Power Drawn by Multiple Impellers in Sparged Agitated Vessels

INTRODUCTION

Recent work's2 has clearly indicated the close link between the power drawn by a single impeller into which gas is being fed from a sparge pipe or ring and the formation of gas-filled cavities behind the impeller blades. Indeed, the variation of P , / P o , the ratio of gassed to ungassed power, with the aeration number, N u (Fig. I ) can be directly predicted from the number of large cavities, which is itself a function of N , and the size of the i m ~ e l l e r . ~ . ~

Although the problem is complicated by the bulk flow regimes of flooding and r e c i r ~ u l a t i o n , ~ the study of cavity formation has provided a valuable insight into the fluid mechanics of the sparged, agitated vessel and has helped in the rationalization of calculation procedures for estimating the gassed power drawn by a single im- ~ e l l e r . ~ . ~ However, little data are available for the gassed power drawn by multiple impellers even though these are often used industrially, particularly in fermentors.6

For ungassed conditions the power number for n impellers is approximately n(N,) , where ( N p ) l is the power number of a single impeller, provided the impeller spacing is not less than the impeller diameter.'.* It has been suggested that the relationship between P , / P o and N u obtained for a single impeller may also be used to estimate the gassed power drawn by two or more impellers.6 As part of a recent series of papers by equipment manufacturers, unsupported by references, Hicks and Gatesg adopted a similar approach to the calculation of ungassed power but they indicated that, while the power drawn by the bottom impeller is reduced by gassing as for a single impeller (Fig. I ) , the reduction for the second and subsequent impellers should be related to the gas-liquid density. In other words

( P g / P o ) n = i = f ( N u ) (1)

and

(Pq = ( N p )1pdN3D5 (2 )

where p d is the density of the dispersion, o r

~ P g / P o ) n > , = ( 1 ~ E H ) ( 3 )

where e,, is the gas hold-up. Values of c H are typically less than about 10% for all realistic gassing rates SG that (P,),,, > ( f g ) n = l .

Since no measurements of cavity formation in multiple impeller systems have been reported, it is not possible to relate ( P , / P o ) to Nu and to the number of cavities in these cases. However, P , / P o and the type and number of cavities formed are directly related to the gas flow through the impeller region whether from the sparger or from rec i r~ula t ion . '~~ This note reports data that elucidate the qbove question.

RESULTS

A cylindrical tank (0.56 m diam) containing O.Z%(w/v) NaCl solution to a depth equal to the tank diameter when unaerated, and fitted with two Rushton turbines (each with a diameter f of that of the tank) was used for the present experiments. The lower impeller was placed at f of the liquid height above the base and the upper

Biotechnology and Bioengineering, Vol. XXI, Pp. 2341-2345 ( 1979) @ 1979 John Wiley & Sons, Inc. 0006-3S92/79/0021-2345$01 .OO

2342 BIOTECHNOLOGY AND BIOENGINEERING VOL. XXI (1979)

0 N,- Q / ND'

Qualitative relationship between P , / P o and Q / N D 3 (numerical values Fig. 1. depend on ~ c a l e , ~ , ~ impeller type,4 and flow reg i~ne~ .~ ) .

impeller either at I or 14 impeller diameters above the lower one. The gassed and ungassed power drawn were measured with an accurate air-bearing d y n a m ~ m e t e r . ~ Results for the single impeller system had also been obtained previously giving data for impellers of both f and f of the tank d i a ~ n e t e r . ~ . ~

The ungassed power number for the single impeller (Np)l was 4.9 while that for the two impellers ( N p ) z was found to be 10.2 for both impeller spacings used.

The correlation between P , / P , and N , obtained from this and previous work for single impellers for gassing rates from about 0.15 to 0.76 vlvim (0.36 to 1.76 x mYsec) is shown in Figure 2. Also shown are the predicted curves for P , / P o from cavity formation data3 for impellers of 0.10 and 0.19 m diam. As can be seen, there is reasonable agreement between the predicted values and the two independent sets of experimental data. The accuracy of the experimental measurements and the complexity of the phenomenon do not allow the difference between the two impeller sizes to be detected.

The equivalent data for the double impeller configurations (with each spacing giving identical results) are shown in Figure 3. Clearly, the use of two impellers produces a very different relationship between P u l p o and N , as compared to a single impeller.

DISCUSSION

The results reported here are in good accord with those previously reported7** for ungassed power numbers, i.e., ( N p ) l = 4.9 and ( N p ) z = 10.2 so that ( N p ) z = 2 ( N p ) , . In addition ( N p I z is unaffected by the impeller spacings used: nor do the impeller spacings affect the gassed power drawn.

On the other hand, the quite marked difference in the P u l p o vs. N u plots for single and double impellers clearly invalidates the design method put forward for estimating the gassed power in such cases which suggests that they should be the same.6 Indeed, an underestimation by as much as a factor of 2 could result, i.e., 1 5 ~ P u / P o ~ z / ( P u / f ' ~ ) l 5 2 over the range of N u covered in this work.

