Modeling of the 3D hydrodynamics of 2-blade impellers in stirred tanks filled with a highly viscous fluid

This paper deals with mixing in stirred tank reactors by paddle agitators and two-blade impellers with different blade widths. Computational Fluid Dynamics (CFD) is used to solve the 3D hydrodynamics and to obtain at every point the flow patterns, the stress components and the viscous dissipation function. From the latter information, the power consumption is calculated. These results are compared with available experimental data: good agreement is observed. For example, for a paddle agitator, the flow is essentially plane far away from the horizontal walls. That means that, in order to create an axial circulation in the volume of the tank, the impeller height has to be decreased. This work documents the ability of CFD to model changes in flow patterns for three dimensional flows in stirred tanks.     

双层涡轮桨搅拌反应器内混合时间的大涡模拟

采用计算流体力学(CFD)方法对直径为0.476m双层涡轮桨搅拌反应器内的流动及混合进行了数值模拟,并实验测试了混合过程。利用大涡模拟(LES)及Smagorinsky-Lilly亚格子模型求解湍流流动与示踪剂传递过程,桨叶区域采用滑移网格技术。研究结果表明,大涡模拟得到的示踪剂响应曲线和混合时间与实验结果吻合良好,其预测精度明显优于基于雷诺平均(Reynolds-averaged Navier-Stokes,RANS)的标准k-ε模型的模拟结果。大涡模拟是研究搅拌反应器内非稳态及周期性湍流流动的有效方法。     

Large Eddy Simulations of Mixing Time in a Stirred Tank

Large eddy simulations （LES） of mixing process in a stirred tank of 0.476m diameter with a 3-narrow blade hydrofoil CBY impeller were reported. The turbulent flow field and mixing time were calculated using LES with Smagorinsky-Lilly subgrid scale model. The impeller rotation was modeled using the sliding mesh technique. Better agreement of power demand and mixing time was obtained between the experimental and the LES prediction than that by the traditional Reynolds-averaged Navier-Stokes （RANS） approach. The curve of tracer response predicted by LES was in good agreement with the experimental. The results show that LES is a reliable tool to investigate the unsteady and quasi-periodic behavior of the turbulent flow in stirred tanks.     

Numerical simulation of turbulent batch mixing in a vessel agitated by a Rushton turbine

In this study, computational fluid dynamics (CFD) modelling of turbulent batch mixing of an inert tracer in a baffled vessel agitated by a six-bladed Rushton turbine has been carried out using the proprietary code FLUENT. The study is intended to evaluate the CFD predictions of key properties related to the mixing against measurements and to provide a detailed insight into the process. Three-dimensional, time-dependent flow and mixing calculations have been performed using the fully predictive sliding-mesh technique for the impeller/tank geometry employed by Distelhoff et al. [M.F.W. Distelhoff, A.J. Marquis, J.M. Nouri, J.H. Whitelaw, Scalar mixing measurements in batch operated stirred tanks, Can. J. Chem. Eng. 75 (1997) 641–652] for mixing studies using a laser induced fluorescence technique. Complementary validation of hydrodynamic predictions in a geometrically similar tank was carried out against the experimental data obtained by Hockey [R.M. Hockey, Turbulent Newtonian and non-Newtonian flows in a stirred reactor, Ph.D. Thesis, Imperial College, London, 1990]. The predicted mean velocity components in the bulk regions of the tank above and below the impeller compare well with the experimental data. However, the turbulent kinetic energy is significantly underestimated in these areas. The predicted tracer concentration variations with time at different locations in the tank, in common with measurements, show initial fluctuations, which eventually approach the fully mixed concentration. However, the time required for the appearance of first peak in the concentration–time plot, peak value of the tracer concentration and the time required for the local tracer concentration to attain the final value depend on the position in the tank. The CFD predicted mixing times at different locations in the tank as well as the overall mixing time show reasonably good agreement with the measured data and with those calculated from published experimental correlations.     

