Mixing analysis in a tank stirred with Ekato Intermig impellers

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

Discrete element simulation of a flat-bottomed spouted bed in the 3-D cylindrical coordinate system

A spouted bed is simulated in three dimensions by a discrete element method (DEM) in a cylindrical coordinate system. The numerical scheme is based on a second order finite difference method in space and a second order Adams-Bashforth method for time advancement. Gas-particle interaction is assumed to obey the Ergun equation (for void fraction less than 0.8) and its corrected model by Wen and Yu (for void fraction greater than 0.8). The spouted bed vessel is a flat-bottomed cylinder in height and in diameter. The gas inlet diameter is . Three hundred thousand monosized spheres of diameter are used in the simulation. The typical characteristics of spouted beds, such as spout, annulus and fountain, are reproduced. Particle velocity profiles show good agreement with experimental results and self-similarity of the radial distribution of axial particle velocities is reported. Gas flow patterns are also studied and the effect a vortex ring fixed at the bottom of the vessel is investigated. The simulation is validated through comparisons with results reported in the literature.     

Characterization of flow phenomena induced by ultrasonic horn

Mean flow and turbulence parameters have been measured using laser Doppler anemometer (LDA) in ultrasound reactor. The effects of the ultrasonic power have been investigated over a power density (P/V) range of 15-. The liquid circulation velocities are dominant in the zone nearer to the source of energy and are substantially low at the walls and at the bottom of the reactor. The levels of turbulence kinetic energy and dissipation rate are high near the horn and decrease rapidly with increasing distance from the horn. Average turbulent normal stresses are larger than the turbulent shear stresses. However, they are much lower than stirred reactors when compared at the same power consumption per unit mass. Comparisons of LDA measurements and computational fluid dynamics (CFD) predictions have been presented. The good agreement indicates the validity of the CFD model. The flow information has been extended for the prediction of mixing time. For uniform mixing in ultrasound-assisted reactors, optimum power density and diameter of the vessel is needed, yet it is far less effective than conventional stirred vessel. The possibility of optimization has been suggested in terms of power dissipation and the vessel size.     

Design of microfluidic slug mixing based on the correlation between a dimensionless mixing rate and a modified Peclet number

A method to design mixing in microfluidic slugs using a modified Peclet number, , has been reported by the authors, but it was limited to mixing at constant diffusivity D. This paper reports an improved method to quantitatively determine the effect of D on a relation between Pe^* and mixing rates. Computational fluid dynamics (CFD) simulations were used for the investigation. We introduce D into the mixing rate term in the relation between Pe^* and mixing rates, and found that (mixing ) becomes a function of only Pe^*. Thus, slug mixing can be designed using the new dimensionless number, (mixing ), and Pe^*. This allows us to use mixing rate data at any value of D to estimate mixing rates at another value of D. Though Pe^* includes effects of D, l, d_s, and U_s, effects of initial arrangements of reactants inside a slug and slug cross-sectional shapes are not considered. Thus, the relations between (mixing ) and Pe^* (referred as Pe^* correlation) are quantitatively determined to cover the effects of these parameters. Furthermore, we used the Pe^* correlation to show theoretically that channel contraction is an effective microfluidic operation to enhance mixing in slugs.     

Liquid mixing in gas-liquid two-phase flow by meandering microchannels

The influence of the channel radius on the mass transfer in rectangular meandering microchannels (width and height of ) has been investigated for gas-liquid flow. Laser induced velocimetry measurements have been compared with theoretical results. The symmetrical velocity profile, known from the straight channel, was found to change to an asymmetrical one for the meandering channel configuration. The changes in the secondary velocity profile lead to an enhanced radial mass transfer inside the liquid slug, resulting in a reduced mixing length. In the investigated experimental range (superficial gas velocity and superficial liquid velocity ) the mixing time was reduced eightfold solely due to changes in channel geometry. An experimental study on the liquid slug lengths, the pressure drop and their relation to the mass transfer have also been performed. Experimental results were validated by a simulation done in Comsol Multiphysics^®. To obtain information for higher velocity rates, simulations were performed up to . These velocity variations in the simulation indicate the occurrence of a different flow pattern for high velocities, leading to further mass transfer intensification.     

