CFD analysis of turbulence in a baffled stirred tank, a three-compartment model

Three-compartment model was used to study non-homogeneity of mixing in a fully baffled stirred tank. Multiple reference frame (MRF) technique was used for calculations. Calculations were performed to study the effects of agitator speed, impeller diameter, baffle width and distance of impeller from bottom of the tank on turbulent flow field. Three different zones of the vessel, that were a small zone near the impeller, another zone around the baffles, and a relatively large zone far from the impeller and baffles, named circulation zone, were investigated. Boundaries of these zones were determined using two different methods. The first method used gradient of energy dissipation rate while the other method used cumulative energy dissipation rate to determine the zone boundaries. Zone boundaries determined by both methods were comparable. The turbulent kinetic energy dissipation rate gradient was the preferred method due to its simplicity. Turbulent kinetic energy dissipation rate increased with agitator speed in all zones. Both turbulent kinetic energy dissipation rate and turbulent kinetic energy showed considerable change with impeller diameter at impeller zone, while no remarkable change was observed at baffle and circulation zones. Three-compartment model parameters, impeller and baffle energy dissipation ratios λ_i, λ_b, impeller and baffle volume ratios μ_i, μ_b and impeller and baffle exchange flow rates Q_i, Q_b were obtained from CFD simulations. Impeller energy dissipation ratio, impeller exchange flow rate and baffle exchange flow rate increased while baffle volume ratio decreased with agitation rate and impeller diameter. Baffle energy dissipation ratio and impeller volume ratio showed no considerable change with agitation rate and impeller diameter.     

Analysis of energy dissipation in stirred suspension polymerisation reactors using computational fluid dynamics

This work evaluates the spatial distribution of normalised rates of droplet breakage and droplet coalescence in liquid–liquid dispersions maintained in agitated tanks at operation conditions normally used to perform suspension polymerisation reactions. Particularly, simulations are performed with multiphase computational fluid dynamics (CFD) models to represent the flow field in liquid–liquid styrene suspension polymerisation reactors for the first time. CFD tools are used first to compute the spatial distribution of the turbulent energy dissipation rates (ε) inside the reaction vessel; afterwards, normalised rates of droplet breakage and particle coalescence are computed as functions of ε. Surprisingly, multiphase simulations showed that the rates of energy dissipation can be very high near the free vortex surfaces, which has been completely neglected in previous works. The obtained results indicate the existence of extremely large energy dissipation gradients inside the vessel, so that particle breakage occurs primarily in very small regions that surround the impeller and the free vortex surface, while particle coalescence takes place in the liquid bulk. As a consequence, particle breakage should be regarded as an independent source term or a boundary phenomenon. Based on the obtained results, it can be very difficult to justify the use of isotropic assumptions to formulate particle population balances in similar systems, even when multiple compartment models are used to describe the fluid dynamic behaviour of the agitated vessel. © 2011 Canadian Society for Chemical Engineering     

On the influence of mixing on crystal precipitation processes—application of the segregated feed model

The segregated feed model (SFM), a compartmental mixing model, is used to predict the influence of mixing on crystal precipitation. In this method, the population balance is solved simultaneously with the mass balances using crystallisation kinetic, solubility and computational fluid dynamics (CFD) mixing data. Mean properties are calculated for the three different zones of the reactor (two feed zones and bulk zone). It is predicted that during continuous operation, the product particle size exhibits oscillating behaviour before reaching steady state after about ten residence times. In contrast, the second moment (surface area) sharply increases during the first residence time and remains constant thereafter.Different mixing conditions are modelled by varying the mesomixing and micromixing times, which can be regarded as convective and diffusive exchange parameters between the compartments of the reactor. The overall nucleation rate is found to strongly depend on the mixing conditions, as it depends in a highly non-linear manner on the level of supersaturation. In consequence, the nucleation rate varies over three orders of magnitude between ‘good’ and ‘poor’ mixing conditions. Using the SFM, the effect of different feed points, feed rates, feed tube diameters, energy dissipation rates, impeller types and vessel sizes on the nucleation rate and the particle size during crystal precipitation is illuminated. Predictions of the model compare favourably with batch and continuous experimental data for calcium oxalate.     

