Coherent structures and axial dispersion in bubble column reactors

Pergamon

Chemical Engineering Science, Vol. 51, No. 10, pp. 2511-2520, 1996 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights re~erved 0009-2509/96 $15.00 + 0.00

S0009-2509(96)00110-8

COHERENT STRUCTURES AND AXIAL DISPERSION IN BUBBLE C O L U M N R E A C T O R S J.S. GROEN, R.G.C. OLDEMAN, R.F. MUDDE and H.E.A. VAN DEN A K K E R Kramers Laboratorium roar Fysische Technologie Delft University of Technology. Prins Bemhardlaan 6. 2628 BW DELFT, The Netherlands

abstract In this paper results of measurementsof the local and lime-dependent behaviour of the two-phase flow in a bubble column are presented. Measurementswith Laser Doppler Anemometry (LDA) and with glass fibre probes were performed in t~vohomogeneously aerated air/water bubble columns, of 15 and of 23 cm dia. These measurements show that considering the flow field as stationary considerably underestimates the velocities present. Although the time averaged liquid velocity profiles resemble textbook data, these averaged values are a result of the passage of coherent structures. LDA measurements showed that these swarms have typical velocities and that at different radial positions, different typical velocities are dominant. The measurementsperformed ~ith sets of glass fibre probes show that these swarms are typically of the order of the column diameter, indicating that dispersive transport in the axial direction is limited to a distance of approximately the column diameter. Axial dispersion in a bubble column is thus regarded as transport ~ith a typical velocity over a typical distance. A simple model is proposed, defining the axial dispersion coefficient as the product of the typical velocities with the column diameter. Agreement of results obtained with this model with existing literature data is good, especially at lower superficial gas velocity conditions. 1. I N T R O D U C T I O N AND B A C K G R O U N D S Bubble columns have many properties that are advantageous for the process industry. The simple construction and absence of moving pans make them cheap and easy to maintain. However, the scale-up of bubble columns still is poorly understood. Scaling up based on time-averaged values of the flow field, on dimensionless numbers or on empirical models have their limited areas of application. Detailed knowledge of -local and dynamic- values of twophase flow parameters in bubble columns at different scales can be of great value for understanding the behaviour of bubble columns and developing accurate scaling rules. In the last few years various techniques have been developed for measuring local values at a data rate sufficiently high to study the dynamic behaviour of the flow in a bubble column. Amongst these are Laser Doppler Anemometry and techniques using glass fibre probes. Recently, results obtained with these (and other) techniques were presented (Groen et al. 1994, 1995). This paper reports on new results and their implications for understanding bubble column behaviour.

F/ow patterns Bubbles dispersed in a bubble column cart}, liquid upwards with them in their wake and, at higher gas loading, in between them (in swarms). This liquid has to flow down again, thus giving rise to overall liquid circulation patterns.

~t

~t

oiO

k._Jl ni

C-hl k..Jl

k_.Jl .-... .~l_ ..... a

b

Figure 1. Liquid circulation patterns in bubble columns, a) large-scale overall circulation; b) donut-model of Joshi and Sharma (1979); c) circulation cells according to Zehner (1986). This effect was firstly reported by De Nevers (1968), who stated that the liquid circulation pattern is induced by density differences caused by maldistribution of the bubbly phase across the cross-sectional area of the bubble column: in the central area of the column the local value o f the gas hold-up is higher than close to the wall, 251l

2512

J.S. GROENetal.

resulting in liquid upflow in the central region and liquid downflow along the wall. This pattern is sketched in Figure l.a. Such a profile is indeed measured and reported in several papers, amongst which the work of Hills (1974) is often cited. The maldistribution of the gas hold-up r, is generally modelled with a power law: ~(*) : ~ 0 ( 1 - * ' ) = ~ m ÷ 2 ( 1 - 4 " ) m

