[MartiÌ-n, Montes, Galan, 2008] Bubbling Process in Stirred Tank Reactors I - Agitator Effect on Bubble Size, Formation and Rising

Chemical Engineering Science 63 (2008) 3212 -- 3222

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Bubblingprocess instirredtankreactors I:Agitatoreffectonbubblesize, formationandrising

Mariano Martn, Francisco J. Montes, Miguel A. GalnDepartamento de Ingeniera Qumica y Textil, Universidad de Salamanca, Pza. de los Cados 1-5, 37008 Salamanca, Spain

A R T I C L E I N F O A B S T R A C T

Article history:Received 19 July 2006Received in revised form 18 March 2008Accepted 21 March 2008Available online 27 March 2008

Keywords:CFDBubblesStirred tanksBioreactorsBubbling processImpellers

The study of the hydrodynamics generated by impellers and its effect on the generation of bubbles andon their rising and dispersion is of key importance to improve the knowledge about the contact betweenphases and the mass transfer rates, particularly in cases where it is the limiting step. CFD simulations andhigh-speed video techniques are used to study the hydrodynamics developed by five different impellers,each located at three different positions above the dispersion device. Furthermore, two dispersion deviceswith one and two holes, respectively, are also used. The effect of the impellers on the characteristicsof the bubbles and of the dispersions generated has been analysed. Bubbles generated under stirringare smaller than those generated in stagnant fluids. It is also shown that the initial bubble size at theorifice determines the contribution of the impeller and the perforated plate to the Sauter mean diameter.Although bubble formation is chaotic, the formation period is predictable based on three variables: thelocation of the impeller, its rotational speed and the gas flow rate. Bubble mean diameter was correlatedto classical equations based on Kolmogorov's theory. Only when impellers are capable of breaking thebubbles, Kolmogorov's theory is completely verified.

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1. Introduction

In order to improve the mass transfer rate between phases, manytimes the gas phase is dispersed into the liquid phase not only usingdispersion devices but also mechanical mixing. This unit operationis widely used in the chemical and biochemical industries. In fer-mentation processes and waste water treatment, the dispersion ofthe gas phase is the most important operation.

The main factors affecting the mass transfer rate in gas--liquiddispersions are the physico-chemical properties of the liquid, thesparger design, the diameter of the orifice, the tank design, the typeof agitator and its relative dimensions, the power input, the gasflow rate, the continuous phase, the presence of a chemical reaction,the electrolyte concentration and the presence of catalysts (Sidemanet al., 1966). Mixing also defines the generation of bubbles insidethe tank (their frequency and initial size), their mean size and thehydrodynamics of the whole system.

Several studies (Hassan and Robinson, 1977; Arjunwadkar et al.,1998; Gogate et al., 2000; Veera et al., 2001; Bouaifi et al., 2001; Alveset al., 2002) have been carried out in order to understand the effect ofthe hydrodynamics on the mass transfer. The typical hydrodynamic

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parameters studied have been the bubble size distribution, the gashold up, G , the rising velocity of the bubbles and the effective powerinput, which is very important for the scale up of the equipment.

However, the effect of the hydrodynamics developed by the im-pellers on the bubbling has barely been studied. It has been reportedby Marshall et al. (1993) that bubbles generated under flow fieldswere smaller in comparison with those growing in stagnant liquids.Only few models try to determine the effect of known liquid flowson the generation of bubbles at submerged orifices (Marshall et al.,1993; Nahra and Kamotani, 2003; Loubire et al., 2004).

Inside stirred tanks, the liquid flow under the impeller is char-acterised by turbulent eddies (McCabe et al., 1991). Bubble forma-tion process and the dispersions generated will be affected by theflow patterns developed by the impeller, which defines the flowover the orifices as well as the stresses acting on the bubbles. Ac-cording to Barabash and Belevitskaya (1995), bubble stability underthese stresses depends on its size. Furthermore, the impeller can alsoguide the gas through preferential paths, so that the resident timeof bubbles is reduced (Parente et al., 2004).

In this paper, high-speed video techniques are used to study thegeneration of bubbles under mixing conditions as well as to studythe mean size of the population of bubbles for five different agitators(two pitched blade turbines, a modified blade, a Rushton turbine anda propeller), two dispersion devices, and several gas flow rates androtational speeds. The position of the impellers was also modified

M. Martn et al. / Chemical Engineering Science 63 (2008) 3212 -- 3222 3213

along the vertical axis. The final aim of this work is to study andcharacterise the hydrodynamics in order to explain its effect on themass transfer rate. This explanation will be carried out in the secondpart of the work.

