Effect of eccentricity on transitional mixing in vessel equipped with turbine impellers

In this paper, the results of the experimental studies of the mixing time, as well as the power consumption and baffle presence in the stirred tank with dual eccentrically located impellers are presented. The experiments were carried out in an unbaffled flat-bottomed cylindrical vessel. Three types of impellers were used: Rushton turbine, six pitched blade turbine and six flat blade turbine. The obtained data show that eccentricity of dual impeller systems leads to reduction of mixing time. Moreover, the experimental data confirmed the enlargement of power consumption in such systems. In the paper the analysis of relation between eccentricity ratio and mixing time has been performed.     

Hydrodynamics and volumetric gas-liquid mass transfer coefficient of a stirred vessel equipped with a gas-inducing impeller

Hydrodynamic and mass transfer characteristics of a gas-liquid stirred tank provided with a radial gas-inducing turbine were studied. The effect of the rotation speed and the liquid submergence on global hydrodynamic and mass transfer parameters such as the critical impeller speed, the induced gas flow rate, the gas holdup, the power consumption and the volumetric gas-liquid mass transfer coefficient were investigated. The experiments are mainly conducted with air-water system. In the case of critical impeller speed determination, two liquid viscosities have been used. The volumetric gas-liquid mass transfer coefficient k_La has been obtained by two different techniques. The gas holdup, the induced gas rate and the volumetric gas-liquid mass transfer coefficient are increasing functions with the rotation speed and decreasing ones with the liquid submergence. The effects of these operating parameters on the measured global parameters have been taken into account by introducing the dimensionless modified Froude number and correlations have been proposed for this type of impeller.     

CFD analysis of a rotor-stator mixer with viscous fluids

The characterization of the hydrodynamics of a rotor-stator mixing head has been carried out in the laminar regime with viscous Newtonian fluids. The rotor-stator considered is a very common design composed of a flat blade rotating in a fixed slotted cage. A numerical methodology has been used based on the virtual finite element method to model the velocity patterns, estimate the distribution of shear stress and the flow rate through the head. We have found that the numerical prediction of the power consumption and flow profiles compare well with experimental data. The generation of a pseudo-cavern around the mixing head and how it scales with the Reynolds number have also been investigated, showing that there is a minimum speed limit below which the rotor-stator cannot be used.     

Mixing studies of non-Newtonian fluids in an anchor agitated vessel

The success of any mixing operation involving liquid–liquid, gas–liquid and gas–liquid–solid systems depends mainly on the geometry of the vessel and impeller, operating conditions and properties of the system. Transformation of laboratory results to commercial scale unit is very difficult due to the complexity of flow phenomena and the scale up is being done by adopting a conservative approach which is based on the geometric, kinematic and dynamic similarities. This approach does not take into account the non-ideal flow behavior of the fluid and the design of commercial unit will be more rational if this information is included in the design of the unit.     

Shear and skin friction on particles in power-law fluids agitated by flat-blade and fluid foil impellers

The shear rates that exert angular deformation on spherical particles have been measured. The particles are mimiced by a spherical probe. The probe has been immersed in various impeller-agitated power law fluids. The fluids are aqueous dispersions of polymers, e.g. CMC, xanthan gum and starch. The probe has been positioned in various points of a stirred vessel and at various angles. Angle-averaged shear rate distributions were produced. The distributions obtained are characteristic for the specific impeller flow patterns. The flow patterns have been identified by computational fluid dynamics (CFD). Two types of impellers representative for the flat and the fluid-foil blade design, i.e., a Rushton flat-blade turbine (RT) and a Narcissus impeller (NS) are studied. The effects of rheological properties and blade design on the ‘shear-rate-on-particles’ distribution are examined. The local shear field non-uniformity has been uncovered and compared in terms of the CFD-generated time-averaged velocity and deformation rate profiles. The ‘shear-rate-on-particles’ distribution apart from the impeller is found to follow qualitatively the time-averaged inner flow shear rate distribution. Referring to impeller speed 5-12.5 Hz, the dimensionless wall shear rate varied between 200 and 1000. In power law fluids, the shear rate on particles decreased up to 50%. The fluid-foil NS-generated shear field was found comparable to the shear field induced by conventional flat-blade turbines and appeared in cases less sensitive to polymer presence. The shear rate produced by the fluid-foil impeller in the highly shear-thinning model solution (n∼0.4) exceeded the flat-blade RT-imposed shear rate. The analysis has been extended to skin friction drag on particles. It is shown that, while exerting an undoubtedly greater angular deformation in water-like fluids, in polymer presence the conventional flat-blade turbine introduces a flow geometry that imposes particle drag that is close or in some cases even less than the one generated by the fluid-foil impeller. The fact implies a weak shape effect of radial turbines on shear-sensitive particles or particle dispersions in power law liquids.     

