study of various curved-blade impeller geometries on power consumption in stirred vessel using...

Journal of the Taiwan Institute of Chemical Engineers 44 (2013) 192–201

Study of various curved-blade impeller geometries on power consumption instirred vessel using response surface methodology

Reza Afshar Ghotli a, A.R. Abdul Aziz a,*, Shaliza Ibrahim b, Saeid Baroutian c, Arash Arami-Niya a

a Department of Chemical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysiab Department of Civil Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysiac SCION, Te Papa Tipu Innovation Park, 49 Sala Street, Private Bag 3020, Rotorua 3046, New Zealand

A R T I C L E I N F O

Article history:

Received 30 July 2012

Received in revised form 12 October 2012

Accepted 21 October 2012

Available online 20 December 2012

Keywords:

Curved blade impeller

Curvature angle

Central disk size, Power number (NP)

Aerated and un-aerated system

RSM

A B S T R A C T

The geometry of an impeller is a determining factor in power demand, which in turn determines the cost

of mixing operation in stirred tanks. In this work, the power requirements for seven types of 6-curved

blade impellers of varying curvature angles and central disk sizes, were analyzed via response surface

methodology (RSM) and compared to a Ruston turbine. The experiments were conducted using water as

the working fluid in a standard mixing vessel. Power consumptions were measured using a load cell

arrangement for a wide range of speeds in both aerated and un-aerated conditions. The data revealed

that the power number (NP) of the elliptical shape curved blade was 2.8 whereas for CB1808, CB1608 and

CB1408 were respectively 21%, 32% and 75% higher. Furthermore, the power number values for the

impeller with a 3/4D central disk size was approximate 3.4, while the impellers with 1/2, 1/4 and without

central disk were respectively 15%, 20% and 23.5% higher. The results under different gas flow rates

illustrated the power reduction of the curved blades impellers, both various central disk sizes and

curvature angles, were in the range of 1–20% meanwhile the Rushton turbine was in the range of 5–45%.

Curvature angle and central disk size found as the significant parameters through variance analysis

(ANOVA). The results also indicated that the significance of the central disk size was less than the other

variables. The R-squared values indicated a fitting of the models with the experimental data. In

conclusion, the curved blade impellers were found to have lower power consumption in both aerated

and un-aerated conditions in comparison with the Rushton turbine.

� 2012 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

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Journal of the Taiwan Institute of Chemical Engineers

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1. Introduction

Several types of impellers have been designed and created forvarious applications in chemical, pharmaceutical, petroleum andfood processes through standard stirred vessels. Paddled; propel-lers and turbines are among some of the common types ofimpellers used in mixing processes. Proper impeller selection foreach process requires precise information about the viscosity offluid, operating conditions, system flow regime, etc. [1]. Powerdrawn by a rotating impeller has a significant role in the design ofthe mixing systems and the best choices for impellers are thosewith the lowest power consumption [2]. Thus, a comparison ofdifferent impellers would be helpful in determining the choice ofan appropriate impeller for a dispersion process. Several worksdetermined the power number of a wide range of impellers designs

* Corresponding author. Tel.: +60 379675300.

E-mail addresses: [email protected] (R. Afshar Ghotli),

[email protected] (A.R. Abdul Aziz), [email protected] (S. Ibrahim),

[email protected] (S. Baroutian), [email protected] (A. Arami-Niya).

1876-1070/$ – see front matter � 2012 Taiwan Institute of Chemical Engineers. Publis

http://dx.doi.org/10.1016/j.jtice.2012.10.010

such as down pumping 458 pitched blade turbines [3–6], uppumping 458 six pitched blade turbine [3] and Sawtooth impeller[6], Rushton turbine [7–11], Concave blade (semi circular) [3,9,12–14], 6SRGT Scaba [3,15,16], Propeller [4,17], Lightnin A6000impellers [18], A310 Fluidfoil impellers [18], prochem T [15,19],Parabolic bladed disc turbine [3] and curved pitched blade turbine[4] have performed through the stirred vessels. Table 1 showssome power number values for various impeller types.

