509329

Chemical Engineering Science 55 (2000) 5881}5896

Mixing in large-scale vessels stirred with multiple radial or radial andaxial up-pumping impellers: modelling and measurements

Peter VraH bel!,1, Rob G. J. M. van der Lans!,*, Karel Ch. A. M. Luyben!,Lotte Boon", Alvin W. Nienow"

!Kluyver Laboratory, Department of Biotechnology, Delft University of Technology, Julianalaan 67, 2628 BC Delft, The Netherlands"Centre for Bioprocess Engineering, School of Chemical Engineering, The University of Birmingham, Birmingham B15 2TT, UK

Received 6 October 1999; received in revised form 16 March 2000; accepted 12 June 2000

Abstract

Mixing phenomena are regarded as one of the major factors responsible for the failure to successfully scale up some bioprocesses.Such phenomena have been investigated within the framework of an EC project &Bioprocess Scale-up Strategy'. Mixing in bioreactorsdepends on energy input, impeller type, reactor con"guration and impeller geometry. Here, two di!erent reactors of volumes 12 and30 m3 were used, and they were equipped with either multiple Rushton turbines or with a combination of a Scaba 6SRGT radialimpeller with multiple 3SHP axial up-pumping hydrofoils above it. Mixing time, power consumption, gas hold-up and liquidvelocities were measured at di!erent stirrer speeds and aeration rates in water. At the same total speci"c power input, aeration did notin#uence the mixing time much unless it changed the bulk #ow pattern. A considerable reduction of mixing time was achieved if theupper impellers were axial instead of radial Rushtons at the same power consumption. The improvement with the axial impellerscould be related to the reduction of axial #ow barriers due to di!erent circulation #ow patterns. The Compartment Model Approach(CMA) was used to develop a #ow model based on the general knowledge of the hydrodynamics of both unaerated and aerated stirredvessels. The model was successfully veri"ed for di!erent impeller and reactor con"gurations and di!erent scales with measured pulseresponse curves, using either a #uorescent or a hot water tracer. The model can be used for process design purposes. ( 2000 ElsevierScience Ltd. All rights reserved.

Keywords: Scale-up; Modelling; Stirred bioreactor; Multiple impellers; Up-pumping and radial stirrers

1. Introduction

Highly non-homogeneous temperature and concentra-tion conditions may appear in a fermenter, especially onthe large scale, because of insu$ciently energetic mixing.Variations in concentration may lead to locally limitingsubstrates, excessive pH excursions and/or product inhi-bition. Such concentration #uctuations may in#uence thephysiology of microorganisms, leading to strain degrada-tion and to a decrease of process yield (Bylund, Collet,Enfors & Larsson, 1998). Due to a lack of detailed know-ledge of both #uid dynamics and physiology, scale-up isperhaps more an art rather than an exact science

*Corresponding author. Tel.: #31-15-278-7654; fax: #31-15-278-2355.

E-mail address: [email protected] (R. G. J. M. van der Lans).1Present address: Faculty of Industrial Technologies, The University

of Trenc\ in, 02032 PuH chov, Slovakia.

(Humphrey, 1998). On the other hand, since homogenisa-tion inevitably deteriorates on scale-up (Nienow, 1998),any improvement in this parameter is worth aiming for atthe large scale.

A primary in#uence on a variety of mixing parametersis the choice of impeller type and reactor con"guration.Rushton turbines were introduced many years ago inindustry, mostly because that con"guration was origin-ally considered to have especially good gas dispersioncapabilities (Tatterson, 1991; Nienow, 1998). Compart-mentalization and consequently strong axial #ow bar-riers are associated with such radial #ow impellers,(Cronin, Nienow & Moody, 1994) which limit homogen-eity. Axial down-pumping, wide blade impellers ap-peared to be promising (McFarlane & Nienow, 1996) forgas dispersion and improved axial mixing (Cooke,Middleton & Bush, 1988; Otomo, Bujalski & Nienow,1995). Another aspect favouring such impellers is theirimproved power e$ciencies (low power numbers) and

0009-2509/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 1 7 5 - 5

satisfactory #ow numbers (Jaworski, Nienow, Kou-tsakos, Dyster & Bujalski, 1991). However, down-pumping impellers inevitably give rise to severe torque#uctuations when aerated (Nienow, 1998). Recent workhas suggested that up-pumping hydrofoils have good gasdispersion characteristics (Nienow, 1998), handling largequantities of air without #ooding, signi"cant power lossor severe torque #uctuations; and when used in pairs,give good homogenisation at an aspect ratio of 2(Hari-Prajitno et al., 1998). In addition, radial/axialdown-pumping combinations give improved axial mix-ing compared to Rushtons (Manikowski, Bodemeier,Lubert, Bujalski & Nienow, 1994) and at the small scale,a radial Scaba 6SRGT with up-pumping Scaba 3SHPshas been shown to have good aerated power character-istics (Boon, 2000).

Relevant qualitative and quantitative knowledge of themixing behaviour of multiple axial and radial impellers isan inevitable requirement for creating and verifying #owmodels. Such models should help a process engineer todesign and run the process in an e!ective manner. An-other aspect of #ow models is that they can be used toinclude models of structured microbial kinetics to obtaina more complex and complete picture of the relevantphenomena occurring in a large-scale fermenter (TraK -ga> rdh, 1988, 1993; Kristiansen, 1993). There are two basicapproaches to the development of liquid #ow models: (i)Computational Fluid Dynamics (CFD) and (ii) Compart-ment Model Approach (CMA). CFD is based either onstatistical turbulent studies (k}e models) or on structuralturbulence studies (Large Eddy Simulations) (Tatterson,1991), while CMA is based on gross #ow studies. Thereare still some signi"cant problems with CFD: (i) Under-standing of the behaviour of two-phase #uid #ow is notyet su$ciently developed to solve the equations ofmotion satisfactorily; (ii) CFD calculations need to beveri"ed (Nienow, 1998) but detailed experimental veri"-cation (velocity measurement) at large scale is extremelydi$cult; (iii) demands on computational power are ex-tremely high. Although CFD is expected to be the designtool for the future, it will take some time before it can beused for #ow predictions in large-scale fermenters withbiological media.

CMA was used in this study because of the followingreasons: (i) Compartment models use, a priori, know-ledge from gross-#ow studies as the basis of the modeland do not need detailed understanding of the #uidmotion; (ii) the experimental veri"cation in multi-phasesystems can be done with pulse response techniqueswhich are not particularly di$cult even at large scale;(iii) computational power is not a limiting factor. Al-though this approach might be regarded as rather crudeand simplistic, its results are quite useful (Tatterson,1991).

This paper reports a comparison of radial Rushtonimpellers with a radial/up-pumping combination of

Scaba impellers at the commercial scale, which con"rmsand extends the ideas outlined above concerning thedi!erent impeller characteristics. Homogenization,power characteristics and gas hold-up were measuredand a consistent compartment model was developed andvalidated for both aerated and non-aerated conditions,for di!erent impeller con"gurations, stirrer speeds, aer-ation rates and scales. Because the model is based onhydrodynamic parameters, it can be easily extended andused by a process engineer for design purposes, or forintegration with microbial kinetics.

