Investigation of Flow Patterns in Continuous-ﬂow Stirred

The Canadian Journal of Chemical Engineering, Volume 80, August 2002 591

The design and geometrical configuration of a stirred vessel isusually geared to some specific process. For example, batch stirredtanks usually have their outlet located at the bottom of the vessel,

to facilitate emptying and cleaning. In continuous-flow stirred vessels, onthe other hand, the outlet is located often at mid-height, or the liquidexits by overflowing, as is the case with flotation cells.

Ideally, one should be able to use an optimally-designed stirred vesselfor a specific task. However, in real life, it is often necessary to make useof a given stirred tank for a variety of recipes, and its configuration maylead to flow pathologies and sub-optimal process performance. Forexample, the inlet tube is often positioned close to the turbine, so thatthe entering liquid is fed straight into the liquid being drawn in theagitator-swept region. In a bottom-outlet vessel, one would expect, evenintuitively, that this might lead to short-circuiting.

One way to investigate the appropriateness of a particular design is bydetermining its effect on the flow patterns in the stirred vessel. However,most of the work published so far is related to batch cases — see Mavrosand Bertrand (2002) and Mezaki et al. (2000), among others. On theother hand, although continuous-flow stirred cells have been used for anextremely long time – a plate in Agricola’s De Re Metallica (1556) depictsa set of stirred tanks connected on series – there is relatively little workpublished on the flow patterns in continuous-flow stirred vessels.Recently, flow patterns have been determined by laser Dopplervelocimetry in continuous-flow stirred tanks for a radial-flow turbine(Alliet et al., 2001) and for an axial-flow impeller (Mavros et al., 1997, 2000,2002; the latter also contains a review of the recent relevant literature).

In this work, the effects of the position of the inlet and of meanresidence time of the flow-through liquid on the flow pattern are studiedby laser Doppler velocimetry (LDV) for a standard-configuration agitatedvessel equipped with a Rushton turbine, in order to determine possibleflow problems and the limits of vessel operability.

Experimental Apparatus and ProcedureThe LDV measurements were taken in a fully-baffled (b = T/10) cylindricalvessel (T = 0.19 m), with a dished bottom (with a curvature radius R = 0.19 m).The height of the liquid (tap-water) in the vessel (H) was kept constantat 0.19 m, resulting in a liquid volume (VL) of 5.15 ¥ 10–3 m3. The vesselwas located inside a square transparent box, with a high-quality optical

*Author to whom correspondence may be addressed. E-mail address: [email protected]

Investigation of Flow Patterns in Continuous-flowStirred Vessels by Laser Doppler Velocimetry

Paul Mavros1*, Catherine Xuereb2, Ivan Fort3 and Joël Bertrand2

1 Department of Chemistry, Aristotle University, Thessaloniki, Greece2 Laboratoire de Génie Chimique, ENSIACET, Toulouse, France3 Department of Chemical and Food Process Equipment & Design, Czech Technical University, Prague, Czech Republic

The flow structure of a continuous-flow reactorstirred by a Rushton turbine was investigated by laserDoppler velocimetry for two different mean residencetime-mixing time ratios. Velocity measurements wereobtained for two inlet locations, corresponding to theincoming liquid stream being fed co-currently orcounter-currently to the flow discharged by theturbine. In all investigated configurations and for alloperating conditions, it was found that the flowdisruption caused by the incoming liquid stream wasobservable mainly in the first vessel quarter, whichfollowed the feed-tube plane. From comparison of thevelocities encountered in the various planes in thecontinuous-flow reactor to the velocities of the batchreactor, it was also concluded that it may be possibleto intensify the usage of the turbine-stirred vessel bydecreasing the characteristic times ratio, withoutconsiderable flow by-pass and/or short-circuitingproblems.

