Two-Phase Flow and Bubble Size Distribution in ... - ACS Publications

Ind. Eng. Chem. Res. 2010, 49, 2613–2623

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Two-Phase Flow and Bubble Size Distribution in Air-Sparged and Surface-Aerated Vessels Stirred by a Dual Impeller Giuseppina Montante, Fabio Laurenzi,† Alessandro Paglianti, and Franco Magelli* Department of Chemical, Mining and EnVironmental Engineering, UniVersity of Bologna, Via Terracini 28, Bologna I-40131, Italy

The aim of this work is to investigate the turbulent hydrodynamic features of a fully baffled gas-liquid stirred vessel equipped with a dual turbine consisting of a radial concave-blade turbine and a downflow pitched blade turbine (PBT). Two different operating modes are analyzed, namely air sparged and surface aerated. A two-phase particle image velocimetry (PIV) technique, based on a single laser sheet source and two cameras, each provided with a filter for separately catching the light scattered by the liquid seeding particles or the bubbles, was adopted for detecting independently and simultaneously the liquid and bubble phase velocities. The mean flow fields of the gas and liquid phases, the rms velocity fluctuation maps of the two phases, and a comparison with the corresponding velocity measurements effected in single-phase conditions are presented. The typical bubble size distribution (BSD) in the two gas-liquid systems obtained by a digital image processing method is also presented, and its dependency on the gas feeding configuration and on the dimensionless Weber number is shown. The effects on the hydrodynamic behavior of the gas-liquid dispersion of liquid viscosity as well as of gas flow rate or impeller speed for the air-sparged and surface-aerated systems, respectively, are discussed. The results suggest that simultaneous detection of the flow fields of the two phases is required for appropriate, detailed evaluation of the system features. Even a limited viscosity change has a significant impact on the system hydrodynamics, since it affects both the flow field and the BSD. 1. Introduction Gas-liquid stirred vessels are widely adopted in several processes of the chemical, mining, pharmaceutical, and biotechnological industries. The performance of such equipment depends greatly on the fluid dynamic behavior, in that the mean flow generated by the impeller(s) determines the convective transport of momentum, heat and mass, while turbulence determines dispersive and interphase transport. Impeller type and number, vessel configuration, liquid properties, and operating conditions affect strongly the fluid dynamic performance.1,2 In recent years the features of two-phase flow have been studied with advanced experimental techniques, primarily laser Doppler velocimetry (LDV) and particle image velocimetry (PIV). For sparged vessels of standard geometry mainly the behavior of the liquid phase has been investigated,3-7 while limited data are available on bubble velocities and on the turbulent features of the gas phase.8-12 Similar information for more complex geometric configurations (such as dual or multiple impellers, surface aerators, self-inducing aerators, jet-loop systems, etc.) is even less available and is restricted to the liquid phase.3 Data have also been provided about the spatial distribution of bubble size and bubble size distribution (BSD) in equipment stirred with a single agitator12-19 or a dual or triple turbine.16,18,20-22 The local hydrodynamics of surface-aerated reactors has not been characterized so far, with the exception of a study relative to the onset of surface air entrainment, where the root-mean-square (rms) velocity fluctuations were shown to be the key parameter for modeling.23 Indeed, detailed data on the mean and fluctuating velocity components of the liquid and gas phases as well as the typical size of the bubbles will help to improve design rules, optimize * To whom correspondence should be addressed. Tel.: +39 051 2090245. Fax: +39 051 6347788. E-mail: [email protected]. unibo.it. † Present address: Methanol Casale sa, 6900 Lugano, Switzerland.

the configurations, and validate the modeling techniques, especially those based on computational fluid dynamics (CFD) methods. In this work, an investigation is carried out about the turbulent flow field of both phases in a dual impeller gas-liquid stirred tank consisting of a radial concave-blade turbine at the bottom and a pitched blade turbine (PBT); both sparged and surface-aeration modes are considered. The mixing behavior and the bubble size distribution have been evaluated by means of the PIV technique and digital image analysis, respectively; two liquids of different viscosities and three gas flow rates have been considered. 2. Experimental Section The experiments were carried out in a fully baffled flatbottomed cylindrical vessel of diameter T ) 23.2 cm, whose geometric configuration is depicted in Figure 1. Agitation was provided by a dual impeller: the lower agitator was a radial

Figure 1. Geometric configurations of the stirred vessel: left, air-sparged system; right, surface-aerated system.

