Uniform Flow in Bubble Columns - ACS Publications - American

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Ind. Eng. Chem. Res. 2009, 48, 148–158

Uniform Flow in Bubble Columns R. F. Mudde,* W. K. Harteveld,† and H. E. A. van den Akker Kramers Laboratorium Voor Fysische Technologie and J.M. Burgers Center for Fluid Mechanics, Delft UniVersity of Technology, Pr. Bernhardlaan 6, 2628 BW Delft, The Netherlands

Uniform bubbly flow in a 15 cm bubble column is investigated. We use a special needle sparger consisting of 559 separate needles, uniformly distributed over the bottom. With this sparger, we can ensure that all bubbles generated are of the same size and that the bubble injection is very uniform over the entire bottom of the column. Detailed experiments are reported, using optical glass fibers to measure the local gas fraction and bubble size and velocity and using laser Doppler anemometry to measure the liquid axial velocity field. We find that the homogeneous flow regime extends up to a gas fraction of 55% well beyond the predictions of theory. The superficial gas velocity at which the homogeneous regime looses its stability depends on the water quality: fresh water looses its stability much earlier than old water. However, the gas fraction as a function of the superficial gas velocity is in the homogeneous regime independent of the water quality. The overall gas fraction can be described by a Richardson and Zaki type of relation or by the proposal by Garnier et al. We have indications that, at the point of instability, the bubble size has increased to a critical value at which the lift force reverses sign. This causes the radial gas fraction to change from flat with a small wall peaking to core peaking provoking the instability as suggested by Lucas et al. [Chem. Eng. Technol. 2005, 60, 3609]. Alternatively, at higher gas fractions, the swarm gets denser and the bubble wakes get suppressed. According to Fox and co-workers [Chem. Eng. Sci. 2007, 62, 3159], this causes the flow to lose its stability. 1. Introduction In bubble columns, two basic flow regimes are possible: the homogeneous and the heterogeneous regime (see, e.g., refs 3–6). The latter prevails at the higher gas flow rates and is generally characterized by transient flow, a net circulation, and a wide bubble size distribution. Bubble columns operate in most cases in the heterogeneous regime. The homogeneous regime is found at low superficial gas velocities. In this regime, the bubble size has a narrow distribution and the liquid motion is restricted to small scales induced by the passing bubbles. At some point, the homogeneous regime becomes unstable and a transition sets in to the heterogeneous one. Numerous papers have appeared that deal with one or more of the aspects of this transition from homogeneous to heterogeneous. One way to study this transition is by constructing a gas fraction (R) vs superficial gas velocity (Usup) plot from experimental data,4,7–11 and find the inflection point in the plot. Here the transition to the heterogeneous regime sets in. Linear stability analysis is also frequently employed to investigated the stability of the homogeneous regime, see e.g., 1, 2, and 12–16. An extensive review is presented by Joshi et al.17 In their review, they discuss the one-dimensional linear stability of the homogeneous flow in various dispersed systems, like fluidized beds and bubble columns. The authors present a relation for the maximum gas fraction in the bubble column in the homogeneous regime. This maximum is reached when the gas fraction versus superficial gas velocity is at its maximum. However, the system may become unstable before this point is reached. The stability analysis provides the critical gas fraction at which small disturbances of the homogeneous regime get amplified. Various parameters influence the critical gas fraction calculated from the stability analysis. For bubble sizes above 3 mm, the critical gas fraction is found to decrease with increasing * To whom correspondence should be addressed. E-mail address: [email protected]. † Present address: Shell Global Solutions, Amsterdam, The Netherlands.

size. Furthermore, the critical gas fraction peaks at db ≈ 3 mm. The predicted peak values range from as small as 10% to 100% (i.e., always stable), depending on the closure relations used in the hydrodynamic description. In the same paper, also the experimental data from the literature are collected. For air-water columns at ambient conditions, the maximum critical gas fraction reported is 36.5%. However, the majority of data are around a value of 20-25% with critical superficial velocities of about 3-4 cm/s. Leoń-Becerril et al.13,14 report that, according to their stability analysis, the homogeneous flow becomes unstable at R ≈ 30% for spherical bubbles. This critical gas fraction reduces to 10% to 15% for ellipsoidally shaped bubbles. Lucas and co-workers1,15 investigated the role of the lift force and concluded that the influence of the lift force on stability is much higher than that of the turbulent dispersion force. Moreover, for small bubbles that have a positive lift coefficient, the lift force is stabilizing, whereas for the larger bubbles, that have a negative lift coefficient, this force is destabilizing. Bhole and Joshi16 collected a lot of literature data for pure systems as well as for systems with additives. A wide range of critical gas fractions was reported. For water, the maximum critical gas fraction is as high as 45.8%.11 The theoretical result of the work of Bhole and Joshi gave a good prediction of the transition from homogeous to heterogeneous flow for a wide range of systems. Joshi12 also conducted a linear stability analysis for a 2-dimensional air-water bubble column. From this work, it follows that the critical gas fraction follows from a simple relation: Rcrit ) 1/(n + 1) with n bing the Richardson and Zaki coefficient. According to the authors, a typical value for n is 1.4, leading to a critical gas fraction of 42%. Finally, Monahan and Fox2 inspected instability from both horizontal and vertical modes in the bubbly flow. Different from e.g. Lucas et al. they find that the instability is associated with the bubble induced turbulence production. A lot of work on the transition between homogeneous and heterogeneous flow in the bubble columns has been done by Drahos and co-workers. Zahradnik9 already in 1979 investigated

