基于不同亚格子尺度过滤模型下提升管内颗粒流动的数值模拟

固相亚格子尺度过滤模型是在高精度的网格下,系统地过滤了基于结合颗粒动理学的双流体模型的模拟结果而得到的曳力和固相应力等本构关系的计算模型。今分别采用固相亚格子尺度过滤模型(Filtered Model I)、壁面修正固相亚格子尺度过滤模型(Filtered Model II)和改进的固相亚格子尺度过滤模型(Filtered Model III)模拟NETL/PSRI挑战问题中的提升管内的颗粒流动特性,得到了时均气体压力梯度和时均轴向颗粒速度等分布。亚格子尺度模型和均匀流动模型(Huilin-Gidaspow model)的研究结果相比,改进的固相亚格子尺度过滤模型(Filtered Model III)与实验值更接近,尤其是对于高颗粒浓度流动。壁面修正可以提高压力梯度,从时均轴向颗粒速度分布曲线,可以看出在提升管内颗粒流动结构呈现更为明显的环核流动结构;同时,研究了提升管内气体压缩性、壁面修正和计算网格对模拟结果的影响,分析表明气体的可压缩性对提升管内轴向气体压力梯度有影响,在模拟计算时考虑气体的压缩性,可以提高计算精度。     

网格尺寸对循环流化床内气固两相流动的影响

将基于能量最小多尺度方法(EMMS)的曳力模型耦合到双流体模型中,并针对循环流化床内的气固两流动进行了模拟研究。采用全滑移壁面边界条件处理颗粒相,考察了3种网格尺度对轴向空隙率和出口颗粒循环量等气固流动特性的影响。计算结果表明,应用EMMS曳力模型处理相间作用力,同时在采用全滑移壁面边界条件处理颗粒相时,双流体模型能够正确预测轴向空隙率分布。采用网格尺寸为2.325 mm×20 mm时,模拟结果和实测数据吻合较好,表明在循环流化床的数值模拟中选择恰当的网格尺度是极为重要的。     

亚格子湍动能模型及循环流化床气固湍流特性分析

以气相大涡-颗粒相二阶矩双流体模型为框架,基于单相流亚格子湍动能推导方法,考虑固相影响推导气相亚格子湍动能方程,建立了适用于气固两相流动的气相亚格子湍动能模型;同时考虑气相亚格子湍动能与颗粒相速度脉动二阶矩之间的脉动能量传递,补充了气固相间脉动能量作用模型。模拟了循环流化床内气固两相湍流流动过程,模拟结果与实验数据吻合较好,并较未考虑湍流模型的模拟结果更接近实验值。比较了不同亚格子湍流模型对颗粒运动的影响,与Smagorinsky亚格子涡黏模型相比,亚格子湍动能模型能够更好地模拟两相流的湍流特性。分析了气体表观速度对湍流作用的影响。研究表明,随着气体表观速度的增加,气相亚格子湍动能和亚格子能量耗散逐渐增加,径向分布的非均匀性增强。     

循环流化床气固两相流动数值模拟的研究进展

对循环流化床气固两相流动数值模拟的研究进展进行介绍,包括传统的欧拉双流体模型、基于颗粒动力学理论的双流体模型、基于拉格朗日坐标系下的颗粒轨道模型、能量最小多尺度模型和小室模型,并对上述模型的原理、发展和优缺点进行了描述。     

流化床内颗粒流体两相流的CFD模拟

采用先进的CFD模拟技术分析流化床内两相复杂体系的非线性流体动力学特征已得到普遍认同,但是由于不同研究者对颗粒与颗粒以及颗粒与流体之间相互作用力认识的差异,导致欧拉-欧拉框架下动量守恒方程的不同表达形式。本文在总结文献中有关颗粒黏性力、固相压力和两相间作用力的基础上,从双流体理论出发,提出了一个考虑拟平衡态下固体颗粒对流体相和固相动量守恒方程均有影响的简捷流体动力学模型。该模型的主要特点是表征颗粒离散属性的特征长度视为颗粒直径的同一数量级。随后在CFX4.4商业化软件平台上通过增加用户自定义子程序,对网格尺度、时间步长和最大颗粒堆积率的无关性进行检验,介绍了作者近年来采用该模型模拟二维/三维流化床内液固体系的散式流态化、气固Geldart A类物料的散式/聚式流态化和床层塌落特性以及Geldart B/D类物料的鼓泡/射流流态化和床层塌落的研究进展。模拟的主要结果与经典理论、本研究实验和文献报道数据相一致,说明该模型可以用来预测流化床内密相颗粒流体体系的动力学特性。     