O)

where tt(q~) is the local gas hold-up as a function of the dimensionless radial coordinate q~, ao is the gas hold-up at the column centreline, ~ is the cross-sectional area averaged gas hold-up and m is a constant (usually taken between 2 and 7). This power law has formed the basis for various models which describe the flow field in terms of a largescale circulation pattern (Ueyama and Miyauchi 1979, Geary and Rice 1992). Joshi and Sharma (1979) modelled the flow pattern in a bubble column as a stack of donut-shaped circulation cells (Figure l.b). The model of Zehner describes a bubble column in terms of circulation cells that span the total column diameter (Figure l.c, this pattern is not axiymmetric). The occurrence of these cells is shown by a visual study ofChen et al. (1989). Dudukovi6 and coworkers (Devanathan et al. 1990) showed the presence of one large liquid circulation pattern. All these models essentially present time-averaged values of two-phase parameters. Only a few descriptions of non-steady behaviour are found in literature (e.g. Franz et al. 1984, Chen et al. 1994, Groen et al. 1994, 1995). The application of Computational Fluid Dynamics (CFD) in calculating the flow in a bubble column has recently emerged due to the immense increase in computational power. Steady-state calculations, in terms of one overall circulation pattern (e.g. Grienberger and Hofmann 1992) or with the donut-cells as starting point (Millies and Dewes 1995) have been presented. Time dependent calculations have given some promising results (Sokolichin and Eigenberger 1994, Lapin and UJbbert 1994). Recent results of calculations of the latter bear some resemblance to the experimental work of the group of Dudukovi6 (Devanathan et al. 1995). Axial dispersion

Axial dispersion (or backmixing of the phases) is a major effect determining the performance of bubble column reactors and a phenomenon that considerably complicates scale-up. Many empirical models describing the axial dispersion coefficient of the liquid phase EL have been presented (reviewed in Deckwer 1992 and in Deckwer and Schumpe 1993). These models usually describe EL as a function of the reactor diameter D R and of the superficial gas velocity Uc,s: y

EL :k, 9 duos

(2)

where x ranges from 1 to 2 and y is taken to be between 0.3 and 1.5; hence the factor k~ generally is not dimensionless. Baird and Rice (1975) used Kolmogorov's theory of isotropic turbulence to estimate dispersion coefficients. They took the column diameter as the specific size of a bubble column and, by dimensional analysis, arrived at the following model for the axial dispersion coefficient:

E~ : k., D R4/3 C1/3

(3)

in which ¢ is the specific power input and k., is dimensionless and has a value of about 0.35. In the case of a bubble column it is easily shown that £ equals g.uG.~ (g denoting gravity). Usually, equation (3) is made dimensionless and thus presented as follows:

DR] : 2.83

(4)

EL ) The dimensionless group on the left hand side ofeq. (4) is the Bodenstein number, the group on the right hand side is a Froude number. Many models, usually coming quite close to eq. (4) have since been presented, summarized by Deckwer (1992) and by Groen (1994). 2. EXPERIMENTAL TECHNIQUES Laser Doppler Anemometry

The application of Laser Doppler Anemometry (LDA) in two-phase flows has already been known for some time (Mahalingam et al. 1976). The major restriction for using LDA in two-phase flow is the fact that each bubble essentially acts as a mirror which scatters the light. For that matter, the application of LDA in its most powerful form, i.e. forward scatter mode, is restricted to low gas hold-up systems. The group of Durst (see e.g. Durst et al. 1986) have shown that LDA is a valuable measuring technique in these systems. At higher gas hold-up conditions though, the use of LDA is restricted to backscatter mode, a consequence of which is a relatively low data rate. Some attempts have been presented to employ LDA in determining both the liquid and the bubble velocities, but these attempts did not prove accurate for bubbles larger than about 2 mm and for higher hold-up conditions. Simple experiments on LDA measurements in a single bubble train showed that no signal is obtained from bubbles passing the measuring volume, but that the bubble wake can be observed as a short period of relatively high velocity