Les écoulements dans une cuve agitée par uneturbine de Rushton opérant en mode continu ont étéétudiés par vélocimétrie à rayons laser à effet Doppler,pour le cas de deux taux de temps de résidence /temps de mélange. Les champs de vitesses ont étéobtenus pour deux points d’alimentation, l’unintroduisant le liquide dans le courrant d’aspiration dela turbine, et l’autre à contre-courrant du jet sortantdu coté des pales de la turbine. Pour toutes lesconfigurations étudiées et tous les modes opératoires,l’effet de la présence du jet d’alimentation du liquideont été observé surtout dans le quart de la cuve enaval du plan du tube d’alimentation. La comparaisonentre les vitesses dans le cas de l’opération de la cuveen mode « batch » et en mode continu avec la turbinede Rushton a démontré qu’il serait possible d’intensifierl’utilisation de la cuve agitée, en augmentant le débitd’alimentation sans causer des problèmes auxécoulements par court-circuit ou par déviations.

Keywords: mixing, agitation, continuous, stirred tank,laser Doppler velocimetry, Rushton turbine, Mixel.

592 The Canadian Journal of Chemical Engineering, Volume 80, August 2002

glass (altuglass) window, which allowed the laser beams tofocus inside the stirred liquid with minimal distortion; the boxwas also filled with tap-water.

The impeller used was a standard Rushton turbine (D = T/2),located at a clearance of C = T/2 from the vessel bottom. Theshaft used for these measurements had an o.d. (dS) equal to0.008 m, and extended to the bottom of the vessel. The agitatorrotation speed was held constant at N = 3 rps (= 180 rpm).

Liquid was fed into the vessel via a tube, with an i.d. of 10 mmand an o.d. of 12 mm, positioned in the q = 45º plane (betweentwo adjacent baffles). In the first set of LDV measurements, the tubewas located above the impeller, with its tip 48 mm from theliquid free surface and 11 mm from the agitator shaft (Figure 1a);this is termed the co-current configuration, since the enteringliquid joins the liquid flowing in the upper primary circulation

loop. In the second set of LDV measurements, the tube waspositioned so as to face the side of the Rushton turbine blades;this is termed the ‘counter-current’ configuration, since theliquid fed into the vessel opposes the liquid being ejectedsideways by the rotating turbine. In both cases, the liquid outletwas located at the center of the dished bottom of the vessel.

The LDV apparatus (Dantec) had two laser beams, allowingthe simultaneous determination of two of the three velocitycomponents. From 35 to 89 points were measured in each ofthe three planes: the feed plane, the one 90° in front, and theone 180° in front of the feed plane (Figures 1b to 1f). At leasttwo thousand points were validated at each LDV measurement.The flow was seeded periodically with small seed particles[Iriodin 111 Rutile Fine Satin (Merck), dp = 15 mm].

The data yielded by the Flow Velocity Analyser were collectedand stored in a PC. The Floware software (v. 3.2) calculateddynamically the mean velocity (Ui) from the instantaneous fluidvelocity (ui):

where r, z, and t refer to the radial, axial and tangential velocitycomponent, respectively. In this equation, the bias of the fast-movingseed particles is accounted for by taking into consideration thetime (tk) spent by the particle inside the measuring volume.It should be noted also that the calculated velocities include thevariations due to turbulence and to the periodic blade passage.

In continuous-flow processes, one major variable is the timespent by the through-flowing liquid in the vessel; a typicalmeasure of this is the mean residence time (t). Usually, this ischosen in relation to the mixing time, i.e., the time necessaryfor the homogenization of the vessel contents. The latter hasbeen related to the vessel and agitator dimensions and thepower number (Po) (Ruszkowski, 1994; Nienow, 1997):

(1)U t u t i r z ti k ikk

nk

k

n= Â Â =

= =1 1, , ,

Figure 1. (a) Location of the inlet tubes and of the vessel outlet. (b-f)Planes of LDV measurements (plan view); the small circle indicates theposition of the liquid feed tube. The inlet tubes are located at the mid-planebetween two adjacent baffles.

