Search

Gas–liquid two phase flows are widely encountered in industry. The design parameters include two phase pressure drop, mixing and axial mixing in both the phases, effective interfacial area, heat and mass transfer coefficients. Currently, there is a high degree of empiricism in the design process of such reactors owing to the complexity of coupled flow and reaction mechanism. Hence, we focus on synthesizing recent advances in computational and experimental techniques that will enable future designs of such reactors in a more rational manner by exploring a large design space with high-fidelity models (computational fluid dynamics) that are validated with high-fidelity measurements (hot film anemometry (HFA), Laser Doppler anemometry (LDA), particle image velocimetry (PIV), etc.) to provide a high degree of rigor. Understanding the spatial distributions of dispersed phases and their interaction during scale up are key challenges that were traditionally addressed through pilot scale experiments, but now can be addressed through advanced modelling. For practically complete knowledge of the fluid mechanical parameters, it is desirable to implement direct numerical simulations (DNS). However, the current computational power does not permit full DNS for real bubble columns. Therefore, we have been using simplified turbulence models (such as large eddy simulation, Reynolds stress, k – ε , etc.) which need the knowledge of turbulence parameters. For the estimation of these parameters, currently semi-empirical procedures are being used pending the knowledge of turbulence. Further, the formulation of governing equations in all the CFD models (except DNS), the knowledge of interface forces (drag, lift, virtual mass, Basset, etc.) is needed and for their estimations empirical correlations are being employed, again pending the knowledge of fluid mechanics under turbulent conditions in bubble columns. In gas–liquid dispersions, the gas is sparged in the form of bubbles. During the bubble rise, the mechanism of wake detachment creates turbulence which can be called as wake generated turbulence. In addition, energy gets transferred from the gas phase to liquid phase. The quantitative amounts are negligible when bubble motion is not hindered and the gas–liquid dispersion is homogenous. The amounts increase with an increase in the extent of hindrance. However, in the homogenous regime, even under extreme conditions, the extent of energy transfer in the bulk gas–liquid dispersions (volume other than wake volume) is fairly limited. On contrast, in the heterogeneous regime, the rates of energy transfer become sizeable. The energy received by the liquid (in both the regimes) also creates turbulent motion and termed as bulk generated turbulence. In turbulent flows a compendium of eddies (flow structures) of different length and time scales contribute towards improved/enhanced mixing, momentum transfer, heat transfer, and mass transfer (transport phenomena). Hence, a proper understanding of the dynamics of these turbulent flow structures, and their role in the transport phenomena, can bring substantial improvement in the scale-up and design procedures. The present paper brings out the current status of knowledge on bubble generated turbulence. All the published literature in experimental measurements and DNS simulations has been critically analysed and coherently presented. [ABSTRACT FROM AUTHOR]

Abstract: Turbulence intensity, or hydromechanical stress, is a controlling parameter in many industrially relevant processes. Especially fermentation processes are often characterized by intense aeration and agitation, operating conditions for which the measurement of turbulence intensity is extremely difficult. Since the maximum stable drop diameter in a break-up controlled dispersion is directly correlated with turbulence intensity, the measurement of drop sizes can enable an indirect access to the intensity of turbulence under such operating conditions. This work presents the constraints and the development of a method for the measurement of maximum stable drop size in aerated liquid–liquid dispersions in stirred tanks for the purpose of characterizing turbulence intensity. Continuous and dispersed phase properties were selected to achieve a break-up controlled dispersion with negligible coalescence. This was accomplished mainly by applying a dilute dispersion, a low ionic strength and by incorporating a dispersed phase, paraffin oil, with a negative spreading coefficient. The negative spreading coefficient prevents coalescence due to drop–bubble interactions for aerated operating conditions. It was demonstrated that the off-line measured drop size distributions are representative for the conditions in the bioreactor and are not altered by sample handling. The sampling and measurement procedure was found to be highly reproducible with a standard deviation for the maximum stable drop size for independent experiments of approximately 10%. Relevant constraints for the application of the method in large-scale experiments were discussed and accounted for during method development to allow a later application in production scale equipment. [Copyright &y& Elsevier]

Abstract: This paper deals with the velocity distribution and friction factor of polymer drag reducing flows in smooth pipes. By applying the concept of elastic shear stress or the Reynolds shear stress deficit, the equations of velocity distribution and friction factor in turbulent drag reducing flows are derived. Based on the derived equations, the onset Reynolds number for drag reduction is discussed which shows that the onset of drag reduction depends on the polymer type and its concentration. The optimal polymer concentration for Maximum Drag Reduction (MDR) is obtained, and it depends only on the polymer species. The effect of polymer mechanical degradation is discussed in the current paper. [Copyright &y& Elsevier]

Abstract: Turbulence in bubbly flows is of utmost practical and theoretical interest. In the current work, particle image velocimetry (PIV) measurements have been carried out in a rectangular bubble column. The superficial gas velocity was varied from 2mm/s to 20mm/s, with the gas hold-up values up to 4.75%. Both the homogeneous and heterogeneous regimes of operation were covered for the bubble column. Prior to turbulence measurement with PIV the bubble size distribution, time averaged velocity profile, and gas hold-up profile were measured with high speed camera and modified Pitot tube probe. In order to resolve low speed (large scale) and high speed (small scale) flow structures in a column properly, measurements were carried out with a low speed (7Hz) and high speed (900Hz) PIV system. Image processing program to identify bubbles from PIV image and mask the PIV vector field was developed. The energy spectrum of the liquid phase turbulence was calculated from PIV velocity field with FFT. Wavelet transform was used to separate small scale fluctuations from large scale fluctuations in liquid velocity field. Energy spectrum of large scale fluctuations was found to be dependent on the sparger type, while energy spectrum of small scale fluctuations was found to be similar for all spargers. The spectral slope of inertial subrange was found to be close to −5/3. The spectral slope for wavenumber higher than inertial subrange was found to be −3. Reasoning for this behavior based on energy transfer and energy dissipation rate has been provided. [Copyright &y& Elsevier]

Abstract: The statistics of the scalar dissipation rate (SDR) in gaseous flows with Schmidt numbers close to unity were examined in a joint numerical and experimental effort, in a shearless mixing layer in the presence of decaying turbulence using three-dimensional Direct Numerical Simulations (DNS), and in an axisymmetric plume formed by the continuous low-momentum release of an acetone-laden stream (used as a tracer to measure the passive scalar) along the centreline of a turbulent pipe flow of air downstream of a turbulence generating grid using Planar Laser-Induced Fluorescence (PLIF). For the flows examined good agreement was found between the DNS and the experiment, both of which indicate that: (i) the probability density functions of the unconditional and conditional SDR show small departures from lognormality; (ii) the ratio of the standard deviation of the unconditional SDR to its respective Reynolds-averaged mean, as well as the ratio of the standard deviation of the conditional SDR to its conditional mean (these ratios do not vary strongly with the value of the mixture fraction at which it is evaluated), both increase over a few Kolmogorov time scales from zero (at the injector nozzle in the experiment and initially in the DNS) to some value downstream and at later times; (iii) the long-time values of the ratios of the standard deviation to the mean of the conditional and unconditional SDR increase with the turbulent Reynolds number; (iv) for the same turbulent Reynolds number, the DNS and the experiment showed that the ratio related to the unconditional SDR increases to a long-time value of approximately 2.3 (±20%), while the ratio related to the conditional SDR increases quickly to a value that stays within the range 1.0–1.4 (or, 1.2±0.2) and reaches a maximum value of 1.3–1.4 by the end of the DNS run and at the downstream edge of the experimental domain. The development of the conditional SDR fluctuations is discussed by comparing the early and late stages of mixing. The agreement between the PLIF measurements, which can only resolve two-dimensional fields, and the DNS, which provides access to the fully resolved three-dimensional field, suggests that the present conclusions are not limited by resolution or the lack of measurement in the third dimension. The results are useful for the development and validation of turbulent reacting flow models such as advanced flamelet, Conditional Moment Closure (CMC), and transported Probability Density Function (PDF) closures. [Copyright &y& Elsevier]

