Ind. Eng. Chem. Res. 2005, 44, 9695-9704
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Just Because It’s Small Doesn’t Mean It’s Well Mixed: Ensuring Good Mixing in Mesoscale Reactors J. F. Hall,†,‡ M. Barigou,† M. J. H. Simmons,*,† and E. H. Stitt§ Centre for Formulation Engineering, Department of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, U.K., and Johnson Matthey Catalysts, P. O. Box 1, Belasis Avenue, Billingham, Cleveland TS23 1LB, U.K.
The advent of high throughput experimentation (HTE) for molecular discovery and rapid screening of new catalyst formulations has led to interest in the mixing characteristics of small stirred vessels at scales below those previously studied. In this paper, particle image velocimetry (PIV) is used to obtain macromixing characteristics for single phase fluids of two different viscosities (µ ) 0.001 and 0.433 Pa s) and for two-phase air-water mixtures in a 45 mm diameter vessel using a 6 blade up-pumping pitched-blade turbine. Eccentric agitation is examined as a means of improving the mixing performance since the vessels are used without baffles, and the global circulation of the fluid was comparable with that of a conventional baffled configuration for single-phase mixing at a constant power input per unit mass (0.168-5.5 W kg-1). For high viscosity fluids, the characteristic flow patterns resembled those for a radial device. For twophase mixing at gassing rates of 0.25 and 0.5 vvm, two sparger configurations were used with the sparger being placed either beneath the impeller axis (R) or away from the impeller (β). The β configuration appeared to be a better choice because of the smaller size of bubbles generated compared with the R configuration and the satisfactory levels of global mixing observed in the vessel. 1. Introduction The control of the degree and rapidity of mixing is essential for the successful operation of any industrial process. The complex nature of the flow field within most industrial equipment, in particular, the ubiquitous stirred tank, has led to considerable research effort to obtain an understanding of the mixing length-scales and time-scales of both single and multiphase mixtures. Several books have been written on the subject.1-3 The general approach taken for the translation of a developmental process from the initial laboratory scale to the industrial scale of production is to attempt to mimic the operational conditions in the pilot vessel at the production scale. This has been a perfectly valid assumption for scenarios involving the development and testing of a process at vessel scales on the order of 10-3 to 10-2 m3 upward, as the large number of previous studies (both academic and industrial) have proved. However, the advent of revolutionary high throughput experimentation (HTE) techniques requires a reexamination of this approach. HTE offers the potential to dramatically reduce the time-scales currently required for the screening of novel molecules and catalysts, and as such, significant benefits are anticipated via the implementation of the HTE protocol in the worldwide chemicals industry. Many commercially available HTE units are based upon small agitated stirred vessels with typical volumes of 10-5 to 10-4 m3, an order of magnitude below existing well-researched lab-scale mixers. * Corresponding author. Dr. Mark Simmons. Tel.: +44 (0) 121 4145371. E-mail:
[email protected]. † University of Birmingham. ‡ Current address: Johnson Matthey Catalysts, P. O. Box 1, Belasis Ave, Billingham TS23 1LB, U.K. § Johnson Matthey Catalysts.
The mixing performance of these units is not optimal because of two primary factors:4-6 First, the small scale of the reactors precludes the generation of high Reynolds numbers, even at high agitation speeds. Second, the HTE reaction vessels are generally unbaffled, to facilitate automated loading and cleaning cycles by robotic server units, as well as to prevent fouling/contamination and excessive particle attrition. Without baffles to break up the dominant tangential flow, efficient mixing cannot be achieved in conventional unbaffled vessels where the impeller shaft is placed at the vessel axis. Since decisions regarding the viability of a certain process or operating condition requirements are often made based on the information generated by the HTE unit, it is vital that the hydrodynamic behavior and fluid mixing performance of these small vessels are fully quantified. Without this information, there is no way for the operator to discern the parametric sensitivity of the process under investigation and differentiation between mass transfer effects and/or kinetic effects becomes impossible. Studies by previous authors based upon conventional vessel configurations at the laboratory and pilot scale (H ) T, C ) 1/3H, D ) 1/3T, fully baffled conditions) for both radial and axial impeller types using flow visualization techniques and computational fluid dynamics have characterized the macroflow behavior in terms of mean flow patterns,7-12 the microflow qualities in terms of the turbulence parameters,13-18 and the mixing performance in terms of the concentration fields.19-23 Laser Doppler velocimetry (LDV) and particle image velocimetry (PIV), in particular, have enabled researchers to obtain high-resolution velocity fields and, hence, develop a thorough understanding of both the global flow patterns and the behaviour of the fluid within the highly energetic regions, such as the impeller discharge jet.