Published literature on mixing showed the employment ofdifferent types of impellers for various applications but theRushton turbine is still a very common and applicable type.However, there are several drawbacks associated with the Rushtonturbine such as a considerable drop in the power input and masstransfer in the aerated system [9,20,21], in addition to high levelsof shear stress in the district of the impeller and a nonhomogeneous spatial distribution of the energy dissipation rateinside the tank [22]. Compared to the Rushton turbine, Hydrofoilimpellers, such as Prochem Maxflow T and Lightnin A315 show amuch lower power reduction over a wide range of gas flow rates[23]. Moreover, the curved or hollow blade impellers, such asSCABA and concave blade turbines, also provide better gassed

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Nomenclature

NRe Reynolds number, dimensionless

P power required by the impeller, kg m2/s3

r density, kg/m3

N rotational speed of impeller, rev/s

D impeller diameter, m

m viscosity, kg/s m

t torque, Nm

m mass defined by the load cell, kg

g acceleration of gravity, 9.8, m/s2

d a distance from the motor to the central rod (Fig. 1),

m

Q flow rate of discharged gas through the impeller

region, m3/s

D impeller diameter, m

n number of variables

a distance of axial point from the center point

Y response value be predicted by the model

b0 constant coefficient

bii quadratic coefficient

bi linear effect

bij interaction coefficients

xi and xj coded values

R. Afshar Ghotli et al. / Journal of the Taiwan Institute of Chemical Engineers 44 (2013) 192–201 193

power characteristics and shaft stability performance than thestandard Rushton impeller with much less reduction in powerdrawn [3,15,16,24,25]. For example, Couper et al., described thatthe gas handling capacity for Chemineer CD-6 is 200% more thanthe six bladed disk turbines, prior to flooding and at flooding theaerated power reduction is only around 30% [26].

Consequently, large differences in power consumption can beseen among various designs, while the effect of small changes in aparticular geometry such as blade angle and central disk size hasnot been widely established. Literature reviews suggest thatpublished works on curved blade impellers are very limited. Thus,in this work the effects of various curvature angles and central disksizes for the six curved blade impellers on power in both aeratedand un-aerated conditions were investigated. Finally, a compari-son was made with the results of the Rushton turbine.

Table 1Some of previous power number values for different types of impellers.

Impeller type NP values Reference

Down pumping 458 pitched blade turbines (PBT) 1.7 [5]

Down pumping 458 four pitched blade turbine 0.99 [6]

Down pumping 458 six pitched blade turbine 2.1 [4]

Sawtooth impeller 0.32 [6]

Concave blade (semi circular) impeller 2.8 [9]




Lightnin A6000 impellers 0.23 [18]

A310 fluidfoil impellers 0.30 [18]

Propeller 0.67 [17]

Propeller 0.89 [4]

Curved pitched blade turbine 2.41 [4]

Standard six blade Rushton turbine 5.0 [45]

Convex pitched blade turbine 2.29 [4]






Experimental design technique is a very helpful technique toprovide statistical models and giving better recognition of theinteractions between the parameters. Furthermore, responsesurface methodology (RSM) is a compilation of mathematicaland statistical techniques which can be employed to determine theimportance of affecting parameters [27–29]. There is no informa-tion available in literature regarding the modeling of theinteraction between angles, central disk size and Reynolds numberwith power number. Therefore, in this work central compositedesign (CCD) based on response surface methodology (RSM) wereused to evaluate the effects of blades curvature angles and centraldisk sizes on power consumption in different Reynolds and flownumbers in stirred vessels and to prepare a model throughexperimental data.

2. Experimental setup

2.1. Setup

All the measurements were carried out in a 0.4 m diameter (T)flat bottom vessel which was constructed from a transparentscratch proof Perspex. The tank was equipped with four equallyspaced wall mounted baffles (B) of width, B = T/10. The ratio ofimpeller clearance (C) to tank diameter (T) followed the standardgeometries and was equivalent to 0.133 m. The sparger wasprovided with 24 equally spaced holes of 0.002 m in diameter withthe same outer diameter and impellers equivalent to 0.133 m. The

Fig. 1. Schematic of the load cell set-up to determine power number: (A) load cell;

(B) connector; (C) rod; (d) a distance from the motor to the central rod; (E) panel; (F)

motor; and (G) weight.

R. Afshar Ghotli et al. / Journal of the Taiwan Institute of Chemical Engineers 44 (2013) 192–201194

sparger was located concentrically to the impeller at a verticalposition of 0.13 m below the turbine at the bottom of the vessel.Regardless of the position, the sparger always discharged gastoward the turbine region. Tap water was used directly as aworking fluid and the liquid height was equal to the tank diameter(T). In advance of each test, the tank was filled with fresh waterregularly. Meanwhile, the temperature was at about 25 8C (roomtemperature). A load cell was employed to measure weight or forcefor the determination of power. The load used in this work haddifferent standard weights and the calibration curve was plottedusing averaged mV and grams so as to increase the accuracy andthe performance of the system. A schematic of the experimental setup and load cell design are illustrated in Fig. 1. Based on theobjectives of this project, i.e., to use six curved blade turbines, itfocused on six curved blade impellers with different bladecurvature angles and central disc sizes. In addition, a comparisonwas also made with the well-known six straight bladed Rushtonturbine. The description and schematic of each impeller is given inFig. 2 and Table 2.