2. Material and methods

2.1. Production-scale fermenters

Two fermenters were used: 30 m3 (Biocentrum, StatoilStavanger, Norway) and 12 m3 (Pharmacia & UpjohnAB, Sweden). The 12 m3 vessel was equipped with eitherthree, 6-blade Rushton turbines, RT, (Fig. 1A) (Con"g-uration A); or with a 6-blade Scaba radial turbine,6SRGT, (Fig. 1B) combined with two, 3-blade Scabaaxial hydrofoil impellers 3SHP (Fig. 1C) pumping up,(Con"guration B). The 30 m3 vessel had either fourRushton turbines (Con"guration C) or a 6SRGT andthree, 4-blade Scaba hydrofoils 4SHP, pumping up,(Con"guration D). Con"guration A}D are given in detailin Table 1 and a general layout is presented in Fig. 2.More detailed drawings can be found in VraH bel, Van derLans, Cui and Luyben (1999) and Bylund et al. (1998).

2.2. Pulse-response experiments

Tap water was used as the #uid for pulse-responsemeasurements with a #uorescent tracer in con"gurationB}D (Groen, 1994; Cui, Van der Lans, Noorman& Luyben, 1996a; VraH bel et al., 1999). The tracer wasinjected below the liquid surface and detected at theout#ow of the bottom impeller (see Fig. 2). This injectionand detection position gives the maximum response time(VraH bel, Van der Lans, Hoeks & Luyben, 1998) and themixing time at the 95% homogeneity level was deter-mined after processing the response curve (VraH bel et al.,1999). In addition, in the earlier work, three di!erentdetection positions were used (VraH bel et al., 1999). In thatcase, the probe position in Fig. 2 swamped the otherreadings and was most reproducible. Therefore, it wasdecided that, given the di$culties of large-scale experi-mentation, only one detection position should be usedhere. Four repeats were carried out at each operatingcondition and the experimental error was de"ned as themean standard deviation. Standard deviations of allsingle experiments are given in Figs. 9}11 and the mean

experimental standard deviations, SDEXP

are given in

5882 P. Vra& bel et al. / Chemical Engineering Science 55 (2000) 5881}5896

Fig. 1. Radial Rushton turbine, RT (A); Radial Scaba impeller,6SRGT(B); Axial Scaba impeller, 3SHP (C).

Table 3. The absolute values of experimental deviationsare about proportional to the scale: 3 s to 9 s in the 8 to22 m3 cases, respectively.

For reactor con"guration A, mixing experiments wereundertaken using the temperature pulse method (Nagy,1994). The method is described in detail by Mayr, Nagy,Horvat and Moser (1994). In this case, the detection wasmade simultaneously at eight di!erent reactor locations.

The mixing time was derived from the average of all eightmultiple responses, processed on the basis of an `in-homogeneitya curve (Mayr et al., 1994). Data from thatstudy are also included here.

2.3. Overall gas hold-up

Gas hold-up was estimated from the di!erence of dis-persion level of an aerated and a non-aerated reactor.

2.4. Power measurement

The electrical power supplied to the agitator motorwas measured using a Fluke 41B Power HarmonicsAnalyser and converted to mechanical power, P, trans-mitted to the #uid. All measurements constitute an aver-age of 100 samples taken at 10 s intervals. Calibration ofthe electric power measurement is based on the thermaldata of Noorman et al. (1993). The speci"c power inputdue to the air #ow, gvc

Gs, is the second relevant compon-

ent of the total speci"c power contribution to the liquidin an aerated mixed vessel, e

T(Groen, 1994) so that the

total mean speci"c power is given by

eT"

PG

mL

#gvcGs

. (1)

Here PG

is the mechanical power consumption of theimpellers under aeration, m

Lis the mass of liquid and

vcGs

is the super"cial gas velocity averaged over axialliquid depth. It is calculated from a barometric gas #owrate measured by a mass #ow controller (Heijnen, Hols,van der Lans, Leeuwen & Weltevrede, 1997).

2.5. Liquid velocity measurements

An electromagnetic probe (the 3-Axis ElectromagneticCurrent Meter ACM-300; Alec Electronics Co., Ltd, Ja-pan) was used to measure velocities in three directions.Measurement position: 22 cm below the dispersion sur-face, 20 cm from the reactor wall (Fig. 2). The probe isbased on Faraday's law: a conductive medium #owingthrough a magnetic "eld induces a voltage di!erence,which is proportional to the velocity of the medium. Theadvantage of this probe is that it works equally wellunder both unaerated and aerated conditions. The disad-vantage is that it is quite large, i.e. the measurementvolume was spherical with a diameter of 6 cm. It also hada limited frequency response, the highest possible fre-quency of measurement being 50 Hz. Both average, u6 ,and, in spite of the inherent limitations, root mean square(r.m.s.) velocities, u, were obtained from the recordedsignal. Though clearly, the r.m.s. velocities were notstrictly equivalent to those obtained by LDA, they wereutilised for assessment of axial turbulent intensities in thebulk region. This usage is discussed later in this paper.

P. Vra& bel et al. / Chemical Engineering Science 55 (2000) 5881}5896 5883

Table 1Geometry of studied reactor con"gurations. Ba%e width B

W"0.08¹; Rushton blade height D

H"0.20D and blade width D

W"0.25D; For

explanation of primary and secondary loops, see Fig. 3

Con"guration A B C! D(RT/12 m3) (Scaba/12 m3) (RT/30 m3) (Scaba/30 m3)

NI

3 3 4 4¹ (m) 1.876 1.876 2.09 2.09<

L(m3) 8 8 22 22

Bottom impeller (D) RT (0.41¹) 6SRGT (0.56¹) RT (0.33¹) 6SRGT (0.45¹)Upper impellers (D) RT (0.41¹) 3SHP (0.61¹) RT (0.33¹) 4SHP (0.50¹)H

L1.59¹ 1.59¹ 3.13¹ 3.13¹

CB

0.30¹ 0.30¹ 0.55¹ 0.55¹C

I0.45¹ 0.45¹ 0.70¹ 0.70¹

No. of primary loops 3]2 2#2]1 4]2 2#3]1No. of secondary loops 1" 1" 1" 1"#2

!See also VraH bel et al. (1999)."Secondary loop in the top of the reactor.

Fig. 2. Fermenter con"guration for mixing experiments. Injection anddetection locations for tracer and position velocity probe indicated. Seefurther Table 1.

3. Model

3.1. Global yow pattern of radial impellers

Compartment modelling is based on knowledge of theglobal #ow pattern (Mann & Hackett, 1988; Reuss

& Jenne, 1993). Flow patterns with multiple radial tur-bine impellers have been obtained in many studies forboth non-aerated and aerated reactors e.g., Hudcova,Machon and Nienow (1989); Rous\ ar and Van den Akker(1994) and have been discussed in detail in a previouspaper (VraH bel et al., 1999). In short, the #ow structurecreated by a disc turbine in a ba%ed vessel consists of twocirculation loops, one in the upward and one in thedownward direction. The #ow pattern depicted in Fig. 3(left-hand side) is an accurate diagrammatic representa-tion if the impeller clearance is larger than 1.2}1.5 timesthe impeller diameter (Hudcova et al., 1989; Cronin et al.,1994; Cui, van der Lans & Luyben, 1996b). Moreover,a secondary vortex maintaining a minimal macromixingwas detected in the uppermost region of the reactor usingthe LDV technique (SchaK fer, Hofken & Durst, 1997). Inaddition to these mean circulation loops, axial turbulentliquid exchange occurs in the reactor.

