investigaciones experimentales, distribución de partículas

8/2/2019 investigaciones experimentales, distribucin de partculas

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Chemical Engineering Science 61 (2006) 28642870www.elsevier.com/locate/ces

Experimental investigations of stirred solid/liquid systems in three differentscales: Particle distribution and power consumption

R. Angst, M. Kraume

Technische Universitt Berlin, Fachgebiet Verfahrenstechnik, MA 5-7 Strae des 17. Juni 136, 10632 Berlin, Germany

Available online 26 January 2006

Abstract

In this paper, experimental results of power consumption as well as phase distribution measurements in stirred solid/liquid systems arepresented. The local dispersed phase volume fraction in three geometrically similar vessels with the diameters of 0.2, 0.4 and 0.9m wasinvestigated at up to 69 different local positions by means of an endoscope technique. The results are compared and show a good agreementbetween the different vessel sizes under comparable conditions. The power number was investigated and found to decrease remarkably withincreasing mean solids concentrations. 2005 Elsevier Ltd. All rights reserved.

Keywords: Mixing; Multiphase flow; Particle distribution; Scale-up; Suspension

1. Introduction

Although solid/liquid systems are among the most common

apparatuses in the process industry there is still a remark-able gap between the industrial demand and the ability to pre-dict the fluid dynamics of the solid/liquid flow. Despite thefact that numerous publications on the matter exist (e.g. Penazet al., 1978; Einenkel, 1979; Barresi and Baldi, 1987; Bilek andRieger, 1990; Mak and Ruszkowski, 1990; Heywood et al.,1992; Godfrey and Zhu, 1994; McKee et al., 1994; Brucatoet al., 2002; Spidla et al., 2004) the transferability of the re-sults is low due to the strong dependency of the flow field onthe geometry as well as on the properties of the dispersed andthe continuous phase. Even the prediction of an extensively in-vestigated topic like the impeller speed necessary for complete

suspension (Zwietering, 1958) can turn out to be difficult whennon-standard geometries are utilized.Major reasons for the complex behaviour of stirred

solid/liquid systems are the occurrence of macro-instabilities,chaotic eddy structures of varying time scale and size, as wellas the tendency of fluidised particles to segregate and exhibitlarge concentration gradients like e.g. in fluidised beds. Thetime scales of macro-instabilities are significantly larger than

Corresponding author. Tel.: +49 30 314 23701; fax: +4930 314 21134.E-mail address: [email protected] (M. Kraume).

0009-2509/$ - see front matter 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ces.2005.11.046

the turbulent fluctuations in single-phase flow. This complicatesboth the experimental detection of a mean local concentrationand the prediction by means of CFD. While the experimental

techniques have to be able to detect fluctuations of timescalesranging from 100 down to 0.05 Hz as measured for the largestinvestigated geometry in this study, transient CFD simulationswould have to capture a long period of time to resolve theselarge fluctuations correctly. To avoid the loss of the smaller timescales this has to be done with a sufficiently fine discretisationof time, thus leading to very long calculating times. Since forindustrial applications this is not feasible at all, advanced meth-ods have to be developed to predict stirred solid/liquid systems.The data provided in this contribution are meant to increase thegeneral understanding of the complex fluid dynamics as wellas to validate existing and new CFD models.

2. Method

The experimental investigations were carried out in threegeometrically similar vessels with diameters of 0.2, 0.4 and0.9m(Fig. 1). The vessels featured a dished bottom, four bafflesand a pitched blade turbine with six blades pumping downward.The liquid levels inside the vessels were equal to their respectivediameters.

An endoscope system developed by the authors workgroupwas applied to measure the local concentration of the dispersed
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R. Angst, M. Kraume / Chemical Engineering Science 61 (2006) 2864 2870 2865

Fig. 1. Investigated geometry.