Figure 2. 2-D flow maps for the co-current liquid inlet (t/tM = 9.6) and comparison with the batch-case flow map (data taken from Mavros et al., 1996).

although an even simpler empirical correlation holds for themost common impellers (Roustan and Pharamond, 1988;Tatterson, 1991):

Customarily, the two times have been chosen so as to obtaina ratio of t/tM ≈ 10, which is considered to correspond to aCSTR. However, one possible question is whether it would bepossible to force the stirred vessel by increasing the through-flowrate, which corresponds to lower values of the mean residence

(3) Nt T DM = ( )4

2

(2) Nt Po T DM = ( )-5 3 1 3 2. / time and the t/tM ratio. In order to investigate the limits of

vessel operability, two different volumetric flow-through rateswere also chosen, to simulate a normal and an intensified vesselutilization: FL = 6.1 L min–1 (corresponding to a near-normalvessel utilization: t/tM = 9.6), and FL= 12.1 L min–1 (correspondingto an enhanced utilization: t/tM = 4.8). In calculating characteristictimes ratio, the simpler Equation (3) was used.

Results & DiscussionCo-Current Liquid FeedFigure 2 presents the 2D flow patterns in three planes — thefeed tube plane and the 90° and 180° downstream planes —and compares them to the batch-case flow pattern. Asexpected, below the tip of the tube a high velocity region maybe observed, with the incoming jet joining the circulating liquidand flowing towards the upper side of the turbine disk. It is


Figure 3. Spatial distribution of 2-D composite velocity ratios (U*rz,cont / U*

rz,batch) for the lower liquid feed flow rate in the co-current mode (t/tM = 9.6).

Figure 4. Spatial distribution of tangential velocity ratios (U *t,cont / U *

t,batch) for the lower liquid feed flow rate in the co-current mode (t/tM = 9.6).

interesting to note that, at this lower flow rate, the typical twoprimary-loops flow pattern induced by the Rushton turbine isobserved, with only slightly higher velocities found below theturbine disk. The two downstream-plane (90° and 180°) flowmaps look similar to the batch-case one, indicating that theeffect of the incoming liquid is restricted to the immediatevicinity of the feed tube plane.

A better way of utilizing the LDV data to visualize the changesinduced by the incoming liquid jet is by plotting the 2D-compositedimensionless velocity (U*

rz) ratio, i.e., the ratio U*rz,cont /U*

rz,batch.The composite velocity is obtained from Equation (4):

where U*r and U*

z are the dimensionless mean radial and axialvelocities, respectively, obtained by dividing the mean velocitiesby the agitator tip speed:

(4) U U Urz r z

* * * /= +( )2 2 1 2

Figure 3 presents the spatial distributions of this ratio for thethree planes studied in this work; the batch-case flow pattern isalso provided for comparison (Figure 3a). For the low flow rate,corresponding to the high characteristic times ratio, the feed-tube plane (Figure 3b) shows a difference in velocitymagnitudes close to the feed tube tip, with velocities in thatregion about nine times higher than the spatially-correspondingbatch-mode velocities. All over the other regions of this plane,the differences seem quite small, and U*

rz,cont are found to be ofthe same order of magnitude as U*

rz,batch. Moving downstream,at the 90° plane (Figure 3c), a region of high velocities incomparison with the batch case, is seen in the upper circulationloop, close to the vessel walls. However, the maximum velocityratio is lower (@6), indicating that the effect of the incomingliquid stream is gradually attenuated. Again, in the other parts of

(5)U U U i r z ti i tip* , , ,= =


Figure 5. 2-D flow patterns for the increased liquid flow rate (t/tM = 4.8) and the co-current mode of operation.

Figure 6. Spatial distribution of 2-D composite velocity ratios (U*r z,cont / U*

rz,batch) for the higher liquid feed flow rate in the co-current mode (t/tM = 4.8).


the vessel, the 2D-flow pattern seems to remain similar to thebatch case. Further downstream (180° plane, Figure 3d), a regionof higher U*

rz velocities is identified, in the same place as previouslybut with velocity magnitude differences practically halved.