10.1021/ie9006276  2010 American Chemical Society Published on Web 02/05/2010

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Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010

Figure 2. Dimensionless flow field of the liquid in single-phase conditions, H ) 2T configuration. (a) Water, N ) 305 rpm; (b) water-glycerine solution, N ) 160 rpm.

Figure 3. Dimensionless flow field of water under sparged aeration. N ) 305 rpm. (a) QG ) 0.02 vvm; (b) QG ) 0.25 vvm.

Scaba 6SRGT turbine of diameter equal to 12.1 cm, placed at a distance T/3 from the vessel base; the upper one was a downflow four-bladed PBT of diameter equal to 9.4 cm, placed at a distance T above the Scaba turbine. Optimization of the geometric configuration was not attempted. Two operating modes were investigated, namely air-sparged conditions, where air was fed into the liquid through a point sparger placed on the vessel axis at a distance Cs equal to T/6 from the vessel bottom (underneath the lower turbine), and surface aeration. The liquid level in the ungassed vessel was maintained at a height H equal to 2T for the air-sparged configuration, while a lower level equal to 1.44T was fixed for the surface-aeration setup so that the submergence of the upper edge of the impeller blades below the liquid level (under ungassed conditions) was equal to 1.5 cm (0.066T); in both cases the vessel was open at the top. Water and a water-glycerine solution of 5 mPa · s viscosity were used as the liquid phase. In the air-sparged experiments different gas flow rates, QG, ranging from 0.02 to 0.25 vvm (volumetric air flow/minute per volume of liquid) were considered for both the air-water and the air-water/glycerine systems; the impeller rotational speed, N, was fixed at 305 and 160 rpm for the former and latter liquids, respectively. For the surface-aerated configuration, liquid gassing is based on bubble entrainment due to agitation and the impeller rotational speed was varied in the range 385-435 rpm for water, while only the condition N ) 305 rpm could be studied for the water-glycerine solution. The vessel was contained inside a square tank filled with the working liquid for minimizing optical errors. The liquid and gas velocity fields were measured using a PIV system based on a single laser sheet source (pulsed Nd:YAG laser, λ ) 532 nm light wavelength, f ) 15 Hz, frequency) and two cameras provided with appropriate light filters for separately

capturing the light scattered by the seeding particles for the liquid (polymeric particles coated with fluorescent RhodamineB) with one camera (HiSense MK II, 1344 × 1024 pixels CCD) and that scattered by the bubbles with the other (PCO, 1280 × 1024 pixels CCD). The time interval between two laser pulses was varied in the range 150-500 µs, depending on the impeller speed, and that from a pulse pair to another was equal to a few seconds. At least 1000 image pairs were required to obtain sample-independent velocity fluctuation measurements. The interrogation area was set at 64 × 64 pixels, and the crosscorrelation of the image pairs was performed on a rectangular grid with 50% overlap between adjacent cells. For determining the bubble size, the gas-liquid stirred vessel was illuminated with diffused light from the back and images were captured with a digital camera placed at the vessel side opposite the lamps with a small aperture. For each operating condition, 150 images were acquired. Each picture was processed with Shadow processing software (Dantec Dynamics) to determine bubble size and bubble size distribution (BSD). The bubble edges were identified by the Canny method, which is based on the detection of local maxima of the image gradients, with the gradient being calculated using the derivative of a Gaussian filter. The edges weaker than a fixed sensitivity threshold were discarded, and those included in the output were further analyzed for retaining only the edges with closed contours. Finally, the area of each detected bubble was calculated summing up the total number of pixels contained inside the edge. The bubble equivalent diameter, db, was evaluated as the diameter of a spherical bubble having the same area as the measured object. It is to be noted that bubbles smaller than 1 pixel (0.35 mm) could not be detected with this method: this size cutoff affects the BSD but does not seem to have practical consequences since tiny bubbles do not actually