Coherent structures and axial dispersion

2513

directly following a bubble (see also Sheng and Irons 1991). It was thus assumed that LDA measures the liquid phase only. Glass Fibre Probes The use of glass fibres in determining local two-phase hydrodynamic parameters has gathered a lot of attention in the past years. The technique is described by Frijlink (1987) and is treated in detail in earlier papers (Groen et al. 1994, 1995). A glass fibre probe distinguishes between the gas phase and the liquid phase by means of the difference in refractive indices. Light from a LED is set into one end of a glass fibre, the other end of which is submerged in the two-phase flow to be studied. When the glass fibre tip is surrounded by water, the light proceeds into the flow more or less undisturbedly. When a bubble hits the probe tip, the light will be reflected back into the fibre and can thus be detected by a light sensitive cell. From the time signal, the local value of the gas hold-up can be obtained. If the signals of sets of glass fibres are registered simultaneously, correlation techniques can be applied to study the dynamics of the two-phase flow in a bubble column, e.g. to determine parameters of bubble swarms. If a bubble swarm is modelled to have size 1, velocity v and lifetime T, the cross covariance function R of a pair of glass fibre probes at the same radial position qb and a small vertical distance - apart has the form:

RU) = A "e

--;

"e- - 7

(5)

in which x is the time shift between the two signals and A represents the intensity of the gas fraction fluctuations. 3. EXPERIMENTAL SETUP Measurements were performed in two bubble columns, one of 15.2 cm i.d. and one of 23.4 cm i.d. Both columns were filled with tap water and were aerated homogeneously by means of a sintered polyethylene porous plate (pore dia 40 lain, porosity 40%). In operating the 15 cm column, the gassed dispersion height was kept constant at 152 cm (i.e. 10 DR). The 23 cm column was operated at a constant gassed dispersion height of 187 cm (8 DR). Both columns were operated at superficial gas velocities up to 7 cm/s, which is clearly in the heterogeneous bubbly flow regime. The LDA equipment consisted ofa 4W Spectra-Physics argon-ion laser and a TSI 9201 colorburst multicolor beam separator. In this project 2D measurements were performed, but in this paper only results of the axial velocity measurements are presented (using green light, wavelength 514.5 nm). The system operated in backscatter mode; the emittor and detector equipment were all fitted into a single probe which was connected to the laser system with a fibre. The detected light was sent into a TSI 9230 colorlink beam separator, after which the bursts were processed in a TSI IFA 750 digital burst correlator. The measurements were controlled from and stored on a 486/66 PC. The LDA measurements were performed at different heights above the distributor plates: H/Dn = 2.6, 4.2 and 6.6 in the 15 cm column and H/Dk = 2, 4 and 6 in the 23 cm column. The maximum laser power employed was ca. 2W, aluminium coated polyethylene particles (spherical, 4 gm dia) were used as seeding. The laser was operated in random mode and every measurement consisted of at least one series of 360000 independent bursts (resulting in 'raw data files' of ca. 3.6 MB per measurement). Of each series always 200000 or more bursts were in the axial direction. Close to the wall of the columns the 360000 points were collected in about 6 minutes, while towards the centreline of the column the acquisition took longer. If the number of 360000 was not reached within about 10 minutes (which happened in the central region of the columns at high gas hold-up) the measurements were stopped. Although this data rate is relatively low compared to the rate obtained with forward scatter mode, it is still large enough to study the flow dynamics. The glass fibres used in the probes were made of Fybropsil quartz fibre. This fibre (dia 0.2 mm) is covered by a silicon cladding and a teflon protective layer. These layers were removed from the fibre tip over a distance of about 1 cm. Two probes were used, both fitted in a traversing system, ensuring that the probes could be accurately traversed over the column radius. Measurements were performed at various heights above the distributor plate and at varying vertical distances z between the probes. The signals of the fibre probes were simultaneously registered using an HP workstation (2 × 15000 samples at 200 Hz). Since the accurate calculation of cross covariance functions requires quite some data, 50 series were acquired in the 15 cm column, while 80 series were necessary in the 23 cm column. Both the LDA and the glass fibre data were processed using VEE-Test software (HP trademark) and some inhouse developed processing routines, all in a unix environment. 4. RESULTS Laser Doppler AnemomeoT Typical results of time averaged linear liquid velocity profiles as measured with LDA are shown in Figure 2. It can be seen that these profiles indeed show the circulation characteristics as mentioned above: upward liquid movement

2514

J. S. GROEN et al.

0.4

0.4

0.2

0.2 o tl 5 c m column I

-a IT

0

o >= -o ~-

NN

123cm columnJ ,

0

P,

== Q

-0.2

E >~

1.3 cm/=

<;

