentally studied in a conical fluidized bed and the results compared with numerical simulations. Local solid velocities in the bed have been measured by means of an optical fiber technique under different operating conditions of particle loading and air velocity. The radial profiles of axial solid velocities have been simulated to assess the sensitivity of grid size, and different drag models, namely, those by Syamlal and O'Brien, Ahmadi and Ma, Arastoopour et al., and Gidaspow, for no‐slip, partial‐slip, and free‐slip boundary conditions (BCs). The different drag models record almost similar results, but those provided by the Gidaspow and Ahmadi–Ma models, together with free‐slip BCs, are in somewhat better agreement with the experimental data for conical fluidized beds with smooth walls. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4502–4518, 2013     

bubble-based EMMS/PFB模型的建立及在加压流化床浓相段的应用

基于多尺度分解和能量消耗分析方法,结合压力下锥形分布板射流床气泡直径关联式,建立了一个适于加压流化床（PFB）的能量最小多尺度模型--bubble-based EMMS/PFB模型。应用此模型模拟一个二维加压射流床,分析了操作压力、位置高度、空隙率及剩余速度对非均匀因子的影响。通过模拟结果与实验数据的对比,发现该模型相比于Gidaspow模型,能够更准确地模拟加压射流床内颗粒浓度的分布状态及颗粒靠近壁面处的速度变化;将这种曳力模型应用到流化床浓相段的模拟,预测了床内颗粒浓度瞬时分布及沿轴向的时均值分布、颗粒的速度分布等流动行为,使流化床浓相段的气固流动行为可视化,对流化床的设计、放大有一定的指导作用。     

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.     

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。     

Fluidization of micronic particles in a conical fluidized bed: Experimental and numerical study of static bed height effect

The numerical simulations and experimental data of bed hydrodynamics in a conical fluidized bed unit are compared. Experimental studies have been carried out in a bed containing TiO₂ particles belonging to A/C boundary of Geldart's classification with a wide particle‐size distribution. Thus, pressure measurements and an optical fiber technique allowed determining the effect of static bed height on the fluidization characteristics of micronic particles. Numerical simulations have then been performed to evaluate the sensitivity of gas‐solids drag models. The Eulerian multiphase model has been used with different drag models and three boundary conditions (BC) consisting of no‐slip, partial‐slip, and free‐slip. The numerical predictions using the Gidaspow drag model and partial‐slip BC agreed reasonably well with the experimental bed pressure drop measurements. The simulation results obtained for bed expansion ratio show that the Gidaspow model with the free‐slip BC best fit with the experimental data. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

湍动流化床过渡段固含率分布特征的实验及数值模拟

在湍动流化床中,过渡段对于包括甲醇制烯烃在内的气固催化快反应有着重要的作用。采用PV6D反射型光纤探针对内径95 mm的湍动流化床内过渡段的固含率分布和脉动参数进行了测量,分别考察了表观气速和静床高的影响,并采用修正的基于颗粒动力学的三段曳力双流体模型进行模拟。实验表明,湍动流化床过渡段中固含率的轴向分布呈现S型和指数型两种类型,固含率轴向与径向分布都在过渡段内出现最大梯度,表明过渡段中固体浓度分布比稀相段和密相段更不均匀。表观气速和静床高的变化将导致S型和指数型分布的相互转变,并且对过渡段底部与壁面附近的固体高浓度区影响最为显著。局部固含率脉动概率密度分布表明,在静床高较小时,随着气速的增大,床层下部气含率最大值位置将从中心区移动至环隙区,呈现气含率的双峰型分布。本文提出的修正三段曳力模型考虑了颗粒团聚的影响,对过渡段中分布板影响区之外的固含率分布均能较好地模拟。     

气固垂直并流向上两相流流体动力学模型

运用能量最小多尺度 (EMMS)模型 ,推导出滑移速度及颗粒速度的径向分布 ,并进一步计算了径向空隙率、流体速度、团聚物直径、流体对颗粒的悬浮输送能量和颗粒的质量流率等相关的动力学参数 .模型计算结果反映了气固垂直两相流的径向不均匀性 (稀、密两相共存 )及环 /核结构的存在 .计算值与实验结果相吻合 .滑移速度的计算结果表明在核心区内也存在着团聚物 ,并不是呈现单一颗粒运动形态 ,这与实验现象一致 .该模型不仅克服了原有EMMS模型求解困难的问题 ,而且其计算不依赖于核心区半径等任何待定参数 ,只需物性参数、床层截面平均空隙率和操作参数即可 ,方便了实际应用 .     

不同曳力模型及颗粒碰撞恢复系数对短接触旋流反应器内气固流场的影响

为考察曳力模型和颗粒碰撞恢复系数对短接触旋流反应器内流动特性的影响,基于双流体模型, 结合颗粒动力学理论,对反应器内气固两相流场进行模拟研究。分别采用Gidaspow、Wen & Yu和Syamlal-O’Brien 3种曳力模型, 考察颗粒速度特性以及固含率径向分布。对比分析不同曳力模型的计算结果表明,Syamlal-O’Brien模型计算结果与实验结果误差较大,Wen & Yu模型在反应器边壁附近区域的计算结果误差较大,Gidaspow模型计算结果与实验结果最为吻合。此外,颗粒碰撞恢复系数较小时,所得计算值小于实验测量值,当恢复系数为0.95时颗粒扩散效果最好,计算结果与实验数据吻合度最高。     

On the development of flow pattern in a bubble column reactor: Experiments and CFD

A comprehensive analysis of the development of flow pattern in a bubble column reactor is presented here through extensive LDA measurements and CFD predictions. In the LDA measurements, the simultaneous measurements of 2D velocity-time data were carried out at several radial locations and many axial cross-sections of the column for two different spargers. The profiles of mean axial liquid velocity, fractional gas hold-up and bubble slip velocity showed excellent agreement between the predictions and the experimentally measured values. The experimental results showed that the mean tangential velocity varies systematically in the radial as well as along the axial co-ordinates. The turbulence parameters viz. turbulent kinetic energy, energy dissipation rate and eddy diffusivity were also analysed. The estimated values of local energy dissipation rate obtained using eddy isolation model were used for establishing the energy balance in the column. The experimental data were used for the estimation of normal and shear stress profiles. For the case of single point sparger, just above the sparger region, the bubble plume was seen to have a strong tangential component of motion thereby yielding higher gas hold-up slightly away from the centre. This visual observation was well captured in profiles of all the hydrodynamic parameters obtained from the experimental data. CFD simulations of the mean velocities, gas hold-up and turbulent kinetic energy compared well with the experimental results.     

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.     

EMMS曳力模型及其颗粒团模型的构建和检验

准确描述颗粒团聚特性是发展完善基于多尺度最小能量原理（EMMS）的曳力模型的重要方向之一。提出描述颗粒团聚特性的数学模型,不仅符合物理判断,而且与实验结果吻合。采用颗粒团模型,改进EMMS曳力模型,与实验及直接数值模拟结果吻合较好。改进的曳力模型与欧拉-欧拉双流体方法耦合,实现了不同工况下A、B类颗粒流化床流动特性的数值模拟。成功预测了颗粒非均匀分布特性、局部滑移速度、局部非均匀度以及噎塞状态。