Experimental Analysis of Hydrodynamics Induced by a Moritz HAS Impeller in Laminar and Turbulent Regimes

The hydrodynamics induced by a Moritz HAS impeller are investigated using the PIV technique. The purpose of this study is to extend the knowledge of this kind of impeller, well known in turbulent flow, to the transition regime and laminar flow. Measurements of instantaneous velocity fields are synchronized with the position of the blade of the impeller. The periodic motion induced by the impeller blade rotation is measured by this conditional averaging. A triple decomposition is used to analyze the levels of turbulent kinetic energy and periodic kinetic energy induced by the impeller. In a turbulent regime, the impeller induces axial flow: the magnitude of periodic fluctuation is low compared to the turbulent one. In a laminar regime, the impeller induces a tangential‐radial discharge flow, and periodic velocity fluctuations are limited to the vicinity of the impeller.     

Simulation of laminar and turbulent impeller stirred tanks using immersed boundary method and large eddy simulation technique in multi-block curvilinear geometries

Impeller stirred tanks are commonly used in the chemical processing industries (CPI) for a variety of mixing and blending technologies. Such processes require accurate modeling of the turbulent flow in the tank over a range of operating conditions (e.g. impeller speed), and in addition, require a computationally efficient solution strategy that can represent moving rigid geometric parts (impellers) in the tank. In the present study, a methodology is proposed that combines the advantages of the immersed boundary method (IBM) to represent moving rigid geometries with the efficiency of multi-block structured curvilinear meshes (to minimize wasted grid points) for the representation of overall complex domains. The IBM implementation on a multi-block curvilinear mesh is advocated for the simulations of impeller stirred tank reactors (STR) and has distinct advantages over other competing methods. In the present work, the curvilinear-IBM methodology is further combined with the curvilinear coordinate implementation of large eddy simulation (LES) technique to address the issue of modeling unsteady turbulent flows in the STR. To verify the implementation of IBM in a multi-block curvilinear geometry, a laminar STR with a stack of four pitched blade impellers on a single shaft is simulated and compared against experimental data. Verification of the combined IBM-LES implementation strategy in curvilinear coordinates is done through comparisons with the measurements of turbulent flow in a baffled STR with a single pitched blade impeller. For both laminar and turbulent STR, the predictions are in very good agreement with measurements. It is suggested here that this methodology can be reliably used as a predictive tool for the flow fields in STRs with complex geometries.     

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.     

Impeller power draw during turbulent operation in solid‐liquid suspensions

Experimental measurements with six impeller types in solid‐liquid suspensions indicate that impeller power draw in the turbulent regime is approximately proportional to the solid‐liquid suspension density when the solids are distributed throughout the liquid; however, the accuracy of this approach is limited and there are clear differences in the behaviours of the various impellers. In general, power draw increases are less than suspension density increases for impellers with large blade‐trailing vortices, while power draw increases are equal to or greater than suspension density increases for impellers with smaller blade‐trailing vortices. The power draw data is well‐described using linear relations between the impeller power number and the density difference correlating parameter proposed by Micheletti et al.,^[9] with the slope of the relation being dependent on impeller type. More extensive testing with a pitched‐blade turbine, using a greater variety of solids, found that the relation between the impeller power number and the density difference correlating parameter is independent of particle size for particles as large as 1 mm (1000 microns). For particles larger than 1.7 mm (1700 microns), in addition to suspension density, the solid volume fraction affects the pitched‐blade turbine power number; however, it is difficult to determine if this effect exists at all scales or if it is a result of the large particle size relative to the impeller dimensions in the experimental system. For large particles, the power draw is increased by the addition of neutrally‐buoyant particles that do not change the suspension density, with the magnitude of the increase being dependent on impeller type.     

Power Consumption in the Turbulent Regime for a Coaxial Mixer

The power consumption of a new coaxial mixer composed of an anchor impeller and a pitched‐blade turbine impeller, and a series of rods operated in a contra‐rotating mode has been characterized experimentally in the turbulent regime. It is shown that both the power curve and the turbulent power number vary significantly with the speed ratio between the impellers. Likewise with single impeller mixers, the transition regime starts at a Reynolds number above 100 and the turbulent regime between 10³ and 10⁴ irrespective of the definition of the Reynolds number used.     

