Experimental and Numerical Investigation on Gas Holdup and

Ind. Eng. Chem. Res. 2006, 45, 1141-1151

1141

Experimental and Numerical Investigation on Gas Holdup and Flooding in an Aerated Stirred Tank with Rushton Impeller Weijing Wang,†,‡ Zai-Sha Mao,*,† and Chao Yang† Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100080, China, and Department of Chemistry and Chemical Engineering, Dalian UniVersity, Dalian, Liaoning 116622, China

The spatial distribution of gas holdup in a stirred tank with a Rushton impeller and i.d. of 380 mm was measured by the fiber optic technique to show the different gas-liquid flow patterns including flooding. The data on loading/flooding transition are found consistent with the general correlation. The experiments were also simulated numerically by the Eulerian-Eulerian approach with the control volume formulation with the k--Ap two-phase turbulence model, and different flow patterns in the gas-liquid stirred tank were well demonstrated. It is found that the gas holdup in the impeller discharge stream is underpredicted, but in the broad bulk flow region the results of simulation are in good agreement with the experimental data. 1. Introduction Stirred tank reactors are widely used in chemical and processing industries. In a stirred tank, the swirling flow driven by the impeller interacts with the stationary wall baffles, and complex three-dimensional unsteady flow is resulted. The flow becomes more complex if aerating gas is introduced. Tremendous efforts, including experiment and numerical simulation, have been devoted to understanding the flow in a gas-liquid stirred tank, and great progress has been achieved to date. There are different flow regimes in a gas-liquid stirred tank, which are closely related to the rate of aeration and the pumping power of the stirring impeller. A stirred tank reactor is expected to operate in the completely dispersed regime or at least the loaded regime (the bubbles are dispersed by the impeller into the upper bulk region). Flooding of the tank (the gas phase is not well dispersed and rises up in a limited region around the stirrer shaft) is the least desired operating condition. The flow pattern influences significantly the gas-liquid mass transfer1 and the micromixing efficiency.2 Therefore, it is essential for chemical engineers to know under what conditions the tank is flooded and how it can be avoided. Many investigations have been conducted mainly by experimental approaches. Nienow et al. (1977) conducted a series of experiments on gas-liquid flow in tanks stirred by Rushton disk turbines.3 They investigated the relationship between gas-liquid flow pattern and input power and found there are five different flow patterns in gas-liquid stirred tanks as shown in Figure 1, among them pattern a was the flooding pattern. Bruijin et al. showed the parallelism between the pattern of gas cavity behind the impeller blades of Rushton turbine and the rate of sparging gas.4 As the gas flow rate is increased beyond a critical level, large cavities are formed behind the blades to result in flooding of the tank. Paglianti et al.5 studied the flooding/loading transition in a stirred tank and pointed out that the transition can be correlated in terms of a dimensionless function of pumping capacity versus aeration rate. However, the existing study on flooding remains insufficient. * To whom correspondence should be addressed. Tel: +86-1062554558. Fax: +86-10-62561822. E-mail: [email protected]. † Chinese Academy of Sciences. ‡ Dalian University.

Figure 1. Bulk flow patterns with increasing stirring speed.3

Several studies reported the spatial distribution of gas holdup in the stirred tanks. Lu et al.6 measured the liquid velocity and gas holdup in impeller discharge stream using hot film anemometry and showed that the values of liquid velocity components and gas holdup decrease in the radial direction. Greaves and Kobbacy7 also measured the gas holdup and diameter of bubbles at different locations in the gas-liquid stirred tank and calculated the interfacial area at the same position. Bombac et al.8 presented systematic data of the local gas holdup distribution in an aerated stirred tank (T ) 0.45 m), and a detailed analysis of the gas cavity structures near the impeller blade tips indicated that the transition from loading to flooding status corresponded well with the transition from the loading condition to the state of ragged cavities. Numerical simulation is also an efficient tool for studying the gas-liquid flow in stirred tanks. Harvey and Greaves9 attempted the two-dimensional numerical simulation of singlephase flow in a stirred tank by treating the impeller region as a “black box”. This approach was later adopted by most investigators in simulating the single-phase flow in stirred tanks.10-12 Many new approaches not relying on experimental data and empirical formulas were attempted. Ranade and van den Akker13 and Ranade and Dommeti14 proposed a computational snapshot of the flow field at particular instant. Brucato et al.15 developed the inner-outer iterative procedure with combination of the “black box” approach. Wang and Mao16 improved the inner-outer iterative procedure and kept the pseudoperiodical turbulence without averaging the flow parameters exchanged between the inner and outer regions in the azimuthal direction. When this was used to simulate singlephase flow in a stirred tank, good results were obtained.16,17

10.1021/ie0503085 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/07/2006

1142

Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006

Figure 2. Skematic of stirred tank and Rushton impeller.