10.1021/ie050224w CCC: $30.25 © 2005 American Chemical Society Published on Web 07/08/2005
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While much previous literature has been devoted to the characterization of this “standard” stirred tank geometry, the ubiquitous nature of the stirred tank within the chemicals industry has resulted in a huge number of variations in the design which may not always be adequately described by conventional reactor models. Although it has been shown that the turbulent parameters of the flow in conventional fully baffled vessels may be predicted via validated computational fluid dynamics (CFD) models, comparatively little confidence may be held in the application of such techniques to situations concerning unbaffled or otherwise unconventional configurations, since few previous studies have concentrated upon these vessel designs. While some works have sought to characterize mixing in unbaffled vessels either via analysis of the power characteristics24-26 or via the evaluation of the tracer concentration profile,27-28 no thorough examination of the fluid hydrodynamics within unbaffled vessels exists. In addition, the vast majority of previous works have concentrated upon vessels in the size range 200-500 mm diameter, which corresponds to the average size of vessel encountered in academic laboratories. While vessels smaller than this scale have held little relevance for the development of scaling rules in the past, with the advent of these HTE techniques it is vitally important that the hydrodynamic behavior and mixing performance in such vessels is thoroughly understood. In this paper, we review our recent investigations into the hydrodynamics of these small-scale vessels4-6 and present the use of eccentric agitation as a means of obtaining more effective mixing for a range of operational scenarios, namely, the mixing of a single-phase low viscosity fluid (water), a single-phase high viscosity fluid (PPG 2000), and a two-phase air-water mixture. This paper focuses on the fluid hydrodynamics and the mixing performance of a miniature agitated vessel of 45 mm diameter; this scale corresponds to approximately the midrange of those encountered within high throughput experimentation (HTE) laboratory equipment. The time-averaged flow fields within the vessels have been obtained using PIV; full details of the implementation of this technique for the HTE vessels used can be found in Hall et al.5 2. Materials & Methods 2.1. Single-Phase Mixing Vessel. A schematic of the 45 mm diameter vessel used (T45) is given in Figure 1. The vessel was constructed of optically perfect borosilicate glass, and to minimize refractive effects distorting the images produced from the PIV, the vessel was enclosed within a square glass box filled with the fluid under investigation. A removable baffle module allowed for experiments to be carried out for two configurations, namely, conventional baffled centerline agitation (B) and unbaffled eccentric agitation (E). The baffle module itself consisted of four equally spaced baffles of width 0.1T and thickness 0.01T secured to supporting rings top and bottom and constructed from polyamide powder via a selective laser sintering (SLS) process. The uppumping, 6-bladed pitched-blade turbine impeller (PBT; D/T ) 0.5; Cw/T ) 0.5 (B); Cw/T ) 0.7 (E); Cimp/T ) 0.33; and W/T ) 0.1) was constructed from stainless steel by HEL Group (Barnet, U.K.), and the angle of the blades was 45° to the impeller axis. Up-pumping PBTs provide versatility with respect to process applications; specifically, they suppress the formation of a surface vortex and surface aeration.
Figure 1. Schematic diagram of the vessel used in this study. Greyed lines denote eccentric impeller location.
2.2. Gas-Liquid Mixing Vessel. To perform an investigation into the processes of two-phase gasliquid mixing and hydrodynamics, the initial T45 vessel was modified to allow the introduction of gas at a suitable location. Conventional vessels generally rely upon a ring or pipe sparger located centrally beneath the impeller. The introduction of any vessel fitting standing proud of the vessel base will have some effect upon the fluid flow field in the region; for centerline vessels, the location of the sparger within the central forced vortex region below the impeller may not significantly alter the flow field, but for an eccentrically configured vessel, with a powerful swirling flow component below the impeller, no intrusion may be made into the flow without creating a substantial distortion within the flow field. Therefore, instead of relying upon a ring or pipe sparger fitting to supply gas to the vessel, sintered glass or frit panels were fitted flush into the base of the vessel to deliver gas directly below the eccentrically located impeller. To determine the effect of sparger location on gas-liquid hydrodynamics, two configurations of sparged vessel were examined. The R configuration (Figure 2a) has the sparger directly below the impeller, whereas the β configuration (Figure 2b) has the sparger 180° out of phase with the impeller and the gas is delivered directly into the bulk fluid region. The average pore size of the sintered panels used was ∼10 µm, leading to the generation of bubbles ∼100 µm in size at the sparger. Air was introduced via a rotameter calibrated using a soap film air flow meter. For all two-phase experiments, the fluid used was distilled water. The vessels were washed out several times to ensure their cleanliness and to ensure that no traces of surfactant or other contaminant that could have an adverse effect upon the coalescent behavior of the system were present. 2.3. Particle Image Velocimetry. Two-dimensional PIV data were obtained for each vessel configuration using a TSI Powerview PIV system (TSI Inc., Shoreview, MN) connected to a Dell Precision 620 twin-processor
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Figure 2. Schematic representation of the sparger configurations used in this study: (a) R configuration and (b) β configuration.