10.1021/ie8000748 CCC: $40.75  2009 American Chemical Society Published on Web 09/06/2008

Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 149

this problem and found that for a perforated plate the critical gas fraction was higher for smaller hole diameter. They reached a value of 39% for a perforated plate with a hole size do ) 0.5 mm. Locket and Kirkpatrick8 also experimentally investigated the stability of bubble flows. They operated in a countercurrent mode such that the swarms could be kept stationary. This way they managed, in a pipe of 76 mm diameter, to obtain a critical gas fraction of 66%. However, this is not directly comparable to the homogeneous bubble column, as now there is a distinct liquid velocity profile close to the wall creating a lift force on the bubbles. Furthermore, the liquid flow is turbulent and thus also a turbulent dispersion force is action on the bubbles. Drahos et al.18 studied pressure fluctuations in a bubble column. They report a maximum hold up of 30% in their equipment. Zahradnik et al.4 found in a 14 cm diameter bubble column from residence time distribution measurements and from the gas fraction that for a perforated plate the homogeneous flow could easily be obtained for superficial gas velocities up to 4 cm/s. They also reported that the stability of the homogeneous flow could be significantly enhanced by adding surface active solutes to the liquid. They used a 14 cm diameter bubble column with different perforated plates for sparging the gas. For water, they found a critical gas fraction of 32%, but this could easily be increased to 63% by adding 0.5% of ethanol. Also for electrolytes, the critical value was higher, e.g. they report 38% for KI. Ruzicka and co-workers11 made an extensive study of the transition from homogeneous to heterogeneous flow. They provided an extensive literature review on the topic and gave a model description for the critical prediction. From this, it followed that the maximum gas fraction for the homogeneous regime has a value of 55%. However, this was found for shallow columns with a height of diameter ratio of 3. In a subsequent paper in 2001,19 the same group of researchers investigated the effects of the diameter and of the mixture height on the stability. They reported that both an increase in the diameter and the height had a destabilizing effect on the homogeneous regime. In most cases, the critical gas fraction was 30% or below. Also this research group reported20 the effect of the liquid viscosity on the stability: for µl ) 1-3 mPa s, no big difference was found, but for the range of 3-22 mPa s, the stability decreased with increasing viscosity. Finally, in a recent paper,21 the effect of surfactants was investigated. It was found that addition of e.g. CaCl2 at low concentrations stabilized the homogeneous regime. However, for larger concentrations a destabilizing was observed. In this paper, the authors conclude that the important problem of the prevailing flow regime in bubble column reactors has been paid only very little attention. The flow regimes are in most studies not specified at all, or mentioned only marginally. If mentioned, so usually vaguely, based on the authors intuition and experience. If specified, so usually based only on the visual inspection of experimental data, mainly on the shape of the e(q) graph. Virtually all the above-mentioned papers used rather course experimental techniques. The number of papers on the homogeneous bubble regime that reported detailed hydrodynamic experiments have been rather limited. Yao et al.22 preformed experiments using a conductivity probe for the bubble size and velocity and for the gas fraction and an ultrasonic Doppler anemometer also for the bubble velocity (i.e., for 2 components of the velocity vector). Furthermore, they employed a hot wire anemometer for the liquid velocity. They report that a large scale liquid circulation, characteristic for the heterogeneous regime, sets in above a superficial gas velocity of 4 cm/s. Garnier

23

et al. measured, using a hot wire, the liquid velocity in a bubble column of 8.0 cm diameter equipped with a needle sparger consisting of 271 needles. Very uniform flows could be obtained. They also measured the local gas fraction using a double optical probe. A small cocurrent liquid flow was used in the experiments; hence, this is not literally a bubble column. They found very flat gas fraction profiles for gas fractions as high as 40%. They also gave a scaling law for the bubble rise velocity in the swarms. It scales with R1/3, like sedimenting particles in the dense regime. Harteveld and co-workers24 also used a needle sparger to achieve very uniform inlet conditions. They reported experiments using the laser Doppler anemometry (LDA) and optical glassfibers and showed very uniform flow at gas fractions of 10%. In a later paper25 these authors reported in the same column very uniform flow up to a gas fraction of 25%. Kulkarni and Joshi26 performed 2D laser Doppler anemometry measurements in a 15 cm diameter column using two different spargers: a single-point and a multipoint one. The superficial gas velocity was kept constant at 2.0 cm/s during all experiments. The results were compared to CFD (computational fluid dynamics) simulations of the flow. The flow showed large scale circulation already at a gas fraction of about 7%. More importantly for the present paper, the authors made an attempt to incorporate a real sparger in the CFD simulations. They conclude that “still [a] lot of scope exists for the development of generalized codes, possibly by understanding the physics of the flow”. The present paper aims at providing detailed, reliable data on the hydrodynamics in the homogeneous regime. CFD simulations should be able to capture this type of flow relatively easy as the modeling of phenomena such as turbulence does not play a crucial role here. Monahan et al.27 performed CFD simulations of a bubble column and paid special attention to the homogeneous regime. They showed that indeed the simulations can reproduce the homogeneous regime at relatively high superficial gas velocities. From the above, it does not become clear where the border between the two regimes is exactly located. In general, it is found that the homogeneous flow goes through a transition regime toward the heterogeneous regime at gas fraction between 15-25%. Theoretical work28 suggest that at gas fractions beyond 30% the homogeneous flow is inherently unstable and, in smaller diameters, a transition to slug flow sets in. However, stability analysis also resulted in higher predections. Although for industrial practice the heterogeneous regime is the most important one, proper experimental data on the homogeneous regime are relevant. Nowadays, bubbly flows are also studied via CFD. In particular, for bubble columns, CFD simulations of the heterogeneous regime have been reported.27,29–32 A good test of the codes and models used is to see if a code can predict the right homogeneous flow, when the gas is introduced uniformly over the bottom of the bubble column. It is an open question up to which gas fractions the flow can be homogeneous and whether or not CFD can predict this. Moreover, the onset of the instability triggering the change from homogeneous to heterogeneous flow is not completely understood. The number of detailed experiments with well-defined and controlled inlet conditions is rather limited. In almost all cases, porous plates or perforated plates have been used. With these spargers, the inlet conditions are not accurately controlled, nor are they known with high accuracy. Therefore, the present paper revisits the homogeneous bubbly flow. We aim at providing detailed data of the gas fraction distribution (using glass fibers) and liquid velocity (using LDA) that can, e.g., be used to test CFD simulations of the homogeneous regime. Our sparger is capable of providing a very uniform inlet condition to the bubble

