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Chaotic flow in bubble column reactors
00000000000000o0000000000000000000000000000000000000000000000000000oo000000ooo
Pergamon
Chemical Enoineerin0 Science, Vol. 50, No. 16, pp. 2661 2667, 1995 Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0009 2509/95 $9.50 + 0.00
0009-2509(95)00070-4
Chaotic flow in bubble column reactors (Received 14 October 1994; accepted in revised form 17 January 1995)
INTRODUCTION Bubble column reactors are favored in chemical and biochemical industries when gas-liquid reactions are to be performed in large volumes at low mixing energy levels. Although simple in construction, scale up of these reactors remains a problem. The models actually used in practice suffer from being extremely simplified (Deckwer and Schumpe, 1993); most of the essential physical details of the two-phase gas-liquid flow have not been considered. The main reason for this unfavorable situation is limited computing power; it was not possible to solve the governing equations, which are principally known, for realistic boundary conditions and with sufficiently high numerical resolution. The advent of high-speed workstations now becoming available, initiated an increasing activity in computational fluid dynamics. This development was reflected by renewed investigations of the flow in bubble column reactors. The two-phase gas-liquid flow in bubble columns has recently been adressed by many investigators (Gasche et al., 1990; Svendsen et al., 1992; Webb et al., 1992; Grienberger and Hofmann, 1992; Hjertager and Morud, 1993; Lapin and Liibbert, 1994a,b; Sokolichin and Eigenberger, 1994). Computational fluid dynamics, however, will only be accepted in practice when it is possible to validate the computer code, or at least the results of the program packages, for a particular application. This indispensibly requires highly informative measurement results from the real systems that are modelled. The difficulty in the stochastical flow systems we are dealing with is that there are only a few measurement techniques which are capable of providing detailed information on the transient fluid flow patterns. Particle image velocimetry (Chen and Fan, 1992) is one example of such an advanced technique. One central aspect, however, is difficult to investigate with advanced visualization techniques: the three-dimensional path of a representative particle, the central quantity of the Lagrangian representation of the flow, cannot easily be obtained with such techniques on the scale of the entire reactor. Particle paths are a prerequisite for estimating the changes in the environment a chemical reactant fluid element experiences on its journey through the reactor. This type of information is needed to estimate the reactor performance. Such a path information can be obtained with single particle tracking techniques such as computer aided radioactive particle tracking [CARPT: Yang et al. (1993)]. In this paper particle paths through a bubble column reactor as observed experimentally are compared with paths simulated. The results are discussed in the context of the transient flow structures which dynamically change in a real bubble column. Some features of the complex flow in simple bubble column reactors are easier to understand in the light of this comparison.
METHODS Experimental Experiments have been performed in a simple bubble column of about 251 volume. The column was equipped with a sparger covering the entire flat bottom, consisting of a sintered metal plate. Gas supply was kept constant with a mass flow controller. The most important data about the column are summarized in Table 1.
Table 1. Data of the bubble columns used System Distributor Column diameter Superficial air velocity Static liquid height Mean gas holdup
air-water sintered plate 20.3 cm 2.0 cm/s 57 cm 0.100
Air-in-water dispersions were used in these experiments. St. Louis tap water was taken without additions. Superficial gas velocity of 2cm/s was adjusted in the experiments reported. The hydrodynamical characteristics have been measured by means of the CARPT-technique. The measurement technique is discussed in detail by Devanathan et al. (1990), Moslemian et al. (1992) and Yang et al. (1993); hence we only briefly mention the aspects that are of importance in this paper. CARPT is a particle tracking technique, in which the position of an essentially neutrally buoyant tiny particle suspended in the two-phase gas-liquid flow is pin-pointed by a set of detectors properly arranged around the bubble column. The particle used is a small fully wettable pill, containing a scandium-46 sample transmitting 7-radiation with an activity of about 300/zCi. The 16 detectors used are NaI-based scintillation counters. Since it is possible to determine the particle's position with a high sampling rate, its path through the column can be determined and recorded. In the experiment reported the sampling frequency was 33 Hz. Flow simulations For the experimental setup described, a numerical threedimensional dynamic flow simulation was performed based on the Euler-Lagrange representation of the two-phase flow as described by Lapin and Lfibbert (1994a, b). Hence, it will be described only very briefly.
