Reynolds number scaling of flow in a stirred tank with Rushton turbine. Part II — Eigen decomposition of fluctuation

We consider the question of scaling of flow within a stirred tank with increasing Reynolds number. Experimental results obtained from two different tanks of diameter 15.25 and 29.21 cm with a Rushton turbine operating at a wide range of rotational speed is considered for the scaling analysis. The resulting Reynolds number of the flow ranges from 4000 to about 80,000. Phase locked stereoscopic PIV measurements have been performed in order to obtain all three components of velocity on three different vertical planes close to the impeller. The scaling of plane-averaged mean flow was explored in the companion part-I of the paper. The scaling of rms and skewness of fluctuation about the mean is investigated here. The fluctuation about the mean is explained in terms of time-dependent oscillation of the impeller-induced jet and tip vortex components of the flow. The spatial structure of the instantaneous fluctuation about the mean is investigated in terms of eigenmodes obtained using proper orthogonal decomposition with the method of snapshots. The scaling of energy content of the dominant eigenmodes with Re is investigated.     

Laser-Doppler measurements of the turbulent flow in stirred vessels to establish scaling rules

A laser-Doppler velocimeter, equipped with a frequency shift so as to eliminate directional ambiguity, has been used to measure the turbulent flow in stirred vessels with diameters of 0.12, 0.29 and 0.90 m of the same geometry. The vessels contained water and measurements were done in the impeller stream region. Scaling rules have been derived for average velocity, the periodic component, turbulent intensities and turbulence power spectra.It appears that close to the impeller the flow is dominated by the periodically fluctuating flow of the trailing vortices behind the impeller blades. The normalized mean velocity in the trailing vortices, and therefore the turbulence intensity close to the impeller, is very sensitive to impeller geometry and shows a slight increase with size of the vessel. In the greater part of the impeller stream region the power spectra have a section with a ?$\text{5}\text{2}$ slope on a log-log scale and consequently the energy of the small eddies decreases with increasing scale. At the vessel wall the vortices have decayed completely to random turbulence and the spectrum shows a ? $\text{5}\text{3}$ slope.     

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.     

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     

Analysis of dominant flow structures and their flow dynamics in chemical process equipment using snapshot proper orthogonal decomposition technique

Snapshot proper orthogonal decomposition (POD) technique has been applied to reveal the dominant flow structures, their dynamics and length scales in six widely used industrial equipments (stirred tank, bubble column, Taylor-Couette flow (annual contactor), ultrasonic reactor, jet reactor, and channel flow). The variation in length scale of structures within an equipment, with change in its operating conditions (Reynolds number and power input) or change in its geometric configuration (sparger and impeller designs), has been brought out in this work. The planar data set for POD analysis was obtained from particle image velocimetry (PIV) and large eddy simulation (LES) studies. The dominant spatial topology was analyzed by using the velocity and vorticity POD modes. The modes have revealed the following flow structures: the ascending streaks and bursts in channel flow, the vortex tube and leading edge vortices in jets, the irregular small chaotic vortices in Taylor-Couette flow, the variation in plume oscillation and flow structures in the vortical region of bubble column resulting from changes in sparger design, the high intensity vortices near the source of ultrasound in the ultrasonic reactor and the effect of impeller designs on dominant flow structures and near blade vortices in the stirred tank. The length scales of structures are obtained by applying image processing on the spatial modes. The dynamics of these flow structures in each of the items of equipment is captured by reconstructing the flow field using appropriate spatial and temporal modes that contribute to these structures. Further, a unique attempt has been made to correlate the length scale distribution with the mixing time.     

TURBULENT FLOW IN STIRRED TANKS: SCALE-UP COMPUTATIONS FOR VESSEL HYDRODYNAMICS

A numeric model for turbulent flow was used to compute the flow patterns in Rushton turbine agitated vessels. The cases considered cover two orders of magnitude for the three different scaling criteria of constant impeller Reynolds number, power input per unit mass, and impeller tip speed. The constant power input scale-up criteria maintains the turbulence levels throughout the vessel during scale-up. The circulation times, however, increase with vessel size for this scaling criteria. The other scaling criteria of constant impeller tip speed and impeller Reyonds number lead to decreasing turbulence levels in the tank along with further increases in circulation times.     

Numerical simulation of fluid dynamics in the stirred tank by the SSG Reynolds Stress Model

The Speziale, Sarkar and Gatski Reynolds Stress Model (SSG RSM) is utilized to simulate the fluid dynamics in a full baffled stirred tank with a Rushton turbine impeller. Four levels of grid resolutions are chosen to determine an optimised number of grids for further simulations. CFD model data in terms of the flow field, trailing vortex, and the power number are compared with published experimental results. The comparison shows that the global fluid dynamics throughout the stirred tank and the local characteristics of trailing vortices near the blade tips can be captured by the SSG RSM. The predicted mean velocity components in axial, radial and tangential direction are also in good agreement with experiment data. The power number predicted is quite close to the designed value, which demonstrates that this model can accurately calculate the power number in the stirred tank. Therefore, the simulation by using a combination of SSG RSM and MRF impeller rotational model can accurately model turbulent fluid flow in the stirred tank, and it offers an alternative method for design and optimisation of stirred tanks.     