Flow regimes and gas holdup in paper pulp-water-gas three-phase slurry flow

Hydrodynamic flow characteristics of solid-liquid-gas slurry made by intimately mixing fibrous paper pulp with water and air were investigated in a short, vertical circular column. The pulp consistency (weight fraction of pulp in the pulp-water mixture) was varied in the low consistency range of 0.0-1.5%. The test section was long, with inner diameter. Mixing of the slurry prior to entering the test section was done using a patented mixer with controlled cavitation that generated finely dispersed micro-bubbles.Flow structures, gas holdup, and the geometric and population characteristics of gas bubbles in the gas-pulp-liquid three-phase flow were experimentally investigated, using visual observation, Gamma-ray densitometry, and flash X-ray photography. Superficial velocities of the gas and liquid/pulp mixture covered the ranges 0- and 21-, respectively.Five distinct flow regimes could be visually identified. These included dispersed bubbly, characterized by isolated micro-bubbles entrapped in fiber networks; layered bubbly, characterized by bubbles rising in a low consistency annular zone near the channel wall; plug; churn-turbulent; and slug. The dispersed and layered bubbly regimes could be maintained only at very low gas superficial velocities or gas holdups. Flow regime maps were constructed using phasic superficial velocities as coordinates, and the regime transition lines were found to be sensitive to consistency.The cross section-average gas holdup data showed that both the dispersed and the layered bubbly regimes could best be represented by the homogeneous mixture model. The drift flux model could best be applied to the reminder of the data when the plug and churn-turbulent flow regimes were treated together, and the slug flow was treated separately. The drift flux parameters depended on the pulp consistency.     

Solids mixing in the riser of a circulating fluidized bed

Gas/solid and catalytic gas phase reactions in CFBs use different operating conditions, with a strict control of the solids residence time and limited back-mixing only essential in the latter applications. Since conversion proceeds with residence time, this residence time is an essential parameter in reactor modelling. To determine the residence time and its distribution (RTD), previous studies used either stimulus response or single tracer particle studies.The experiments of the present research were conducted at ambient conditions and combine both stimulus response and particle tracking measurements. Positron emission particle tracking (PEPT) continuously tracks individual radioactive tracer particles, thus yielding data on particle movement in “real time”, defining particle velocities and population density plots.Pulse tracer injection measurements of the RTD were performed in a 0.1 m I.D. riser. PEPT experiments were performed in a small ( I.D.) riser, using ¹⁸F-labelled sand and radish seed. The operating conditions varied from 1 to 10 m/s as superficial velocity, and 25- as solids circulation rate.Experimental results were compared with fittings from several models. Although the model evaluation shows that the residence time distribution (RTD) of the experiments shifts from near plug flow to perfect mixing (when the solids circulation rate decreases), none of the models fits the experimental results over the broad (U,G)-range.The particle slip velocity was found to be considerably below the theoretical value in core/annulus flow (due to cluster formation), but to be equal at high values of the solids circulation rate and superficial gas velocity.The transition from mixed to plug flow was further examined. At velocities near U_tr the CFB-regime is either not fully developed and/or mixing occurs even at high solids circulation rates. This indicates the necessity of working at U> approx. ( to have a stable solids circulation, irrespective of the need to operate in either mixed or plug flow mode. At velocities above this limit, plug flow is achieved when the solids circulation rate . Solids back-mixing occurs at lower G and the operating mode can be described by the core/annulus approach. The relative sizes of core and annulus, as well as the downward particle velocity in the annulus (∼U_t) are defined from PEPT measurements.Own and literature data were finally combined in a core/annulus vs. plug flow diagram. These limits of working conditions were developed from experiments at ambient conditions. Since commercial CFB reactors normally operate at a higher temperature and/or pressure, gas properties such as density and viscosity will be different and possibly influence the gas-solid flow and mixing. Further tests at higher temperatures and pressures are needed or scaling laws must be considered. At ambient conditions, reactors requiring pure plug flow must operate at and . If back-mixing is required, as in gas/solid reactors, operation at and is recommended.     