Characterization of flow phenomena induced by ultrasonic horn

Mean flow and turbulence parameters have been measured using laser Doppler anemometer (LDA) in ultrasound reactor. The effects of the ultrasonic power have been investigated over a power density (P/V) range of 15-. The liquid circulation velocities are dominant in the zone nearer to the source of energy and are substantially low at the walls and at the bottom of the reactor. The levels of turbulence kinetic energy and dissipation rate are high near the horn and decrease rapidly with increasing distance from the horn. Average turbulent normal stresses are larger than the turbulent shear stresses. However, they are much lower than stirred reactors when compared at the same power consumption per unit mass. Comparisons of LDA measurements and computational fluid dynamics (CFD) predictions have been presented. The good agreement indicates the validity of the CFD model. The flow information has been extended for the prediction of mixing time. For uniform mixing in ultrasound-assisted reactors, optimum power density and diameter of the vessel is needed, yet it is far less effective than conventional stirred vessel. The possibility of optimization has been suggested in terms of power dissipation and the vessel size.     

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     

仿柳叶形静态混合器的流动及混合特性

对仿柳叶形静态混合器内混合气流进行了速度场与浓度场的试验研究,结果表明该混合器内速度场与浓度场偏差均达到了非常理想的效果（优于国家标准偏差值）。同时采用CFD软件对该静态混合器内的流场进行了数值模拟,试验与模拟的数值结果以及两者的浓度云图分布都有着较好的一致性。随后的研究结果表明：在混合元件尾迹区域出现了纵向涡和发卡涡来促进混合;在经过混合元件区域时因为湍流动能耗散率增加形成的高湍流动能耗散率区能够使物质交换更加频繁;整个静态混合器的流动阻力也主要发生在该区域,随之出现的返混现象也在一定程度上加强了混合效果。     

搅拌混合中的循环与剪切

搅拌混合中的循环与剪切被定量化,搅拌功率分解为P=Q∑S_k,分解后的循环流量和总剪切强度,以及剪切强度在空间的分布应匹配．混合对偶合反应过程影响的实验结果表明,循环／剪切比适中的搅拌桨能较好地满足偶合反应工艺的需要,其分隔指数最小.用修正的拉格朗日法进行过程模拟,结果表明团块的循环经历影响其局部分隔指数,增大单位体积功耗、循环／剪切比以及循环区与桨叶区的能耗分配比能降低偶合反应的分隔指数．     

运用粒子图像测速仪研究双层Rushton桨搅拌槽内湍流特性

Particle Image Velocimetry （PIV） has been used to investigate turbulence characteristics in a 0.48 m diameter stirred vessel filled to a liquid height （ H = 1.4T ） of 0.67 m. The agitator had dual Rushton impellers of 0.19 m diameter （ D = 0.4T ）. The developed flow patterns depend on the clearance of the lower impeller above the base of the vessel, the spacing between the two impellers, and the submergence of the upper impeller below the liq- uid surface. Their combinations can generate three basic flow patterns, named, parallel, merging and diverging flows. The results of velocity measurement show that the flow characteristics in the impeller jet flow region changes very little for different positions. Average velocity, trailing vortices and shear strain rate distributions for three flow patterns were measured by using PIV technique. The characteristics of trailing vortex and its trajectory were described in detail for those three flow patterns.
Since the space-resolution of PIV can only reach the sub-grid rather than the Kolmogorov scale, a large-eddy PIV analysis has been used to estimate the distribution of the turbulent kinetic energy dissipation. Comparison of the distributions of turbulent kinetic energy and dissipation rate in merging flow shows that the highest turbulent kinetic energy and dissipation are both located in the vortex regions, but the maxima are at somewhat different lo- cations behind the blade. About 37% of the total energy is dissipated in dual impeller jet flow regions. The obtained distribution of shear strain rate for merging flow is similar to that of turbulence dissipation, with the shear strain rate around the trailing vortices much higher than in other areas.     