Fig. 2. The Schematic of different types of impellers utilized in this work: (

2.2. Power and power number determination

In the same geometrical systems, Reynolds number has acritical correlation with power consumption due to the dependen-cy of flow regimes, whether it is laminar or turbulent. In otherwords, the power drawn is extremely dependent on Reynoldsnumber [7,10,30]. Reynolds number (NRe) is demonstrated inEq. (1) which reveals the ratio of inertial forces to viscous forces.

NRe ¼rND2

m(1)

The power variances have been investigated in aerated and un-aerated conditions with various types of impellers, speeds, tankgeometries, etc. by several researchers [7,20,31,32]. The powernumber of impellers is evaluated using the following expression[7,33]:

NP ¼P

rN3D5(2)

1) 6RT; (2) 6 curved blade impellers; and (3) various curvature angles.

Table 2Type of impellers investigated in the experimental part.

No. Impeller Outer dia. (D)

(cm)

Curvature

angle

Central disk

size

Blade length

(mm)

Blade thickness

(mm)

D/T

1 6 curve blade without central disk (ND) 13.3 1808 0 4.3 2.0 1/3

2 6 curve blade with 1/2D central disk (CB1/2D) 13.3 1808 1/2D 4.3 2.0 1/3



5 6 curve blade with 3/4D central disk (CB1808) 13.3 1808 3/4D 3.3 2.0 1/3

6 6 curve blade elliptical shape with 3/4D central disk (CB(e)) 13.3 E 3/4D 3.3 2.0 1/3



9 6 flat blade Rushton turbine with 3/4D central disk (RT) 13.3 0 3/4D 3.3 2.0 1/3


Generally, the power consumption is calculated directly fromthe measurements of the torque and the shaft speed onto whichthe impeller had been mounted using the following equation:

P ¼ 2pNt (3)

In this work, the power consumption was evaluated by the loadcell setup. When a force is applied to it in a definite manner, a loadcell produces an output signal that is relative to the applied force[34]. The following expression was used to determine the powerconsumption.

P ¼ 2pNmgd (4)

2.3. Flow number determination

The relationship between the aerated and un-aerated powerratio (Pg/P0) and the gas flow number, NQ, at a constant impellerspeed, is commonly employed to express the effect of variations inthe gas flow rate on the cavity structure and vessel hydrodynamics[35]. The Aeration number or gas flow number, NQ, is proportionalto the gas flow divided by the impeller pumping capacity.

NQ ¼Q

ND3(5)

2.4. Statistical analysis

Response surface methodology (RSM) is a compilation ofmathematical and statistical techniques for modeling, analysis anddetermination of regression model equations and operatingconditions through quantitative data of appropriate experiments[36,37]. RSM has already been verified as a reliable statistical toolin the investigation of some chemical engineering processes[27,38–41]. In this study, RSM design called central compositedesign (CCD) was employed as a proper experimental design with aminimum number of experiments to analyze the effect of thecurvature angle and Reynolds number in addition to central disksize and Reynolds number on the power number [41,42].Furthermore, this method was applied to analyze the effect ofthe curvature angle and flow number as well as central disk sizeand flow number on power ratio (Pg/P0). With this method, a core

Table 3Independent variables and their coded levels for the CCD.

Variables Code Coded variable level

�1 0 1

Reynolds number (�103) X1 89 182 275

Angle size X2 140 160 180

Disc size X3 3.325 6.65 9.975

Flow number (�10�2) X4 0.71 3.01 5.31

factorial is created that forms a cube with sides that are two codedunits in length (from �1 to +1 as noted in Table 3).

The coded values of each factor level, which are independentvariables consisting of the Reynolds number, X1, angle size, X2, discsize, X3, Flow number, X4, and their coded levels for the CCD areillustrated in Table 3.

