Suspension of solid particles in multi‐impeller three‐phase stirred tank reactors

Solids suspension characteristics in gas—liquid–solid three‐phase stirred tanks with multi‐impellers were experimentally examined. Minimum impeller speeds for ultimately homogeneous solid suspension have been measured stirred tank reactors. Three impellers were installed: two four‐pitched blade downflow disk turbines and one Pfaudler type impeller chosen to provide good gas dispersion and to accomplish off‐bottom suspension of solid particles, respectively. Gas dispersion causes an increase in particle sedimentation associated with a decrease in power consumption and as a result, minimum impeller speeds for ultimately homogeneous solid suspension increase with increasing gas flow rates. A correlation was developed to predict minimum impeller speeds for ultimately homogeneous solid suspension. The proposed correlation, which agrees satisfactorily with the experimental results, is expected to be useful in design and scale‐up.     

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.     

Large Eddy Simulation of Flow in Stirred Vessels

Large eddy simulations (LES) of the flow in stirred tanks were performed. One of the advantages with LES is that it can provide details of the flow field that cannot be obtained with so‐called Reynolds averaged equations and the corresponding models. Simulations were done on both single and multi‐impeller systems. Both Rushton and curved‐blade radial impellers were studied in both a fixed and a rotating frame of reference. The results show that the periodicity is much stronger and present in a larger part of the vessel for the Rushton turbine than for a curved‐blade turbine.     

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.     

Particle‐resolved PIV experiments of solid‐liquid mixing in a turbulent stirred tank

Particle Image Velocimetry (PIV) experiments on turbulent solid‐liquid stirred tank flow with careful refractive index matching of the two phases have been performed. The spatial resolution of the PIV data is finer than the size of the spherical, uniformly sized solid particles, thereby providing insight in the flow around individual particles. The impeller is a down‐pumping pitch‐blade turbine. The impeller‐based Reynolds number has been fixed to Re = 10⁴. Overall solids volume fractions up to 8% have been investigated. The PIV experiments are impeller‐angle resolved, that is, conditioned on the angular position of the impeller. The two‐phase systems are in partially suspended states with an inhomogeneous distribution of solids: high solids loadings near the bottom and near the outer walls of the tank, much less solids in the bulk of the tank. The liquid velocity fields show very strong phase coupling effects with the particles increasingly attenuating the overall circulation patterns as well as the liquid velocity fluctuation levels when the solids volume fraction is increased. © 2017 American Institute of Chemical Engineers AIChE J, 63: 389–402, 2018     

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.     

LDA measurements and CFD simulations of an in‐line high shear mixer with ultrafine teeth

Hydrodynamics of a pilot‐scale in‐line high shear mixer (HSM) with double rows of ultrafine rotor and stator teeth, including the velocity profiles and power consumptions, were measured using laser Doppler anemometry and a torque transducer, respectively. Computational fluid dynamics simulations were conducted using the standard k‐ε turbulence model with first‐ and second‐order accuracy and large eddy simulation (LES) with the standard Smagorinsky–Lilly subgrid scale model. Predictive capabilities of the different turbulence models and discretization schemes were assessed based on the experimental data. It is found that the current LES can predict accurately the flow patterns for the strongly rotating and locally anisotropic turbulent flows in the complex in‐line HSM. The results obtained are fundamental to explore potential applications of the in‐line teethed HSMs to intensify chemical reaction processes. © 2013 American Institute of Chemical Engineers AIChE J, 60: 1143–1155, 2014     

The Two‐Phase Flow in an Axially Stirred Vessel Investigated Using Phase‐Doppler Anemometry

The phase‐Doppler technique has been used to characterize the two‐phase flow of liquid and particles in a stirred vessel agitated by a pitched blade turbine. The number of measurement locations used is considerably larger than in previous investigations and the behaviour of four different types of particles is studied. The fluid phase and particle phase flow is studied with particular emphasis on the relative velocities of the two phases. The largest slip velocities in the tank were found just beneath the impeller, and large slip velocities generally coincide with large velocity gradients. Generally, particles lag in relation to the fluid when the fluid flow is directed upwards, and vice versa, but exceptions to this are not unusual.     

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.     