If the system is aerated (Fig. 3A right-hand side), anadditional steady liquid stream appears, which connectsadjacent impeller zones, and a secondary circulatoryliquid cell in the top of the reactor is observed (Rous\ ar& Van den Akker, 1994). Therefore, three #ows (circula-tion, exchange of liquid and induced #ow by aeration)should be taken into account in order to model themixing phenomena in a multiple impeller system witha compartment model.

3.2. Global yow pattern of axial up-pumping impellers

The main circulation pattern involving axial up-pump-ing hydrofoils were described recently, based on LDAmeasurements of single impellers (Mishra, Dyster,Jaworski, Nienow & McKemmie, 1998) and CFD predic-tions with single and multiple impellers under unaeratedconditions (Jaworski et al., 1998). In addition, visual


Fig. 3. Schematic representation of global #ow pattern for (A) multipleRushton con"guration and (B) multiple Scaba con"guration (bottomradial 6SRGT and upper axial (3SHP or 4SHP) up-pumping impellers).Situation of a non-aerated and an aerated reactor is depicted on the leftand right side of the reactors, respectively. Solid lines: circulation #owCF (thin lines: secondary circulation #ow SCF); dashed lines: gasinduced #ow IF. Axial exchange #ow EF not shown.

observation of #ow patterns with single, dual and tripleup-pumping impellers under both aerated and unaeratedconditions have been made (Hari-Prajitno et al., 1998).For a single impeller, the #ow consists of (i) a dominantloop going up at about 453 to the vertical, continuingtowards the tank wall and down along the wall beforerecirculating back to the impeller with the eye of the loopbelow the impeller; (ii) a secondary smaller loop going upwith the main loop but then continuing "rstly up the walland then in towards the shaft and back down to theimpeller (Mishra et al., 1998). If more impellers are used,the secondary loops create a transition between contra-acting primary loops (Hari-Prajitno et al., 1998) in a sim-ilar way to that found with downpumping hydrofoils(Manikowski et al., 1994; Mavros and Badou, 1997).

A simpli"ed scheme of these #ows is depicted inFig. 3B, which is close to the con"guration of combina-tion B. In reality, the upper secondary loop is positionedcloser to the primary loop and the shape of both are moreelliptical (Hari-Prajitno et al., 1998). However, CMAcannot handle such detailed phenomena. Therefore, therepresentation of Fig. 3B is a suitable simpli"cation. The

signi"cance of the secondary loop increases with increas-ing clearance between the impellers, C

I. At C

I"0.6¹,

the secondary loop is less pronounced than at CI"0.8¹

(Hari-Prajitno et al., 1998) as it is with dual down pump-ing impellers (Mavros & Badou, 1997); and the mixingtime has been shown to be shorter when the secondaryloop is missing (Hari-Prajitno et al., 1998). Therefore, inthe case of C

I"0.6¹, secondary circulation loops were

assumed to be negligible. In addition, secondary loopswere not observed between the radial and the bottomaxial up-pumping impeller, probably because the respect-ive primary loops are co-current where they meet (suchan e!ect with co-current loops has also been found withup/down-pumping hydrofoil combinations (Hari-Prajitno et al., 1998)). Fig. 3B shows the proposed #owstructure showing the existence of secondary loops fora reactor con"guration with high impeller clearance(equivalent to con"guration D), though with only 3impellers.

Finally, for these di!erent circulation #ow patterns,the same concept of two additional #ows with con"g-urations B and D was used as in the case of Rushtonturbines, i.e., (i) axial turbulent exchange; and (ii) aliquid stream induced by the air when the system isaerated.

The exact number of primary and secondary loops forall four impeller con"gurations is given in Table 1.

3.3. Physical structure of the model

3.3.1. Radial yow Rushton impellersThe physical model for the radial #ow Rushton impel-

lers has already been developed, being published "rst in1996 (Cui, van der Lans, Noorman & Luyben, 1996a),and recently extended (VraH bel et al., 1998, 1999). There-fore it will only brie#y be outlined here in order to setthose earlier papers into the context of the present workand to show how it can be extended to the axial/radialcombination.

The most important region that has to be modelled isthe impeller region. The complexity depends on the pur-pose of the model and it has to be stressed that thenumber of compartments and the magnitude of the #owsare related variables in compartment modelling. Ideally,real #ow parameters such as circulation, exchange andinduced #ow rates should be used when applying thistype of model in order to maximise the connection withphysical reality. Therefore, the number of compartmentsis a dependent variable. Three layers of compartmentsper impeller region was found to be suitable to model the#ow structure observed in a vessel mixed by radial impel-lers. In addition, sensitivity analysis (Cui et al., 1996a;VraH bel et al., 1999) showed that the use of 15 compart-ments per impeller region was su$cient to model over-shoot response curves. Therefore, this number wasadopted here and is depicted in Fig. 4A.


Fig. 4. Axi-symmetric compartment structures: (A) top radial impellerand secondary circulation loop in the top of the reactor; (B) axialpumping-up impeller and secondary circulation between adjacent axialimpellers. The axis of symmetry is at the left side of the "gure. Forsymbols see Fig. 3.

Experimentally, the Rushtons were studied in two con-"gurations, A and C (see Table 1) with three and fourturbines at 12 and 30 m3, respectively. According to theglobal #ow pattern, one impeller produces two circula-

tion liquid loops (Cui et al., 1996a). The region Hlin Fig.

4A corresponds to any one of the impellers on Fig. 3A.Under aerated conditions, the loops are modelled asideal mixed tanks-in-series with axial exchange and eachloop is expressed as the sum of a circulation #ow, CF(mechanical power) and as a result of density di!erences,gas induced #ow IF (pneumatic power). The volumes ofthe compartments in one row are taken as equal. With-out aeration, no IF mean #ow is observed and the zonesare separated (Rous\ ar & Van den Akker, 1994). Thesetwo #ows are modelled as one-way #ows only. However,axial turbulent exchange #ows between compartments inthe axial direction also occur (EF). These are not one-directional #ows but occur within the impeller zone andbetween the zones as long as the #ow layers contacteach other. This axial turbulent exchange plays an im-portant role in this kind of compartment modelling andcannot be equivalently replaced by radial back-mixing orby changing the number of tanks in series (Cui et al.,1996a).

The secondary vortex in the uppermost part of thereactor in Fig. 3A was modelled as a circulation loopconsisting of secondary circulation #ow, SCF, and in-duced #ow, IF plus an exchange #ow EF (the upper partof Fig. 4A). The secondary circulation #ow, SCF, shouldhave a lower value then the primary circulation #ow,CF/2, but higher than the exchange #ow due to turbu-lence, EF. It was shown previously (VraH bel et al., 1998),that EF values in this region are very similar for bothaerated and non-aerated systems and, therefore, thenon-aerated values of EF were used for the secondarycirculation #ows.

