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.     

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.     

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。     

Assessment of large eddy and RANS stirred tank simulations by means of LDA

Large eddy simulations (LES) and Reynolds-averaged Navier-Stokes (RANS) calculations were performed on the flow in a baffled stirred tank, driven by a Rushton turbine at Re=7300. The LES methodology provides detailed flow information as velocity fluctuations are resolved down to the scale of the numerical grid. The Smagorinsky and Voke subgrid-scale models used in the LES were embedded in a numerical lattice-Boltzmann scheme for discretizing the Navier-Stokes equations, and an adaptive force-field technique was used for modeling the geometry. The uniform, cubic computational grid had a size of 240³ grid nodes. The RANS calculations were performed using the computational fluid dynamics code CFX 5.5.1. A transient sliding mesh procedure was applied in combination with the shear-stress-transport (SST) turbulence closure model. The mesh used for the RANS calculation consisted of 241464 nodes and 228096 elements (hexahedrons). Phase-averaged and phase-resolved flow field data, as well as turbulence characteristics, based on the LES and RANS results, are compared both mutually and with a single set of experimental data.     

Stereo‐PIV experiments and large eddy simulations of flow fields in stirred tanks with Rushton and curved‐Blade turbines

The flow characteristics in pilot‐scale stirred tanks with Rushton and curved‐blade turbines were investigated by using stereoscopic particle image velocimetry (SPIV) experiments and large eddy simulation (LES) methods. The velocity and turbulent kinetic energy (TKE) in the impeller discharge regions were carefully resolved with a high resolution SPIV system, and the detailed phase‐resolved velocity and TKE profiles were used to validate the LES results. The effects of Reynolds number and blade shape on the flow characteristics were discussed. The LES results of velocity, TKE, and the evolution of trailing vortices were compared with the SPIV experimental data, and good agreement was obtained at various phase angles. The effects of subgrid scale model and hybrid grid with different mesh resolutions on the LES results were investigated. LES is a computationally affordable method for the accurate predictions of the complex flow fields in pilot‐scale stirred tanks is presented. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3986–4003, 2013     

PIV experiments and large eddy simulations of single-loop flow fields in Rushton turbine stirred tanks

The single-loop flow fields in Rushton turbine stirred tanks with clearance C=0.15T (T is tank diameter) were investigated by using particle image velocimetry (PIV) experiments and large eddy simulation (LES) methods. The velocity and turbulent kinetic energy (TKE) were carefully measured and resolved with high resolution camera. The regions with high TKE are affected by the movement of the trailing vortices generated behind the impeller blades. The effects of both geometrical configuration and Reynolds number were discussed. It is found that the Reynolds number has little effect on the mean flow for the configuration of impeller diameter D=T/3, C=0.15T. However, the single-loop flow pattern is changed into a double-loop one if D is increased from T/3 to T/2. The LES results were compared with the PIV experiments and the laser Doppler anemometry (LDA) data in the literature. The effect of the grid was validated, and the levels of local anisotropy of turbulence near the impeller discharge regions were investigated. Both the phase-averaged and phase-resolved LES results are in good agreement with the PIV experimental data, and are better than the predictions of the k–ε model. The agreement shows that the LES method can be used to simulate the complex flow fields in stirred tanks.     

大涡模拟搅拌槽中的液相流动

采采用大涡模拟湍流模型对有档板的Rushton 桨搅拌槽进行了数值模拟研究。控制方程采用控制容积法进行离散,对流项用三阶QUICK格式,扩散项是二阶中心差分。压力 速度耦合方程在交错网格上采用SIMPLE算法进行求解。小尺度流动的模化采用动力学（dynamic）亚格子模型。搅拌桨与档板之间的相互作用采用改进的内外迭代法进行处理。计算结果和文献值吻合得很好。     

用大涡模拟结合改进的内外迭代法数值模拟搅拌槽中的液相流动

1 INTRODUCTION Stirred tank reactors are widely encountered in the chemical, pharmaceutical, and hydrometallurgical proc- esses. The fluid motion in stirred tanks is three-dimensional, complex, and covers a wide range of spatial and temporal scales. In the area surrounding the impeller, the flow is highly turbulent and swirling. The numerical simulation of such reactor systems is helpful in quantifying the effects of the impeller type, geometry, and the operational conditions in order to …     

涡轮桨搅拌槽内单循环流动特性的大涡模拟

利用大涡模拟方法研究了涡轮桨搅拌槽内的单循环流动特性,采用Smagorinsky-Lilly动力亚格子模式,与文献实验及模拟数据进行了详细的比较. 结果表明,叶片后方的双尾涡偏向槽底运动,上尾涡在30o处已开始衰减. 800000个非均匀分布的计算网格和30个桨叶旋转周期的样本数据统计可获得准确的大涡模拟数据. 时均速度、均方根速度和湍流动能的大涡模拟值与实验数据一致,而k-e模型的模拟值与实验不符. 桨叶区呈现较强的各向异性,这是导致k-e模型预测不准确的主要原因. 对于搅拌槽内的复杂流动,大涡模拟方法是一个非常有效的工具.     

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.     