Application of extended quadrature method of moments for simulation of bubbly flow and mass transfer in gas‐liquid stirred tanks

In the present paper, two gas‐liquid stirred tanks, one agitated by a radial impeller and another by an axial impeller, are modelled using the open‐source computational fluid dynamic (CFD) package OpenFOAM (open source field operation and manipulation). The combined effect of the bubble break‐up and coalescence in the tank is considered by a population balance model (PBM) called extended quadrature method of moments (EQMOM). The three‐dimensional simulation is made using a multiple reference frame (MRF), a well‐established method for the modelling of mixers. Dispersed gas and bubble dynamics in the turbulent flow are modelled using the Eulerian‐Eulerian approach (E‐E) with mixture k‐epsilon turbulent model and the modified Tomiyama drag coefficient for the momentum exchange. The model is developed to predict the spatial distribution of gas phase fraction, Sauter mean bubble diameter (), number density function (NDF), dissolved oxygen (DO) evolution, and flow structure. The numerical results are compared with experimental data and a fair agreement is achieved. The results of the axial impeller are discussed based on four impeller rotational speeds with different volumetric mass transfer coefficients.     

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。     

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     

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     

Flow structure and the effect of macro-instabilities in a pitched-blade stirred tank

Turbulent flow inside a dished bottom baffled stirred tank reactor (STR) with a 45° pitched blade impeller is studied numerically and experimentally. Three different impeller rotational speeds are studied corresponding to impeller Reynolds numbers of 44,000, 88,000 and 132,000, respectively. The numerical study is based on a large-eddy simulation (LES) technique with a fixed body-fitted curvilinear mesh. The moving impeller geometries are modeled using an immersed boundary method (IBM). The experiments consist of particle image velocimeter (PIV) measurements of the flow field. The instantaneous as well as the time-averaged flow field suggests the formation of trailing vortex structures which are associated with higher levels of turbulent kinetic energy relative to the remaining flow field. Instabilities occurring at a frequency lower than the frequency of impeller rotation are identified from the time signal of the velocity components. The role of these lower frequency macro-instabilities (MI) is explored by observing changes in the three-dimensional circulation pattern within the stirred tank. The growth and dissipation of trailing edge vortices are shown to be appreciably influenced by the macro-instability. A significant amount of kinetic energy (velocity fluctuations) is observed to be associated with the low frequency dynamics of the trailing edge vortices during an MI cycle.     

Impeller characterization and selection: Balancing efficient hydrodynamics with process mixing requirements

Current literature relies almost exclusively on the power number to compare and characterize impellers. Industrial mixing requirements may rely on conditions far away from the impeller. A protocol is proposed to compare impellers designed for turbulent mixing on the basis of impeller hydrodynamic performance and mixing process objectives. A hydrofoil impeller (KPC), and a mixed‐flow impeller (45^° down‐pumping PBT), each at two diameters, were used to test the protocol. Fourteen measures were considered. Five are recommended for full characterization: power number, momentum number, and peak rate of dissipation of turbulent kinetic energy to characterize conditions at the impeller; power at just‐suspended speed to compare the efficiency of solids suspension at the bottom of the tank; and point of air entrainment as a measure of turbulence penetration to the free surface. These five measures provide complete information about mixing performance and good differentiation between the impellers and geometries. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2573–2588, 2012     

Flow and Turbulence in the Discharge of Radial Pumping Turbines: Influence of the Turbine Type

Velocity measurements were made in the impeller discharge of 6SRGT‐ and Rushton‐type impellers in a 0.6 m³ tank using constant temperature anemometry with a direction sensitive split‐film probe. The reproducibility error of the measurement system was found to be greater than 5 % for all measured properties. The main flow and turbulent parameters measured at three agitation rates in the impeller discharge are compared for the two turbines with respect to both agitation rate and the measured power input. For comparison of the flow properties in the centerline of the two turbines having different diameter and blade height, a uniform representation was used treating the impeller stream as a special kind of free jet. Using this representation, we obtained similar results for both turbines on all measured parameters. The profile measurements showed a similar main flow field for both turbines, but significant differences were found in the axial distribution of turbulent kinetic energy and the energy dissipation rate.     