contribute significantly to mass transfer. Further details on both experimental techniques can be found elsewhere.12 A vertical plane placed midway between two baffles was always considered for the measurements; an overall plane including both impellers was investigated for both configurations, namely the full liquid height for the free-surface-aeration mode (H ) 1.44T) and up to H ) 1.6T for the air-sparged system. For improving image resolution, the view area of the cameras was restricted to a number of axial positions in both the PIV and the bubble size measurements. The data obtained at various axial positions were subsequently merged into a single plane. The selection of the above-mentioned operating conditions was forced by the intrinsic limitations of the PIV technique, whose operability is strictly dependent on the extent of the gas holdup.24 Specifically, the experiments in the air-water/ glycerine system could be run only at an impeller speed lower than that adopted for air-water: in the former system at high rotational speed the presence of an extremely large number of tiny bubbles made the medium opaque and, therefore, the PIV technique useless. Similarly, in the same conditions the BSD could not be measured by the Shadow processing software. On the other hand, complete gas dispersion could not be attained at the lower impeller speed in pure water. In the following, r and z are the radial and axial coordinates, respectively, and the origin of the coordinate system is fixed at the center of the vessel bottom. The mean and rms velocities are made dimensionless by dividing by the Scaba impeller tip speed, Vtip, unless differently specified. The mean axial and radial velocities, U and V, are positive if directed upward and toward the vessel center, respectively. Overall gas holdup was also evaluated by measuring the liquid-gas interface rise. At the reported operating conditions with water, its value was lower than about 3%: this figure cannot be taken as an accurate estimate because of the measurement errors associated with a limited interface rise, but it is consistent with the literature6 concerning the upper limit of gas holdup measurable by means of PIV. 3. Results and Discussion 3.1. Single-Phase Flow. The reference flow fields in water and in the water-glycerine solution under ungassed conditions and at the same impeller rotational speeds adopted in the airsparged measurements are shown in Figure 2. The vectors, which represent the dimensionless liquid mean velocity on a vertical plane placed midway between two baffles, show that the radial jet produced by the lower impeller gives rise to a typical double loop of similar shape for both fluids, slightly better defined for the viscous solution; while the upper PBT pumping downward produces a single circulating loop with a stronger, more coherent jet in the case of water. As a result, the discharge streams of the two impellers interact directly with each other in the case of water, while for the water-glycerine solution an almost independent mixing action is exerted by each impeller. The reason for the observed differences could lie in the flow regime, as in the water-glycerine solution the impeller Reynolds numbers, based on the liquid physical properties, are 1 order of magnitude smaller than in water (7.5 × 104 and 4.5 × 104 for the lower and the upper impeller, respectively, in water versus 7.8 × 103 and 4.7 × 103 in the water-glycerine solution). The Reynolds numbers in the surface-aerated configuration were similar (i.e., 9.44 × 104 and 5.7 × 104 in water vs. 1.5 × 104 and 8.9 × 103 in the water-glycerine solution for the lower

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Figure 4. Dimensionless flow field of gas in water under sparged aeration. N ) 305 rpm. (a) QG ) 0.02 vvm; (b) QG ) 0.25 vvm.

and the upper impeller, respectively), which makes the comparison between the two systems meaningful. 3.2. Hydrodynamics of the Air-Sparged Configuration. The fluid dynamic behavior of the two gas-liquid systems in the air-sparged configuration is affected by the air bubble presence even at a very low gas rate. In the case of water (Figure 3), when the gas flow rate is increased the shape of the circulation loops of the Scaba turbine changes, the discharge stream of the PBT is weaker and less coherent, and its circulation center is closer to the turbine. A similar shift of the PBT recirculation loop toward the turbine tip under aeration has also been reported by Aubin et al.10 As a result, the zone between the two impellers becomes less and less agitated as QG increases. For QG ) 0.25 vvm, two corotating recirculation loops appear underneath the Scaba turbine. Their presence can also be noticed in the experimental data of Khopkar et al.,24 who performed PIV experiments using a Scaba impeller working at QG ) 0.2 vvm in a fully baffled tank with a dished bottom. The gas flow fields that are shown in Figure 4 exhibit general features similar to those of the liquid ones, although the gas rate increase does not produce the same effect detected in the liquid. For the investigated gas rates, the loop shape typical of the radial 6SRGT turbine takes place below the impeller, while above it the air bubbles follow the liquid stream close to the vessel wall. A more marked effect of QG is visible in the PBT region, due to the modification of the discharge stream already observed for the liquid phase. Finally, wide almost stagnant zones in the middle of the vessel between the two turbines indicate that the buoyancy of the bubbles is about equal to the drag exerted on them by the downflowing liquid. The radial liquid velocity profiles close to the impeller tip are only slightly affected by the gas at any impeller speed investigated so that the two-phase pumping capacity is expected

