Hydrodynamic Characteristics of Dual-Impeller ... - ACS Publications

Aug 17, 2009 - The mixing modes (axial and radial) are proposed in the light of ... the combination taking pitched blade turbine downflow (PBTD) as th...
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Ind. Eng. Chem. Res. 2010, 49, 1001–1009


Hydrodynamic Characteristics of Dual-Impeller Configurations in a Multiple-Phase Stirred Tank Tao Wang,† Gengzhi Yu,† Yumei Yong,† Chao Yang,*,†,‡ and Zai-Sha Mao† Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China, and Jiangsu Marine Resources DeVelopment Research Institute, Lianyungang 222005, China

Experiments are carried out in a baffled flat-bottom stirred tank to test five dual-impeller configurations, including a new type of impeller, alternate blade disk turbine (ABDT). Power consumptions in gas-liquid, liquid-solid, and gas-liquid-solid systems are determined by the shaft-torque method. It is found that the configuration with an axial impeller consumes less energy than that with a radial one in all multiple-phase systems. The correlations between power input and gas flow rate or solid concentration are also discussed. Power number reaches a limit with the increase of Reynolds number in liquid-solid systems. Aeration is proved to be harmful to solid suspension. Mixing time and solid particle concentration are measured by the electric conductivity method and Powder Voidmeter PC-6, respectively. The mixing modes (axial and radial) are proposed in the light of impeller types and flow patterns. The experimental results show that the mixing time of the double radial impeller configuration is the shortest, while the double axial impeller combination performs worst. Judging from the axial solid particle concentration distribution and overall suspension uniformity, the combination taking pitched blade turbine downflow (PBTD) as the lower impeller achieves the best solid suspension. 1. Introduction The dual-impeller configuration is often used in stirred tanks. Compared with single impellers, dual combination has more advantages, such as efficient gas distribution, longer gas phase residence time, increased gas hold-up, superior liquid flow (plug flow) characteristics, and lower power consumption per impeller.1 Especially for uniform suspension of solids, the dualimpeller system is more energy-effective than the singleimpeller. Furthermore, multiple-impeller systems need lower rotational speed,2 which is very important in some systems sensitive to shear (e.g., in biometallurgical reactors). Accordingly dual-impeller combinations are widely employed in industrial reactors. As each impeller produces its own flow pattern, the coupling becomes more intricate and the regularities in singleimpeller systems are no longer valid for dual-impeller combinations. Consequently the research on dual-impeller agitators is with great significance. The dual-impeller should be considered when the height-to-diameter ratio (H/D) exceeds 1.0. Nienow et al.3,4 gave a summary of experimental studies on the gas-liquid-solid systems with a single impeller in the turbulent regime. Impeller type, solid distribution, mixing time, mass transfer characteristics, and just-off-bottom suspension were discussed in detail. Besides single-impeller, Kasat and Pandit5 reviewed the mixing characteristics of multiple impeller systems in solid-liquid and gas-liquid-solid tanks. Special consideration was given to the complete off-bottom suspension state (termed as Njs) and solid concentration values (local and overall). The measurement methods, effect of gas sparger, impeller and off-bottom clearance, and empirical expression for Njs were discussed thoroughly. As conclusion, the authors emphasized the necessity of systematic study of multiple impellers in threephase systems and comparison with CFD results. An uncon* To whom correspondence should be addressed. Tel.: +86-1062554558. Fax: +86-10-62561822. E-mail address: chaoyang@ home.ipe.ac.cn. † Chinese Academy of Sciences. ‡ Jiangsu Marine Resources Development Research Institute.