Modelling mass transfer in an aerated 0.2 m vessel agitated by Rushton, Phasejet and Combijet impellers

We assembled a set of models that allows investigation of local variables that are difficult to measure, validation of mechanistic physical models, and comparison of different numerical solutions. Population balances (PB) for bubbles were combined with local flow modelling in order to investigate G–L mass transfer in an air–water system. Performance of three different impeller geometries was investigated: Rushton (RT), Phasejet (PJ) and Combijet (CJ). Simulations were compared against experimental mixing intensity, gas hold-up, vessel-averaged volumetric mass transfer rates (k_La), and local bubble size distributions (BSDs).The simulations qualitatively predict k_La's with different impellers at the fully dispersed flow region and gave new insight on how k_La is formed and distributed in the stirred vessels. The used bubble breakage and coalescence models are able to describe both air–water and viscous non-Newtonian G–L mass transfer. Difference between experimental mass transfer rates of the three impellers was within experimental error, even trough the flow patterns, gas distribution, and local BSDs differ considerably. The population balance for bubbles was modelled in two different ways, with multiple size groups (MUSIGs) and with the bubble number density (BND) approach. MUSIG calculations took over twice as much computational time than BND, but there was little difference in the results. The Rushton turbine k_La was described with best accuracy, which is not surprising since most phenomenological models are fitted based on RT experiments. We suggest that these models should be validated over a wider range of vessel geometries and operating conditions.     

Mixing analysis in a tank stirred with Ekato Intermig impellers

The mixing performance of a batch stirred tank with four Ekato Intermig^® impellers is investigated in this paper by experimental and computational methods. We considered three impeller speeds corresponding to Reynolds numbers 37, 50 and 100, all in the laminar regime. For the purposes of model development and flow validation, Newtonian rheology is assumed, where the fluid density and viscosity is set to and , respectively. The computed velocity field and mixing patterns are validated using Particle Image Velocimetry, acid-base visualization experiments and Planar Laser-Induced Fluorescence. All three techniques reveal excellent agreements between the experiments and computations. Also, detailed Lagrangian analysis of mixing, using particle tracking and stretching simulations, is presented for two flowrates in the laminar regime. It is shown that severe compartmentalization exists in the vessel and transport in the axial direction is very slow. Characterization of local micromixing intensities is presented by computing the distribution of intermaterial area density and striation thickness distribution (STD) from the stretching field. It is found that the STDs at both flowrates are identical despite significant differences in the stretching field, suggesting that at low stirring rates micromixing performance is independent of agitation speed.     

Using CFD to predict the behavior of power law fluids near axial-flow impellers operating in the transitional flow regime

