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Impellers in stirred vessels are often characterized by dimensionless numbers such as the power and flow numbers. These are often crucial in determining mixing performance. Previous studies for high-shear mixers have yielded correlations between the power, flow, and mixer geometries, since in these mixers the flow can be independently varied. For stirred vessels, dimensional analysis is typically used to develop such correlations, leading to less accurate predictive models. Here, we combine an analysis based on a balance of angular momentum balance with computational fluid dynamics simulations to comprehensively study the effect of impeller geometry on the relationship between power and flow. The results allow for the prediction of the flow generated by the impeller based on the easily measurable impeller power consumption and the geometrical dimensions of the impeller. The models are accurate over a wide range of geometries. Furthermore, we are able to predict both the primary and total flows.

Accelerated growth of scale was studied in a baffled agitated reactor, which could be disassembled into nine sections, allowing quantitative determination of scale thickness. A coordinate measuring machine was used to determine the scale thickness on individual wall segments. The growth pattern of the scale was found to be nonuniform due to the variation of fluid velocity near the wall at various heights. Computational fluid dynamics (CFD) simulation showed that fluid flow is time-dependent and has two distinct flow zones, one involving recirculation through the impeller in the lower part of the vessel and the other involving lower velocities due to the flow separation at the wall in the upper part. CFD simulation also showed the presence of macroinstabilities, which manifest as asymmetrical and chaotic flow structures with relatively long-time scales. Scale growth is found to be prominent in regions where the fluid velocity and wall shear stresses are low.

The Anton Paar Powder Cell was used to measure the torque necessary to rotate an impeller in beds of glass beads, sand and alumina powders aerated between no aeration to the minimum for fluidization. Measured torque values depend on the material tested, on the air flow rate applied, on the impeller depth and on the height of the impeller blade. The effect of the impeller depth is linear for low impeller depth and is less than linear at high depth values. A model was developed for the interpretation of the experimental results based on the idea that the material is shearing on the surface described by the impeller rotation. The model allows to estimate an effectiveness of the impeller in the torque determination and also to predict the torque for the impeller at the at deepest positions at which the wall effects have to be considered. © 2017 American Institute of Chemical Engineers AIChE J, 2017

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

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

Local and temporal variations of the particle cloud formed in a cylindrical mixing vessel were investigated experimentally. Different particle sizes (0.5, 1, and 2 mm) and volumetric concentration up to 20 vol % were evaluated at different impeller speeds. The time-averaged cloud height was linear with impeller frequency and with volume concentration. Suspensions with larger particles had a lower average cloud height, while the standard deviation for the temporal cloud height variation was larger. Two strong periodic phenomena were identified to be dominating the particle cloud height variations. The frequencies were linear with impeller speed, resulting in dimensionless frequencies of S-1 = 0.02-0.03 and S-2 = 0.05-0.06. The frequencies were affected by neither the particle size nor the volumetric concentration. The amplitude showed no dependency on the particle size, but the S-2 amplitude significantly decreases and S-1 increases with increasing solid concentration. The results were compared to LES/discrete element method simulations and showed a fair agreement.

CO2 hydrate formation experiments are performed in a 20 L semi-batch stirred tank reactor using three different impellers (a down-pumping pitched blade turbine, a Maxblend™, and a Dispersimax™) at various rotational speeds to examine the impact of the flow conditions on the CO2 hydrate formation rate. An original mathematical model of the CO2 hydrate formation process that assigns a resistance to each of its constitutive steps is established. For each experimental condition, the formation rate is measured and the rate-limiting step is determined on the basis of the respective values of the resistances. The efficiencies of the three considered impellers are compared and, for each impeller, the influence of the rotational speed on the rate-limiting step is discussed. For instance, it is shown that a formation rate limitation due to heat transfer can occur at the relatively small scale used to perform our experiments. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4387–4401, 2015

The influence of impeller type in a mechanically stirred airlift bioreactor was analyzed in relation to the non-Newtonian viscous fluids. The agitation was carried out through a marine impeller (axial impeller) and a paddle impeller (radial impeller) located along with the gas sparger in the region comprised by the riser. The bioreactor was sparged with air under different velocities (0.036–0.060 m s−1). Carboxymethylcellulose 1.94% and xanthan 1.80% were used as a fluid model. The gas holdup and volumetric mass-transfer coefficient increased in up to five and three times, respectively, when compared to a conventional airlift bioreactor; however, better results were obtained when the straight paddle impeller type was used. The results suggest that the studied bioreactor can be used successfully in viscous fluid, and it can be more efficient than conventional airlift bioreactors. The results obtained suggest the use of radial impellers. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3159–3171, 2015