Considering Figs. 3A and 4A in more detail, Fig. 4A isan axi-symmetric picture of the impeller region with 15compartments and the secondary circulation loop in thetop of the reactor with 10 compartments. The reactorshaft is the axis of symmetry and the whole of Fig. 4Acorresponds to the #ow pattern in the upper right quarterof Fig. 3A. If more impellers are present, each is modelledas being equivalent to the height H

lin Fig. 4A. Thus,

following this structure, the reactors of con"gurationA and C from Table 1 were modelled with 3]15#10and 4]15#10 compartments, respectively. Because ofaeration, the total volume under consideration varied asthe hold-up changed. The geometrical size of the com-partments in the impeller regions was kept constant, butthe size of the ten compartments in the top zone waschanged to allow for the enhanced hold-up. However, theamount of liquid in each compartment was also adjusted(reduced) in proportion to the overall hold-up.

3.3.2. Scaba conxgurationThe same concept was used as in the case of Rushton

turbines. The di!erences in the compartments (Fig. 4B)follow only from the di!erence in global #ow structure asshown in Fig. 3B based on the work of Hari-Prajitno


et al. (1998) and Boon (2000): (i) there is only one primarycirculation loop per upward pumping impeller; (ii) thereis a secondary circulation #ow (SCF) in the top of thevessel; (iii) secondary circulation #ows also exist betweenimpeller zones for con"guration D where the impellerspacing was large (C

I"0.7¹) (and as with the Rushtons',

the value of SCF was taken as equal to EF) but withouta secondary #ow for con"guration B (C

I"0.45¹); (iv)

a stagnant zone (one layer of compartments) with axialexchange #ows only was introduced between the radialimpeller and the axial up-pumping impeller immediatelyabove it, thereby maintaining roughly uniform size com-partments throughout the reactor.

The main circulation loop was expressed by a series of12 ideally mixed compartments connected with circula-tion #ow, CF, and induced #ows, IF (Fig. 4B). In contrastto radial impellers (Fig. 4A), the three compartmentsinside the circulation loop are connected to the neigh-bouring compartments only by axial exchange #ow, EF(Fig. 4B). This #ow structure resulted from the di!erent#ow pattern of axial and radial impellers and a sensitivityanalysis (Cui et al., 1996a; VraH bel et al., 1999) showed that15 compartments per impeller region is suitable for mod-elling axial impellers as well as radial.

Therefore, according to the above analysis, the bio-reactor of con"guration B was modelled with 3 (12#3)compartments for the impeller zone (lower part of Fig.4B), 5 compartments for the stagnant region between theradial and lower axial impeller and 10 for the top second-ary circulation loop (Fig. 4B). For con"guration D, thereare 4]15 impeller compartments, 2]10 between axialimpellers and 1]10 top of vessel secondary circulationdrops and 5 radial/axial stagnant loops. The volume ofthe ten compartments in the top zone was adjusted toaccommodate the hold-up when the system was aerated,as described for the Rushton turbines.

3.4. Determination of parameters

Four parameters are required in the model to describethe #ow phenomena; the number of compartments andthree main #ow parameters, circulation #ow rate, CF,exchange #ow rate, EF, and induced #ow rate, IF. All ofthem can be derived from the present knowledge of thehydrodynamics (VraH bel et al., 1999). Non-aerated sys-tems are regarded as a special case of aeration with gas#ow equal to zero and P

G/P equal to 1. Application to

the Rushton turbine con"guration and parameter sensi-tivity analysis has been presented previously (VraH belet al., 1999) and, therefore, they are only brie#y sum-marised here.

3.4.1. Circulation yowCirculation #ow, CF, is determined from the liquid

discharge #ow (pumping capacity) of the impeller(TraK ga> rdh, 1988; Rous\ ar & Van den Akker, 1994; Vas-

concelos, Alves, Nienow & Bujalski, 1998):

CFG"A

PG

P BbK

CND3 (2)

where CFG

is the circulation #ow under gassed condi-tions, N the stirrer speed, D the impeller diameter, andP and P

Gthe impeller power consumption under non-

gassed and gassed conditions, respectively; b, determinedby the LDA method, has a value of 0.34 (Rous\ ar & Vanden Akker, 1994). The discharge #ow of Rushton tur-bines, Q

L, is de"ned as the integral of the velocities just

over the blade height (Van 't Riet & Tramper, 1991;Nienow, 1998) through the area swept by the blade tip. Inthe case of axial up-pumping impellers, Q

Lis the volume

#ow rate through the swept circle directly above theupper edge of the impeller (Jaworski et al., 1991; Mavros,Xuereb & Bertrand, 1996; Nienow, 1997, 1998). Thecirculation #ow is usually expressed using the typicalhydrodynamic parameter, impeller #ow number,Fl ("Q

L/ND3). However, a complete circulation #ow

should take into account entrained #ow out of the impel-ler blade (F

E-factor) (Nienow, 1997, 1998). Because CF is

considered constant in the whole circulation loop, theaverage circulation rate in the whole path is used (F

A-

factor). Therefore, for each geometry, KC"F

A]F

E]Fl

and the actual value of the parameters used are given inTable 2. Table 2 also shows that in certain cases, valuesfor the precise geometry under study are not available inthe literature. Therefore, data from the closest equivalentcon"gurations were employed. Assessment of the sensi-tivity of these choices (data not shown) indicated that themodel predictions are not very sensitive with respect tothese parameters.

Eq. (2) allows modelling of the whole agitation systemprovided the drop of mechanical power (P

G/P) for di!er-

ent agitation and aeration rates for each impeller withindi!erent impeller combinations is known. For Rushtonturbines, separate correlations for the bottom impeller(Cui et al., 1996b) and upper impellers (Abrardi, Rovero,Sicardi, Baldi & Conti, 1988) were utilised. For Scabaimpellers, the present measurements were used (Fig. 5), asdiscussed later.

3.4.2. Exchange yowThe exchange #ow rate EF can be considered to be a

result of the #ow induced by turbulence through the tankcross-sectional area. Under unaerated conditions, Vascon-celos et al. (1995) and Otomo et al. (1995) have shown

EFU"K

END3. (3)

Thus, this #ow can be considered to be related to theimpeller pumping capacity. Vasconcelos, Alves andBarata (1995) suggested that K

E"0.236 ¹/D for Rush-

ton turbines and Otomo et al. (1995) found KE"0.4 for

a 0.5¹ Rushton turbine.


Table 2Characteristics of impellers used in mixing experiments

RT 6SRGT 3SHP/4SHP

Po 5.8! 1.5! 0.65!

Fl 0.75 (Revill, 1982) 0.56! 0.66!

FA

0.8 (Cui et al., 1996a) 0.8" 0.7#

FE

2.0 2.0 (Nienow, 1998) 2.0" 1.3$

KE

KE"0.236 ¹/D K

E"0.236 ¹/D Eq. (14)

(Vasconcelos et al., 1995) (Vasconcelos et al., 1995)

!Po based on power measurement undertaken in co-operation with Scaba AB, Sweden and Fl values provided by them."Since both are radial #ow agitators, assumed equal to Rushton turbines.#Assume equal to the axial averaged value for a PBD impeller (from Fig. 7, Jaworski et al., 1991).$Assumed equal to the value for an axial Lightnin A 310 impeller (from Table 2, Mavros et al., 1996).