ventional gas-liquid-solid stirred tank called a vortex-ingesting reactor was reported by Conway et al.,6 which was equipped with two impellers and a concentric draft-tube. The vortexingesting reactor is an advanced gas reactor and also suitable for solid suspension compared with other gas-self-inducing agitators. Li et al.7 discussed the gas dispersion in a gas-liquid surface aerator tank with H/D ) 1.4. Three dual-impeller configurations were studied with the combination of surface aeration and sparger aeration at different gas superficial velocities. The results show that the combination is beneficial to gas dispersion and gas-liquid mass transfer. Power consumption is always a key issue in studying and designing stirred tanks. The early researches were mostly carried out with traditional impellers, such as standard Rushton turbine, and down-(up-)pumping 45°-pitched blade turbines. Armenante and Chang8 studied the power consumption in vessels agitated by one-, two-, or three-Rushton disk turbines under turbulent conditions. It is found that the dissipated overall power was proportional to the off-bottom clearance of the lowest impeller and the impeller spacing. Dohi et al.9 measured the power consumption in a boiling stirred tank with three pitched blade downflow turbines. Kuzmanic et al.10 reported the power consumption, mixing time, and critical impeller speed of a double down-pumping pitched blade turbine combination in a liquid-solid system. With more energy-effective impellers developed like Scaba 6SRGT, A-310, A-315, A-340, “elephant ear” agitator,11 and Maxblend and Fullzone impellers12 in recent years, the investigation was focused on inventing more new types with better performances. The hydrodynamic performances of a dual-shaft mixer composing of a Paravisc-type impeller and a Deflo disperser in a viscous Newtonian continuous phase were investigated by Pour et al.13 Dohi et al.12 employed two types of large-scale impellers called Maxblend and Fullzone in a triple-impeller system to investigate power consumption and solid suspension performances. The experiments were carried out in five different scale vessels (with diameters from 200 to 800 mm) to examine the scale-up problem. A correlation for

10.1021/ie9006886  2010 American Chemical Society Published on Web 08/17/2009


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thepowerconsumptionoflarge-scaleimpellersingas-liquid-solid systems was proposed. Moreover, CFD (computational fluid dynamics) was also employed to predict power consumption.14 However, most papers are on two-phase (gas-liquid or liquid-solid) systems, and simulations of gas-liquid-solid systems are relatively rare. Mixing time (tm) is also one of the most significant parameters in expressing the performances of stirred tanks. The shorter the mixing time, the better the reactor performance. There are many means to determine tm, for example, electric conductivity method, temperature difference method, decolorization method, and chemical neutralization. Manna15 provided the comparison between physical (electric conductivity) and chemical methods for the measurement of mixing time both in theory and experiment. Bouaifi and Roustan16 concluded that the conductivity method and decolorization technique gave similar mixing time under the same operating conditions. It is revealed that the mixing mechanisms were strongly dependent on flow patterns, impeller type, and diameter in dual-impeller gas-liquid reactors. The presence of a solid phase prolongs mixing time obviously because of the decreased circulation velocity. Kraume17 found the experimental results by the decolorization method in liquid-solid systems were about 10 times longer than that of single-phase state. For aeration condition, Hari-Prajitno et al.18 concluded that gassing increased only slightly the total mixing time for dual APV-B2 impellers. The effect of many factors on mixing time such as sensor location, impeller speed, spacing between impellers, boiling, gassing (cool and hot), and floating solids were discussed in detail, and many equations proposed for mixing time were also provided.13,16-20 However, most authors attempted to provide the correlations between mixing time and vessel geometry or operating conditions. It seems that little is reported about the detailed influences of flow pattern and mixing mode on mixing time. In research of liquid-solid systems, many studies (experiment or simulation)21-26 were focused on agitator speed for just-offbottom suspension, and relatively less attention was paid to solid particle concentration distribution in recent literature. Optics is often adopted to measure local solid concentration. Angst and Kraume27 measured the local particle concentrations in three geometrically similar vessels with an endoscope technique. Shan et al.28,29 determined the solid concentration distribution in an unbaffled stirred tank equipped with a 70° pitched 3-blade turbine downflow using a Powder Voidmeter PC-6.30 Gonzalez et al.31 measured the exit and mean solid concentration by weighting the samples in a 5 L aerated glass tank fixed with single pitched blade turbine or marine propeller. The vessel was operated with 3 L of 6% (w/v) slurry. The mathematic models predicting the solid concentration based on operating conditions were provided. In addition to optics and weighting methods, Micale et al.32,33 developed a simple technique called the “pressure gauge technique (PGT)” to measure the overall fraction of suspended solids. The new method is based on the measurement for pressure variation on the bottom as a result of the presence of suspended solids. According to the report, PGT can be extended to gas-liquid-solid and liquid-solid systems at any agitation speed. But it is difficult to apply PGT in axial or radial solid concentration distributions. Moreover, CFD was also developed in solid suspension in liquid-solid systems. Kasat et al.34 simulated the solid hold-up distribution and suspension quality in a baffled flat-bottom reactor with a standard Rushton turbine. Shan et al.28,29 gave both numerical simulation and experimental research of liquid-solid flow in an unbaffled elliptical stirred vessel with a pitched blade turbine