phase (Ritter and Kraume, 2000; Angst and Kraume, 2005). Asimilar system was applied by Alban et al. (2004). The endo-scope has a diameter of 7 mm and was inserted vertically intothe vessels with diameters of 0.2 and 0.4 m, while in case ofthe vessel with a diameter of 0.9 m it was inserted horizontallythrough the side wall of the vessel. In the latter case the lens ofthe endoscope can be adjusted to be flush with the wall of thevessel when the concentration at the wall is to be measured. Inthis case, the two-phase flow field remains entirely undisturbedof the otherwise invasive measuring technique. That is espe-cially interesting, since endoscope-related disturbances of thesolid/liquid flow field at the wall will have a significantly largerimpact than in other regions of the vessel. The entire set-up for

the vertical application is depicted in Fig. 2.The endoscope system is based on the principle of back

scattering. The particles of the dispersed phase at the measuringpoint in front of the endoscope tip are temporarily illuminatedby a flashlight connected to the endoscope via fibre optics. Anamount of light that is proportional to the number of particlesin front of the endoscope tip is scattered back into the front lensand to an attached CCD camera. Via a computational grey-scaleanalysis with the software IMAGEJ (Fig. 3), the mean value ofthe back-scattered light intensity is calculated that correspondsdirectly to the particle concentration at the measuring point.At each measuring position, 50 to 150 images were taken with

a repetition frequency of 1 Hz. In the three different vessels,pictures of the suspended particles scattering back the flash lightfrom the endoscope were taken at up to 69 discrete measuringpoints located at identical related bottom clearances.

Despite the invasive nature of the measurement technique andthe probe diameter of 7 mm, the remarkable agreement of themeasured local concentrations in the different scales (Fig. 4)indicates that the flow field in the smaller scales is not signi-ficantly disturbed by the probe. The fact, that the applied back-scatter method does not use an additional reflector opposing thelens, like a transmission method, certainly contributes to this.

The larger related distances between the measuring probe andshaft or wall for the smaller scales were chosen in order to avoid

additional reflections from objects other than the particles.

Fig. 2. Endoscope system.

To calibrate the system, fluidised beds were applied since

they allow a homogeneous distribution of the dispersed phase.The system was calibrated with mean particle concentrationsof 115vol% in steps of 1vol%. The calibration as well asthe measurements in the different vessels was carried out inan obscured environment to prevent day light from interferingwith the optical measuring technique.

Glass beads with a mean diameter of 200m were used as thedispersed phase. The mean dispersed phase volume fractionsapplied were 210vol%. The particle size distribution of theglass beads were narrowed down in a fluidised bed. Severalimpeller speeds were investigated. Unless otherwise noted, theimpeller speed applied provided a mean suspension height of

90% of the liquid level, also referred to as the H90 criterion(Kraume and Zehner, 2001).In all investigated vessel sizes, the power consumption for the

single- and two-phase flow was measured. Since the tendency ofthe results is identical, only results of the vessel with a diameterof 0.4 m are included in this contribution. The vessel itselfwas mounted on a pneumatic bearing to eliminate the bearingfriction. A lever arm with a commercial load cell was appliedto measure the force. A commercial torque metre was appliedas well (Ascanio et al., 2004). The torque measurements werecorrected for frictional losses using measurements taken in anempty vessel. The latter values were in the magnitude of lessthan 2% of the values measured with water at the investigated

impeller speed.
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2866 R. Angst, M. Kraume / Chemical Engineering Science 61 (2006) 28642870

Fig. 3. Block diagram of the computational grey-scale analysis of an endoscope image.

Fig. 4. Local particle volume fractions measured in vessel diameters on 0.2,0.4 and 0.9 m with 5 and 10 vol% mean dispersed phase volume fraction.

The torque measurements were used to calculate the powernumber NP

NP=P

Susn3d5

with the mean density Sus of the suspension calculated as

Sus = LL + SS= L +S(S L).

The influence of the dispersed phase on the mean kinematicviscosity and thereby on the Reynolds number Re accordingto Weinspach (1969) is smaller than 6% and was thereforeneglected.

3. Results

3.1. Particle distribution

In Fig. 4, selected results obtained at identical related bottomclearances in the three investigated vessels of different scalesare shown. The abscissas of the diagrams indicate the dimen-sionless radial and vertical positions of the measuring points in-side the vessel. The ordinates indicate the local dispersed phasevolume fraction at each measuring point.