There is significant progress in the gas-liquid flow simulation.13,18-24 Lane et al.18 improved the formulations of ineterphase forces and bubble size. Khopkar et al.19 provided CARPT/CT data on gas holdup measurements and confirmed the applicability of numerical simulation to predict the main features of gas-liquid flow in stirred tanks. Deen et al. investigated gas-liquid flow in a stirred tank with Rushton impeller experimentally, simulated the same tank using the slide grid technique, and found the results of numerical simulation in satisfactory agreement with the experimental data.22,23 Wang and Mao24 simulated the gas-liquid flow in stirred tank using the improved inner-outer iterative procedure,16 and the simulation agreed well with the literature data. To date the practical application of numerical simulation, especially to the scale-up of gas-liquid reactors, is very limited. The flow structure is different for a gas-liquid stirred tank operated at different conditions. The transition from one pattern to another case is complicated and this phenomena is observed by Nienow et al.,3 but the existing investigations on gas-liquid flow in stirred tanks, either experimental or numerical, are not comprehensive: there are no systematic experimental data on stirred tanks. Due to lack of experimental data, the simulation by the “black box” approach fails to demonstrate the flow patterns in gas-liquid stirred tanks and their transitions. It seems that more experimental studies are desired to accumulate the basic data on hydrodynamics and transport behavior in gasliquid stirred tanks, so that the ability of numerical procedure for simulating all the flow patterns of gas-liquid stirred tank may be demonstrated. To this end, a series of experiments on gas-liquid stirred tank with a Rushton turbine were carried out to get the measurements of gas holdup distribution throughout the tank under quite different operation conditions. The experimental study was also complimented with numerical simulation using the improved inner-outer iterative procedure to check the applicability of the numerical procedure adopted in this work. 2. Techniques and Numerical Method 2.1. Experimental Apparatus. The diameter of the stirred tank, T, is 380 mm, having four baffles on the wall with a width of T/10. The impeller is a standard Rushton turbine, and the dimensions are shown in Figure 2. The experimental media are ambient air and water. The gas sparger ring is made of a copper tube with 5 mm i.d., the sparger ring diameter is ds ) 76 mm, and it has 20 φ 1 mm holes. The spacing between the gas sparger and the tank bottom is 50 mm. The experimental apparatus is shown in Figure 3. The compressed air enters the stirred tank through the gas sparger and then is dispersed by the Rushton turbine. The gas flow rate is measured by a rotameter. The turbine is driven by a motor with speed control.

Figure 3. Scheme for the experimental apparatus. Key: 1, speed controllable motor; 2, torque transducer; 3, fiber optic probe; 4, Rushton turbine; 5, gas sparger; 6, stirred tank; 7, optic instrument; 8, A/D converter; 9, PC computer; 10, rotameter.

Figure 4. Schematic for the fiber optic probe. Key: 1, light source; 2, fiber coupler; 3, light detector; 4, amplifier; 5, A/D converter; 6, computer; 7, probe.

The local gas holdup is measured by a fiber optic probe, and the signals are sampled by the A/D converter at the frequency of 23 kHz. The collecting period is 90 s for the gas holdup measurement with about 1000 bubbles sampled at each measurement location. The signals are transformed into a digital stream by an A/D converter and then processed and stored by a PC computer. 2.2. Measurement Techniques. Available methods for the measurement of local gas holdup include the photoelectric capillary method,7 hot-film anemometry,6 electric capacity method,3 electric conductance method,8,25 and more expensive CARPT/CT measurements.19 Because a fiber optic probe has the advantage of quick response and low disturbance to flow field and works well for either electroconductive or nonconducting system,26 it was chosen for this experiment. The structure of the fiber optic probe is shown in Figure 4. It is consisted of light source, fiber coupler, light detector, amplifier, A/D converter, computer, and probe. The probe is made of optic fiber whose diameter is 62.5 µm with a conic end, and therefore, the light may be reflected back at the probe end. The intensity of reflected light is relied on the fluid medium in contact with the conic end. The light detector converted the

Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1143

Figure 5. Typical signal from the optical fiber probe.