downflow. For the scale-up criteria of liquid-solid stirred tanks, Montante et al.35 got experimental and simulated (using commercial CFD code CFX-4.3) axial solid concentration distributions in some geometrically similar vessels. In this work, the hydrodynamic performances of five dualimpeller combinations (including a new type of impeller) are studied. The power consumption as a function of gas flow rate and solid concentration are discussed in gas-liquid, liquid-solid, and gas-liquid-solid systems. The mixing time in both single liquid and gas-liquid systems are obtained. Novel analysis on the impact of flow pattern and mixing mode on mixing time is suggested, too. In addition, the experiments for solid particle concentrations are conducted to explore the local solid hold-up and overall mixing of the tank. The instrument Powder Voidmeter PC-6 (manufactured by the Institute of Process Engineering, Chinese Academy of Sciences) is first used in dualimpeller systems. Ultimately, the optimum dual-impeller combination is suggested for different operations and goals. 2. Experimental Section 2.1. Measurement Method. The measurement of power consumption (P) was by the shaft-torque method: P ) 2πMN


where M presents the torque and N is the rotational speed. The torque was obtained following the procedure proposed by Chapple et al.:36 at the beginning of each set of experiments, the motor was run at the desired N for half an hour with only the shaft mounted without the liquid phase filled. After the torque reached a constant, the initial baseline torque was recorded and the motor stopped, then the impeller was mounted on the shaft, and the motor was restarted with liquid injected into the tank. The dynamic response for each point varied from a few minutes at the lowest speed to an almost instantaneous response at the highest speed. The difference of the power and the baseline gave the net stirring power. This method is effective and generally used, because it is not influenced by the friction within the motor, bearing, and shaft.8,36,37 The electric conductivity method is taken for the measurement of mixing time (tm) in this work. The electrolyte solution of high concentration (250 g/L NaCl solution) as the tracer is injected into the system from the liquid surface near the wall. The monitoring position is located at the opposite location with a clearance of 0.08 m from the bottom. The electric conductivity will not be stabilized at the monitoring position until the electrolyte solution is dispersed uniformly into the vessel. If the time trace of electric conductivity versus time is plotted, tm may be determined as the time between the injection of electrolyte and the time when the instant conductivity never biases over 5% from the final constant value. While dealing with the experimental data, the dimensionless conductivity Y is adopted:38 Y)


C(t) - C0 C∞ - C0



where C0 is the initial average conductivity of liquid, C∞ is the final average conductivity of well-mixed liquid phase, and C(t) is the instant conductivity at time t. If Y starts to remain in the range between 0.95 and 1.05, the mixing is considered complete. Every experimental condition was tested repeatedly 6-10 times to get an average of tm. Optical technique was used to examine the local solid particle concentration X (g/100 mL). The fiber optic reflection probe of

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Figure 1. Experimental setup. Figure 3. Measuring points in the stirred tank for local solid concentration experiment (units: centimeters).

Figure 2. Four impellers used in experiments. Table 1. Configurations of Five Dual-Impeller Combinations configuration