150 Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009

Figure 1. System used to provide the bubble column with air.

Figure 2. Top view of needle sparger (left) and picture showing bubble formation with one-third of the needles in operation (right, gas fraction about 15%).

column, something that is easily implemented in computer simulations and can serve as a good test as discussed in the work of Monahan et al.27 Furthermore, the sparger is capable of generating a very narrow bubble size distribution and maintain that over a relatively wide range of superficial gas velocities. Experiments like this are very limited in the literature but, in our opinion, provide a well defined “test case”. Moreover, we estimate the bubble size and measure the bubble velocity using a four point optical probe. We have carried out experiments in a 15 cm diameter column and found that the uniform flow can be present up to 55% volume fraction of the bubbles. Finally, at the onset of instability, we find an intriguing duality in the flow that may give a clue to the instability we observed.

teristics of the needles stay the same during the experiments. Eleven electronic mass flow meters (VPInstruments VPFlowmate with a range of 0-5 slm) have been used in combination with metering valves to obtain accurate control over the flow to the groups. For an accurate measurement of the total flow rate, another electronic mass flow meter (VPInstruments VPFlowmate with a range of 0-100 slm) has been used. A schematic representation of the setup is given in Figure 1. Note that upstream of each group of needles a so-called group-needle (inner diameter 0.6 mm, length 10 cm) is placed, in order to obtain a very uniform flow to each of the groups of needles. A picture of the sparger operating with one out of every three needles is given in Figure 2.

2. Experimental Setup

3. Experimental Techniques

All experiments are carried out in a cylindrical column of 15 cm inner diameter, filled with tap water to an ungassed height of 130 cm. A special bubble distributor is used for the injection of the bubbles. It consists of 559 needles, with an inner diameter of 0.8 mm and a length of 20 cm where each needle exit is 5 mm above the column bottom. More details can be found in ref 25. The needles are placed in a triangular pattern, with a pitch of 6 mm. The flow through the needles is controlled in small groups. In total, the needles are grouped in eleven groups. The number of needles operating is a function of the required gas fraction. In order to obtain a uniform bubble size, the gas flow rate through each needle needs to be between 1 and 3 mL/ s. Therefore, for gas fractions below 15%, 187 needles are used, i.e. one out of every three. For larger gas fractions, all needles are in operation. This split ensures that the bubbling charac-

Glass Fiber Probes. Optical glass fibers are used to probe the bubble phase. The probe’s working principle is the difference in refraction index between glass (the probe material), water, and air. Light is sent into the glass fiber. At the tip, it will reflect back when the tip (size 200 µm) is surrounded by air. Most of the light will propagate into the water phase if the tip is surrounded by water. By detecting the reflected light, the phase present at the probe tip is detected (see, e.g., refs 33–35). Gas fraction profiles are measured using a single point optical probe. First, the time series recorded is made binary via an appropriate threshold (thR). The latter is set at 10% of the difference between the output value of the tip in air (sa) and that in water (sw). b(tj) )

{

1 0

if s(tj) > thR ) 0.1(sa - sw) + sw else

(1)


Figure 3. Typical signal of the piercing of a single bubble. The noise levels of the probe are very low. The binary version of the signal is also given.

Figure 4. Effect of small departures from vertical alignment on the axial liquid velocity profile (R ) 8.1%).

Next the (local) gas fraction is obtained as follows: N

∑ b(t ) · ∆t j

R)

j)1

N∆ts

s

(2)

with N the total number of samples, and ∆ts ) 10 µs, the sample time. The threshold should not be too high as this would cause bubbles that touch the tip rather than being pierced to be filtered out, thus underestimating the gas fraction. Obviously, it can not be too close to 0 as then unwanted noise would cause an overestimate of the gas fraction. An example of the signal (and its binary) of a single bubble passage is given in Figure 3. Note that when the tip of the probe leaves the bubble the response is very fast: the original signal and the binary step almost completely overlap. The measuring time per data point was set at 900 s. The number of bubbles detected scales roughly linearly with the gas fraction and is in all cases above 5000. The experimental error of measurements with the glass fibers is made of two parts. The first part is the statistical error associated to the measuring time. It is proportional to the square root of the measuring time. Repeated experiments show that in our case the absolute uncertainty in the gas fraction is 0.001-0.003 for the gas fraction range studied. The second part is a bias error due to the difficulties of piercing a bubble at the bubble edge. This is caused by the surface tension force that makes the bubble deviate from its vertical path upon colliding with the glass fiber. This error depends on the approach velocity of the bubble and on the swarm density surrounding the bubble: the higher the velocity, the smaller the bias; the denser the swarm, the less room there is for the bubble to flow around the glass fiber tip. In the literature,36,35 it is reported that this bias caused an underestimate of 5-10% of the actual gas fraction. In the present case, the swarm gets much denser than used in the studies mentioned. We expect that the bias will be smaller and estimate it to be 5%. Note that this effect causes a systematic underprediction of the gas fraction.