Maximum effective hydrodynamic stress, τmax, responsible for the breakup of aggregates with size comparable to Kolmogorov eddies, was experimentally determined in an aerated stirred tank. The proposed method is based on the measurement of the maximum stable aggregates size consisting of poly(methyl methacrylate) nanoparticles. The fractal aggregates were broken under various operating conditions in an aerated stirred tank and calibrated with known flow conditions using contracting nozzles to convert the measured aggregate sizes into hydrodynamic stress. It was found that τmax⁡ can vary substantially among studied conditions and its magnitude depends on the controlling mechanism including gas jet during bubble formation, bubble rise, bubble burst at the gas–liquid interface or the turbulence generated by the impeller. The measured values are in good agreement with literature data which supports the applicability of this method to characterize the maximum effective hydrodynamic stress in complicated multiphase flow. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1735–1744, 2015

Based on conventional turbulent jet theory and the general theoretical framework of scalar dispersion in turbulent shear flows, a novel formulation of the radial impeller's jet in stirred tanks is introduced. Whereas previous studies considered the impeller's jet as developed, it is now comprised of two separate spatial regions along the radial axis: the zone of flow establishment (ZFE) and the zone of established flow (ZEF). This formulation is accompanied with semi-analytical expressions for the prediction of turbulent key parameters including the random part of k and e in the ZFE. The new theoretical framework is validated both with laser Doppler anemometry measurements and with 3-D numerical simulations using the standard k−e turbulent model. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1413–1426, 2015

Scale-up of agitated drying processes to minimize particle size changes in active pharmaceutical ingredients (API) can be challenging. Particle agglomeration or attrition problems due to agitated drying are often discovered on the initial scale-up from the lab to the plant. Traditional laboratory drying equipment has not successfully reproduced the degree of agglomeration or attrition observed at scale. This discrepancy may be attributed to the ability of particulate solids, such as crystalline API's to transfer stresses from the normal direction into the shearing direction. As batch size increases during scale-up, the compressive and shearing forces experienced by the API increase. To overcome this limitation, a modified laboratory setup was constructed which reproduces the range of hydrostatic pressures observed during scale-up. This work highlights the use of the modified setup to characterize the propensity for particle attrition to occur at different stages of the drying process by measuring impeller torque. Torque measurements of the API powder at different hydrostatic pressures revealed a behavior consistent with Coulomb's law of friction. The torque data obtained from these measurements were used to determine the bulk friction coefficient for API powder beds at different liquid content. Additionally, the amount of work done by the impeller blades was correlated to the degree of particle attrition observed. A workflow for assessing risk of API attrition at scale is described. © 2014 American Institute of Chemical Engineers AIChE J, 61: 407–418, 2015

Crystallization processes in a 500 mL stirred tank crystallizer with computational fluid dynamics (CFD) and population balances toward estimating how crystal size distributions (CSDs) are influenced by flow inhomogeneities was explored. The flow pattern and CSD are presented here though extensive phase Doppler particle analyzer measurements and CFD predictions for three different impeller designs (disc turbine, pitched blade turbine, and Propeller) and each rotated at three different speeds (2.5, 5, and10 r/s). As crystallization processes in practice could involve break-up and aggregation of crystals, some selected break-up and aggregation kernels are incorporated. Extensive comparison of simulations with experimental data showed consistent trends in the proper quantitative range. An attempt has also been made to develop scaling laws: (a) mean particle size with average power consumption per unit mass and (b) particle-size distribution with the turbulent energy dissipation distribution. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3596–3613, 2014

Prediction of cavern formation in yield stress fluids in stirred tanks is of great importance for optimization. A new torus model is developed and then validated by experimental data and computational fluid dynamics simulation. Unlike existing mathematical models, the new torus model assumes that the circular center of the torus should not be outside the impeller swept region as the Reynolds number (Re) increases. Hence the cavern boundary is shaped like an apple torus rather than a horn torus. The new model also considers the cavern-vessel interactions. At relatively high Re, the new model predicts cavern shape and size better than other models. It correctly captures the cavern outline at various Re, which verified the assumption about torus center. The new model is then used to identify the influence of rheological parameters on cavern formation, and further extended to the cavern prediction of the dual-impeller system. (C) 2014 American Institute of Chemical Engineers