upper impeller lower impeller






the Powder Voidmeter PC-6 emits an infrared beam, which is reflected while encountering solid particles. The received signal is treated by the instrument to get the estimate of solid concentration. The diameter of the probe is just 3 mm; therefore, the effect of the probe on the whole macro flow field is negligible.28-30 2.2. Experimental Setup. The experimental setup is shown in Figure 1. The stirred tank with diameter of 0.38 m and total height of 0.6 m is equipped with four wall baffles with the width of 0.038 m. Air, tap water, and quartz sand are used as the gas, liquid, and solid phases, respectively. The density of water is 998.2 kg/m3, and the viscosity is 1.005 × 10-3 Pa · s. The bulk density of solid particle is 2403 kg/m3, and the particle size is 0.3-0.7 mm. A ring aerator with 16 holes (diameter of 2 mm) is installed 10 mm underneath the lower impeller if aeration is needed. The diameter of the aerator is 0.12 m. Four impellers with the same diameter of 0.127 m are employed in the experiments (Figure 2): Rushton disk turbine (RDT), alternate blade disk turbine (ABDT),39 45°-pitched blade turbine upflow (PBTU), and pitched blade turbine downflow (PBTD). Five dual-impeller configurations are listed in Table 1 and labeled as upper impeller + lower one when experimental results are presented. 2.3. Experimental Condition Analysis. A dual-impeller combination is often used in the stirred vessel with a high H/D ratio, hereby the liquid height is set to be 0.5 m (H/D ) 1.3). In mixing time experiments, the clearance between the bottom and lower impeller (CI) is D/3, and the distance between impellers is also D/3 (CII). But for solid particle concentration

Figure 4. PV as a function of Ug at different agitation speeds.

and power consumption experiments, it is very difficult to attain the just-off-bottom state with the clearance of D/3 (CI) because of the high density of quartz sand. Therefore D/5 (CI) is adopted and CII is 3D/5. The measuring point distribution for solid particle concentration is shown in Figure 3. As the daylight is influential to the probe, the stirred tank is covered with black cloth. The overall average solid particle concentration is set at 2 g/100 mL. 3. Results and Discussion 3.1. Power Consumption. 3.1.1. Gas-Liquid Systems. In gas-liquid systems for some given rotational speeds, the power consumptions per volume (PV) at different gas flow rates (Ug) are shown in Figure 4. It is found that configuration C with both radial impellers costs the most energy and the power input of configuration A composed of two axial impellers is the least. There is a great difference between A and C: PV of both radial impellers (C) is nearly three times more than that of both axial impellers (A). These results agree with that of Bouaifi and Roustan.16 It might be explained that the global power consumption is the sum of two impellers. It is concluded that the configuration with the axial impeller is more energy-efficient


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Table 2. Vaules of kp for Different Configurations in Gas-Liquid Systems N (rpm)






600 700

-109.7 -117.9

-114.1 -143.3

-123.9 -232.8

-215.9 -277.1

-145.1 -250.6

than that taking the radial one in aerated dual-impeller systems. Besides, it is obvious that PV is decreased with an increasing superficial gas velocity (Ug). The correlation between PV and Ug may be simply linked with straight lines for the five configurations of this work. Similar results were also obtained by Bouaifi and Roustan16 in a dual-impeller system: 1-

Pg Ug ) CFrg )C P0 √gD


where Frg is the Froude number of gas and C is a constant. From eq 3, it is easy to find that the correlation between PV and Ug is also linear. The slope of the line, kp, could be used for evaluating the power consumption reduction and the sensitivity to the aeration of the dual-impeller (Table 2). For all the five configurations, kp at faster rotational speed (700 rpm) is smaller than that at 600 rpm, which means that the power reduction is more at larger agitation speeds. It is observed that the power reduction of configuration D is more than that of other configurations. The power input of configuration A is not sensitive to aeration. Thus, it is noted that the power inputs of axial impellers are stable and not sensitive to aeration relative to radial ones. 3.1.2. Liquid-Solid Systems. Figure 5 shows the effect of overall solid concentration (X) on PV with the agitation speed of 700 rpm. For different configurations, the tendency of plots is similar. When solid concentration is lower, the correlation between PV and X can be expressed by a straight line simply, implying that the complete off-bottom or full suspension is obtained. But with more and more solid particles loaded into the tank, some particles settle on the bottom. Solid suspension becomes incomplete, i.e., the given 700 rpm is less than Njs (critical agitation speed for just-off-bottom suspension), so the added solids probably fall down to the bottom. The agitation with the constant speed (700 rpm) has no influence on the particles staying in the bottom. That is why the curves become leveled at the end part. Generally speaking, the whole tendency might be characterized by a quadratic curve (in Figure 5).

Figure 6. Power consumption versus agitation speed in liquid-solid systems (2 g/100 mL).