Abstract: Particle deposition in fully developed turbulent square duct flows is simulated using large eddy simulation for Reynolds numbers, based on the bulk velocity and duct width, equal to 250k, 83k and 10,320. A particle equation of motion including Stokes drag, lift, buoyancy and gravitational forces is used for particle trajectory analysis. Results obtained for the fluid phase show good agreement with experimental data and the predictions of direct numerical simulations. Predictions for particles show that the secondary flow established in the duct cross-section plays an important role in the particle deposition process. Under the influence of this flow, high-inertia particles (particle Stokes number, St>12.38) tend to deposit close to the corners of the duct floor, while low-inertia particles (St<6.43) deposit near the floor centre. It is shown that the flow Reynolds number, particle size, drag force, shear-induced lift force and gravity all affect the particle deposition process. Particle deposition in the vertical direction increases with flow Reynolds number but simultaneously decreases in the horizontal direction. The particle deposition velocity is found to increase with both the particle size and the flow Reynolds number, with the tendency for deposition at the duct corners increasing with both variables. From a dynamic analysis, gravity most significantly affects particle deposition in the vertical direction, while in the horizontal direction the drag force dominates. The influence of the lift force increases with particle size, and its effect becomes significant as particles approach the duct floor; hence, it can act as another important factor causing particles to accumulate at the corners of the duct. Generally, and for all particle populations in the three flows considered, the particle deposition process can be described by the free-flight model. [Copyright &y& Elsevier]

Abstract: Monolithic reactors employed in automotive exhaust gas aftertreatment typically operate under fluctuating flow conditions. These fluctuations in the volumetric flow rate through the catalyst are caused by engine pulsations and the upstream exhaust gas turbulence. In the current work, the effects of the turbulent-to-laminar transition on the conversion of pollutants under mass-transfer limited operation of a monolithic reactor are investigated using numerical simulations. The most notable effect of the turbulence is an introduction of temporal fluctuations to the observed conversion at the outlet. These fluctuations are attributed to variations in the axial velocity (and thus the retention time) in the channel. A simplistic model for a single monolith channel in a tanks-in-series framework is suggested that captures this effect of the upstream turbulence on the dimensionless heat and mass transfer numbers in automotive catalysts. The model can be used to resolve the transient variations of the heat and mass transfer when the upstream turbulent characteristics are known. The effects of such variations on the catalytic conversion are likely to be most pronounced for reactions with negative-order kinetics when operating close to ignition or extinction. [Copyright &y& Elsevier]

Abstract: This paper presents the state of the art regarding the understanding of axial mixing in pulsed columns. Residence Time Distribution (RTD) experiments carried out mainly between 1986 and 2002 are reviewed in connection with fluid mechanics studies and CFD simulations. Based on prior work by Buratti (1988), a new model is established to correlate the continuous phase axial dispersion coefficient with the operating conditions in a wide range of operating (pulse intensity up to 7.5cms−1) and geometric conditions (0.17≤H/D≤1.33), thereby reducing the estimation error from 143% to 21% in the case of small-aspect ratio columns (H/D<1), such as those used in nuclear research, and from 95% to 27% in the case of (possibly annular) industrial size columns. Experimental results are relatively well reproduced by RANS-type computational fluid dynamics (CFD) simulations, provided a low-Reynolds model is used for the turbulent viscosity estimation. [Copyright &y& Elsevier]

Abstract: The aim of this study was to find models for turbulent fragmenting forces in the high-pressure homogeniser from data available in Computational Fluid Dynamics (CFD) simulations with Reynolds Averaged Navier Stokes (RANS) turbulence models. In addition to the more common RANS k–ε turbulence models, a Multi-scale k–ε model was tested since experimental investigations of the geometry imply large differences in behaviour between turbulent eddies of different length-scales. Empiric models for the driving hydrodynamic factors for turbulent fragmentation using the extra information given by multi-scale simulations were developed. These models are shown to give a more reasonable approximation of local fragmentation than models based on the previously used RANS k–ε models when comparing to hydrodynamic measurements in an experimental model. [Copyright &y& Elsevier]

Abstract: Micromixing of viscous systems in a stirred-tank reactor with Rushton turbine is investigated numerically. It is characterized by the product selectivity of parallel competitive reactions. Flow fields inside the reactor are determined by the Reynolds Stress Model (RSM). A computational fluid dynamics (CFD) method combining the standard E model and Finite-Rate/Eddy-Dissipation (FR/ED) model is implemented and is validated using experimental data in the literature. The simulations show that a higher agitation speed, a lower fluid viscosity and/or a feeding location closer to the discharge area of the impeller favor micromixing and the reaction rate. The trajectory of the reaction plume also influences the micromixing performance. The value of the FR/ED model parameter determined by lab-scale experiments decreases with increasing fluid viscosity. However, it is little affected by the agitation speed. These results provide useful guidelines for the scale-up of industrial reactors with complex chemical reactions. [Copyright &y& Elsevier]

Abstract: Since the emulsification in the High-Pressure Homogenizer (HPH) is controlled by hydrodynamic forces, the turbulent flow field in the valve region is of significant interest. Computational Fluid Dynamics (CFD) simulations have been used for this in many studies. However, there are reasons to question if the utilized turbulence models, with their inherent assumptions and simplifications, could accurately describe the influential aspects of the flow. This study compares CFD simulations using the methods from previous studies with experimental measurements in a model HPH valve. The results show that the region upstream of the gap can be described accurately regardless of turbulence model and that the gap region can be captured by using one of the more refined k−ε models. None of the studied turbulence models were able to describe the details of the highly turbulent region downstream of the gap. The obtained results are also discussed in relation to generalizability and limitations in using CFD simulations for understanding the emulsification in the HPH. [Copyright &y& Elsevier]

Abstract: This paper proposes that a diesel oxidation catalyst (DOC) operating within the fully turbulent flow regime is an efficient means of reducing the contents of particulate matter in the exhaust gases. The suggested mode of operation is in contrast to the fact that the DOCs are typically operated within the laminar flow regime. In the paper, the particle trapping efficiency and pollutant conversion in turbulent ceramic DOCs are calculated using both mass-transfer correlations available in the literature and computational fluid dynamics (CFD). It is shown that a turbulent DOC substantially increases the removal of small particulates from the exhaust gases. This indicates the potential of the aftertreatment system to comply with the forthcoming number-based emission legislations on particulate matter. In addition, the turbulent DOC can be used to optimize the overall performance of a combined system consisting of a DOC and a diesel particulate filter. [Copyright &y& Elsevier]