Flow mixing of a non-Newtonian fluid in a stirred tank equipped with a side-entry impeller was observed using particle image velocimetry (PIV). The effects of some geometrical parameters including the mixer shape and impeller type and position on the flow pattern were studied on velocity fields obtained at different locations inside the mixing domain. The different flow structures revealed that the ratio of inertial and viscous forces largely defines the flow pattern. Dead zones were observed inside the tank due to the rheological properties of the fluid. The size of the dynamic regions and the average velocity near the impeller were enhanced by increasing the suction area. Likewise, large pitch ratios were found to improve the active mixing zone and the axial discharge. Curves for the power and pumping numbers are reported for different axial flow impellers. © 2013 American Institute of Chemical Engineers AIChE J, 60: 1156–1167, 2014

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

Simulations of solid–liquid flow in an agitated tank have been performed. The simulations fully resolve the mildly turbulent liquid flow (Re � 2000) in the tank, and the spherical solid particles suspended in the liquid. Full resolution of the particles sets the grid spacing and thereby limits the tank size and the number of particles (up to 3600 in this article) that are computationally affordable. The solids volume fraction is some 8%. The lattice-Boltzmann method has been used to solve the flow dynamics; the particles move under the influence of resolved hydrodynamic forces, unresolved lubrication forces, net gravity, and collisions (with other particles, the tank wall, and the impeller). We show the start-up of the suspension process, demonstrate its dependency on a Shields number (that we interpret in terms of the Zwietering correlation) and show the impact of polydispersity on the suspension process. V

A detached eddy simulation (DES), a large-eddy simulation (LES), and a k-"-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-" 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. V C 2011 American Institute of Chemical Engineers AIChE J, 00: 000–000, 2011

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

In-line rotor stator mixers differ from in-tank versions because the flow is often controlled independently of the rotor speed. For in-tank devices the turbulent power can be adequately described by single impeller type power number. For an in-line rotor-stator mixer it is found that the power transmitted by the rotor consists of a power term and a flow term. The constants in this expression are normally obtained from a multilinear regression of a large matrix of experiments. Two simplified methods of obtaining these constants from limited data sets by (1) torque measurement and (2) by heat balance are described herein. These are used to determine the constants for a Silverson 150/250 MS inline mixer with different rotor stator arrangements from the laminar to turbulent regimes. The power and Metzner-Otto constants determined are shown to be in good agreement to data for a larger matrix of experimental data. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1683–1692, 2012

The flow variations or macroinstabilities (MIs) occurring in a vessel stirred by a pitched blade turbine (PBT) are studied through particle image velocimetry (PIV) experiments. Proper orthogonal decomposition and fast Fourier transform techniques are applied to the PIV velocity data at one vertical and nine horizontal planes below the impeller, to identify and characterize the flow structures present in the vessel. It is shown that the PBT MI is manifested as a precessional movement around the impeller axis and an oscillation in the direction of the axial mean stream around the shaft axis. The identified flow structures are similar to those previously observed in vessels stirred by Rushton impellers and are characterized by two dominant frequencies, equal to one-tenth and one-fifth of the impeller rotational speed. The nature and extent of these structures and their interaction with the trailing vortices emanating from the turbine blades are discussed. © 2011 American Institute of Chemical Engineers AIChE J, 2011

By using mixing intensification involving high solids concentration as a means to achieve process intensification for the mineral process industry is discussed here. Improving agitator energy efficiency is essential for operating at high solids concentrations. It is shown that improved agitator energy efficiency can be achieved by removing baffles and using higher power number impellers at high solids loadings. Power consumption (50–80%) reductions were demonstrated in the experiments. It is also suggested that slurry stratification in tanks can be used to boost either solids residence time or slurry mass flow. Basic equations related to solids residence time and solids throughput are presented for guidance toward minerals process intensification. An example on doubling throughput via intensification is presented. © 2010 American Institute of Chemical Engineers AIChE J, 2011