Figure 7. Power number versus Reynolds number in liquid-solid systems: (solid symbol) in a logarithmic coordinate; (hollow symbol) in a normal coordinate. Table 3. Results of Fitting Np as a Function of Re in Double Log Coordinates configuration

fitting quadratic curve



Np ) 21.27 - 6.859Re + 0.5602Re2 Np ) 26.96 - 9.626Re + 0.8838Re2 Np ) 28.61 - 10.16Re + 0.9363Re2 Np ) 24.67 - 8.517Re + 0.7620Re2 Np ) 27.33 - 9.759Re + 0.8964Re2

0.9995 0.9999 0.9999 0.9997 0.9999

Figure 6 shows the correlation between PV and N with the solid concentration of 2 g/100 mL. The power number (Np) is usually adopted if power consumption is discussed: Np )

Figure 5. PV as a function of solid concentrations in liquid-solid systems (N ) 700 rpm).

P FN3d5


In the baffled single liquid phase with one impeller, when the flow becomes completely turbulent (Re > 2 × 104), the power curve is a smooth line in double log coordinates. That means that Np becomes constant and independent of Re. In Figure 7 (hollow symbols), in the baffled liquid-solid system with a dual-impeller, Np drops off to an asymptotic value with increasing Re in all solid suspension states. For different combinations, the correlations between Np and Re can be

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Figure 8. PV as a function of Ug with different solid concentrations in gas-liquid-solid systems. (a) Configuration A (PBTU + PBTD). (b) Configuration B (PBTU + ABDT). (c) Configuration C (RDT + ABDT). (d) Configuration D (RDT + PBTD). (e) Configuration E (ABDT + PBTD).

expressed very well by quadratic curves in double log coordinates (Table 3). The curves are approximately parallel except for configuration B (Figure 7, solid symbols). It is concluded that the Np-Re quadratic curve under a logarithmic coordinate may be the power consumption characteristic curve for dual-impeller combinations in liquid-solid systems.

3.1.3. Gas-Liquid-Solid Systems. Figure 8 shows the variation of PV with Ug at different solid concentrations with the rotational speed of 700 rpm. Complete off-bottom conditions are achieved for different values of Xavg. For configurations C, D, and E, aeration is of little effect on the linearity of power input as a function of superficial gas


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Table 4. Mixing Time (units: seconds) in Single Liquid Systems N (rpm)






100 200 300 400

18.43 10.67 7.00 6.28

16.00 10.00 6.00 4.84

12.50 5.60 5.50 3.60

12.75 8.89 6.20 5.50

14.71 9.36 6.75 4.46

Table 5. Mixing Time (units: seconds) in Gas-Liquid Systems (Gassing Rate ) 0.6 m3/h) N (rpm)






100 200 300 400

14.60 11.00 7.20 7.28

12.37 13.38 6.28 5.27

13.00 8.60 5.67 4.80

11.60 11.90 6.38 6.00

14.18 13.56 7.27 5.92

velocity. Because axial impellers are not sensitive to aeration as is discussed in gas-liquid systems, the reduction of PV for configuration A is not obvious with lower gas flow rates. But with more and more gas entering into the tank, bubbles may pass through the impeller region vertically as a result of poor ability of axial impellers for dealing with air. Consequently PV is to fall down rapidly (in Figure 8a). With gas introduced into the liquid-solid systems, as observed clearly in Figure 8a, c, and e, the power input does not always increase as more and more solid particles are loaded in the tank (X from 1 to 3 g/100 mL). So it may be concluded that aeration is not beneficial to solid suspension because gas is to decrease power input. Another reason might be that the gas mixing into liquid system is to lower the total density of fluid, i.e., greater disparity in weight between fluid and solid may accelerate the settlement of solid particles. 3.2. Mixing Time. The mixing times in single liquid and gas-liquid systems are both examined under different rotational speeds for 5 configurations at the same gassing rate of 0.6 m3/ h, as shown in Tables 4 and 5. 3.2.1. Single Liquid Systems. In single liquid systems, the double radial impeller combination C performs the best. The tm of the double radial impeller configuration is the shortest of all in the whole range of 100-400 rpm. Meanwhile, tm of double axial impeller combination A is the longest. It is about 21.4-42.7% more than that of configuration C. The difference among radial + axial and axial + radial combinations is little and their tm values are between those of configurations A and C. These results may be explained by their own flow pattern and mixing mode (Figure 9a and b), in which the tracer

Figure 9. Mixing modes of different configurations in mixing time experiments. (a) Mixing mode of double axial impellers: more-disperseweak-shear. (b) Mixing mode of double radial impellers: break-priordisperse-secondary.