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.     

Hydrodynamics Characterization of an Ellipse Gate Impeller by Experimental and Numerical Studies

Hydrodynamics characteristics like flow pattern, shear rate distribution, power consumption, axial pumping capacity, mixing time, and mixing efficiency of an ellipse gate (EG) impeller were investigated by experimental and numerical methods. The numerical simulation results were validated by experimental data of power consumption and mixing time. Results indicate that the axial pumping number of the EG impeller is larger than that of any other reported large‐scale impeller under laminar regime, and that the shear rate formed by this impeller is less sensitive to Reynolds numbers. In‐depth analysis reveals the different function of each part of the EG impeller under different flow regimes. This impeller provides an almost similar mixing efficiency like the double‐helical ribbon impeller under laminar regime, but much higher mixing efficiency both under transitional and turbulent flow regimes.     

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     

Numerical Investigation of the Effect of Impeller Design Parameters on the Performance of a Multiphase Baffle‐Stirred Reactor

The turbulent gas‐liquid flow field in an industrial 100‐m³ stirred tank was calculated by using computational fluid dynamics based on the finite‐volume method. Turbulent effects were modeled with the shear stress transport model, and gas‐liquid bubbly flow was modeled with the Eulerian‐Eulerian approach using the Grace correlation for the drag force interphase momentum transfer. The relative motion between the rotating impeller and the stationary baffled tank was considered by using a multiple frames of reference algorithm. The effects of Rushton and pitched‐blade impeller design parameters such as blade geometry, location, and pumping direction on the mixing performance were investigated. It was found that a combination of Rushton turbines with up‐pumping pitched‐blade turbines provides the best mixing performance in terms of gas holdup and interfacial area density. The approach outlined in this work is useful for performance optimization of biotechnology reactors, as typically found in fermentation processes.     

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     

基于CFD的轴流泵内部流场模拟

利用数值流体动力学CFD（computational fluid dynarnics）软件对轴流泵内部的非稳态三维湍流流动进行了模拟,以研究其内部流动规律。计算域由转动的叶轮、固定的导叶体、进口流道和出口流道组成,使用了多重参考坐标系（MRF）和混合面（rnixingplane）把旋转区域和静止区域分开。计算得到了轴流泵转子叶片速度等值线,轴流泵转子叶片和轮毂的全压等高线。根据数值计算数据对轴流泵的外特性进行定量的预估。计算结果有助于深入了解轴流泵的内部流动机理,指导轴流泵的水力设计。     

Effect of Particle Image Velocimetry Setting Parameters on Local Velocity Measurements in an Agitated Vessel

Although they are obtained under the same conditions, results on the flow field in an agitated vessel achieved using particle image velocimetry (PIV) may vary due to differences in the PIV conditions. The influence on turbulence characteristics of the main PIV setting parameters, i.e., PIV spatial resolution, sampling frequency, and recording time, was investigated. Tests were performed with three different liquids in a developed turbulent field for a Rushton turbine impeller using two‐dimensional time‐resolved PIV. To obtain the relevant velocity gradients, a minimum recording time is needed. No effect of sampling frequency was observed if the sampling frequency was higher than approximately 17 times the impeller frequency, which is about three times the impeller blade frequency.     

Prediction of the Induced Gas Flow Rate from a Self‐Inducing Impeller with CFD

The complex task of describing computationally two‐phase turbulent flows in aerated stirred‐tank reactors was overcome by proposing that the gas flow rate in the hollow impeller can be estimated from single‐phase flow simulations of the liquid phase in the reactor: the pressure at the impeller surface obtained from liquid phase simulations can be related to the gas induction rate. A commercial lab‐scale reactor with a radial six‐bladed hollow impeller was chosen for the study. To validate the presented methodology, the induced gas flow rate was measured experimentally from the tracking of the position of bubbles in a dynamic sequence of flow images. Notwithstanding the simplifications assumed in the presented CFD methodology, good agreement has been obtained between numerical results and experiments.