Figure 7. Positions for gas holdup measurement.

is used for simulating the two-phase turbulence flow in the stirred tank as previously.24 The partial differential equations for velocity components of phase k were

Fk

(

+ Figure 6. Calibration of the fiber optic probe. Key: 1, flowmeter; 2, bubble column; 3, fiber optic probe; 4, A/D transducer; 5, computer; 6, manometer.

intensity signal of reflected light to electric signal, which is then amplified by an amplifier to a voltage signal suitable for A/D conversion. The typical signal is shown in Figure 5. The local gas holdup is defined as the fraction of the time when the probe tip is inside bubbles in a sufficiently long measurement period.8 When the probe tip penetrates into a bubble, the signal jumps from low voltage level Vl to highlevel Vh, and vice versa when the bubble detaches from the probe. A threshold voltage V0 is needed to judge whether the probe is in liquid phase or gas phase. The value of V0, lying between Vl and Vh, can be defined with parameter β:

V0 ) Vl + β(Vh - Vl)

(1)

The value of β is determined to be 0.15 after calibrating the probe against uniform bubbly flow in a vertical pipe. The calibrating setup is sketched in Figure 6. The bubble column gas holdup between two pressure measurement taps can be gotten by U-tube manometer, and the radial profile of gas holdup is also measured by the optical fiber probe. The value of β is updated until the gas holdup measured by the optical fiber probe equals the gas holdup measured by U-tube manometer. All the measurement points are on a vertical plane in the middle between two wall baffles, with the points uniformly arranged in a 10 × 20 grid as shown in Figure 7. The distance between each point is T/20. The gas holdup is measured at every point except in the region swept by the Rushton turbine. 2.3. Brief Account of the Numerical Scheme. In this work, a “two-fluid” model27 together with the k- two equation model

)

∂ ∂ ∂P (R u ) + (Rkukiukj) ) -Rk + FkRkgi + Fki ∂t k ki ∂xj ∂xi 2∂(Rkk) Fk 3 ∂xi

( (

)) ( (

∂uki ∂ukj ∂ Ru + ∂xj k ke ∂xj ∂xi

+

))

∂Rk ∂Rk ∂ µkt u + ukj ∂xj σt ki ∂xj ∂xi

(2)

in which µt is turbulent viscosity and µe is the total effective viscosity. The dominant body forces include gravity, buoyancy, and interphase drag force. In gas-liquid flow, the interphase drag force Fki on an average bubble is

1 F ) FlCDA|ul - ug|(ul - ug) 2

(3)

where A is the projected area of the bubble and CD is the drag coefficient. Ishii’s expression28 for CD, which takes account of bubble-bubble interaction and bubble distortion, can be used here:

4 CD ) r b 3

xg∆Fσ (1 - R ) g

-0.5

(4)

Assuming that bubbles are spherical and have the same ul ug in an infinitesimal unit volume, the total interphase friction/ tank volume reads24

xg∆Fσ (1 - R )

1 -Fli ) Fgi ) Fl 2

g

-0.5

Rg|ul - ug|(uli - ugi) (5)

It is noted that the interphase drag force becomes irrelevant of the bubble size. The centrifugal force Frk ) RkFκ(ω × r) × ω and the Coriolis force Fck ) 2RkFκω × uk arise when a noninertial reference frame is used but do not appear in the inertial reference frame. The influence of other types of phase interaction is neglected.

1144


Figure 8. Computational domains for inner-outer procedure: (a) inner domain; (b) outer domain, shaded region excluded from the computation.

In a stirred tank, the fluctuating liquid velocity is the main source of turbulence, while the presence of dispersed gas bubbles does contribute to the turbulence in two-phase dispersion due to the interphase friction. Moreover, the turbulence model used here24 is an extension of the standard two equation k- model for single phase flow, namely the two-phase k--Ap model29, with Ap indexing the turbulent eddy viscosity for gas phase is related to that of the liquid phase through an algebraic formulation by Hinze-Tchen30 (also cited in refs 29 and 31). Also the contribution to liquid-phase turbulence due to the relative motion of gas phase to liquid is included as did by Ranade and van den Akker.13 The flow in the impeller region is strongly swirling, so a swirl correction is made on the source term of the equation as described in ref 24. The wall functions32 are applied to the near-wall nodes. This two-phase k--Ap model requires the local average bubble diameter db in the stirred tank, which can be approximated by the Sauter mean diameter d32 without much error. Some investigators estimated the ratio of d32 over dmax for bubbles. Hesketh et al. suggested the ratio of d32/dmax to be 0.62 for the bubbles in horizontal pipeline flow.33 Partharathy and Ahmed determined experimentally the ratio of d32/dmax for bubbles at different positions in the gas-liquid stirred tank and found it to be 0.785.34 Various d32/dmax values have been reported for droplets in liquid-liquid dispersions. Brown and Pitt found a linear relationship between d32 and dmax in the kerosene-water system in stirred tanks, and the d32/dmax ratio was determined to be 0.7.35 Calabrese et al. report a d32/dmax value of 0.6 for the dispersion of moderate viscosity oils in stirred vessels.36 It is to be noted that, despite the diversity of systems, the reported d32/dmax values do not show considerable scatter. An average value is determined to be 0.68 for these above-mentioned cases and is used in this investigation. Thus, dmax can be obtained by the following equation:37

dmax ) 0.725

() σ Fl

3/5

-2/5

Figure 9. Simulated results using different grids at z ) 0.094 m: (s) 36 × 36 × 90; (2) 36 × 36 × 75; (b) 30 × 36 × 60; ([) 0 × 18 × 45 (Q ) 3.43 × 10-4 m3/s, ω ) 62.8 rad/s, T ) 288 mm, D ) 96 mm).