This article investigates ways of modeling the homogenization mechanism occurring when mixing highly viscous Newtonian fluids with a planetary mixer. In particular, an arrangement of ideal reactors containing a perfect‐mixed zone sweeping out a torus reactor is proposed to represent the dynamics of the mixing process. The originality of the arrangement of ideal reactors developed is due to the time–dependent location of the perfect‐mixed zone in the torus which mimics the periodic revolution motion of the agitator around the vertical and central axis in the vessel. To ascertain the reliability of the method proposed, tracer injections were carried out with a planetary mixer named TRIAXE® system. It is shown that modeling results are in close agreement with experimental ones on the whole range of impeller revolution speeds tested. The model proposed captures well the physical mixing phenomena. © 2010 American Institute of Chemical Engineers AIChE J, 2011 57;7

Solid suspension in stirred tank reactor is widely used in process industries for catalytic reactions, dissolution of solids, crystallization, and so on. Suspension quality is a key issue in design and operation of stirred reactor and its determination is not straight forward. Cloud height measurements of solid suspension provide a relatively simple way to quantify quality of suspension. In this work, experiments were carried out to quantify variation of cloud heights with impeller speed and particle characteristics. These measurements were carried out using visual observations, image analysis, and ultrasound velocity profiler techniques. The obtained data demonstrated the existence of hysteresis in cloud heights with respect to impeller speed. Apart from possible applications in reducing power required for achieving desired solid suspension quality, the existence of hysteresis also provides a new way to evaluate computational fluid dynamics (CFD) simulations of solid liquid flows in stirred vessels. An attempt was made to capture observed hysteresis in cloud heights in CFD simulations. The simulated results were compared with the experimental data. The presented models and results (experimental and computational) will he useful for simulating complex solid liquid flows in stirred reactors. (C) 2010 American Institute of Chemical Engineers AIChE J, 56: 2795-2804, 2010

Numerical simulations of granular flow in a cylindrical vessel agitated by a four-blade impeller were performed using the discrete element method. Velocity, density, and stress profiles within the mixer displayed a periodic behavior with a fluctuation frequency equal to that of the blade rotation. Blade orientation was found to affect flow patterns and mixing kinetics. For an obtuse blade pitch orientation, a three-dimensional recirculation zone develops in-front of the blade due to formation of heaps where the blades are present. This flow pattern promotes vertical and radial mixing. No recirculation zone was observed when the blade orientation was changed to an acute blade pitch. The system's frictional characteristics are shown to strongly influence the granular behavior within the mixer. At low friction coefficients, the 3-D recirculation in front of the obtuse blade is not present reducing convective mixing. Higher friction coefficients lead to an increase in granular temperature which is associated with an increase in diffusive mixing. Normal and shear stresses were found to vary with mixer height with maximum values near the bottom plate. Additionally, a strong dependence between the magnitude of the shear stresses and the friction coefficient of the particles was found. The stress tensor characteristics indicate that the granular flow in our simulations occurs in the quasi-static regime. At the same time, the averaged pressure was found to vary linearly with bed height and could be predicted by a simple hydrostatic approximation. © 2009 American Institute of Chemical Engineers AIChE J, 2009

A computational fluid dynamics (CFD) model is proposed, based on ANSYS-CFX tools coupled to optimization models inside the commercial optimization software mode-FRONTIER in order to obtain an optimal design of a high-efficiency impeller for solids suspension. The aruzlysis of impeller shape performance was carried out using the shear-stress transport (SST) turbulence model with streamline curvature correction. This turbulence model combined the advantages of the κ―e and κ―ω models, ensuring a proper relation between turbulent stress and turbulent kinetic energy, allowing an accurate and robust prediction of the impeller blade flow separation. The multiple frames of reference and the frozen rotor frame change models were used for the rotor/stator interaction inside the mixing vessel. The optimization procedure used seven design variables, two nonlinear constrains and two objective functions. The objective functions chosen (among many other possible options) to evaluate the impeller performance were the maximum solid distribution throughout the vessel (homogeneous suspension) reflected by a low variance between local solid concentration and average solid concentration inside the vessel and the higher pumping effectiveness, which was defined as the quotient of the flow and power numbers. The first objective function searches for impeller configurations able to provide good solid suspension, since it aims to achieve homogeneous suspension. The second objective function aims to reduce power consumption for a high-pumping capacity of the impeller. These criteria were considered enough to characterize the optimized impeller. Results indicated that the optimized impeller presented an increase of the pumping impeller capacity and homogeneous solid suspension with low-power consumption, especially when compared with the PBT 45° impeller.