Modeling spatial distribution of floc size in turbulent processes using the quadrature method of moment and computational fluid dynamics

A study was performed that utilizes the quadrature method of moments (QMOM) to model the transient spatial evolution of the floc size in a heterogeneous turbulent stirred reactor. The QMOM approach was combined with a commercial computational fluid dynamics (CFD) code (PHOENICS), which was used to simulate the turbulent flow and transport of these aggregates in the reactor. The CFD/QMOM model was applied to a 28 l square reactor containing an axial flow impeller and 100 mg/l concentration of 1 μm nominal clay particles. Simulations were performed for different average characteristic velocity gradients (40,70,90, and 150 s^-1). The average floc size and growth rate were compared with experimental measurements performed in the bulk region and the impeller discharge region. The CFD/QMOM results confirmed the experimentally measured spatial heterogeneity in the floc size and growth rate. In addition, the model predicts spatial variations in the aggregation and breakup rates. Finally, the model also predicts that the transport of flocs into the high shear impeller discharge zone was responsible for the transient evolution of the average floc size curve displaying a maximum before decreasing to a steady-state floc size.     

Simulation of fine particle formation by precipitation using computational fluid dynamics

The 4‐environment generalized micromixing (4‐EGM) model is applied to describe turbulent mixing and precipitation of barium sulfate in a tubular reactor. The model is implemented in the commercial computational fluid dynamics (CFD) software Fluent. The CFD code is first used to solve for the hydrodynamic fields (velocity, turbulence kinetic energy, turbulent energy dissipation). The species concentrations and moments of the crystal size distribution (CSD) are then computed using user‐defined transport equations. CFD simulations are performed for the tubular reactor used in an earlier experimental study of barium sulfate precipitation. The 4‐EGM CFD results are shown to compare favourably to CFD results found using the presumed beta PDF model. The latter has previously been shown to yield good agreement with experimental data for the mean crystal size at the outlet of the tubular reactor.     

An Analysis of Mixing in a Typical Experimental Set‐up to Measure Nnucleation Rates of Precipitation Processes

Mixing in a typical experimental setup to measure nucleation rates in precipitation processes was assessed. To determine these rates as a function of the driving force for concomitant polymorphs, it is necessary to perform these experiments at constant supersaturation. Therefore, the mixing time must be shorter than the time for the first nuclei to appear. For fast precipitation processes complete mixing has to be achieved within milliseconds. The mixing performance of a wide angle Y‐mixer was studied to see whether this is possible. An analysis of characteristic mixing times as a function of the average energy dissipation rate showed that turbulent dispersion of the feed streams determined the rate of the mixing process. The characteristic time for turbulent dispersion was of the same order as an arbitrarily set residence time in the Y‐mixer. However, CFD simulations of the flow showed large variation in the spatial distribution of the dissipation rate and revealed unsatisfying macromixing.     

管型混合澄清槽内的液-液两相流的数值模拟

管型混合澄清槽在工业生产中具有广阔的应用前景。通过计算流体力学分别对管型混合澄清槽内的混合室和澄清室进行数值模拟,系统地探究了分散相液滴尺寸（d₃₂₌ 100~500 μm）、进料油水比（O∶A = 1∶1~1∶5）、入口挡板及入口位置对混合澄清效果的影响,并将模拟结果与传统方型混合澄清槽进行对比。结果表明,管型混合室内的流场分布更合理,不易形成流动死区。管型混合室内搅拌桨上方和下方形成压力更小的低压区,流体的湍动能更大,搅拌性能更好。在混合室中,降低分散相d₃₂和进料油水比能够提高混合性能。在澄清室中,提高分散相d₃₂和降低进料油水比能够提高澄清性能,入口挡板能够有效提高澄清性能。     

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.     

Validation of CFD simulations of a stirred tank using particle image velocimetry data

Methods for validating CFD simulations based on the Reynolds Average Navier-Stokes equation (RANS) against Particle Image Velocimetry (PIV) measurements are investigated and applied to one of the most common problems in the chemical process industry — the prediction of flow field in a stirred vessel. A total of 1024 sequential instantaneous 2D velocity fields along the central axial plane of a stirred vessel with a P-4 axial impeller are obtained through PIV measurement. From the PIV data, the mean velocity, turbulent kinetic energy, Reynolds stresses and dissipation rate fields are extracted. By introducing several tools to quantify the similarities and differences between two-dimensional fields, CFD predictions of the flow field are validated against PIV data. Furthermore, using PIV and LDV data, the effect of boundary conditions on CFD simulation results is examined. The effect of different Reynolds stress closures on the flow prediction is also studied.     