LDA. The LDA equipment consists of a 4W Spectra-Physics Ar+ laser and a TSI 9201 colorburst multicolor beam separator. The beam pairs are focused using a backscatter probe with a lens of 0.132 m focal length. Detected light is sent to a TSI 9230 colorlink. The Doppler bursts have been processed by a TSI IFA-750 processor. The application of LDA in bubbly flows is far from straightforward. Upon measuring deeper in the bubbly flow, the data rate gets strongly reduced due to blockage of the laser beams by the bubbles. This reduction is approximately proportional to exp(-c[Rl/db]), where c is a constant in the range of 1.5-3, l is the distance of the measuring volume in the bubbly flow, R is the void fraction, and db is the bubble diameter (see, e.g., the work of Groen et al.37). Apart from blocking the laser beams, the bubbles can also cause Doppler bursts that will lead to a velocity measurement. From a given burst, it is very difficult to tell whether it is caused by a seeding particle or by a bubble. In the present experiments, we used neutrally buoyant hollow glass particles with a diameter of about 8 µm as seeding. It is discussed by Groen et al.37 that under these conditions the number of velocity measurements that actually comes from a bubble is negligible. It is therefore safe to assume that the LDA measures the liquid velocity. Typical data rates for void fractions near 10% are 150-400 Hz near the wall and 0.8 Hz in the column center. This shows the difficulty of experiments deeper inside the column, especially at the higher void fractions, where experiments in the center are no longer possible. The measuring time per point was set at 900 s. Close to the wall a single data set contains more than 200 000 data points, whereas at a radial position r/R ≈ 0.5 at a gas fraction of 30% this number has dropped to less than 5000. LDA data are not bias free. First, due to increased noise levels caused by the bubbles multiple validation, i.e. measuring the burst of a single seeding particle multiple times, occurs more often than in single phase flow. The multiple data points are removed by rejecting those data points that are outside 4 times the standard deviation of the data set. Next, for all two data points within a time interval of 1 ms, the second data point is removed. Second, a velocity bias correction is employed. This correction is based on the so-called 2D+ weighing: the weighing factor is inversely proportional to the magnitude of the velocity vector that is estimated from two of the three velocity components. For a full discussion, see, e.g., the work of Tummers.38 These corrections amount to about 2 cm/s, reducing the velocity. It brings the measured net cross-sectional flow of the liquid down from 1 or 2 cm/s to values of 0.3 cm/s or less. Column Alignment. Rice and co-workers39,40 have shown that very small deviations from vertical alignment result in the creation of a large scale liquid circulation in the column and an increase in the axial dispersion of the bubble phase. Tinge and Drinkenburg41 discuss the maximum inclination angle before this circulation sets in. Extrapolation of their results gives a maximum inclination of 0.05° in our case. Careful alignment made it possible to have a horizontal deviation at a position of 1.5 m above the bottom of the column with respect to the vertical of less than 1 mm, which indicates a maximum inclination angle of 0.04°. We have run a test with an average gas fraction of 8.1% (measured from the liquid level increase) to see the influence of the inclination angle on the axial liquid velocity as measured by the LDA. Results are shown in Figure 4. It is clear that even angles as small as 0.04° are visible. Note further that, for “perfect” alignment, we measure a slightly nonzero mean flow. This is a consequence of a small bias in the LDA measurements.

152 Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 Table 1. Fit Parameters

RZ Garnier

Figure 5. Void fraction as a function of the superficial gas velocity with time t after filling the bubble column with fresh tap water. Note that both theoretical lines (RZ and Garnier) almost overlap.

4. Gas Fraction and Liquid Velocity 4.1. Overall Gas Fraction. The overall gas fraction is plotted in Figure 5. For low superficial velocities, the bubbly flow is in the homogeneous regime and the gas fraction raises more or less linearly with the gas flow rate. However, at a certain point, this linearity breaks down and the gas fraction only slowly increases with the superficial gas velocity. This marks the change from homogeneous to heterogeneous flow.11 Where exactly this happens, depends on the purity of the water. As can be seen in Figure 5, for fresh tap water, we find the transition around 30-35%. But as the water stays longer in the column, this point shifts until we finally can reach gas fractions of 55% before the uniform flow becomes unstable. This is surprising as all reports so far on bubble columns have this transition much lower: at or below 30%. Moreover, linear stability analysis of the uniform flow predicts instability from 25-40% for spherical bubbles or as low as 10-15% for ellipsoidal bubbles (see, e.g., refs 28 and 13). We have measured the surface tension of the water in the column as a function of time, using the Du Nouÿ Ring method. We find, that according to this method the surface tension stays constant: σ ) (71.6 ( 0.5) × 10-3 N/m. No decreasing trend with time has been found. The data, presented in Figure 5, can be analyzed based on the slip velocity between the gas and liquid phase. Both the Richardson and Zaki (RZ) relation for the slip velocity and the proposal by Garnier et al.23 are used. The slip velocity (Vs), defined as the bubble velocity (Vd) minus the velocity of the continuous phase (Vc), is connected to the superficial velocities: Vs ≡ Vd - Vc f Vs(R) )