Both the large eddy simulation (LES) technique and the k-epsilon turbulent model were used to simulate the gas-liquid turbulent flow in a stirred tank driven by a Rushton impeller. A Eulerian-Eulerian two-fluid model for gas-liquid two-phase flow, was developed using the large eddy,v simulation for both gas (aid liquid phases. The relative baffles was accounted for through the movement of the rotating impeller to the static baffles 'improved inner-outer iterative algorithm. The spatial discretization of the governing equations was performed on a cylindrical staggered grid. For the LES, a conventional Sniagorinsky,v sub-grid model was adapted to modeling the turbulence of the liquid phase. The momentum and continuity equations were discretized using the finite diffrence method, ",ij'h a third order QUICK (Quadratic Upwind Interpolation tor Convective Kinematics) scheme used for convective terms. The phase-resolved predictions of the LES were compared with the experimental data and the simulation results by the standard k-epsilon model, suggesting that the LES has much better accuracy than the k-epsilon model. (c) 2008 American Institute of Chemical Engineers.

Turbulent flow and bubble coalescence in water at the leeward side of a baffle in a stirred tank reactor have been studied with PIV and a high-speed CCD camera. A large stationary vortex was revealed at the leeward side of the baffle. At impeller speeds of 400–600 RPM, the maximum tangential velocity at the vortex was proportional to the impeller tip speed (uθ ≈ 0.27 Utip), giving a pressure difference in the vortex of as much as a few hundred pascal. The main mechanism for coalescence in this area was trapping of bubbles in the vortex, increasing the local hold-up and coalescence probability by forcing the bubbles together. The force on the bubbles resulting from the local pressure gradient makes the bubbles move fast to the centre, within 10–20 ms. The coalescence efficiency was very high and more than 85% of the coalescence occurred within 2 ms. Bouncing of bubbles was mainly seen for large bubbles moving up in the centre of the vortex. The trapping of the bubbles was modeled successfully by a drag coefficient model corrected for nonspherical bubbles and turbulent continuous phase. © 2007 American Institute of Chemical Engineers AIChE J, 2007

The present work involves Computational Fluid Dynamics (CFD) modeling and validation of head and power characteristics of a Top Shrouded Turbine with Nonradial Rectangular Blades (TSTNRB) operated in backswept mode. Following the successful validation reported here and in two previous studies by the authors. CFD has been used to simulate the performance of different kinds of impellers viz. Straight Blade Paddle (SBP), Rushton Turbine (RT), Top Shrouded Turbine with Radial Rectangular Blades (TSTRRB), Top Shrouded Turbine with Radial Trapezoidal Blades (TSTRTB), Top Shrouded Turbine with Non-radial Rectangular Blades (TSTNRB), Top Shrouded Turbine with Curved Blades (TSTCB), and Both side Shrouded Turbine with Radial Trapezoidal Blades (BSTRTB), to compare them for pump-mix action. Baffle-impeller interaction has been modeled using the sliding mesh approach. Standard k-e model has been used for turbulence modeling. The power number, head number, and flow number have been computed for each impeller. The impellers have been rated on the basis of head generated by them for equal specific power input. An attempt has been made to explain why different impellers operating at the same speed and handling the same inlet flow rate should give different heads. How this insight can be used to conceptualize better designs of pump-mix impeller is illustrated. © 2007 American Institute of Chemical Engineers AIChE J, 2008

The precession of macroinstability (MI) vortices in stirred vessels has been investigated with vortex tracking methodologies, and utilized to enhance mixing performance. The techniques used are presented and employed to determine the instantaneous and average location, size and vorticity of the MI vortex for Re = 3,200 and 32,000 in 80 and 294 mm dia. vessels stirred by a Rushton impeller. Measurements of mixing time are performed in a 588 mm dia. vessel with surface insertion of a passive scalar tracer either inside or outside the precessing MI vortex. The data indicate that in-vortex insertion can result in a mixing time reduction of 20%, and even possibly 30%. © 2007 American Institute of Chemical Engineers AIChE J 2007

In this study, the spatial distribution and significance of macro instabilities in two cylindrical tanks of different size, and one square tank, stirred with standard six bladed Rushton impellers, are investigated. The instabilities of the flow structure are investigated by searching for significant frequencies using the Lomb algorithm on instantaneous velocity data collected using laser Doppler anemometry at various locations in the tanks. The investigation of the energy levels shows that the harmonics of the blade passage differ in both magnitude and spatial distribution for different tank sizes, geometries, and energy input. Several significant dimensionless frequencies, that is, frequency Strouhal numbers, are detected and identified both in relative magnitude and spatial range. © 2006 American Institute of Chemical Engineers AIChE J, 2006