- e - - 3.2 ¢rn/=

-0.4

-0.2 3.4 crn/$

._._ 5.7 ¢m/I

._._- 5.4 cm/I

-0.4

Dimensionless radial coordinate

(-)

Dimensionless radial coordinate (-)

Figure 2, Time-averaged linear liquid velocity profiles in bubble columns measured with LDA. in the centre of the column and downflow along the wall. The profiles agree well with the results of Hills (1974). One of the measured liquid velocity profiles in the 23 cm column (marked with e) does not show 'textbook behaviour'; oddly enough Hills measured the same phenomenon. He reckoned this to be caused by the presence of an asymmetric flow field. Integration over the column area of the "neat" velocity profiles showed that the net liquid velocity is zero, which supports the assumption of the presence of an overall liquid circulation pattern. From Figure 2 it becomes clear that already at very low superficial gas velocities (below 1 cm/s) a clear circulation pattern is measured. It can be seen as well that at high superficial gas velocity conditions in the 23 cm column it is not possible to reach into the central region anymore. Strikingly enough, it appeared to be very well possible to measure in high (nearly 30%) gas hold-up conditons and still reach some 8 cm into the column. Of course these measurements should be interpreted with care: since the data rate under these conditions is so low these data may certainly not be used for determining any flow dynamics: where close to the wall it was possible to obtain data at an average rate of ca. 1200 Hz, during a radial traverse towards the column centreline the data rate dropped to a few 100 Hz in low gas hold-up conditions and to the order of i Hz in the case of high gas hold-up. In the latter case, calculation of the time averaged velocity is the only statistical calculation allowed. It was quite clear that the concept of the liquid flow field as being stationary does not describe the actual flow a

I I

°0.5

0 0.5 axial liquid velocity (m/s)

c o l u m n wall

Figure 3. Liquid velocity pdfs over a radial traverse accross the 15 cm bubble column (u~;s = 0.6 cm/s, H/Dk = 2.6).

Coherent structures and axial dispersion

2515

field present very well. On-screen real-time monitoring of the probability density function (pdf) of the velocities measured (by means of a time window) showed a strongly fluctuating flow field. This pdfwas indeed changing all the time, but rather than one peak shifting up- and downwards, continuously new peaks emerged and disappeared after a few seconds.Looking closer into the positions of these peaks in the pdf showed that in the case of low gas hold-up they emerged (not only, but preferentially) at two positions, one at a negative and one at a positive velocity. This phenomenon is depicted in Figure 3. Figure 3.a shows an impression of an alternating velocity pdf like it was seen on screen. In figure 3.b, a series of time-averaged pdfs of measurements during a radial traverse across the 15 cm column (from the wall towards the centre, U~s = 0.6 cm/s) is shown. Close to the wall the peak at negative velocity is dominant, though an upward velocity is clearly present as a "shoulder" at the right hand side of the peak.In traversing towards the centreline, the proportion of the negative peak slowly decreases and the positive peak gains importance. This effect continues right up to the centre, where the upward velocity is dominant, but negative velocities are still present as well. It is clear though that the distinction between the two peaks is less pronounced in the central region. It can thus be seen that the time-averaged value of the liquid velocity should really be seen as the time averaged value of the two velocities that occur in an alternating sequence. Note the "tail" at the right hand side of all pdfs; this tail is most likely caused by the wake of the bubbles. It is striking that the pdfs are dominated by just a few velocity peaks. The velocities corresponding to these peaks are called 'typical' velocities. Each of these typical velocities may well correspond to the passing of a coherent structure (i.e. a bubble swarm). Apparently, only a few -preferential- velocities determine the entire average flow field. It may be expected that the values of these typical velocities are dependent on geometry and operating conditions.

t~

•-0.~

0 0.5 axial liquid velocity (m/s)

Figure 4. Time dependent behaviour of the liquM velocity, a) velocity p d f at a certain moment (time span - 5 s); b) velocity p d f during the same measurement, ~10 seconds later (lhne span -5 s). 23 cm column, Uas = 3.4 cm/s, H/DR = 6, O0 = 0.8.

