1-s2.0-S0263876204726052-main

8/11/2019 1-s2.0-S0263876204726052-main

1/9

LIQUID HOMOGENIZATION CHARACTERISTICS IN

VESSELS STIRRED WITH MULTIPLE RUSHTON TURBINESMOUNTED AT DIFFERENT SPACINGSCFD Study and Comparison with Experimental Data

G. MONTANTE and F. MAGELLI

DICMA, Department of Chemical, Mining and Environmental Engineering, University of Bologna, Bologna, Italy

The purpose of this work is to investigate the capability of the currently available CFDtools to correctly forecast the homogenization process in a baffled vessel stirred withsets of identical Rushton turbines mounted with different spacings. The results of the

simulations are compared with experimental data for the validation of the computational pro-

cedure. The simulations provide a good prediction of the time evolution of tracer dispersioninside the vessel volume for all the geometrical configurations. The differences in mixingperformance due to flow variations occurring as a result of the modification of the impellernumber and spacing are correctly forecasted.

Keywords: mixing; homogenization; multiple Rushton turbines; impeller spacing; CFD.

INTRODUCTION

Mixing in stirred vessels is a common operation in thechemical, pharmaceutical and food industry as well as inbiotechnology, environment reclamation, etc. The flowfield prevailing in a stirred vessel is of paramount import-ance for the specific process(es) to be accomplished as itaffectsamong other tasksthe homogenization leveland, therefore, the performance that can be achieved. Theclassic classification of impellersnamely radial, axial-flow and purely axialis just a first step for the descriptionof their actual behaviour. It is well known, for instance, thatthe typical double-loop flow pattern produced by verticalflat-blade and concave-blade turbines in baffled stirredvessels degrades to a mostly axial single loop when the tur-bine clearance from the vessel base is less than a given

critical value (Conti et al., 1981; Montante et al., 1999).The use of multiple-impeller agitation systems has

attracted great attention because they allow easier heatremoval, better gas utilization when using sparingly solublegases, less variable shear rate in the stirred liquid and morecompact equipment. If the stirrers are sufficiently distantfrom each other as well as from the vessel base, no signifi-cant interaction exists between the adjacent impellers, sothat the flow pattern produced by each of them in the setis similar to that determined by a single one (Smith et al.,1987; Komori and Murakami, 1988; Bouaifi et al., 1997;

Hiraoka et al., 2001). Instead, deviations from this con-dition have been determined when the impellers are close

to each other. For Rushton turbines, Mahmoudi andYianneskis (1991) and Rutherford et al. (1996) showedthat the trailing vortexes structure and flow periodicitydecrease significantly when impeller spacing is as smallas T/3 or lower and the region between the turbines ismarkedly anisotropic; the definitions of merging or diver-ging flows have also been introduced. A similar analysiswas conducted by Mishra and Joshi (1994) for dual impel-ler systems consisting of either identical Rushton turbinesor a Rushton turbine and a pitched-blade disc turbine andby Baudou et al. (1997) for axial impellers. Impeller spa-cing was shown to profoundly affect liquid circulation(Mukatakaet al., 1981; Fort et al., 1987), power consump-

tion (Taguchi and Kimura, 1970; Komori and Murakami,1988; Hudcova et al., 1989; Cronin et al., 1994; Hiraokaet al., 2001) and mixing time (Mukataka et al., 1981;Magelli et al., 1986; Komori and Murakami, 1988;Cronin et al., 1994).

The complex fluid dynamics of multiple impeller sys-tems was modelled by various authors as a means todescribe the flow behaviour in a more complete way thanwith only mixing time. Both simple stage models (Magelliet al., 1986; Manna et al., 1991; Vasconcelos et al., 1995;Linek et al., 1996; Alves et al., 1997) and multiple-compartment models (Mann et al., 1981, 1997; Mayret al., 1993; Reuss and Jenne, 1993; Vrabel et al., 1999,2000; Cui et al., 1996) were adopted for this purpose in

the case of multiple radial turbines. This approach wasassociated to the study of impeller spacing influence by

Correspondence to: Dr F. Magelli, DICMA, Department of Chemical,Mining and Environmental Engineering, University of Bologna, vialeRisorgimento 2, 40136 Bologna, Italy.E-mail: [email protected]

1179

02638762/04/$30.00+0.00# 2004 Institution of Chemical Engineers

Trans IChemE, Part A, September 2004Chemical Engineering Research and Design, 82(A9): 11791187

8/11/2019 1-s2.0-S0263876204726052-main

2/9

Magelliet al.(1986), who showed that a unique model para-meter (viz., the backflow rate between adjacent stages)suffices to interpret the overall, gross behaviour of thesesystems provided that the number of stages is taken asequal to the number of the turbines. For axial flow impel-lers, the axial dispersion model behaves slightly betterthan stage models (Jahoda et al., 1994). The modelling of

these systems with advanced CFD tools has also beenattempted in the last few years: Micale et al. (1999) wereable to predict the flow behaviour corresponding to differ-ent impeller spacing (i.e. with parallel, merging or diver-ging flows), while Jaworski et al. (2000), Bujalski et al.(2002) and Montante et al. (2004) studied the transienthomogenization process following an injection of a certainamount of tracer for standard impeller spacings and wereable to predict the mixing timealthough with differentsimulation techniques and with different accuracies. Nostudy is available on the use of this approach to predictthe homogenization characteristics in connection withdifferent impeller spacings.