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Figure 5. Axial velocity component of the gas and liquid phases at various heights under sparged aeration (H/T ) 2 configuration). Water, N ) 305 rpm, QG ) 0.05 vvm. Open symbols, gas phase; solid symbols, liquid phase.

to be roughly equal to the single-phase value. However, the grid for the velocity measurements at the impeller tip was not fine enough as to allow accurate pumping capacity evaluation. Based on the reported measurements, it is also possible to make estimates between the local velocity of the bubbles and the liquid phase (slip velocity). For this purpose the axial, dimensionless velocity components of the two phases have been plotted as a function of the dimensionless radius at different heights for a given condition (water, N ) 305 rpm, QG ) 0.05 vvm) in Figure 5. As can be observed, in the inner zone of the lower vessel portion (H/T ) 0.17, 0.5, and 0.83) the gas velocity is higher than that of the liquid, with the difference being as high as 0.8Vtip (and even twice at H/T ) 0.83); in the upper vessel portion the slip velocity is negligible, except in few intermediate zones at the vessel top (H/T ) 1.4). This finding can be explained by the fact that large and tiny bubbles in PIV experiments give the same contribution to the evaluation of the mean gas phase velocity. Indeed, at each location the gas phase velocity vector is calculated as the arithmetic mean (over the

total number of image pairs) of the velocity of the bubbles contained in the interrogation area (Montante et al.11). Keeping this aspect in mind, the different behaviors in the two vessel regions seem to be associated with the different bubble sizes in the upper and lower vessel parts (see section 3.4). This enforces the concept that the lower radial turbine in dual agitator systems is mainly responsible for turbulence and gas dispersion, while the upper axial impeller provides mostly circulation.2 The presence of the bubbles determines a change in the turbulent features of the liquid that can be described by means of the ratio of the liquid rms velocity components in aerated and single-phase conditions. As depicted in Figure 6 for QG ) 0.05 vvm, wide zones are characterized by values of this ratio lower than unity, thus indicating turbulence dampening by aeration, which agrees with the results of Aubin et al.10 though obtained for a different geometry; instead, turbulence is enhanced especially in the upper vessel part due to the change in the PBT circulation loop induced by the bubbles. A small increase in the rms velocity fluctuations is also observed close


Figure 6. Ratio of the rms velocity fluctuations for air-sparging to singlephase conditions in water; QG ) 0.05 vvm. (a) Contours of the axial component; (b) contours of the radial component. 6

to the PBT blade tip, as already found by Khopkar et al. These turbulence modifications seem to be mostly due to changes in the liquid flow pattern induced by bubble motion rather than to local small-scale interaction between the bubbles and the turbulent eddies. For this reason, the relationship between the ratio of bubble size to turbulent length scale and the liquid turbulence intensity25 is not investigated in the present study. The behavior of the water-glycerine solution under aeration is similar to that determined with water, as can be observed in Figure 7. In particular, the same qualitative modification of the circulation loops is observed at the same gas flow rates and the presence of two corotating loops is confirmed below the turbine for QG ) 0.25 vvm. Differently from the water-air system, at a higher gas flow rate a new circulation loop appears in the middle of the vessel region (r/T ) -0.45, z/T ) 0.85) that results from the interaction of the discharge streams of the two impellers. The effect of QG on the gas flow fields is less marked than that exhibited by the liquid phase. The two vector plots (Figure 8) are very similar, and in both cases the extent of the stagnant zone is more limited than found for the air bubbles in water. Indeed, a circulation loop with the center placed at r/T ) -0.32 and z/T ) 0.52 can be clearly noticed, while with the air-water system that zone is practically stagnant. The effect of the bubbles on the turbulent velocities of the water-glycerine solution can be appreciated in Figure 9, where the same parameters are given as in Figure 6. Values lower than unity, indicating turbulence reduction, characterize most zones of the upper vessel region, while those mixed by the Scaba turbine are mostly featured by turbulence enhancement, probably due to flow field variations. Indeed, the presence of the dispersed phase does not change the flow pattern of the liquid significantly in the case of water (Figures 2a and 3), while with the glycerine solution, probably due to the higher gas holdup, the flow pattern of the liquid phase changes significantly (Figures 2b and 7): two corotating loops appear underneath the Scaba impeller also

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Figure 7. Dimensionless flow field of the water-glycerine solution under sparged conditions. N ) 160 rpm. (a) QG ) 0.02 vvm; (b) QG ) 0.25 vvm.