As a first approach to the problem, the hydrodynamics of theliquid will be simulated using computational fluid dynamics (CFD).This approach is easy and saves time and money (Aubin et al., 2004;Brucato et al., 1998; Montangne et al., 2001). It has already beenverified by visual methods such as Doppler velocimetry (LCD), orparticle image velocimetry (PIV), for typical geometries and agita-tors such as Rushton or pitched turbines (Ranade et al., 1992; Donget al., 1994; Hockey and Nouri, 1996; Nienow, 1997; Sahu et al.,1999; Baldi and Yianneskis, 2004).

2. Theoretical considerations

Bubble initial volume is responsible for its stability in the fluidflow and it will determine whether the bubbles are going to bebroken or not (Barabash and Belevitskaya, 1995). The breakageof the bubbles is what provides contact area between phases.Therefore, bubble dispersion depends strongly on the bubblingprocess.

Although themodels available in the literature for bubble growingin non-stagnant fluids consider only the effect of known liquid flowrates over the orifice (Marshall et al., 1993; Nahra and Kamotani,2003; Loubire et al., 2004), they conclude that the flow reduces thebubble initial volume since it drags the bubble from the orifices andso it detaches sooner.

The theoretical study for the mean diameter of the bubbles inan agitated gas--liquid dispersion has traditionally been carried outaccording to Kolmogorov's theory of isotropic turbulence. The max-imum stable diameter for a bubble or a drop is a function of theWeber number of the system (Pacek et al., 1998).

The Sauter mean diameter, d32, is widely considered to be pro-portional to the maximum stable diameter (Calderbank, 1958; Paceket al., 1998; Alves et al., 2002; Garca-Ochoa and Gmez, 2004), andcan be expressed as

d32 = C13/5

3/52/5(1)

where is assumed to be the input power per unit mass (Alves et al.,2002). Calderbank (1958) also considered the effect of the gas holdup on the mean diameter of the bubbles.

Although the Sauter mean diameter has traditionally been con-sidered to be proportional to the maximum stable diameter, thisassumption is valid only if the bubble size is controlled by break-up processes. On the other hand, when coalescence processes playan important role, d32 has been reported to be proportional to theminimum diameter of the dispersion (Shinnar, 1961):

d32 = C2 0.25 (2)However, since 1967, most authors have used the first consider-

ation. Looking for simple equations for predicting bubble mean sizein stirred tanks and avoiding theoretical considerations, the typicalequation used is

d32 = kd (PgV

)(3)

The constants in the former equations depend on the dispersiondevice as well as on the impeller type.

These equations can also be obtained as the solution of a popula-tion balance in which bubbles are broken due to turbulence whereastheir stability depends on the surface tension (Galindo et al., 2000). in Eq. (3) would depend on the balance between break-up andcoalescence processes, and thus it is smaller next to the impeller.

Meanwhile, coalescence increases (Bouaifi et al., 2001; Alves et al.,2002).

3. Materials and methods

3.1. Experimental setup

The experimental setup is shown in Fig. 1. Bubbles are generatedinside a laser-sealed glass tankwhose dimensions are 151515 cm.In the middle of the tank, there is a gas chamber with dimensions5 5 5 cm divided into two equal chambers. On the gas chamber,a substructure, 2 2 2 cm, is placed in order to accommodate thesieve plate on it. The liquid level reaches 8 cm of water over theperforated plate. Deionisedwaterwas used as liquidmedia (20 C, =998kg/m3, =0.073N/m, L =1.037103 Pa s). This configurationallows an accurate visualisation of the bubbling process as well asthe study of the dispersions generated by different impellers anddispersion devices.

Air bubbles are generated at two different perforated plates. Thefirst has only one orifice of 2mm of diameter. The second has twoorifices of 2mm each. In order to avoid coalescence between growingbubbles, the separation between holes was 6mm. However, bubbledeformation due to liquid flow makes coalescence easier (Martinet al., 2008). Nevertheless, the big bubble resulting from coalescenceat the perforated plate would be easily broken by the impeller andthe reported cases of coalescence were of no statistical importance.In the first case, only one of the two gas chambers was used while theother was sealed. When the two-holed perforated plate was used,each hole was the exit for each of the gas chambers. Due to theconfiguration of the experimental setup, three gas flow rates of 0.6106, 1.4106 and 2.8106 m3/s were used with the one-holeddispersion device along with one gas chamber. Meanwhile, for thetwo-holed dispersion device, lower flow rates were to be used, 0.3106, 0.6 106 and 1.4 106 m3/s, since the air flow can breakthe seal between chambers. A constant pressure regime has beenused.