偏心组合桨搅拌槽内层流混合过程的数值模拟

目前,处理高黏流体和对剪切敏感介质的层流搅拌槽的报道并不多见。本文建立了描述双层组合桨搅拌槽内高黏非牛顿流体层流流动、混合过程的数学模型,利用Laminar模型、多重参考系法（MRF）和示踪剂浓度法对其流场特性、示踪剂扩散过程进行数值模拟,分析搅拌槽内轴向速度曲线、示踪剂浓度响应曲线和混合时间。结果表明：中心搅拌中间面将介质阻隔在各自的半层内运动,偏心搅拌介质作全局运动,轴向混合能力突出;转轴中心搅拌依靠上下半层浓度差的增大向下扩散,转轴偏心搅拌通过不对称结构扩散示踪剂,叶轮相对转轴偏心搅拌则利用叶片的不对称分布;距离加料点较近和较远的监测点浓度响应曲线因振荡和调整,混合时间较长,处于中间面的监测点拥有最短的混合时间。     

Agitation and mobilization of thixotropic liquids

Direct numerical simulations of transitional and turbulent flows of purely viscous thixotropic liquids in stirred tanks have been performed. The simple thixotropy model used is based on the notion of a network in the liquid with an integrity that builds up with finite rate under quiescent conditions, and breaks down under liquid deformation. We solve a transport equation for the network integrity which is two‐way coupled to the lattice‐Boltzmann‐based flow solver. The liquid's time scale characterized by the dimensionless Deborah number shows a profound impact on the level of mobilization and the flow patterns in the mixing tanks, especially if the time scale of the liquid is of the same order as the circulation time in the tank. It is also demonstrated to what extent increasing the impeller speed improves mobilization and mixing. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Laminar Mixing in Eccentric Stirred Tank Systems

Laminar flow structure and mixing patterns in stirred tanks with eccentrically located impellers is examined using tracer visualization techniques and laser induced fluorescence (LIF). The displacement of the shaft from the centerline of the tank has a remarkable effect on the manifold structure of the flow: segregated regions of regular motion observed in concentric systems are destroyed, impeller mid‐plane separatrices are eliminated, and the axial circulation is greatly improved even in systems agitated even by radial impellers.     

搅拌反应器气液两相流混合过程的涡旋效应数值模拟

为研究气液两相搅拌釜桨叶对釜内流动结构及气液混合性能的影响,本文以直叶片和推进叶片为研究对象,采用ICEM软件对搅拌釜流场进行六面体结构网格划分,基于SST-DDES湍流模型及欧拉-欧拉多相流模型对搅拌釜内部流场进行三维非定常计算,获得两种桨叶下搅拌釜内部涡结构及其演化过程,并分析搅拌釜内瞬态气相分布和瞬时流场的分布规律。研究结果表明：由于叶片旋转而产生的涡有撕裂、合并、衰减和耗散的演化过程;直叶片相较于推进叶片,其涡耗散速度较快,涡产生到消失的周期较短;由于叶片结构不同,主流的运动方向也随之改变,直叶片沿径向分布,推进叶片沿轴向分布。前者在釜内形成上下两层循环区,不利于气相扩散。后者在釜内形成一个大循环区,加剧釜内流动循环,造成后者的气相扩散能力大于前者。比较两者T_0.95分布,推进叶片要小于直叶片,推进叶片搅拌釜T_0.95近似为直叶片搅拌釜T_0.95的50%。     

搅拌釡中层流流场的模拟

Stirred tanks are used extensively in process industry and one of the most commonly used impellers in stirred tanks is the R.ushton disk turbine. Surprisingly few data are available regarding flow and mixing in stirred-tank reactors with Rushton turbine in the laminar regime, in particular the laminar flow in baffled tanks.In this paper, the laminar flow field in a baffled tank stirred by a standard R.ushton turbine is simulated with the improved inner-outer iterative method. The non-inertial coordinate system is used for the impeller region, which is in turn used as the boundary conditions for iteration. It is found that the simulation results are in good agreement with previous experiments. In addition, the flow number and impeller power number calculated from the simulated flow field are in satisfactory agreement with experimental data. This numerical method allows prediction of flow structure requiring no experimental data as the boundary conditions and has the potential of being used to scale-up and design of related process equipment.     

半圆管曲面涡轮搅拌槽内混合特性的数值模拟

在商业化软件ANSYS CFX 10.0平台上,采用多重参考系法来解决挡板与桨叶之间的相对转动问题,由标准k-ε模型对半圆管曲面涡轮搅拌槽内流动和混合过程进行了详细的数值模拟,本模拟所得的功率准数和设计值以及相关文献值吻合良好。结果表明：当搅拌桨离底距离由搅拌槽直径的1/2处变为1/3处时,搅拌槽内的流型均为典型的“双循环流型”,而当搅拌桨离底距离由搅拌槽直径的1/3处降低至1/6处时,槽内流型由典型的“双循环流型”转变为“单循环流型”;通过对不同时刻不同桨叶离底距离下的示踪剂浓度分布图分析表明槽内的混合过程与流动场密切相关;加料点位置对于最终的流场混合效果有着显著影响,对于混合时间数据的采集应注意不同加料位置时监测点的选取。CFD模拟结果表明本文所采用的模型可以很好的预测半圆管曲面涡轮搅拌槽内的混合特性,为进一步改进和优化半圆管曲面涡轮的设计提供了一定的参考。     

