Large Eddy Simulation of Turbulent Flow in a Rushton Impeller Stirred Reactor with Sliding‐Deforming Mesh Methodology

The unsteady turbulent flow in a mixing vessel stirred by a Rushton impeller is predicted using the Large Eddy Simulation technique. The interaction between the moving impeller and the static baffles is accounted for explicitly through a sliding‐deforming mesh methodology, thus, eliminating approximations used to account for the effect of the moving impeller. Large‐scale structures associated with the trailing vortices are assessed via the vorticity and the turbulent kinetic energy distributions. The phase‐resolved predictions are compared with measurement data obtained by laser‐Doppler anemometry and favourable agreement is reported both for mean as well as turbulence quantities.     

Liquid Homogenization in Aerated Multi‐Impeller Stirred Vessel

The macroflow of fluid in a tall cylindrical vessel stirred with multiple stirrers was studied in the case of aeration of a liquid charge. The time of homogenization of the charge (mixing time) was calculated from the time dependency of the tracer concentration measured at various locations. Two types of stirrer were used in the experiments: six‐bladed Rushton turbines and/or pitched‐blade turbines with inclined blades pumping the liquid down or up. Four stirrers of the same type were located on the shaft. Other variables during the experiments were the stirrer frequency and the gas flow rate. It was found that the liquid macroflow in the vessel could be interpreted by the cell model or by the axial dispersion model for unaerated as well as for aerated systems. The influence of the aeration on the macroflow and mixing time was explained by the interaction of buoyancy and radial forces, and equations for the model parameters were proposed containing gas flow numbers and Froude numbers.     

CFD Prediction of Flow and Homogenization in a Stirred Vessel: Part II Vessel with Three and Four Impellers

This article deals with CFD simulations of flow inside stirred vessels equipped with three and four radial or axial impellers mounted on the same shaft. A comparison was made between simulated data and experiments for one‐ and two‐impeller systems and was presented in Part I [1]. The effect of the lowest impeller off‐bottom clearance, number of impellers used, and impeller type on the tracer distribution was studied. The simulations were mainly focused on the grid size and type and the analysis of the concentration curves in each impeller section. The predicted velocity fields, power and pumping numbers, concentration curves, and mixing times were validated with experimental data. The simulation results show the significant influence of the grid density on the velocity profiles and power and pumping numbers in contrast to the low impact on the concentration curves. A better prediction of the concentration curves was reached when radial impellers were used; the mixing times were generally over‐predicted.     

CFD Prediction of Flow and Homogenization in a Stirred Vessel: Part I Vessel with One and Two Impellers

A simulation of flow field and tracer homogenization was performed using the commercial CFD software FLUENT 6.1. The aim is to investigate the potential of CFD software to predict concentration distribution of added tracer in cylindrical vessels. The calculated results – dimensionless velocity profiles, power and pumping numbers, dimensionless concentration curves, and mixing times – were compared with experiments in stirred vessels. In Part I, the study was performed for vessels agitated by one or two impellers on a centric shaft. Two different impellers were used – a 6‐bladed 45° pitched blade turbine and a standard Rushton turbine. The standard k‐? turbulence model and multiple reference frames method were used for the simulations. The influence of the grid type was also investigated; three types of grid – a structured, unstructured and a special user‐defined grid – were studied.     

Estimation of kLa Values in Bench‐Scale Stirred Tank Reactors with Self‐Inducing Impeller by Multiphase CFD Simulations

A multiphase computational fluid dynamics (CFD) simulation methodology is developed and proposed for the estimation of the spatial distribution of k_La values in a bench‐scale reactor equipped with a self‐inducing impeller. The importance of estimating an apparent drag coefficient, which considers the effect of turbulence on the gas bubble rising velocity, is also tackled by applying different correlations available in literature, namely, Brucato, modified Brucato, and Pinelli correlations. The spatial distribution of k_La values in the agitated vessel is found from the CFD results using Danckwert's surface renewal model. An analysis of the gas volume fraction distribution obtained from the simulations is performed in order to choose the most suitable drag model. The modified Brucato correction correlation for the drag force exhibits the best agreement with experimental data.     

Effect of Dual Impeller‐Sparger Geometry on the Hydrodynamics and Mass Transfer in Stirred Vessels

The understanding of the effect of impeller‐sparger configurations on gas dispersion and mass transfer is very important to improve the performance of gas/liquid contactor systems. The influence of the impeller positions, the upper turbine diameter, the sparger ring diameter and its location in regard to the lower impeller on the power consumption, the volumetric mass‐transfer coefficient and the overall oxygen transfer efficiency were studied in a nonstandard curved bottomed reactor with an agitated system with dual disk style turbines. In the range of the gas flow rates studied, the most efficient impeller‐sparger arrangement for the oxygen transfer is the impeller system with turbines of different diameters located at C = 0.25 and IC = 0.5, and with the sparger of smaller diameter than the lower impeller settled below the impeller. A new model to estimate the k_La with an average relative error of 8 %, which takes the reactor operation conditions and the influence of the impeller‐sparger geometry into account, was also proposed.     