That indeed various peaks (i.e. bubble swarms) in the pdfs can be observed is shown in Figure 4, where the time dependent behaviour of the flow can be seen more clearly. Figure 4.a shows a 'snapshot' of a measured pdf at a certain moment (the pdf spanning about 5 s), in Figure 4.b a pdf snapshot from the same time series, but now about 10 s later is shown. The dynamic behaviour is clear. The occurrence of such peaks can be observed at higher superficial gas velocity conditions as well, though the view becomes somewhat more complicated. Apart from the typical velocities increasing, more peaks arise in the time-averaged velocity pdf, so apparently more typical velocities play a role. Even though, the concept remains the same, as can be seen in the time-averaged pdfs shown in Figure 5: close to the wall the velocity with the largest (negative) value is dominant, but more towards the centre, other peaks become more important. At least two peaks at negative velocities can be observed and one positive one. In this case it is difficult to determine whether this sequence continues up to the centreline of the column, since at higher gas hold-up conditions the data rate quickly decreases, so the pdf cannot be determined with great accuracy. By monitoring the time dependent behaviour of the pdf (as shown in Figure 4), it is possible to estimate the typical velocities for the different conditions. The results are shown in Table l (u denoting the typical velocity). Note that the 'direction' (upward or downward) of the velocities is not taken into account, i.e. the values reported in Table I are the absolute values of the velocities.

2516

J. S.

GROENet aL

4,=0.93]

re--

-1

o I._..axial liquid velocity (m/s)

wall

centrelin~

Figure 5. The occurrence o f multiple peaks in velocity pdfs over a radial traverse across the 15 cm bubble column (Ucs = 3.2 cm/s, H/DR = 4.2)

Table 1. Typical velocities as measured with LDA.

15 cm column

23 cm column

Uos (cm/s)

a (%)

u (cm/s)

U~s (cm/s)

a (%)

u (cm/s)

0.6

3.8

$

1.3

4.0

12

1.9

9.1

11

2.0

8.7

10

2.5

12.0

18

3.4

17.4

19

3.2

16.3

12, 29

4.4

22.8

30

5.7

29.0

14, 32

5.5

25.5

12, 34

6.5

28.3

14, 29, 50

The results presented above lead to a mechanistic flow field description that essentially treats a bubble column as an unsteady system. The flow field in a bubble column should be conceived as being constructed by the passage of various dominant coherent structures (or bubble swarms) having a vertical size typically in the order of the column diameter and a typical velocity. These swarms are the major characteristic determining axial dispersion in bubble columns. It might be concluded from visual observations that these swarms originate right at the distributor plate. This was seen very clearly in the 15 cm column, even at low gas hold-up. Though the aeration took place homogeneously over the entire cross-sectional area of the column, the bubbles coming from the distributor always started their journey upwards in the form of a swarm in a priority direction, creating a large-scale liquid vortex-like structure of aspect ratio l directly above the distributor plate (comparable to the "first vortex" in figure I.c). After a couple of seconds, this priority direction would suddenly change over into another which could be any direction over the column perimeter. This changing over would go on and on, resulting in the unsteady flow field described above, which was propagated throughout the bubbly flow. It does not seem, however, that this changing over takes place with a certain frequency. More likely, this occurs in a chaotic way, in the long run resulting in the timeaveraged liquid circulation pattern as shown in Figure l.a. In the case of the 23 cm column, this effect was present as well, though considerably less pronounced. This concept might well explain the observations ofChen et al. (1989, 1994), and the work of Devanathan et al. (1995). It is in agreement with the calculations of Lapin and Ltlbben (1994) and of Sokolichin and Eigenberger (1994).

Coherent structures and axial dispersion

2517

0.002 7"

C nl 1. m > 0

I

0.001

Ir, ,r lr"r t r ; v "1"

m m

a -0,001

-2

-1

0

1

Time shift (-)

0.004 m

0.003

C

•1_ ~=

0.002

o

0.001

8

0 -0.001 -2

-1

0

1

2

Time shift (-)