primary variables. The FORTRAN computer code was developed by the present authors on the basis of the long-time accumulation of numerical programs in our laboratory, and all the computation was done on a personal computer. It was essentially validated previously for single phase and gas-liquid flows.16,17,24 Four grids with various fineness, 30× 18 × 45 (radial × axial × azimuthal), 30 × 36 × 60, 36 × 36 × 75, and 36 × 36 × 90 were tested24 in the numerical simulation of the case with Q ) 3.43 × 10-4 m3/s, ω ) 62.8 rad/s, and T ) 288 mm as operated by Lu et al.6 The simulated radial profiles of gas holdup and velocity component are shown in Figure 9. It is noted that the difference between the results on grid 36 × 36 × 90 and grid 36 × 36 × 75 is very small, indicating that on the 36 × 36 × 90 grid is sufficiently fine so that the numerical error due to discretization may be neglected. Therefore, this grid is chosen for all subsequent simulation work. 3. Results and Discussion

(6)

In this work the three-dimensional gas-liquid flow in a stirred tank is simulated. Because the stirred tank has four baffles and six impeller blades, half of the stirred tank is selected as the computational domain. In this approach, the whole axial section of the tank is subdivided into two partly overlapped zones: an inner domain enclosed by surface Σ2 and an outer one that only excludes the surface Σ1 enclosed impeller region in the tank (Figure 8). The numerical procedure has been elaborated previously in ref 24. To solve above equations, the power-law scheme recommend by Patankar38 is adopted to discretize the momentum equations, and the pressure field is solved by the SIMPLE algorithm. Discretization of the partial differential equations is realized by integration over each cell with a staggered arrangement of

3.1. Gas Holdup Contour Maps. Figure 10 is the gas holdup contour maps from the present experimental measurements at the same gas flow rate but different stirring speed. The gas is dispersed by the turbine and gradually spread into the whole upper bulk region as the stirring speed is increased. Meanwhile, the recirculation of liquid is also intensified and some gas is entrained into the lower bulk region. The faster the stirring speed, the more gas is entrained to the lower bulk region. In general, the gas holdup in the impeller stream is greater than that in the bulk regions, and it decreases gradually with the radial position. When the turbine fails to disperse the gas (in Figure 10a), the gas holdup is the highest around the impeller shaft in the upper bulk flow region. As flooding occurs when gas flow rate is raised above the dispersion capacity of the impeller, the gas holdup presumes a spatial distribution of the similar feature. On the other hand, the nonflooding normal


Figure 10. Gas holdup contour maps (Q ) 2.222 × 10-4 m3‚s-1 and ω ) 8.17, 14.0, 24.2, and 30.8 rad‚s-1, respectively).

Figure 11. Gas holdup contour map (Q ) 7.5 × 10-4 m3‚s-1, ω ) 44.7 rad‚s-1)

operation (Figures 10b-d) is observed to feature with quite lower gas holdup at the shaft than the broad region of the upper bulk region. Figure 11 presents the case with large gas sparging rate and high stirring speed; the topological structure is similar with Figure 10d, but the level of gas holdup is raised significantly. Observation in Figures 10 and 11 suggests that, except for the case of flooding (Figure 10a with low stirring speed), there is always an area of high gas holdup a little distance off the outer edge of impeller blades. The maps are topologically similar to those reported by Bombac et al.8 From these contour maps, it is apparent that Figure 10a is identified as the flooding regime, Figure 10b,c presents the loaded regime, and Figures 10d and 11 are completely dispersed patterns. 3.2. Comparison between Experiment and Simulation. The simulation results under different gas flow rates and stirring speeds for gas holdup and flow field are shown in Figure 12ae, with the experimental conditions corresponding to Figures 10a-d and 9, respectively. The gas holdup distribution simulated is topologically similar to the experimental results, and the transition from the gas being dispersed by the turbine only around the impeller region (Figure 12a), and then the upper bulk region becoming full of bubbles (Figure 12b,c), to finally