Uliq Ug R 1-R

(3)

The superficial liquid velocity can be set to zero as we are in the homogeneous regime. Hence, no liquid circulation is induced and the local, averaged liquid velocity is zero. Thus, we obtain a direct relation between the void fraction and the superficial gas velocity: Ug ) R · Vs(R) )

{

V∞R(1 - R)n-1

RZ

V∞R(1 - CµR1⁄3) Garnier

(4)

with V∞ being the slip velocity of a single bubble, n the Richardson and Zaki power () 2.39 for bubbles of the present size in the original RZ model), and Cµ a parameter set to 1 in

V∞(m/s)

n(-)

0.195 0.280

1.40

Cµ(-) 0.60

Garnier’s model.23 Both models are fitted to the data of Figure 5. The results are given in Table 1. Clearly, we find a much lower power for the Richardson and Zaki slip velocity than according to the original model for particles with a single particle Reynolds number above 500. However, the value of n ) 1.4 is in agreement with the one mentioned by Joshi.12 Moreover, the single bubble rise velocity needs to be set at 0.195 m/s. This is too small: the bubbles in the present experiment have an equivalent diameter of 4 mm (see section 4.4). These bubbles have a terminal rise velocity of 0.25 m/s, significantly higher than the value needed for a proper fit of the Richardson and Zaki relation to our data. If we use the power n ) 1.4, the maximum possible gas fraction of the homogeneous regime (Rmax ) 1/n) is 0.71,8,17 and the critical value12 is Rcrit ) 1/(n + 1) ) 0.42. This underestimates our findings. Joshi17 provides a more extensive analysis and arrives at a different expression for the critical gas fraction: Vs2Cv(1 + Cv) ) Ddbg(Rcrit + Cv)

(5)

in which Vs(R) is the slip velocity between the two phases, Cv is the virtual mass coefficient, D is a dispersion constant given a value of 1.2, db is the bubble size, and g is gravity’s acceleration. If in eq 5, the Richardson and Zaki relation is substituted with n ) 1.4 and the virtual mass is set to 0.5, then for 3 mm sized bubbles the critical gas fraction is 0.19. For larger bubbles, this value decreases. Again, we have an underestimate of our maximum stable gas fraction found in the experiment. The Garnier model uses an R1/3 dependence. This reflects the bubble-bubble distance in the swarm. Garnier et al. report that their bubbles have an equivalent diameter ranging from 3.4 to 5.5 mm. This is in the same range as the bubble size in our case. For the model of Garnier, we find a value of 0.28 m/s for the slip velocity of a single bubble which is in reasonable agreement with the actual velocity of a single bubble (≈ 0.25 m/s) and is the same value as reported by Garnier. However, the coefficient, Cµ, in the Garnier model is found to be 0.60 in our experiments, rather than close to 1 as Garnier et al. report. A difference with the Garnier experiments is that in our case the liquid velocity is 0, whereas in their case, it is not. From their results, it can be observed that their findings are different for different liquid velocities: the lower the liquid velocity, the quicker the slip velocity drops as a function of the gas fraction. In contrast, our data show a slower decrease. It is not clear why we observe such a difference. The single bubble rise velocity is almost the same in both Garnier and our experiment. Furthermore, the bubble size is quite comparable. If we use the Joshi criterion of eq 5 with the same parameters as given above, we find for the critical gas fraction a value of 0.2. This is almost equal to the prediction using the Richardson and Zaki expression for the slip velocity. Again, this value is much smaller than our experimental one and it decreases with increasing bubble size. Joshi et al.17 performed a parameter variation study on all variables in the criterion of eq 5. They show in their paper that the dispersion coefficient, D, needs to be as small as 0.5 to get a critical gas fraction above 0.5. This seems to indicate that at the high gas fraction we can reach, the dispersion of the gas phase is reduced significantly compared to the more dilute cases. An explanation for this may be that,

Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 153 Table 2. Superficial Gas Velocities for the Various Gas Fractions Studied

Figure 6. Void fraction profiles in the entrance region (Ug ) 0.023 m/s).