The 2-D velocity vectors plotted in these figures miss theimportant third dimension of the flow in the stirred vessel,especially in the neighborhood of the turbine. Hence, plots ofdimensionless tangential velocity ratios are also necessary toobtain a fuller and more meaningful view of the flow structure

in the stirred tank and the effect of the flow-through liquidstream. Figure 4a presents the spatial distribution of tangentialvelocities in the batch case. As expected, the highest velocities arefound close to the agitator blade tips. In the case of continuous-flowoperation, measurements were obtained only in the twodownstream planes and the ratio U*

t,cont / U*t,batch distributions

are plotted in Figures 4b and 4c. It is interesting to note that inthese two downstream planes, for the lower liquid flow rate, thechanges brought to the tangential velocities are located almost

Figure 7. Spatial distribution of tangential velocity ratios (U *t / U *

tip) for the higher liquid feed flow rate in the co-current mode (t/tM = 4.8).

Figure 8. 2-D flow patterns for the lower liquid feed flow rate (t/tM = 9.6) and the counter-current mode of operation.

at the bottom of the vessel, as if the incoming stream has beendiverted sideways and downwards in a spiral-like deviation. Amore important feature is the region of liquid circulatingcounter-clockwise in the upper part of the vessel, seen from thelarge negative U*

t ratios. This pattern may be indicative of a suctioneffect caused by the incoming jet, which becomes apparent in thevessel quarter downstream from the feed tube plane.

From these figures, it may be deduced that at lower volumet-ric flow rate, the effect of the co-currently fed stream isrestricted to the upper part of the vessel, where it joins therecirculating liquid, and that this effect is observable mainly inthe region of the feeding tube. As one moves downstream,following the agitator rotation, the effect of the flow-throughliquid is gradually lost.

When the flow rate of the co-current feed is increased, thehigh-velocity jet is deflected radially and at the same time

upwards by the rotating disk, and this is observed clearly at the90°-downstream plane (Figures 5c, 6c). The typical two-loopflow structure appears again to be recovered at the 180°-downstream plane (Figures 5d, 6d). The tangential velocityratio distributions (Figure 7) show the effect of the incomingliquid stream more clearly: this time, the changes appear closeto the rotating impeller, with velocities considerably higherthan in the batch case (Figure 7b). Further downstream, in the180° plane (Figure 7c), the region with velocity differences isdiminished, but retains similar top velocity differences.

From these flow maps it may be deduced that in the case ofthe Rushton turbine, the introduction of the liquid stream in theupper part of the vessel and co-current with the liquid beingdrawn in by the impeller rotation, only partially affects the flowstructure. This region seems to be limited to the vessel quarterbetween the feeding-tube plane and the one 90° downstream.


Figure 9. Spatial distribution of 2-D composite velocity ratios (U *r z,cont / U *

r z,batch) for the lower liquid feed flow rate in the counter-current mode(t/tM = 9.6).

Figure 10. Spatial distribution of tangential velocity ratios (U*t,cont / U*

t,batch) for the lower liquid feed flow rate in the counter-current mode (t/tM = 9.6).


Figure 11. 2-D flow patterns for the higher liquid flow rate (t/tM = 4.8) and the counter-current mode of operation.

Figure 12. Spatial distribution of 2-D composite velocity ratios (U *r z,cont / U *

r z,batch) for the higher liquid feed flow rate in the counter-current mode(t/tM = 4.8).

Figure 13. Spatial distribution of tangential velocity ratios (U*t,cont / U*

t,batch) for the higher liquid feed flow rate in the counter-current mode (t/tM = 4.8).

It should be noted that this discussion is limited to thepresent geometrical configuration; it is obvious that a differenttube outlet, e.g., a wider tube, or a diffuser-type outlet, wouldresult in different local incoming jet velocities, and perhapswould affect the overall flow patterns in a different way.

Counter-current Liquid FeedThe second set of LDV measurements was made with the tip ofthe feeding tube positioned at the side of the Rushton turbineblades, with the tube set against the vessel walls, equidistantfrom two neighboring baffles (Figure 1). Thus, the liquid exiting

from the feeding tube faced the stream of liquid being ejectedradially outwards and towards the vessel walls by the rotatingturbine — the counter-current feed mode, since the incomingstream flows against the pumped-out stream. This creates aregion of intense turbulence and mixing in the space betweensuch regions are usually created in practice by two opposing jets,in order to achieve appropriate conditions for the crystallizationprocess (Stavek et al., 1990; Benet et al., 1999; Mumtaz et al., 2000;among others).