A computational fluid dynamics (CFD) model of flow in a mixing tank with a single axial-flow impeller was developed with the Fluent^TM software. The model consists of an unstructured hexagonal mesh (158,000 total cells), dense in the region from the surface of the impeller. The flow was modeled as laminar and a multiple reference frame approach was used to solve the discretized equations of motion in one-quarter of a baffled tank. A solution of 0.1% Carbopol in water, a shear-thinning fluid, was found to be clear enough to measure impeller discharge angles using laser Doppler velocimetry. This is the first time that impeller discharge angles have been reported in the literature for a shear-thinning fluid with a hydrofoil impeller. Rheological measurements indicated that the Carbopol solution can be characterized by the power law (K=9,n=0.2) under the range of shear conditions (0.1- expected near the impeller in the mixing tank. The CFD model accurately predicted the dependence of power number and discharge angle on Reynolds number (as predicted by Metzner and Otto), for an A200 (pitched blade turbine or PBT) and an A315 (Hydrofoil) impeller operating in the transitional flow regime (Reynolds numbers: 25-400) with glycerin and 0.1% Carbopol solutions. Subsequently, the results of a systematic CFD study with power law fluids indicated that the power number and discharge angle of an axial-flow impeller in the transitional flow regime depends not only on the Reynolds number (as determined by Metzner and Otto's method) but also on the flow behavior index n. Consequently, an alternative to Metzner and Otto's method was pursued. The results of converged CFD simulations indicate that the near-impeller “average shear rate” increases not only with increasing RPM (as proposed by Metzner and Otto), but also with decreasing flow behavior index (n) and discharge angle in the transitional flow regime. Considering this result, an improved method of estimating the power number and discharge angle for power law fluids in the transitional flow regime is proposed.     

Design of multiple impeller stirred tanks for the mixing of highly viscous fluids using CFD

The effect of multiple Intermig impeller configuration on hydrodynamics and mixing performance in a stirred tank has been investigated using computational fluid dynamics. Connection between impeller stages and compartmentalisation has been assessed using Lagrangian particle tracking. The results show that by a rotating the Intermig impeller by 45^° with respect to its neighbours, instead of a 90^° rotation as recommended by manufacturers, enables a wider range of operating conditions, i.e., lower Reynolds number flows, can be handled. Furthermore by slightly decreasing the distance between the lower two impellers, fluid exchange between the impellers is ensured down to Re=27.     

Solids distribution and rising velocity of buoyant solid particles in a vessel stirred with multiple impellers

The distribution of buoyant solid particles in agitated suspensions has been studied. The investigation was carried out in a baffled vessel characterised by an aspect ratio equal to four and stirred with four radial impellers. Dilute suspensions of single-sized spherical particles of expanded polystyrene (density equal to 90.7 kg/m³) in water were used. Solid concentration was measured with a non-intrusive optical technique. Measurements were performed along the axis of the reactor to obtain steady-state vertical profiles (that increase from the vessel base to the top) as well as at fixed elevations to determine their transient after a pulse of solids injected at the bottom.Both the steady-state profiles and the transient concentration curves were interpreted in terms of the axial dispersion model with sedimentation. By data treatment the rising velocity in the agitated system could be determined, which proved to be significantly smaller than the rising velocity in a still liquid. The ratio of these two velocities is in reasonable agreement with a correlation of the ratio of the settling velocities for heavy particles with the ratio of the Kolmogorov microscale to particle diameter established in the past.     

Mixing analysis in a coaxial mixer

The performance of a coaxial mixer in the laminar-transitional flow regime was numerically investigated with Newtonian and non-Newtonian fluids. These mixers comprised two shafts: a central fast speed shaft mounted with an open turbine, and a slow speed shaft fitted with a wall scraping anchor arm. To model the complex hydrodynamics inside the vessel, the virtual finite element method (POLY3D^TM software) coupled with a Lagrange multiplier approach to cope with the non-linearity coming from the rheological model was employed. Co-rotation and counter-rotation mode were compared, based on several numerical criteria, namely, mixing time, power consumption and pumping rate. It was found that co-rotating mode is more efficient than counter-rotating mode in terms of energy, pumping rate and homogenization time.     