The experimental conditions have been selected in order to gen-erate normal flow patterns inside the tank. The impeller must belocated neither close to the dispersion device nor close to the freesurface. The mixing must be turbulent and it is desirable for the ro-tation velocity to be low in order to avoid flooding due to eithercavitation or central vortexes (Placek et al., 1986).

Therefore, the impeller was situated in the middle of the tankat three different distances, h, from the dispersion device of 0.02,0.035 and 0.05m. Three rotational speeds, 180, 280 and 430 rpm,were used and this experimental scheme was used for five differentimpellers, a Rushton turbine, a propeller, a modified blade and twodifferent pitched blade turbines.

The dispersion generated as well as the individual bubbles wererecorded by means of a high-speed video camera able to record upto 1000 frames per second. Motionscope software was used to editand study the images and to carry out the measurements of thebubble sizes and formation time and frequency.

The Sauter mean diameter of the dispersion was calculated us-ing Eq. (4), counting up to 200 bubbles. In case there was no suchnumber in a single frame, several frames, separated enough in timenot to study the same bubbles, were analysed in order to obtain arepresentative value:

d32 =

nid3eqi

nid2eqi

(4)

where ni is the number of bubbles with an equivalent diameter deqi.It is determined considering the bubbles as ellipsoids, Fig. 2.

3214 M. Martn et al. / Chemical Engineering Science 63 (2008) 3212 -- 3222

Fig. 1. Experimental setup: 1. High-speed video camera; 2. optical table; 3. bubble column; 4. illumination source; 5. air bottles; 6. rotameter; 7. computer; 8. impeller.

Fig. 2. Equivalent diameter calculus.

3.2. Power number calculation

3.2.1. Theoretical modelThe power number determines the real power input in the sys-

tem. Due to the fact that in the experimental setup the dissipatedenergy was kept low, so that bubbles could be recorded as individ-ual entities, the experimental measurements were not reliable andan alternative method was used. The hydrodynamics of the systemhas been modelled using CFD.

Ansys CFX solves the momentum transport equations,Navier--Stokes equations and continuity equation using the finiteelement method. The turbulence method used is known as k.. Thevalue for the model constants are C = 0.09, C1 = 1.44, C2 = 1.92,k = 1.0 and = 1.3. The normal stress (2/3) k, is added to thehydrostatic pressure. The equations solved can be found in Brucatoet al. (1998).

The boundary conditions to be imposed correspond to the tankwalls, the impeller geometry, both defined as smooth walls, and thefree surface that correspond to the atmosphere.

3.2.2. GeometriesFig. 3 represents the geometries of the five different impellers

with their photographs. These 3-D geometries, as well as the tank,were created using CFX. The dimensions of the geometries are onthe figures so that it is possible to clone the stirrers and the tank.As it can be seen in the representation of the tank, a hole has to bedesigned in order to make a way for the impeller. Its boundaries willbe coupled with the boundaries of each of the impellers.

4. Results

4.1. Power number verification

Table 1 shows the calculated power number for the different agi-tators at different positions using CFD. Since the results for the threerotational speeds at each position were similar, a mean value wascalculated. The values in Table 1 are small. However, they are inaccordance with the fact that in case of regions in the tank withrelative low flow velocity, in spite of high turbulence near the im-

peller, the energy required to move the flow is small (McCabe et al.,1991). The liquid velocity was much lower below and surroundingthe gas chamber than that in the impeller region, due to the loca-tion of the dispersion device, in order to record the generation ofthe bubbles. This effect is similar to that shown for non-Newtonianfluids for fluid regions far from the impeller (McCabe et al., 1991).Furthermore, in the absence of baffles, the power number decreaseswith the Reynolds number (McCabe et al., 1991).

Although Ranade et al. (1992) and Ranade (1997) have success-fully compared experimental values of the power number resultingfrom their simulations with calculated values, it is desirable to con-firm the power numbers calculated due to the non-standard geome-tries used in this work.