Microdynamic analysis of the particle flow in a cylindrical bladed mixer

A microdynamic study of the particle flow in a vertical axis mixer with slowly rotating flat blades has been performed by means of a modified discrete element method. The conditions are comparable to recent experiments conducted using positron emission particle tracking, with a mixer being in diameter, filled by 16,000 monosized spheres of diameter, and two blades rotating at a speed of . The dependence of flow behaviour on particle-particle and particle-wall sliding and rolling frictions is quantified and the results are used to establish the spatial and statistical distributions of microdynamic variables related to flow and force structures such as velocity, porosity, coordination number, particle-particle and particle-wall interaction forces. While the geometry and operational conditions are relatively simple, the particle flow is shown to be very complicated. There is a three-dimensional zone in front of a blade where particles have a strong recirculating flow. Increasing sliding friction coefficient or decreasing rolling friction coefficient can promote the formation of this zone. The flow and force structures of particles in the mixer are not uniform, although macroscopically steady flow is reached readily. The results show that increasing the rolling friction coefficient and, in particular, the sliding friction coefficient can increase the bed porosity and decrease the mean coordination number. The recirculating flow and the mixing kinetics are promoted by increasing the sliding friction coefficient or decreasing the rolling friction coefficient. Furthermore force arching is strong in the particle bed, with large inter-particle forces concentrating near the bottom corner just in front of the blade and propagating into the bed. Increasing the sliding or rolling friction coefficient increases the potential energy of particles in the mixer, but the kinetic energy is not sensitive to these coefficients. The increased potential energy gives increased particle-particle and particle-wall interaction forces and hence an increased torque required to drive the system. The results highlight the capacity and usefulness of numerical simulation in developing an understanding of the interplay of structure, forces, velocities and mixing in granular systems.     

Use of angle resolved PIV to estimate local specific energy dissipation rates for up- and down-pumping pitched blade agitators in a stirred tank

Up-pumping pitched blade turbines (and similar impellers) have recently been shown to be particularly effective for achieving a variety of mixing duties. Here, their turbulent flow characteristics are analysed by angle-resolved particle image velocimetry (PIV) for the first time and compared with their down-pumping equivalent, the usual time-averaged parameters also being determined for each. The work was conducted in 0.15 m diameter vessel (T) with a 45° impeller of diameter D (=0.45T) in water. The angle-resolved PIV enables a number of novel features to be identified. Firstly, the two pumping directions are shown to give very different vortex structures, even though the flow numbers, Fl, are the same (=0.79). In addition, the ‘spottiness’ of the normalized kinetic energy along a radius as the trailing vortex moved away from each impeller can be identified, which is not shown from time-averaged data. Often, the most important parameter for processing is the local normalized specific energy dissipation rate, and this is estimated using three methodologies: by measurement of the components of the stress tensor directly, ; by dimensional analysis, , with measured integral length scales (ILS); and by the Smagorinsky closure method, , to model unresolved scales (with a Smagorinsky constant used in the literature on stirred vessels). Again, only the angle-resolved results show the spottiness of and also higher values than the time-averaged. Differences in the values obtained by the three methods are discussed and compared with the existing literature. Most importantly, for the first time, the power input in the PIV-interrogated region is calculated from the three methods and compared to the input based on the impeller torque. Both DA and SGS methods are shown to overestimate the true power by a factor of 5 and 2, respectively, whilst the DE method provided a significant underestimate (1/5th) due to the limitation of the resolved length scales. The SGS method shows the greatest promise and by changing the value of the Smagorinsky constant in accordance with recent recommendations, good agreement is obtained. Nevertheless, it is concluded that there is still a need for improved methods for determining the important mixing parameter, .     