Studies of a mixing process induced by a transverse rotating magnetic field

This study reports on research results in the field of a mixing process under the action of a transverse rotating magnetic field (TRMF). The main objective of this paper is to present the effect of this type of a magnetic field on the mixing time. The proposed dimensional analysis of Navier–Stokes equation including the Lorentz force allows describing the analyzed process by means of the relationships basing on the dimensionless numbers (the mixing time number, the magnetic Taylor number, and the rotational Reynolds number). The possibility of using the magnetic particles (Fe₃O₄) as active micro-stirrers under the influence of a TRMF for active enhancement of a mixing process was considered. Moreover, the effect of a particle content on homogenization efficiency by applying a TRMF was also investigated. The obtained experimental results suggest that the mixing time under the TRMF and MDF conditions may be worked out by using the relation between the mentioned mixing time number and the modified Reynolds number (particle Reynolds number). Important conclusions referring to the discussion of experimental studies of a mixing process are also specified.     

Effect of eccentricity on laminar mixing in vessel stirred by double turbine impellers

Laminar mixing is often conducted in industrial processes, for example in polymerization reactors or in biotechnological processes. The laminar flow conditions caused problems of inefficient mixing due to some mixing anomalies like occurrence of the isolated mixing regions (IMR), segregation or compartmentalization phenomena. In this paper, flow visualization experiments are used to examine the size, positions and structure of the IMR regions as a function of Reynolds number and eccentricity ratio in the vessel equipped with double turbine impellers. It was found that the eccentricity brings deformation and reduction of the IMR volume. Moreover another benefit of using eccentrically located impeller systems is an improvement of axial flow. Two types of IMR regions are found: undulated IMR (UIMR) and ribbon-like IMR (RIMR). The structure of IMR depends on the eccentricity ratio defined as E/R. At the low eccentricity values the structure of single filament wrapped around core of the IMR is found. Additionally, the IMR region is inclined to the impeller plane.     

Tomographic imaging during reactive precipitation in a stirred vessel: Mixing with chemical reaction

Electrical resistance tomography (ERT) allows the user to non-invasively ‘see inside their process’ through the manipulation and measurement of electrical properties enabling a powerful real-time visualisation of the time evolving three-dimensional conductivity distributions within the process unit. A 4-plane 16-sensor ERT array retrofitted to a 7.5 l stirred vessel has been used to rigorously interrogate the single feed semi-batch precipitation of barium sulphate, providing over 1000 spatially varying data points per ‘captured’ frame. A variety of reactant concentrations and agitation intensities were investigated. The results obtained reflect both the hydrodynamics and complex reaction kinetics involved with reactions and detail a number of very distinct regions during the experimental runs. This is achieved through the direct visualisation of the induced feed plume, quantification of the homogeneity (‘mixedness’) within the vessel, time evolving conductivity trends and a further analysis into the rates of conductivity changes as the reaction proceeds. For some experimental runs the predicted conductivity trends for a perfectly mixed state have been calculated using a conductivity-concentration correlation. ERT offers many spatially varying data points as opposed to point wise measurements which offers a significant improvement for the validation of mathematical models which attempt to deal with reactive crystallisation. As well as data collection, specifically for model validation, ERT may offer the means to control the spatio-temporal distributions of reactants and phases within the reactor to aid the suppression of unwanted by-products for industrial processes whilst offering a means to monitor the process unit to ensure the required mixing intensity is always achieved. Also included is an analysis of the mean volume diameter of the precipitate for each experimental run with scanning electron microscope (SEM) images.     

Improvement of granular mixing of dissimilar materials in rotating cylinders

We have found that periodic flow inversions of free-flowing materials may be used to effectively eliminate both size and density segregation in free-surface flows. In a rotating cylinder, these inversions may be induced by placement of an axially located baffle within the flow. In this work, we report on an experimental study of radial mixing and segregation for binary mixtures of granular materials in a rotating cylinder both with and without an axially-located baffle. Qualitative and quantitative measures of the segregation/mixing are shown via digitized images and the intensity of segregation, respectively. We define a mixing improvement factor (ψ) to quantify the relative impact of the axial baffle for a variety of baffle placements and geometries. We find that the maximum extent of mixing is achieved when the baffle size is equal to the radius of the cylinder and fixed either at the free surface or within the shear layer. In contrast, we show that segmenting the baffle, baffle placement outside the shear layer (in fixed bed), or placement at the periphery of the cylinder resulted in an insignificant increase in mixing. Mixing was found to be independent of the shape of a baffle.     