To verify the values of the power number (P0), we tried to mea-sure the power input. However, it turned out to be a very smallvalue and within the experimental error of the clamp AC/DC currenttester. Therefore, the simulated values of P0 were validated measur-ing mixing times.

The power number and the dissipated energy are related to themixing time in a tank, . Several empirical correlations have beenproposed to determine : Eq. (5) (Van't Riet and Tramper, 1991), andEq. (6) (Nienow, 1997):

= 3(

T

D

)3 P1/30 N1 (5)

= 5.9(

T

D

)1/3 1/3 D2/3 (6)

To experimentally determine , the concentration of a colorant(blue of methylene) will be monitored after its injection in the tank.Five ml will be injected at a corner of the tank and every 5 s a sampleof 2.5ml will be extracted. The volumes of the samples are negligi-ble with respect to the total volume of the tank and the dilution alsoallows the verification of Beer's law. The concentration will be mea-sured using UV-V spectrophotometry at 590nm, the wavelength atwhich the maximum of absorption of the colorant is obtained, anda HITACHI U-2000 Spectrophotometer. The colorant verifies Beer'sLaw (Atkins, 1991). The mixing time is that for which the concentra-tion after the injection differs less than 5% with that at time infinity.

The experimental conditions for which the mixing time was mea-sured were h=2 cm for each of the first five impellers at an impellerspeed of 180 rpm. Under these conditions, the experimental relativeerror is the smallest, since the biggest mixing time is obtained andthe injection is performed without directing the colorant into theimpeller blades.

The measured mixing times were compared with those obtainedusing the power number in empirical equations (5) and (6) (seeFig. 4). The experimental results agree well with the predicted byEqs. (5) and (6), so that the simulated power numbers can be nowused in the study.


Fig. 3. Impellers (a) Pitched blade turbine: T = 6 cm, Tj = 0.6 cm, Wa = 1.5mm, Wb = 1mm, Re = 5.1 cm, Rb = 6.5 cm, Di = 5mm; (b) Modified blades: T = 4.8 cm, Ti = 0.35 cm,Tj = 0.4 cm, R = 0.25 cm, Tk = 0.5 cm, D = 1 cm; (c) Rushton turbine: T = 5.2 cm, Td = 3.2 cm, Ti = 1.5 cm, Tj = 1 cm; (d) Pitched blade turbine: T = 5.6 cm, Tj = 0.7 cm, 45 ,Di = 0.5 cm, R = 11.15 cm, W = 0.6 cm; (e) Propeller: T = 5 cm; Tlobulus = 1.7 cm, 30 .

Table 1Simulated Power number

h (m) Pitched blade (impeller 1) Modified blade (impeller 2) Rushton turbine (impeller 3) Pitched blade (b) (impeller 4) Propeller (impeller 5)

0.02 0.075 0.07 0.11 0.036 0.040.035 0.083 0.06 0.10 0.034 0.0360.05 0.076 0.09 0.10 0.034 0.036

Fig. 4. CFD code verification.

Table 2Bubble formation without agitation

Qc (m3/s) tf (ms) tt (ms) deqi (mm)

1 orifice 0.6 106 31 170 7.01.4 106 30 88 7.92.8 106 30 47 8.7

2 orifices 0.3 106 33 186 4.80.6 106 33 145 5.31.4 106 32 99 5.1

4.2. Bubbling process

The aeration number for all the impellers was kept low so thatthe study of bubbles in dispersions generated is possible. Otherwise,bubbles could not be visually identified as entities. According tothe empirical equations for the aeration number (Hughmark, 1980;Walas, 1990), the aerated and the unaerated power can be consideredas equal under our experimental conditions.

Table 2 summarizes the results of the characteristics of the bub-bles in the absence of stirring as a starting point for the comparisonof the effect of stirring on the bubbles.


Although the generation of a single bubble under stirring is achaotic process, bubble formation time and size change from onebubble to another under the same experimental conditions. In thiscontext, several patterns can be found.

Bubbles generated under stirring are affected by the flow devel-oped in the tank and by turbulent eddies. In the first place, bubbleson the dispersion device can be dragged due to the liquid flow de-veloped by the impeller (see Fig. 5). Furthermore, it can also be seenthat for the same experimental conditions, bubble shape and forma-tion time vary from one bubble to another, supporting the chaos be-hind bubbling. Second, the motion of bubbles depends on the maindriving force and the flow pattern generated by the impeller. Forthe highest gas flow rate experimentally used, the initial bubble di-ameter is approximately 9mm. In this case, bubbles are big and the

Fig. 5. Bubbles swept by the impeller (t, ms). Modified blade h=2 cm; N =180 rpm;Qc = 0.6 106 m3/s.