The required number of experiments for the CCD methodconsists of 2n factorial runs with 2n fixed axial runs and replicatetests at the center; where n is the number of variables. Thus, thetotal number of tests (N) is evaluated from:

N ¼ 2n þ 2n þ nC (6)

Hence, for the two variable sets consisting of ‘‘curvature angle,Reynolds number’’ and ‘‘disk size, Reynolds number’’, 4 factorialruns, 4 fixed axial runs and 5 replications of center points werechosen. Replication numbers of center are employed to predict theexperimental standard error of prediction. Therefore, the totalnumber of experiments for each set of experiments of curvatureangle, Reynolds number and disk size, Reynolds number with fourvariables is 13. The same operations were established on ‘‘flownumber, disk size’’ and ‘‘flow number, angle’’ variables sets. Thelow and high levels are coded as �1 and +1, the independentvariables are coded to the (�1, 1) interval, respectively. The axialpoints are placed at (�a, 0) and (0, �a), where the distance of theaxial point from center is a. The value of a depends on the number ofpoints in the factorial portion of the design. In fact, the value of a canbe calculated by Eq. (7) [36].

a ¼ ð2nÞ0:25(7)

In this study, the value of a was fixed at 1. Modification of theexperimental data is done by a second-order polynomial regres-sion model:

Y ¼ b0 þX3

i¼1

bixi þX3

i¼1

biix2i þ

X2

i¼1

X3

j¼iþ1

bi jxix j (8)

The variance analysis (ANOVA) is applied to verify thesignificance of the models, factors, coefficients and regression,statistically [41,43]. Design expert software (DOE) (version 8.0.7.1,Stat-Ease, Inc., Minneapolis, USA), was employed to performstatistical analysis, and regression models. The complete designmatrices of the experiments performed, together with the resultsobtained for both un-aerated and aerated system, are shown inTables 4 and 5.

3. Results and discussion

3.1. Power number

In this study, the value of 5.9 was obtained for the powernumber of Rushton turbine in a Reynolds number range of

Table 4Experimental design matrix and response results for un-aerated system.

Run Type Reynolds number, X1 Angle, X2 Central disk size, X3 Yield, Y1 Yield, Y2

1 Axial 272,000 160 6.65 4.32 4.09

2 Axial 180,300 140 9.97 5.12 3.48

3 Center 180,300 160 6.65 3.76 3.88

4 Center 180,300 160 6.65 3.8 3.85

5 Center 180,300 160 6.65 3.72 3.91

6 Factorial 272,000 140 9.97 4.97 3.54

7 Center 180,300 160 6.65 3.77 3.81

8 Center 180,300 160 6.65 3.71 3.86

9 Factorial 88,600 140 3.33 4.05 3.59

10 Factorial 88,600 180 9.97 3.15 3.15

11 Axial 180,300 180 3.33 3.36 4.15

12 Factorial 272,000 180 3.33 3.4 4.49

13 Axial 88,600 160 9.97 3.54 3.15

Table 5Experimental design matrix and response results for aerated system.

Run Type Flow number, X4 Angle, X2 Central disk size, X3 Yield, Y3 Yield, Y4

1 Factorial 0.007 140 3.33 1.035 1.007

2 Center 0.030 160 6.65 1.001 1.0375

3 Center 0.030 160 0.65 1.003 1.0380

4 Center 0.030 160 6.65 1.004 1.0300

5 Factorial 0.007 180 9.97 1.021 1.0210

6 Axial 0.007 160 6.65 1.019 1.0200

7 Axial 0.053 160 6.65 0.822 0.8990

8 Center 0.030 160 6.65 0.99 1.0371

9 Axial 0.030 140 9.97 0.915 1.0290

10 Factorial 0.053 180 9.97 0.868 0.8680

11 Center 0.030 160 6.65 1.001 1.0365

12 Axial 0.030 180 3.33 1.028 0.9940

13 Factorial 0.053 140 3.33 0.734 0.8590


0.88 � 105 to 2.75 � 105. These results proved to be in a goodagreement with literature reported power number values in arange of 5.0–6.0 [7,11,44–46]. In order to improve the accuracy ofthe results, the experiments were repeated three times. Aftercomputing the data, the power numbers against Reynolds numberwere plotted for various impellers.

3.1.1. Development of regression model for power number

The correlations between responses (NP) and three independentparameters, Reynolds number, central disk size and curvatureangle, were investigated through central composite design. Fiveruns were performed at the center point to determine theexperimental error. Sequential model sums of squares wereselected the highest order polynomial where the additional terms

Fig. 3. Predicted vs. actual value of power number (NP) in

are significant and the model is not aliased. Experimental designsoftware suggested a quadratic model. Table 4 displays the resultsof the experimental design as well as the experimental results.Regression analysis was performed to fit the quadratic model tothe power number response in terms of central disk size andcurvature angle.