workstation (Dell Corp., U.S.), running TSI Insight 5.0 software, which performed the tasks of both controlling the experimental procedure and managing the data capture/processing. Image capture was achieved via a single 1024 × 1024 pixel frame-straddling charged coupled device (CCD) camera (TSI PIVCam 10-30, TSI Inc.), linked to an image grabber board in the workstation. Full details of the implementation of the PIV technique and the algorithms used for the data analysis may be found in Hall et al.5 The seeding used for both single and two-phase experiments with water as the working fluid were fluorescent 3 µm diameter particles (Duke Scientific Corp., U.S.). An ALP545 high-pass wavelength optical filter (TSI Inc.) was used in front of the camera to prevent detection of incident laser light. For the two phase air-water experiments, this filter acted to separate incident true particle images from light scattered by the bubbles contained within the flow. This prevented bubble images from being considered as particle images by the correlation software, since this would lead to the generation of false vector data. The captured images from the two-phase air-water experiments were used to estimate the average bubble diameter within the vessel. The diameters of all bubbles that were in focus (camera field focused on plane of laser light sheet) were manually measured from high-resolution printed images and the Sauter mean diameter calculated from the bubble size distributions via
d32 )
∑nibdib3 ∑nibdib2
(1)
where nib is the number of bubbles with diameter dib. Global gas hold-up, φg, was calculated from the increase in the liquid free surface elevation upon gassing, which was also obtained from the PIV images. If hu and hg represent the free surface elevation of the fluid
for ungassed and gassed conditions, respectively, then the holdup fraction is given by
φg )
(hg - hu) hg
(2)
Hence, the interfacial area, a, for the system can be estimated as
a)
6φg d32
(3)
where a is defined as the ratio of the bubble surface area (gas-phase surface area) to the combined (total) volume of gas and liquid (m2 m-3). The seeding particles used for the single-phase, laminar flow regime experiments were 10 µm silvered hollow glass spheres (Dantec, U.S.), which were premixed with 5 mL of the working fluid to form a dilute suspension before being added to the vessel contents. The seeding suspension was added incrementally until a suitable number of particle images were recorded in each interrogation cell. 2.4. Experimental Conditions. 2.4.1. Low-Viscosity Experiments. To facilitate valid comparisons between both single- and two-phase experiments at differing operating conditions, the constant power input per unit volume protocol was selected as the scale-up criterion. The gassed power input, Pi, was determined from measurements made of the torque on the impeller shaft (using a Eurostar PowerVisc, IKA, Bremen, Germany) coupled with a term to represent the hydraulic power supplied to the fluid by the action of the sparged gas, to give a total power input per unit volume, Pg where g ) 9.81 m s-2 (gravitational constant) and Ug is the gas superficial velocity, which is defined as
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Ug )
4Qg πT2
(5)
where Qg is the volumetric gas discharge. Two gas discharge rates were considered, 0.25 and 0.5 vvm (where vvm is defined as vessel volume per minute). For all experiments, P/VL ) Pg/VL ) 168 W m-3 (equivalent to 0.168 W/kg). Power input measurements were performed independently for both R and β configurations. The experimental parameters are given in Table 1a. 2.4.2. High-Viscosity Experiments. The working fluid used for the high-viscosity experiments was polypropylene glycol 2000 (PPG 2000) with a dynamic viscosity, µ, of 0.433 Pa s. The experiments were performed over a range of power input per unit mass, P/FVL, from 0.6 to 5.5 W kg-1. The much higher power inputs were needed in order to get satisfactory movement of the viscous fluid within the vessel. A range of power inputs was used in order to ascertain the range which would lead to satisfactory mixing. The experimental parameters are given in Table 1b. 3. Results & Discussion 3.1. Mean Flow Behavior. The mean flow structure for both B and E configurations with water as the working fluid are shown in Figure 3 parts a and b, respectively. The magnitude of the radial and axial velocities for both configurations are comparable. The flow field in the B