Fig. 6. Period of bubble formation. 1 orifice dispersion device.

buoyancy force has an important contribution. However, at the sametime, the drag force increases because the cross area of the bubbleis also large. Therefore, bubble motion results from the combinationof both diving forces together with the flow lines generated by theimpeller, which depend on its geometry. Finally, the flow patterncan lead the bubbles through preferential paths. The impeller loca-tion plays an important role in bubble suction from the orifice. Thehigher the location of the impeller, the greater the pressure differ-ence between the position of the impeller and that of the dispersiondevice.

Based on the experimental results exposed before, the formationperiod of the bubbles, tt , is almost predictable because it depends onthe gas flow rate and it is directly related to the flow pattern over theholes of the dispersion devices as well as to the pressure differencebetween the impeller and the dispersion device. Apart from the well-known effect of the gas flow rate, which decreases tt , an incrementin power input also reduces tt for all the impellers. Bubbles aresucked by the upwards vertical flow lines generated by the impeller.The position of the impeller does not always modify tt ; however,in general terms, the higher the impeller is located, the shorter theperiod time, due to the suction effect of the central ascendant currentunder the impellers and the pressure difference generated betweenthe impeller and the perforated plate. Fig. 6 shows the experimentalresults for the one-holed dispersion device.

In contrast, bubble formation time, tf , is not so predictable. Nev-ertheless, tf usually decreases slightly with the gas flow rate and thepower input. Bubbles are sucked and dragged from the dispersiondevice and their detachment is earlier comparedwith stagnant fluids.


Fig. 7. Initial bubble size. 1 orifice dispersion device.

As it can be seen in Fig. 7, in general, the power input reduces theinitial bubble size. Bubbles are swept and helped detach from thedispersion device due to the impeller agitation. Since tf decreasesslightly with the impeller speed, so does the initial bubble size. Thegas flow rate across the orifice also has an important effect on themean bubble size. Since tf remains almost constant with the gas flowrate, bigger bubbles are generated as the gas flow rate increases.Initial bubble size is important to determine whether the bubblesare going to be dragged by the flow or could be broken.

Both the raising of the bubbles and the path followed are influ-enced by the initial size of the bubbles along with the flow patterngenerated by the impeller. The movement of big bubbles is deter-mined not only by the buoyancy force, but also by drag forces due tothe large cross-sectional areas, considering that the bubbles do notbreak. Both contributions and the flow lines generated by the differ-ent impellers, as a result of the particular geometry of their blades,can make the bubble rise in zig-zag (pitched blade turbines) or ina line (Propeller and two modified blades). In the case of smallerbubbles, both effects reduce their contribution to the movementof the bubbles. As a result, bubbles can easily be dragged by theflow. Fig. 8 represents the rising paths for the pitched blade tur-bine and the propeller. To the right, the gas flow rate increases from0.6 106 to 2.8 106 m3/s. Meanwhile, downwards the rota-tional speed increases from 180 to 430 rpm. The photographs aretaken at the highest distance (h=0.05m). The rising path generatedby both can be fitted to a Fourier transform. The particular flow pat-tern developed by the propeller makes the bubbles rise almost in aline. For lower positions of the impeller, the paths are barely devel-oped, since the bubbles are generated in the zone of influence of theimpeller.

From these results, the bubble mean size and the effect of theposition of the impeller on the mass transfer rate can be easily ex-plained. Bubbles will be broken either by deformation due to theflow or by direct impact with the blades. According to the particu-lar rising path, the bubbles can even avoid the effect of the bladesin certain conditions; therefore, it can be predicted that as the im-peller is placed higher, bubbles will be broken mainly as a result oftheir deformation, and if it is located lower, the direct effect of theimpeller will be the main break-up mechanism.

4.3. Bubble dispersions

Mean bubble size depends on the capability of the impeller ofbreaking the bubbles generated at the dispersion device. Meanwhile,bubble stability in a tank depends on its size. Big bubbles are easilydeformed and broken while smaller ones are dragged by the flowacross the tank with little deformation. Fig. 9 represents the defor-mation of a bubble generated under a Rushton turbine. The regularshapes shown in stagnant fluids are no longer seen under stirring.

