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     

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.     

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     

Experimental Study of Influence of the Impeller Spacing on Flow Behaviour of Double‐Impeller Stirred Tank

The flow fields in the stirred tank with three different kinds of combined double‐impeller agitators: disc turbine + disc turbine (DT‐DT, radial impeller), pitched blade turbine + pitched blade turbine (PTD‐PTD, axial impeller) and pitched blade turbine + disc turbine (PTD‐DT), were investigated in detail by using laser Doppler anemometry. The two‐dimensional mean velocity field and the distribution of turbulence intensity were obtained for different impeller spacings. The experimental results show that the impeller spacing has a significant influence on the flow field. To improve flow homogeneity and agitator efficiency, the appropriate impeller spacing should be in the range of 1/2 to 2/3 of the tank diameter.     

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     

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.     

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     

Characterisation of three different impellers using the LDV-technique

A characterisation of three commonly used impellers was made in this study by measuring local mean velocities and the fluctuations of these velocities with the LDV technique. The data was used to estimate volumetric flow, velocity fluctuations and turbulent intensity in the impeller region of the tank. The impellers investigated were a high flow impeller, a pitched blade turbine and a Rushton turbine. The cylindrical vessel used was made of Perspex, had a dished bottom (DIN 28013), was equipped with four baffles and had an inner diameter of 0.45 m. It was found that the bulk velocities could be scaled with the tip-speed of the impeller (ND). The flow rate at constant impeller speed increased in the order high flow impeller — Rushton turbine — pitched blade turbine. The corresponding order for the turbulence fluctuation is: high flow impeller — pitched blade turbine — Rushton turbine. The velocity profile of the flow out from the high flow impeller was furthermore, not as smooth as could be expected.     

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.     

Importance of using the correct impeller boundary conditions for CFD simulations of stirred tanks

Two experimentally determined sets of impeller boundary conditions were used to simulate the flow generated by a pitched blade turbine in a cylindrical baffled tank. Use of these two sets of boundary conditions in simulations with two different off bottom clearances led to the conclusion that the flow generated by a pitched blade impeller cannot be successfully predicted without considering the impeller location. Correct prediction of velocity fields in the tank required the correct specification of velocity boundary conditions. Successful prediction of the turbulent energy distribution required proper specification of the turbulence boundary conditions. There was almost no interaction between the velocity and turbulence fields. The turbulet kinetic energy dissipation rate was at a maximum close to the impeller in both geometries. Within this region the average dissipation rate was five and a half times greater that the average dissipation rate in the tank.     

Angle-resolved stereo-PIV measurements close to a down-pumping pitched-blade turbine

The present work employs a stereoscopic-PIV technique to obtain angle-resolved fields of all three velocity components close to a T/3, 45^° down-pumping pitched-blade turbine operated at 300 rpm in a 0.29 m diameter vessel. The measurements were made at blade angles 7.5^° apart, with 300 measurements taken at each blade position, in order to calculate angle-resolved mean velocity fields and turbulence quantities. Turbulent kinetic energy (k) distributions were obtained using (i) a pseudo-isotropic approximation, from two velocity components and (ii) a full calculation from all three velocity components. The two calculation methods for k yielded similar results, indicating that data from 2-D PIV measurements yield reasonable estimates of the turbulence kinetic energy. The tangential velocity components at the impeller discharge from PIV were in good agreement with data from LDA analysis. A kinetic energy balance across the impeller was performed (i) rigorously and (ii) using approximations which neglected second- and higher-order velocity cross-correlations. Both analyses show that around 44% of the total power consumed by the impeller is dissipated in the impeller region. The average rate of dissipation of kinetic energy is about 40 times higher in the impeller region than the volume-average dissipation rate in the whole vessel.     

The Use of Positron Emission Particle Tracking in the Study of Multiphase Stirred Tank Reactor Hydrodynamics

This paper describes the use of positron emission particle Tracking (PEPT) in the analysis of local particle and fluid velocities in solid‐liquid stirred tank reactors agitated with a Rushton turbine and an upward‐pumping pitched blade turbine. PEPT captures the full three‐dimensional characteristics of hydrodynamics and mixing in stirred vessels, allowing the analysis of the two‐phase flow fields. Furthermore, by comparing the liquid and particle velocities, the spatial and temporal variation of the relative particle‐liquid velocity can be estimated. Such information reveals considerable heterogeneity in the vessel and facilitates the evaluation of impeller design, particularly with the aim of minimizing mass transfer limitations.     