Mixing of stabilised drops in suspension polymerisation

In suspension polymerisation it is sometimes necessary to add material to the reactor after the reaction has started. When that happens, the new material and existing drops can remain segregated for significant amounts of time. Hashim and Brooks (Chem. Eng. Sci. 57 (2002) 3703) showed that the viscosity of drops affects both their sizes and their rates of coalescence. In the work reported here, further clarification of the drop mixing process is achieved by using pairs of stabilised dispersions. Solutions of polystyrene (PS) in styrene formed the dispersed phase and the tracer die technique was used to determine the extent of drop mixing. Drop mixing rate increased when the polymer content of all the drops increased from 0 to but further increases in polymer content lead to a reduction in mixing rate. Drop viscosity affected the mixing rate both directly and indirectly, because viscosity affected drop size and that influenced the drop-mixing rate. With increased polymer content, the larger drops made little contribution to the mixing. Experimental results were compared with the prediction of a model developed previously by Alvarez et al. (Chem. Eng. Sci. 49(1) (1994) 99). The model is consistent with the initial coalescence rates that were deduced from the experimental measurements. Drops containing PS mixed more quickly with drops containing PS than with drops containing PS. In those cases, the initial drop size distribution was relatively wide but, gradually, became narrower (the larger drops disappeared). With no polymer in the dispersed phase, the mixing of pre-dispersed drops was slower than the mixing that occurred when a batch of non-dispersed material was added to a stabilised dispersion (i.e. batch mixing). But, with of polymer in the dispersed phase, the mixing rate of two stabilised dispersions was similar to the batch mixing rate (even though the added polymer solution was not initially protected by the stabiliser). Mixing of two stabilised dispersions, with drops containing different amounts of PS, indicated that drop viscosity influences the mixing rate more than the difference in drop sizes.     

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

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

Transition between stratified and non-stratified horizontal oil-water flows. Part II: Mechanism of drop formation

The conditions and mechanism of drop formation at the interface of oil-water wavy stratified flows that lead to the onset of drop entrainment and the transition to dual continuous flow pattern were investigated both experimentally and theoretically. Experimentally, high-speed video imaging was used to capture the mechanism of drop detachment from waves during oil and water stratified flow in a diameter horizontal acrylic pipe. The visual observations revealed that the faster phase undercuts the other one while the waves present in both phases deform until drops are detached. The wave deformation was attributed to the drag force, that originates from the relative movement between the two phases, exceeding the stabilising surface tension force. Based on this force balance an equation was developed that related the wavelength to the amplitude that can lead to drop detachment. This drop entrainment equation and the wave stability equation suggested in part I of the paper [Al-Wahaibi, T., Angeli, P., 2007. Transition between stratified and non-stratified horizontal oil-water flows. Part I: Stability analysis. Chemical Engineering Science, in press, doi:10.1016/j.ces.2007.01.024 ], defined three regions in a wave amplitude versus length graph, namely the stable waves, the unstable waves and the drop entrainment region. The intersection of the lines produced by these two equations gives the critical minimum wave characteristics for drop formation. These agreed well with experimental data when a new correlation for the drag coefficient on the waves was used, suitable for liquid-liquid flows. Also the characteristics of waves that were experimentally found to form drops fell within the predicted entrainment region.     