The Sauter mean diameter for both dispersion devices, one-holedand two-holed perforated plates, was determined considering thebubbles as ellipsoids and calculating the equivalent diameter of eachbubble, deqi, of the dispersion according to Fig. 2. The definition ofthe Sauter mean diameter was used, Eq. (4), so that the experimentalresults could be fixed to Eq. (3). Table 3 summarizes the results.

The results presented in Table 3 can be explained based on theobserved hydrodynamics. Big bubbles generated from the one-holeddispersion device can be easily deformed and broken. As a result, thevalues of are large, in absolute terms. Smaller bubbles are morestable in the flow and this leads to smaller values of , in absolute


Fig. 8. Bubbles rising under pitched blade and propeller. h = 0.05m.

Fig. 9. Bubble deformation under a Rushton turbine (t, ms). h = 0.05m; N = 430 rpm; Qc = 1.4 106 m3/s.

Table 3Sauter mean diameter versus power input

One-holed Two-holed

kd 103 kd 103 Pitched blade 5.2 0.26 5.0 0.30Modified blade 3.4 0.35 4.8 0.22Rushton turbine 4.6 0.38 3.7 0.26Pitched blade (b) 4.0 0.34 3.4 0.23Propeller 4.2 0.25 4.5 0.04Air--water system 4.4 0.25 3.8 0.16

The effect of the five impellers.

terms. As a result, the dispersion device has a higher contribution tothe mean size of the dispersion.

Considering all the impellers for each dispersion device, meanvalues of kd or were obtained. As it can be seen in Table 3, themean values of kd and are similar to those reported by Bouaifiet al. (2001) and Alves et al. (2002), for the air--water system.

Furthermore, the results obtained impeller by impeller are alsoin accordance with Alves's results, which reveal that if break-upmechanisms determine bubble size, increases, in absolute terms.Meanwhile, coalescence and lack of breakage decrease , in absoluteterms.

The location of the impeller along the vertical axis for h = 0.02and 0.035 cm, the locations of the impeller where it was possibleto measure a complete dispersion in the experimental setup, haslow effect on the break-up efficiency of the power input for thedispersions generated from the one-holed perforated plate. Bub-bles are big enough to be easily broken. The only impeller whoseresults were clearly affected by the position of the impeller wasthe first pitched blade turbine, impeller 1. A higher position ofthe impeller resulted in a loss of break-up efficiency due to thefact that the bubbles could avoid the effect of the impeller. How-ever, if the bubbles generated at the dispersion device are smaller,such as those generated from the two-holed perforated plate, ahigher position of the impellers reduces the break-up efficiencyfor almost all the impellers. Table 4 summarizes the experimentalresults.


Table 4Effect of the location of the impeller on the break-up efficiency

h (cm) One-holed Two-holed

Pitched blade 2 0.23 0.353.5 0.27 0.275 0.30 0.35

Modified blade 2 0.33 0.293.5 0.33 0.12

Rushton turbine 2 0.37 0.323.5 0.38 0.20

Pitched blade (b) 2 0.32 0.273.5 0.35 0.18

Propeller 2 0.24 0.053.5 0.26 0.07

Fig. 10. Bubble mean size one-holed dispersion device.

Fig. 11. Bubble mean size two-holed dispersion device.

Figs. 10 and 11 show the effect of the power input on the meanbubble size of the dispersion for the two different dispersion deviceswith all the impellers. decreases as the generated bubbles at theorifice are smaller since they are more stable in the flow.

Table 5Sauter mean diameter versus power input

One-holed Two-holed

kd kd

Pitched blade 0.62 0.26 0.78 0.29Modified blade 0.46 0.32 0.54 0.20Rushton turbine 0.67 0.34 0.71 0.20Pitched blade (b) 0.52 0.35 0.57 0.20Propeller 0.54 0.24 0.82 0.03Air--water system 0.57 0.25 0.65 0.15The effect of the five impellers and the initial bubble size.

Since the initial bubble size determines the stability of the bub-bles, and this size depends on the dispersion device and the gas flowrate impeller, it is convenient to use the following equation to isolatethe effect of the impeller on the bubbles:

d32db

= kd (PgV

)(7)

The empirical coefficients are presented in Table 5. The values of show almost no change for the one-holed perforated plate and a littlechange for the two-holed perforated plate. However, kd increaseswhen the stability of the initial bubble increases. Meanwhile, thevalues of kd in Table 3 remain stable.