The purpose of this work is to investigate the capabilityof the currently available CFD tools to correctly forecastthe homogenization process in a baffled vessel stirredwith sets of identical Rushton turbines mounted with differ-ent spacings. A fully predictive simulation approach isadopted and the role of the relevant parameters is studied.The results of the simulations are compared with experi-mental data for the validation of the computationalprocedure.

STIRRED VESSEL CONFIGURATIONS ANDEXPERIMENTAL CONDITIONS

The stirred vessel considered in this work was a tall

cylindrical tank of diameter Tequal to 13 cm and height,H, equal to 52.6 cm (about 4T), provided with four T/10baffles attached to the wall. The vessel had a flat bottomand was closed at the top with a lid. The stirring actionwas provided with identical, evenly spaced Rushton tur-bines of diameter D T/3 mounted on the same shaft.Different geometrical configurations were considered forthe agitation system, namely an impellers number, J,equal to 4, 8, 10 and 12; since the vessel height wasfixed, this allowed investigation of the effect of the impellerspacing. For all the experimental conditions,Swas alwaysequal to H/J, and the off-bottom clearance of the lowestimpeller was equal to S/2 (Figure 1).

Experiments were conducted with water at room temp-erature at selected impeller speeds (Magelli et al., 1986)and therefore the same conditions were adopted for thesimulations. The transient concentration (homogenizationcurves) of an electrolytic tracer was measured by a conduc-tivity probe. The experimental procedure consisted ofinjecting a small amount of aqueous KCl solution at thebase of the vessel and measuring the resulting concen-tration transient very close to the vessel top by means ofa conductivity probe and meter. The injection point andprobe location were at about 1 cm from the base and thetop, respectively, between two baffles. From the wholehomogenization curve, the mixing time value was also cal-culated: in particular, the so-called t95 was considered, i.e.

the time necessary to reach 95% homogeneity after tracerinjection. Both the whole curve and the mixing time

value will be considered in the following for the evaluationof the CFD simulation results.

CFD SIMULATIONS

The CFD simulation of the homogenization experimentsin the stirred vessel described above was performed foreach geometrical configuration, i.e. J 4, 8, 10, 12, atselected operating conditions by means of a fully predictiveprocedure. In all cases, the simulations refer to the fully tur-

bulent regime (with the rotational Reynolds number, Re,ranging from 2.8 104 to 3.4 104). The homogenizationcurves were obtained by a computational procedure repli-cating the experimental one quite closely. The fully devel-oped liquid flow field was determined first; then, thedistribution of a passive tracer introduced rapidly into thevessel was calculated until the attainment of (almost) com-plete homogenization.

The liquid flow field was calculated using the well-known transient sliding grid method (SG), implementedin the commercial CFD code CFX-4. The grids employedfor the simulations consisted about 350,000 cells, thevessel volume being the same in all cases. The compu-

tational domain was divided into two blocks, the innerone containing the impellers and the external one contain-ing the baffles, as required by the SG procedure. The inter-face between the two blocks covered the whole azimuthaland axial extension of the tank, while the radial positionwas fixed at 3.68 cm from the vessel centre, i.e. half-waybetween the impeller blade tips and the baffles. A fixedazimuthal and radial grid spacing was adopted for all thegeometrical configurations of the stirred vessel, while thecells axial distribution was varied for taking into accountthe different number of impellers: in fact, the grid wasrefined close to the impellers, where the bigger flow vari-ations were expected to take place. In all cases, thewhole 2pazimuthal extent of the stirred vessel was consi-

dered. The Reynolds averaged Navier Stokes (RANS)equations coupled with the standard k1 turbulence

Figure 1. Geometrical characteristics of the experimental vessel.

Trans IChemE, Part A, Chemical Engineering Research and Design, 2004, 82(A9): 11791187

1180 MONTANTE and MAGELLI

8/11/2019 1-s2.0-S0263876204726052-main

3/9

model were solved using a finite volume method (Burnsand Wilkes, 1987) and the SIMPLEC algorithm for coup-ling pressure and velocity (Van Doormal and Raithby,1984). The hybrid-upwind discretization scheme was usedfor the convective terms. On solid walls, conventionallinearlogarithmic wall functions (Launder and Spalding,1974) were used.