Figure 10. Electrical conductivity versus time. (a) Combination A (PBTU + PBTD). (b) Combination C (RDT + ABDT).

electrolyte solution is injected into the liquid surface. It is known that the axial-flow produced by PBTD or PBTU is of weak shear. Consequently, the electrolytic solution of high concentration moves with the main axial flow to the bottom undispersed. As suggested by the peaks of time traces of conductivity sensored by the probe (Figure 10a), so more full cycles of circulation are necessary to reach the standard of the mixing time. But in the system with a radial-flow impeller like RDT or ABDT, the mixing process may be different. The injected electrolyte lump is broken into elements of small size by the great shear from the radial-flow impeller. Better dispersion results; therefore, the probe will not detect the peak in the conductivity curves (Figure 10b). The break-prior-dispersesecondary way should be more effective than more-disperseweak-shear, and the mixing time is shorter. 3.2.2. Gas-Liquid Systems. In aerated systems, the double radial impeller combination C is still superior to other combinations, but the dominance is not as evident as that in single liquid systems. The tm of configuration A is 10.96-34.06% more than that of configuration C. The influence of aeration on tm for all combinations is the same (Figure 11). Under lower rotational speed (about 100 rpm), aeration is helpful for gas-liquid dispersing, because the power input is little. The main force for the dispersion of electrolytic tracer is the up-rising movement of the gas phase. It is to result in the axial movement of the water, so the motion may accelerate the diffusion of electrolyte solution and shorten tm. But with the increase of rotational speed,

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Figure 11. Mixing time versus agitation speed. (a) Configuration B (PBTU+ABDT). (b) Configuration E (ABDT+PBTD).

the main force for dispersion becomes the input power from the impellers. Aeration reduces the power input on the contrary, which is going to prolong the mixing time. 3.3. Solid Particle Concentration in Liquid-Solid Systems (X). 3.3.1. Distribution of X. Figure 12 shows axial local solid particle concentration distributions at different radial positions (r ) 90, 130, 170 mm) with the rotational speed of 400 rpm. The combinations that take PBTD as the lower impeller obtain the relatively equal mixing (A, D, and E), and a larger value of X is achieved in the upside of the tank. For combinations B and C, it is difficult to make many particles move up to the middle and top of the vessel, and most particles stay near the bottom. The conclusion is that the lower impeller contributes more than the upper one in a solid suspension. 3.3.2. Overall Mixing Equality. There are many criteria in judging the uniformity of suspension in the whole tank. The standard deviation σ is frequently used:26,34,40 σ)

 ( ) 1 n


∑ i)1

ci -1 c0



where n is the number of sampling locations used for measuring the solid holdup, ci is the local instantaneous solid concentration, and c0 means the overall average solid concentration in the tank. A smaller value of σ indicates better solid dispersion and suspension. Murthy et al.26 predicted Njs in a gas-liquid-solid stirred tank with CFD simulations and used σ to quantify the suspension quality, too. The value of 0.75 was considered to

Figure 12. Axial solid concentration distributions in liquid-solid systems (N ) 400 rpm). (a) r ) 170, (b) 130, and (c) 90 mm. Table 6. Comparison between Experiment and Simulation Results of Njs Based on σ configurations σ Njs (rpm)






0.72 0.78 0.80 0.70 0.73 290 480 490 250 280

PBTDa DTa PBTUa 0.76 405

0.76 615

0.78 558

a Simulation results from the work of Murthy et al.:26 a gas-liquid-solid system with a single impeller.

reach the critical impeller speed suspension. Another value of 0.8 was suggested by Kasat et al.34 and Panneerselvam et al.40 Table 6 gives the comparison between experiment and simulation results of Njs based on the value of the standard deviation of solid concentrations. It is noted that the difference of both methods is small and the critical impeller speed for suspension