The selected measuring points presented in Fig. 4 are locatedat distances of 0.25D, 0.55D and 0.75D from the bottom. Sev-eral radial positions were investigated. In each diagram concen-tration profiles for mean dispersed phase volume fractions of 5and 10 vol% are displayed. The impeller speed in each case was

adjusted to meet the H90 criterion except for the vessel with adiameter of 0.9 m, where the impeller speed chosen provideda suspension height of 95% of the liquid level. With impellerspeeds of 678 min1 (0.2 m vessel, 5 vol%), 877 min1 (0.2mvessel, 10 vol%), 419 min1 (0.4 m vessel, 5 vol%), 538 min1

(0.4 m vessel, 10 vol%) and 275min1 (0.9 m vessel, 5 vol%)the local particle concentrations in the different vessels werefound to be remarkably similar. Larger deviations can only beobserved for the vessel with a diameter of 0.9 m at a bottomclearance of 0.75D. Here the local particle concentrations arehigher which corresponds to the fact that the suspension heightin this case was larger than 90%. The results indicate local par-ticle concentrations higher than the mean concentration at the

wall in the lower half of the vessel, as well as local concentra-


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0

4

8

12

0.6 0.8

0

4

8

12

0.2 0.4 0.6 0.8

0

4

8

12

0.2 0.4 0.6 0.8

r/R [-]

[%v

ol.]

0.7

5D

0.5

5D

0.2

5D

10 vol.%

8 vol.%

6 vol.%

4 vol.%

2 vol.%

Fig. 5. Local particle volume fractions measured in a vessel with D=0.2 m,mean particle volume fractions of 210 vol% and a stirred speed of 877 min1

(50 images per measuring point).

tions lower than the mean concentration at the shaft and at thewall in the upper half of the vessel.

In Fig. 5 various mean dispersed phase volume fractionsfrom 2 to 10 vol% are depicted for a constant stirrer speed of877min1. This is the stirrer speed necessary to meet the H90criterion for a mean dispersed phase concentration of 10 vol%.While the results for mean concentrations of 2, 4 and 6 vol% ex-hibit a fairly homogeneous distribution of the dispersed phase,at higher particle loadings a substantial decrease of the lo-cal concentration at bottom clearances of 0.55D and 0.75D

near the shaft was found. In all investigated regions lower than0.55D, the measured local particle concentration was close tothe mean concentration.

Contrary to the investigations of other authors (Einenkel,1979; Barresi and Baldi, 1987), no pronounced accumulationof particles at the stirrer level was found.

A comparison of the local particle concentration at njs(Zwietering, 1958) and nH90 is given in Fig. 6. In most in-vestigated regions the local concentration achieved with theimpeller speed nH90 was closer to the mean concentration of5 vol%. For all investigated mean volume fractions and ves-sel diameters the stirrer speed nH90 was higher than njs andtherefore provides a better distribution of the dispersed phase.

Although the H90 criterion has been proven to be more sub-

0

4

8

12

0.6 0.8

0

4

8

12

0.2 0.4 0.6 0.8

0

4

8

12

0.2 0.4 0.6 0.8

r/R [-]

[%Vol.]

0.7

5D

0.5

5D

0.2

5D nH90

njs

Fig. 6. Local particle volume fractions measured in a vessel with D=0.4 m,mean particle volume fractions 5 vol% and impeller speeds of nH90:419min1 and njs : 338 min

1.

jective due to the strongly transient behaviour of the particlewaves that develop beneath the clear liquid layer (Kraume andZehner, 2001), the H90 criterion qualifies as a criterion forcomplete suspension and is, unlike measurements ofnjs , alsoreproducible in opaque vessels.

To give a detailed impression of the particle distribution, inFig. 7 all 69 measuring points investigated in the vessel with adiameter of 0.9 m are shown. The dispersed phase with a meanconcentration of 5 vol% was in the state of complete suspensionwith an impeller speed of 275 min1. In Fig. 7, the abscissas

again represent the vertical and radial position in the vesselbut subtend the ordinates, indicating the local dispersed phasevolume fraction, at the mean concentration of 5 vol%.

Local particle concentrations above the mean concentrationwere observed especially at the wall but also in the downstreamregion of the secondary vortex in the vicinity of the shaft andat the level of the stirrer. Furthermore, in the lowest investi-gated measuring plane at a bottom clearance of 0.15D, a slightbut rather homogeneous increase of the local particle concen-tration can be stated. While there is a reduction of the particleconcentration at the shaft above the impeller, the concentrationis increased at positions with similar radii below the impeller.Larger areas with a local concentration below the mean con-

centration were only found at the highest measuring plane at
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0.15 0.35 0.55 0.75 0.95

r/R [-][%v

ol.]

DN900. 5 %vol.

0

5

10

Fig. 7. Local particle volume fractions measured in D = 0.9 m with a meanparticle volume fraction of 5% at stirrer speed of 275min1, suspensionheight > 0.9D.