the bubbles being entrained into the lower bulk region (Figure 12d,e) is well demonstrated by the simulated contour maps of gas holdup. The local nonuniformity and the trend of decrease in the radial direction of gas holdup are also clearly reflected in Figures 10 and 11. It can be seen from Figure 12 that the liquid flow form an eddy in the upper bulk region of stirred tank driven by the gas at first. Two eddies are formed in liquid flow above and below the impeller stream gradually with the increasing of stirring speed. The eddy formed by the buoyancy of rising gas disappears gradually because of strengthened circulation of liquid flow. Most gas rises up from the bottom to up. At high speed, part of the gas is entrained into the lower bulk region, and a small amount of gas is sucked into impeller. The whole transition process is the same as Nienow’s observation illustrated by Figure 1a-d.3 In experiment, only the flow of gas is visually observable, and it is difficult to observe the flow of liquid. The simulation shows that liquid flow varies in a complicated way. At first, the liquid flow generates only one eddy (Figure 12a), but three eddies appear as the stirring speed increases (Figure 12b). The uppermost eddy is due to the buoyancy of rising gas, which will disappear gradually with the increase of stirring speed. Liquid flow will have two eddies eventually, and this flow pattern is the same as in most investigators’ simulations.13,20,21 In experiment, it is observed that the main gas stream flows up in upper space close to the shaft and little gas reaches the lower space of the tank when flooding occurred, no matter whether it is caused by low stirring intensity (Figure 10a) or high rate of aeration. This is somewhat different from that the Rushton’s result that the flooding is the transition of flow pattern from Figure 1c to Figure 1b39 and that flooding resulted as the transition from Figure 1d to Figure 1c.3 When operation is approaching flooding, the flow in the stirred tank is observed very unstable. 3.3. Transition from Loaded to Flooding Regime. In this investigation, the flows in a stirred tank under the flooding and critical conditions are simulated respectively, and it was found that the computation was difficult to converge: the numerical residues decreased to certain levels and then fluctuated numerically, in accordance to the physical flow instability. Figure 13a,b shows the stabilized but not converged results of simulation, and we can observe that the simulated dispersion of gas is similar to Figure 12b (the main bubble stream rises in parallel to the shaft) and somewhat between Figure 10 parts a and b,

1146


Figure 12. Simulation on gas holdup distribution and flow structure of gas-liquid flow: (a) radial profile of gas holdup (Rg) and (b) radial profile of velocity component (ulr). Legend: left, the gas holdup distribution; middle, gas flow field; right, liquid flow field Key: (a) Q ) 2.222 × 10-4 m3‚s-1, ω ) 8.17 rad‚s-1; (b) Q ) 2.222 × 10-4 m3‚s-1, ω ) 14.0 rad‚s-1; (c) Q ) 2.222 × 10-4 m3‚s-1, ω ) 24.2 rad‚s-1; (d) Q ) 2.222 × 10-4 m3‚s-1, ω ) 30.8 rad‚s-1; (e) Q ) 75.0 × 10-4 m3‚s-1, ω ) 44.7 rad‚s-1.

but the value of gas holdup in the lower tank has been decreased largely. The flow pattern of liquid phase is also similar to Figure 12b, and the impeller stream is more inclined upward as the gas flow increases. Also in experiment, transition to flooding occurs as a sudden deterioration of liquid pumping capacity and gas holdup uniformity. Some gas can circulate to the lower space of stirred tank before flooding happens, while no gas appears in the lower bulk region when the stirred tank is flooded. In our opinion, the striking feature of flooding is the channeling of gas stream around the impeller shaft rather than the transition from a better distribution to nonuniform one or the disappearance of gas bubbles in the lower bulk region. Careful reexamination of the measured holdup contour maps (Figures 10 and 11) and the simulation of gas-liquid flow (Figures 12 and 13) reveals that, along with the increase of stirring speed, a gas velocity vortex is gradually formed and finally becomes very obviously located at the outer-upper corner, indicating that the gas bubbles are discharged along with liquid

stream away from the impeller blades. Corresponding to this, a region of high gas holdup appears beyond the outer edge of turbine blades. When flooding is going to occur or has occurred, the gas velocity vortex center is shifted to above the blade (Figure 13). The correspondence between the gas holdup distribution and the gas velocity vector map seems very regular and informative. In an attempt to correlate the critical condition for the transition between loaded and flooding regimes, Paglianti et al.5 proposed to plot the Froude number Fr ) N2D/g against the flow number Flg ) Qg/ND3 at the flooding/loading transition. The present experiment identified two data points on the transition. Point A in Figure 14 is the transition from the flooding (Figure 10a) to the loaded regime (Figure 10b), corresponding ω ) 12.5 rad‚s-1, and point B is the critical condition for the transition from the complete dispersion (Figure10d) to the flooding regime due to the increase of Qg at the constant agitation of ω ) 30.8 rad‚s-1. It is observed that in Figure 14 our data are in very good accordance with the data


