群体平衡方程在搅拌反应器模拟中的应用

群体平衡方程(population balance equation,PBE)是描述多相流体系中分散相大小与分布随时空变化的通用方程。搅拌反应器内多为多相流体系,考虑到颗粒聚并、破碎等微观机制对颗粒大小、分布、粒数密度等宏观参量的影响,采用PBE对搅拌槽内多相流体系进行数值模拟,可以较准确预测搅拌槽内流场和颗粒的大小与分布。对群体平衡方程在搅拌反应器数值模拟中的应用进行了综述,在简要介绍PBE的基本形式后,讨论了PBE的主要数值求解方法,然后着重介绍近年来采用PBE对搅拌槽内液固沉淀过程、气液及液液体系进行数值模拟的情况,并对今后的研究方向进行了展望。     

分解槽搅拌过程数值模拟研究

建立了一个工业分解槽的计算流体力学CFD模型,采用稳态多重参考系法以及欧拉一欧拉多相流模型对槽内固液两相搅拌过程进行数值模拟计算。分析了流体速度分布、颗粒相分布以及搅拌功率变化过程。     

搅拌槽内多相流动数值模拟研究进展

综述了过程工业中广泛应用的搅拌槽反应器内多相流动数值模拟研究的进展.讨论多相湍流模型、相间作用力模型及搅拌桨处理方法等重要的数值模拟技术和方法,并对有关的计算模型进行了比较分析.针对搅拌槽内的各种多相体系,论述了不同研究者在桨区处理、相间动量传递描述和分散相的引入对体系湍流特性影响等方面的模拟方法并对结果作了比较.提出了需要进一步深入研究的课题.     

半弧面斜叶桨的流体力学性能与氧传质特性

氧传质系数是气液搅拌反应器设计的关键参数,研究新型搅拌桨的氧传质性能对气液两相搅拌反应器的强化有着重要的意义。本文实验研究了气体分布器、搅拌转速、气量对氧传质系数、搅拌功耗及气含率的影响,结果表明,氧传质系数随搅拌转速和气量的增加而增加;并建立了氧传质系数与搅拌功耗和表观气速的经验公式,为进一步放大应用提供了基础。采用欧拉-欧拉多相流模型及群体平衡模型对半弧面新型斜叶桨进行了计算流体力学（CFD）数值模拟研究,模拟研究了不同结构、搅拌转速、气量下的流体力学性能和氧传质系数,模拟计算结果与实验值的相对偏差在20%以内;这为研究这一半弧面新型斜叶桨提供了一种可靠的数值模拟方法;优化了半弧面新型斜叶桨的结构,提高了搅拌釜的氧传质效率。     

多相搅拌槽内宏观混合研究进展

多相搅拌槽反应器广泛应用于化工、冶金等过程工业中,而多相混合状态对于多相搅拌槽反应器的设计、优化和放大具有重要意义.混合时间是表征其宏观混合过程的一个重要参数.文中从实验和数值模拟二方面对多相搅拌槽反应器的液相混合时间研究进行综述,对气液、液固、液液、气液固4种体系的多相搅拌槽进行了分类总结,讨论了分散相、桨型、转速、...     

不同黏度下气液体系流体力学行为的PBM模拟

基于Eulef-Euler双流体模型,分别采用均一气泡尺寸和PBM方法对鼓泡床内气液两相流体系中的流体力学行为进行了数值模拟,经与实验结果比较表明,采用PBM方法获得的模拟结果更为准确,表明了PBM方法的优越性.采用PBM模型模拟了不同黏度气液体系中的流体力学行为,获得了包括平均及局部气含率分布、气泡尺寸分布,循环液速和大小气泡的空间分布等流体力学信息,并将模拟结果与相应操作条件下的实验结果进行了比较,吻合较好,说明PBM方法不仅可以用于鼓泡床反应器内气液两相流体系的模拟研究,还能对不同液相黏度下气液体系中的流体力学行为作出正确的预测和描述,为多相流反应器的设计和放大提供了有益的参考.     

改进Intermig桨种分槽搅拌性能的数值模拟

利用商业CFD软件Fluent 12.0和并行计算系统图形工作站,对改进的Intermig桨种分槽内部流场进行了三维数值解析.采用Realizable κ-ω流模型和欧拉-欧拉多相流模型对槽内不同桨叶离底距离C、桨叶直径D下的氢氧化铝颗粒悬浮规律以及搅拌桨功率消耗进行了模拟.结果显示,搅拌转速一定的条件下,桨叶直径越大...     