0.85D. No evidence was found of a pronounced minimum ofthe local particle concentration in the centre of the secondaryflow field as it is predicted by some CFD simulations (e.g.Sommerfeld and Decker, 2003).

3.2. Power number

The experimental results of the power number shown in thiscontribution were obtained in the mid-sized vessel with a di-ameter of 0.4 m. The general tendency of the results, however,

was confirmed by measurements with the other two vessel sizesof 0.2 and 0.9 m as well.Fig. 8 shows the related power number NP Sus/NPWater vs.

Reynolds number for 5 and 10 vol% mean dispersed phase vol-ume fraction. Furthermore, njs and nH90 are indicated. Themeasurements were carried out with the vessel mounted on apneumatic bearing with a lever arm, load cell combination todetermine the torque.

The results in Fig. 8 show the related power numbers ofboth particle volume fractions to be lower than the power num-bers of the single phase system for higher Reynolds numbersabove approximately 105. This was not expected and is opposedto other publications (Niesmak, 1982; Bujalski et al., 1999;

Greaves and Loh, 1984; Wu et al., 2002). A decrease of the

5

0.75

1

1.25

1.5

1.0E+04 1.0E+05 1.0E+06

Re [-]

10 %Vol.

5 %Vol.

H90njs

NP

Sus

/NPWater

[-]

Fig. 8. Related power number, njs and nH90 for mean dispersed phasevolume fractions of 5% and 10% for a vessel diameter of 0.4m.

power number in suspensions so far has only been reported forRushton turbines and very high dispersed phase concentrationsof 49 vol% where a non-Newtonian behaviour of the mixturecan be assumed (Wu et al., 2002).

For clarity, the progression of the curves can be divided intothree different sections. In Section 1, at Reynolds numbers be-low 6104, a decrease of the related power number can be ob-served with rising Reynolds numbers. This is probably causedby the reduced bottom clearance of the impeller due to the sed-imented particles on the bottom of the vessel leading to a largerpower number (Bates et al., 1966). According to Liepe et al.(1998), a reduction of the bottom clearance can increase thepower number up to 25%. With an increasing Reynolds num-ber the thickness of the solids layer on the bottom is reducedand therefore the power number decreases also due to an in-creased bottom clearance of the stirrer. Accordingly, this ef-

fect is more pronounced for the mean particle volume frac-tion of 10%. At the impeller speed for complete suspensionnjs all particles are suspended thus the available bottom clear-ance of the stirrer has reached its maximum. Although the bot-tom clearance of the stirrer with no particles at the bottomis identical to the bottom clearance of the single-phase sys-tem, a power number smaller than the one of a single-phasesystem can be observed. At this Reynolds number a com-plete suspension has been achieved, but it is not homogeneous,yet.

In Section 2, for an impeller speed between njs andnH90, the related power numbers remain almost constant.

As a result of the upward-directed secondary flow fieldof the stirrer and the natural behaviour of the particles tosettle, a clear liquid layer between the suspended parti-cles and the surface is formed (Einenkel, 1979; Kraumeand Zehner, 2001). In consequence the stirrer is rotatingin a local particle concentration that is significantly higherthan the mean concentration. The increased mean densityin the proximity of the stirrer in consequence should leadto a higher related power number that decreases with anincreasing stirrer speed and thereby increased suspensionheight.

What we observe in Fig. 8 is the opposite. In all investigatedcases for impeller speeds larger than njs the related power num-

ber rises with higher impeller speed and an increasing height
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of the suspension (Section 3). The effect observed here is notentirely understood, but several known phenomena can be em-ployed to explain this behaviour.

Firstly, the reduction of the solids fraction between the bladesof the stirrer due to centrifugal effects can reduce the powernumber to a degree where it is equal to the one of a single-

phase system (Nienow, 1992).Secondly, the influence of the particles on the turbulence ofthe continuous phase is likely to have an impact on the powerconsumption. Particles with a diameter smaller than the Kol-mogorov scale are able to follow even the smallest eddies (Goreand Crowe, 1989). Due to the additional mass of the particles,more kinetic energy is dissipated and the turbulence of the con-tinuous phase is reduced (Graham, 2000). Since the increaseof shear stress in a turbulent fluid is comparable to a fluid withhigher viscosity (Lee and Brner, 1987), a reduction of the tur-bulence would lead to smaller shear stress and to reduced powerconsumption.