It is possible to explain the coefficients of the correlation (Tables 3and 5) based on the photographs of the bubbles (Fig. 12).

When the impeller is capable of breaking the bubbles, in generalfor big initial bubbles, for example, those generated from the one-holed perforated plate, was next to that predicted by Kolmogorov'stheory (0.4). For these cases the mean bubble diameter of the dis-persion is defined by the break-up process.

However, if the impeller cannot break the bubbles, this coefficientis lower, in absolute terms. There are four different reasons for ob-taining a low value of . The first reason is if the bubble size is withinthe stable range for the operating conditions. In general, those gen-erated from the two-holed perforated plate are small bubbles whichfollow the flow lines. The blades of the impeller can barely deformthem. The second reason is if the bubbles can avoid the blades. Thisoccurs when the rising path of the bubbles, resulting from the hy-drodynamics generated by each impeller combined with the effect ofdrag and buoyancy forces on the bubbles, allows them to bypass theimpeller blades. The third reason is in case the blades of the impellercannot break the bubbles. This occurs when either the geometry ofthe blades does not allow developing a wake where the bubbles canbe retained or the bubbles are not hit by the impeller blades. Thepropeller and the three-blade turbine named as impeller 1 show thisfact. The last reason can be the coalescence processes taking placedue to bubble collisions. However, they were rarely found in therecording. As a result, the dependency of the Sauter mean diameteron the power input is less important.

Using these principles, it is possible to justify the break-up effi-ciency of each impeller:

For the pitched blade turbine (impeller 1) the change in theregime with the rotational speed can be seen in Fig. 12(a). At lowrotational speeds, bubbles cannot be broken and rise almost as if nointerference with the impeller exists. Bubbles can avoid the blades.An increase in the rotational speed increases the break-up processesand leads to the generation of a true dispersion. The sharp blades ofthis impeller allow a small loss of break-up efficiency when the ini-tial bubbles are small, such as those generated from the two-holedperforated plate, since bubbles are deformed until they break up inthe discharge of the gas or cut.

The particular geometry of the modified blade impeller, im-peller 2, determines its effect on the bubbles. The peaks generate a


Fig. 12. (a) Pitched blade turbine: rotational speed effect h = 0.02m, Qc = 0.6 106 m3/s; (b) Modified blade: rotational speed effect---h = 0.02m, Qc = 2.8 106 m3/s; (c)Gas dispersion generated by a Rushton turbine (d) Gas dispersion generated by a pitched blade turbine. Effect of gas flow rate---h = 0.02m, N = 430 rpm. (e) Gas dispersiongenerated by a propeller.

low-velocity region along which the bubbles rise. The geometry ofthe blade determines the break-up mechanism, whether the bub-bles are broken due to the deformation at the end of the impeller

or due to the direct cut with the blade. This impeller suffers froma high loss of efficiency in bubble break-up when their initial sizeis smaller, because they can either avoid the blades in their rising


movement, so that they are neither cut by the blades nor retainedat the end of the blades to be broken at the discharged, or cannotbe deformed (Fig. 12(b)).

In the case of the Rushton turbine, the most used impeller for fer-mentation processes, two results can be reported. In the first place,the disk retains the bubbles up to their break-up. This fact increasesthe gas hold up and also the fact that when bigger bubbles are gener-ated, break-up processes are easier. Fig. 12(c) represents the disper-sion of gas generated by a Rushton turbine. This impeller has almostthe same break-up efficiency no matter the initial size of the bubble,the effect of the disk retaining the bubbles until their breakage inthe discharge of the gas phase is the key, maintaining the value of next to that predicted by Kolmogorov's theory for both dispersiondevices.

The second pitched bladed turbine breaks the bubbles due todeformation of the gas at the concave blade. Fig. 12(d) shows thegeneration of the dispersion of bubbles in this particular case. Theblades are more hydrodynamic than those of the first turbine.The bubbles are not cut by the blades. The flow pattern developed,able to deform the bubbles, and the accumulation of gas at theend of the impeller allow a small loss of efficiency in the break-upprocess with the initial size of the bubble.

