Impeller Stream Research Articles

Near-wall resolution and wall modeling for lattice Boltzmann simulations of mechanically agitated vessels

We demonstrate the importance of near-wall treatment in lattice Boltzmann models (LBM) for mechanically agitated vessels at high Reynolds numbers typical of industrial mixing. LBM simulations were performed with and without wall models at multiple resolutions. Results were compared to experimental data in the impeller stream and the near-wall region. Neglecting wall models when under-resolving the wall regions, which is the typical practice for LBM simulations of stirred vessels, led to incorrect flow prediction. Either extreme spatial resolution in the near-wall region or the use of wall models improved predictions when comparing to other software methodologies (Finite Volume Method) and experimental data. However, the use of wall stress-based models in this work led to a small bias that persists even at higher resolutions whether using finite volume or lattice Boltzmann methods. More accurate wall models should be investigated for more accurate predictions in turbulent mechanically agitated vessels.

PIV and dynamic LES of the turbulent stream and mixing induced by a V-grooved blade axial agitator

The hydrodynamic behavior of a turbulent flow and the mixing characteristics generated by a V-grooved axial impeller inside an agitated tank reactor were investigated both experimentally and numerically. Angle resolved Particle Image Velocimetry (PIV) techniques with an angular displacement Δθ = 5° have been applied and two aerodynamic planes along the blades were considered. PIV-based results were compared to those obtained by Large Eddy Simulation (LES), used with the dynamic Smagorinsky-Lilly sub-grid scale (SGS) model. Results showed the existence of distinctive recirculation zones in the aerodynamic planes, and new additional frequencies in the impeller stream, induced by the grooves. A decrease of mixing time of about 11% was obtained experimentally, consequence of the better suction induced by the grooved blades in the early stages of mixing. Mean velocities, vorticity, TKE obtained from LES showed a good agreement with the PIV-based results. The distributions of turbulence dissipation rate ε were similar to those obtained from PIV, however showing high under-predicted magnitudes.

CFD simulation of single-phase flow in flotation cells: Effect of impeller blade shape, clearance, and Reynolds number

A series of numerical simulations of turbulent single-phase flows are performed to understand the flow and mixing characteristics in a laboratory scale flotation tank. Four impeller blade shapes covering a wide range of surface areas and lip lengths are considered to highlight and contrast the flow behavior predicted in the impeller stream. The mean flow close to the impeller is fully characterized by considering velocity components along the axial direction at different radial locations. Normalized results suggest the development of a comparatively stronger axial velocity component for a blade design with the smallest lip length, called big-tip impeller here. Normalized turbulent kinetic energy profiles close to the impeller reveal the existence of an asymmetric trailing vortex pair. The highest turbulence kinetic energy dissipation rates are observed close to the impeller blades and stator walls where the radial jet strikes the stator walls periodically. Furthermore, liquid phase mixing in the flotation cell is studied using transient scalar tracing simulations providing mixing time data. Finally, pumping capacity and efficiency of different impeller designs are calculated based on which the impeller blade design with a rectangular blade design is found to perform most efficiently.

Analysis of PIV measurements using modal decomposition techniques, POD and DMD, to study flow structures and their dynamics within a stirred-tank reactor

The present work is a comparative analysis of Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) computed on experimental turbulent velocity fields measured in a 20L-tank stirred by two Rushton impellers at two rotating speeds, N = 150 and 300 rpm. POD identifies flow structures that optimally capture the total kinetic energy of the flow, while DMD identifies structures that significantly contribute to the dynamics of the flow. The experimental data, i.e. the instantaneous velocity fields Ur(r,z,t) and Uz(r,z,t), come from 2-D Particle Image Velocimetry (PIV). The flow motion is turbulent, and it occurs over a wide range of length and time scales, from equipment-dependent large-scale coherent structures to the smallest-scale eddies where energy dissipation takes place. It thus provides an interesting benchmark case for the comparison between POD and DMD, which are based on energy and dynamic analysis, respectively. POD analysis reveals that the most energetic structures are related to the inherent periodic unsteadiness due to the relative motion between the rotating impeller blades and the non-moving baffles. Apart from the mean field, the first most energetic group of modes is related to trailing vortices induced by the Rushton turbines and is associated to a frequency equivalent to the blade passage frequency and its overtones. The second most energetic group of modes is related to vortical structures in the impeller stream and is associated to a frequency equivalent to the rotating speed. DMD analysis identifies flow structures that are found similar to these most energetic modes, although differences appear due to the fact that DMD isolates structures associated to a single frequency and their corresponding growth/decay rate. As in POD, the relative importance of each DMD mode can be estimated using an appropriately defined energy criterion. Comparison of the results from both modal decomposition methods points out their complementarity and their potential for describing the spatial and time characteristics of the flow within a stirred tank.