LDA‐Measurements in a Stirred Tank With a Liquid‐Liquid System at High Volume Percentage Dispersed Phase

The purpose of this study is to evaluate how the flow is influenced by the volume percentage of dispersed phase in a liquid‐liquid system. A novel model system consisting of two refraction index matched immiscible liquids is presented along with experimental velocity vector fields of the continuous phase that utilises the non‐intrusive Laser‐Doppler‐Anemometry technique. Three velocity components have been measured inside a baffled cylindrical tank, stirred with a six‐bladed Rushton‐impeller. The experiments show that the vortex below the impeller is stretched, primarily in the radial direction, with increasing dispersed phase content. A small change in the shape of the vortex above the impeller can also be observed. The turbulence is dampened with increasing dispersed volume fraction.     

CFD Modelling of Mixing Effects on the Course of Parallel Chemical Reactions Carried out in a Stirred Tank

Effects of turbulent mixing on the course of two fast parallel chemical reactions (neutralization of sodium hydroxide and hydrolysis of ethyl chloroacetate) carried out in a semibatch stirred tank reactor are experimentally investigated and numerically simulated. The flow pattern in the stirred tank is predicted using CFD and experimentally validated using Laser Doppler Anemometry. Mixing effects are modelled using three CFD based models. In the first and the second model the Beta probability distribution and the spiked distribution are used respectively; in the third model concentration fluctuations are neglected.     

Multi‐Phase‐Multi‐Size‐Group Model for the Inclusion of Population Balances into the CFD Simulation of Gas‐Liquid Bubbly Flows

A CFD model for the simulation of gas‐liquid bubbly flow is developed. In the model, the multi‐phase flow is simulated by an Eulerian‐Eulerian approach using several phase definitions (from 3 to 10). The bubble size distribution is simulated by a solution of the discretized population balance equation with coalescence and break‐up of bubbles. The number of the discretized population balance equations in the model is larger than the number of the phases used in the flow field simulation. A desired accuracy in the simulation can be achieved by choosing a suitable number of phases as a compromise between accuracy and computational cost. With this model, more detailed flow hydrodynamics and bubble size distribution can be obtained. The model was tested with different operating conditions and for different numbers of dispersed phases in a bubble column, and was verified with a bubble size distribution obtained experimentally.     

Effect of Impeller Vertical Position on Drop Sizes in Agitated Dispersions

The effect of impeller height relative to the vessel bottom was studied by measuring the drop size distributions of kerosene dispersions in water at two positions inside a stirred tank. Measurements were taken at 1/3, 1/ 2, and 2/3 of total vessel height for rotational speeds 250, 300, 350 and 400 RPM and for hold‐up fractions 0.02 and 0.04. Results show an influence of impeller height on drop sizes ranging from a Sauter mean diameter decrease of 7.8 % to an increase of 35 % relative to the ones obtained with the impeller at the center of the vessel     

Micromixing of Solid‐liquid Systems in a Stirred Tank with Double Impellers

The effect of solid particles on micromixing has been studied using the competitive iodide/iodate reaction system in stirred, multi‐impeller, solid‐liquid systems. The influences of particle size, impeller speed, solid holdup, feed position, and energy input have been investigated. The change of the segregation index with the power input was more distinguishable only for the 450–600 μm particles as compared with the large ones, at the same solid holdups. Also, for the small ones, cloud formation was observed at a particle concentration of 12.1 wt %. However, the influence of larger particles of 1–1.25 mm on micromixing was negligible, though both energy input and solid loading were increased. Besides, the optimal feed position was identified, and multiple feeds were also explored.     

Testing the Well-Mixed Model for a Gas-Liquid Stirred Ozonization Reactor

A “well-mixed” model was developed for a semi-batch gas-liquid reactor designed to study the mechanisms of ozonation of organic compounds in aqueous media, and tested against unsteady-state absorption data. In the (experimental range examined for the superficial gas velocity (v)Q < 0.30 cms(1),) this model fairly describes the fluid dynamic behavior of the reactor for stirring speeds not greater than about 400 rpm. To minimize the effects of the physical factors on the computed kinetic parameters, the kinetic experiments should be carried out in these operating conditions.     