Eqs. (9) and (10), shown below, express the ralationshipbetween NP (Y1) with Reynolds number (X1) and curvature angle(X2) and also the relationship between NP (Y2) with Reynoldsnumber (X1) and central disk size (X3) in terms of coded factorsis:

Y1 ¼ 3:824483 þ 0:325X1 � 0:705X2 � 0:1675X1X2

� 0:07569X21 þ 0:23431X2

2 (9)

terms of: (a) curvature angle and (b) central disk size.

Fig. 4. Comparison of NP values curved blade impellers with various curvature

angles.


Y2 ¼ 3:885517 þ 0:275X1 � 0:34333X3 � 0:1275X1X3

� 0:03431X21 � 0:12931X2

3 (10)

Fig. 3a and b illustrates the predicted power number valuesthrough developing Eqs. (9) and (10) in terms of the actual resultvalues. The close position of points to the line proved theprofitability of quadratic models. In this case X1, X2 and X3 aresignificant model terms.

3.1.2. Statistical analysis on experimental data for power number

Determination of the coefficients of model equations inaddition to analysis of variance (ANOVA) was investigatedthrough DOE software. The models could determine theinteraction and effect of experimental factors on power numbervalues. Tables 6 and 7 display the analysis of variance (ANOVA)for response surface quadratic models for power number valuesof curved blade impellers with different curvature angles andcentral disk sizes, respectively. The models represent high R-squared (R2) values of 0.93 and 0.96 for Eqs. (9) and (10),respectively, those are close to unity. Thus, it reveals that both ofthem can give close estimated values to the actual values. As canbe seen from Table 6, the F-value of 18.08 for Eq. (9) implies themodel is significant. There is only a 0.07% chance that a ‘‘Model F-Value’’ this large could occur due to noise. Values of ‘‘Prob > F’’less than 0.05 indicate the model terms are significant. In thiscase X1 and X2 are significant model terms. Table 7 shows theModel F-value of 34.32 for the equation 10 which indicates thatthis model is also significant and there is only a 0.01% chance thata ‘‘Model F-Value’’ could happen due to noise. Values of‘‘Prob > F’’ less than 0.05 for X1, X3, X1X3 and X2

3 shows thesignificancy of the model terms. Adequate Precision measures thesignal to noise ratio. A ratio greater than 4 is desirable. In thesecases the ratios of 14.635 and 20.957 for model equations (9) and(10) indicate sufficient signal and the ability of these models tonavigate the design space.

Table 6Analysis of variance (ANOVA) for response surface quadratic model for power number

Source Sum of squares Degree of freedom Mean of

Model 3.880352 5 0.77607

X1 0.63375 1 0.63375

X2 2.98215 1 2.98215

X1X2 0.112225 1 0.112225

x21 0.015823 1 0.015823

x22 0.151632 1 0.151632

Residual 0.300478 7 0.042925

Lack of fit 0.294998 3 0.098333

Pure error 0.00548 4 0.00137

Cor total 4.180831 12

R-squared 0.9281


Source Sum of squares Degree of freedom Mean o

Model 1.294788 5 0.2589

X1 0.45375 1 0.4537

X3 0.707267 1 0.7072

X1X3 0.065025 1 0.0650

X21 0.003251 1 0.0032

X23 0.046182 1 0.0461

Residual 0.052812 7 0.0075

Lack of fit 0.047332 3 0.0157

Pure error 0.00548 4 0.0013

Cor total 1.3476 12

R-squared 0.9608

3.1.3. The effect of curvature angles on power number

The influence of varying curvature angles in the curved bladeimpellers are presented in Fig. 4. The curved blade impellers withcurvature angles of 1808, 1608 and 1408 are noted by (CB1808),(CB1608) and (CB1408), respectively. The results were comparedwith RT and elliptical shaped curved blade (CB(e)) impellers(Table 8).

The power number decreases with the enhancement in thecurvature angle and the elliptical blade had the lowest powernumber value compared to the other curved blades. The averagepower numbers value of the elliptical shape curve blade was 2.8and it was 21%, 32% and 75% less than CB1808, CB1608 and CB1408,respectively. The results proved that the power number values forcurved blade impellers are much less than for the Rushton turbinefor the same rotational speed and number of blades. Fig. 4 andTable 8 illustrate that after NRe reaches a value of 1.75 � 105, exceptfor the CB140 the NP values for curved blade impellers wererelatively constant between 3.4 and 3.5; meanwhile a reduction isseen in the range of 6.3 to 5.2 for RT when the Reynolds number

(curvature angle).

square F-value p-Value Prob > F Remarks

18.07948 0.0007 Significant


69.4727 <0.0001 Significant


0.368609 0.5629 Not significant


71.77578 0.0006

(central disk size).

f square F-value p-Value Prob > F Remarks

58 34.32385 <0.0001 Significant

5 60.14283 0.0001 Significant

67 93.7455 <0.0001 Significant

25 8.618815 0.0218 Significant

51 0.430949 0.5325

82 6.121283 0.0426 Significant

45

77 11.51625 0.0195

7

Table 8NP values for the curved blade impellers with various curvature angles.