To test the other design method,s hold-up values are required. Measurements of hold-up in this vessel have been reported elsewhere,'o.ll and it was found that e H was proportional to (P,)1'3(Q)1'2. In spite of this dependence on power input and gassing rate, for the range of these values examined here e H never exceeded 10%

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0 . 9

0.8 P

'''0 0.7

0.6

0 .5

and was generally less. For any particular agitation speed and gassing rate, the power for the upper impeller is given by

(4) (P,),=z = (PO)l(l - E H )

for the lower impeller by

( P g ) x = t = (Pn)i(Pg/Pn)i (5 1

-

-

-

- -

and for the ungassed condition by

(Po )z = 2(Pn )I

where ( P g / P n ) , and e H correspond to the relevant operating conditions. Rearranging eqs. (4)-(6) gives

Taking e H = 0 and estimating ( P g / P o ) l for any particular value of N and Q (i.e., of N , ) from Figure 2 allows (Pg /Pn)2 to be estimated as shown in Table I and plotted in Figure 3. The agreement between the experimental data and the predicted values seems to indicate that this method of calculation is very satisfactory.

It is interesting to postulate why the power drawn by the second impeller is so large. The presence of gas in the system ensures that gas-tilled cavities will form behind the impeller blades and their type and size for any value of N will depend uniquely2 on the quantity of gas passing through them. Since

( P g ) n = 2 = (P0)l (8)

the amount of gas passing through the upper impeller must be surprisingly small. A

'"1 A B 8

0.4 l I I I I I 1 0 1 2 3 4 5 6

N, lo2

Fig. 2. P g / P n vs. No for a single turbine impeller. Experimental data from Refs. 3 and 5 for D = 0.14 m (v) and D = 0.19 m (0). (A) Data from present work. Curves predicted from cavity formation (Ref. 3) for D = 0.10 m (- . -) and D = 0.19 m (- - -).

2344 BIOTECHNOLOGY AND BIOENGINEERING VOL. XXI (1979)

0.4' ' ' ' ' ' ' ' ' " ' I 0 I 2 3 4 5 6 7 8 9 10 II 12

N, 40'

Fig. 3. Comparison of P,/Pn vs. N , for single and double turbine impellers. Best line from Figure 2 for a single impeller (- . -). Experimental data for double impellers (M). Curve predicted from eq. (7) for double impellers (- - -).

recent paperx2 on recirculation in stirred tanks indicated that the ratio of the gas recirculation rate ( Q R ) to the gas sparge rate ( Q ) was small over quite a wide range of agitator speeds above that which just prevents flooding, and was always less than 0.2 for the N , values covered in this work. If it is assumed that the gas flow that passes directly through the second impeller is approximately Q R , then this might offer a physically acceptable explanation for what is observed, i.e.,

Clearly more work remains to be done if these measurements are to be given a satisfactory explanation. I t would be useful to examine other ratios of impeller and tank diameters and to extend the measurements to fermentation broths. However, now it is important to point out that, of the only two d e s i p procedures recommended for estimating the gassed power requirements for multiple impellers, one seriously underestimates that requirement,6 while the other appears to be sa t i s f a~ to ry .~

TABLE I Estimating ( P g / P o ) z from ( P , , / P , ) ,

(%) *OZ (2), (2)2 3.0 0.66 0.83 4.0 0.56 0.78 5.0 0.52 0.76 X -0.4 0.70

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Nomenclature

impeller diameter (m) number of impellers (dimensionless) impeller rotational speed (sec-') ungassed power number (dimensionless) aeration number (= Q / N D 3 ) (dimensionless) Q R / N D 3 (dimensionless) gassed power (W) ungassed power (W) gas sparge rate (m3/sec) recirculation gas rate (see Ref. 12) (m3/sec) gas hold-up (defined by Refs. 10 and 1 I ) (dimensionless)

P d Subscripts

l , 2 , . . . n = 1, 2, . . .

average density of dispersion (kg/m3)

refer to the effect of the total number of impellers refers to the effect of a particular impeller where n = 1 is the lowest, n = 2 the next, etc.

References

I . A. W. Nienow and D. J. Wisdom, Chem. Eng. Sci., 29, 1043 (1974). 2. W. Bruin, K. van Riet, and J . M. Smith, Trans. Inst . Chem. Eng., 52, 88

(1974). 3. A. W. Nienow and D. J . Wisdom, Institution of Chemical Engineers, 3rd

Annual Research Meeting, Salford, 1976. 4. K. van Riet, J. M. Boom, and J . M. Smith, Trcrns. Inst. Chern. Eng. , 54, 124

(1976). 5. A. W. Nienow, D. J. Wisdom, and J . C. Middleton, Procwdings of the 2nd

G/ropc,rrn C o q f i r e n c ~ on Mixing, Ctrmhridgc, (BHRA, Cranfield, 1978), pp. FI- I-FI- 16.

6. S. Aiba, A. E . Humphrey, and N . F. Millis, Bioc~hc,mic.tr/ Etigi/zc,c~ririg (Aca- demic, New York, 1973).

7. H. Fukuda, Y. Sumino, and T. Kanzaki ,J . Fermcnt. Techno/., 46,838 (1968). 8. H. Taguchi and T. Kimura, J. fc,rmcnt. Tcchnol.. 48, I17 (1970). 9. R. W. Hicks and L. E. Gates, Chem. Eng.. July 19, 141 (1976).

10. V. Machon, A. W. Nienow, J . Vlcek, and J . Solomon, Chrm. Eng. J . , in

I I . A. W. Nienow and V. Machon, Biotcdi /7o/ . B i o e i i ~ . . 21, 1483 (IY7Y). 12. A. W. Nienow, C. Chapman. and J . C . Middleton, C'hc,m. h g . J . . 17, 1 I I

(1979). A. W. NIENOW M. D. LILLY

press.

Department of Chemical and Biochemical Engineering University College London, Torrington Place London, W C l E 7JE, England

Accepted for Publication May 25, 1979