Abstract: Large Eddy Simulations (LESs) were performed for a confined rectangular liquid jet with a co-flow and compared in detail with particle image velocimetry (PIV) measurements. A finite-volume CFD library, OpenFOAM, was used to discretize and solve the filtered Navier–Stokes equation. The effects of grid resolution, numerical schemes and subgrid models on the LES results were investigated. The second and fourth order schemes gave similar performance, while the fourth order scheme costs much more computationally. Subgrid model comparison showed that the locally dynamic procedure is necessary for complex flow simulation. Model validation was performed by comparing LES data for the point-wise velocity statistics such as the mean and the root-mean-square velocity, shear stress, correlation coefficient, velocity skewness and flatness with the PIV data. In addition, LES data for the two-point spatial correlations of velocity fluctuations that provide structural information were computed and compared with PIV data. Good agreement was observed leading to the conclusion that the LES velocity field accurately captures the important characteristics of all the turbulent length scales present in the flow, from the fully resolved energy-containing eddies to the subgrid-scale dissipative eddies. [Copyright &y& Elsevier]

Abstract: To investigate the behavior of inter-particle collision and its effects on multiphase flow, the direct numerical simulation of a three-dimensional gas–solid two-phase plane mixing layer is conducted. The flow is assumed to be temporally evolving and incompressible. The particle trajectories are traced by the one-way or two-way coupled Lagrangian method separately. The deterministic hard-sphere model is used to describe the inter-particle collision. Calculations are performed for a particle Stokes numbers of 3. The results show that the preferential concentration phenomenon of particles is found after the beginning of the rolling up of the large-scale vortex structures due to the influence of the vortex. It is also found that the inter-particle collision occurs frequently in the local regions with higher particle concentration of the flow field. The evolution of inter-particle collision can be divided into 3 stages under the influence of the growth of the vortex and the particle dispersion. The results under the two-way coupling show that the particle distribution is more uniform. The modifications of the mixed fluid thickness, the Reynolds stresses, and the mean stream-wise velocity of two phases due to inter-particle collision are quantitatively investigated. [Copyright &y& Elsevier]

Abstract: This work presents a comprehensive study of different turbulence models, including the k–ε, SST, SSG–RSM and the SAS–SST models, for simulating turbulent flow in a baffled tank stirred with a Rushton turbine. All the turbulence models tested predict the mean axial and tangential velocities reasonably well, but under-predict the decay of mean radial velocity away from the impeller. The k–ε model predicts poorly the generation and dissipation of turbulence in the vicinity of the impeller. This contrasts with the SST model, which properly predicts the appearance of maxima in the turbulence kinetic energy and turbulence energy dissipation rate just off the impeller blades. Curvature correction improves the SST model by allowing a more accurate prediction of the magnitude and location of these maxima. However, neither the k–ε nor the SST model is able to properly capture the chaotic and three-dimensional nature of the trailing vortices that form downstream of the blades of the impeller. In this sense, the SAS–SST model produces more physical predictions. However, this model has some drawbacks for modelling stirred tanks, such as the large number of modelled revolutions required to obtain good statistical averaging for calculating turbulence quantities. Taking into consideration both accuracy and solution time, the SSG–RSM model is the least satisfactory model tested for predicting turbulent flow in a baffled stirred tank with a Rushton turbine. [Copyright &y& Elsevier]

Abstract: The flow pattern in process machinery has a significant impact on the product quality, because it influences the residence time, the mixing of components and the stability of chemical reactions. Hence the determination of the residence time and the measurement of the flow patterns have been the emphasis of many studies. The work presented shows a novel approach for the determination of the tangential and axial velocity profiles in a tubular bowl centrifuge. For the first time, flow velocities inside a fast rotating centrifuge have been measured using Laser-Doppler-Anemometry. The rotor of the centrifuge is made of carbon fibre reinforced plastic with an inner diameter of 100mm and a length of 200mm. The maximum rotational speed is 20,000rpm, creating the multiple of 22,400 times the earth gravitational force. No failure of the material was detected at any process parameters. The centrifuge is operated with two different setups. One setup employs an assembly of two coaxial cylinders, in which the void between them is entirely filled with water. In the second arrangement, only the outer rotor is assembled and the centrifuge is operated like an overflow centrifuge. The Laser-Doppler measurements of the axial fluid velocity are confirmed by determining the residence time distribution at various parameters. The results obtained show an effective tangential acceleration; the liquid exhibits a rigid body rotation for rotational speeds up to 8000rpm for throughputs between 0.5 and 1.8l/min. The axial flow pattern depend on the volume flux and the rotational speed. The cross-section through which the liquid flows was in most cases between 60% and 100% of the overall area. The influence of the inlet subsides towards the outlet with an inlet zone of 15% of the length of the rotor. No boundary layer flow was detected in the overflow setup, which is due to the plunged inlet and the effective tangential acceleration of the incoming liquid. [Copyright &y& Elsevier]

Abstract: The bubble column reactors are usually operated in a heterogeneous regime where the liquid phase turbulence is generated by the bubble motion and the velocity gradients in the mean motion. The turbulent flow comprises of fluid elements moving in a random fashion with different sizes and energies, called ‘flow structures’. Both the large and small scale flow structures within a reactor play an important role in governing the local momentum, heat and mass transfer. The current work is focused on the estimation of the time averaged flow pattern and flow structures. The experimental data has been collected using miniature pressure sensors, PIV+shadowgraphy and LDA. The data was subjected/analyzed to/with multipoint linear stochastic estimation (MLSE), wavelet transforms, image processing and eddy isolation (EIM) to identify the flow structures. Two bubble columns have been used: a narrow rectangular (2D) column and a cylindrical (3D) column. Wavelet transforms (WT) were applied to isolate individual structures from PIV data to get their shape, size and energy in the 2D column. MLSE has been used to obtain the velocity profiles from pressure fluctuation signals. This data, augmented by PIV and LDA data, is subjected to WT and EIM to get the eddy age and its energy distribution. The data of the eddy shape size and energy was used to predict the mass transfer coefficient in the cylindrical bubble column as a test case. Overall, in this work we present a methodology to utilize the experimental data to get a better insight of the dynamics of flow structures, and propose a path forward for the deeper understanding of transport phenomena in bubble columns. [Copyright &y& Elsevier]

Abstract: An experimental study and numerical investigation of thermal mixing are carried out on tandem twin jets in cross flow. Experiments were carried out for velocity ratios 1, 2 and 4 for 15°C temperature difference between main pipe and jet fluid. Velocity and temperature fields are measured using Hot Film Anemometer (HFA). Three dimensional steady state Computational Fluid Dynamics (CFD) simulations have been carried out to predict the velocity and temperature fields. The predicted velocity and temperature fields are in good agreement with the experimental measurements. Temperature fluctuations have been predicted using temperature variance model. The effect of jet spacing for different velocity ratios is studied. For jet spacing equal to twice the jet diameter, both the jets influence each other. Increase in the jet spacing decreases the effect of jets on each other. [Copyright &y& Elsevier]