Impeller type NP

Re number

0.886 � 105 1.803 � 105 2.72 � 105

6 CB(e) 2.04 2.90 3.01

6 CB(ND) 3.60 4.35 4.50

RT 6.27 6.20 5.18


increases from 0.886 � 105 to 2.72 � 105 (Table 8). The reduction isassociated with an increase in the trailing vortex intensity behindthe Rushton turbine blades [16,47]. This is likely to be due to cavityformation behind the blades from air being entrained from thesurface, which is intensified when increasing the speed or theReynolds number. Thus, this results in greater power consumptionvalues for the Rushton turbine. Moreover, a tendency of thebubbles to accumulate at the low pressure area causes anextension in the gas cavity effect and results in higher powervalues under un-aerated condition [48]. However, the curved bladeshape reduces the effect of gas cavity and trailing vortex in the rearside of blades [16,47]. Since, a smaller curvature angle has a biggercurvature width, it causes decrease in this particular effect [9]. Thesmaller curvature angles have wider curvature and consequence inlarger swept areas and this may lead to higher power consumption.At last, the high volumes of air bubbles were observed around theRushton turbine region which leads to an increase in the cavityeffect and higher power consumption in higher Reynolds numbers[9,48]. Moreover, observation proved that the smaller curvatureangle results in air bubbles intensification around the impellerregion and higher power consumption at higher Reynoldsnumbers.

3.1.4. The effect of different central disk sizes on power number

Fig. 5 and Table 8 represent the power number against theReynolds number for six semi circular blade impellers with variouscentral disc sizes. The impeller without central disk CB(ND), 1/4D

central disk (CB1/4D), 1/2D central disk (CB1/2D) and 3/4D centraldisk (CB3/4D) were investigated. The results indicated the lowestNP value was 3.4 for CB3/4D, whereas the impeller without centraldisk obtained the highest NP value of 4.2. As can be seen from Fig. 5and Table 8, after Reynolds number of 1.75 � 10�5, the NP valuesfor CB(ND) and CB1/4D were nearly the same. Although the plotsshow that increasing the central disc size results in a lower powernumber value, except for the CB3/4D, the average of NP values forthese impellers are nearly the same and the lowest value was

Fig. 5. Comparison of the power number vs. the Reynolds number

obtained for CB3/4D. The results specified that the NP value for theimpeller with 3/4D, central disk size, is 15%, 20% and 23.5% lessthan the impellers with 1/2, 1/4 and without central disk,respectively. From the hydrodynamic point of view, reducingthe central disk size while the impeller diameter is constant causesa higher net swept area and accordingly results in higher powernumbers. Reduction in central disk size results in a larger amountof air bubbles traveling through the impeller blades and moreturbulence. The disk can accumulate the gas under the impellerand leads it to high shear zone near the blades where bubbleformation occurs. Moreover, the disk can decrease he flowinstabilities occurred by impellers without central disk [47].Therefore, the power values for the impellers with bigger centraldisk size were fairly lower.

3.2. Aerated power determination

3.2.1. Development of regression model for power reduction ratio

The relationship between response (Pg/P0) and three indepen-dent parameters consisting of flow number, central disk size andcurvature angle were also determined through central compositedesign. Five runs were performed at the center point to determinethe experimental error.

Similarly as last two models, sequential model sums ofsquares were selected the highest order polynomial where theadditional terms are significant and the model is not aliased. Aquadratic model was recommended by the Experimental designsoftware. The results of experimental design are demonstratedwith the experimental results through Table 5. Regressionanalysis was performed to fit the quadratic model to the powerratio response in terms of central disk size and curvature angle.Eqs. (11) and (12), shown below, demonstrate the relationshipbetween Pg/P0 (Y3) with the flow number (X4) and the curvatureangle as well as the relationship between Pg/P0 (Y4) with theflow number (X4) and the central disk size (X2) based on codedfactors.