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to mixing at lower rotational speeds, and aeration becomes disadvantageous at higher N. Generally speaking, faster rotational speed is to produce more uniform mixing in solid particle suspension. The configuration taking PBTD as the lower impeller is superior to other combinations. The lower impeller contributes more to solid suspension than the upper one in solid suspension. Acknowledgment The financial support from the National Natural Science Foundation of China (Nos. 20990224, 20306028), 863 Program (2007AA060904), 973 Program (2007CB714305), the National Project of Scientific and Technical Supporting Program (2008BAF33B03), and the Project of Scientific and Technical Supporting Program in Jiangsu Province (BE2008086) is gratefully acknowledged. Figure 13. Standard deviation of solid concentrations versus agitation speed in liquid-solid systems.

is therefore achieved when the value of σ reaches the range of 0.7 to 0.8. Figure 13 presents the relation between σ and rotational speed, showing that the combinations that adopted PBTD as the lower impeller perform better and that the critical solid suspension state is obtained (σ < 0.8). On the contrary, the combinations with a radial-flow impeller as the lower impeller, like configurations B and C, cannot suspend the solid particles to desired state; σ is still above 0.8 (incomplete suspension) even with high rotational speeds. Some points are to be made here. First, the above results and observations may not be valid for the systems with higher solid concentrations. The stronger interactions among the phases may make the behaviors more complicated and ruleless. That is one of the reasons why there is little literature on the research of liquid-solid and gas-liquid-solid systems with high solid concentrations. Second, the present study presents the effects of the continuous phase on the behavior of solid phase, but the back interactions of the solid phase on the continuous phase are not demonstrated. Therefore, more tests on systems with higher solid phase concentrations are necessary for achieving a comprehensive understanding of stirred tanks applied in industrial processes. 4. Conclusions The configuration taking axial impellers consumes less energy than that with radial ones in all multiple-phase systems. In gas-liquid systems, the correlation between PV and Ug is linear. The input power of axial impellers is stable and not sensitive to aeration. The power reduction is more significant at larger agitation speed. The overall variation tendency of PV with different X is characterized by quadratic correlations in liquid-solid systems. Np seems to drop off to an asymptotic value with increasing Re, and the relationship between Np and Re is expressed very well by quadratic curves in a logarithmic coordinate. Aeration is harmful to solid suspensions, and the correlations between PV and Ug (or X) are dissimilar for different configurations. The mixing in a dual-impeller tank is investigated and the mixing modes of impellers with different flow patterns (axial and radial) are proposed. The analysis of experimental results suggests that the radial impeller is better for macromixing. The impacts of aeration on mixing time for different combinations are alike. The up-rising movement of air bubbles is beneficial

Notation ci ) local instantaneous solid concentration, g/100 mL c0 ) overall average solid concentration in the tank, g/100 mL CI ) clearance between tank bottom and lower impeller, m CII ) clearance between two impellers, m d ) diameter of impeller, m D ) diameter of tank, m E ) electrical conductivity, µS/cm Frg ) Froude number of gas g ) acceleration of gravity, m2/s h ) axial coordinate in solid concentration experiment, m H ) height of liquid surface, m H/D ) height to diameter ratio of the stirred tank kp ) slope of fitting lines in gas-liquid systems M ) torque value, N · m N ) rotational speed, rpm Njs ) critical speed for just-off-bottom suspension, rpm Np ) power number n ) the number of sampling locations for measuring the solid holdup P ) power consumption, W Pg ) power consumption with gassing, W P0 ) power consumption without gassing, W PV ) power consumption per volume, kW/m3 R ) correlation coefficient Re ) Reynolds number r ) radial coordinate, cm tm ) mixing time, s Ug ) superficial gas velocity, m/s X ) local solid particle concentration, g/100 mL Xavg ) overall solid particle concentration, g/100 mL F ) density, kg/m3 σ ) standard deviation

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ReceiVed for reView April 29, 2009 ReVised manuscript receiVed July 26, 2009 Accepted July 30, 2009 IE9006886