Abstract: An experimental investigation of a vertical upward, two-phase pipe flow was undertaken to measure kinematic parameters of the fluid and solid phases. The kinematic parameters included Reynolds stress distributions based on quadrant analyses that provided insight in understanding the behavior of two-phase kinematic correlation profiles. The data collected was based on a two-color digital particle image velocimetry (DPIV) technique that simultaneously measured the velocity fields of the fluid and solid phases. From quadrant analysis results, differences in Reynolds stress quadrant profiles between the single- and two-phase conditions were observed near the wall in the range 0.8>r/R>0.55, corresponding to wall distances between 35 and 75 viscous lengths (y+). Correlation coefficients between the two phases were then calculated, using the fluctuating velocity components of each phase. The extent of the interaction between the two phases was tracked by the changing correlation values versus distance from the wall. The correlation of the fluid and solid phase velocities was highest in the core region of the pipe (y+∼120), where the effect of turbulent events is reduced; low correlation coefficient values were found at y+<75, where differences of magnitudes, inflection points, etc. of burst and sweep event quadrant analysis profiles were observed. The extent of the influence of wall dynamic turbulent events on the solid phase was observed both by the differences in the relative Reynolds stress quadrant profiles and, more readily, by the changing values of two-phase axial and radial correlation coefficients determined from the simultaneous fluid and solid fluctuating velocities measured by the two-color DPIV methodology. These changing values of the correlation coefficients across the tube reflect the different responses of low inertia (fluid tracers) and high inertia (solid phase glass spheres) particles to the turbulent events. Similar profiles of the axial and radial correlation coefficients were observed, indicating that for the geometry and flow conditions considered, one velocity component of each phase was sufficient to track the spatial extent of turbulent event effects and their interactions with the fluid and solid phases. It is found that the two-color DPIV methodology and two-phase correlation results can give critical insight into the performance of thermal-fluid processes, as burst and sweep events have a large impact on the kinematics and dynamics of particles in the two-phase flow. [Copyright &y& Elsevier]

Abstract: Discrete vortex simulations of a dilute two-dimensional particle-laden shear layer with one-way coupling were performed to study fluid–particle correlated motion and the transfer of turbulent kinetic energy between the phases. The resulting modification of carrier phase turbulence, estimated according to current computational models, was evaluated. Particle Stokes numbers were between 1.0 and 4.5, so that the particles showed considerable temporal concentration fluctuations due to centrifuging by the fluid flow structures, and the mass loading was 12% corresponding to a volume fraction of 6.0×10−5. Fluid velocities and particle concentration and velocities and their covariances, which appear in a commonly used model equation for carrier phase turbulence modification, were evaluated. Additionally, the probability density functions of fluid velocity fluctuations viewed by the particles are presented and compared with their Eulerian counterparts. It was found that particles view reduced velocity fluctuations due to preferential clustering. The model for carrier-phase turbulence modification predicted turbulence reduction, depending on the particle Stokes number. The mechanism responsible for turbulence reduction was the correlated velocity fluctuations of fluid and particles and this reduction could reach values up to one third of the fluid flow dissipation. Preferential particle concentration together with a relative velocity between the phases could generate turbulent kinetic energy of the gas phase, however this production was nearly an order of magnitude smaller compared to reduction of turbulence due to the correlated motion. The findings were compared with experiments available in the literature and help to clarify the view when turbulence reduction or augmentation occurs. [ABSTRACT FROM AUTHOR]

Abstract: A combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) system was employed to investigate the turbulent mixing in a confined liquid-phase rectangular-wake flow with a Reynolds number based on hydraulic diameter of 37,500 and a Schmidt number of 1250. The simultaneous velocity and concentration field data were analyzed for flow statistics such as turbulent fluxes, turbulent viscosity and diffusivity, and turbulent Schimdt number. The streamwise and transverse turbulent fluxes were found to be of the same magnitude. The turbulent flux vector was not aligned with the mean concentration gradient. The turbulent Schimdt number was about 0.8. The spatial correlations of turbulent fluxes and concentration fluctuations were evaluated. In the correlation field, there were a positive and a negative vertically oriented elliptical correlation region, which were symmetric around the basis point. The correlation region was a horizontally oriented ellipse with negative values of the correlation coefficient. The correlation field of was also an ellipse with a horizontal major axis. The behavior of large-scale structures in both the velocity and concentration field was studied using linear stochastic estimation with a defined event of concentration fluctuation. Vortex streets were observed in the estimated velocity fields. The streamwise growth of the structure size increased linearly initially but then grew more slowly. [Copyright &y& Elsevier]

Abstract: A Lagrangian marker particle (LMP) method is applied to measure the toroidal large-scale eddies (LSEs) and their enveloping stagnation surfaces in a 280l bottom-sweeping model crystallizer. The trajectories of a 0.4cm diameter LMP show that these stagnation surfaces inhibit transport. Analysis shows that the velocity component normal to stagnation surfaces vanish. Therefore, stagnation surfaces act as a semi-permeable barriers to particle transport. Microconductivity measurements show that the stagnation surfaces are leaky at the molecular scale. Thus particle transport through stagnation surfaces is size-dependent. The LMP measurements reveal the structure of the LSEs. This consists of (1) an upward-swirling flow adjacent to the tank perimeter extending from the bottom to the top of the tank, (2) a central, quiescent zone, and (3) a downward return flow between (1) and (2) through a system of nested, smaller diameter, secondary toroidal flows concentric with the impeller axis. A cylindrical stagnation surface surrounds the central quiescent zone. These results are corroborated by measurements of inhomogeneous concentration profiles in an industrial scale 2000l batch crystallizer. This leads to an understanding of the effects of LSEs on silver halide microcrystal particle size distribution in the industrial scale crystallizer. [Copyright &y& Elsevier]

Abstract: Turbulent fluid flow and related solid particle behaviour in the direct vicinity of the heat exchanging (HE) surface of a scraped heat exchanger crystallizer was studied. The liquid flow is visualized by dye injection and the particles are monitored directly for two types of commonly used scraper geometries. In conjunction with this experimental work, we performed direct numerical simulations of the two-phase (solid–liquid) flow system. Our main goal is the design of scraper geometries that enhance heat transfer by perturbing the thermal boundary layer, and effectively scrape off particles that nucleate, grow and adhere onto the HE surface. Also the turbulent flow generated by the moving scrapers should direct the particles into the bulk of the tank. The experiments and simulations show good qualitative resemblance which enables the design of scrapers based primarily on numerical predictions. [Copyright &y& Elsevier]