Y3 ¼ 1:0 � 0:11X4 � 0:039X2 � 0:037X4X2 � 0:069X24

� 0:018X22 (11)

Y4 ¼ 1:04 � 0:071X4 þ 0:009667X3 � 0:00125X3X4

� 0:073X24 � 0:024X2

3 (12)

Fig. 6a and b illustrate the predicted Pg/P0 values usingexpressions (11) and (12) with the actual result values. The closepositions of points to the line verify the effectiveness of the

for six curved blade impellers with various central disk sizes.

Fig. 6. Predicted vs. actual value of power ratio (Pg/P0) in terms of: (a) curvature angle and (b) central disk size.


quadratic models. In this case X4, X2 and X3 are significant modelterms.

3.2.2. Statistical analysis on experimental data for power reduction

ratio

Determination of the coefficients in the models equations wascalculated via DOE software, as well as, analysis of variance(ANOVA). The interaction and influence of experimental factors onthe power number value could be specified through the models.Tables 9 and 10, illustrate the analysis of variance (ANOVA) for theresponse surface quadratic models for the Pg/P0 values of curvedblade impellers with different curvature angles and central disksizes, respectively. High R-squared values (R2) of 0.98 and 0.99 forEqs. (11) and (12) are signified the models. Therefore, both modelscan give proper estimated values close to the actual values. The F-values of 85.57 for Eq. (11) and 177.87 for Eq. (12) from Tables 9and 10 showed the significancy of these models. There is only a0.01% chance that a ‘‘Model F-Value’’ this large could occur due tonoise. Values of ‘‘Prob > F’’ less than 0.05 for X2, X4, X2X4 and X2

4


Source Sum of squares Degree of freedom Mean

Model 0.10 5 0.21

X4 0.071 1 0.071

X2 0.009048 1 0.009

X2X4 0.005476 1 0.005

X24 0.013 1 0.013

X22 0.00008492 1 0.000

Residual 0.001706 7 0.000

Lack of fit 0.001597 3 0.000

Pure error 0.0001268 4 0.000

Cor total 0.11 12

R-squared 0.9839


Source Sum of squares Degree of freedom Mean

Model 0.054 5 0.011

X4 0.030 1 0.030

X3 0.0005607 1 0.000

X3X4 0.00000625 1 0.000

X24 0.015 1 0.015

X23 0.0015649 1 0.001

Residual 0.0004285 7 0.000

Lack of fit 0.0003850 3 0.000

Pure error 0.00004355 4 0.000

Cor total 0.055 12

R-squares 0.9922

shows the significancy of the model terms in Eq. (11). Moreover, X3,X4, X2

3 and X24 were the significant model terms in Eq. (12).

Adequate Precision measures the signal to noise ratio. A ratiogreater than 4 is desirable. The ratio of 29.26 and 33.24 for modelequations (11) and (12) shows sufficient signal and the ability ofthese models to navigate the design space.

3.2.3. The effect of curvature angles on power reduction ratio

The effects of curvature angle variance in six curved bladeimpellers also studied the aerated condition. Fig. 7, illustrates theeffect of curvature angles for CB180, CB160 and CB140 on a ratio ofaerated to un-aerated power (Pg/P0) against the aeration number,NA and the results compared with the Rushton turbine. The resultsfor the CB(e) and the Rushton turbine are demonstrated in Table11. The data was achieved under a constant speed of 10 rps andvarious superficial gas velocities in the range of 0–10 mm/s.

Fig. 7 shows that the Pg/P0 values increase when increasing thecurvature angle. Moreover, the aerated to un-aerated power valuefor the curved blade impellers becomes nearly constant around 1.0

(curvature angle).

of square F-value p-Value Prob > F Remarks


289.81 <0.0001

048 37.12 0.0005

476 22.47 0.0021

53.23 0.0002

08492 3.48 0.1042

2437

5264 16.61 0.0101 Significant

0317

(central disk size).

of square F-value p-Value Prob > F Remarks


496.42 <0.0001

5607 9.16 0.0192

00625 0.10 0.7586

242.44 <0.0001

5649 25.56 0.0015

06121

1283 11.79 0.0187 Significant

01089

Fig. 7. The effect of various gas flow rate on power ratio for curved blade impellers

with various curvature angles.