for these dense systems, the motion of individual bubbles is greatly reduced by the presence of all other bubbles. In essence this is the well-known mutual hindrance that restricts the bubble mobility. 4.2. Radial Gas Fraction Profiles. Radial void fraction profiles were determined with single glass fiber probes for various superficial gas velocities at various heights in the column. Figure 6 gives an impression of the uniformity of gas injection that is achieved with the needle sparger. The result shows that the void fraction profile contains small nonuniformities at z ) 0.07 m, introduced by imperfections in the sparger, but that these nonuniformities quickly even out: at z ) 0.15 m, the void fraction distribution is very uniform. This shows that the needle sparger can provide very uniform gas injection. Typically, the gas fraction for bubbles of the present size (equivalent diameter about 4 mm) is underestimated by 5-10%, see, e.g., refs 33 and 35. This is due to the difficulty of piercing a bubble at its side: in many cases, this results in a bouncing off from the tip rather than being pierced. Surface tension forces are responsible for this bouncing. Small peaks are observed in the void fraction at distances of 5 mm from the wall (about one bubble diameter). At smaller distances to the wall, the void fraction drops more or less linearly. The drop near the wall may be explained with a local force driving bubbles away from the wall, such as that modeled by Antal et al.42 This model is employed quite frequently in modeling studies for the estimation of, e.g., void fraction profiles for bubbly pipe flow or bubble columns.43,44 It is not clear, however, if such a force is really present: the derivation by Antal42 is performed for small bubble Reynolds numbers. The works by Takemura and Magnaudet45 and De Vries46 suggest that, instead, for larger bubble Reynolds numbers, bubbles may be attracted to and bounce against the wall. An alternative explanation for the drop in void fraction near the wall may be the fact that bubbles cannot overlap with the wall. This way, their shape determines the variation in void fraction. A simple check with the assumption of an ellipsoidal shape shows that this gives a reasonable approximation for the decrease in void fraction near the wall. Next, the shape of the void fraction profile is investigated for various heights, superficial gas velocities, and water contamination levels. Since the gas injection is very uniform, the nonuniformities observed in the profiles are due to hydrodynamic effects and not due to the sparger. First, results are shown for tap water of several days old (large vortical structures occur for Ug > 0.06 m/s) and an ungassed liquid height of 1.3 m. This water is still relatively clean. (The water in the column is in a batch and will get contaminated over time by contamination from the surroundings and, more importantly, from the air supply; air needs to be sparged continuously as otherwise water would seep into some of the needles, blocking air flow through

Ug (m/s)

R (-)

no. of needles

0.015 0.017 0.025 0.032 0.039 0.049

6.1% 7.6% 11% 16% 20% 25%

187 187 187 559 559 559

them. Moreover, some bacterial growth can not be completely excluded over the long time that the water is in the column.) The superficial gas velocities that have been used are given in Table 2. This table also shows the number of needles that have been used. The flow rates through the needles for these conditions give equivalent bubble diameters in the size range 3.5-5.0 mm. If the superficial gas velocity is increased from 0.015 to 0.025 m/s, the bubble size increases due to the larger flow rates through the needles. If the superficial velocity is increased further, the number of needles is tripled, the flowrate through the needles decreases, and the bubble diameter drops again. As a result, the bubble diameter variation over the entire void fraction range is reduced and attains a local maximum value for R ) 11%. Figure 7 shows void fraction profiles for superficial gas velocities of 0.015 and 0.049 m/s. Figure 8 shows more profiles for the superficial gas velocities without large scale structures for z ) 1.2 and 0.6 m. The figures show that the inside of the bubble column is very uniform for all superficial velocities, except close to the surface for R ) 25%. The low superficial gas velocities show a wall peaking behavior for all heights. The same peaking behavior is observed for Ug > 0.035 m/s (R > 18%) for z < 0.9 m. In higher parts of the column, the peak disappears. A small dip occurs near x/R ) 0.7 for all experiments with Ug > 0.03 m/s. This small dip is due to an artifact of the experiments with the probe. We have used 5 different probes simultaneous to speed up the measurements. The one positioned at x/R ) 0.7 systematically slightly underpredicts the void fraction. Additional void fraction profiles for more contaminated tap water of two weeks old are shown in Figure 9. For all the experiments from this point on, the ungassed liquid height was 1.0 m, unless noted otherwise. The behavior is similar to that observed in Figures 7 and 8. For the superficial gas velocities, that are significantly below the critical superficial gas velocity where the onset of vortical structures occurs (Ugcrit ≈ 0.07 m/s), again wall peaking is observed for all heights (e.g., Figure 9a with Ug ) 0.047 m/s). For the superficial gas velocities somewhat below the critical superficial gas velocity (Figure 9b with Ug ) 0.066 m/s), the wall peaking disappears near the top of the bubble column. For the case where dynamic large scale structures are present (Figure 9c with Ug ) 0.076 m/s), the familiar core-peaking void fraction profile is found. In this case, an additional underestimation of the void fraction is present: bubbles rising downward have a smaller probability of being pierced.47 Wall peaking behavior has been reported for bubbly pipe flows by e.g. Serizawa et al.48 Similar void fraction wall peaking is observed in model predictions for bubble columns and pipe flow by Guet et al.43 The behavior is explained by the effect of the lift force, which causes accumulation of small bubbles (i.e., smaller than 5 mm) in the negative velocity part of the flow, which is close to the wall. The position where the peaking is observed in the current experiments is at 5 mm from the wall. The lift force acting on the bubbles at this location is significant


Figure 7. Void fraction profiles for 6.1% void fraction (Ug ) 0.015 m/s) (a) and 25% void fraction (Ug ) 0.049 m/s) (b). The tap water is several days old.

Figure 8. Void fraction profiles for various gas fractions at z ) 1.2 m (a) and z ) 0.6 m (b). The tap water is several days old.