configuration is dominated by a flow loop in the vicinity of the impeller discharge stream. Velocity magnitudes are noticeably higher below the impeller plane.6 The dominant flow features for the E configuration (Figure 3b) consist of an upward directed discharge from the impeller at r/R ) -0.9 and a high vorticity loop located around the impeller tip at r/R ) 0, which swirls below the impeller before re-entering the impeller inlet at -1.0 e r/R e -0.6 (referred to as the subimpeller loop from here on). The mean velocities are much more evenly distributed throughout the eccentrically agitated vessels, particularly above the impeller plane; Hall et al.6 demonstrated that macromixing times for the E configuration were at least as short as those obtained for the B configuration at the same scale. The flow maps for both B and E configurations with PPG 2000 as the working fluid are shown in Figure 4 parts a and b, respectively. The flow pattern has subtle differences compared with that obtained for water. The characteristic flow pattern for the B configuration (Figure 4a) consists of an angled discharge jet emanating upward (increasing z/H) and outward (toward vessel wall, increasing r/R) from the impeller region, which splits into two distinct streams upon approaching the wall, and the subsequent formation of two recirculation loops returning fluid to the upper and lower impeller inlets. For the E configuration (Figure 4b), the flow map is slightly more complicated; the asymmetric design of the eccentric vessel configuration results in a highly asymmetric flow map; the discharge from the impeller zone is directed into the bulk fluid zone at z/H
) 0.33 for the region 0.0 e r/R e 0.75, from where the characteristic flow pattern develops into a subimpeller loop (centered upon r/R ) 0.1 and z/H ) 0.25), feeding back into the impeller inlet and the forced vortex zone located directly below the impeller. A secondary discharge jet emanates from the impeller at r/R ) -0.9, forming a subsidiary loop to the left above the plane of the impeller. Thus, the characteristic flow pattern observed in both vessel configurations (B & E) for a high-viscosity fluid is similar to the type of flow pattern commonly associated with radial-type impellers such as the Rushton turbine or flat-blade paddle, rather than axial or mixed flow discharge patterns that are generally observed with PBT impellers. Such behavior has been observed for mixed-flow hydrofoil impellers operating in viscous fluids.9 In the upper sections of the vessel for the E configuration (Figure 4b), velocities are generally negligible, with little suggestion of the upward transport loop noted for these vessel configurations in low-viscosity applications (Figure 3b), even allowing for a higher energy dissipation rate; overall mixing performance would be expected to suffer as a consequence. The feeding of fluid into the impeller inlet at -0.4 e r/R e 0.2 is delivered from a subsidiary upper recirculation loop from the main impeller discharge stream, which is augmented by fluid swirling into this section of the vessel from the secondary discharge jet above the plane of the impeller. For the two-phase experiments, the agitation speed (N) and gassing rate (Qg) were set so as to place the vessel operating conditions in the completely dispersed regime.1 The point on the aeration number curve representing the onset of the complete dispersion flow regime is displayed in Figure 5. The measured values of gas holdup, bubble size, and interfacial area are given in Table 1a for all the experiments. The effect of aeration upon the mean velocity field for the R configuration is shown in Figure 6, representing Qg ) 0.25 and 0.5 vvm, respectively. The main effect of gassing upon the mean velocity field is the generation of a powerful upward flow into the region directly below the impeller. The addition of pressurized gas from the sparger into the region -1.0 e r/R e -0.3 supplies energy to the liquid due to the pneumatic lift of the bubbles, and fluid is entrained by their rising motion. The presence of a powerful upward axial flow stream into the inlet of the impeller results in an enhanced axial discharge above the impeller in the region -1.0 e r/R e -0.4; this effect is similar at both gassing rates employed. A powerful mean flow is also observed throughout the region below the impeller (z/H e 0.33). In the bulk fluid zones in the upper reaches of the vessel (-0.2 e r/R e 1.0, 0.5 e z/H e 1.0), the fluid velocities are relatively low, particularly with respect to those observed below the impeller plane or those on the “closed” side of the eccentric vessel (corresponding to the location of the main impeller discharge stream). Interactions between the fluid and the semidisengaged floc of large postcoalescence bubbles that congregate at the liquid surface are responsible for the increased magnitude of the mean velocity vectors in the very upper section of the vessel at both gassing rates. If the β sparger configuration (Figure 7) is used, then there is no energy supplied to the fluid by the sparged