This #ow can also be considered to be due to thevertical r.m.s. turbulent #uctuating velocity, u@

z, which

has been measured for some systems. Thus,

EF"u@z(p¹2/4) (4)

where p¹2/4 is the cross-sectional area through whichthe exchange #ow passes. Since the turbulent #uctuatingcomponent can be made dimensionless to give

u@z,3%-

"u@z/pND (5)

then

EF"u@z,3%-

(p2¹2/4)ND. (6)

For axial impellers in the bulk region away from theimpeller, Jaworski et al. (1991) showed that u@

z,3%-"0.05

and velocity measurements made here in the bulk withthe magnetic probe give similar values (see later underResults and Discussion (Fig. 12)).

A third approach may also be used, based on Kol-mogoro!'s theory of isotropic turbulence. The r.m.s. #uc-tuating velocity of the energy containing eddies, u@(Davies, 1972) is given by

u@"(eTle)1@3 (7)

where eT

is the speci"c energy dissipation rate (W/kg)and l

eis the length of the energy containing eddies for

which a value of 0.08D has been suggested (Davies, 1972).For unaerated conditions,

P"Po oN3D5 (8)

and therefore

eT"e

T,U"A

4Po N3D5

p¹2HiB (9)

for multiple impeller systems where Hi

is the impellerspacing. For aerated systems, the energy dissipation as-sociated wtih gas #ow must also be considered (Groen,1994) as well as the change in power compared to theunaerated case, (P

G/P), and the hold-up of the gas, e.

Thus, the total mean speci"c power is

eT"(P

G/P)

eT,U

(1!e)#gvc

Gs(10)

where vcGs

is super"cial gas velocity (based on the volume#ow rate averaged over the liquid depth allowing for thestatic head). Substituting Eq. (10) in Eq. (7) and sincethere is also gas hold-up so that the area available for#ow is (p/4)¹2(1!e) and assuming u@

z"au@ (Cui et al.,

1996a; VraH bel et al., 1999), then from Eq. (4) after suitablemanipulation,

EFG"0.34a¹2D1@3(1!e)C

(PG/P)Po N3D5

(p/4)¹2Hi(1!e)

#gvcGsD

1@3. (11)

For the unaerated case, vcGs"0, e"0 and P

G/P"1, so

that

EFU"0.367a Po1@3A

Hi

D B~1@3

A¹

DB4@3

ND3. (12)

By inspection with Eq. (3), it can therefore be seen thatthis approach suggests

KE"0.367a Po1@3A

Hi

D B~1@3

A¹

DB4@3

. (13)

Thus, since for Rushton turbines (Vasconcelos et al.,1995), K

E"0.236 ¹/D, a can be determined knowing

the geometry and Po. For the Rushton turbines forcon"guration A and C, these parameters in Table 1 givea values of 0.294 and 0.315, respectively (VraH bel et al.,1999). Since for axial impellers, a K

Ecorrelation was not

available, KE

was obtained by combining Eqs. (3)}(5) togive

KE"

u@z,3%-4 A

p¹

D B2

(14)


Fig. 5. Measured power reduction in tap water due to aeration fordi!erent con"gurations (Table 1) and at di!erent stirrer speeds asfunction of the gas #ow number. Filled symbols: Scaba/12 m3 reactor(con"guration B); open symbols: Scaba/30 m3 (D). Open circles:RT/30 m3 (C).

and thus a could again be determined. Finally, with theappropriate values of a for the system geometry (A}D)and #ow regime, Eq. (11) or Eq. (12) was used to calculateEF. Overall, since 5 compartments are used at any level,EF in Fig. 4 is equal to EF from Eq. (11) or Eq. (12)divided by 5 for each con"guration.

3.4.3. Secondary circulation yow (SCF )This #ow was taken as equal to the exchange #ow

under unaerated conditions, Eq. (12), as discussed earlierin the paper and in accordance with previous work onRushton turbines (VraH bel et al., 1999).

3.4.4. Induced yowThe induced #ow rate, IF, due to aeration, is depen-

dent upon the aeration intensity and impeller pumpingcapacity under aerated conditions [Eq. (2)] (Vasconceloset al., 1995; VraH bel et al., 1999). Thus,

IF"kAX

"

QG

APG

P BbND3

(15)

where QG

is the sparged gas #ow rate. Instead of a valueof b"1 as proposed by Vasconcelos et al. (1995, 1998), inorder to be consistent with Eq. (2), the value of 0.34 wasadopted. However, this coe$cient has a very small e!ecton model prediction. k

AXbalances the important e!ects

of aeration and pumping and it has to be estimated froma comparison of predicted and measured values of mix-ing time for each reactor/impeller con"guration.

For Rushton turbines, a geometry-independent cor-relation was reported (Vasconcelos et al., 1995):

kAX

"vAX

A[1!(D/¹)2]~4.75 (16)

where A is the cross-sectional area of the gap betweenturbines and tank wall. v

AXis a parameter with the

dimension of velocity also found to be geometry indepen-dent with a mean value of 0.066 m s~1 (Vasconcelos etal., 1995) though more recently, a value of 0.07 m s~1 wasrecommended based on work with multiple Rushtonturbines at di!erent scales up to 600 L (Vasconcelos et al.,1998). Therefore, this parameter might be regarded asscale independent in the investigated range of volumes.Eq. (16) was originally derived for Rushton turbines butit was also used here for the Scaba impellers.

4. Results and discussion

4.1. Power measurement

It is known from previous measurements with Rushtonturbines (Hudcova et al., 1989; Tatterson, 1991; Cui et al.,1996b) that there is a considerable reduction of mechan-ical power consumption at higher aeration rates. Ratio ofgassed to ungassed power, P

G/P, can have values as low

as 0.4 at higher gas #ow numbers. A similar result wasfound here (Fig. 5) for con"guration C.

For hollow type radial #ow impellers such as Scaba6SRGT, the fall in power is generally negligible for speci-"c energy dissipation rates of the order used here (Saito,Nienow, Chatwin & Moore, 1992). A similar result hasrecently been found when using wide-blade, up-pumpinghydrofoil impellers (Hari-Prajitno et al., 1998). The re-sults for the radial/up-pumping axial combination isshown in Fig. 5. The fall in power is much less than withthe Rushtons. However, since it is reasonable to assumethat the fall with the 6SRGT is negligible (P

g/P"1),

most of the fall must be attributed to the 3SHP and4SHP impellers. This fall would probably be reduced ifwider blades were used.

There are several correlations of PG/P for single Rush-

ton impellers (e.g., Hughmark, 1980; Cui et al., 1996b),but few for multiple impeller systems (Nienow & Lilly,1979; Abrardi et al., 1988). Here, for Rushton turbines,the correlation of Cui et al. (1996b) was used for thebottom impeller and that of Abrardi et al. (1988) for theothers. For the Scaba con"gurations, the measuredvalues were used assuming: P

G/P"1 for Scaba 6SRGT

(Saito et al., 1992) and that, as for Rushton turbines(Abrardi et al., 1988), the fall on the upper SHP hydro-foils was evenly distributed i.e., P

G/P was the same for

each SHP to give overall PG/P values in Fig. 5.