Each simulation regarding the flow field was started fromthe initial condition of fluid at rest. At the beginning of everysimulation a time step size corresponding to an impellerrotation ofpwas selected for achieving the complete fluidmotion within a reasonable computational time; sub-sequently, the time step was considerably reduced to provideone impeller rotation of a single cell in the azimuthal direc-tion for allowing the refinement of the solution. For eachtime step a variable number of internal iterations were per-formed, ranging from 25 to 50, thus ensuring low andunchanging residuals of all variables. The cut off point inthe residuals was fixed to 1027. Overall, a number of timesteps corresponding to about 15 s of real impeller rotational

time was found to be sufficient to obtain a satisfactory per-iodic solution for J 4 and 8, while for J 10 and 12 alonger time was required (about 20 s). The attainment ofthe solution was verified by checking the invariability ofthe mean flow field at selected locations after subsequentcomplete impeller revolutions. Then, the dynamic distri-bution of the tracer after its injection inside the stirredvolume was calculated by solving a time-dependent Rey-nolds averaged scalar transport equation:

@rF

@t rrUF r(G Gt)rF (1)

where F is the tracer mean volumetric fraction, U is the

mean velocity vector, ris the fluid density, G is the molecu-lar diffusivity and Gt is the turbulent diffusivity. In all thesimulations, G was assumed to be equal to 1029 m2 s21,which is a typical value for the liquids. Equation (1) incor-porates the gradient-diffusion hypothesis:

ruf GtrF (2)

according to which the turbulent flux of the scalar is linearlyproportional to the mean scalar gradient, this implying thatthe scalar flux vector is aligned with the mean scalar gradi-ent vector. The turbulent diffusivity, G t, has to be specifiedfor closing the problem. Usually, this parameter is calcu-

lated from the ratio of the turbulent viscosity, mt, and the tur-bulent Schmidt number, st, for which the definition is:

st mtrGt

(3)

Therefore, the st value has to be fixed. If turbulence trans-ports passive scalars as fast as momentum, stis close to 1.Generally, the turbulent Schmidt number expresses thedifference between the transport rate of momentum and pas-sive scalars. For simple shear flow (e.g. axisymmetric jets,channel flow) a value of 0.70 was found to provide goodagreement with experimental data and it is usually assumedas a default value. Different values have been recommended

for other cases. Rodi (1980) suggested the value of 0.90 fornear-wall flows and of 0.50 for jets and mixing layers.

He et al. (1999) recommended a value of 0.20 for jet incrossflow. Nagata and Komori (2001) have proved that theassumption of identical eddy diffusivity for heat and passivemass does not hold true for a plume under stably stratifiedconditions. Overall, different stvalues have been suggesteddepending on the particular application (Yimeret al., 2002).To the best of the authors knowledge, no investigation for

identifying the more appropriatest value in stirred vesselshas been carried out. For this reason, in this work theeffect of the turbulent Schmidt number on the tracer simu-lation results has been investigated. In the case ofJ 12,two different simulations were performed by using a turbu-lent Schmidt number equal to 0.10 and 0.70, the firstvalue being recommended on the basis of previous findings(Montante et al., 2004) and the second being that usuallyadopted as a default value. For all the other cases (J 410)onlyst 0.10 was considered, for reasons that will be dis-cussed in the next sections.

The initial condition was that of zero tracer concen-tration in the whole vessel volume, except for the injection

region, which was defined as close as possible to theexperimental one. The standard time step adopted forthese simulations was equal to 0.01 s, which is very smallas compared with the experimental time evolution of thetracer distribution. Zero scalar flux boundary conditionswere imposed on solid walls. Once the three-dimensionaltime-dependent map of tracer volume fraction had beencalculated, its time evolution at the same position of theexperimental probe was monitored, in order to allow thesubsequent direct comparison with the correspondingexperimental homogenization curves.

RESULTS AND DISCUSSION

The computational procedure described above had pro-duced accurate forecasts of homogenization curves andmixing times for stirred vessels equipped with multipledown-pumping PBTs (Montanteet al., 2004), all character-ized by impellers spaced wide enough to ensure no inter-action between adjacent impellers. In that work, the mostcritical factors in the selected computational procedure toobtain good predictions were identified as the liquid flowfield prediction and the turbulent Schmidt number. In con-trast, those having a minor impact on the predictions werevarious computational options (such as the discretizationscheme) as well as the exact location of probes and tracerinjection. For this reason, only the effect of the former will

be discussed in the following, while little attention will bedevoted to the influence of this last group of parameters.The expected flow patterns for the four geometrical con-

figurations under study can be inferred from the results ofRutherford et al. (1996). These authors identified the criti-cal impeller arrangements for a dual Rushton turbine lead-ing to either the parallel, merging or diverging flowconfigurations as defined by the values of the lower impel-ler clearance,C1, and impeller spacing,S, both normalizedwith T. These critical values are reported in the lower partof Table 1, while in the upper part the values calculated forthe four case studies are given. For J 4 and J 8 theexpected flow pattern is the parallel one, a situation inwhich each impeller acts independently from the others.