Abstract: The normalized Reynolds (NR-) stress is a symmetric, non-negative, dyadic-valued operator. An analysis of the hydrodynamic equation governing velocity fluctuations of a constant property Newtonian fluid shows that this operator is related to a prestress operator that is also symmetric and non-negative. The prestress operator accounts for local spatial changes in the fluctuating pressure and in the fluctuating instantaneous Reynolds stress. The Cayley–Hamilton theorem from linear algebra is used to complete the closure with a non-negative mapping of the normalized Reynolds stress into the prestress. The non-negative mapping between the prestress operator and the Reynolds stress depends on a scalar-valued turbulent transport time related to the relaxation of a Green''s function associated with a convective–viscous parabolic differential operator and the relaxation of a two-point, space–time correlation related to turbulent velocity fluctuations. The preclosure equation also depends on a kinematic operator related to the average velocity gradient and a rotational operator related to the angular velocity of the frame. The resulting universal realizable anisotropic prestress (URAPS-) closure is realizable for all non-rotating and rotating turbulent flows, provided the complementary transport equations for the turbulent kinetic energy and the turbulent dissipation are formulated to yield non-negative solutions. Experimental data and DNS results previously reported in the literature for non-rotating homogeneous simple shear and for non-rotating and rotating homogeneous decay are used to determine the closure constants. For rotating homogeneous simple shear, the URAPS-closure predicts the existence of self-similar states for finite positive and negative rotation numbers. The URAPS-closure for the NR-stress predicts anisotropic states consistent with expected behavior. [Copyright &y& Elsevier]

Abstract: Three-compartment model was used to study non-homogeneity of mixing in a fully baffled stirred tank. Multiple reference frame (MRF) technique was used for calculations. Calculations were performed to study the effects of agitator speed, impeller diameter, baffle width and distance of impeller from bottom of the tank on turbulent flow field. Three different zones of the vessel, that were a small zone near the impeller, another zone around the baffles, and a relatively large zone far from the impeller and baffles, named circulation zone, were investigated. Boundaries of these zones were determined using two different methods. The first method used gradient of energy dissipation rate while the other method used cumulative energy dissipation rate to determine the zone boundaries. Zone boundaries determined by both methods were comparable. The turbulent kinetic energy dissipation rate gradient was the preferred method due to its simplicity. Turbulent kinetic energy dissipation rate increased with agitator speed in all zones. Both turbulent kinetic energy dissipation rate and turbulent kinetic energy showed considerable change with impeller diameter at impeller zone, while no remarkable change was observed at baffle and circulation zones. Three-compartment model parameters, impeller and baffle energy dissipation ratios λ i, λ b, impeller and baffle volume ratios μ i, μ b and impeller and baffle exchange flow rates Q i, Q b were obtained from CFD simulations. Impeller energy dissipation ratio, impeller exchange flow rate and baffle exchange flow rate increased while baffle volume ratio decreased with agitation rate and impeller diameter. Baffle energy dissipation ratio and impeller volume ratio showed no considerable change with agitation rate and impeller diameter. [Copyright &y& Elsevier]

Abstract: Large regions of inhomogeneous mixing have been observed in industrial, bottom-sweeping impeller crystallizers. To investigate this phenomenon, we conducted experiments on a one-tenth volume model of this kind of mixing tank. Results are reported of Lagrangian marker particle (LMP) and microconductivity measurements using the model mixing tank with impeller tip Reynolds numbers of 25,000. Surprising structure is found in this high Reynolds number flow. Using the LMP trajectory data, we show the flow consists of a narrow region of rapidly moving, upward spiralling flow at the tank perimeter. This flow returns slowly through a vertical stack of tori and through a quiescent region centered on the impeller. These tori are concentric with the impeller and exist at loci of regions of shear found adjacent to the quiescent central region and the tank perimeter. Conditional analysis of the microconductivity signals reveals that large concentration fluctuations occur in the perimeter flow. In contrast, only small diffusive-like concentration fluctuations occur in the center of the tank. This segregation of regions of rapid transport in the perimeter flow from regions of micromixing in the quiescent region results in inhomogeneous mixing in the tank. The complexity of the flow is reflected in the large dynamical dimension () of the flow obtained from the calculation of the Kolmogorov entropy production rate. The return-time distribution was found to be composed of a superposition of two log-normal distributions. Period doubling phenomenon was also found in these distributions. [Copyright &y& Elsevier]

Abstract: Eddy viscosity models (EVM) constitute a powerful approach for turbulence modeling in engineering applications. However, the correct formulation of EVM models is still subject to discussion, in particular the impact of model parameters on the practical relevance of models in different classes of application scenarios is not fully understood. A systematic approach for assessing parameter impact involves optimization methods for computational fluid dynamics that allow for quantitative model analysis by rigorous comparison with experimental data. In order to illustrate this systematic approach, the – turbulence model is analyzed on the basis of laser Doppler velocimetry measurements for the flow between two plates. It is shown that ad hoc approaches for adapting parameter values for the – model may easily fail due to over-parameterization of the underlying model or insufficient data. Therefore, an a priori method for the identification of potential problems is important which is based on the sensitivity coefficients of the measurements with respect to the model parameters. The commercial software package FLUENT employed in our application is augmented using the automatic differentiation system ADIFOR for efficient sensitivity computation. Taken together, this results in reliable a priori methods for model assessment and calibration. Noteworthy, the choice of turbulence parameters on the basis of the formal a priori analysis agrees well with the physical understanding of the – model. [Copyright &y& Elsevier]

Abstract: In this study, we are interested in deriving time-smoothed governing and constitutive equations for gas–solids flow in moderately dense systems where particle–particle collision is the main energy dissipation mechanism. Results obtained from dynamic simulations of a gas–solids flow in a 1D channel are used to show that it is possible to obtain expressions for the time-averaged constitutive relations based on Taylor series expansion. We demonstrate, by comparing with time-averaged transient results, that the 1st term (or laminar) in the series expressions of most non-linear constitutive relations can yield inaccurate quantitative and qualitative results. This means that steady-state models derived by simply removing the partial time derivative from the governing equations are not suitable for gas–solids flows. This study shows that it was necessary to include many terms of the Taylor series expression of non-linear constitutive relations (such as the granular energy dissipation term) due to large-scale oscillations that were computed for all flow variables at all locations in the 1D domain. In some cases, the Taylor series expansion diverged and the Euler transformation was used to improve the convergence of these series. In this moderately dense flow system, turbulence in the gas-phase was found to be just a reaction to turbulence in the solids phase that resulted from the large-scale motion of solids clusters. This resulted in a negative turbulent gas viscosity computed due to the fact that gas (in the horizontal direction) flows only to occupy regions vacated by clusters of solids. The steady-state results obtained using the time-smoothed gas–solids flow model compared well with the time-averaged results obtained using the transient model for all flow variables. [Copyright &y& Elsevier]

Abstract: A three-dimensional Eulerian–Eulerian two-phase approach has been used for the simulation of a cross-flow gas–liquid wastewater treatment reactor. Two different turbulence models have been tested: the and Reynolds Stress Model (RSM) models. Bubble induced turbulence source terms have been added to these models. Numerical results have been validated using Laser Doppler Velocimetry (LDV) measurements. Simulations with both turbulence models successfully predicted the hydrodynamics of the reactor. Then particle tracking with a stochastic approach has been used to calculate residence time distributions (RTD) with the flow previously simulated. It has been shown that dispersion in the reactor is primarily due to turbulence. Results have been compared with experimental RTD for various liquid and gas flowrates both on a bench scale and full scale plant. The RSM model accurately predicted the dispersion whereas the standard model slightly underestimated the dispersion. [Copyright &y& Elsevier]