Figure 13. Simulation on gas holdup distribution and flow pattern for gas-liquid under the critical and flooding conditions: left, the gas holdup distribution; middle, gas flow field; right, liquid flow field. Key: (a) Q ) 11.11 × 10-4 m3‚s-1, ω ) 30.8 rad‚s-1; (b) Q ) 13.89 × 10-4 m3‚s-1, ω ) 30.8 rad‚s-1.

et al.40 is also plotted as a reference:

Fr )

Figure 14. Comparison of the present data for the flooding/loading transition with the data and correlation of Nienow et al.40 and Paglianti et al.5

from Nienow et al.40 and Paglianti et al.5 Except in the high range of Flg, the correlation of Fr against Flg is very significant, suggesting the similarity of the flooding mechanism in gasliquid stirred tanks. A curve based on the correlation by Nienow

1 T 3.5 Flg 30 D

()

(7)

It seems that a new correlation based on more parameters and more data is desired. 3.4. Gas Holdup in the Impeller Discharge Stream and Bulk Flow. The measured gas holdup profiles are presented and compared with the numerical predictions to check the accuracy and capacity of the present numerical procedure. Impeller Discharge Stream. Figure 15 shows the radial profiles of gas holdup in the impeller stream at increasing impeller speed, revealing that the holdup decreases in the radial direction and assumes rather high level near the impeller swept region. But the simulation underpredicts the gas holdup largely, although in the same trend. The reasons for difference are possibly the following: (1) The model for gas-liquid interaction in the impeller stream and the impeller region needs improvements. (2) The standard k- turbulence model used in this investigation needs to be improved to account for the anisotropic in nature of turbulence in the impeller stream. (3) A re-

1148


Figure 15. Comparison between the simulation and experiment in impeller discharge stream.

cent development of numerical simulation of turbulence twophase flow is the turbulence correction of bubble drag coefficient as implemented in Lane et al.18 This correction has not been incorporated in the present program, and it is believed that the extent of underprediction of gas holdup in the impeller stream would be alleviated with this correction. (4) The tap water used in the experiment is very possible to produce more bubbles than in the demineralized water, and the difference has not been embodied in the mathematical model. Bulk Region. The gas holdup is generally below 0.1 in the bulk regions (Figure 16), and the radial profiles of gas holdup are rather flat. The simulation meets the experimental data well in the bulk flow region because turbulent gas-liquid flow in the bulk flow region is more likely to be isotropic, and the k--Ap model describes such flow reasonably well. Although the present numerical method give reasonable agreement with experiments only in the semiquantitative sense, it is still a useful tool in analysis and design of gasliquid chemical reactors, for example, in selecting operating conditions and tank geometry and avoiding nonuniform gas distribution and flooding. In this simulation, no empirical formula and experimental data are required as impeller region boundaryconditions; hence, the numerical procedure may be

applicable to more general cases than the “black box” approaches. 4. Conclusions Experiment was conducted to measure the spatial distribution of gas holdup in the stirred tank and presented typical patterns of distribution in a wide range of stirring speed and gas holdup level. The data are consistent and in accordance with the literature observations and provided reference data for analysis of performance of gas-liquid stirred tanks and for validation of numerical scheme for simulating gas-liquid flow in stirred tanks. On the basis of these measurements, the flooding/loading transition is addressed. The critical condition is that the main gas stream rises up in parallel to the stirrer shaft. By this criterion, the present transition data are well consistent with the general Fr versus Flg correlation. The gas holdup in the stirred tank are simulated under the experimental operating conditions. The three-dimensional simulation based on two-fluid model and the k--Ap two-phase turbulence model demonstrates the different flow patterns in gas-liquid stirred tanks that have been observed experimentally.The gas holdup distribution simulated is topologically sim-


Figure 16. Measurements of gas holdup in the bulk flow region and the numerical predictions.

ilar to the experimental data under different gas-liquid flow conditions. The simulation can describe well the gasliquid flow pattern transition as the stirring speed or rate of aeration is changed. Gas holdup nonuniformity and decrease with the radial position are also clearly reflected by the simulation. Although the simulation results compare reasonably with the experimental data, further improvement for quantitative application is necessary and demands more sophisticated two-phase turbulence model and more accurate formulation of gas-liquid interaction at large gas holdup.

Acknowledgment The authors acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 20236050) and the National Basic Research Priorities Program (Grant No. 2004CB217604).