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.     

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.     

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.     

Energy Dissipation Rates of Newtonian and Non‐Newtonian Fluids in a Stirred Vessel

Energy dissipation rates of water and glycerol as Newtonian fluids and carboxyl methyl carbonate solution as non‐Newtonian fluid in a stirred vessel are investigated by 2D particle image velocimetry and compared. Mean velocity profiles reflect the Reynolds (Re) number similarity of two flow fields with different rheological properties, but the root mean square velocity profiles differ in rheology at the same Re‐number. Energy dissipation rates are estimated by direct calculation of fluctuating velocity gradients. The varying energy dissipation rates of Newtonian and non‐Newtonian fluids result from the difference in fluid rheology and apparent viscosity distribution which decides largely the flow pattern, circulation intensity, and rate of turbulence generation.     

Numerical Investigation of Three‐Dimensional Bubble Column Flows: A Detached Eddy Simulation Approach

Numerical simulations were performed employing detached eddy simulation (DES) in a three‐dimensional transient Euler‐Euler framework for bubble columns, and all the computational fluid dynamics results were compared with a k‐? model and available experimental data. The numerical results are in good agreement with the experiments in predicting the time‐averaged axial velocity and turbulent kinetic energy profiles. The flow‐resolving capabilities of the DES model are highlighted, and it is shown that the DES turbulence model can be efficiently used for simulating flow field and turbulent quantities in the case of bubble columns.     

FLOW GENERATED BY PITCHED BLADE TURBINES II: SIMULATION USING κ-ε MODEL

Experimental data on average velocity and turbulence intensity generated by pitched blade downflow turbines (PTD) were presented in Part I of this paper. Part II presents the results of the simulation of flow generated by PTD

The standard κ-ε model along with the boundary conditions developed in the Part 1 have been employed to predict the flow generated by PTD in cylindrical baffled vessel. This part describes the new software FIAT (Flow In Agitated Tanks) for the prediction of three dimensional flow in stirred tanks. The basis of this software has been described adequately. The influence of grid size, impeller boundary conditions and values of model parameters on the predicted flow have been analysed. The model predictions successfully reproduce the three dimensionality and the other essential characteristics of the flow. The model can be used to improve the overall understanding about the relative distribution of turbulence by PTD in the agitated tank     

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.     

Estimation of the turbulent kinetic energy dissipation rate from 2D-PIV measurements in a vessel stirred by an axial Mixel TTP impeller

The turbulent dissipation rate is a key parameter in stirred tanks and its local values may have a strong influence on the performance of many processes. However, the local dissipation rate estimation is far from easy in a stirred tank, especially near the impeller discharge where maximum values are encountered. The aim of this work is to estimate the dissipation rate in a vessel used for animal-cell cultures and stirred with a down-pumping axial impeller (Mixel TTP) from velocity fields measured by 2D-PIV. Special attention is paid to the assumptions necessary to estimate the dissipation rate from 2D measurements and to the influence of measurement spatial resolution on the estimated values. The analysis of isotropy ratios measured on vertical, horizontal and tangential planes shows that the turbulence in the impeller discharge is far from isotropic. Isotropy assumptions classically used to estimate the dissipation rate from 2D measurements may thus lead to erroneous values. Based on the measured isotropy ratios, a new relationship is proposed to estimate the dissipation rate in the impeller discharge. This relationship is then used to estimate the dissipation rate on a vertical plane located in the impeller discharge zone. In order to analyze the influence of the measurement spatial resolution on the estimated values of the dissipation, a total of 12 spatial resolutions are tested. Results show that if the spatial resolution is divided by a factor 2, the dissipation rate increases by 220%. For the smallest spatial resolution value used, the maximum dissipation rate estimated is 50 times higher than the mean overall dissipation rate and the corresponding minimum value of the Kolmogorov scale is nearly 3 times smaller than the Kolmogorov scale computed from the mean overall dissipation rate.