The most peculiar dispersion generated by any of the impellers isthat generated by the propeller. This impeller, typical in ship propul-sion, develops a flow pattern in which the bubbles are barely brokenbut retained under the impeller. Tables 3 and 5 present the absenceof break-up processes for small bubbles, those generated at the two-holed perforated plate, where is almost zero. The propeller canonly smack the bubbles; meanwhile, the geometry of the blades ofthe turbine does not generate a wade wide enough so as to retainthe bubbles up to their break-up by deformation. The positive valueis due to the deformation of the bubbles in the flow. An explana-tion can be found in the flow pattern developed by the impeller. Alow-pressure region under the impeller is obtained and therefore,bubbles remain there for a while.

Furthermore, the physical effect of the impellers on the gas phase,shown in the equations, whether they are theoretical or empirical,is responsible for their break-up. This is the reason why there aredifferences between the empirical fitting coefficients obtained fordifferent geometries and impeller configurations.

5. Conclusions

Since mass transport processes depend on the hydrodynamicsof the system, its characterisation allows a better understanding ofthe process. CFD has proved to be a powerful tool in order to studydifficult geometries in an easy and safe way.

The mixing in a tank is used to improve the contact betweenphases by dispersion of the gas phase. The dispersion generated byeach impeller depends on its geometry, responsible for the dominantbreak-up mechanism (bubble deformation or elongation, direct cut),and it is conditioned by its effect on the bubbling, which, althoughis a chaotic process, determine the initial bubble size. In general,the gas flow rate increases the initial bubble size; at the same timepower input and a higher location of the impeller reduces it. Fur-thermore, although the effect of the position of the impeller on thecharacteristics of the growing bubbles is not well defined, a higherposition allows the bubbles to avoid the direct effect of the impeller,reducing its efficiency. This is a very important result regarding themass transfer rate.

The dispersion device determines the mean bubble size and thegenerated dispersion if the power input is unable to break the bub-bles. Small bubbles, such as those generated in the two-holed dis-persion device, are difficult to be broken and move with the flow.Bigger bubbles are easily deformed and broken.

The performance of the impellers in the breakage of the bub-bles can be compared with the results of Kolmogorov's theoryof turbulence. Coalescence processes as well as stable bubbles,small bubbles unable to be broken, reduce the dependency ofthe mean bubble diameter on the power input, and only whenthe break-up of the bubbles domain the process of gas disper-sion, the theory of Kolmogorov is verified. The use of Calderbank'sequation for the specific area (Calderbank, 1958) is limited to theimpellers able to break the bubbles, where coalescence processescan be neglected, since it is somehow based on Kolmogorov'stheory.

The rising path of the bubbles depends on the flow pattern ofeach of the impellers as well as on the bubble size, which determinesthe contribution of the drag and buoyancy forces to the movementof the bubble.

Notation

a specific superficial area, m1a horizontal bubble diameter, mb vertical bubble diameter, mC1, C2, C model constantsd32 Sauter mean diameter, mmdb initial bubble diameter, mdeqi equivalent diameter, m, deqi = (a2 b)(1/3)D0 orifice diameter, mDC tank diameter, mDi shaft diameter, mFr , F volume forces, Nm

3FlG aeration number FlG = QcNT3h impeller height above the dispersion device, mH blade height, mk kinetic turbulent energy J kg1L impeller characterists, mni number of bubbles of class iN rotational speed, s1P unaerated power, WPg aerated power, WP0 Power number P0 = PT5N3Qc gas flow rate, m3 s1R blades curvature, m

Re Reynolds number, Re = T2NT impeller diameter, mTi blades length, mtM mixing time, stf formation time of a bubble, mstt formation period of bubbles, msuG gas superficial velocity, ms

1V liquid volume, m3

w blade velocity, ms1W blade width, m

We Weber number, We = N2T3Greek letters

, , , empirical coefficients dissipated energy, Wkg1g gas hold up, eff , T laminar, effective and turbulent viscosities, Pa sG gas density, kgm

3 liquid density, kgm3 superficial tension, Nm1 stress, Nm2 angular velocity, rad s1


Acknowledgements

The support of the Ministerio de Educacin y Ciencia of Spainproviding an F.P.U. fellowship to M. Martn is greatly acknowledged.The funds from the project reference CTQ 2005-01395/PPQ are alsoappreciated. We thank Prof. J. Cuellar, Chemical Engineering Depart-ment, University of Salamanca, for lending us some of the impellersused in this paper.

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