In the case of J 10, C1/T is equal to the boundaryvalue, 0.20, as given by Rutherford et al. (1996) and the


LIQUID HOMOGENIZATION CHARACTERISTICS 1181

8/11/2019 1-s2.0-S0263876204726052-main

4/9

expected flow pattern is, therefore, more uncertain to fore-cast than for the previously mentioned geometrical con-figurations. According to Montante et al. (1999), the flowpattern transition for a single impeller takes place at C1/T 0.17 and a double-loop configuration is still estab-lished for C1/T 0.20. Moreover, very small changes in

the geometrical configuration can produce slight variationin the boundary value so that no firm conclusion can bedrawn forJ 10. Instead, for J 12 the merging flow pat-tern should take place, i.e. a situation in which the lowestimpeller pumps axially upward rather than producing thetypical double-loop configuration: therefore, the mergingof the loops coming out from the lower and the upper adja-cent impellers takes place.

The analysis of the flow field predicted in each of thefour cases investigated in this work has confirmed thatthe expected flow patterns were predicted correctly. Aplot of the flow fields for the cases ofJ 4 and 12 impel-lers is shown in Figure 2(a) and (b), respectively, where theflow patterns on a vertical plane extending from the vessel

base up to aboutz/T 1.6 are reported. For J 4 the par-allel flow pattern is apparent, where each turbine behavesindependently of each other. For J 12 merging flowcan be recognized for impeller pairs: the lower turbine ofeach pair pumps upwards and the upper one downwards,so that merging of these streams takes place and onesingle double-loop configuration is obtained for the pairinstead of two typical of parallel flow, with two stagnationpoints instead of four. These results are in good agreementwith those published by Micale et al.(1999), but as a differ-ence from the two impellers system the two loops do notmerge mid-way between two impellers. Scrutiny ofFigure 2(b) shows that each turbine pair exhibits parallel

flow relative to the others, a behaviour that could not bechecked experimentally. Also, each vessel module is notequal to the others and, therefore, the analogy with theexperiments of Rutherford et al. (1996) is not complete.A more quantitative description of these different flow pat-terns can be obtained by comparing the three mean velocitycomponents at selected elevations. As an example the axial,radial and tangential velocity radial profiles relevant toelevation A, B, and C (see Figure 2) are plotted inFigure 3: they refer to an axial position mid-way betweenthe first and the second impeller for J 4 (A) and

J 12 (B) and between the second and the third impellerfor J 12 (C). It is worth noting that the curve at C for

J 4 coincides exactly with that at A. The profiles at

planes A and C are very similar to each other (only a limi-ted axial velocity distortion being apparent for the C curve

due to the influence of the lowest turbine pair), while majordifferences can be noticed in all the velocity components atplane B. In addition, the axial profiles of the radial velocitynormalised with the impeller tip speed,Vtip, are reported inFigure 4 (J 4, thin line and J 12, thick line), at a fixedradius not far from the blade tip. In the figure the axialcoordinate is limited to z/T 1 for a clearer represen-tation, since the behaviour repeats almost identically foreach turbine pair. The predicted profiles exhibit the typical

experimental trend determined by Rutherford et al.(1996),with a radial velocity peak between two consecutive

Table 1.Lower impeller clearance,C1, and impeller spacing,S, for the fourcase studies (upper part) and critical arrangements identified by Rutherfordet al. (1996) for a dual Rushton turbine (lower part).

J C1/T S/TType of flow(Rutherfordet al., 1996)

4 0.51 1.012 Parallel8 0.25 0.506 Parallel

10 0.20 0.405 Merging12 0.17 0.337 Merging

.0.20 .0.385 Parallel

.0.17 ,0.385 Merging,0.15 .0.385 Diverging

Figure 2. Velocity vector plot on a vertical plane mid-way between twobaffles extending from the vessel base up to about z/T 1.6. (a) J 4;(b) J 12. The elevations A, B, C are shown, to which the velocityprofiles of Figure 3 refer.



8/11/2019 1-s2.0-S0263876204726052-main

5/9

impellers for J 12 and the peak corresponding to theimpeller disk elevation for J 4. The same qualitativeresults of the J 4 case were obtained also for the stirredvessel equipped with eight impellers. For the uncertain caseofJ 10 a merging flow pattern was obtained after 20 s ofimpeller revolution: notably, after about 10 s the flow fieldappeared to be parallel, while after a longer agitation time a

stable merging flow pattern was established. It is worthmentioning that the same behaviour could be observedexperimentally by flow visualizations of the single impellersystem investigated by Montante et al. (1999): during theinitial agitation period the flow pattern started as a parallelone also in the case of single loop flow configurations.Once stabilized, the same behaviour as of the J 12 casewas also obtained for the vessel equipped with 10impellers.