Mixing of shear-thinning fluids with yield stress is investigated in a three-dimensional (3-D) flow both in experiments and in simulations. Experiments are conducted in a stirred tank using tracer visualization and velocity measurements. Bulk flow visualization shows the familiar cavern formation around the impeller with stagnant zones surrounding it. Detailed flow visualization inside caverns reveals the main ingredients of chaotic flow: lobe formation, stretching, folding, and self-similar mixing patterns. For multiple impeller systems, however, we find strong compartmentalization characterized by robust segregation between adjacent caverns, hindering mixing performance. Mixing efficiency is enhanced by moving the shaft off-center, which breaks spatial symmetry. The displacement of the shaft from the tank centerline has a beneficial effect on manifold structure: segregated regions are destroyed, separatrices are eliminated, and axial circulation is improved. Numerical simulations are performed by solving the incompressible Reynolds Averaged Navier Stokes equation with a Galerkin Least-Squares finite-element formulation and a macroscopic rheological model. Simulations are able to capture the main features of the flow and are used to investigate stretching statistics and scale behavior. © 2006 American Institute of Chemical Engineers AIChE J, 2006

DOI 10.1002/aic.10997Published online September 26, 2006 in Wiley InterScience (www.interscience.wiley.com).In turbulent liquid mixing, the performance of a stirred tank is usually expressed as thetime it takes to homogenize a passive scalar concentration starting from a segregatedstate. Numerical prediction of mixing times requires solving the flow field and theassociated passive scalar. A novel numerical approach is presented to passive scalarmixing in an agitated tank. In addition to a large-eddy simulation based on lattice-Boltzmann discretization of the Navier-Stokes equations, the convection-diffusion equa-tion governing passive scalar transport has been solved by finite volume discretization.Numerical diffusion has been effectively eliminated by applying a TVD scheme. With thishybrid approach we study mixing in a Rushton turbine stirred vessel at Re 24,000. Thesimulations were designed such that their results can be critically assessed with experi-mental data. The simulations are in (at least) qualitative agreement with the experiments,and allow for assessment of how mixing times defined in various ways relate. Also the roleof the impeller size has been investigated. The numerical method needs improvement inthe sense that it is not exactly mass conservative, which likely is due to the fixed-gridapproach in combination with a non-fixed (revolving) impeller.

Laboratory laser Doppler velocimetry (LDV) measurements were conducted to measure the shear rate coefficient KS of a range of impellers. Equations correlating KS with NQ (flow number) are provided for axial flow and radial flow impellers. Theoretical formulations based on the classic boundary layer theory are developed to estimate the shear rate at the blade surface. Calculations show that the shear rates at the blade surface are many orders of magnitude higher than those in the flow at the impeller outlet. The software code XFOIL was used to illustrate typical distributions of the shear rates along the blade surfaces. Effects of viscosity, non-Newtonian shear-thinning index, agitator design, and scale-up on shear rates are illustrated. © 2006 American Institute of Chemical Engineers AIChE J, 2006

The ensemble-averaged kinetic energy viscous dissipation rate was determined with a multipoint LDA technique in a vessel stirred by a Rushton turbine. Nine out of the total of 12 mean squared velocity gradients constituting the dissipation rate were directly measured in the impeller stream, and the deviation of the flow from local isotropy was investigated. The dissipation rate normalized with N3D2, where N and D are the impeller rotational speed and the impeller diameter, respectively, was found to be approximately constant for Reynolds numbers of 20,000–40,000, whereas the fluctuating gradients were found to vary significantly, by up to three times the ensemble-averaged values, with blade angular position. The ensemble-averaged dissipation rate values were also assessed through a local turbulence kinetic energy balance. © 2005 American Institute of Chemical Engineers AIChE J, 2005