4.2. Gas hold-up

Fig. 6 gives gas hold-up data for both the Scaba andRushton impeller con"gurations in the 30 m3 reactor at


Fig. 6. Gas hold-up data at di!erent characteristic (axial averaged)super"cial gas velocities as a function of power input measured in10 kg m~3 NACl solution for Scaba (con"guration D) and Rushtonturbines (con"guration C) in the 30 m3 reactor. Solid lines represent gashold-up correlation according to Eq. (17).

Fig. 7. Mixing time versus total (mechanical and pneumatic) speci"cpower input for both aerated and non-aerated reactors of con"gura-tions B}D. Open and closed symbols depict aerated and non-aeratedexperimental data, respectively. Lines represent correlation of mixingtime versus total speci"c power input to the power of minus 1/3(Corrsin, 1964; Nienow, 1997; Cooke et al., 1988).

the same characteristic super"cial gas velocity and mech-anical power consumption of the impellers. Though thedata are somewhat limited, Fig. 6 shows that equal gashold-up was obtained under these conditions for eachimpeller type. Others, e.g. Whitton and Nienow (1993),reported similar results to Fig. 6 when radial impellerswere used in two geometrically similar vessels of di!erentscale. This present result provides further support, there-fore, to the concept that the gas hold-up is not generallyin#uenced by the impeller type at equal vc

GSand speci"c

energy dissipation rate (Nienow, 1998).The data in Fig. 6 are best correlated by the equation:

e"0.37(PG/<)0.16(vc

Gs)0.55. (17)

The exponents in Eq. (17) on (PG/<) and (vc

GS) are very

similar to those published previously (0.13 and 0.55,respectively) by Nienow, Buckland and Hunt (1994).These latter exponents were based on experimental dataobtained in 14 m3 bioreactors agitated by either multipleRushton turbines or multiple wide-blade hydrofoil Light-nin' A315 or Prochem Max#o T impellers pumpingdownwards. Most of the literature is based on work ona much smaller scale, with single impellers in vessels ofaspect ratio 1 at a lower super"cial gas velocity. A typicalcorrelation for such conditions gives exponents +1/3and +2/3, respectively, in Eq. (17) (see, for example,Van 't Riet & Tramper, 1991). The present results andthose of Nienow et al. (1994) would suggest that quitedi!erent functionalities between (P

G/<) and (vc

GS) and

hold-up apply at the large scale, at least when multipleimpellers are used. At present, the reason for the di!er-ence is not clear.

Given this di!erence between large-scale and small-scale results and the fact that hold-up is very sensitive tochemical composition (Martin, McFarlane & Nienow,1994), it was decided that though there are many gashold-up correlations available in literature for single im-pellers (e.g., Tatterson, 1991; Van 't Riet & Tramper,1991), for the CMA calculations, the experimentalmeasurements would be used.

4.3. Mixing

The mixing time data are shown in Figs. 7}11. Thedata cover all four con"gurations, both unaerated andaerated and the results are expressed both in terms of thegas #ow number and total speci"c energy dissipation rate(including the pneumatic contribution according to Eq.(1)). These results will now be discussed, in terms of theirrelationship to the literature covering a comparison ofimpeller types and scale-up to the present modelling.

4.3.1. The impact of scale, impeller type and specixcenergy dissipation rate

Nienow (1997) has shown based on turbulence theory(Corrsin, 1964) that, with single impellers, the mixingtime is independent of the impeller type and can becalculated from

hm"5.9¹2@3(e

T)~1@3(D/¹)~1@3. (18)

Cooke et al. (1988) found a similar expression for dualimpeller systems, though h

mwas correlated in terms of


Fig. 8. Mixing time in all non-aerated reactors versus speci"c powerconsumption. Open symbols depict experimental data of 95% mixingtime (Con"gurations B}D) and "lled symbols depict 80% mixing time(Con"guration A) (Nagy, 1994). Solid lines represent CMA predictionof 95% mixing time and dashed line prediction of 80% mixing time.

Fig. 9. Mixing time (80% homogeneity) for reactor con"guration A.Symbols: measurements; Lines: CMA predictions. For calculation ofthe induced #ow, the value of k

AX"0.36 was estimated form Eq. (16)

(Vasconcelos et al., 1995).

Fig. 10. Mixing time (95%) for reactor con"guration B. Symbols:measurements; Lines: CMA predictions. For calculation of the induced#ow, the value of k

AX"1.1 was estimated from Eq. (16) (Vasconcelos et

al., 1995).

Fig. 11. Mixing time (95%) for reactor con"guration D. Symbols:measurements; Lines: CMA predictions. For calculation of the induced#ow, the value of k

AX"13.1 was obtained by optimization.

the power number, whether aerated or unaerated. Thus,for Rushton turbines

hm"3.3Po~1@3

GN~1A

H

DB2.43

. (19)

Eqs. (18) and (19) did not take into account the contribu-tion of pneumatic power, probably because in the work

which led to them, the contribution was rather small. Theform of Eq. (19) was also found to apply to down-pumping axial #ow impellers but the time was typicallyreduced by a factor of 2. Recent work by Otomo et al.(1995) found results that broadly "t in with the "ndings ofCooke et al. (1988); and Hari-Prajitno et al. (1988) alsoobtained similar reductions when comparing dualup-pumping, wide blade hydrofoils to dual Rushtonturbines.


Fig. 12. Measured rms velocities in axial direction, u@z, in the non-

aerated 30 m3 reactors of con"gurations C ("lled symbols) andD (axial/radial) (open symbols) in a bulk region. The values of averagedrelative #uctuation velocity, u@

z,3%-, ("u@

z/pND) for con"gurations C and

D are 0.047$0.002 and 0.049$0.004.

Fig. 7 shows that in the 30 m3 fermenter, the mixingtime under unaerated and aerated conditions with fourRushton turbines and the Scaba axial/radial combina-tions are both proportional to e~1@3

T. In addition, through

the increased diameter of the Scaba impellers should leadto a reduction h

mof +10% on the basis of Eq. (18), from

the experiments hm

for the four radial impellers is ap-proximately twice as large as h

mfor the axial/radial

combination. Cooke et al. (1988), Otomo et al. (1995) andHari-Prajitno et al. (1998) all ascribed this reduction inmixing time to the loss of zoning as indicated in thechange from Fig. 3A to Fig. 3B as shown here.

From Eq. (19), the reduction in mixing time due to thechange from 4 impellers in the 30 m3 to 3 impellers at the12 m3 can be considered as being due to the change infermenter diameter, i.e. (2.09/1.876)2@3 which is close to 1,and in height, i.e., (3.13/1.59)2.43+5. Thus, the calcu-lation would suggest a 5 fold reduction in h

mrather than

4 fold seen in Fig. 7. Clearly, Eqs. (18) and (19) cannot beextended inde"nitely and the present work also suggeststhat pneumatic power should be included. On the otherhand, they show the trends well and highlight the impor-tance of height compared to diameter of fermenter. Fig.8 shows only the unaerated data plotted with h

mon

linear co-ordinates (hm&1/N) plus experimental data

based on 80% mixing time for con"guration A. If thistime is increased using the present model (CMA predictsthe response of the whole pulse experiment (VraH bel et al.,1999)) to give the 95% mixing time, then all the data "t inquite well with the trends in Fig. 7.

