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.     

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.     

用改进的内外迭代法数值模拟Rushton涡轮搅拌槽流场

在有挡板的搅拌槽中，受搅拌桨驱动的液体在挡板的作用下会产生复杂的三维湍流流动.利用“快照”法思路和改进的内外迭代法及k–e湍流模型对Rushton涡轮有挡板的搅拌槽进行了整体数值模拟. 同文献中的实验数据进行了比较，模拟值同实验值基本吻合. 改进后的内外迭代法不依赖经验公式和实验数据，有一定的通用性.     

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.     

Experimental determination and numerical simulation of mixing time in a gas-liquid stirred tank

In this work, mixing experiments and numerical simulations of flow and macro-mixing were carried out in a 0.24 m i.d. gas-liquid stirred tank agitated by a Rushton turbine. The conductivity technique was used to measure the mixing time. A two-phase CFD (computational fluid dynamics) model was developed to calculate the flow field, k and ε distributions and holdup. Comparison between the predictions and the reported experimental data [Lu, W.M., Ju, S.J., 1987. Local gas holdup, mean liquid velocity and turbulence in an aerated stirred tank using hot-film anemometry. Chemical Engineering Journal 35 (1), 9-17] of flow field and holdup at same conditions were investigated and good agreements have been got. As the complexity of gas-liquid systems, there was still no report on the prediction of mixing time through CFD models in a gas-liquid stirred tank. In this paper, the two-phase CFD model was extended for the prediction of the mixing time in the gas-liquid stirred tank for the first time. The effects of operating parameters such as impeller speed, gas flow rate and feed position on the mixing time were compared. Good agreements between the simulations and experimental values of the mixing time have also been achieved.     

Detached eddy simulation on the turbulent flow in a stirred tank

A detached eddy simulation (DES), a large‐eddy simulation (LES), and a k‐ε‐based Reynolds averaged Navier‐Stokes (RANS) calculation on the single phase turbulent flow in a fully baffled stirred tank, agitated by a Rushton turbine is presented. The DES used here is based on the Spalart‐Allmaras turbulence model solved on a grid containing about a million control volumes. The standard k‐ε and LES were considered here for comparison purposes. Predictions of the impeller‐angle‐resolved and time‐averaged turbulent flow have been evaluated and compared with data from laser doppler anemometry measurements. The effects of the turbulence model on the predictions of the mean velocity components and the turbulent kinetic energy are most pronounced in the (highly anisotropic) trailing vortex core region, with specifically DES performing well. The LES—that was performed on the same grid as the DES—appears to lack resolution in the boundary layers on the surface of the impeller. The findings suggest that DES provides a more accurate prediction of the features of the turbulent flows in a stirred tank compared with RANS‐based models and at the same time alleviates resolution requirements of LES close to walls. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3224–3241, 2012     

Numerical simulation of turbulent flow in a baffled stirred tank with an explicit algebraic stress model

An explicit algebraic stress model (EASM) was used to simulate anisotropic turbulent flows in baffled stirred tanks equipped with a standard Rushton turbine. The quantitative predictions of velocity components, turbulence kinetic energy, Reynolds stresses and turbulence energy dissipation rate in the context of anisotropic turbulence were conducted to assess the comprehensive performance of the EASM. A lot of efforts have been made to ensure numerical stability during the calculations such as using a good initial flow field, manipulating source terms and adjusting under-relaxation factors. The predicted results were also compared with experimental data and other simulation results obtained using the standard k–ε model, algebraic stress model (ASM), Reynolds stress model (RSM) and large eddy simulation (LES). All the simulations were run with in-house codes. The simulation results show that agreement between the EASM predictions and experimental values is satisfactory. The EASM is consistently superior to the standard k–ε model when predicting both peak values and trend of variation in velocities and turbulence quantities. In comparison to the RSM, the EASM has almost the same predictive accuracy. The EASM is inferior to the LES on the prediction of turbulence kinetic energy. Nevertheless, the computational cost of the EASM is significantly lower than that of the LES, which is an obvious advantage in practical applications.     

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.     

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.     

γ-CT measurement and CFD simulation of cross section gas holdup distribution in a gas–liquid stirred standard Rushton tank

Cross section gas holdup distributions at 3/4 dimensionless static liquid height in a gas–liquid stirred standard Rushton tank were measured using ¹³⁷Cs γ-CT scan measuring technology at larger gas flow rates and higher impeller rotating speeds. The obtained CT scan images and digital distribution curves of gas holdup with dimensionless radius based on the CT images could explain the fluctuation changes of gas holdup distribution. The dense area of gas holdup distribution appeared in the upper space of impeller blades. Gas holdup increased both with gas flow rate and impeller rotating speed, but gas flow rate had more influence on gas holdup than impeller rotating speed. The Eulerian–Eulerian two-fluid model coupling with the bubbles' coalescence and break-up models, and the drag coefficient model were established to make CFD simulation of gas holdup distributions for the gas–liquid stirred Rushton tank under different gas flow rates and impeller rotating speeds.     