The goal of this report is to analyze the relationship between characteristic floc size and hydrodynamics in a mixing tank. The first question addressed concerns the relation between an average floc size and the viscous dissipation rate of kinetic energy. A first series of flocculation experiments were conducted in a mixing tank with two impellers (a Rushton turbine and a Lightnin A310 impeller) for equivalent dissipated power conditions. The average floc size is shown to depend on the global dissipation rate; it does not depend on the impeller type. However, the floc size distributions are significantly different for each impeller. The second question addressed concerns the dependency of the floc size on the history of mixing. A second series of experiments consisted of flocculation, breakup, and reflocculation stages. These experiments showed that the average floc sizes are similar after flocculation or reflocculation steps, but, once again, the floc size distributions can be very different with different impellers. The flocculation phenomena analyzed in this study mainly occur in the viscous subrange, with maximum floc size on the order of Kolmogorov microscale. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2064–2081, 2004

The discharge flow of a Rushton turbine is characterized by a counter-rotating vortex pair generated behind the impeller blade. The objective here is to characterize these trailing vortices. To this end, PIV measurements were synchronized with blade position. These measurements were performed to identify and locate the trailing vortices, according to an identification technique proposed to detect a vortical region. The advantage of this method for determining the trailing vortex is highlighted after comparison to previous techniques. The trajectory of the vortices is deduced and it is shown to follow the phase-averaged velocity field induced by the impeller. The trailing vortices were characterized in terms of size and velocity circulation within the vortex. The interactions between these organized structures and turbulence were also illustrated. © 2004 American Institute of Chemical Engineers AIChE J, 50: 75– 86, 2004

Low-frequency mean flow variations, identified experimentally in various stirred-tank geometries, are studied by means of large eddy simulations in a Rushton turbine stirred tank. The focus is on flow structures, and the spectral characteristics of the velocity components. The lattice-Boltzmann Navier-Stokes solver, and the Smagorinsky subgridscale model, are adopted for solving the stirred tank flow, and boundary conditions are imposed by means of an adaptive force-field technique. Simulations performed at Reynolds numbers 20,000 and 30,000 on grid sizes of 120 3 , 180 3 , and 240 3 grid nodes confirm the experimentally found flow variations at various monitoring points in the bulk flow. The period of the flow variations found in the bulk of the tank corresponds to approximately 250 blade passage periods. A simulation performed at a Reynolds number of 12,500 showed pronounced flow variations with a timescale of about 65 blade passage periods, which is consistent with experimental observations. Transient flow field results in the bulk flow of the tank uncover a whirlpool type of precessing vortex, of which the impact on the kinetic energy of the velocity fluctuations is further analyzed. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2383–2393, 2004

Flow instability phenomena in stirred vessels were studied with laser anemometry and flow visualization. The effects of fluid density and viscosity, impeller Reynolds number (Re), impeller design, diameter, and off-bottom clearance were investigated in order to quantify the frequencies (f) of the macroinstabilities stemming from precessional motions. The instabilities are characterized by two frequencies, one present at low Re, and another at high Re values. For intermediate Re values, both frequencies were present. In all cases, f was proportional to the impeller speed (N). The parameter f′ = f/N was shown to be linearly related to the impeller diameter in the low Re range; f′ was not affected by impeller clearance. At constant Re, a change in fluid density and viscosity did not affect f′. The energy contained in the instability frequencies was shown to vary across the vessel. The implications of the results mixing practice are discussed. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2050–2063, 2004

Helical ribbon impellers are widely used in chemical and process industries for the mixing of pseudoplastic fluids of high viscosity. The design of such impellers is based on an assumed linear relation between shear rate and the rotation speed of the impeller. A number of computational fluid dynamics (CFD) simulations of the flow field have been carried to verify this hypothesis. It is shown that while the shear rate varies greatly within the mixing vessel, there does exist a linear relationship between the impeller speed and the local shear rate near the tip of the impeller. The proportionality constant K s associated with this linear relation is found to be dependent on the geometric parameters of the system, but is largely independent of the flow behavior index. Based on these results, a new correlation, applicable to both Newtonian and power-law fluids for power consumption, is proposed.

A PIV technique is used to analyze the local hydrodynamics generated by a Rushton turbine. Different types of motion coexist in the tank: the mean flow (or global circulation), the periodic fluctuations (or trailing vortices) induced by the blade rotation in the impeller region, and the turbulent fluctuations (that dissipate the kinetic energy). These three kinds of motion can be estimated after experiments as soon as a triple decomposition of the velocity is performed. The mean velocity, the periodically induced stress, and the Reynolds stress are analyzed in the agitated tank, close to the impeller. These data are used for two purposes: to identify and quantify the transfer of kinetic energy between mean flow, periodic flow, and turbulence; and to estimate the dissipation rate of turbulent kinetic energy (TKE) from the balance of TKE, in which each term will be derived from experiments. Characteristics of turbulence are also presented and discussed.