Overall, the improvement in mixing is mostly due tothe reduction in the amount of zoning (or axial barriers(Groen, 1994)). However, it is also worth noting thatimproved mixing would also be achieved by enhancedturbulent exchange. Axial #uctuating velocities weremeasured in the bulk using the magnetic probe (Fig. 12)and the relative axial velocities for both impellers,u@Z,3%-

("u@Z/pND), were +0.05. Surprisingly, this value is

in good agreement with that found by Jaworski et al.(1991) for axial #ow impellers based on LDA measure-ments, since LDA measures to a much "ner scale andhigher frequency. Nevertheless, because of the larger dia-meter, the absolute axial #uctuating velocities u@

zwere

25% higher at the same speci"c energy dissipation rate incon"guration D in the region of the axial Scaba impellersthan in con"guration C with the Rushton turbines. Thisenhancement in u@

zalso contributes somewhat to the

predicted shorter mixing time through Eq. (4).

4.3.2. The ewect of aerationFig. 7 shows that aeration did not in#uence the mixing

time much at the same speci"c power input. Figs. 9}11show the e!ect of aeration on mixing time in more detail,plotting h

mversus Fl

G"(Q

G/ND3) at constant stirrer

speed for con"gurations A, B and D. Also, as discussedlater, predictions from the modelling are included. The

trends regarding the e!ects of aeration, which are in-dicated in these plots, are lost when the data are plottedagainst total speci"c energy dissipation rate (Fig. 7).

With the Rushton turbines in con"guration A (Fig. 9),aeration did not in#uence the mixing time much, if #ood-ing of the reactor was prevented (data not shown). Thereseem to be two important factors explaining this phe-nomenon: (i) a minimal change of the total power input(mechanical plus pneumatic) and (ii) the particular #owstructures. The drop in power with the Rushton turbinesunder aeration (Fig. 5) which would perhaps tend toincrease h

mis more or less compensated for by the in-

duced liquid #ow from aeration (Rous\ ar & Van denAkker, 1994; Vasconcelos et al., 1995; VraH bel et al., 1999).Thus, overall, there is in a minimal change of the qualityof mixing. Similar results were shown previously for the30 m3 vessel with four Rushtons (con"gurations C)(VraH bel et al., 1999) where a slight maximum in mixingtime with increasing aeration intensity was found. In thatcase, at low gas #ow numbers, the reduction in mechan-ical power is larger than the increase in pneumatic power.At higher aeration rates, the pneumatic component be-comes more important and compensates for the lossof mechanical power. A small maximum can also beobserved in the 12 m3 reactor with 3 Rushton turbines(Fig. 9).

The power consumption of the combination of Scabaimpellers is less dependent on aeration than that of theRushtons (Fig. 5). Again, the gas-induced liquid #owcompensates for this smaller drop of mechanical powerconsumption, resulting in a minor change of mixingquality for con"guration B (Fig. 10). (It should also be


noted that the gas #ow numbers are smaller in Fig. 10than in Fig. 9 mainly due to the e!ect of D3 (where anarithmetic mean of the impeller diameters was used)).However, in the case of three axial pumping-up and oneradial impeller in the 30 m3 vessel (con"guration D), thereduction in mixing time on aeration was considerable at75 rpm (Fig. 11). In this case, where the mechanical powerinput is low, aeration produced a 35% increase in thetotal power input, when the non-aerated and aeratedsystem at Fl

G"0.03 are compared. Since h

m&(e

T)~1@3

from turbulence theory (Corrsin, 1964; Groen, 1994;Nienow, 1997), only an 11% decrease of mixing is pre-dicted whilst a 20% decrease was observed (Fig. 9). Thisdecrease, therefore, is probably caused by a change of#ow pattern under these conditions. In particular, thezoning associated with the secondary circulation loopsfound under unaerated conditions between impeller re-gions at this large impeller spacing may be broken downby aeration (Hari-Prajitno et al., 1998). Such loops rep-resent zones with low axial exchange. In the axial}radialcombination (con"guration B) with low clearance be-tween impellers, such loops do not form (Jaworski et al.,1998) and thus, the aeration did not change mixing timesigni"cantly as a change of global #ow pattern did notoccur.

4.4. Model calculations

The model was used to calculate pulse-response curves(and subsequently mixing times) in di!erent parts of thereactors for all four con"gurations A}D.

4.4.1. Non-aerated reactorThe calculated CMA pro"les of h

mversus speci"c

energy dissipation rate "t experimental data very well. InFig. 8, three di!erent reactor con"gurations are com-pared on the bias of 95% mixing time whilst for con"g-uration A, the 80% mixing times (Mayr et al., 1994) werecompared. To enable the latter data to be more easilyrelated to the situation with the other con"gurations, thecorresponding 95% mixing time was also calculated. Thecalculations followed all the trends determined experi-mentally: (i) Axial con"gurations (B and D) reducedmixing time at the same power consumption by a factorof about two, compared to the radial con"gurations(A and C); (ii) The increased scale, impeller number andvessel aspect ratio at equal speci"c energy dissipationrate for the same impeller con"guration increased themixing time, cf. con"guration A with C and B with D.

Two theoretical approaches have been used to derivemixing time correlations for non-aerated systems forsingle impellers based on either turbulence or bulk circu-lation #ow (Corrsin, 1964; Nienow, 1997). For singleimpellers, a turbulence model (Nienow, 1997) which ledto Eq. (18) has been shown to be superior. However, formultiple impellers, both concepts are required and CMA

incorporates them. If one of these phenomena is neglect-ed, it is di$cult to explain mixing behaviour in suchcases. The reasons for the higher mixing e$ciency of axialcon"gurations compared to Rushton turbines accordingto CMA arise from a combination of two points:(i) a di!erent #ow structure (less axial #ow barriers) and(ii) di!erent #ow values (higher values of circulation andexchange #ows) at the same power consumption. Thoseaspects re#ect the hydrodynamic knowledge availablea priori and are a fundamental part of the CMAapproach.

Under unaerated conditions, all hydrodynamic para-meters necessary for the calculations were availablea priori, the geometry of the reactor and impellers, stirrerspeed and impeller characteristics such as power num-bers and #ow numbers. No "tted parameters were used.This use of literature data allows the CMA approach tobe used as a design tool for large reactors with multipleimpellers of di!erent type and con"gurations. It has beenvalidated on liquid volumes from 5 m3 (Cui et al., 1996a)to 22 m3 (here) with di!erent numbers of radial andradial/axial up-pumping impellers. Within this range ofoperating conditions, the relative average standard devi-ation between calculated and measured mixing times hasbeen found to be less than 6%.

4.4.2. Aerated reactorCMA predictions of mixing in aerated vessels for four

con"gurations (Figs. 9}11 here and Figs. 7A}D (VraH belet al., 1999)) are within the range of experimental error(Table 3), though the experimental variations were higherthan in the non-aerated cases. The in#uence of aerationon mixing time did not prove to be large for threecon"gurations (A}C). A slight increase of mixing time atlow aeration intensity and slow decrease of mixing athigher values was observed with both Rushton con"g-urations (data for Con"guration C not given). The modelshowed that this shape of curve was the result of thecompeting e!ect of reduced agitator power consumptionand increased induced liquid #ow by aeration.