Figure 9. Void fraction profiles for tap water which is 2-3 weeks old. Large scale structures are found for Ug > 0.07 m/s.

since these bubbles experience a shear due to the down flow close to the wall. This downward liquid motion is caused by the slightly lower gas fraction very close to the wall and thus a higher local mixture density. 4.3. Axial Liquid Velocity Profiles. Mean axial liquid velocity profiles for various gas fractions are shown in Figures 10 and 4. The profiles show that for all superficial gas velocities, upflow occurs in the central region with r/R
0.9 and has a typical velocity of around -0.04 m/s. The downflow is most likely caused by the low void fraction very close to the wall, which causes a density difference between the inner bubble column regions and the wall region. Most publications on bubble columns (e.g., refs 49 or 50) report that the inversion point (i.e., the point where uax,liq ) 0) is located around r/R ) 0.7, whereas


Figure 10. Mean axial liquid velocity profile for various void fractions. The tap water is several days old. The ungassed liquid height is 1.3 m.

the present study finds the inversion point near r/R ) 0.9. This shows the very strong homogeneity for the present flow. The difference is most likely caused by the absence of any large scale structure in the flow. For the other studies, the gas injection may not have been uniform enough to achieve this. The results close to the wall show no trend with Ug. This is probably due to the presence of a strong preshift frequency bleed through in the LDA signal for measurements near the wall. This affects the mean velocity. In addition, since the wall location is determined by locating positions where zero velocity is found, a small error in the radial alignment is created, which manifests itself strongest close to the wall where the velocity gradient is largest. 4.4. End of Homogeneous Regime. In the previous sections, wall peaking of the void fraction profiles was found, which is generally associated with a lift force driving the smaller bubbles closer to the wall. Close to the wall a narrow region with liquid down flow exists, providing a velocity gradient that can produce a significant lift force. In the higher parts of the column, and for the higher superficial gas velocities approaching the critical gas velocity where the first large structures are observed, the velocity of the down flow increases. Nevertheless, for these conditions, the wall peaking disappears. This indicates that the lift force toward the wall is decreasing in magnitude. Since the actual velocity gradient is increasing, the decrease in the lift force is probably caused by a decrease of the lift coefficient, which may possibly even reach a negative value. The results in ref 51 show that the lift coefficient decreases if the horizontal bubble diameter approaches a critical value, which is approximately 5.8 mm for air-water. The results, therefore, could indicate that the mechanism for the transition that was proposed by Lucas et al.1 plays an important role. These authors argue that small, local disturbances of the state of uniform bubble distribution get positive feedback from the lift force if the bubble size is larger than the critical size. Consequently, the disturbance grows and the homogeneous regime looses its stability. Fox and co-workers2 proposed a different mechanism. From their stability analysis, they concluded that the transition from homogeneous to heterogeneous flow could be caused by an instability triggered by a reduction of the bubble induced turbulence. This reduction is a consequence of the suppression of bubble wakes in the more dense swarms. The authors found no need to link the transition to a change in lift coefficient as has been proposed by Lucas and co-workers. The mechanism proposed by Fox and co-workers is interesting and requires additional experiments in which the focus should be on retrieving turbulence data. Figure 11 shows images of the bubbles close to the wall. It is evident from these pictures that with increasing gas fraction the bubble size increases. If this continues, then according to the Lucas criterion, the uniform flow looses its stability when

the bubble size has increased beyond a critical size. To further investigate this, measurements of the actual bubble size have been conducted. However, at the same time, the swarm becomes denser and the wakes may be suppressed causing a transition toward homogeneous flow according to the Fox mechanism. Figure 12 shows the means and standard deviations for the major (a) and minor (b) axis lengths of the bubbles obtained with a photographic technique. For the horizontal diameter, clear differences are observed between the case of “fresh” tap water and the case of contaminated tap water. For the relatively clean water, the horizontal bubble size is increasing for Ug < 0.05 m/s, whereas it is more or less constant for the contaminated water. In this range, the bubble shape for the contaminated water is more or less ellipsoidal, whereas the bubbles in the relatively “clean” water have much more irregular shapes and exhibit strong shape oscillations. As soon as the horizontal diameter reaches a value around 5.8 mm in the region near the free surface, the increase levels off and strongly increased liquid downflow is observed close to the wall in the top regions of the bubble column (“A” for fresh, “a” for contaminated water). If the superficial gas velocity is increased slightly further, large scale instability is observed, first in the top parts of the column (“B” for fresh water) and for a small further increase in the entire bubble column (“C” for fresh, “c” for contaminated water). The results could be explained by the reversal of the liftforce direction as proposed by Lucas et al.1 The graph in Figure 13 reproduces the results of the stability analysis by Lucas et al.1 for a Gaussian bubble size distribution. If the standard deviation of the bubble diameter exceeds a certain critical value, the flow becomes unstable. This critical standard deviation is a function of the mean bubble diameter. The mean and standard deviation that were observed in the present experiments at the onset of dynamic large scale structures are also plotted in the same figure. The agreement with the result of the stability analysis is good, although the good match is not very sensitive to the precise value of the standard deviation for the present conditions. In addition, the result shows that the width of the bubble diameter distribution is quite small in terms of lift-force behavior. When the gas flowrate is increased to about Ug ) 0.08 m/s, the uniform flow looses its stability. However, at this setpoint, the flow starts to oscillate between homogeneous and heterogeneous, with a period of some 20 s. The gas fraction as a function of time is for this condition given in Figure 14. After reaching its highest gas fraction of about 55%, an instability quickly develops: from the free surface, the liquid starts flowing rapidly downward in the wall region and the entire flow becomes “turbulent”. Note that at these high gas fractions it is even close to the wall difficult to measure with the LDA. The downward velocity is high enough to drag bubbles downward. This can be seen in Figure 15 that shows the time trace of the vertical component of the liquid velocity in a point close to the wall as obtained with the LDA. After a few seconds, the gas fraction reaches a minimum and the downward liquid velocity a maximum. Then, the flow starts to relax, the gas fraction starts to climb, and the homogeneous flow is restored. When the gas fraction reaches 55%, the cycle repeats in a sawtooth manner. From visual observation, we tend to conclude that the bubble size is decreased during the “turbulent” stage. This makes sense as the large scale liquid circulation will strip the bubbles somewhat earlier from the needles of the sparger. Therefore, the bubble size decreases. This fits with the picture that the onset


Figure 11. Images of bubbles close to the wall for increasing void fraction (contaminated water of three weeks old).