分布孔大小对环流反应器内流动影响数值模拟

采用k-ε二方程模型和欧拉多相流模型,对一种气升式环流反应器内的湍流气液二相流进行了全尺寸的数值模拟研究,考察了采用具有不同大小分布孔气体分布器时反应器内气含率和流速分布的细节。模拟结果表明采用小分布孔的反应器内的平均气含率较高,气液二相接触效果较好,对于反应过程有利。计算所得的整体气含率与实测的整体气含率进行了对比,吻合较好。     

多相流搅拌反应器研究进展

综述了近五年冷态气液固三相搅拌反应器的研究成果,阐明近期研究热点已转为热态多相流搅拌反应器的流体力学行为。概述了热态气液两相体系中通气功率、混合时间、局部及总体气含率的研究结果。指出今后研究重点应为热态的固液悬浮、气液传质过程及其机理,同时说明用计算流体力学（CFD）对气液固三相搅拌反应器的数值模拟仍属起步阶段。     

搅拌反应器内气液两相流的CFD研究进展

搅拌式气液反应器因其操作灵活、适用性强等优点,在过程工业中应用广泛.综述了采用计算流体力学CFD技术对搅拌反应器内气液两相流动行为的数值模拟研究.Euler-Euler双流体模型作为主要方法用于描述气液两相流动,在其基础上耦合相对简单的气泡数密度函数模型或复杂的群体平衡模型,可较为准确地预测搅拌反应器内气泡尺寸和局部气含率及其分布规律.CFD模拟结果可用以分析和评价不同搅拌桨叶、搅拌桨组合和气体分布器的气液分散性能,对气液反应器的结构优化和过程强化提供了有效手段.     

Two Analytical Approaches for Solution of Population Balance Equations: Particle Breakage Process

Various particulate systems were modeled by the population balance equation (PBE). However, only few cases of analytical solutions for the breakage process do exist, with most solutions being valid for the batch stirred vessel. The analytical solutions of the PBE for particulate processes under the influence of particle breakage in batch and continuous processes were investigated. Such solutions are obtained from the integro‐differential PBE governing the particle size distribution density function by two analytical approaches: the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM). ADM generates an infinite series which converges uniformly to the exact solution of the problem, while HPM transforms a difficult problem into a simple one which can be easily handled. The results indicate that the two methods can avoid numerical stability problems which often characterize general numerical techniques in this area.     

Numerical simulation of stirred tanks using a hybrid immersed-boundary method

Conventionally, multiple reference frame (MRF) method and sliding mesh (SM) method are used in the simulation of stirred tanks, however, both methods have limitations. In this study, a hybrid immersed-boundary (IB) technique is developed in a finite difference context for the numerical simulation of stirred tanks. IBs based on Lagrangian markers and solid volume fractions are used for moving and stationary boundaries, respectively, to achieve optimal efficiency and accuracy. To cope with the high computational cost in the simulation of stirred tanks, the technique is implemented on computers with hybrid architecture where central processing units (CPUs) and graphics processing units (GPUs) are used together. The accuracy and efficiency of the present technique are first demonstrated in a relatively simple case, and then the technique is applied to the simulation of turbulent flow in a Rushton stirred tank with large eddy simulation (LES). Finally the proposed methodology is coupled with discrete element method (DEM) to accomplish particle-resolved simulation of solid suspensions in small stirred tanks. It demonstrates that the proposed methodology is a promising tool in simulating turbulent flow in stirred tanks with complex geometries.     

Dispersion coefficient and settling velocity of the solids in agitated slurry reactors stirred with multiple rushton turbines

The feature of solids distribution in tanks stirred with multiple Rushton turbines was investigated. Both transient and steady-state experiments were performed in tanks of two scales with a variety of suspensions. The data were analysed with the axial sedimentation-dispersion model. The axial dispersion coefficient of the solid phase was found not to differ from that of the liquid by more than 20%. The effective particle settling velocity in the stirred medium was then determined. It is confirmed that this parameter is different from the terminal settling velocity. Their ratio exhibits the same dependence on Kolmogoroff microscale and particle size as obtained previously with an indirect, approximate approach.     

搅拌反应器中液相混合时间研究进展

搅拌反应器是一种在化工、医药、能源和废水处理等领域应用比较广泛的设备.其中混合时间是表征搅拌反应器内物料混合状况的一个重要参数.本丈从实验测量方法和数值模拟两个方面综述了近50年来对混合时间的研究,并展望了未来混合时间测量方法和数值计算的发展方向.     