Simulating the mixing and segregation of solids in the transverse section of a rotating kiln

Rotating kilns are widely used in industry to process granular material. These processes include calcination of mineral ores, drying of foods and grains, combustion of wastes and manufacturing of pharmaceuticals. Since models developed for a particular process are often unique to that process there is a need to develop more generic models to predict the mixing and segregation in the transverse section of a rotary kiln.This paper presents a mathematical simulation - based on experimental observations - to estimate the mixing rate, final extent of mixing and the final distribution of material due to segregation. The models used in the simulation allow for scale-up of processes to produce a simulation that is applicable to a broad range of industrial processes. Independent experiments were used to verify the simulation and it was found that the mixing rate, the final extent of mixedness and the final segregated state could be predicted to within acceptable errors.     

Tomography measurements of gas holdup in rotating foam reactors with Newtonian, non-Newtonian and foaming liquids

Rotating solid foam reactors have already proven to show high mass transfer rates and to be a potential alternative to slurry reactors. The rotation of a foam block stirrer results in a high mass transfer and in the development of different reactor sections showing specific hydrodynamics and gas holdup distributions. In order to optimize the reactor system the hydrodynamics in a lab scale reactor are studied using γ-ray tomography, a powerful method to measure the gas holdup in three-phase reactors. The influence of liquid properties, such as viscosity and surface tension, and the rotational speed on the gas/liquid distribution in the different reactor sections is investigated. Especially the viscosity has a strong effect on the entrapment of gas bubbles in the foam block structure, while the surface tension is the dominant parameter in the outer reactor section. The influence of these parameters on the inset of foaming and the collapse of the gas/liquid dispersion is investigated. Conclusions on the mass transfer performance are drawn and recommendations for further optimizations of the reactor design and the operational conditions depending on the liquid properties are developed.     

Liquid phase mixing and gas hold-up in a multistage-agitated contactor with co-current upflow of air/viscous fluids

A hydrodynamic study is carried out in a multistage-agitated contactor with cocurrent upflow of air/viscous fluids. The liquid phase backmixing is characterized through a residence time distribution study in various viscous fluids (up to 20 mPa s). The liquid Reynolds number with respect to the impeller applied in the investigation ranges from 1000 to 50 000. A cascade of stirred tanks with back flow model satisfactorily fits all experimental residence time distribution curves in the present study. It is found that the increase in the liquid viscosity reduces the backmixing in the liquid phase due to its dampening effect on turbulence. The presence of the gas phase helps in reducing the backmixing by the straightening effect and entrainment effect in a co-current operation manner. The gas hold-up measured in the present study is comparable to the literature data. A new type of correlation taking into account the influence of the gas phase is proposed to predict the backmixing in a multistage-agitated contactor.     

Energy dissipation and macro instabilities in a stirred square tank investigated using an LE PIV approach and LDA measurements

In this study, the hydrodynamics and turbulence in a square tank stirred with a hydrofoil impeller, a Lightnin A310, is investigated using a large eddy particle image velocimetry (LE PIV) approach. The particle image velocimetry data are used as the large scale part of a large eddy simulation and the small scales are modelled assuming that the turbulent kinetic energy production is limited to the large scale structures, the turbulent energy dissipation is confined to the small scale structures and the transfer of energy takes place in the inertial sub-range. The small scale turbulence was modelled by direct calculation of the turbulent stress tensor using filtered particle image velocimetry data. The spatial distribution of the calculated dissipation rate tensors showed good agreement with previous work.

The macro instabilities of the flow structure were investigated by means of spectral analysis. Low frequency phenomena separated from the mean flow were detected. The cause of these could partly be explained by the circulation time for the tank, which corresponded to the low frequency phenomena found at 0.03N Hz, where N is the rotational speed.