Abstract: A computational fluid dynamics (CFD)-code has been developed using finite volume method in Eulerian framework for the simulation of axisymmetric steady state flows in bubble columns. The population balance equation for bubble number density has been included in the CFD code. The fixed pivot method of Kumar and Ramkrishna [1996. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chemical Engineering Science 51, 1311–1332] has been used to discretize the population balance equation. The turbulence in the liquid phase has been modeled by a model. The novel feature of the framework is that it includes the size-specific bubble velocities obtained by assuming mechanical equilibrium for each bubble and hence it is a generalized multi-fluid model. With appropriate closures for the drag and lift forces, it allows for different velocities for bubbles of different sizes and hence the proper spatial distributions of bubbles are predicted. Accordingly the proper distributions of gas hold-up, liquid circulation velocities and turbulence intensities in the column are predicted. A survey of the literature shows that the algebraic manipulations of either bubble coalescence or break-up rate were mainly guided by the need to obtain the equilibrium bubble size distributions in the column. The model of Prince and Blanch [1990. Bubble coalescence and break-up in air-sparged bubble columns. A.I.Ch.E. Journal 36, 1485–1499] is known to overpredict the bubble collision frequencies in bubble columns. It has been modified to incorporate the effect of gas phase dispersion number. The predictions of the model are in good agreement with the experimental data of Bhole et al. [2006. Laser Doppler anemometer measurements in bubble column: effect of sparger. Industrial & Engineering Chemistry Research 45, 9201–9207] obtained using Laser Doppler anemometry. Comparison of simulation results with the experimental measurements of Sanyal et al. [1999. Numerical simulation of gas–liquid dynamics in cylindrical bubble column reactors. Chemical Engineering Science 54, 5071–5083] and Olmos et al. [2001. Numerical simulation of multiphase flow in bubble column reactors: influence of bubble coalescence and breakup. Chemical Engineering Science 56, 6359–6365] also show a good agreement for liquid velocity and gas hold-up profiles. [Copyright &y& Elsevier]

A novel type of photo-bioreactor is being studied. The main feature in this system is the inclined tube in which most of the photosynthesis occurs. Two phase gas–liquid counter-current flow takes place in this environment. The flow configuration in the range of interest has not been described previously. The trajectories of the liquid phase are the target of the present work. These trajectories are needed for a proper mathematical representation of the process. Experimental studies where carried out using two methods: studying the response of the system to a pulse disturbance, and tracking an optical tracer with a system developed in our laboratory. The influence of tube inclination and of gas flow rates was studied. A rough compartmental model is presented, which fits the transient experimental data. The mass transfer rate from the gas phase to the liquid was studied since it is needed to assess the capacity of providing enough CO2 to match the light captured by photosynthesis. Both gas holdup and mass transfer rates are reported as a function of tube inclination and gas flow rates. [Copyright &y& Elsevier]

Abstract: A new experimental approach has been developed for the identification of reasonable break-up mechanisms in stirred dispersions and of a physically based model for the daughter drop size distribution. In the experiments, breakage of a single organic droplet and the subsequent fragments formation are analyzed by image processing techniques. The experimental data are then fitted by means of a daughter drop size distribution function written in terms of a probability density function (pdf). The mathematical approach that matches the theoretical requirements and that provides the best fit of the experimental data is the pdf proposed by Diemer and Olson [2002. A moment methodology for coagulation and breakage problems: part 3—generalized daughter distribution functions. Chemical Engineering Science 57(19), 4187–4198]. This is a purely statistical model that does not contain any dependence on physical parameters, such as turbulence intensity and mother drop size. Based on the experimental results, an extension of the Diemer and Olson model is proposed, in which dependence on the Weber number as well as on the mother drop diameter can be inserted. Other models appeared in the literature [. Description of interaction processes in agitated liquid–liquid dispersions. Chemical Engineering Science 32(11), 1289–1297; . Scale effect on breakup process in liquid–liquid agitated tanks. Journal of Chemical Engineering of Japan 16(4), 312–319; . On the breakup of an air bubble injected into a fully developed turbulent flow: part 2. Size PDF of the resulting daughter bubbles. Journal of Fluid Mechanics 401, 183–207] are also discussed and compared with experimental data. Out of them, the only model that approaches experimental data in a satisfactory way is the model by Martínez-Bazán et al. [1999. On the breakup of an air bubble injected into a fully developed turbulent flow: part 2. Size PDF of the resulting daughter bubbles. Journal of Fluid Mechanics 401, 183–207]. Eventually, the presence of the maximum break-up probability for symmetric breakage, in contrast with some theoretical models published in the literature, is explained and justified by means of energy considerations. [Copyright &y& Elsevier]

Abstract: This paper discusses the simulation of bubbling gas–solid flows by using the Eulerian two-fluid approach. Predictions of particle motion, bed expansion, bubble size and bubble velocity in bubbling beds containing Geldart B particles are compared with experimental results and correlations found in the literature. In addition, gas mixing in a bed of Geldart A particles is investigated. An in-house code has been developed based on the finite-volume method and the time-splitting approach using a staggered grid arrangement. The velocities in both phases are obtained by solving the 2D Reynolds-averaged Navier/Stokes equations using a partial elimination algorithm (PEA) and a coupled solver. The turbulence model is used to describe the turbulent quantities in the continuous phase. In general, the model predictions are in good agreement with experimental data found in the literature. Most important observations are: the level of the restitution coefficient was found to be crucial in order to obtain successful results from 2D axisymmetric simulations of a system containing Geldart B particles. Bubble size and bubble rise velocities are not as sensitive to the restitution coefficient. The turbulence model is of outmost importance concerning gas mixing in a fluidized bed of Geldart A particles. From these numerical analyzes an optimized granular flow two-fluid model can be designed for the purpose of simulating reactive systems in fluidized bed reactors. [Copyright &y& Elsevier]

In order to represent radial dispersion phenomena in packed beds a three-dimensional network model is proposed based on characteristic structural properties of the packing. As shown by a detailed sequential experimental study, the model is able to predict radial Peclet numbers for the turbulent regime in good agreement with experimental data without adjusting any model parameter. [Copyright &y& Elsevier]

An analysis of a sequencing batch reactor (SBR) from a fluid mechanical point of view, used in the cultivation of granular activated sludge (GAS), is carried out by experimental, computational fluid dynamics (CFD) and artificial neuronal networks (ANN) methods. Due to the complexity of the three-phase problem, new hybrid methods are developed in order to shorten the calculation time and to improve the numerical prediction. In the numeroexperimental hybrid, experimentally obtained velocities from particle image velocimetry (PIV) method are implemented as initial conditions for the numerical simulation. This operation causes improvement of multiphase flow results and save CPU time of about 40% in comparison with the standard calculation. In the neuronumerical hybrid, numerically obtained results and process parameters are employed for training of an ANN. With the trained ANN, several geometrical and physical entities are calculated for a range of SBRs. In this case, the acceleration, in the prediction of several process parameters, reaches the factor . [Copyright &y& Elsevier]