Flow behavior and regime transition in a high-density circulating fluidized bed riser

Flow behavior and flow regime transitions were determined in a circulating fluidized bed riser (0.203 m i.d. × 5.9 m high) of FCC particles (, ). A momentum probe was used to measure radial profiles of solids momentum flux at several heights and to distinguish between local net upward and downward flow. In the experimental range covered (; ), the fast fluidization flow regime was observed to coexist with dense suspension upflow (DSU). At a constant gas velocity, net downflow of solids near the wall disappeared towards the bottom of the riser with increasing solids mass flux, with dense suspension upflow achieved where there was no refluxing of solids near the riser wall on a time-average basis. The transition to DSU conditions could be distinguished by means of variations of net solids flow direction at the wall, annulus thickness approaching zero and flattening of the solids holdup versus G_s trend. A new flow regime map is proposed distinguishing the fast fluidization, DSU and dilute pneumatic transport flow regimes.     

A new method to determine the microbial kinetic parameters in biological air filters

This paper presents a new method to determine kinetic parameters of the biodegradation of various pollutants in a biofilter. Toluene, a readily biodegradable volatile organic compound, and methane, a hydrocarbon and a greenhouse gas, have been chosen as the target pollutants. The new protocol utilized biomass immobilized on bed pellets; these directly sampled from a continuous steady-state biofilter. The comparison of this method with the conventional experimental protocol utilizing micro-organisms suspended in a liquid medium was made using the pollutant toluene. Indeed, with both methods, the kinetic parameters have been evaluated by following the microbial growth in batch, thermostated reactors, using determined amounts of pollutant substrate. This experiment has confirmed the pertinence of the new procedure. The interesting features of the new method are that: (1) it is easy to operate (no preliminary treatment of the bed samples) and (2) it provides reproducible parameters that represent the real biofilter case more adequately than liquid cultures. In addition, modeling of the experimental specific growth rates in the case of toluene has shown that the values obtained with the use of solid extracts can be correlated by a Haldane's formulation, where , , and . The maximum specific growth rate was reached for an initial concentration of toluene near . The determination of the experimental specific growth rates of micro-organisms in the methane biofilter has also been performed. This study allowed highlighting two methane concentrations’ ranges: from 1000 to 14 500 ppmv and from 14 500 to 27 000 ppmv. For the first range, the Monod model proves to be suitable with the kinetic parameters: and . For the second range, neither the Monod nor the Haldane's formulation could directly be used. However, a mathematical adjustment of the Monod model allows to find kinetic parameters and . The biomass yields for the tested methane concentrations have also been determined and showed two different tendencies, depending on the same two ranges. For the first range of methane concentrations, the biomass yield was quite constant with an average value around while for the second range, it could be approached by a polynomial second-order regression. The maximum value of the biomass yield obtained on the second range was at a methane initial concentration of 20 000 ppmv.     

Liquid phase catalytic hydrodechlorination of 2,4-dichlorophenol over carbon supported palladium: an evaluation of transport limitations

The catalytic hydrodechlorination (HDC) of aqueous 2,4-dichlorophenol (2,4-DCP) solutions over Pd/C catalysts (1-10% w/w Pd) has been investigated at 303 K in a stirred slurry reactor. The experimental results have shown that 2,4-DCP is converted to phenol quantitatively and 2-chlorophenol (2-CP) is the only intermediate product within detect limitations . The system is 100% selective in terms of dechlorination and phenol hydrogenation only proceeds once complete dechlorination has been attained. The reaction pathway is illustrated and HDC progress is related to pH changes in solution. The mass-transfer limitations have been evaluated experimentally using the diagnostic criteria associated with varying hydrogen flow rate, stirring speed, catalyst concentration and particle size. Experimental results combined with parameter estimation have revealed the influence of mass transfer at the liquid/solid interface and intraparticle diffusion in limiting HDC rate. These effects can be minimized for the less active 1% w/w Pd/C catalysts where the stirring speed , hydrogen flow , catalyst concentration and particle sizes . The selectivity trends associated with 1% w/w Pd/C were the same whether the system operated under physical transport or chemical control. The selectivity with respect to 2-CP was however limited by mass-transfer processes in the HDC reaction using higher Pd loadings.