Nomenclature b ) length of the blade (m) C ) spacing between the impeller and the bottom of stirred tank (m) CD ) drag coefficient d ) diameter (m) d32 ) Sauter mean diameter (m) dmax ) maxim diameter (m) ds ) diameter of sparger (m) D ) diameter of impeller (m) D0 ) diameter of impeller disk (m) f ) width of baffle (m) Fck ) Coriolis force (N‚m-3) Frk ) centrifugal force (N‚m-3) Flg ) gas flow number ()Q/ND3) Fr ) Froude number ()N2D/g) g ) gravity acceleration (9.81 m‚s-2) H ) height of liquid in stirred tank (m) k ) turbulent kinetic energy (m2‚s-2)

1150


N ) impeller speed (rev‚s-1) P ) pressure (Pa) Q ) gas flow rate (m-3‚s-1) r ) radial coordinate (m) R ) radius of stirred tank (m) RT ) radius of Rushton turbine (m) T ) diameter of stirred tank (m) u ) velocity (m‚s-1) V ) volume (m3) V0 ) threshold voltage (V) Vh ) high voltage of signal (V) Vl ) low voltage of signal (V) w ) width of blade (m) z ) axial coordinate (m) Greek Letters R ) phase fraction β ) parameter ) energy dissipation (m2‚s-3) θ ) azimuthal coordinate (rad) µ ) viscosity (Pa‚s) F ) density (kg‚m-3) σ ) surface tension (N‚m-1) ω ) angular speed (rad‚s-1) Subscripts i, j ) direction i, j k ) phase k eff ) effective r, θ, z ) radial, azimuthal and axial direction b ) bubble e ) eddy t ) turbulence l ) liquid g ) gas tip ) impeller tip Literature Cited (1) Warmoeskerken, M. M. C. G.; Smith, J. M. Flooding of disc turbines in gas-liquid dispersin: A new description of the phenomenon. Chem. Eng. Sci. 1985, 40, 2063. (2) Lin, W. W.; Lee, D. J. Micromixing in aerated stirred tank. Chem. Eng. Sci. 1997, 52, 1837. (3) Nienow, A. W.; Wisdom, D. J.; Middleton, J. C. The effect of scale and geometry on flooding, recirculation, and power in gassed stirred vessels. Presented at the 2nd European Conference on Mixing, Cambridge, England, 1977, F1.1-F1.16. (4) Bruijn, W.; van’t Riet, K.; Smith, J. S. Power consumption with aerated Rushton turbines. Trans. IchemE 1974, 52, 88. (5) Paglianti, A.; Pintus, S.; Giona, M. Time-series analysis approach for the identification of flooding/loading transition in gas/liquid stirred tank reactors. Chem. Eng. Sci. 2000, 55, 5793. (6) Lu, W. M.; Ju, S. J. Local gas holdup, mean liquid velocity and turbulence in an aerated stirred tank using hot-film anemometry. Chem. Eng. J. 1987, 35, 9. (7) Greaves, M.; Kobbacy, K. A. H. Measurement of bubble size distribution in turbulent gas-liquid dispersions. Chem. Eng. Res. Des. 1984, 62, 3. (8) Bombac, A.; Zun, I.; Filipic, B.; Zumer, M. Gas-filled cavity structure and local void fraction distribution in aerated stirred vessel. AIChE J. 1997, 43, 2921. (9) Harvey, P. S.; Greaves, M. Turbulent flow in an agitated vessel, Part II: Numerical solution and model prediction. Trans. IchemE 1982, 60A, 201. (10) Middleton, J. C.; Piece, F.; Lynch, P. M. Computations of flow fields and complex reaction yield in turbulent stirred reactors, and comparison with experimental data. Chem. Eng. Res. Des. 1986, 64, 19.