Ind. Eng. Chem. Res., Vol. 44, No. 25, 2005 9699 Table 1. Experimental Parameters (a) Low-Viscosity Experiments (Pg/VL ) 168 W m-3 for all experiments) config. (R or β) & gassing rate Qg (vvm)
rotation speed N (rev min-1)
impeller tip speed Utip (m s-1)
Reynolds number Re
holdup fraction φg (%)
Sauter mean bubble diameter d32 (mm)
interfacial area a (m2 m-3)
0 R, 0.25 R, 0.5 β, 0.25 β, 0.5
575 612 666 564 558
0.72 0.75 0.82 0.69 0.69
5520 6360 5880 5350 5390
0 7.6 8.2 7.7 8.4
0 0.83 0.87 0.74 0.69
0 549 566 624 730
(b) High-Viscosity Experiments config. B&E
power input P/FVL (W kg-1)
rotation speed N (rev min-1)
Reynolds number Re
impeller tip speed Utip (m s-1)
0.611 1.25 2.22 3.60 5.50
478 708 907 1114 1313
11.1 16.3 21.2 26.0 30.7
0.60 0.89 1.14 1.40 1.65
gas directly below the impeller. Instead, the gas is delivered in the region 0.3 e r/R e 1.0, away from the impeller inlet region. Consequently, no strong axial flow is observed in the vicinity of the sparger, as the dominant flow behavior in this region comprises the
recirculation of fluid below the plane of the impeller; bubbles emanating from the impeller are advected by this fluid stream and carried up to the plane of the impeller in a tangential spiral. Mean velocity values are very low in the bulk fluid zone above the plane of the impeller in the region -0.4 e r/R e 1.0, z/H g 0.33. Energy is delivered into the fluid by the impeller, but upon gassing, the formation of trailing gas cavities behind the blades precludes efficient transfer of energy and momentum from the impeller to the dispersion. The streamlining of the fluid flow around the gas cavities reduces drag on the impeller blade, and therefore, a higher agitation speed under aerated conditions than under ungassed conditions is required to maintain a constant power input per unit volume. However, it is clear from examination of Figures 6 and 7 that the higher tip speed alone is not sufficient to develop a well-defined macrotransport loop throughout the entire vessel volume, such as that observed in single-phase studies6 (Figure 3b), because the presence of the additional gas phase disrupts the global fluid recirculation loops. 3.2. Mixing Characteristics and Energy Distribution. The turbulent kinetic energy, k′, may be obtained for turbulent (i.e., low viscosity) flow field data from the 2-D fluctuating velocity components, u′ and v′, by the following equation which takes account of the lack of information in the third (tangential) direction.5,16
k′ ) 0.75(u′2 + v′2)
Figure 3. Liquid-phase mean velocity vectors with water as the working fluid, jT) 0.17 W kg-1, Utip ) 0.72 m s-1, µ ) 0.001 Pa s: (a) for the baffled configuration (B) and (b) for the eccentric configuration (E)6.
(6)
The turbulent kinetic energy (TKE) distribution for the E configuration, shown in Figure 8, shows that the dominant flow pattern consists of a powerful discharge jet leaving the impeller in the region -1e r/R e -0.8 and extending vertically from the impeller to a point in the vicinity of z/H ) 0.6. Whether the jet is fully dissipated at this point or simply leaves the plane of measurement is not clear from the present data, but this would appear to be the case, as a further region of higher energy fluid is observed for all vessels: the region r/R ) 0.2, z/H ) 0.8 for T35E and T60E; r/R ) -0.2, z/H ) 0.8. The appearance of this fluid is strongly suggestive of a continuum from the discharge jet noted leaving the impeller previously. Fluid is recirculated back to the impeller, from where it then passes back into the primary discharge jet. Hall et al.6 observed similar patterns in the distributions of TKE for ec-
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Figure 5. Ratio of gassed/ungassed power against aeration number NA ) Qg/ND3. Values of (NA)CD are 2 × 10-3 and 4.5 × 10-3 for Qg ) 0.25 and 0.5 vvm, respectively.