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Shorter Communications
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On the column scale, the flow of the two-phase gas-liquid dispersion is simulated as a single phase flow using the Navier-Stokes equations. The linear mesh size in such numerical calculations are large as compared with the mean bubble diameter. It is thus not possible to resolve the bubbles on that scale. Consequently, it is assumed that the dispersion is a single phase flow with spatially varying density. At the lower gas holdups considered the effective viscosity is nearly equal to the liquid viscosity. Within the control volumes of the column scale representation, individual bubbles or bubble clusters are described by spatial density distributions. Due to buoyancy effects they are travelling through the dispersion. Their paths are calculated on the basis of force balances. In this Lagrangian way, more than 100,000 bubbles or bubble clusters can simultaneously be tracked on their way through the column. The motion of both phases are coupled in the following way: for a single time step the paths of the gas-phase elements lead to a pattern of cluster positions. They can be converted into density distributions on the column scale. This density field is used in the Navier-Stokes equations. Then the velocity and pressure fields which result as solutions of these equations are used to update the cluster positions. This cycle is repeated until convergence is obtained, i.e. until the error in all equations is lower than a predefined value. The spatial resolution of the simulation is high enough to obtain the chaotic motion of the two-phase flow shown in the figures without any artificial assumption about fluid turbulence; all flow structures are an immediate result of the Navier-Stokes equation system.
RESULTS
Flow patterns Velocities were calculated on a three-dimensional numerical grid of 34 × 34 x 100 nodes. Figure 1 depicts a typical velocity pattern of the two-phase gas-liquid flow in the bubble column. Velocity vectors taken at points on two perpendicular planes (x-y plane and x-z plane) through the column axis (x-axis) are shown. The arrows are projections of the three-dimensional velocity vectors onto the two planes. The velocity scale is shown as an arrow at the lower left side of the left graph. The velocity pattern depicted in Fig. 1 represents the flow computed for a particular instant in time. It shows a typical situation which appears after the system had sufficient time to reach a quasi-stationary state. However, the structure of the flow pattern is by no means stationary but is continuously changing in a chaotic way, although the assumed superficial gas velocity, Wsg = 2 cm/s, is rather low. At the time the result shown in Fig. 1 was obtained, 135,518 bubbles represented by spatial density distributions of roughly 3 mm width were within the system, they led to a gas holdup of about 10%. Figure 2 depicts a momentary situation of the bubble cluster locations within a thin slide parallel to the x-y plane and the corresponding density distribution of the dispersion. Of course, this cluster position pattern is also changing considerably with time. Similar structures can be observed by visual inspection of a laboratory bubble column in operation (e.g. Denk and Stern, 1979). Since the motion is chaotic, it is difficult to compare images calculated for different times. Quantitative comparisons of the flow patterns are possible on a statistical basis only. The easiest way is time averaging over many characteristic time-constants of the hydrodynamic motion, i.e. over periods which are long enough to average out all stochastically appearing flow structures. Such an averaged velocity pattern is shown in Fig. 3. A fairly (but not exactly!) symmetric flow profile appears after averaging. This profile is the type of flow patterns usually discussed in literature. It was
obtained after averaging over a period of 4 min only. Only in small columns like the one investigated, such short averaging times lead to reproducible patterns.