Figure 14. Alternating regimes for Ug ) 0.08m/s: time series of the gas fraction.

Figure 15. Alternating regimes for Ug ) 0.08m/s: time series of the axial liquid velocity close to the wall.

Figure 12. Evolution of mean and standard deviation of the major and minor bubble axis lengths for two levels of water contamination. The dimensions were obtained with a photographic technique.

Figure 13. Comparison of the maximum stable standard deviation of the bubble diameter according to ref 43 and the conditions in the current experiment at the onset of transition.

of the instability is caused by a reversal of the direction of the lift force. The bubbles at the top are slightly larger than in the

rest of the column due to the lower hydrostatic pressure. Hence, we can expect the first instability to occur at the top of the column, with the bubbles moving away from the wall. The relatively heavy layer close to the wall then starts moving downward, creating the large scale instability and moving more bubbles to the center at the position where it “bends inward” (for continuity reasons). Finally, when the liquid circulation reaches the sparger, the bubbles formed are smaller and the lift force regains its original sign but is now stronger and can restore the uniform distribution. This takes several seconds as both the small bubbles will have to move to the top of the column and, more importantly, the liquid flow will have to decay. Once this flow has decayed, the uniform gas distribution can be reestablished. However, at the same time, the bubbles formed at the sparger will get bigger as they no longer feel the drag from the liquid flow trying to pull them off. Thus slightly larger bubbles will move upward, reaching the critical size at the top of the column and the cycle repeats. The wake suppression (as proposed by Fox et al.) could equally well explain the above observation. Now the critical swarm density with the required turbulence reduction also starts at the top of the column, as due to the reduced hydrostatic pressure, the bubble size is increased, and the gas fraction is slightly higher in the top region. Also with this model, the flow


may become in a transitional state. Now due to the circulation, the swarm gets less dense and the turbulence level may be restored. Additional experiments are required to sort out the cause of the instability. 5. Concluding Remarks In this paper, we have reported experiments on bubbly flow in a 15 cm-diameter cylindrical column. The continuous phase (water) is in a batch. The air bubbles (equivalent diameter about 3.5-5 mm) are injected via a special needle sparger that generates a very uniform input of the bubbles. We employed optical glass fiber probes and LDA to assess the uniformity of the flow. After careful alignment of the column, we obtained flat gas fraction profiles up to gas fractions as high as 55%, with a small wall peaking. As a consequence of this flat gas fraction profile, the liquid shows hardly any circulation: liquid velocities close to the wall are a few centimeters per second downward, and in the center, we measure typically 1-2 cm/s upward flow, which is partly a bias error in the LDA measurements. The downflow at the wall results in a shear field that will via a lift force push bubbles smaller than about 5-6 mm toward the wall. This could be responsible for the wall peak we observe. The flow is steady: only small scale fluctuations are observed. Our findings are in contrast to predictions from linear stability analysis. Generally, the latter predicts a transition from the uniform regime into a heterogeneous one for gas fractions in the range of 25-35%. However, if we let the water “age”, we find stable uniform flow up to 55%, i.e. well beyond the stable regime predicted by the linear stability analysis for air-water bubbles of the present size. In the homogeneous regime, the gas fraction and the superficial gas velocity are coupled by a Richardson and Zaki (RZ) type of relation, i.e. the slip velocity can be described by Vs ) V∞(1 - R)n-1 with V∞ ) 0.195 m/s, which is too low for the present bubbles, and n ) 1.4. However, also the relation proposed by Garnier et al.23 gives an adequate fit to the data with Vs ) V∞(1 - CµR1/3) with V∞ ) 0.28 m/s and Cµ ) 0.6. At a gas fraction of 55%, the flow becomes unstable. Instabilities at the top develop and propagate downward. The nature of the flow changes drastically: the gas profile is no longer flat, but core peaking is found instead. This causes large density differences within the mixture and gravity will act, making the flow unstable. Our findings could be explained by the reversal of the lift force once the bubble size passes a critical diameter,51 resulting in a flow instability as proposed by Lucas et al.1 However, care should be taken, as at these high gas fractions the bubble-bubble distance is small and the wakes cannot develop in a similar way as in the case of isolated bubbles. Therefore, the instability may also be triggered by the suppression of the wake as proposed by Fox and co-workers.2 Acknowledgment This work has been done via a grant from the Dutch Foundation for Fundamental Research on Matter (FOM) under the Dispersed Multiphase Flow programme. Literature Cited (1) Lucas, D.; Prasser, H. M.; Manera, A. Influence of the lift force on the stability of a bubble column. Chem. Eng. Technol. 2005, 60, 3609– 3619. (2) Monahan, S. M.; Fox, R. O. Linear stability analysis of a two-fluid model for air-water bubble columns. Chem. Eng. Sci. 2007, 62, 3159–3177.

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ReceiVed for reView January 16, 2008 ReVised manuscript receiVed June 24, 2008 Accepted July 3, 2008 IE8000748

Uniform Flow in Bubble Columns - ACS Publications - American

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