Simulation of laminar and turbulent impeller stirred tanks using immersed boundary method and large eddy simulation technique in multi-block curvilinear geometries

Impeller stirred tanks are commonly used in the chemical processing industries (CPI) for a variety of mixing and blending technologies. Such processes require accurate modeling of the turbulent flow in the tank over a range of operating conditions (e.g. impeller speed), and in addition, require a computationally efficient solution strategy that can represent moving rigid geometric parts (impellers) in the tank. In the present study, a methodology is proposed that combines the advantages of the immersed boundary method (IBM) to represent moving rigid geometries with the efficiency of multi-block structured curvilinear meshes (to minimize wasted grid points) for the representation of overall complex domains. The IBM implementation on a multi-block curvilinear mesh is advocated for the simulations of impeller stirred tank reactors (STR) and has distinct advantages over other competing methods. In the present work, the curvilinear-IBM methodology is further combined with the curvilinear coordinate implementation of large eddy simulation (LES) technique to address the issue of modeling unsteady turbulent flows in the STR. To verify the implementation of IBM in a multi-block curvilinear geometry, a laminar STR with a stack of four pitched blade impellers on a single shaft is simulated and compared against experimental data. Verification of the combined IBM-LES implementation strategy in curvilinear coordinates is done through comparisons with the measurements of turbulent flow in a baffled STR with a single pitched blade impeller. For both laminar and turbulent STR, the predictions are in very good agreement with measurements. It is suggested here that this methodology can be reliably used as a predictive tool for the flow fields in STRs with complex geometries.     

Numerical Simulation of Gas‐Liquid Flow in a Stirred Tank with Swirl Modification

Although the standard k‐? model is most frequently used for turbulence modeling, it often leads to poor results for strongly swirling flows involved in stirred tanks and other processing devices. In this work, a swirling number, R_S, is introduced to modify the standard k‐? model. A Eulerian‐Eulerian model is employed to describe the gas‐liquid, two‐phase flow in a baffled stirred tank with a Rushton impeller. The momentum and the continuity equations are discretized using the finite difference method and solved by the SIMPLE algorithm. The inner‐outer iterative algorithm is used to account for the interaction between the rotating impeller and the static baffles. The predictions, both with and without R_S corrections, are compared with the literature data, which illustrates that the swirling modification could improve the numerical simulation of gas‐liquid turbulent flow in stirred tanks.     

轴流桨搅拌槽三维流场数值模拟

利用k -ε湍流模型预测了搅拌槽在不同操作条件下宏观速度场 ,模型成功预测了搅拌槽内速度分布 ,计算结果与实验结果吻合较好 .模型预测结果表明 ,搅拌槽内宏观流动场受搅拌桨槽径比影响较大 .对单层搅拌桨 -槽体系 ,挡板前后宏观流动场差别很大 ,在挡板以前区域 ,轴向流动较强 ,在整个r -z断面上形成一个整体循环 ;而在挡板后面区域 ,流体在桨叶安装位置高度附近转向轴心流动 ,槽体上半部区域形成二次循环区域 ,且二次循环区域内流体以向下流动为主 .     

A THREE-PARAMETER MODEL FOR THE DISTRIBUTED FEED REACTOR

The distributed feed reactor has been analysed as a linear array of alternate plug flow and stirred tank reactors. Three parameters in the model serve to describe fluid flow characteristics and the concentration profile. The parameters allow design flexibility and in their extremities the physical situation approaches a train of stirred tanks or a plug flow reactor. The parameters have been estimated so as to maximize the yield. For a parallel reaction scheme it is shown that both plug flow and stirred tank features are significant, and that the present model predicts greater yield than models which consider only plug flow or complete mixing.     

Experimental and CFD investigation of power consumption in a dual Rushton turbine stirred tank

Power consumption of a mixing system is a key variable in chemical and bioprocess engineering, the determination of which is of interest of many processes. Besides, prediction of the flooding-loading transition in an aerated stirred tank is crucial for the correct design of aerated stirred tank reactors. In this research, laboratory investigation has been carried out on local and total power consumption of a single phase as well as gas-liquid phase systems in a fully baffled stirred tank equipped with dual six-blade Rushton turbines; moreover, the flow regime behavior of a gas-liquid system was investigated. Results have been compared with data obtained from CFD simulation of experimental setup and the data available in the literature. Reasonable agreement between the experimental and simulation results indicates the validity of the CFD model. Using predicted data some empirical correlations have been derived which present new relations in estimation of power consumption and flow regime transitions in stirred tanks with dual Rushton impellers.     