Two commercial CFD codes were used to simulate the strongly swirling single-phase flow with core recirculation within an axial hydrocyclone. Both packages used a Differential Reynolds Stress Model with default constants for the turbulence closure. The effect of omitting wall reflection terms was also investigated and it was generally found that this lead to better agreement with experiment. Interestingly, the predicted velocity profiles from the two CFD codes did not agree with each other. Possible reasons for this are different turbulence modelling approaches with different terms for the turbulent diffusion and rapid pressure–strain terms. [Copyright &y& Elsevier]

Abstract: Experiments of oil–water upward and downward flows have been carried out in a 38mm ID pipe to investigate the modifications of turbulent flow characteristics by the presence of dispersed phase, i.e., mean and turbulent velocity profile of the continuous phase and mean velocity profile of the dispersed phase. Results for both oil-in-water (o/w) and water-in-oil (w/o) dispersions are presented. In o/w upward flow, the axial mean velocity profiles are found to be flatter than in single-phase flow and then change to centre peaked as the input oil fraction increases; a flatter profile is seen in w/o upward flow. In downward flow, the presence of oil drops always tends to flatten the continuous phase velocity profile in o/w dispersions, while a slightly centre peaked profile is observed in all cases of w/o systems. For both upward and downward flows, the presence of the dispersed phase tends to flatten the turbulence intensity profile and to result in a more uniform distribution of the turbulent energy over the pipe cross-section. It is also found that turbulence is more likely to be enhanced in the pipe centre area, where the volume fraction and the size of the dispersed phase are larger, while suppressed in the area close to the wall. Turbulence intensity is increased with mixture velocity and is slightly higher in upward than in downward flows. The current study suggests that local dispersed phase fraction and size as well as dispersed phase velocity seem to affect turbulence characteristics in oil–water flows. Previous models based on particle-laden flows for the prediction of turbulence enhancement or suppression were examined and agreement was found to depend on the type of dispersion (i.e., whether oil or water constitute the continuous phase). [Copyright &y& Elsevier]

Abstract: Liquid-phase turbulent transport in a confined rectangular wake was investigated for a Reynolds number of 37,500 based on bulk velocity and the hydraulic diameter of the test section and a Schmidt number of 1250 using particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF). The velocity and concentration field data were analyzed for flow statistics such as the mean velocity, Reynolds stresses, turbulent kinetic energy, turbulent dissipation rate, mixture-fraction mean, mixture-fraction variance and one-point composition probability density functions (PDF). Computational fluid dynamics (CFD) models, including a two-layer – turbulence model, a scalar gradient-diffusion model and a scalar dissipation rate model were validated against PIV and PLIF data collected at six downstream locations. Low-Reynolds-number effects on turbulent transport were taken into consideration through the mechanical-to-scalar time-scale ratio. The experimental and computational results were found to be in satisfactory agreement. [Copyright &y& Elsevier]

Abstract: The friction factor, evaluated from the Colebrook and White equation, is traditionally computed iteratively. An analytical solution of the Colebrook and White equation for the friction factor can be obtained, using the Lambert function. Also, the equation relating the outlet pressure to the inlet pressure of an ideal gas flowing through a straight pipe under isothermal, steady state conditions has been hitherto considered in literature to be implicit in these variables, probably due to its inherent non-linear nature. However, it can be shown that an analytical solution to the above equation for the pressure drop (or alternatively, outlet pressure) can also be obtained using the Lambert function. [Copyright &y& Elsevier]

Abstract: For the cultivation of microorganisms, baffled shake flasks are employed when increased levels of oxygenation and mixing are required. Their use has been discouraged, however, due to the danger of a wetted sterile plug and the lower reproducibility of the experimental results. Consequently, there are only few studies dealing with this type of shaken bioreactor, and there is practically no characterization of this reactor type from a chemical engineering viewpoint. Therefore, a systematic study to elaborate the basic characteristics of the volumetric power consumption and the unfavorable out-of-phase phenomenon in baffled shake flasks is undertaken. A new type of measuring device was developed to measure the volumetric power consumption in a single shake flask. The volumetric power consumption was found to increase with increasing shaking frequency and with decreasing filling volume. Further, an independency of power consumption on the shaking diameter was observed as long as the fluid motion is in-phase. A comparison of two different baffle geometries demonstrated that deeper baffles cause more resistance to fluid flow. For the commonly employed shaking diameter of 25mm, the investigated baffled flask types may not be operated in the in-phase state. A larger shaking diameter must therefore be employed. It was found for the first time that for all in-phase conditions, the dimensionless Newton number is independent of the Reynolds number Re. Power consumption in baffled shake flasks may therefore be described by a characteristic only dependent on the filling volume and the flask type. Even though there are quantitative differences, a qualitative similarity between fluid flow in stirred tanks and shake flasks has been demonstrated. [Copyright &y& Elsevier]

Abstract: A CFD (computational fluid dynamics) model of a solvent extraction pulsed column has been developed and run with a single water phase. The results are compared with experimental measurements taken on a pilot scale column using PIV (particle image velocimetry). The pulsed column investigated had disk–doughnut internals and was operated under pulsing intensities ranging from 10 to 32.5mm/s. PIV measurements of velocity were used to validate the CFD model and to characterise the pulsing flow of a single phase through the column. The CFD modelling was performed for the same geometry and operating conditions using a 2D computational grid and a low Reynolds Number – turbulence model. An improved velocity prediction was achieved by adding a gap between the doughnut internal and the pulsed column wall. The combined measurements and predictions give insight into the effect of the geometry internals on the flow hydrodynamics in the pulsed column. [Copyright &y& Elsevier]

Abstract: In order to gain a better understanding of the scalar dissipation rate in turbulent flows and to test available models for this quantity, high-resolution two-dimensional planar laser-induced fluorescence measurements were undertaken in the mixing field formed by the axisymmetric injection of a fluorescent tracer (acetone) into a confined turbulent co-flow of air, with emphasis on the less explored early region close to the nozzle and on the spatial resolution and level of image denoising necessary for the correct measurement of . In the mean, the resulting plumes had Gaussian profiles and axial decay as expected from previous investigations. It was found that, with Kolmogorov lengthscale resolution and careful image processing prior to the calculation of the scalar gradients, the measured satisfied global conservation of scalar energy across the plume to within 20%. The estimated mean three-dimensional scalar dissipation rate was used to calculate (twice the timescale ratio) that was found to decrease from values higher than 10 adjacent to the nozzle, to approximately 2 at an axial distance of 2–3 nozzle diameters (corresponding to residence times of 0.1–0.2 turbulent timescales) and retaining this value further downstream. The data can assist the validation of models for . [Copyright &y& Elsevier]