An indirect confirmation of the good reliability of thesimulated mean flow field in all the four simulated geo-metric configurations derives from the comparison of thepredicted and experimentally available power number,

Np. The Np values relevant to the four cases, normalizedwith the impeller number and with the power number cor-responding to a single impeller system, (Np)J/J(Np)J1, areplotted in Figure 5 against S/D. The simulated values werecalculated from the torque on the four baffles, while theexperimental ones were taken from the literature (Magelliet al., 1986). As can be observed, the simulations predictthe Np values very closely and, apart from a slight over-estimation for the case J 8, the decreasing trend of thepower draw with decreasing impeller spacing is predictedcorrectly. It is worth observing that the sharp power dropcorresponds to the flow pattern change from parallel tomerging.

Further analysis of the single-phase flow fields is not

reported here as the computational strategy adopted pre-sently for single phase baffled stirred tanks has been thesubject of a number of works and RANS-based simulationsperformed adopting the k1 turbulence models and the SGimpeller simulation strategy have already been validatedwidely, especially for vessels stirred with Rushton turbines

Figure 3. Radial profiles of axial (U), radial (V) and tangential (W) meanvelocity normalized with Vtip. Thin line:J 4, elevation A (half-way bet-ween the first and the second impeller). Thick line: J 12, elevation B(half-way between the first and the second impeller). Thick dotted line:

J 12, elevation C (half-way between the second and the third impeller).

Figure 4.Axial profiles of mean radial velocity normalised with Vtipin thelower vessel part. Thin line: J 4; thick line: J 12.

Figure 5. Comparison of the experimental (O) and computed Np (W)

values normalized with the impellers number and the Np value for asingle impeller system for various spacings S/D.



8/11/2019 1-s2.0-S0263876204726052-main

6/9

for the case of single (Brucato et al., 1998; Montanteet al.,2001) and dual turbine stirred tanks (Micale et al., 1999).

As anticipated in the Introduction, computational pro-cedures for predicting the time evolution of a tracer in stir-red vessels are, in contrast, much less well validated. Forthis reason, the transient tracer concentration distributionfrom the injection to homogeneity condition (as well as

the computed mixing time) will be examined in the follow-ing and compared with relevant experimental data. In allthe simulations, the tracer was assumed to be injectedfrom the vessel bottom into the previously calculatedflow field, thus reproducing the experimental injection posi-tion as closely as possible. Then, the tracer concentrationcalculated at each time step was recorded at every positionand, in particular, in the small volume corresponding to theposition of the experimental probe that, in the experiments,was inserted inside the vessel through the top lid.

A qualitative overall picture of the tracer distribution cal-culated inside the vessel for J 4 and 12 is shown in theplots reported in Figures 6 and 7, respectively, at different

times. The maps refer to the dimensionless concentrationon a vertical plane between two baffles: after a few instantsfrom the injection the tracer is spread up to the first impel-ler forJ 4 and up to the second forJ 12. The high con-centration in these zones following the injection and itslevelling out with time is a well-documented phenomenon(Mayr et al., 1993; Jahoda and Machon, 1994; Jaworskiet al., 2000). Apparently, the tracer follows different

patterns depending on the geometrical configuration. Nota-bly, compartmentalization produced by radial turbines(Cronin et al., 1996) can be easily noticed in bothconfigurations.

As regards the influence of the turbulent Schmidtnumber, the default value st 0.70 was taken first forthe simulations and additional calculations with st 0.10

were run later, this last value having been found by trialand error in a previous study (Montante et al., 2004). Theresulting concentration curves at the vessel top normalizedwith respect to the concentration value corresponding to thefully homogeneous condition are plotted vs time inFigure 8, together with the experimental data obtained forthe same condition used in the simulation (fluid: water,

N 860 rpm). As can be observed, the calculated transienttracer concentration reproduces the experimental trendquite well for st equal to 0.10, while much slower tracerdispersion is predicted for the higher value of the sameparameter. The system behaves as if material exchangebetween the different impeller regions was underpredicted

if using the standard st value, as suggested by Bujalskiet al. (2002) and Jaworski et al. (2000). It should beremembered that an eddy diffusivity hypothesis has beenintroduced for closing the problem equations, equation(2), and that, according to such a modelling approach, theparameter controlling the turbulent transport of the traceris the turbulent diffusivity, Gt. The turbulent Schmidtnumber contributes to determining Gt together with the

Figure 6.Maps of dimensionless tracer concentration in a vertical plane mid-way between two baffles. J 4. (a)t 0.07 s; (b)t 4.94 s; (c) t 8.69 s;(d) t 80 s.