Figure 6. Cross correlation functions of the signals of two glass fibre probes with the fit according to eq. (6). a) in the centre of the column; b) close to the wall. 23 cm column, UGs = 7 cm/s, H/DR = 5, z = 5.8 cm. Glass fibre probes The glass fibre probe measurements were carried out under the same exprimental conditions as the LDA measurements. The probes were placed at radial positions varying from the column centre to close to the column wall. Typical examples of cross covariance functions R(x) as calculated from pairs of glass fibre probe signals are shown in Figure 6. In the central region a distinct peak at a positive time shift is observed, thus on average an upward directed bubble swarm is present. Close to the wall, a peak at negative time shift is observed, indicating downward flowing bubble swarms. The cross correlation functions are the result of processing and averaging data of at least 80 minutes. So it Should be kept in mind that only the dominant swarm is showing up in Figure 6. The cross covariancefiinctions were fitted with the following function:

R(',:)

0.8

=

a'e

(6)

• 15 cm cotumn I o 23 cm column

A vm

~

0.6

I 0

.¢2_ "¢:

0.4

E

0

i.7. 0.2 0

0

I

I

I

I

I

5

10

15

20

25

Axial distance (cm)

Figure 7. Dependence of the value of c with increasing axial distance z. 15 cm column (uGs = 5.6 cm/s, H/D R = 6) and 23 cm column (UGs = 7 cm/s, H/Dn = 5). Comparing eq. (6) to eq. (5) shows that the fit parameters a, b and c should be interpreted as follows:

2518

J. S. GROENet al. a = A'e

; b =

T -I +

; c = z

(7)

V

Thus the value ofc determines the swarm velocity v. This parameter is by far the easiest one to get. That c does denote a velocity is shown in Figure 7 in which the value ofc is given for different values of z; the linear dependence is striking. Values ofv calculated in this way quite neatly correspond with the average liquid velocity as measured with LDA p l u s a swarm rise velocity estimated with the Barnea-Mizrahi (1973) model. The value of the Lagrangian swarm lifetime Tcan be estimated by evaluating the value of a as a function ofz. The typical swarm size / is then calculated by means of the value ofb. Both in the 15 cm column and in the 23 cm column the value of Tis in the order of 0.5 s. In the 15 cm column, the value for I calculated in this way was between 12 and 13 cm, the value of/for the 23 cm column comes strikingly close to 23 cm. This is in agreement with our previous results (Groen et al. 1994,1995). Note that these measurements do not say anything about the horizontal size of the structures. These should not be seen as spherical over the entire column diameter, since this would e.g. not allow the presence of net liquid upflow in the column centre ar}d therefore would disagree with the LDA results. A x i a l dispersion

Axial dispersion should be regarded as transport with a typical velocity over a typical axial distance. As demonstrated with the LDA measurements, the flow field is dominated by a few typical velocities. As shown in the previous paragraph, the maximum vertical distance bubble swarms span is of the order of the column diameter. In this view, the axial dispersion coefficient can be modelled with these two parameters:

EL = k , . o .

(8)

This model is dimensionally correct; it does not involve powers for u or DR, although most likely u will show a dependence on column diameter. The calculation o f EL using eq. (8) is straightforward for low superficial gas velocities, since only one distinct typical velocity is present. At higher superficial gas velocities the presence of multiple peaks complicates things. As a first estimate a dispersion coefficient is assigned to each of the typical velocities, since they all induce axial dispersion. Given the mechanistic setup of this model, a first estimate would be that EL is e q u a l to the product of u and DR, in other words, k3 = 1. Dispersion coefficients can thus be calculated by multiplying the typical velocities of Table 1 with the respective column diameters. As a consequence, the Bodenstein number becomes equal to the ratio of

1E+01 i i

i

t_

1 E+O0

.Q

i

E c

=

e~

i

r

I

I

1 E-01

I¢t

i

C "U

o

i

_,

1E-02

~ i ,

q

*

i

P

i * * i

i t t i

~ I i i

I I p I

t

I

111 •

15 cm column

o 23 cm column

1 E-03 1 E-06

1E-05

1E-04

1E-03

J

J

1E-02

1E-01

1E+O0

Froude number (-)

F i g u r e 8. A x i a l dispersion results c o m p a r e d to the model o f eq. (4) a n d existing literature data.