CFD simulation of stirred tanks: Comparison of turbulence models. Part I: Radial flow impellers

A critical review of the published literature regarding the computational fluid dynamics (CFD) modelling of single‐phase turbulent flow in stirred tank reactors is presented. In this part of review, CFD simulations of radial flow impellers (mainly disc turbine (DT)) in a fully baffled vessel operating in a turbulent regime have been presented. Simulated results obtained with different impeller modelling approaches (impeller boundary condition, multiple reference frame, computational snap shot and the sliding mesh approaches) and different turbulence models (standard k ? ε model, RNG k ? ε model, the Reynolds stress model (RSM) and large eddy simulation) have been compared with the in‐house laser Doppler anemometry (LDA) experimental data. In addition, recently proposed modifications to the standard k ? ε models were also evaluated. The model predictions (of all the mean velocities, turbulent kinetic energy and its dissipation rate) have been compared with the experimental measurements at various locations in the tank. A discussion is presented to highlight strengths and weaknesses of currently used CFD models. A preliminary analysis of sensitivity of modelling assumptions in the k ? ε models and RSM has been carried out using LES database. The quantitative comparison of exact and modelled turbulence production, transport and dissipation terms has highlighted the reasons behind the partial success of various modifications of standard k ? ε model as well as RSM. The volume integral of predicted energy dissipation rate is compared with the energy input rate. Based on these results, suggestions have been made for the future work in this area.     

CFD Prediction of the Critical Agitation Speed for Complete Dispersion in Liquid‐Liquid Stirred Reactors

A computational fluid dynamics (CFD) model is adopted to simulate the turbulent immiscible liquid‐liquid flow in a stirred vessel based on a two‐fluid model with a k‐ϵ‐A_P turbulence model. An improved inner‐outer iterative procedure is adopted to deal with the impeller rotation in a fully baffled stirred tank. Different drag formulations are examined, and the effect of the droplet size on both the dispersed phase holdup distribution and the velocity field is analyzed. Two different numerical criteria are tested for determining the critical impeller speed for complete dispersion. The simulated critical impeller speeds are generally in good agreement with the correlations in the literature when the fixed droplet size is properly selected. This demonstrates that the modeling approach and the numerical criteria proposed in this work are promising for predicting the dispersion characteristics in liquid‐liquid stirred tanks.     

Analysis of stirred tanks with two‐zone models

Stirred tank turbulence and fluid flow characteristics are analyzed based on a two‐zone model. Instead of using the zonal model for stirred tank performance prediction as often proposed in the literature, the zoning is used here as a tool for mixing analysis. A systematic zoning approach is proposed, where the tank is divided into two nested regions. By gradually increasing the inner zone volume, continuous curves can be obtained for turbulent energy dissipation distribution and pumping numbers between the zones as functions of the zone sizes. It is shown here that these curves can be used as a powerful tool for visualizing stirred tank performance. They can be used, e.g., in impeller performance comparisons and analysis of mixing characteristics with changing rheology, or to examine various numerical aspects related to stirred tank CFD modeling. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Transitional flow in a Rushton turbine stirred tank

The way in which the single phase flow of Newtonian liquids in the vicinity of the impeller in a Rushton turbine stirred tank goes through a laminar‐turbulent transition has been studied in detail experimentally (with Particle Image Velocimetry) as well as computationally. For Reynolds numbers equal to or higher than 6000, the average velocities and velocity fluctuation levels scale well with the impeller tip speed, that is, show Reynolds independent behavior. Surprising flow structures were measured—and confirmed through independent experimental repetitions—at Reynolds numbers around 1300. Upon reducing the Reynolds number from values in the fully turbulent regime, the trailing vortex system behind the impeller blades weakens with the upper vortex weakening much stronger than the lower vortex. Simulations with a variety of methods (direct numerical simulations, transitional turbulence modeling) and software implementations (ANSYS‐Fluent commercial software, lattice‐Boltzmann in‐house software) have only partial success in representing the experimentally observed laminar‐turbulent transition. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3610–3623, 2017     

半椭圆管盘式涡轮桨搅拌槽内湍流结构的时间解析PIV研究(英文)

The turbulence structure in the stirred tank with a deep hollow blade (semi-ellispe) disc turbine (HEDT) was investigated by using time-resolved particle image velocimetry (TRPIV) and traditional PIV. In the stirred tank, the turbulence generated by blade passage includes the periodic components and the random turbulent ones. Traditional PIV with angle-resolved measurement and TRPIV with wavelet analysis were both used to obtain the random turbulent kinetic energy as a comparison. The wavelet analysis method was successfully used in this work to separate the random turbulent kinetic energy. The distributions of the periodic kinetic energy and the random turbulent kinetic energy were obtained. In the impeller region, the averaged random turbulent kinetic energy was about 2.6 times of the averaged periodic one. The kinetic energies at different wavelet scales from a6 to d1 were also calculated and compared. TRPIV was used to record the sequence of instantaneous velocity in the impeller stream. The evolution of the impeller stream was observed clearly and the sequence of the vorticity field was also obtained for the identification of vortices. The slope of the energy spectrum was approximately &;#61485;5/3 in high frequency representing the existence of inertial subrange and some isotropic properties in stirred tank. From the power spectral density (PSD), one peak existed evidently, which was located at f0 (blade passage frequency) generated by the blade passage.     