Figure 8. Dimensionless flow field of gas in the water-glycerine solution under sparged conditions. N ) 160 rpm. (a) QG ) 0.02 vvm; (b) QG ) 0.25 vvm.

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Figure 9. Ratio of the rms velocity fluctuations for air-sparged to singlephase conditions in the water-glycerine solution; QG ) 0.05 vvm. (a) Contours of the axial component; (b) contours of the radial component.

for the case of QG ) 0.05 vvm, while a modification of the flow field occurs above the impeller, similarly to the case of QG ) 0.25 vvm as can be noticed by comparing Figures 2b and 8b. This difference, which is negligible for the water system and significant for the glycerine case, seems to be the reason for the notable differences in turbulence enhancement in the two air-sparged cases when comparing Figures 6 and 9. 3.3. Hydrodynamics of the Surface-Aerated Configuration. In general terms, the fluid dynamic behavior of the stirred vessel working under surface-aerated conditions is similar to that of the air-sparged system; the more important differences are addressed in the following. The velocity fields of the liquid measured at N ) 385 and 435 rpm are shown in Figure 10a and 10b, respectively. Underneath the Scaba impeller and at the lower impeller speed, the flow pattern coincides with the typical shape produced by any radial impeller, with the center of the circulation loop positioned at about r/T ) -0.35 and z/T ) 0.18, while at the higher impeller speed, which corresponds to an increased gas holdup, two circulation loops appear. Therefore, the same behavior already observed in the case of the air-sparged system (Figure 3) is confirmed for this operating mode, too. Minor differences induced by a gas rate increase can be noticed in the discharge stream from the PBT: when the impeller speed is increased, the center of the circulation loop moves toward the impeller and the magnitude of the liquid velocity vectors decreases. The main liquid flow field differences with respect to the air-sparged configuration are in the central region of the vessel: in the surface-aerated case the upper loop of the Scaba reaches the elevation z ) 0.8T, while in the air-sparged system it merges with that of the upper turbine. A comparison of the flow fields obtained in the sparged and surface-aerated systems at three elevations is shown in Figures 11 and 12 for the axial and radial velocity components of the liquid phase, respectively. A line showing the values for the ungassed system is also plotted for reference. As is apparent,

Figure 10. Dimensionless flow field of water under surface-aeration conditions. (a) N ) 385 rpm; (b) N ) 435 rpm.

in most locations significant differences with respect to the single-phase flow are present, while the trend of the axial and radial components for low aeration conditions (N ) 305 rpm and QG ) 0.02 vvm for the sparged system and N ) 385 rpm for the surface-aerated system) and intermediate aeration conditions (N ) 305 rpm and QG ) 0.25 vvm for the sparged system and N ) 435 rpm for the surface-aerated system) are remarkably similar below the Scaba turbine. However, this similarity is less evident in the other two upper sections. The gas flow field shown in Figure 13 exhibits some differences with respect to the liquid phase. As can be noticed, a larger zone at midvessel height is characterized by low velocities and a different size of the loop discharged from the PBT is found. Moreover, at N ) 435 rpm the gas flow field underneath the Scaba impeller is featured by a single loop instead of the two loops found with the liquid phase at the same operating conditions. This behavior agrees with that of the airsparged system for QG ) 0.25 vvm, as can be observed by comparing Figures 10b and 13b with Figures 3b and 4b. Scrutiny of the vector plots shown in Figures 13 and 4 shows that also the bubble loops of the Scaba and the PBT interact less vigorously than in the sparged system, probably due to the different distributions of the gas holdup. The dimensionless radial and the axial rms velocity fluctuations at the two impeller speeds are shown in Figures 14 and 15. The effect of the gas phase on the rms velocity fluctuations is smaller than that determined in the air-sparged system. When the impeller speed is increased, which increases the fraction of the gas ingested into the liquid, the water velocity fluctuations decrease in the whole measurement plane except in the zones close to the Scaba impeller; the increase in the dimensionless fluctuating velocities in these last regions is probably associated


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Figure 11. Dimensionless axial liquid velocity components for the water system at different elevations. Open symbols: air sparged, N ) 305 rpm (squares, QG ) 0.02 vvm; triangles, QG ) 0.25 vvm). Solid symbols: surface aerated (circles, N ) 385 rpm; diamonds, N ) 435 rpm). Lines: ungassed vessel (H ) 2T, N ) 305 rpm).