In the case of con"guration D, the e!ect of aeration onmixing was substantial (Fig. 11). As discussed earlier, thissensitivity is a consequence of the breaking of weaksecondary circulation #ows between impellers (Fig. 3B).CMA is #exible enough to cope with this modi"cation ofthe #ow structure by changing the parameter, k

AX, the

coe$cient of induced #ow. Values taken from the litera-ture [Eq. (16)] (Vasconcelos et al., 1995) were applied inall four cases studied. Those values led to an accuratedescription of the experiments for con"gurations A,B and C but for con"guration D, a k

AXvalue of 1.3 (again

estimated from Eq. (16)) failed (Table 3). To achievea proper prediction, k

AXhad to be set to 13.1 in order to

obtain the "t in Fig. 11. This change in kAX

would meanthat the induced #ow has obtained such a high value thatthe weak secondary loops (associated with low values of


Table 3

Quality of mixing time predictions by CMA model, if kAX

is given by correlation of Vasconcelos et al. (1995). SDEXP

is mean standard deviation of

experimental results and SDEXP~MOD

is mean standard deviation between experimental results and model predictions. Values in brackets representabsolute deviations in seconds

Con"guration A B C D!

(RT/12 m3) (Scaba/12 m3) (RT/30 m3) (Scaba/30 m3)

SDEXP~MOD

16% (3.5 s) 15% (2.5 s) 5% (9 s) 19% (16 s)

SDEXP

15% (3 s) 17% (3 s) 5% (9 s) 9% (7 s)Reference Fig. 9 Fig. 10 (VraH bel et al., 1999) -

!If kAX

is "tted to the experiments, then SDEXP~MOD

"6% (5 s) (see Fig. 11).

axial #ow) do not represent an axial #ow barrier any-more (Fig. 3B). The induced #ow parameter allows animplicit adaptation of the model #ow structure in sucha way that the measurements are described in a consis-tent matter. A more appropriate approach would havebeen to change the model structure explicitly, since the#ow structure probably has changed. Although thiswould result in improved predictions, it is not attractiveto change the model structure as a function of gas #owrate.

This means that, under aerated conditions, a "ttedvalue of the parameter (k

AX) can be used to adapt the

model when needed for a speci"c reactor con"guration.This parameter is regarded as geometry dependent. How-ever, the correlation for calculation of k

AX(Eq. (16), with

vAX

"0.066 (Vasconcelos et al., 1995)) could be success-fully applied (averaged relative standard deviation of11%) in three (A}C) out of four studied con"gurations.

5. Conclusions

Accurate physical measurements on large-scale bi-oreactors are rarely available and are di$cult to obtain.Here, many mixing characteristics associated with fourdi!erent large scale multiple impeller con"gurations arereported. Many of the results "t in well with earlier,smaller scale work, and therefore, this study highlightsthe value of small-scale work as a means of predictinglarge-scale performance. Thus, retro"tting high Po, lowD/¹ radial #ow Rushton turbines by low Po, high D/¹up-pumping axial/radial impeller combinations resultedin less loss of mechanical power and gave the same gashold-up at equal aeration and speci"c power input(Nienow, 1998; Boon, 2000). Up-pumping/radial combi-nation of axial impellers also improved bulk mixingcompared to radial Rushton turbines in vessels withH/¹*1 (Hari-Prajitno et al., 1998). The improvementwith axial impellers could be related to their capability tocreate lower and less intensive axial #ow barriers. As withsingle impellers whether radial (Saito et al., 1992) or axial(Hass & Nienow, 1989), aeration does not have much

in#uence on mixing quality in large-scale reactorsstirred with multiple radial or axial pumping-up/radialimpeller combinations provided the aeration does notlead to a change of bulk #ow pattern (Hari-Prajitno et al.,1998).

In addition, CMA modelling of these large-scale mix-ing time transients based on a general knowledge of thehydrodynamics of both non-aerated and aerated stirredvessels obtained at di!erent scales, predicts the experi-mental results well. It highlights very clearly that thereduction of mixing time is closely related to the reduc-tion of axial #ow barriers with the Scaba radial/axialcombination. The importance of such barriers was alsoindicated by a recent `k}ea CFD analysis of concentra-tion transients and mixing time for dual Rushton tur-bines (Jaworski et al., 1999). However, that analysisgreatly underpredicted the rate of mixing and mixingtime (by a factor of 2 to 3 compared to the experimentalresults), probably because large-scale #ow instabilities,which enhance exchange #ow rates, are not consideredin `k}ea-based CFD codes. Therefore, it would appearthat the present empirical CMA approach leads to morerealistic results; and that it should be useful as a designtool for the prediction of mixing in large-scale reactorswith combinations of multiple radial and axial #owimpellers.

Notation

c concentration, kg m~3

CB

clearance between bottom impeller and bottomof the reactor, m

CI

clearance between impellers, mCF circulation #ow rate, m3 s~1

D impeller diameter, mEF exchange #ow rate, m3 s~1

FE

coe$cient of entrained #owFA

coe$cient of path-averaged #ow rateFl

Ggas #ow number ("Q

G/ND3)

g gravitational acceleration, m s~2

HL

total liquid dispersion height, m


Hi

height of the impeller region, mIF induced #ow rate, m3 s~1

le

length of energy-containing eddies, mkAX

coe$cient of induced #ow, m3 s~1

KC

coe$cient of circulation #ow capacityK

Efraction coe$cient of the #ow in the axial direc-tion induced by impeller

KP

impeller discharge coe$cientm

Lmass of liquid, kg

N stirrer speed, s~1

NI

number of impellersP impeller power input in non-aerated system, WPo power numberQ

Ggas #ow rate, m3 s~1

QL

liquid discharge #ow rate, m3 s~1

SCF secondary circulation #ow rate, m3 s~1

¹ reactor diameter, mt time, su@ root mean square #uctuation velocity, m s~1

u@3%-

relative #uctuation velocity in a bulk region("u@/pND)

< volume of liquid, m3

vAX

parameter with velocity dimension, m s~1

vcGs

characteristic super"cial gas velocity, m s~1.

Greek letters

a proportionality constantb scaling exponent [Eq. (2)]e gas hold-upeT

mean speci"c energy dissipation rate or powerper unit mass, W kg~1

oL

density of liquid, kg m~3

hm

mixing time, s

Subscripts

G aerated system (gassed)i number of compartment stage; non-aerated system (ungassed)Z axial co-ordinate

Acknowledgements

This research was supported by the EC-project&Bioprocess Scale-Up Strategy Based On Integrationof Microbial Physiology and Fluid Dynamics' (ECproject BI04-CT95-0028). We would like to speciallyacknowledge Dr. Sven Hjorth (Scaba AB, Sweden)for power measurements, Asa Manelius and Jan-PeterAxelsson (Pharmacia & Upjohn AB, Sweden) for provid-ing us with mixing data for reactor con"guration A andFrans Hoeks (Lonza, AG, Switzerland) for valuable dis-cussions.

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