Numerical optimization for blades of Intermig impeller in solid–liquid stirred tank

The multiphase flow in the solid-liquid tank stirred with a new structure of Intermig impeller was analyzed by computational fluid dynamics(CFD).The Eulerian multiphase model and standard k-ε turbulence model were adopted to simulate the fluid flow,turbulent kinetic energy distribution,mixing performance and power consumption in a stirred tank.The simulation results were also verified by the water model experiments,and good agreement was achieved.The solid-liquid mixing performances of Intermig impeller with different blade structures were compared in detail.The results show that the improved Intermig impeller not only enhances the solid mixing and suspension,but also saves more than 20% power compared with the standard one.The inner blades have relatively little influence on power and the best angle of inner blades is 45°,while the outer blades affect greatly the power consumption and the optimized value is 45°.     

Effect of swirling addition on the liquid mixing performance in a T-jets mixer

Swirling addition to the stream is beneficial for the fluid mixing. This work aims to study the mixing process intensification in a conventional T-jets mixer by the swirling addition. After experimental verification by the planar laser-induced fluorescence technique, large eddy simulation with the dynamic kinetic energy sub-grid stress model is used to predict how the swirling strength (in terms of swirling number, S_w) and swirling directions affect the mixing performance, e.g. the tracer concentration distribution, mixing time, and turbulent characteristics in the T-jets mixers. Predictions show that the swirling strength is the key factor affecting the mixing efficiency of the process. The overall mixing time, τ₉₀, can be significantly reduced by increasing S_w. Vortex analysis shows that more turbulent eddies appear in the collision zone and the turbulent kinetic energy dissipation rate increases obviously with the swirling addition. When S_w is kept constant, the mixing process can be accelerated and intensified by adding swirling to only one stream, to both streams with the opposite swirling directions, or to both streams with the same swirling directions. Amplification of the mixing process by enlarging the mixer size or increasing the flow rates is also optimized. Thus, this work provides a new strategy to improve the mixing performance of the traditional T-jets mixers by the swirling addition.     

A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow

Several models for the daughter bubble/droplet size distribution are reviewed and a detailed discussion is given to get a better understanding of the daughter size distribution. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow, based on an eddy-bubble/droplet collision method, is developed. It takes into account the energy distribution of turbulent eddies, effect of capillary pressure and surface energy increase during bubble/droplet breakup. An increase in the mother bubble/droplet size and energy dissipation rate increases the probability of unequal breakup. The model prediction is in good agreement with experimental results and the underlying physical situation.     

Energy dissipation and macro instabilities in a stirred square tank investigated using an LE PIV approach and LDA measurements

In this study, the hydrodynamics and turbulence in a square tank stirred with a hydrofoil impeller, a Lightnin A310, is investigated using a large eddy particle image velocimetry (LE PIV) approach. The particle image velocimetry data are used as the large scale part of a large eddy simulation and the small scales are modelled assuming that the turbulent kinetic energy production is limited to the large scale structures, the turbulent energy dissipation is confined to the small scale structures and the transfer of energy takes place in the inertial sub-range. The small scale turbulence was modelled by direct calculation of the turbulent stress tensor using filtered particle image velocimetry data. The spatial distribution of the calculated dissipation rate tensors showed good agreement with previous work.

The macro instabilities of the flow structure were investigated by means of spectral analysis. Low frequency phenomena separated from the mean flow were detected. The cause of these could partly be explained by the circulation time for the tank, which corresponded to the low frequency phenomena found at 0.03N Hz, where N is the rotational speed.     

Effect of blade pitch on the structure of the trailing vortex around rushton turbine impellers

Effect of blade number on the structure of the trailing vortex around the Rushton turbine impeller is examined by analyzing the data of mean velocities, deformation rates, turbulent kinetic energy and energy dissipation rates for 2-, 4-, 6- and 8-straight blades disk turbine impellers in a baffled standard geometry stirred tank. The data of Sauter mean bubble diameter near the blade tip are combined with the turbulent characteristics around the vortex to discuss how the blade number and the strength of the vortex affect the performance of the gas dispersion around the Rushton turbines under a low gassing rate. The results of this analysis show that if power input per each blade is the same, the impeller having four blades not only has the strongest average mean deformation rates and the largest turbulent kinetic energy, but also disperses the smallest average bubbles under the same gassing rate.