Figure 12. Dimensionless radial liquid velocity components for the water system at different elevations. Open symbols: air sparged, N ) 305 rpm (squares, QG ) 0.02 vvm; triangles, QG ) 0.25 vvm). Solid symbols: surface aerated (circles, N ) 385 rpm; diamonds, N ) 435 rpm). Lines: ungassed vessel (H ) 2T, N ) 305 rpm).

with the two corotating loops below the impeller and with the change in flow pattern shape above it. Figure 16 shows the ratio of the vertical rms velocity fluctuations to tip speed detected 1 cm below the ungassed liquid surface at three impeller speeds. The shape and the main curve feature for N ) 385 rpm are similar to those given by Bhattacharya et al.23 at the onset of gas entrainment, thus supporting the mechanism proposed by these authors, while at higher rotational speeds this ratio is smaller and flatter over the whole radius. The effect of the liquid viscosity in the surface-aerated system has been investigated at the impeller speed of 305 rpm, which is lower than that used with water: indeed, at higher impeller speeds the gas-liquid system becomes opaque, so that the laser light sheet is completely blocked. The flow fields of the liquid phase and of the gas phase at N ) 305 rpm, which are shown in Figure 17, are almost identical and exhibit features similar to the single-phase case (Figure 2b). As compared with those

of the air-water system, a small zone appears between the two impellers that is almost stagnant. 3.4. Bubble Size Distribution. For the air-sparged system, the cumulative distributions of the bubble equivalent diameter, deq, are shown in Figure 18 in the plane from z/T ) 1.0 to the vessel top for two gas flow rates measured. The minimum detectable size, which is equal to the pixel size, is deq ) 0.35 mm. As can be observed, about 50% of the bubbles are characterized by an equivalent diameter lower than 0.5 mm and 90% of them are smaller than 1.3 mm. A slight gas rate increase gives a very small increase in bubble size that is likely due to coalescence. For the air-water/glycerine system, the BSD analysis was carried out at three different gas flow rates; the results at the same plane portion considered for the air-water system are shown in Figure 19. The effect of coalescence is clear: at the lowest gas rate about 90% of the bubbles are characterized by deq lower than 2.8 mm, while this parameter is equal to about 3.5 mm at the highest flow rate.

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Figure 15. Dimensionless rms velocity fluctuations in water in surfaceaerated conditions; N ) 435 rpm. (a) Contours of axial component; (b) contours of radial component. Figure 13. Dimensionless flow field of the gas in water under surfaceaeration conditions. (a) N ) 385 rpm; (b) N ) 435 rpm.

Figure 16. Ratio of the axial rms fluctuations and impeller tip speed at z/T ) 1.4 (1.5 cm below the liquid surface under ungassed conditions) in water for the surface-aerated configuration. Circles, N ) 385 rpm; triangles, N ) 400 rpm; diamonds, N ) 435 rpm.

decreases to 2.3 mm when the impeller speed rises to 435 rpm. It is also worth noticing that in the surface-aerated system the bubble size is greater than that measured in the air-sparged case, though at a higher impeller speed. To better compare the data relevant to different systems and conditions, a simplified analysis based on the Weber number is adopted.2 The Weber number is Figure 14. Dimensionless rms velocity fluctuations in water in surfaceaerated conditions; N ) 385 rpm. (a) Contours of axial component; (b) contours of radial component.

The results obtained for the surface-aerated configuration and the air-water system in the vertical plane between z/T ) 0.8 and the vessel top are shown in Figure 20. The effect of bubble breakup due to the increment of impeller speed seems to be slightly more important than that of coalescence due to the increase of the gas holdup: in fact, about 90% of the bubbles have a diameter equal to 2.6 mm at N ) 385 rpm, while db

We )

τdeq σ

(1)

where τ is defined as τ ) 2F(εdeq)2/3

(2)

F is the liquid density and σ is the surface tension; ε is the average energy dissipation per mass of fluid:


ε)

P FVtank

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(3)

The power consumption, P, has been evaluated as the sum of the power supplied by the two individual impellers; in turn, the literature values for ungassed conditions were used because of the high contribution to the overall power demand of the 6SRGT (80%) relative to the PBT (20%) and the very limited power drop of the former on gassing (so that the error in the We number was estimated to be less than 10%). The bubble cumulative number distributions have been replotted against the Weber number in Figure 21. As can be observed, for the airsparged system, all the curves recorded at the two lower gas rates overlap, while the curve representing the highest gas flow Figure 19. Cumulative distribution of bubble equivalent diameter for the air-water/glycerine system at three different gas flow rates. Air-sparged conditions, N ) 160 rpm, from z/T ) 1.0 to vessel top.