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     

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.     

An assessment of different turbulence models for predicting flow in a baffled tank stirred with a Rushton turbine

This work presents a comprehensive study of different turbulence models, including the k–ε, SST, SSG–RSM and the SAS–SST models, for simulating turbulent flow in a baffled tank stirred with a Rushton turbine. All the turbulence models tested predict the mean axial and tangential velocities reasonably well, but under-predict the decay of mean radial velocity away from the impeller. The k–ε model predicts poorly the generation and dissipation of turbulence in the vicinity of the impeller. This contrasts with the SST model, which properly predicts the appearance of maxima in the turbulence kinetic energy and turbulence energy dissipation rate just off the impeller blades. Curvature correction improves the SST model by allowing a more accurate prediction of the magnitude and location of these maxima. However, neither the k–ε nor the SST model is able to properly capture the chaotic and three-dimensional nature of the trailing vortices that form downstream of the blades of the impeller. In this sense, the SAS–SST model produces more physical predictions. However, this model has some drawbacks for modelling stirred tanks, such as the large number of modelled revolutions required to obtain good statistical averaging for calculating turbulence quantities. Taking into consideration both accuracy and solution time, the SSG–RSM model is the least satisfactory model tested for predicting turbulent flow in a baffled stirred tank with a Rushton turbine.     

Numerical investigation of bend and torus flows—Part II : Flow simulation in torus reactor

Flow in a torus reactor with straight parts fitted with a marine impeller is investigated. The laser Doppler anemometry (LDA) is first employed to achieve experimental measurements of mean velocity profiles. Next, a numerical resolution of the steady-state flow is performed using a multiple reference frames (MRF) approach to represent the particular flow induced by the marine impeller in the geometry. A comparison of predictions using different turbulence models to LDA measurements is made, and a k-ω model is assessed.The numerical tool is used to investigate in more details the particular flow induced in the torus geometry. Evolution of the axial and rotating motions when moving away from the impeller is especially investigated, showing the complex hydrodynamical interaction between the main rotating swirl motion involved downstream the impeller, and bend curvature effects. Two different flow conditions can be considered in the torus geometry, with a main swirling motion close to the impeller, which freely decays and vanishes when Dean vortices appear in bends. Simulations for two rotation velocities of the impeller and comparison with the study with simple bends (first part) reveal pertinence of the swirl number Sn to describe the change of flow conditions along the reactor axis. When this parameter decreases below a threshold value around 0.2 in a bend entry, centrifugal effects due to bend curvature are more important than the swirl motion, and Dean vortices appear in bend outlet. One main consequence is the axial distance of the swirl motion persistence, which is found to be smaller for the higher impeller rotation velocity, due to the dual effect of the marine impeller that generates simultaneously both axial and rotating motions.     

CFD simulation and PIV measurement of the flow field generated by modified pitched blade turbine impellers

The hydrodynamics generated by modified pitched blade turbine (m-PBT) impellers with down-pumping mode were systematically investigated through particle image velocimetry (PIV) measurements and computational fluid dynamics simulations. The simulated mean axial velocity, mean radial velocity, and turbulent kinetic energy by the standard k–? turbulent model were validated against the measured PIV data. This shows that the standard k–? turbulent model predicts mean velocity well, but underestimates turbulent kinetic energy near the blade. The flow field and power consumption as well as pumping number for the m-PBT and the standard PBT impeller were predicted. The simulation results demonstrate that a few simple changes of the blade shape influence the velocity distribution, i.e., increasing the magnitude of mean velocity in the vicinity of impeller, and that the m-PBT impeller has a higher pumping efficiency than the standard one.     