Figure 4. Liquid-phase mean velocity vectors with PPG 2000 as the working fluid, jT ) 3.6 W kg-1, Utip ) 1.56 m s-1, µ ) 0.433 Pa s; (a) for the baffled configuration (B) and (b) for the eccentric configuration (E).
centrically agitated vessels of diameters from 35 to 88 mm. However they found that the local magnitudes of the TKE values were scale-dependent. For the high-viscosity fluid, the extent of the penetration of the impeller-sourced high shear- and extensionalflow regions throughout the entire vessel volume is considered. Obviously, mixing performance in any vessel will improve with an increase in the relative velocity of the fluid, as disparate fluid elements are brought into contact with each other with increasing frequency and at higher relative or impact velocities. (Note: Large absolute velocities are not necessary for good mixing,
Figure 6. Liquid-phase mean velocity vectors for R sparger configuration, jT ) 168 W m-3, NA ) (NA)CD: (a) Qg ) 0.25 vvm, φg ) 7.6%; (b) Qg ) 0.5 vvm, φg ) 8.2%.
but large relative velocities between different fluid packets are, as these constitute large velocity gradients.) The presence of increased localized velocities will lead to the formation of localized regions of high velocity gradient, leading, in turn, to increased shear rates and elongation of fluid elements:1 these velocity gradients are the true mechanisms of mixing in laminar fluids. In the r-z plane of measurement, two shear rate components and two deformation strain components will
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Figure 8. TKE distribution for the eccentric configuration (E) with water as the working fluid: jT ) 0.17 W kg-1, Utip ) 0.72 m s-1, µ ) 0.001 Pa s.
Figure 7. Liquid-phase mean velocity vectors for β sparger configuration, jT ) 168 W m-3, NA ) (NA)CD: (a) Qg ) 0.25 vvm, φg ) 7.7%; (b) Qg ) 0.5 vvm, φg) 8.4%.
exist and may be calculated from the ensemble-averaged PIV velocity gradient field as
Shear rate components: ∂Ur ∂Uz , ∂z ∂r
(7)
Deformation strain components: ∂Ur ∂Uz , ∂r ∂z
(8)
To examine the distribution of shear gradients, the two distinct shear gradients are combined into a single “rate of strain” parameter to take into account both radial and axial shear via a single distribution. The distribution of this parameter for the E configuration is shown in Figure 9.
(
)
1 ∂〈Ur〉 ∂〈Uz〉 〈Srz〉 ) + 2 ∂z ∂r
(9)
The most significant regions of high shear within the flow are in the impeller plane (z/H ) 0.33), the central section of the vessel base, and the impeller inlet-outlet on the “closed” side of the vessel (-1.0 e r/R e -0.4). The distribution of the regions of high shear is similar
Figure 9. Rate of strain contours for the eccentric configuration (E) with PPG 2000 as the working fluid: jT ) 3.6 W kg-1, Utip ) 1.56 m s-1, µ ) 0.433 Pa s.
to the distribution of TKE, as shown in Figure 8, except that the region of high shear in Figure 9 extends radially to a greater distance (r/R ≈ 0.9) than the region of TKE in Figure 8 (r/R ≈ 0.5). This result echoes the differences observed between the flow fields in both cases (Figures 3b and 4b).
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Figure 10. Evolution of pseudocavern volume (xUr2 + Uz2 g 0.01Utip) with increasing dissipation rate using PPG 2000 as the working fluid, µ ) 0.433 Pa s.
The extent of the penetration of the impeller-sourced high shear- and extensional-flow regions may be considered by the definition of a “pseudocavern”,29 a representation which is more usually applied to viscous, non-Newtonian shear-thinning fluids. The spatial dimensions of the pseudocavern about the impeller have been determined from the distribution of the combined instantaneous velocity magnitude at each point within the vessel. A pseudocavern is defined below for all contiguous cells with a characteristic velocity magnitude greater than 0.01Utip.29
xUr2 + Uz2 g 0.01Utip
(10)
The variation in pseudocavern occupancy with changes in power input in the range 0.6-5.5 W kg-1 is shown for the E configuration in Figure 10. It can be clearly seen that pseudocavern volume is directly dependent upon energy dissipation: the increased shear gradients developed at higher agitation speeds result in a more powerful mechanism for the transfer of energy and momentum away from the impeller region into the bulk fluid domain. At low dissipation rates (jT ) 0.611 W/kg), the pseudocavern is centered upon the impeller shaft, although the pseudocavern is at its widest below the plane of the impeller (z/H e 0.33) where the subimpeller loop maintains higher velocity magnitudes within the local fluid flow pattern. As the power input increases, the effective center of the pseudocavern moves away from r/R ) -0.4 toward the center of the vessel at r/R ) 0.0 and increases in the axial dimension, particularly in the region 0.0 e r/R e 1.0. Figure 10 shows that the pseudocavern quickly expands once P/FV ) 1.25 W/kg and is essentially constant in volume once P/FV g 2.22 W/kg. For P/FV g 3.6 W/kg, the pseudocavern expands into the bulk fluid region in the upper half of the vessel (0.0 e r/R e 1.0, 0.5 e z/H e 0.8). For the two-phase air-water experiments, the turbulent nature of the flow has been characterized by the