Numerical simulation of a pitched‐blade turbine stirred tank with mirror fluid method

Mirror fluid method [Yang and Mao, Phys. Rev. 2005; E 71:036704] combined with local grid refinement is proposed to deal with the numerical simulation of turbulent flow in a pitched‐blade turbine stirred tank. By such a novel method, the domain occupied by the impeller is assigned suitable flow parameters explicitly by the mirror relation, so that the correct shear and normal forces on the fluid side of an interface segment is eventually guaranteed. Satisfactory agreement between our predictions and the reported experimental data is achieved both in single‐phase baffled or unbaffled stirred tanks and solid–liquid two‐phase systems. © 2012 Canadian Society for Chemical Engineering     

A Multi‐Block Approach to Obtain Angle‐Resolved PIV Measurements of the Mean Flow and Turbulence Fields in a Stirred Vessel

Two‐dimensional Particle Image Velocimetry (PIV) measurements have been used to characterize the complex turbulent flow generated by a T/3 45° pitched‐blade down‐flow turbine, operated at Re ≈ 5 · 10⁴, in a fully turbulent stirred vessel. To maintain high spatial resolution when viewing the whole vessel, a multi‐block approach has been developed, which combines data from different fields of view into a composite flow map. Using 500 measurements of instantaneous u and v velocity fields, angle‐resolved mean velocity maps and turbulence properties, such as the RMS velocities and the turbulence kinetic energy, have been estimated near to the blade, as well as in the bulk of the vessel, at a spatial resolution of between 1 and 2 mm. Vorticity maps have also been calculated to help visualize the trailing vortex structures close to the impeller blades and integral length scales have been estimated from the two‐dimensional spatial auto‐correlation function. It is shown than the common assumption that the integral length scale is about half the blade width is an overestimate close to the impeller and an underestimate far from the impeller.     

Multiphase Stirred Tank Bioreactors – New Geometrical Concepts and Scale‐up Approaches

Mainly with respect to biotechnological cases, current developments in the field of impeller geometries and findings for multistage configurations with a specific view on aerated stirred tanks are reviewed. Although often the first choice, in the given case the 6‐straight blade disc turbine is usually not the best option. Furthermore, quantities usable for scale‐up, specifically applicable in this field are discussed. Only quantities taking local conditions into account appear to be able to actually compare different stirrer types and scales.     

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。     

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.     

涡流桨搅拌槽内流动非稳定性的大涡模拟

The aim of this work is to investigate the flow instabilities in a baffled, stirred tank generated by a single Rushton turbine by means of large eddy simulation （LES）. The sliding mesh method was used for the coupling between the rotating and the stationary frame of references. The calculations were carried out on the ＂Shengcao-21C＂ supercomputer using a computational fluid dynamics （CFD） code CFX5. The flow fields predicted by the LES simulation and the simulation using standard κ-ε model were compared to the results from particle image velocimetry （PIV） measurements. It is shown that the CFD simulations using the LES approach and the standard κ-ε model agree well with the PIV measurements. Fluctuations of the radial and axial velocity are predicted at different frequencies by the LES simulation. Velocity fluctuations of high frequencies are seen in the impeller region, while low frequencies velocity fluctuations are observed in the bulk flow. A low frequency velocity fluctuation with a nondimensional frequency of 0.027Hz is predicted by the LES simulation, which agrees with experimental investigations in the literature. Flow circulation patterns predicted by the LES simulation are asymmetric, stochastic and complex, spanning a large portion of the tanks and varying with time, while circulation patterns calculated by the simulation using the standard κ-ε model are symmetric. The results of the present work give better understanding to the flow instabilities in the mechanically agitated tank. However, further analysis of the LES calculated velocity series by means of fast Fourier transform （FFT） and/or spectra analysis are recommended in future work in order to gain more knowledge of the complicated flow phenomena.     

Turbulent flow field in a stirred vessel agitated by an Impeller with flexible blades

In order to reveal the effect of the blades normal vibration on flow turbulence in the stirred vessel, we designed three kinds of blades: the flexible, flat‐rigid and curved‐rigid blades. The flow fields produced by the impellers with these three kinds of blades were measured by two‐dimensional particle image velocimetry. The results showed that the calculated turbulent kinetic energy (TKE) based on the pseudo‐isotropic assumption is slightly higher than that by the three fluctuating velocities for the flexible and curved‐rigid impellers, and the difference between above two calculations is smaller for the former impeller. For the flexible blades, the trailing vortices slightly move outwards in radial direction than those for the curved‐rigid blades, enhancing TKE transport from the blade to the bulk region of the vessel. For the flexible impeller, the phase‐averaged TKE differs slightly from that for the flat‐rigid impeller, but is higher than that for the curved‐rigid impeller. © 2018 American Institute of Chemical Engineers AIChE J, 64: 4148–4161, 2018     

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.     

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.