Investigation of gas dispersion characteristics in stirred tank and flotation cell using a corrected CFD-PBM quadrature-based moment method approach

In this study, the population balance model (PBM) is coupled with computational fluid dynamics (CFD) to investigate the steady-state bubble size distribution in two types of process equipment namely, a standard Rushton turbine stirred tank reactor and a generic lab-scale flotation cell. The coupling is realized using Fluent 15.07 software, and the numerical model is validated for the stirred tank reactor. The population balance equation (PBE) is solved using the quadrature method of moments (QMOM) technique along with a correction procedure implemented to check and correct invalid moment sets. The breakage and coalescence of bubbles due to turbulence are considered. The breakage rate and daughter size distribution models proposed by Laakkonen et al. (2007) are considered. For modeling coalescence rate, models proposed by Coulaloglou and Tavlarides (1977) are considered. The interaction between the phases is handled by considering the drag model proposed by Lane et al. (2005) while ignoring the other interphase forces. The correction algorithm has been successfully implemented, and improved predictions of gas volume fraction and Sauter mean diameter (SMD, d32) have been observed with a good match between the predictions and experimental measurements. The local SMD predictions are compared against predictions from the past studies and the superiority of the current approach for moderate gassing rates is established. The CFD-PBM approach is then used to study and characterize different flow regimes occurring in a generic mechanical flotation cell at different aeration rates and impeller rotation speeds. Also, power numbers are calculated from torque data and are found to drop considerably with an increase in aeration rate and impeller rotation speed as the flow regime approaches recirculating flow. The predicted SMD for flotation cell indicates that smaller bubbles are concentrated near the high turbulence impeller stream, the lower recirculation region, and close to the tank walls. On the other hand, large bubbles are formed in the upper tank region and are concentrated around the shaft during the flooding, loading, and transition flow regimes. In the future, the corrected QMOM approach will be further extended by implementing kinetic models capable of predicting the flotation rate constant using local bubble size information obtained from CFD-PBM simulations.

PIV Measurements to Study the Effect of the Reynolds Number on the Hydrodynamic Structure in a Baffled Vessel Stirred by a Rushton Turbine

Turbulent flow inside a cylindrical baffled stirred vessel is studied experimentally for different Reynolds numbers. A set of speed was selected ranging from 100 rpm to 350 rpm. These speeds gave high turbulence but without significant surface vortex formation. Vector field’s maps and contours of time averaged velocities, for both radial and axial components in the impeller stream of a vessel stirred by a Rushton turbine, were determined by means of 2D PIV technique. This study reveals the importance of choosing the whole flow field of the entire vessel in order to provide comprehensive understanding of the flow pattern and mixing conditions which is essential for reliable design.

Effect of the Tank Design on the Flow Pattern Generated with a Pitched Blade Turbine

The effect of the tank design on the hydrodynamic structure is carried out in three tanks; cylindrical tank, curved tank and spherical tank; equipped with a six-pitched blade turbine (PBT6). The hydrodynamic behaviour is numeri- cally predicted by the resolution of the Navier-Stokes equations in conjunction with the Renormalization Group (RNG) of the k-e turbulence model. These equations are solved by a control volume discretization method. The numerical results from the application of the CFD code Fluent with the Multi Reference Frame (MRF) model are presented in the impeller stream region. Particularly, the velocity components and the turbulent characteristics are presented in different planes con- taining the blade. The power consumption of these stirred tanks was calculated to choose the most effective system. The comparison between the numerical results and the experimental data showed a good agreement.