偏心搅拌槽内宏观不稳定性的分离涡模拟

为研究偏心搅拌槽内的宏观不稳定性,基于分离涡模型建立了偏心搅拌数值模拟方法。采用滑移网格法模拟搅拌桨的旋转,实现了偏心搅拌流场的非稳态模拟。对不同工况时的宏观不稳定性进行了频谱分析,讨论了偏心率、雷诺数和桨径比对宏观不稳定频率的影响,并进行了PIV实验验证。研究表明,偏心搅拌槽内存在明显的宏观不稳定现象,其变化周期约为桨叶通过周期的10倍;PIV实验结果与分离涡模拟结果吻合较好,都表明偏心搅拌槽内的宏观不稳定频率随雷诺数的升高而增大,随偏心率的增大而减小,随桨径比的增大而增大。     

Dimensional analysis for planetary mixer: Mixing time and Reynolds numbers

Mixing time number is a convenient parameter to characterize mixing performance of stirred tanks. This dimensionless number is now well established for agitated vessels equipped with vertically and centrally mounted impeller for Newtonian as well as for non-Newtonian fluids. To our knowledge, there is more ambiguity concerning its definition for planetary mixers especially when they have dual motion (around two perpendicular axes) to achieve homogenization. In this study, dimensional analysis of mixing time and reliability of the modified Reynolds and mixing time numbers are proposed for such a planetary mixer particularly named as TRIAXE^® system. These two numbers are based on the maximum tip speed of mixer as the characteristic velocity. Modified dimensionless numbers are consistent with the definition of conventional Reynolds and mixing numbers (when only one revolving motion around the vertical axis of the mixing device occurs in the vessel).Mixing time experiments with TRIAXE^® mixer for highly viscous Newtonian fluids showed that the proposed modified Reynolds and mixing time numbers succeeded to obtain a unique mixing curve irrespective of the different speed ratio chosens. This agreement proves that the proposed modified dimensionless numbers can be well adapted for engineering purposes and they can be used to compare the mixing performance of planetary mixers.     

Continued self-similar breakup of drops in viscous continuous phase in agitated vessels

Drop breakup in viscous liquids in agitated vessels occurs in elongational flow around impeller blade edges. The drop size distributions measured over extended periods for impellers of different sizes show that breakup process continues up to 15–20 h, before a steady state is reached. The size distributions evolve in a self-similar way till the steady state is reached. The scaled size distributions vary with impeller size and impeller speed, in contrast with the near universal scaling known for drop breakup in turbulent flows. The steady state size of the largest drop follows inverse scaling with impeller tip velocity. The breadth of the scaled size distributions also shows a monotonic relationship with impeller tip velocity only.     

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。     

内插梯形扰流片的矩形通道内涡流和传热特性

利用Realizable k-ε湍流模型对带缺口的梯形扰流片进行流动和传热特性的数值模拟,研究了梯形扰流片的缺口位置及流动方式对矩形通道内流场以及传热的影响,同时通过对涡量、流线、流速分布、压力变化、湍流强度等的分析,揭示了扰流片强化传热的机理。结果表明,逆流时Nusselt数比顺流时提高了21.7%,同时摩擦因子也提高了25%。顺流时内侧缺口绕流片提高了传热系数的同时也增加了摩擦阻力,而外侧缺口的绕流片降低了传热系数同时也降低了形状阻力。研究发现较低Reynolds数下(10000相似文献   

Characterization of the bubble swarm trajectory in a jet bubbling reactor

The bubble swarm trajectory in the jet bubbling reactor is measured through the bubble image velocimetry (BIV) technique. The result shows that the bubble swarm rises straightly when the jet Reynolds number is lower than 7,000. However, when the jet Reynolds number exceeds 14,000, the bubble swarm exhibits vortex-like motion, and the bubble vortices oscillate periodically. The oscillating frequency of bubble vortices under the gas bubbling condition is lower than the flapping frequency of pure liquid jet. Moreover, the moving region and oscillating frequency of bubble vortices increase with the jet Reynolds number. The superficial gas velocity has little effect on the bubble swarm trajectory and the oscillating frequency. An empirical correlation between the oscillating frequency of bubble vortices and the jet Reynolds number is built based on the simple harmonic vibration theory.     

Experimental and numerical characterization of viscous flow and mixing in an impinging jet contactor

The laminar flow in an impinging jet contactor is examined as a first step toward the development of new technology for fast mixing of viscous fluids. The flow, velocity, and stretching fields in an impinging jet contactor are quantified for low Reynolds number flow using three-dimensional numerical simulations and particle image velocimetry measurements. Computational and experimental velocity fields are in close agreement, as quantified by the velocity probability density functions. Two steady-state flow regimes are found to exist: for jet Reynolds numbers (Re_j) < 10, the jets do not impinge and the velocity field scales linearly with Reynolds number; for Re_j > 10, the jets begin to impinge and recirculation regions form above and below the impingement point. The magnitude of the rate-of-strain tensor is calculated as a function of Re_j. While areas of essentially zero stretching occupy most of the flow domain, very high rates of stretching occur at specific locations in the flow. The maximum and average rates of stretching in the contactor increase roughly linearly as a function of Reynolds number. Mixing simulations show that no mixing occurs for the steady flow in a symmetric-jet contactor. However, mixing is improved substantially by a slight modification of the impinging jet geometry that disrupts geometric symmetry.