The third effect is related to the known fact that the velocityof the secondary flow and thereby the circulation number isreduced with an increasing solids content (Angst et al., 2001;Kohnen and Bohnet, 2001). The effect in a stirred vessel canbe explained in analogy to a centrifugal pump. If the flowrate of a centrifugal pump is reduced by a reduction of thein- or outlet cross-section, a drop in the power consumptionwill occur because less fluid is being accelerated. A simi-lar behaviour can be assumed for an axial pumping stirrerin a vessel with the flow rate being reduced by particles(Zehner, 2005).

This correlates with the experimental results in Fig. 8 wherethe related power number was consistently lower for 10 vol%

than for 5 vol% mean particle volume fraction at higherReynolds numbers.

As noted above, between the impeller speed for completesuspension njs and the homogeneous suspension, the particleconcentration in the proximity of the stirrer is higher than themean concentration. Fig. 8 indicates that an increasing stirrerspeed leads to an increasing related power number although thesuspension height is rising thus the local solids concentrationaround the stirrer is reduced. To understand this phenomenonthe clear layer of continuous phase above the suspension heighthas to be taken into account. This layer is not involved in thecirculation induced by the stirrer (Bujalski et al., 1999; Kraume,

1992) and in consequence has little influence on the powerinput.At any stirrer speed higher than njs , the entire solids content

is circulated, but only the volume of the continuous phase sit-uated below the suspension height is circulated as well. Thus,a low suspension height not only reduces the power numberdue to the reduced circulation because of the increased solidsconcentration around the stirrer, it also circulates onlys a lim-ited amount of the continuous phase. This leads to an increasedvelocity of the continous phase in the region where the circula-tion hoop is reaccelerated by the stirrer. Therefore, in Section3, for impeller speeds higher than nH90 an increasing stirrerspeed leads by a rising suspension height to a decreasing solids

concentration around the stirrer and a decreasing velocity of

0.8

0.9

1

0 10 15 20 25

NP

Sus

/NPWater

[-]

Particle volume fraction [%vol.]

5

Fig. 9. Related power numbers for mean dispersed phase volume fractionsfrom 1.625.1vol% at a Reynolds number of 2 105 for a vessel diameterof 0.4m.

the circulated continuous phase which both result in a risingpower number.

These results are confirmed by the measurements presentedin Fig. 9. In this case, the torque was measured with a com-mercial torque metre. Here, the related power number at a fixedReynolds number of 2 105 is shown for various mean dis-persed phase volume fractions from 1.6% to 25.1%. The cor-responding impeller speed was in all cases larger than njs .Fig. 9 shows a steady decrease of the related power numberwith increasing particle volume fraction. As mentioned before,these findings do not confirm the results of other workgroups.It is likely that the geometry and proportions chosen, the com-bination of and axially, downward pumping impeller and adished bottom are responsible for the reduction of the powernumber.

4. Conclusions

At a stirrer speed matching the H90 criterion, the local par-ticle concentrations at the measuring points located between0.3D and 0.8D, 0.25H and 0.75H are quite close to the meanconcentration of particles in the vessel under comparable con-ditions. In the investigated systems with a particle diameter of200m, the H90 criterion is a good indicator for a homoge-neous distribution below the suspension height.

The local particle concentrations in the different vessels with

impeller speeds meeting the H90 criterion were found to beremarkably similar. In all investigated systems no evidence ofa pronounced local minimum in the centre of the toroidal vor-tex formed by the secondary flow field were found. Significantinhomogeneities were detected in the direct proximity of thewall as well as at the shaft above the stirrer. There is a reduc-tion of the local particle concentration with increasing bottomclearance and decreasing radius.

The power number of all investigated scales and mean par-ticle volume fractions was less than the power number for theequivalent single-phase systems at impeller speeds higher thannjs . The observed reduction of approximately 10% of the powernumber (Fig. 8) may have no impact on design and construc-

tion of vessels but is certainly remarkable.
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Notation

d diameter of the stirrer, mD diameter of the vessel, mH height of the vessel, mn stirrer speed, 1/min

NP power number, dimensionlessr radius of measuring point, mR radius of the vessel, m

Greek letters

density, kg/m3

volume fraction, vol%

Indices

H90 90% suspension heightjs just suspendedL liquid phase

S solid phaseSus suspension

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