(11) Hou, S. D.; Zhang, Z.; Wang, Y. C.; Shi, L. T. Numerical simulation of turbulent flow in stirred tank agitated by axial impeller. J. Chem. Ind. Eng. (China) 2000, 51, 70 (in Chinese). (12) Go¨tz, S.; Sperling, R.; Liepe, F.; Jembere, S. Numerical determination of the three-dimensional velocity distribution in the baffled pitched blade impeller stirred vessel. Chem. Eng. Technol. 1997, 20, 596. (13) Ranade, V. V.; van den Akker, H. E. A. A computational snapshot of gas-liquid flow in baffled stirred reactors. Chem. Eng. Sci. 1994, 49, 5175. (14) Ranade, V. V.; Dommeti, S. M. S. Computational snapshot of flow generated by axial impellers in baffled stirred vessels. Trans. IchemE 1996, 74A, 476. (15) Brucato, A.; Ciofalo, M.; Grisafi, F.; Micale, G. Numerical prediction of flow fields in baffled stirred vessels: a comparison of alternative modeling approaches. Chem. Eng. Sci. 1998, 53, 3653. (16) Wang, W. J.; Mao, Z.-S. Numerical simulation of the whole flow field in a stirred tank with a Rushton turbine using the improved innerouter iterative procedure. Chin. J. Process Eng. 2002, 2, 193 (in Chinese). (17) Sun, H. Y.; Wang, W. J.; Mao, Z.-S. Numerical simulation of the whole three-dimensional flow in a stirred tank with anisotropic algebraic stress model. Chin. J. Chem. Eng. 2002, 10, 15. (18) Lane, G. L.; Schwarz, M. P.; Evans, G. M. Numerical modelling of gas-liquid flow in stirred tanks. Chem. Eng. Sci. 2005, 60, 2203. (19) Khopkar, A. R.; Rammohan, A. R.; Ranade, V. V.; Dudukovic, M. P. Gas-liquid flow generated by a Rushton turbine in stirred vessel: CARPT/CT measurements and CFD simulations. Chem. Eng. Sci. 2005, 60, 2215. (20) Morud, K. E.; Hjertager, B. H. LDA measurements and CFD modeling of gas-liquid flow in a stirred vessel. Chem. Eng. Sci. 1996, 51, 233. (21) Gosman, A. D.; Lekakou, C.; Politis, S.; Issa, R. I.; Looney, M. K. Multidimensional modeling of turbulent two-phase flow in stirred vessels. AIChE J. 1992, 38, 1946. (22) Deen, N. G.; Hjertager, B. H. Particle image velocimetry measurements in an aerated stirred tank. Chem. Eng. Comm., 2002, 189, 1208. (23) Deen, N. G.; Solberg, T.; Hjertager, B. H. Flow generated by an aerated Rushton impeller: Two-phase PIV experiments and numerical simulations. Can. J. Chem. Eng. 2003, 80, 638 (24) Wang, W. J.; Mao, Z.-S. Numerical simulation of gas-liquid flow in a stirred tank with a Rushton impeller. Chin. J. Chem. Eng. 2002, 10, 385. (25) Gao, Z. M.; Wang, Y. C.; Shi, L. T.; Fu, J. F. Determination of bubble parameters by dual electric conductivity probe. Chem. React. Eng. Technol. 1992, 8, 105 (in Chinese). (26) Wang, T. F.; Wang, J. F.; Yang, W. G.; Jin, Y. Experimental study on bubble size distribution in three-phase circulating fluidized beds. J. Chem. Ind. Eng. (China) 2001, 52, 197 (in Chinese). (27) Ishii, M. Thermo-fluid Dynamic Theory of Two-phase Flows; Eyrolles: Paris, 1975; p 164. (28) Ishii, M.; Zuber, N. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE J. 1979, 25, 843. (29) Zhou, L. X. Theory and Numerical Modeling of Turbulent Gasparticle Flows and Combustion; Science Press and CRC Press: Beijing and Boca Raton, FL, 1993; p 165. (30) Hinze, J. O. Turbulence; McGraw-Hill: New York, 1959. (31) Fan, L.; Mao, Z.-S.; Wang, Y. D. Numerical simulation of turbulent solid-liquid two-phase flow and orientation of slender particles in a stirred tank. Chem. Eng. Sci. 2005, 60, 7045-7056. (32) Gosman, A. D.; Ideriah, F. J. K. Teach T: A general computer program for two-dimensional, turbulent, recirculating flows; The Lecture in Imperial College: Imperial College, London, 1976. (33) Hesketh, R. P.; Fraser Russell, T. W.; Etchells, A. W. Bubble size in horizontal pipelines. AIChE J. 1987, 33, 663. (34) Parthasarathy, R.; Ahmed, N. Sauter mean and maximum bubble diameters in aerated stirred vessels. Chem. Eng. Res. Des. 1994, 72A, 565. (35) Brown, D. E.; Pitt, K. Drop size distribution of stirred noncoalescing liquid-liquid system. Chem. Eng. Sci. 1972, 27, 577. (36) Calabrese, R. V.; Chang, T. P. K.; Dang, P. T. Drop breakup in turbulent stirred-tank contactors. Part I: Effect of dispersed-phase viscosity. AIChE J. 1986, 32, 657.

Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1151 (37) Hinze, J. O. Fundamentals of the hydrodynamic mechanism of splitting in dispersion process. AIChE J. 1959, 1, 289. (38) Patankar, S. V. Numerical Heat Transfer and Fluid Flow; McGrawHill: New York, 1980; p 79. (39) Rushton, J. H.; Biminet, J. J. Hold-up and flooding in air liquid mixing. Can. J. Chem. Eng. 1968, 46, 16. (40) Nienow, A. W.; Warmoeskerken, M. M. C. G.; Smith, J. M.; Konno, M. On the flooding/loading transition and the complete dispersal condition

in aerated vessels agitated by a Rushton-turbine. In Proceedings of the 5th European Conference on Mixing, Germany, BHRA Fluid Eng., Cranfield, June 1985; p 143.

ReceiVed for reView March 4, 2005 ReVised manuscript receiVed November 24, 2005 Accepted December 1, 2005 IE0503085

Experimental and Numerical Investigation on Gas Holdup and

Recommend Documents