Motion of typical liquid fluid elements In order to see what a representative fluid element travelling through the two-phase gas-liquid flow in bubble columns will experience, measurements and simulations of the path of a neutrally buoyant flow follower were performed. The experiments were performed with the 7-activated particle tracked on its course through the column with the CARPT-technique described. In the simulations a single (artificial!) particle of neutral buoyancy was tracked. A typical result is shown in Fig. 4. Both results shown in Fig. 4 are paths of the fluid element taking about 5 min real time. Obviously, it is not possible to directly compare two concrete paths of a particle within a chaotic flow. However, it can easily be seen by visual inspection that the gross structure of both paths shown in Fig. 3 are obviously not regular. In order to quantify the behavior of the flow follower by a measure which is meaningful in terms of chemical engineering, we determined the mean distance R(~) the particle travels within a given time interval of length T. R(z) = (Ix(t) - x(t + ~)1) where x(t) is the 3D-position of the particle at time t. The averaging is taken over all times t available in a data set. Hence, R(z) is a measure of how far the particle can move away from an arbitrarily chosen origin within a time span z. In Fig. 5 a comparison is made of the measured and the simulated distances R(z) as a function of the travelling time r based on the paths depicted in Fig. 4. The averaging time was about 4 min. The asymptotic behavior of the curves reflects that the size of the local flow structures is limited by the finite column dimension. The experimental path is slightly more irregular. At small time spans T, the distances R(z) are a little bit larger for the real particle since it makes additional stochastical motions on the smaller scale which cannot be resolved in the simulation. However, it can be seen that both functions have very much the same character. This confirms the similarity between the experimental and the theoretical results.
DISCUSSION AND CONCLUSIONS The two-phase gas-liquid flow in bubble columns appears to be, as shown in Fig. 1, a chaotic flow. Nevertheless, it contains local flow structures of different sizes. The largest and most prominent of them have characteristic length scales in the order of the column diameter. Detailed simulations showed that the vortex-like structures may accumulate gas. Then their density decreases relative to their surrounding. Consequently, they rise within the column. The structures are thus not stable neither with respect to their location nor to their form and size. The results shown clearly demonstrate that the flow in bubble column reactors is transient and chaotic even if the reactor is operated at low superficial gas velocities. Obviously, this influences the mixing properties of these columns. It is to be expected that larger industrial bubble columns are even more susceptible to flow instabilities since the same superficial velocities then lead to much higher Reynolds numbers. An example was shown by Lapin and Liibbert (1994b) for the case of a production-scale beer fermenter. At the current state of the simulation technique, it is not possible to resolve the detailed flow of liquid around individual bubbles. Hence, the transport of the flow follower in bubbles wakes could not be considered. However, the gross motion of the flow particle is reproduced rather well as was demonstrated in Figs 4 and 5.
Shorter Communications
2663
10 [cm/s]: A
X-Y-Plane
X-Z-Plane
Velocity Pattern in an A i r / W a t e r C o l u m n (D = 8 in, wsg : 2 cm/s) Fig. 1. Typical instantaneous flow structure of the dispersion in the bubble column. Two mutually perpendicular cuts through the axis of the bubble column are shown. The scale at the lower left marks the velocity of 10 cm/s. Since the arrow length is not easy to see, the velocity is additionally represented by the size of the triangle which marks the position of the origin of the arrow. Blue color indicates that the vectors have a component coming out of the plane, red arrows are directed into the plane, black ones fairly remain within the plane. The graph above the two figures depicts the velocities within the cross section of the column's top.
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Shorter Communications
Transient Density Pattern
Transient Cluster Positions
Pattern of the Gas-Phase Distribution (D = 8 in, w~8 = 2 cm/s) Fig. 2. Momentary density pattern of the dispersion corresponding to the velocity pattern on left-hand side of Fig. 1. The corresponding bubble cluster position pattern is shown in the right part of the figure. The different densities are marked by colors. Ten classes have been distinguished: white corresponds to the smallest density, black to the highest.
Shorter Communications
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2665
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,,tlTllllllllltlllltIIt ,,i
,, IIIIllllllllllllIIrr,,, ,, Illtllllllltllllr r,, ,, TI11IIIIIIIIIIIIITTr ,, ,, tltttTtlTtllllllll , ,,,ttrttrTtllttltttltttlf, .,ftt~IIIlltttltttttttl~,
,,~rrtttttlltltliltlttt,, ,, ttt/lt/tttttttttttl ,, _.,z~.:,i/Z/i/lltll!~\\\\\\,. i
Fig. 3. Left: velocity pattern in one of the planes depicted in Fig. 1, but averaged over a time period of about 4 min. The upper part shows the velocity pattern in the top surface of the column. Right: in order to make the result more transparent, typical velocity profiles across the column diameter are additionally shown. The scale, 10 cm/s, is shown in form of the arrow at the lower left side of the graph. This graph was made from the data shown on the left part of the figure.