Effects of baffle length on turbulent flows generated in stirred vessels

Abstract The aim of this paper is to study the effect of baffles length on the turbulent flows in stirred tanks. The hydrodynamic behaviour induced by a Rushton turbine (RT6) is numerically predicted by solving the Navier-Stokes equations in conjunction with the Renormalization Group (RNG) of the k-ɛ turbulence model. These equations are solved by a control volume discretization method. The numerical results from the application of the computational fluid dynamics (CFD) code Fluent with the multi-reference frame (MRF) model are presented in the vertical and horizontal planes in the impeller stream region. Our studies were carried out on three different systems. The most effective system was selected based on its calculated power consumption figure. All numerical results showed good agreement with experimental data.

Modeling Erosion Wear Rates in Slurry Flotation Cells

In processes using slurry as the working fluid, wear due to solid particles impinging on elements of the process units is a serious reliability issue. This study considers modeling wear damage in flotation cells, which are widely used in mineral processing. Flotation cells are typically cylindrical vessels where an impeller is used to agitate the fluid, enabling the liberation of the minerals from the slurry. Some solids, particularly those entrained in the impeller stream, can impact on the wall of the cell, leading to material loss and eventually to loss of structural integrity. The problem of predicting the remaining life of the unit due to erosion requires understanding of various sub-processes: flow modeling, particle–fluid interaction, energy interactions at the surface, and the mechanism of erosion itself. In this study, empirically developed equations for the flow field of cylindrical mixing vessel with a Rushton turbine are used in formulating a model relating and the damage accumulation rate to a simple set of measurable variables. To validate a model, a PIV technique was used to measure velocities in the flow field and near the wall on a physical model of the cell with transparent walls and particles that match the refractive index of the fluid. An Eulerian–Langrangian approach has been used to determine the particle trajectories and the effect of a squeeze film is incorporated into the model to modify the velocity distribution of particles prior to impacts. An analytical model based on equations of impulse and momentum for a particle of any shape striking a flat massive surface has been used to describe the energy lost at the walls. Finally, a damage model is developed that takes into account impact velocity, attack angle, properties of the impinging particles and the surface. This model is verified against a second physical model that measures material loss rate at different locations within the cell.

Numerical investigation of turbulent flow generated in baffled stirred vessels equipped with three different turbines in one and two-stage system

The aim of this paper is to study the hydrodynamic behavior induced by a three different turbines: the FBT6 (six flat blades turbine), the RT6 (Rushton turbine), the PBT6 (pitched blades turbine). The turbulent flow generated in stirred tanks is numerically predicted by the resolution of the Navier–Stokes equation in conjunction with the RNG (Renormalization Group) of the k-ε turbulent model. These equations are solved by a control volume discretization method. The measurements were carried out for the one-stage and two-stage systems. The numerical results from the application of the CFD (computational fluid dynamics) code Fluent with the MRF (Multi Reference Frame) model are presented in the vertical and horizontal planes in the impeller stream region. The comparison between the numerical results and the experimental data showed a good agreement.

Analysis of Turbulence Structure in the Stirred Tank with a Deep Hollow Blade Disc Turbine by Time-resolved PIV

The turbulence structure in the stirred tank with a deep hollow blade (semi-ellispe) disc turbine (HEDT) was investigated by using time-resolved particle image velocimetry (TRPIV) and traditional PIV. In the stirred tank, the turbulence generated by blade passage includes the periodic components and the random turbulent ones. Traditional PIV with angle-resolved measurement and TRPIV with wavelet analysis were both used to obtain the random turbulent kinetic energy as a comparison. The wavelet analysis method was successfully used in this work to separate the random turbulent kinetic energy. The distributions of the periodic kinetic energy and the random turbulent kinetic energy were obtained. In the impeller region, the averaged random turbulent kinetic energy was about 2.6 times of the averaged periodic one. The kinetic energies at different wavelet scales from a6 to d1 were also calculated and compared. TRPIV was used to record the sequence of instantaneous velocity in the impeller stream. The evolution of the impeller stream was observed clearly and the sequence of the vorticity field was also obtained for the identification of vortices. The slope of the energy spectrum was approximately (5/3 in high frequency representing the existence of inertial subrange and some isotropic properties in stirred tank. From the power spectral density (PSD), one peak existed evidently, which was located at f 0 (blade passage frequency) generated by the blade passage.