Numerical Investigation of Three‐Dimensional Bubble Column Flows: A Detached Eddy Simulation Approach

Numerical simulations were performed employing detached eddy simulation (DES) in a three‐dimensional transient Euler‐Euler framework for bubble columns, and all the computational fluid dynamics results were compared with a k‐? model and available experimental data. The numerical results are in good agreement with the experiments in predicting the time‐averaged axial velocity and turbulent kinetic energy profiles. The flow‐resolving capabilities of the DES model are highlighted, and it is shown that the DES turbulence model can be efficiently used for simulating flow field and turbulent quantities in the case of bubble columns.     

Perturbed turbulent stirred tank flows with amplitude and mode-shape variations

Stirred tank (STR) flows at low and moderate Reynolds numbers show poor mixing behavior due to formation of segregated zones inside which both magnitude and fluctuation level of velocity components show lower values compared to the active fluid regime (i.e., impeller jet stream, circulation loops). Active perturbation of the STR flow using a time-dependent impeller rotational speed can potentially enhance mixing by breaking up these segregated unmixed zones and enhancing the turbulence level throughout the tank volume. In the present study, the effect of different perturbation cycles on an unbaffled turbulent stirred tank flow at a moderate Reynolds number (rotational speed N=3 rps) is studied using a large-eddy simulation (LES) technique coupled with immersed boundary method (IBM). The perturbation frequency (f) is chosen to correspond to a dominant macro-instability in the flow (f/N=0.022). Two different perturbation amplitudes (20% and 66%) and two perturbation shapes (square-wave and sine-wave) are investigated, and changes in the mean flow field, turbulence level and impeller jet spreading are examined. Large-scale periodic velocity fluctuations due to perturbations are noticed to produce large strain rates favoring higher turbulence levels inside the tank. Production of turbulent kinetic energy due to both the mean and periodic component of the velocity field is presented. Fluctuations in power consumption due to perturbation are also calculated, and shown to correlate with the perturbation amplitude.     

涡轮桨搅拌槽内湍流特性的V3V实验及大涡模拟

分别用体三维速度测量技术（volumetric three-component velocimetry measurements,V3V）和大涡模拟（large eddy simulation,LES）方法对涡轮桨搅拌槽内流场进行研究,发现在完全湍流状态下,涡轮桨搅拌槽内流场的量纲1相平均速度及湍动能分布同Reynolds数无关。用V3V方法实现了Rushton桨叶附近三维流场的重构;探讨尾涡的三维结构及运动规律;分析了叶片后方30°截面轴向、径向和环向速度沿径向分布规律。用V3V实验结果对比了2D-PIV（particle image velocimetry）数据中的尾涡涡对位置和涡量,涡对位置吻合度较好,但2D-PIV中涡量较V3V小37.5%;通过大涡模拟得到完整的尾涡结构,发现在叶片上边缘后侧存在一个和尾涡形成方式相同但不成对出现的涡结构;将大涡模拟结果和2D-PIV及V3V实验结果对比发现,大涡模拟在速度分布及尾涡运动轨迹方面均同实验结果吻合较好,表明大涡模拟能较好地预测涡轮桨搅拌槽内流场。     

Unsteady RANS and detached eddy simulation of the multiphase flow in a co-current spray drying☆

A detached eddy simulation (DES) and a k-ε-based Reynolds-averaged Navier–Stokes (RANS) calculation on the co-current spray drying chamber is presented. The DES used here is based on the Spalart–Al maras (SA) turbu-lence model, whereas the standard k-ε(SKE) was considered here for comparison purposes. Predictions of the mean axial velocity, temperature and humidity profile have been evaluated and compared with experimental measurements. The effects of the turbulence model on the predictions of the mean axial velocity, temperature and the humidity profile are most noticeable in the (highly anisotropic) spraying region. The findings suggest that DES provide a more accurate prediction (with error less than 5%) of the flow field in a spray drying chamber compared with RANS-based k-εmodels. The DES simulation also confirmed the presence of anisotropic turbulent flow in the spray dryer from the analysis of the velocity component fluctuations and turbulent structure as il us-trated by the Q-criterion.     

Experiments and Simulations on Bidisperse Solids Suspension in a Mixing Tank

Experiments and simulations of a solids suspension process in a lab‐scale stirred tank under turbulent conditions have been performed. Two impellers have been tested. The liquid‐solid suspension consists of water and a mixture of glass and bronze particles. The simulations are Eulerian‐Lagrangian with the liquid flow as the Eulerian part, being solved by means of a lattice‐Boltzmann method combined with a large‐eddy approach to turbulence modeling. Comparison with experimental visualizations indicates that the simulations are able to represent the start‐up of the suspension process from a zero‐velocity initial condition. Differences between experiment and simulation are observed near the bottom of the tank. The simulation data are used to highlight the collisional interaction between the two different types of solids, the role of baffles, and the effect of impeller type on the suspension process.