Figure 8 illustrates the 2-D flow patterns for the three planes(feed-tube, 90° and 180° downstream) and compares them to


Figure 14. Comparison of 2-D flow maps (U *r z / U *

tip) generated by the Rushton turbine to the flow maps generated by an axial-flow (Mixel TT)impeller (Mavros et al., 2002) in continuous-mode operation: effects of volumetric flow rate and feed position (co-current, counter-current).All maps represent the flow structure in the feed-tube plane.

the batch-case flow map for the lower flow rate (t/tM = 9.6). Asin the case of the co-current feed, the flow map disruption isobserved mainly in the feed-tube plane. In the two downstreamplanes, the double-loop structure is recovered.

The spatial distribution of the relative composite velocities(U*

r z,cont / U*r z,batch ; Figure 9) shows in a more quantitative way

the evolution and change of the regions where the changesinduced by the incoming feed are found. In the feed-tube plane(Figure 9b), the major velocity change is found, as expected,close to the blade edge. In the 90°-downstream plane (Figure 9c),a slight increase in velocities is observed above the turbine disk,indicating that the incoming liquid stream is slightly misalignedwith respect to the horizontal line and the turbine disk plane.However, as one moves further downstream (180°-pane, Figure 9d),the region where changes are observed is found in the uppercirculation loop and close to the vessel walls, indicating thecomplex 3-dimensional movement of the incoming liquidstream. If the maps of tangential velocity ratios are also takeninto account (Figure 10), then it is possible to hypothesize that,at the lower flow rate and given the slight misalignment, theincoming liquid stream is entrained by the strong rotarymovement of the turbine into the upper circulation loop.

However, even when the flow rate of the incoming liquidstream is increased, the changes in flow pattern in the stirredtank are not extreme (Figure 11). Obviously, the flow patterns inthe feed-tube and the 90°-downstream planes are changed byhigh velocity incoming streams, but as the 180°-downstreamplane is reached, the typical double-loop structure is foundagain. The spatial distributions of relative 2-D composite velocities(Figure 12) indicate that, indeed, the regions of majormagnitude change are to be found close to the impeller edge(feed-tube plane) and the upper side of the turbine disk (90°-plane).Interestingly, in the 180°-downstream plane, two regions areobserved with relatively important composite velocity change.The tangential velocity ratio distributions (Figure 13) show asimilar pattern of changes, with most of the flow map differencesobserved in the 90°-downstream plane.

These figures indicate, on the one hand, that at the highervolumetric flow rate, the change in flow structure affects alarger part of the entire vessel, while on the other hand, thetypical double-loop flow structure induced by the Rushtonturbine is only partially disrupted by the incoming liquidstream. Thus, it may be concluded that, for the given vesselconfiguration, with the outlet located at the bottom, andespecially with the simple dip pipe used for introducing theliquid stream into the vessel, it is possible to position the inletfor the incoming liquid either co- or counter-currently to theprimary circulation loop without major flow pattern disruptions.

Comparison with an Axial-Flow ImpellerSince quite a few stirred vessels use axial-flow impellers, aninvestigation of the continuous-mode operation by LDVmeasurement was also carried out (Mavros et al., 2002) with aMixel TT. This three-blade impeller has a relatively low solidityratio of @ 0.40 (Mavros and Bertrand, 2002), which produces acomposite axial-radial discharge (Mavros et al., 1996). Figure 14compares the feed-plane flow maps for both impellers.(Although the power requirements of the two impellers arecompletely different — the Mixel TT has a power number aboutseven times smaller than the Rushton turbine (Aubin et al.,2001) — their comparison remains possible, because all resultsare scaled according to the same Utip).