多层翼形桨搅拌槽内混合过程的CFD模拟

The mixing process in a stirred tank of 0.476m diameter with single, dual and triple 3-narrow blade hydrofoil CBY impellers was numerically simulated by using computational fluid dynamics （CFD） package FLU-ENT6.1. The multi-reference frame （MRF） and standard k-ε turbulent model were used in the simulation. The shaft power and the mixing time predicted by CFD were in good agreement with the experiment. The effects of tracer feeding and detecting positions on mixing time were investigated. The results are of importance to the optimum design of industrial stirred tank/reactors.     

STUDY OF THE TURBULENT FLOW IN AN UNBAFFLED STIRRED TANK BY DETACHED EDDY SIMULATION

Detached eddy simulation (DES) of the liquid-phase turbulent flow in an unbaffled stirred tank agitated by a six-blade, 45°-pitched blade turbine was performed in this study. The tank wall is cylindrical with no baffle and the fluid flow problem was solved in a single reference frame (SRF) rotating with the impeller. For the purpose of comparison, computation based on large eddy simulation (LES) was also carried out. The commercial code Fluent was used for all simulations. Predictions of the phase-averaged turbulent flow quantities and power consumption were conducted. Results obtained by DES were compared with experimental laser Doppler velocimetry (LDV) data from the literature and with the predictions obtained by LES. It was found that numerical results of mean velocity and turbulent kinetic energy profiles as well as the power consumption are in good agreement with the LDV data. When performed on the same computational grid, which is under-resolved in the sense of LES, DES allows better accuracy than LES in that it works better in the boundary layers on the surface of the impeller and the stirred tank walls. It can be concluded that DES has the potential to predict accurately the turbulent flow in stirred tanks and can be used as an effective tool to study the hydrodynamics in stirred tanks.     

Numerical Simulation of Macroscopic Mixing in a Rushton Impeller Stirred Tank

The macroscopic mixing in a stirred tank with different tracer injection locations, impeller speeds and impeller positions is simulated numerically by solving the transport equation of the tracer based on the whole flow field in the baffled tank with a Rushton disk turbine numerically resolved using the improved inner-outer iterative procedure. Predicted mixing time is compared well with the literature correlations. The predicted residence time distribution of the stirred tank is very close to the present experimental results. The effect of the installation of a draft tube on the mixing time and residence time distributions is addressed.     

Modeling of a cokneader for the manufacturing of composite materials having absorbent properties at ultra‐high‐frequency waves. Part 1: Modeling of flow from residence time distribution investigations

The purpose of this study is to gain better understanding of flow patterns and mixing conditions in a particular single‐screw extruder: the Buss Cokneader. To this end, the residence time distribution (RTD) of the polymer was investigated experimentally for different combinations of the operating variables (i.e. feed rate, screw rotation speed). The measurement of RTD used a standard stimulus‐response technique. Two kinds of tracer were used: free anthracene and anthracene grafted on the polymer. It was shown that only the second could characterize the actual flow of the polymer in the extruder. It does not perturb the flow and has the same rheological behavior as the studied fluid. Thanks to the RTD data, a model of the extruder based on the combination of ideal reactors, such as continuous stirred tank reactors or plug flow reactors, was finally set up. The establishment of relationships between model parameters and extrusion conditions allowed the prediction of RTD with good agreement.     

Modeling mixing dynamics in uncovered baffled and unbaffled stirred tanks

This paper presents results of measurements performed in uncovered baffled and unbaffled stirred tanks. The Laser Doppler Anemometry (LDA) set consists of a 300 mW argon-ion laser generating two pairs of blue and green beams. Additionally, three turbulence models are verified to simulate mixing dynamics in uncovered baffled and unbaffled stirred tanks. Simulations are performed using both the steady- and the transient-state approach. The unbaffled tank was modeled using both the single- and the multiphase approaches. The cited correlations of the central vortex depth are used to verify the multiphase calculations. In order to reduce the computational time, a simplified numerical model is proposed. It assumes a single-phase simulation without the central vortex. The flow fields below the central vortex level are compared between the single- and the multiphase approach. The simplified model can be used both to design and optimize the mixing process.