8/11/2019 1-s2.0-S0263876204726052-main

7/9

turbulent viscosity that is defined on the basis of the well-known eddy viscosity hypothesis. Both the eddy diffusivityand the eddy viscosity hypotheses introduce significantapproximations in the problem equations: therefore, findinga physical explanation for the best st value to adopt is notstraightforward matter and more fundamental investigationis required to clarify this issue. In any case, this result is inagreement with the previous results obtained with triple

PBTs (Montante et al., 2004): overall, it seems that theadopted computational procedure can be confidentlyapplied to any stirred vessel configuration, at least in thecase of multiple impeller systems.

The simulations results relevant to the cases of ten, eightand four Rushton turbines are shown in the same form inFigures 911, where the lines represent the tracer concen-tration transient computed using 0.10 as the stvalue. In all

Figure 7.Maps of dimensionless tracer concentration in a vertical plane mid-way between two baffles. J 12. (a)t 0.07 s; (b)t 4.95 s; (c)t 8.71 s;(d) t 80 s.

Figure 8. Experimental and simulated dimensionless tracer concentrationvs time. J 12; N 860 rpm. Symbols, experimental data; lines, simu-

lation results obtained with two different turbulent Schmidt numbers inthe scalar equation. Thin line, st 0.70; thick line, st 0.10.

Figure 9. Experimental and simulated dimensionless tracer concentration

vs time. J 10; N 970 rpm. Symbols, experimental data; line, simu-lation results obtained with st 0.10.



8/11/2019 1-s2.0-S0263876204726052-main

8/9

cases, good agreement with the relevant experimental datacan be observed.

For a quantitative, rapid evaluation of the agreementbetween experiments and predictions the computed andexperimental mixing times t95 were also calculated andare reported in Table 2. The error in the t95 values for thefour cases range from 2.9 to 9.0% with st 0.1, while itincreases to about 140% with st 0.7. In Table 2, thevalues of the dimensionless mixing times N.t95 are alsoreported for easier comparison: as already reported(Magelli et al., 1986), these values are not correlated toimpeller spacing in a clear way, since they first increase

and then decrease at the increasing of J. The qualitativeexplanation given, as based on the staged model adoptedthat time, was that they reflect the competition betweentwo factors: namely, greater stream interaction and moreextensive staging at the same time when decreasing turbinespacing. In view of the detailed flow field simulation, thatinterpretation can be essentially confirmed.

CONCLUSIONS

The homogenization process in a baffled stirred vesselequipped with a different number of identical Rushton tur-bines has been simulated using a RANS based CFDapproach. As a consequence of the impellers number varia-tion, the impeller spacing changed thus producing a varia-tion in both the flow pattern and the mixing time. Overall,the computational strategy and procedure adopted in thiswork allow to correctly predict the flow pattern, the

mixing time and the whole homogenization dynamics pro-cess for all the four geometrical configurations considered.In particular, the differences in mixing performance due toflow variations occurring as a result of the modification ofthe impeller number and spacing are correctly forecasted.Great sensitivity of the simulations results on the turbulentSchmidt number was observed: a turbulent Schmidtnumber of 0.10 had to be adopted for obtaining goodquantitative agreement of the predictions with the exper-imental data.

NOMENCLATURE

C1 lower impeller clearance, mC tracer concentration

D impeller diameter, mH tank height, mJ number of impellersN agitation speed, s21

r radial coordinate, mS impeller spacing, mT tank diameter, mt time, su instantaneous velocity vector, m s21

U mean velocity vector, m s21

U mean axial velocity, m s21

V mean radial velocity, m s21

W mean tangential velocity, m s21

Vtip impeller tip speed, m s21

z axial coordinate, m

Greek symbolsF tracer mean volumetric fractionf tracer fluctuating volumetric fractionr liquid density, kg m23

G molecular diffusivity, m2 s21

Gt turbulent diffusivity, m2 s21

mt turbulent viscosity, Pa sst turbulent Schmidt number

REFERENCES

Alves, S.S., Vasconcelos, J.M.T. and Barata, J.M., 1997, Alternativecompartment models of mixing in tall tanks agitated by multi-Rushtonturbines,Trans IChemE, Pt A, Chem Eng Res Des, 75: 334338.

Baudou, C., Xuereb, C. and Bertrand, J., 1997, 3-D hydrodynamics gene-

rated in a stirred vessel by multiple-propeller system,Can J Chem Eng,75: 653663.

Figure 10.Experimental and simulated dimensionless tracer concentrationvs time.J 8;N 800 rpm. Symbols, experimental data; line, simulationresults obtained withst 0.10.

Figure 11.Experimental and simulated dimensionless tracer concentration

vs time.J 4;N 898 rpm. Symbols, experimental data; line, simulationresults obtained withst 0.10.

Table 2. Experimental and computed t95 for the four stirred vesselconfigurations.