Fig. 8. The effect of various gas flow rate on power ratio for curved blade impellers

with various disk sizes.


with the NQ values up to 1.8 � 10�2. The results were in a goodagreement with the observations of Junker et al. They reported thatthe Pg/P0 will tend to 1 when the impeller reduces cavity at rearside of blades [20]. After this point the value of Pg/P0 for CB140started to reduce from 1.003 to 0.734, meanwhile the otherimpellers kept constant. After NQ reached 2.8 � 10�2, the value ofPg/P0 for CB160 also started to decrease. For CB180 and CB(e) areduction was observed after NQ of 3.2 � 10�2. For the Rustonturbine the Pg/P0 values reduced significantly in the range of 0.864to 0.506 with NQ of 1.8 � 10�2 to 5.3 � 10�2. This happens due tothe development of large gas cavities at the back of the impellerblades [25].

The results clearly showed that the impellers with biggercurvature angles have better efficiency in higher aeration numbersbecause of lower Pg/P0 reduction and a better gas handlingcapacity. Chen and Chen [24], explained that enhancement in thecurvature angle results in a smaller cavity size behind theimpeller’s blades. The same behavior was also reported byVasconcelos et al. [47] in a concave blade (curved blade) impeller.

The results proved the ability of the curved blade impeller for ahigh gas sparging flow rate prior to flooding [47]. Observation of astirred vessel during the experiments showed larger gas bubblesvolume for the Rushton turbine resulting in significant powerreduction. As well as a considerable decrease in power drawn, largecavities also cause a reduction in impeller pumping capacity, andgas dispersion ability [19]. The results proved that the curved bladeimpeller has better gas handling and less power reduction than theRushton turbine.

3.2.4. The effect of central disk sizes on power reduction ratio

The effects of various central disk sizes were also studied inaerated conditions. Fig. 8 illustrates the effect of central disk sizefor CB3/4D, CB1/2D, CB1/4D on aerated to un-aerated power (Pg/P0)values against the aeration number, NA. The results of RT andCB(ND) are also showed as a comparison in Table 11. In this partthe data was also obtained under a constant speed and varioussuperficial gas velocities.

Table 11Pg/P0 values for the 6 CB(e) and Rushton turbine.

Impeller type Pg/P0

Flow number

0.007 0.03 0.053

6 CB(e) 1.008 1.063 0.848

6 CB(ND) 0.993 0.986 0.862

RT 0.923 0.680 0.506

From Fig. 8 and Table 11, it was found that for the givenimpellers, there was no significant variance in the Pg/P0 valueswhen changing the size of the central disk. A reduction in the Pg/P0

values started after the NQ value of 3.2 � 10�2. The results showedthat after this point the values of Pg/P0 changed in the range of0.965 and 0.859. Reduction in the central disk size causes larger netswept areas and produces more air bubbles thus; resulting inlarger cavity sizes. The small difference observed between thevalues of Pg/P0 was due to a larger net swept area for the largercentral disk size.

4. Conclusion

The effects of blade curvature angles and central disk sizes onpower consumption in both aerated and un-aerated stirred tankwere evaluated and central composite design (CCD) based onresponse surface methodology (RSM) was used to model theexperimental data. The validation of experimental data proved thecapability of the quadratic model. Additionally, the R-squaredvalues illustrated the adequate fitting of the models withexperimental data. The results indicate that a reduction in thecurvature angle causes a higher impeller power number. The NP

value of the elliptical shape curved blade obtained at 2.8 gives thelowest value among the others. NP values were 3.4, 3.7 and 4.9 forCB1808, CB1608 and CB1408, respectively. On the other hand, theresults for the different central disk sizes specified that the biggercentral disc size give slightly lower power number values. The NP

values indicated that the CB3/4D with the value of 3.4 has thelowest power number. The NP value of RT was 5.98.

Results from aerated power consumption confirmed Resultsfrom aerated power consumption confirmed that Pg/P0 values forthe curved blade impellers began to reduce after the flow number(NQ) of 3.2 � 10�2, meanwhile the value for the Rushton turbinedropped after NQ of 1.8 � 10�2. Moreover, decreasing in curvatureangle causes a higher level of reduction in Pg/P0 values. However,changes in the central disk size did not show any significant effectson the Pg/P0 value. The increment in the central disk size from 1/4D

to 3/4D was found to moderate the reduction on the power ratio.The results indicated that generally curved blade impellers have ahigher gas handling capacity and a smaller reduction on Pg/P0

values in comparison with the RT. However, changes in the centraldisk size did not show any significant effects on the Pg/P0 value.

Acknowledgments

The authors are very appreciative for the financial supportprovided by the Post Graduate Research Fund (PPP) (PS141/2009C)and Bright Sparks Program, University of Malaya, and High ImpactResearch Grant (HIR).


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