Oxygen transfer and energy dissipation rate in surface aerator

The dissipation rate of turbulent kinetic energy ( ε) is a key parameter for mixing in surface aerators. In particular, determination ε across the impeller stream, where the most intensive mixing takes place, is essential to ascertain that an appropriate degree of mixing is achieved. Present work by using commercial software VisiMix ® calculates the energy dissipation rate in geometrically similar unbaffled surface aeration systems in order to scale-up the oxygen transfer process. It is found that in geometrically similar system, oxygen transfer rate is uniquely correlated with dissipation rate of energy. Simulation or scale-up equation governing oxygen transfer rate and dissipation rate of energy has been developed in the present work.

Evaluation of local kinetic energy dissipation rate in the impeller stream of a Rushton turbine by time-resolved PIV

The present paper is dedicated to the direct measurement of the dissipation rate of kinetic energy, ε ¯ , by means of time-resolved 2D-PIV, in the impeller region of a stirred vessel. Experimental estimation of ε ¯ is carried out without simplifications, since all spatial gradients of the fluctuating velocity components are directly measured. At each point, measurements have thus been realized in three orthogonal planes. The present results have been compared with previous ones and discussed according to experimental techniques. A special attention is focused on the contribution of measurements in each plane and some new ideas have been suggested for the assessment of ε ¯ . In addition, in each measurement plane, the time-variation of the instantaneous fluctuating velocity gradients have been also presented, exhibiting periodicity, with large values of instantaneous dissipation rate, linked to the trailing vortex induced by the blade rotation.

LES and URANS simulations of hydrodynamics in mixing tank: Comparison to PIV experiments

Dissipation rate of turbulent kinetic energy is a key parameter in a number of chemical and biochemical processes. In stirred tank, its overall value is readily estimated; however its distribution is far from homogeneous. The experimental determination of dissipation rate is difficult and often limited to small regions of a reactor. Therefore, CFD appears to be a useful tool to estimate the distribution of the turbulence dissipation rate. In this work, two kinds of simulation have been performed: a simulation based on the URANS equations and a Large Eddy Simulation with the Smagorinski subgrid scale model. The aims of the present paper are (1) to compare URANS and LES simulations to PIV data in terms of velocity, kinetic energy and turbulence dissipation rate and (2) to study the influence of the constant in the subgrid scale model used in LES. In term of mean velocity, URANS simulation and especially LES are in good agreement with PIV experiments. In term of total kinetic energy, both simulations also give good results; however URANS simulation fails to predict the repartition of total kinetic energy between its periodic and turbulent components in the vicinity of the impeller. The mean velocity and the kinetic energy are shown to be independent of the value of the constant CS in the Smagorinski model. The overall dissipation rate is well predicted by URANS simulation but not its distribution in the impeller stream. For LES, the amplitude of local and overall dissipation rate is shown to be strongly dependent of the value of the constant CS. However, its distribution in the stream is similar regardless of the value of CS and best reproduced than by the URANS simulation.

On the optimization of hydrodynamics in fine particle flotation

There is absolutely no question that a key role for an effective fine particle flotation plays the achievement of sufficiently high flotation velocities by means of large collision rates between the value mineral particles and bubbles in the strongly turbulent rotor (impeller) stream of the flotation machines. Therefore, a large ratio ε R m / ν F n has to be aimed at ( ε R is the local energy dissipation rate in the impeller stream; ν F is the kinematic viscosity of the fluid phase), i.e. ε R should be as large and ν F as small as possible. On the one hand, for that it is important to use an impeller–stator system having a large power number and an intensive internal slurry recirculation. On the other hand, a satisfactory dispersion state and thus advantageous rheological properties (low apparent viscosity) of the slurry must be aimed at. The latter effects a substantial reduction of the turbulence damping and with that not only an increase of ε R in the impeller stream but also a decrease of its volume contraction. Furthermore, an adequate control of the entrainment into the froth lamellae plays a role in optimization.