J N, s21 expt95 expN.t95

simt95(st 0.10)

Percentageerror in t95

4 15.0 30.8 461 31.7 2.928 13.3 50.6 675 46.0 9.0910 16.2 32.4 524 30.0 7.41

12 14.3 35.0 502 37.0 5.71



8/11/2019 1-s2.0-S0263876204726052-main

9/9

Bouaifi, M., Roustan, M. and Djebbar, R., 1997, Hydrodynamics of multi-stage agitated gasliquid reactors, in Recents Progres en Genie desProcedes, Vol 11, no. 52 (Lavoisier, Paris), pp 137144.

Brucato, A., Ciofalo, M., Grisafi, F. and Micale, G., 1998, Numerical pre-diction of flow fields in baffled stirred vessels: A comparison of alterna-tive modelling approaches, Chem Eng Sci, 53: 36533684.

Bujalski, W., Jaworski, Z. and Nienow, A.W., 2002, CFD study of homo-genization with dual Rushton turbinescomparison with experimental

results. Part II: the Multiple Reference Frame, Trans IChemE, Pt A,Chem Eng Res Des, 80: 97103.Burns, A.D. and Wilkes, N.S., 1987, A finite-difference method for the

computation of fluid flows in complex three-dimensional geometries,UKAEA Report AERE-R 12342.

Conti, R., Sicardi, S. and Specchia, V., 1981, Effect of the stirrerclearance on particle suspension in agitated vessels, Chem Eng J, 22:247249.

Cronin, D.G., Nienow, A.W. and Moody, G.W., 1994, An experimentalstudy of mixing in a proto-fermenter agitated by dual Rushton turbines,Trans IChemE, Pt C, Foods Bioprod Proc, 72: 3540.

Cui, Y.Q., Van Der Lans, R.G.J.M., Noorman, H.J. andLuyben, K.Ch.A.M., 1996, Compartment mixing model for stirred reac-tors with multiple impellers, Trans IChemE, Pt A, Chem Eng Res Des,74: 261271.

Fort, I., Machon, V., Hajek, J. and Fialova, E., 1987, Liquid circulationin a cylindrical baffled vessel of high height/diameter ratio with two

impellers on the same shaft, Coll Czech Chem Commun, 52:26402653.

He, G., Guo, Y. and Hsu, A.T., 1999, The effect of Schmidt number onturbulent scalar mixing in a jet-in-crossflow, Int J Heat Mass Transfer,42: 3727 3738.

Hiraoka, S., Kato, Y., Tada, Y., Ozaki, N., Murakami, Y. and Lee, Y.S.,2001, Power consumption and mixing time in an agitated vessel withdouble impellers, in Proceedings of 4th International Symposium on

Mixing in Industrial Processes (on CD-ROM) (PROGEP, Toulouse),pp 9297.

Hudcova, V., Machon, V. and Nienow, A.W., 1989, Gasliquid dispersionwith dual Rushton turbine impellers, Biotechnol Bioeng, 34: 617628.

Jahoda, M. and Macon, V., 1994, Homogenisation of liquids in tanks stir-red by multiple impellers, Chem Eng Technol, 17: 95 101.

Jahoda, M., Pinelli, D., Nocentini, M., Fajner, D., Magelli, F. andMachon, V., 1994, Homogenization of liquids and fluid-dynamic beha-viour of vessels stirred with multiple axial impellers, IChemE Symp Ser,136: 113120.

Jaworski, Z., Bujalski, W., Otomo, N. and Nienow, A.W., 2000, CFDstudy of homogenization with dual Rushton turbinescomparisonwith experimental results. Part I: initial studies, Trans IChemE, Pt A,Chem Eng Res Des, 78: 327333.

Komori, S. and Murakami, Y., 1988, Turbulent mixing in baffled stirredtanks with vertical-blade impellers. AIChE J, 34: 932937.

Launder, B.E. and Spalding, D.B., 1974, The numerical computation ofturbulent flows, Comput Meth Appl Mech Eng, 3: 269 289.

Linek, V., Moucha, T. and Sinkule, J., 1996, Gas liquid mass transfer invessels stirred with multiple impellersI. Gasliquid masstransfer characteristics in individual stages, Chem Eng Sci, 51:32033212.

Magelli, F., Fajner, D., Pasquali, G. and Nocentini, M., 1986, Fluid-dynamic behaviour and mixing times of multiple impeller stirredtanks with low viscosity liquids, Proceedings of 5th Yugoslavian

Austrian Italian Chemical Engineering Conference (Kardelj Univer-sity, Ljubljana), pp 323330.

Mahamoudi, S.M.S. and Yianneskis, M., 1991, The variation of flow pat-tern and mixing time with impeller spacing in stirred vessels with twoRushton impellers, in Proceedings of 7th European Conference on

Mixing, Bruxelmane, M. and Froment, G. (eds) (K-VIV, Antwerp),pp 1724.