spatial distribution of TKE. The TKE distribution in the ungassed vessel (as shown in Figure 8) is characterized by a high degree of homogeneity. Values of k′* ≈ 0.06 Utip2 were observed throughout the bulk fluid zone, with a maximum of only k′* ≈ 0.08 Utip2 observed mainly around the tip of the impeller at r/R ) -0.8. Parts a and b of Figure 11 illustrate the spatial distribution of k′* for the R sparger configuration for gassing rates of Qg ) 0.25 and 0.5 vvm, respectively. The TKE distributions are characterized by a prominent, high-energy stream leaving the upper plane of the impeller on the closed side of the eccentric vessel, in the region -1.0 e r/R e -0.6. A subsidiary loop about the impeller tip at location r/R ) 0.0 provides another common zone of high k′* for both gassing rates. Of particular interest is the extension of the high TKE region below the impeller in Figure 11b. At this operating condition (Qg ) 0.5 vvm), the additional energy supplied to the fluid by its entrainment in this region of the vessel into the rising bubble stream exiting the sparger results in a localized increase in k′*. The occurrence of random small points of high k′* (which manifest themselves as red dots in the TKE distribution on Figures 11-12) are indicative of failures of the peak search or cross-correlation algorithms employed by the Insight software to determine valid particle images in regions of high gas fraction. The exceptions are the two permanent red dots on either side of the impeller shaft at z/H ) 0.65, the cause of which are damaged pixels in the CCD array. The use of the β sparger location leads to a slightly different spatial distribution of TKE (Figure 12). A localized region of high k′* is observed at the impeller tip, centered upon r/R ) -0.9, which is in a comparable position to the main discharge stream observed in the R configuration vessel. However, this zone of higher TKE does not extend upward from the plane of the impeller, suggesting that this flow structure either is indicative of a more tangential impeller discharge (leaving the r-z plane measurement below z/H ) 0.5) or is based on fluctuations caused by the heterogeneity of the gas distribution around the impeller due to the gas sparger location. The largest zone of elevated k′* values is found to extend from the impeller in a radial direction, centered about the plane of the impeller, and occupying the r-z plane from r/R ) -0.4 to r/R ) 0.6 (Qg ) 0.25 vvm) and r/R ) 0.8 (Qg ) 0.5 vvm). The axial spread of this flow structure is also found to be dependent upon the gassing rate; at Qg ) 0.25 vvm, the high k′* values are not observed above z/H ) 0.55 (Figure 12a), whereas at Qg ) 0.5 vvm, the axial penetration is increased to z/H ) 0.70 (Figure 12b). The swirling gas-liquid flow centered upon the plane of the impeller is the root cause of the TKE distribution described above for both operating conditions in the β configuration; the increased gas holdup at the higher gassing rate leads to higher levels of fluctuation in the fluid in localized regions of high gas fraction and the subsequent higher values of TKE recorded in such regions of the flow. These results show that the addition of a secondary gas phase has significant effects upon the vessel hydrodynamics. Upon gassing, and regardless of sparger configuration or gassing rate (for the range of Qg used in this study), the magnitude of the k′* values within the TKE distribution are found to increase substan-
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Figure 11. Normalized TKE distribution in R configuration, NA ) (NA)CD, Pg/VL ) 168 W m -3: (a) Qg ) 0.25 vvm and (b) Qg ) 0.5 vvm.
tially. In the bulk fluid region, the TKE is similar for both ungassed (Figure 8) and gassed (Figures 11-12) conditions at k′* ) 0.06Utip2, but in the regions of the flow comprising the main impeller discharge streams and subimpeller loops, k′* is increased to 0.10-0.12 Utip2 for the gassed conditions. The precise distribution of TKE is found to be dependent upon sparger configuration, and although Qg exerts some influence upon the TKE distribution, the sparger configuration is the controlling parameter. The reason behind the increased values of k′* observed in the TKE distributions of the gas-liquid eccentric mixers is increased fluctuations in the global flow field caused by the arbitrarily heterogeneous
Figure 12. Normalized TKE distribution in β configuration, NA ) (NA)CD, Pg/VL ) 168 W m -3: (a) Qg ) 0.25 vvm and (b) Qg ) 0.5 vvm.