Although stirred tanks have been the most commonly used fluid mixing devices since the beginnings of the industrial era, little is known about how and why they mix, and, therefore, about how to improve their performance, particularly when operated in the laminar regime. In laminar conditions, chaos is the only route to achieve efficient mixing. From the body of research in 2-D chaotic flows, very minute perturbations in the velocity field can lead to widespread chaos and substantial enhancement of mixing performance, but these observations have not been systematically applied to industrially relevant 3-D flows. Using planar laser induced fluorescence and direct numerical simulations, the mechanisms of creation and evolution of mixing structures were studied in Newtonian and non-Newtonian flows. The observed dynamical behaviors are related to geometric features of the system. In Newtonian flow systems, the passing of the impeller blades triggers the onset of chaos by introducing small perturbations to the underlying regular 2-D flow that is observed when impellers are substituted with discs. In non-Newtonian viscoelastic systems, nonlinearity in the stress field introduced by the fluid rheology drives the system to spontaneous chaos even when concentric discs are used to stir the fluid.

This paper presents experimental research carried out in a model mixing vessel on suspending solid particles at high concentrations. It was found that the maximum solid concentration at which slurry suspension can be maintained is approximately 0.90 when normalised by the bed packing coefficient. A higher exponent a-value was found for the dependency of just-off-bottom impeller speed on solids loading in the high solids loading range. At high solids loadings, radial impellers require relatively less power than axial flow impellers to suspend solids, the opposite to that observed in the low solids loading range. When operating in high solid concentration, there is an increase in power number for pitch-bladed turbines and a reduction in power number for Rushton turbines, in comparison with operating in water.

Mixing has a major influence on the product ratio of fast competitive reactions, as the product ratio of these reactions is determined by local concentrations. To integrate models from literature for the description of the mean and fluctuating concentration of a continuous reactant flow fed to a stirred-tank reactor, the models are validated against detailed experimental data for a stirred-tank reactor equipped with a Rushton turbine impeller. Application of these models requires information on local hydrodynamic parameters, which are determined by laser Doppler velocimetry. Model calculations are validated by determining the mean concentration and concentration variance of an inert tracer fed with planar laser-induced fluorescence to the studied stirred-tank reactor. To calculate the mean concentration, a combination of a theoretical model, measured mean concentrations and LDV measurements is used to determine the turbulent diffusion coefficient. The turbulent mixer model is used to calculate the concentration variance. Compared to the literature, this model requires adjustment of the constant in the production of the concentration variance to fit the measured concentration variances correctly. For the mean concentration and its variance, measurements agreed reasonably with simulations.

Accurate prediction of power consumption of impeller in an aerated vessel is crucial for a successful scale-up, operation, and design of reactors in general. A mechanistic model with a correlation that can accurately predict power consumption was developed. Taking into account both geometrical parameters and physical properties of the working fluids, this model reduces the number of adjustable parameters better than published empirical relations. It has the advantage of allowing the user to easily scale up agitated vessels and to evaluate power consumption even for large-scale equipment. It has been tested only for Rushton turbines, however, because it is simply based on mass balances, energy balances and continuity equations, it could also be implemented for use with other impellers with very few modifications.

Scale-up of orthokinetic agglomeration in stirred-tank reactors was studied numerically. A computer code based on the lattice-Boltzmann method was used to perform large eddy simulations. To account for the dependence of agglomeration on hydrodynamics, the kinetic relation proposed by Mumtaz et al. was applied locally. The convection-reaction equation governing the evolution of the particle-number concentration was solved at the same resolution as the flow field. Three scale-up rules were studied: scale-up at constant Re-number, constant specific power input, and constant impeller tip speed. Vessel sizes varying from 1 to 10,000 L were simulated. The use of two types of impellers (Rushton turbine and Pitched Blade turbine) allowed for investigating the dependence of agglomeration on the macroscopic flow pattern in a reactor. Inhomogeneities in stirred-tank flow caused unpredictable scale-up behavior. Scale-up at constant power input yielded the most constant reactor performance. Impeller geometry had a drastic impact on the observed agglomeration rate, even if the difference in Po number was taken into account.