Figure 20. Cumulative distribution of bubble equivalent diameter for the air-water system. Surface-aeration conditions, from z/T ) 0.8 to vessel top.

Figure 17. Dimensionless velocity flow fields in surface-aerated conditions; N ) 305 rpm. (a) Water-glycerine solution; (b) gas phase.

Figure 21. Cumulative distribution of bubble equivalent diameter vs Weber number. Vessel upper region.

Figure 18. Cumulative distribution of bubble equivalent diameter for the water-air system at two different gas flow rates. Air-sparged conditions, N ) 305 rpm, from z/T ) 1.0 to vessel top.

rate is slightly shifted to the right probably due to the effect of gas void fraction increase.26 For the surface-aerated system, the critical Weber number is larger than that of the air-sparged system: this implies bubbles of larger diameter, which aspect has already been observed in Figure 20. This effect is less important in the lower vessel region (z/T ) 0.0-1.0), where all the cumulative size distribution curves are close to each other, as shown in Figure 22. Comparison of the results shown in Figures 21 and 22 would allow one to conclude that in a multiple-impeller vessel the bubble size distribution depends not only on the power input but also on the bubble history: if the bubbles flow first through a high-shear-rate impeller (as is the case with the air-sparged system), the bubble size distribution

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Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010 T ) vessel diameter, m U ) mean axial velocity, m/s u′ ) rms axial velocity fluctuation, m/s V ) mean radial velocity, m/s Vtip ) impeller tip speed, m/s Vtank ) vessel volume, m3 We ) τdeq/σ, Weber number z ) axial coordinate, m Greek Symbols

Figure 22. Cumulative distribution of bubble equivalent diameter vs Weber number. Vessel lower region.

is characterized by a size lower than that obtained when the bubbles flow first through a low-shear-rate impeller (as is the case with the surface-aerated system). 4. Conclusions The turbulent fluid dynamic features of a dual impeller stirred vessel for gas dispersion has been investigated, both in an airsparged setup and in a surface-aerated setup. The PIV measurements have provided information on the detailed flow field of the Scaba 6SRGT impeller, for which scant experimental data are available in spite of its successful industrial application. The analysis of the two-phase flow patterns has demonstrated that the air bubbles strongly affect the liquid velocity field; therefore, the simultaneous detection of the liquid and gas velocity fields cannot be renounced for a full description of the gas-liquid system behavior. The effect of liquid viscosity was also investigated: even the slight increase from 0.9 to 5 mPa · s was found to significantly affect the liquid flow pattern, since a secondary loop appears in the middle of the vessel and smaller bubbles are generated. The effect of the bubbles on the turbulent characteristics was assessed for both liquid systems and for the two stirred vessel modes. The BSD of the gas-liquid systems was also measured, and a simplified analysis has shown their dependence on the Weber number and the vessel configuration. Acknowledgment This work was financially supported by the Italian Ministry of University and Research (MIUR) and the University of Bologna under PRIN 2005 and 2006 programs and the Italian Ministry of Agriculture and Forestry (MIPAAF) under the “BioHydro” project. The authors are grateful to Dr. Tamas Kovacs (Scaba Agitators) for supplying the 6SRGT turbine. A portion of these results was presented in an abridged form at the 14th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Lisbon, Portugal, July 2008). Nomenclature C ) impeller clearance, m D ) impeller diameter, m deq ) equivalent bubble diameter, m H ) ungassed liquid height, m N ) rotational speed, 1/s P ) power draw, kg/s m QG ) volumetric gas flow rate, 1/s r ) radial coordinate, m Re ) FND2/µ, rotational Reynolds number

ε ) mean energy dissipation rate per mass of liquid, m2/s3 F ) liquid density, kg/m3 µ ) liquid viscosity, Pa · s σ ) surface tension, kg/s2 τ ) turbulent stress, kg/m s2

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ReceiVed for reView April 20, 2009 ReVised manuscript receiVed January 15, 2010 Accepted January 20, 2010 IE9006276

Two-Phase Flow and Bubble Size Distribution in ... - ACS Publications

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