Coherent structures and axial dispersion

2519

the superficial gas velocity and the typical liquid velocity. In Figure 8, the results of this model are compared with the model ofeq. (4) and with existing literature data. Given the simplicity of the model, the agreement with existing data is quite good, especially for low superficial gas velocities. Thus the assumption of k3 being equal to I seems justified. It is clear though that the model should be refined further for the higher superficial gas velocity cases. It might be expected that structures with different values of u also have different typical sizes. This should follow from a closer look at the time variation of the cross correlation functions of the glass fibre probes. 5. CONCLUSIONS From the results presented in this paper it can be concluded that considering the flow in a bubble column as stationary by far oversimplifies the actual phenomena present. The LDA measurements show that the time averaged liquid linear velocity profiles should be thought of as being constructed out of different typical velocities, caused by the passage of coherent structures (bubble swarms) which occur at any position in an alternating sequence. At lower hold-up conditions, it is shown that the liquid velocity profile is built up from two velocities (opposite in direction) the magnitude of which is larger than the time-averaged value of the liquid velocity. Close to the wall, the downward velocity is dominant, while on traversing towards the central region of the column the influence of the upward velocity increases. At higher superficial velocity conditions this process is qualitatively the same, though more than one typical velocity plays a part. Glass fibre measurements in combination with correlation techniques show that the swarms present in bubble columns have a typical size of close to the column diameter. By considering axial dispersion as transport with a certain velocity over a certain distance a simple mechanistic model is presented, considering the axial dispersion coefficient as the product of the typical velocities with the column diameter. Given the conceptual form of this model, the agreement of results obtained with it with existing literature data is good, especially at lower gas holdup conditions. It is thus clear that the non-stationary behaviour of bubble columns can be measured and quantified. It may be expected that this local and time-dependent description of the flow in a bubble column will be helpful in understanding bubble column behaviour and in developing reliable scaling rules. NOMENCLATURE amplitude of gas fraction fluctuations (-) u a,b,c fit parameters various v D~ column diameter (m) x.y EL axial dispersion coefficient (m2/s) H height above distributor plate (m) kl, k2, k3 proportionality constants various tz(~) 1 swarm size (m) (z0 m parameter in power law model (-) R cross covariance function (-) c T swarm life time (s) "c U~;s superficial gas velocity (m/s) qb

A

typical liquid velocity swarm velocity fit parameters axial distance

(m/s) (m/s) (-) (m)

local gas hold-up (-) centreline gas hold-up (-) cross sectional averaged gas hold-up (-) specific power input (W/kg) time shift (s) dimensionless radial coordinate (-)

REFERENCES Baird, M.H.I. and Rice, R.G., 1975, Axial dispersion in large unbaffled columns, Chem. Engng d., 9, 171-174. Barnea, E. and Mizrahi, J., 1973, A generalized approach to the fluid dynamics of paniculate systems. Part 1: General correlation for fluidization and sedimantation in solid multiparticle systems, Chem. Engng d., 5, 171-189. Chen, J.J.J., Jamialahmadi, M. and Li, S.M., 1989, Effect of liquid depth on circulation in bubble columns, a visual study, Chem. Engng Res. Des., 67, 203-206. Chen, R.C., Reese, J. and Fan, L.-S., 1994, Flow structure in three-dimensional bubble column and three-phase fluidized bed, AIChE J., 40(7), 1093-1104. De Nevers, N., 1968, Bubble driven liquid circulations, AIChE J., 14, 222-226. Deckwer, W.-D., 1992, Bubble Column Reactors, Wiley. Deckwer, W.-D. and Schumpe, A., 1993, Improved tools for bubble column reactor design and scale-up, Chem. Engng Sci., 48, 889-91 I. Devanathan, N., Moslemian, D. and Dudukovi6, M.P., 1990, Flow mapping in bubble columns using CARPT, Chem. Engng Sci., 45(8), 2285-229 I. Devanathan, N., Dudukovid, M.P., Lapin, A. and LUbber't, A., 1995, Chaotic flow in bubble column reactors, Chem. Engng Sci., 50(16), 2661-2667. Durst, F., SchSnung, B., Selanger, K. and Winter, M., 1986, Bubble driven fluid flows, d. Fluid Mech., 170, 53-82. Franz., K., BOrner, T., Kantorek, H.J. and Buchholz, R., 1984, Flow structures in bubble columns, Ger. Chem. Engng, 7, 365-374.

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