2666
Shorter Communications
Measured
Simulated
Fig. 4. Typical path of a neutrally buoyant particle moving through the two-phase gas-liquid flow in bubble columns. On the left the experimental result, on the right the simulated result is shown.
20
N
Simulation
R ( f ) = (I-2(t) - Y.(t + z')l)
o
lo
~~
Travelling Time [s]
3'0 ,~ go Travelling Time [s]
. . . . .
Fig. 5. Average distance R(,) the neutrally buoyant particle travels within a time interval of length ~. The inserted plot depicts the expanded part of R(z) at smaller travelling times.
Shorter Communications The "particles" suspended in the two-phase gas-liquid flow in bubble columns, whether they are liquid fluid elements, inorganic catalyst particles or microbial cells, do see the transient flow structures only and not the averaged ones primarily discussed in literature. This immediately becomes clear from the experiments and the simulations of the particle paths. Thus, there is no physical base for the assumption of a plug flow of the liquid through the bubble column reactor superimposed by a diffusional process as often assumed in chemical engineering discussions. Hence, the essential message which can be extracted from the investigation described here is that the flow in bubble column reactors must be regarded as a transient chaotic flow instead of a simply structured one. Acknowledgement--The financial support of the Deutsche Forschungsgemeinschaft is gratefully acknowledged. N. DEVANATHAN M.P. DUDUKOVIC
Department of Chemical Engineering Washington University St. Louis, MO 63130, U.S.A. A. LAPIN A. LOBBERT* Institut ffir Technische Chemie Universitat Hannover D-30167 Hannover Germany REFERENCES
Chen, R. C., Reese, J. and Fan, L. S., 1992, Flow structure in a three-dimensional bubble column and three-phase fluidized bed. Paper 114b presented at the AIChE annual meeting, Miami Beach 1992. A.I.Ch.E.J. (in press). Chen, R. C. and Fan, L. S., 1992, Particle image velocimetry for characterizing the flow structures in three-dimensional gas-liquid-solid fluidized beds. Chem. Engng Sci. 47, 3615-3622. Deckwer, W. D. and Schumpe, A., 1993, Improved tools for bubble column reactor design and scale-up. Chem. Engng Sci. 49, 889-911. *Author to whom correspondence should be addressed.
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Denk, V. and Stern, R., 1979, Examples of flow visualization in food technology, in Proceedings 2nd International Symposium on Flow Visualization (Edited by W. Merzkirch), Bochum. Devanathan, N., Moslemian, D. and Dudukovic, M. P. 1990, Flow mapping in bubble columns using CARPT. Chem. Engng Sci. 45, 2285-2291. Gasche, H. E., Edinger, C., K6mpel, H. and Hofmann, H., 1990, A fluid dynamically based model of bubble column reactors. Chem. Engng Technol. 13, 341-349. Grienberger, J. and Hofmann, H., 1992, Investigations and modelling of bubble columns. Chem. Engng Sci. 47, 2215-2220. Moslemian, D., Devanathan, N. and Dudukovic, M. P., 1992, Radioactive particle tracking techniques for investigation of phase recirculation and turbulence in multiphase systems. Rev. Sci. Instr. 63, 4361-4372. Hjertager, B. H. and Morud, K., 1993, Computational fluid dynamics simulation of bioreactors, in Bioreactor Performance (Edited by U. Mortensen and H. J. Noorrnan), pp. 47-61. Ideon, Lund. Landau, L. D. and Lifschitz, E. M., 1974, Hydrodynamik, 3rd German Edition. Akademie, Berlin. Lapin, A. and Lfibbert, A., 1994a, Numerical simulation of the dynamics of two-phase gas-liquid flows in bubble columns. Chem. Engng Sci. 49, 3661-3674. Lapin, A. and Liibbert, A., 1994b, Dynamic simulation of the gas-liquid flows in bubble columns, demonstrated at the example of industrial-scale beer fermenters. Chem. Engng Sci. (submitted). Sokolichin, A. and Eigenberger, G., 1994, Gas-liquid flow in bubble columns and loop reactors. Chem. Engng Sci. (submitted). Svendsen, H. F, Jakobsen, H. A. and Torvik, R., 1992, Local flow structures in internal loop and bubble column reactors. Chem. Engng Sci. 47, 3297-3304. Webb, C., Que, F. and Senior, P. R., 1992, Dynamic simulation of gas-liquid dispersion behaviour in a 2-D bubble column using a graphics mini-supercomputer. Chem. Engng Sci. 47, 3305-3312. Yang, Y. B., Devanathan, N. and Dudukovic, M. P., 1993, Liquid backmixing in bubble columns via computer-automated radioactive particle tracking (CARPT). Exp. Fluids, 16, 1-9.