Scale-up behaviour in stirred square flocculation tanks

In this study, non-intrusive measurements of local floc size distributions were performed in square tanks of different sizes (5, 7.3, 28 and 560 l). The scale-up behaviour of the floc size distribution was followed with both spatial and temporal resolution. The data was collected in situ using particle image velocimetry and image analysis. The analysis of the data was done using a connected component labelling technique. It was found that the reproducibility of the flocculation system was adequate. The results show that there are large spatial differences in the mean size and the shape of the floc size distribution within the tanks but that the differences decrease as tank size increases from 5 to 28 l. However, increasing the size further to 560 l increases the spatial variation. This indicates a change in the dynamics of the flocculation between different parts of the tank as size changes. The dynamics between two important growth mechanisms were investigated as the size of the vessels and the energy input changed. The first mechanism was orthokinetic flocculation in the impeller stream and the second mechanism was differential settling growth in the corner jet. It was found that the changes in spatial variation of the steady-state mean size and the local variation of the mean size can be explained by the difference in the relative importance between the two mechanisms as the size of the vessel and energy input change. A consequence of this is that, for a certain impeller-tank configuration and a certain energy input, there is a certain tank size that decreases the spatial variation in the system, thus, narrowing the size distribution produced in the tank.

Analysis of turbulence anisotropy in a mixing tank

The objective of this paper is to analyze the gap between the local turbulence and the 3D isotropic state in a mixing tank stirred with a Rushton turbine. Experiments were carried out using the PIV technique, and phase average treatment permits the calculation of the six components of the Reynolds stress tensor. In order to quantify the gap between the measured local turbulence and the 3D isotropic state, methods based on tensorial analysis are developed. In a turbulent flow, three representations are able to characterize the turbulence anisotropy: representation based on two eigenvalues ( s – t ) of the anisotropy tensor; the Lumley–Newman triangle based on two invariants ( II – III ) of the anisotropy tensor; a representation based on the axisymmetry invariant A and the two-dimensional invariant G . These three visual methods, that quantify the degree of anisotropy from two independent variables are developed and used in the impeller stream region, and the distribution of the turbulence state is thus described. A parameter is proposed to quantify the anisotropy level.

Turbulence kinetic energy transport processes in the impeller stream of stirred vessels

In the present study ensemble-averaged and phase resolved estimations of the production, diffusion and convection of kinetic energy in the impeller stream of a vessel stirred by a Rushton turbine are provided. To determine those terms all Reynolds stresses (normal and shear) as well as most of the triple-velocity correlations terms were also estimated. The measurements were obtained with a two-channel laser Doppler anemometer, LDA, for Re = 32 000 and the region investigated was delimited by the ranges 0.18 ⩽ r / T ⩽ 0.35 and 0.278 ⩽ z / T ⩽ 0.387 . A Reynolds triple decomposition has been employed to determine the amount of turbulent kinetic energy convected by the organised and mean motions and extracted by the turbulent Reynolds stresses from the organised and mean motions. The data presented can provide valuable information for the design of mixing processes and crucial data to validate computational fluid dynamics simulations of stirred vessel flows.

Nanobubbles, hydrophobic effect, heterocoagulation and hydrodynamics in flotation

It has been shown in recent years that the long-range attractive interaction forces between hydrophobic surfaces in aqueous systems are caused by the capillary forces of gas bridges which form at the coalescence of nanobubbles adhering on the surfaces. The coalescence of nanobubbles on selectively hydrophobized particles with coarser bubbles initiates the jump into the three-phase contact at the attachment events in flotation. Therefore, one should no longer speak of hydrophobic forces in these events but of hydrophobic effects because they are caused by capillary forces. However, in the selective hydrophobization of particles by long-chain collectors (surfactants), there is another situation. Here, the association of nonpolar groups in the adsorption layers plays an important role in the energy balance of adsorption. This association is caused by “truly” hydrophobic interactions, which support the spotty distribution of the adsorbed collector ions on the particle surfaces and promote the formation of nanobubbles. This paper is intended to show to what extent the results obtained by basic research on the nanobubble formation as well as the force–distance dependence of collision events can be applied to flotation processes. This particularly requires the consideration of the highly turbulent flow conditions in the impeller stream of the flotation machines, in which the attachments almost exclusively occur. Various phenomena which occur in these machines and affect the reagent regime and the hydrodynamics point to the fact that nanobubbles can form, exist and even grow into microbubbles in that region. Therefore, so-called combined attachment events should predominate as already imagined several decades ago. The highly turbulent pressure fluctuations in the impeller stream in addition to the dispersion of the bubbles effect also their oscillations in size and shape, so that adsorption equilibria in the interfaces liquid/gas cannot be supposed. However, the pressure fluctuations present the possibility to overcome potential barriers in the wetting films at attachment events.

Direct determination of energy dissipation in stirred vessels with two‐point LDA

AbstractThe 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