Mann, R., Mavros, P.P. and Middleton, J.C., 1981, A structured stochasticflow model interpreting flow follower data from a stirred vessel, Trans

IChemE, 59: 271278.Mann, R., Vlaev, D., Lossev, V., Vlaev, S.D., Zahradnik, J. and

Seichter, P., 1997, A network-of-zones analysis of the fundamentalsof gas-liquid mixing in an industrial stirred bioreactor, Recents Pro-gres en Genie des Procedes, Vol 11, no. 52 (Lavoisier, Paris), pp223230.

Manna, L., Chiampo, F., Rovero, G. and Sicardi, S., 1991, Mixing time invessels stirred by multiple impeller, in Proceedings of 7th EuropeanConference on Mixing, Bruxelmane, M. and Froment, G. (eds)(K-VIV, Antwerp), pp 111119.

Mayr, B., Horvat, P., Nagy, E. and Moser, A., 1993, Mixing-modelsapplied to industrial bioreactors, Bioprocess Eng, 9: 112.

Micale, G., Brucato, A., Grisafi, F. and Ciofalo, M., 1999, Prediction offlow fields in a dual-impeller stirred vessel, AICheE J, 45: 445464.

Mishra, V.P. and Joshi, J.B., 1994, Flow generated by a disc turbine. PartIV: multiple impellers, Trans IChemE, Pt A, Chem Eng Res Des, 72:657668.

Montante, G., Lee, K.C., Brucato, A. and Yianneskis, M., 1999, An experi-mental study of double-to-single-loop transition in stirred vessels,Can JChem Eng, 77: 649659.

Montante, G., Lee, K.C., Brucato, A. and Yianneskis, M., 2001, Numericalsimulation of the dependency of flow pattern on impeller clearance instirred vessels, Chem Eng Sci, 56: 37513770.

Montante, G., Mostek, M., Jahoda, M. and Magelli, F., 2004, CFD simu-lations and experimental validation of homogenisation curves andmixing time in stirred Newtonian and pseudoplastic liquids, ChemEng Sci (submitted)

Mukataka, S., Kataoka, H. and Takahashi, J., 1981, Circulation time anddegree of fluid exchange between upper and lower circulation regionsin a stirred vessel with a dual impeller, J Ferment Technol, 59:303307.

Nagata, K. and Komori, S., 2001, The difference in turbulent diffusionbetween active and passive scalars in stable thermal stratification,

J Fluid Mech, 430: 361380.Reuss, M. and Jenne, M., 1993, Compartment models, in Proceedings of

International Symposium on Bioreactor Performance (IDEON, Lund),pp 6377.

Rodi, W., 1980, Turbulence Models and their Application in Hydraulicsa State of the Art Review, (International Association of HydraulicResearch, Delft)

Rutherford, K., Lee, K.C., Mahmoudi, S.M.S. and Yianneskis, M., 1996,Hydrodynamic characteristics of dual Rushton impeller stirred vessels,

AIChE J, 42: 332346.Smith, J.M., Warmoeskerken, M.M.C.G. and Zeef, E., 1987, Flow con-

ditions in vessels dispersing gases in liquids with multiple impellers,in Biotechnology Processes: Scale-up and Mixing, Ho, C.S. andOldshue, J.Y. (eds) (AIChE, New York), pp 107115.

Taguchi, H. and Kimura, T., 1970, Studies on geometric parameters infermentor design. I. Effect of impeller spacing on power consumptionand volumetric oxygen transfer coefficient, J Ferment Technol, 48:117124.

Van Doormal, J.P. and Raithby, G.D., 1984, Enhancements of the SIMPLEmethod for predicting incompressible fluid flows, Numer Heat Transfer,7: 147163.

Vasconcelos, J.M.T., Alves, S.S. and Barata, J.M., 1995, Mixing in gasliquid contactors agitated by multiple turbines, Chem Eng Sci, 50:23432354.

Vrabel, P., Van Der Lans, R.G.J.M., Cui, Y.Q. and Luyben, K.Ch.A.M.,1999, Compartment model approach: mixing in large scale aerated reac-tors with multiple impellers, Trans IChemE, Pt A, Chem Eng Res Des,77: 291302.

Vrabel, P., Van Der Lans, R.G.J.M., Cui, Y.Q., Luyben, K.Ch.A.M.,Boon, L. and Nienow, A.W., 2000, Mixing in large-scale vessels stirredwith multiple radial or radial and axial up-pumping impellers: modelling

and measurements, Chem Eng Sci, 55: 58815896.Yimer, I., Campbell, I. and Jiang, L-Y., 2002, Estimation of the turbulent

Schmidt number from experimental profiles of axial velocity and con-centration for high-Reynolds-number jet flows, Can Aeronaut Space J,48: 195200.

ACKNOWLEDGEMENTS

This work was financially supported by the Italian Ministry of Univer-sity and Education (FIRB 2001 project) as well as by the University ofBologna.

The manuscript was received 29 March 2004 and accepted for publi-

cation after revision 24 June 2004.



Documents

1-s2.0-S0263876204726052-main