nature of the gas-liquid dispersion. The increased instabilities manifest themselves as fluctuations in discrete fluid elements, leading to higher magnitudes of the turbulence parameters of the flow. Aubin et al.30 also found an increase in k′* in their much larger, fully baffled vessel. In this work, a reduction in TKE was observed in the primary recirculation loop, although this could be attributed to a reduction in the number of valid vectors obtained in this part of the vessel because of the extremely high gas fraction in the locality. These data show that the β configuration appears to be a better choice for gas-liquid mixing in the HTE vessel since the values of measured d32 are smaller (Table 1a), leading to a higher interfacial area for mass transfer, a, while the distribution of TKE indicates
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reasonable levels of mixing and movement of fluid throughout the vessel. Hence, it would be expected that mass transfer would be better for this configuration. Conclusions The use of eccentric agitation has been examined as a strategy to improve mixing in small HTE scale unbaffled vessels. Examination of the mean flow field, measured using a PIV instrument, has shown that the global circulation of fluid for eccentric agitation is at least as good as that obtained for a conventional baffled configuration for the mixing of single-phase fluids over a wide range of viscosities. For high-viscosity fluids, the characteristic flow patterns for the axial 6 PBTu impeller used resembled those for a radial device. This effect has been observed previously.9 For two-phase mixing, the β configuration appears to be a better choice for effective mass transfer because of the smaller size of bubbles generated and the satisfactory levels of global mixing observed in the vessel. Acknowledgment The authors wish to acknowledge the technical assistance regarding the PIV experiments offered by Dr. W. Bujalski (University of Birmingham) and Dr. M. Hyde (TSI Inc., Bristol, U.K.). J.F.H. was funded via an EPSRC Industrial CASE award with Johnson Matthey Catalysts. Literature Cited (1) Harnby, N.; Edwards, M. F.; Nienow, A. W. Mixing in the process industries; Butterworth-Heinemann: Woburn, MA, 1992. (2) Zlokarnik, M. Stirring: Theory and practice; Wiley-VCH: New York, 2001. (3) Paul, E. L.; Atiemo-Obeng, V.; Kresta, S. Handbook of Industrial Mixing: Science and Practice; John Wiley & Sons: New York, 2003. (4) Hall, J. F.; Barigou, M.; Simmons, M. J. H.; Stitt, E. H. Flow patterns in mechanically agitated high throughput experimentation (HTE) reactors. Proc. 11th Eur. Conf. Mixing, Bamberg, Germany, October 2003; VDI-GVC: Dusseldorf, Germany, 2003; p 71. (5) Hall, J. F.; Barigou, M.; Simmons, M. J. H.; Stitt, E. H. Mixing in unbaffled high throughput experimentation reactors. Ind. Eng. Chem. Res. 2004, 43, 4149. (6) Hall, J. F.; Barigou, M.; Simmons, M. J. H.; Stitt, E. H. Comparative study of different mixing strategies in small high throughput experimentation reactors. Chem. Eng. Sci. 2005, 60, 2355. (7) Kresta, S. M.; Wood, P. E. The mean flow field produced by a 45° pitched-blade turbine: Changes in the circulation pattern due to off bottom clearance. Can. J. Chem. Eng. 1993, 71, 42. (8) Lamberto, D. J.; Alvarez, M. M.; Muzzio, F. J. Experimental and computational investigation of the laminar flow structure in a stirred tank. Chem. Eng. Sci. 1999, 54, 919. (9) Fangary, Y. S.; Barigou, M.; Seville, J. P. K.; Parker, D. J. Fluid trajectories in a stirred vessel of non-Newtonian liquid using positron emission particle tracking. Chem. Eng. Sci. 2000, 55, 5969. (10) Rammohan, A. R.; Kemoun, A.; Al-Dahhan, M. H.; Dudukovic, M. P. A lagrangian description of flows in stirred tanks via computer-automated radioactive particle tracking (CARPT). Chem. Eng. Sci. 2001, 56, 2629. (11) Fishwick, R. P.; Winterbottom, J. M.; Stitt, E. H. Effect of gassing rate on solid-liquid mass transfer coefficients and particle slip velocities in stirred tank reactors. Chem. Eng. Sci. 2003, 58, 1087.
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Received for review February 22, 2005 Revised manuscript received June 3, 2005 Accepted June 8, 2005 IE050224W