As observed above, in the co-current feed mode there seemsto be no particular problem with the turbine flow maps (Figures14a, b). However, in the case of the Mixel TT, the incomingliquid stream is added to the recirculating liquid from theprimary circulation loop and the two streams emerge combinedfrom the lower side of the TT (Figure 14e). At the lower flowrate, the radial character of the TT discharge remains strong andprevailing, and the primary circulation loop is maintained. But,when the characteristic times ratio is lowered, the high-velocityincoming jet seems to prevail, and the emerging jet fromthe bottom of the TT is directed, most pointedly towards thebottom of the vessel (Figure 14f). And since the vessel outlet islocated at the bottom of the vessel, this combination ofinlet-outlet position and operating conditions seems to lead toproblems with short-circuiting.

When the liquid is fed counter-currently, the resulting flowstructure again depends upon the ratio of characteristic times.At the high t/tM condition, the circulation induced by therotating TT prevails and the incoming stream combine withthe liquid ejected by the impeller. Obviously, a considerableportion of the incoming liquid will be diverted tangentially butthis is missed in the 2-D flow maps. When the t/tM ratio islowered, corresponding to an intensification in vessel usage, theflow structure appears to be disrupted and a secondary loop isestablished in the upper part of the vessel, where liquidcirculates in the opposite direction to the one usually found inaxial agitators. In fact, even simple visual observation showedthat under these conditions, the incoming stream periodicallyreached the free surface of the liquid in the vessel.

Both the flow patterns and visual observations lead to theconclusion that, while it is possible to operate the radialagitator at high or low t/tM values, in the case of the axialagitator, the location of the vessel outlet directly below theimpeller discharge may lead to liquid short-circuiting and vesseldysfunction.

ConclusionsThe flow structure of a continuous-stirred tank reactor wasinvestigated by laser Doppler velocimetry for two mean residencetimes: mixing time ratios and two different inlet locations,corresponding to co-current or counter-current liquid feed withrespect to the liquid stream discharged by the rotating impeller. Theagitator used for these measurements was a standard Rushtonturbine, and the vessel outlet was located at the bottom of the vessel.

In all the investigated configurations and for all operatingconditions, it was found that the flow disruption caused by theincoming liquid stream was observable only in the first vesselquarter, which followed the plane where the feeding-tube waslocated. The typical double-loop circulation generated by theRushton turbine was usually recovered, as illustrated by the flowpatterns observed in the 180°-downstream plane.

From comparison of the velocities encountered in the variousplanes in the continuous-flow reactor with those in the batch reactor,it may be concluded that for either given vessel configuration, it ispossible to intensify the usage of the stirred vessel to someextent by decreasing the characteristic times ratio, which isequivalent to increasing liquid flow-through or volumetric flowrate, without apparent flow pattern problems. Residence timedistribution measurements could reveal whether these flow rateincreases and vessel configurations also lead to flow pathologies interms of short-circuiting or the by-passing of some vessel regions.


AcknowledgementsThanks are due to the European Union (contract BRITE-EURAM BRRTCT97 5035, thematic network "MIXNET") for the partial financialsupport of this work. One of the authors, Prof. Ivan Fort, also acknowl-edges the financial support of this work by the Czech Republic Ministryof Education (Research Project J04/98:212200008).

Part of this work, with only inlet-outlet configuration, was presentedat the 4th Int. Symp. on Mixing in Industrial Processes (ISMIP4,Toulouse, France, May 14-16, 2001).

Nomenclatureb baffle width (m)D agitator diameter (m)dp seed particle diameter (m)dS agitator shaft diameter (m)H liquid height in vessel (m)k turbulent kinetic energy (m2·s–2)N agitator rotation speed (rps)Po power number R vessel bottom curvature radius (m)tk time spent by the seeding particle inside the LDV-measuring

volume (s)tM mixing time (s)T vessel diameter (m)u instantaneous velocity (m·s–1)U mean velocity (m·s–1)U * dimensionless velocity (= U / Utip)Utip agitator tip velocity (m·s–1)VL liquid volume (m3)

Greek Symbolt mean residence time, (s)

Subscriptscont continuous-moder radialt tangentialz axial

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Manuscript received August 9, 2001; revised manuscript receivedApril 11, 2002; accepted for publication May 9, 2002.


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Investigation of Flow Patterns in Continuous-ﬂow Stirred