PDF method for population balance in turbulent reactive flow

Turbulent reactive flows with particle formation, such as soot formation and precipitation, are characterized by complex interactions between turbulence, scalar transport, particle formation and particle transport and inter-particle events such as coagulation. The effect of formation, growth and coagulation on the particle size distribution (PSD) must be modelled by the population balance equation (PBE). While the PBE has been studied extensively in homogeneous systems and, recently, in simple flows, its coupling with turbulent reactive flows poses a wealth of new questions. Processes such as nucleation, growth and coagulation are described by kinetic laws that link them to the local concentrations of the reactive scalars, which are random in a turbulent flow. This accounts for additional mechanisms that induce randomness and fluctuations to the particle concentration and PSD. Furthermore, conventional RANS closure of the coagulation term PDE (which describes the evolution of the PSD) leads to unknown correlations. In this work a new pdf approach is developed, based on the transport of the joint pdf of reactive scalars and particle number densities at different sizes, which overcomes the additional closure problems. It is also shown how the pdf method can be solved numerically via Monte-Carlo methods, and this is demonstrated via two applications in a partially stirred reactor: precipitation via nucleation-growth and coagulation. In each case the pdf method is compared with models that neglect correlations at various levels, and it is demonstrated that the interaction of turbulence with particle formation mechanisms accounts for significant deviations in the PSD.     

Dispersion and Phase Separation of Water‐Oil‐Amphiphile Systems in Stirred Tanks

Drop size distributions and phase separation behavior of water‐oil‐nonionic amphiphile systems are investigated using an in situ endoscope measurement technique and an external camera in stirred tanks in batch mode. The fitting procedure and the simulation results of a phase separation model are analyzed under the condition that either the swarm sedimentation speed or the mean drop size during sedimentation is known. The steady‐state drop size distributions are self‐similar over the whole range of process parameters, but not in the decaying turbulence field after agitation stop. The coalescence rate in the first seconds after agitation stop clearly affects the separation behavior, so that a prediction of the separation time based on the initial conditions in steady state is not trivial.     

Solution of PBE by MOM in finite size domains

A new approach to solve PBE (Population Balance Equations), FCMOM (Finite size domain Complete set of trial functions Method Of Moments), is presented. The solution of the PBE is sought, instead of the [0,∞] range, in the finite interval between the minimum and maximum particle size; their evolution is tracked imposing moving boundaries conditions. After reformulating the PBE in the standard interval [-1,1], the size distribution function is represented as a series expansion by a complete system of orthonormal functions. Moments evolution equations are developed from the PBE in the interval [-1,1]. The FCMOM is implemented through an efficient algorithm and provides the solution of the PBE both in terms of the moments and in terms of the size distribution function. The FCMOM was validated with applications to particle growth (constant, linear, diffusion-controlled), simultaneous particle growth and nucleation, particle dissolution, particle aggregation (constant, sum, product, Brownian kernels) and simultaneous particle aggregation and growth.     

Solution of population balance equation with pure aggregation in a fully developed turbulent pipe flow

This paper presents our preliminary effort in predicting particle size distributions in particulate processes in turbulent flow systems. The focus has been on processes of pure aggregation, occurring in a turbulent environment. A remarkably simple strategy has been used to solve the population balance equation (PBE) for spatially dependent pure aggregation with insignificant diffusive transport of particles in turbulent flow systems. The method makes use of the solution of a batch PBE through a mathematical transformation linking time to spatial variables. Furthermore, we investigate the self-similar solution of batch aggregation to show scaling behavior of particle size distributions in such flow systems using spatially dependent average particle sizes. Average particle sizes across the pipe cross section have been computed using both averaged frequencies as well as spatially varying frequencies. Comparison of the two solutions shows significant differences between them, establishing the sheer inappropriateness of the use of average aggregation frequencies in the prediction of absolute particle size distribution as done in the past.     

NUMERICAL SIMULATION OF LAMINAR SOLID-LIQUID TWO-PHASE FLOW IN STIRRED TANKS

Laminar flow of solid-liquid suspension has been rarely reported in the literature. In this article, the laminar solid-liquid two-phase flow in a lab-scale stirred tank is measured with digital particle image velocimetry (DPIV) and numerically simulated with the improved inner-outer iterative method. The simulation results show good agreement with the present data. In the range of low solid volume concentration under investigation, solid particles have minor impact on two-phase flow, and the simulated flow fields of both phases are similar to the counterpart of single-phase laminar liquid flow. The comparison of simulation with experiments of single-phase laminar flow shows reasonable agreement. These observations suggest that the numerical method employed in the present study is reliable for analysis of stirred tanks. The influence of impeller off-bottom clearance on velocities is found significant: the lower the impeller, the smaller the radial and axial velocities, and the higher the solid concentration.