循环流化床中颗粒聚团特性的模拟

考虑到循环流化床中分散颗粒和颗粒聚团同时存在的多尺度结构,确定了密相和稀相加速度与计算网格局部参数之间的关系,建立了多尺度曳力消耗能量最小的稳定性条件,基于双变量极值理论,构建了考虑颗粒团聚效应的多尺度气固相间曳力模型。结合双流体模型,对循环流化床内气固流动特性以及颗粒聚团特性进行了模拟研究。通过与实验值比较,考虑颗粒聚团影响的计算模型可以更好地贴近实验结果,颗粒聚团直径随颗粒浓度增大呈现先增大后减小的分布趋势,气体和颗粒的加速度在模拟中与重力加速度同处一个数量级,求解过程中不能被忽略。     

循环流化床中颗粒聚团特性的模拟

考虑到循环流化床中分散颗粒和颗粒聚团同时存在的多尺度结构,确定了密相和稀相加速度与计算网格局部参数之间的关系,建立了多尺度曳力消耗能量最小的稳定性条件,基于双变量极值理论,构建了考虑颗粒团聚效应的多尺度气固相间曳力模型。结合双流体模型,对循环流化床内气固流动特性以及颗粒聚团特性进行了模拟研究。通过与实验值比较,考虑颗粒聚团影响的计算模型可以更好地贴近实验结果,颗粒聚团直径随颗粒浓度增大呈现先增大后减小的分布趋势,气体和颗粒的加速度在模拟中与重力加速度同处一个数量级,求解过程中不能被忽略。     

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。     

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。     

65 t/h高低差速循环流化床流动特性模拟

对一台65 t/h高低差速循环流化床炉内流动特性进行二维数值模拟。采用基于颗粒动力学理论的欧拉双流体模型来描述气固流动,湍流模型、气固曳力模型和不同粒径颗粒间曳力模型分别采用RNG k-ε per phase模型、Gidaspow模型和Schiller-naumann模型,并应用商业计算流体力学软件Fluent进行数值计算,得到炉内颗粒速度分布、压力分布和颗粒浓度分布,并将压力分布与实测值进行对比。在欧拉双流体模型中分别采用单粒径固相模型和多粒径固相模型,并对模拟结果进行对比分析。结果表明,单粒径固相模型能够较好预测高低差速循环流化床炉内流动特性,为其优化设计、运行及大型化提供了理论依据。     

Filtered two‐fluid models of fluidized gas‐particle flows: New constitutive relations

New constitutive relations for filtered two‐fluid models (TFM) of gas‐particle flows are obtained by systematically filtering results generated through highly resolved simulations of a kinetic theory‐based TFM. It was found in our earlier studies that the residual correlations appearing in the filtered TFM equations depended principally on the filter size and filtered particle volume fraction. Closer inspection of a large amount of computational data gathered in this study reveals an additional, systematic dependence of the correction to the drag coefficient on the filtered slip velocity, which serves as a marker for the extent of subfilter‐scale inhomogeneity. Furthermore, the residual correlations for the momentum fluxes in the gas and particle phases arising from the subfilter‐scale fluctuations are found to be modeled nicely using constitutive relations of the form used in large‐eddy simulations of single‐phase turbulent flows. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3265–3275, 2013     

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.     

Verification of filtered two‐fluid models for gas‐particle flows in risers

The effect of solid boundaries on the closure relationships for filtered two‐fluid models for riser flows was probed by filtering the results obtained through highly resolved kinetic theory‐based two‐fluid model simulations. The closures for the filtered drag coefficient and particle phase stress depended not only on particle volume fraction and the filter length but also on the distance from the wall. The wall corrections to the filtered closures are nearly independent of the filter length and particle volume fraction. Simulations of filtered model equations yielded grid length independent solutions when the grid length is ～half the filter length or smaller. Coarse statistical results obtained by solving the filtered models with different filter lengths were the same and corresponded to those from highly resolved simulations of the kinetic theory model, which was used to construct the filtered models, thus verifying the fidelity of the filtered modeling approach. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Heterogeneity analysis of gas-solid flow hydrodynamics in a pilot-scale fluidized bed reactor

Mesoscale drag model is of crucial significance for the reliability and accuracy in coarse-grid EulerianEulerian two-fluid model(TFM) simulations of gas-solid flow hydrodynamics in fluidized bed reactors.Although numerous mesoscale drag models have been reported in the literature,a systematic comparison of their prediction capability from the perspective of heterogeneity analysis is still lacking.In this study,in order to investigate the effect of several typical drag models on the hydrodynamic ...     