Effects of the Stirred Tank's Design on Power Consumption and Mixing Time in Liquid Phase

The influence of the stirrer type and of the geometrical parameters of both tank and agitator (clearance of an impeller from tank bottom, impeller diameter, draft tube and geometry of the tank bottom) on power consumption and mixing time in liquid phase under turbulent regime conditions (Re > 10⁴) have been studied. Different types of agitators have been used, namely Rushton turbine, 45° pitched‐blade turbine, MIXEL TT and TTP propellers and 1‐stage or 2‐stage EKATO‐INTERMIG propellers. All these stirrers were tested with the same power consumption per unit mass of liquid. On the basis of measured power consumption per unit mass, which is required to achieve the same degree of mixing, the results obtained in the present work show that the TTP propeller is the most efficient in liquid phase. Recommendations on the optimum geometric configuration have been made for each type of stirrer.     

Laser Doppler Measurements of Turbulent Parameters in Different Multiple‐Propeller Systems

In this study, laser Doppler anemometry (LDA) measurements in the r‐z plane are obtained in two stirred tanks equipped with two downward pumping propellers in the turbulent and the transient flow domains. A new approach of the hydrodynamics generated by this system consists of determining the one‐dimensional energy spectrum and the autocorrelation coefficient function at different locations in each vessel. In the turbulent flow, the integral scales, the Taylor microscales, and the Kolmogorov microscale have been determined. The dissipation rate is obtained with two methods: from the semi‐empirical expression ϵ = A k^3/2/D and from the frequency spectrum. Results show the influence of the rheological properties on the flow patterns, the influence of the blade passage frequency on the frequency spectrum, and the apparition of a low frequency characterizing the production of macro‐instabilities. Comparison of the turbulent characteristics with the values reported in the literature shows that our combination of propellers produces larger eddies than a Rushton turbine.     

翼形桨搅拌槽内混合过程的数值模拟

采用FLUENT软件的多重参考系(MRF)及标准k-ε模型,将速度场与浓度场方程分开进行求解,对单层轴流式三叶CBY翼形桨搅拌槽内的混合过程进行了数值模拟,所得的混合时间的模拟结果与实验值相吻合。同时采用数值模拟的方法研究了不同的示踪剂加料点、监测点位置及操作条件对混合时间的影响规律;模拟结果表明,混合过程主要由搅拌槽内的流体流动所控制,混合时间与示踪剂加料点及监测点位置密切相关。上述的研究结果对于工业搅拌反应器的优化具有一定的参考意义。     

Simulation of Barium Sulfate Precipitation using CFD and FM‐PDF Modeling in a Continuous Stirred Tank

A mixing‐precipitation model combining computational fluid dynamics (CFD), finite‐mode PDF (probability density function) model, population balance and kinetic modeling has been proposed to simulate the barium sulfate precipitation process in a continuous stirred tank agitated by a Rushton turbine. The effect of various operating conditions such as impeller speed, feed concentration, feed position and mean residence time on the barium sulfate precipitation process is clearly demonstrated. It is shown that the mean crystal size increases by increasing the impeller speed and mean residence time. However, when the feed concentration is increased, the mean crystal size decreases. The predictions are in reasonable agreement with the experimental data in the literature.     

Modeling of Mixing and Reaction in Turbulent Multi‐Phase Flows with Distribution Functions

Numerical simulation of turbulent reacting or multiphase flows is gaining popularity as a tool for the analysis and optimization of many complex applications in process engineering. To make possible the accurate modeling of relevant reaction and transport processes, the respective distribution functions of mixture fraction or particle size must be considered in an adequate manner. In the present paper, novel approaches to make possible a more detailed yet efficient representation of distribution functions in turbulent, reacting multiphase flows are introduced. The application of the methods to the example of a system with mixing and reaction among three species is discussed.     

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.     

高固含搅拌槽内临界离底悬浮转速的数值模拟

使用计算流体软件CFX5.5.1对固液搅拌槽内颗粒的临界离底悬浮转速进行了数值模拟. 搅拌槽直径D=0.476 m,搅拌桨为三叶CBY螺旋桨. 桨叶安装高度h=D/3. 固液两相为玻璃珠-水,固体体积浓度为15%~50%. 对临界离底悬浮的速度判据进行了修正,并利用浓度判据与修正的速度判据得到颗粒临界离底悬浮转速Njs,模拟计算结果与实验数据的误差在工业允许的范围内. 同时,对临界离底悬浮状态槽底部不同浓度下的流体湍流动能的分布情况以及大小进行了预测,并对2种固体临界离底悬浮机理进行了验证.