CFD simulation of liquid-phase mixing in solid-liquid stirred reactor

A comprehensive CFD model was developed to gain an insight into solid suspension and its implications on the liquid-phase mixing process in a solid-liquid stirred reactor. The turbulent solid-liquid flow in a stirred reactor was simulated using a two-fluid model with the standard k-ε turbulence model with mixture properties. The multiple reference frames (MRFs) approach was used to simulate impeller rotation in a fully baffled reactor. The computational model with necessary sub-models was mapped on to a commercial solver FLUENT 6.2 (of Fluent Inc., USA). The predicted solid concentration distribution was compared with the experimental data of Yamazaki et al. [1986. Concentration profiles of solids suspended in a stirred tank. Powder Technology 48, 205-216]. The computational model was then further extended to simulate and understand the implications of the suspension quality on liquid-phase mixing process. The computational model and the predicted results discussed here will be useful for understanding the liquid-phase mixing process in stirred slurry reactors in various stages of solid suspension.     

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.     

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.     

Gas-Liquid Mixing in a Grid-Disc Impeller Stirred Tank

To enhance the gas-liquid mixing performance in stirred tanks, the grid-disc impeller was designed by replacing the solid disc of the standard Rushton impeller with a grid disc. Gas-liquid hydrodynamics of the new impeller was studied by employing the Eulerian-Eulerian two-phase model coupled with the dispersed k-ε turbulence model. Rotation of the impeller was simulated with the multiple reference frame method. Flow field, gas holdup, and power consumption were investigated and compared with the standard Rushton impeller. The numerical method was validated by comparing the gas holdup with literature. The grid-disc impeller performed better than the Rushton impeller in terms of gas dispersion performance, axial pumping capacity, and energy requirement, indicating its potential for gas-liquid mixing applications.     

CFD Modeling of Turbulent Jacket Heat Transfer in a Rushton Turbine Stirred Vessel

CFD modelling of the turbulent heat transfer was performed for a stirred tank equipped with a Rushton turbine impeller and four standard baffles. Eight different turbulence models, i.e. the standard k‐?, RNG k‐?, realizable k‐?, Chen‐Kim k‐?, optimized Chen‐Kim k‐?, standard k‐ω, k‐ω SST and Reynolds stress models, were used during the modelling. In all investigated cases, the boundary flow at the vessel wall was described by the standard logarithmic wall functions. The CFD modelling values of the local heat transfer coefficient were compared with the corresponding experimental data. The best agreement was obtained for the standard k‐?, optimized Chen‐Kim k‐? and k‐ω SST models.     

Study on the solid–liquid suspension behavior in a tank stirred by the long-short blades impeller

We investigated the solid–liquid suspension characteristics in the tank with a liquid height/tank diameter ratio of 1.5 stirred by a novel long-short blades(LSB) impeller by the Euler granular flow model coupled with the standard k–ε turbulence model. After validation of the local solid holdup by experiments,numerical predictions have been successfully used to explain the influences of impeller rotating speed,particle density, particle size, liquid viscosity and initial solid loading on the soli...     

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。     

叶片形状对涡轮桨搅拌槽内尾涡特性的影响

Particle image velocimetry technique was used to analyze the trailing vortices and elucidate their rela-tionship with turbulence properties in a stirred tank of 0.48 m diameter,agitated by four different disc turbines,in-cluding Rushton turbine,concaved blade disk turbine,half elliptical blade disk turbine,and parabolic blade disk turbine.Phase-averaged and phase-resolved flow fields near the impeller blades were measured and the structure of trailing vortices was studied in detail.The location,size and strength of vortices were determined by the simplified λ2-criterion and the results showed that the blade shape had great effect on the trailing vortex characteristics.The larger curvature resulted in longer residence time of the vortex at the impeller tip,bigger distance between the upper and lower vortices and longer vortex life,also leads to smaller and stronger vortices.In addition,the turbulent ki-netic energy and turbulent energy dissipation in the discharge flow were determined and discussed.High turbulent kinetic energy and turbulent energy dissipation regions were located between the upper and lower vortices and moved along with them.Although restricted to single phase flow,the presented results are essential for reliable de-sign and scale-up of stirred tank with disc turbines.     

Numerical Simulation of Macroscopic Mixing in a Rushton Impeller Stirred Tank

The macroscopic mixing in a stirred tank with different tracer injection locations, impeller speeds and impeller positions is simulated numerically by solving the transport equation of the tracer based on the whole flow field in the baffled tank with a Rushton disk turbine numerically resolved using the improved inner-outer iterative procedure. Predicted mixing time is compared well with the literature correlations. The predicted residence time distribution of the stirred tank is very close to the present experimental results. The effect of the installation of a draft tube on the mixing time and residence time distributions is addressed.     

Measurement of phase holdups in liquid-liquid-solid three-phase stirred tanks and CFD simulation

Phase holdup is an important hydrodynamic characteristic of multiphase systems relevant to optimization and scale-up of related process equipment. In the present article, measurements of phase distribution of solid particles and oil droplets are conducted in a lab-scale stirred tank by sample withdrawal under various operating conditions. A Eulerian-Eulerian three-fluid model is established for the prediction of phase distribution of two dispersed phases in the agitated liquid-liquid-solid dispersion system. The turbulence structure in the system is described by an extension of the standard k-ε turbulence model to three-phase flow including the influence of presence of two dispersed phases as an additional source of turbulent kinetic energy. Momentum exchange between continuous and dispersed phase as well as between the two dispersed phases are incorporated into the model formulation. Comparison of model predictions with experimental data suggests reasonable agreement for the dispersed oil phase. The predicted distribution of solid particles shows some discrepancies in comparison with the measurements, but the agreement is significantly improved for higher impeller speeds.