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.     

A spatially‐averaged two‐fluid model for dense large‐scale gas‐solid flows

We present a spatially‐averaged two‐fluid model (SA‐TFM), which is derived from ensemble averaging the kinetic‐theory based TFM equations. The residual correlation for the gas‐solid drag, which appears due to averaging, is derived by employing a series expansion to the microscopic drag coefficient, while the Reynolds‐stress‐like contributions are closed similar to the Boussinesq‐approximation. The subsequent averaging of the linearized drag force reveals that averaged interphase momentum exchange is a function of the turbulent kinetic energies of both, the gas and solid phase, and the variance of the solids volume fraction. Closure models for these quantities are derived from first principles. The results show that these new constitutive relations show fairly good agreement with the fine grid data obtained for a wide range of particle properties. Finally, the SA‐TFM model is applied to the coarse grid simulation of a bubbling fluidized bed revealing excellent agreement with the reference fine grid solution. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3544–3562, 2017     

Verification and Validation of Spatially Averaged Models for Fluidized Gas-Particle Suspensions

Two different methods for closure modeling of the unresolved terms appearing in the filtered two-fluid model are discussed and compared. The spatially averaged two-fluid model is based on generalizing the concepts of large eddy simulation to gas-particle flows. In the approximate deconvolution method-two-fluid model approach, the unresolved terms are modeled by an approximate deconvolution method, where an approximation of the unfiltered solution is obtained by repeated filtering. Finally, these models are applied to a lab-scale and a pilot-scale fluidized bed. Both approaches yield fairly good agreement with a highly resolved reference simulation as well as with experimental data. Additionally, both methods deliver reasonable grid-independent solutions up to a grid resolution of 2 cm in the case of Geldart type A particles.     

Conventional and data-driven modeling of filtered drag,heat transfer,and reaction rate in gas–particle flows

This study presents conventional and artificial neural network-based data-driven modeling (DDM) methods to model simultaneously the filtered mesoscale drag, heat transfer and reaction rate in gas–particle flows. The dataset used for developing the DDM is filtered from highly resolved simulations closed by our recently formulated microscopic drag and heat transfer coefficients (HTCs). Results reveal that the filtered drag correction is nearly independent of filter size when including the filtered gas phase pressure gradient. We further find that the filtered HTC correction critically depends on the added filtered temperature difference marker while the filtered reaction rate correction shows weak dependence on the additional markers. Moreover, compared with conventional correlations, DDM predictions agree better with filtered resolved data. Comparative analysis is also conducted between existing HTC corrections and our work. Finally, the applicability of conventional and data-driven models coupled with coarse-grid computational fluid dynamics simulations for pilot-scale (reactive) gas–particle flows is validated comprehensively.     

On the effects of the flow macro-scale over sub-grid modelling in dense gas–solid fluidized flows

Multiscale modelling of gas–particle fluidized flows is frequently approached by means of sub-grid modelling, which provides constitutive closures for filtered formulations applied to large scale simulations. A widely practiced procedure for the derivation of sub-grid models consists of filtering over predictions from highly resolved simulations under two-fluid modelling. The present work is intended as a contribution in this field by providing new supporting evidence for the enhancement of sub-grid closure models. Most of the efforts in the area have been directed to providing sub-grid models dependent on meso-scale filtered effects alone, and under low gas Reynolds number suspension conditions. In this work, macro-scale conditions are added to the analysis thereby accounting for flow topology, particularly for dense gas–solid fluidized flows. Two macro-scale variables are considered in the simulations, namely the domain average solid volume fraction and the domain average gas Reynolds number. So, in addition to the usual meso-scale filtered markers, relevant filtered parameters are also related to those macro-scale conditions. The filtered parameters of interest here are the effective interphase drag coefficient and filtered and residual stresses in both of the phases. Various domain average solid volume fractions and domain average gas Reynolds numbers were enforced, thereby providing for a variety of macro-scale dense conditions. It was found that both these macro-scale parameters considerably affect the meso-scale and the resulting filtered parameters of dense gas–solid flows, even though this occurs in a milder way when compared to results for dilute flow conditions available in the literature.