Abstract: The purpose of the present study is to observe the effect of the blade attack angle on the roll and trailing vortex structures in a stirred vessel via laser-Doppler velocimetry (LDV). In this investigation, four-bladed paddle impellers with four attack angles, which were , , and , respectively, were used. By synchronizing LDV with a rotary encoder coupled to the impeller shaft, angle-resolved measurements of all three velocity components were performed. This experimental method made it possible to capture the details of the vortical structure both behind the impeller blade and discharge region. Our study on the mean flow structure generated by three types of pitched blade turbines (, , and , respectively) found that a single trailing vortex was formed around each turbine blade. Roll-up of the vortex sheet issuing from the blade tip was also observed, which indicated a major roll of trailing vortex generation mechanism for each pitched blade turbine. [Copyright &y& Elsevier]

Abstract: Many mixing applications involve viscous fluids and laminar flows where the detailed as well as overall flow structures are important. In order to understand the fluid dynamic characteristics of low Re laminar flows in mixing vessels, the flow induced by a Rushton impeller for three Re namely, 1, 10 and 28, was studied both experimentally and computationally. It was found that for the highest Re, the flow exhibited the familiar outward pumping action associated with radial impellers under turbulent flow conditions. However, as the Re decreases, the net radial flow during one impeller revolution was reduced and for the lowest Re a reciprocating motion with negligible net pumping was observed. This behaviour has not been reported in the literature in the past and represents a highly undesirable flow pattern from the standpoint of effective mixing. The CFD results successfully reproduced this behaviour. In order to elucidate the physical mechanism responsible for the observed flow pattern, the forces acting on a fluid element in the radial direction were analysed. The analysis indicated that for the lowest Re, the material derivative of radial velocity near the blade tip is small thus a balance exists between pressure and viscous forces; the defining characteristic of creeping flow. The velocity and pressure forces are in phase because the velocity is driven by the pressure field generated by the rotation of the impeller. Based on these findings, a simplified analytic model of the flow was developed that gives a good qualitative as well as quantitative representation of the flow. [Copyright &y& Elsevier]

Abstract: The particulate jet generated by solid particles falling from a circular orifice into an unbounded quiescent air is simulated. The three-dimensional vortex method, proposed for the analysis of particle-laden free turbulent flow in a prior study, is employed for the simulation. It is found that the falling particles induce complicated three-dimensional unsteady air flow involving large-scale eddies. The air takes its maximum velocity at the jet centerline, and the velocity profile satisfies the self-similarity around the centerline. The effect of particle diameter on the velocity distribution for the two phases is investigated. The entrained air flow rate is favorably compared with the value predicted by the analytical models. [Copyright &y& Elsevier]

Abstract: The effect of particle diameter on the gas-particle two-phase compound round jet is numerically analyzed by the three-dimensional vortex method presented in a prior study. The air jet issues from a round nozzle into the co-flowing air stream, where the Reynolds number based on the air velocity at the nozzle exit is and the velocity ratio between the co-flowing stream and the jet at the nozzle exit is 0.27. The flow direction is vertical downward. Spherical glass particles having diameters 60, 80 and are loaded from the nozzle. The mass loading ratio is 0.27. The analysis made clear the air turbulent modulations due to the particles, such as the relaxation of velocity decay, the increment and decrement of momentum diffusion at the developing and developed regions, respectively. It also clarified that the air turbulent modulations become markedly as the particle diameter decreases. [Copyright &y& Elsevier]

Abstract: A study was performed that utilizes the quadrature method of moments (QMOM) to model the transient spatial evolution of the floc size in a heterogeneous turbulent stirred reactor. The QMOM approach was combined with a commercial computational fluid dynamics (CFD) code (PHOENICS), which was used to simulate the turbulent flow and transport of these aggregates in the reactor. The CFD/QMOM model was applied to a 28l square reactor containing an axial flow impeller and 100mg/l concentration of 1 m nominal clay particles. Simulations were performed for different average characteristic velocity gradients (, and 150s). The average floc size and growth rate were compared with experimental measurements performed in the bulk region and the impeller discharge region. The CFD/QMOM results confirmed the experimentally measured spatial heterogeneity in the floc size and growth rate. In addition, the model predicts spatial variations in the aggregation and breakup rates. Finally, the model also predicts that the transport of flocs into the high shear impeller discharge zone was responsible for the transient evolution of the average floc size curve displaying a maximum before decreasing to a steady-state floc size. [Copyright &y& Elsevier]

Abstract: The use of ejectors as a gas–liquid contacting device has been reported to give higher mass transfer rates than conventional contactors. Computational fluid dynamics (CFD) modeling studies were undertaken to understand the hydrodynamic characteristics with reference to the ejector geometry. The CFD model also provides a basis for quantifying the effects of operating conditions on the ejector performance. CFD studies show that at low value of area ratio (ratio of throat area to nozzle area), due to the larger diameter of the water jet, the annular area available for air flow reduces, causing recirculation of the entrained air within the converging section of the ejector. On the other hand, for higher values of area ratio, due to smaller diameter of the water jet, the momentum transfer to the air decreases and all the entrained air cannot be forced through the throat. As a result, the net air flow rate going into the throat for both area ratios is small. Thus there is an optimum area ratio for the maximum air entrainment rate. The air entrainment rate correlates with pressure difference between the air entry and throat exit for a wide variety of ejector geometries and operating conditions. The overall head loss factor and the ejector efficiency can be predicted a priori. [Copyright &y& Elsevier]

Abstract: Theoretical prediction of flow regime transition in bubble columns was studied based on the bubble size distribution by the population balance model (PBM). Models for bubble coalescence and breakup due to different mechanisms, including coalescence due to turbulent eddies, coalescence due to different bubble rise velocities, coalescence due to bubble wake entrainment, breakup due to eddy collision and breakup due to large bubble instability, were proposed. Simulation results showed that at relatively low superficial gas velocities, bubble coalescence and breakup were relatively weak and the bubble size was small and had a narrow distribution; with an increase in the superficial gas velocity, large bubbles began to form due to bubble coalescence, resulting in a much wider bubble size distribution. The regime transition was predicted to occur when the volume fraction of small bubbles sharply decreased. The predicted transition superficial gas velocity was about 4cm/s for the air–water system, in accordance with the values obtained from experimental approaches. [Copyright &y& Elsevier]

Abstract: The accuracy of the estimation of turbulence power spectra from Laser Doppler Anemometry (LDA) signals in bubbly flows is studied. Special attention is paid to the influence of the gaps in the signal created by the bubbles. The performance of reconstruction and slotting techniques for the estimation of the power spectrum is determined by application to synthetic bubbly flow LDA signals, and checked by application to real data. Estimation of spectra of bubbly flow signals with reconstruction techniques is found to give poor results. In general, the application of reconstruction techniques to LDA signals gives bias in the spectrum due to the addition of noise and low-pass filtering. The nature of the filtering and noise for bubbly flow signals differs from that for single phase flows. For bubbly flow signals, the spectrum is reliable up to a cut-off frequency which is lower than the cut-off frequency for single-phase flow signals with similar data rates. In addition, slopes close to may appear for signals which in reality have flat spectra. For single phase flow, it is possible to correct for these artefacts. The work shows that it is not possible to create similar correction techniques for bubbly flow signals. The application of the slotting technique for estimation of power spectra of bubbly flow signals leads to much better results. Estimation of the spectrum beyond the mean data rate is well possible. The performance of several improvements of the slotting technique is discussed. [Copyright &y& Elsevier]