Pergamon
Chemical Enoineerin0 Science, Vol. 50, No. 16, pp. 2661 2667, 1995 Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0009 2509/95 $9.50 + 0.00
0009-2509(95)00070-4
Chaotic flow in bubble column reactors (Received 14 October 1994; accepted in revised form 17 January 1995)
INTRODUCTION Bubble column reactors are favored in chemical and biochemical industries when gas-liquid reactions are to be performed in large volumes at low mixing energy levels. Although simple in construction, scale up of these reactors remains a problem. The models actually used in practice suffer from being extremely simplified (Deckwer and Schumpe, 1993); most of the essential physical details of the two-phase gas-liquid flow have not been considered. The main reason for this unfavorable situation is limited computing power; it was not possible to solve the governing equations, which are principally known, for realistic boundary conditions and with sufficiently high numerical resolution. The advent of high-speed workstations now becoming available, initiated an increasing activity in computational fluid dynamics. This development was reflected by renewed investigations of the flow in bubble column reactors. The two-phase gas-liquid flow in bubble columns has recently been adressed by many investigators (Gasche et al., 1990; Svendsen et al., 1992; Webb et al., 1992; Grienberger and Hofmann, 1992; Hjertager and Morud, 1993; Lapin and Liibbert, 1994a,b; Sokolichin and Eigenberger, 1994). Computational fluid dynamics, however, will only be accepted in practice when it is possible to validate the computer code, or at least the results of the program packages, for a particular application. This indispensibly requires highly informative measurement results from the real systems that are modelled. The difficulty in the stochastical flow systems we are dealing with is that there are only a few measurement techniques which are capable of providing detailed information on the transient fluid flow patterns. Particle image velocimetry (Chen and Fan, 1992) is one example of such an advanced technique. One central aspect, however, is difficult to investigate with advanced visualization techniques: the three-dimensional path of a representative particle, the central quantity of the Lagrangian representation of the flow, cannot easily be obtained with such techniques on the scale of the entire reactor. Particle paths are a prerequisite for estimating the changes in the environment a chemical reactant fluid element experiences on its journey through the reactor. This type of information is needed to estimate the reactor performance. Such a path information can be obtained with single particle tracking techniques such as computer aided radioactive particle tracking [CARPT: Yang et al. (1993)]. In this paper particle paths through a bubble column reactor as observed experimentally are compared with paths simulated. The results are discussed in the context of the transient flow structures which dynamically change in a real bubble column. Some features of the complex flow in simple bubble column reactors are easier to understand in the light of this comparison.
METHODS Experimental Experiments have been performed in a simple bubble column of about 251 volume. The column was equipped with a sparger covering the entire flat bottom, consisting of a sintered metal plate. Gas supply was kept constant with a mass flow controller. The most important data about the column are summarized in Table 1.
Table 1. Data of the bubble columns used System Distributor Column diameter Superficial air velocity Static liquid height Mean gas holdup
air-water sintered plate 20.3 cm 2.0 cm/s 57 cm 0.100
Air-in-water dispersions were used in these experiments. St. Louis tap water was taken without additions. Superficial gas velocity of 2cm/s was adjusted in the experiments reported. The hydrodynamical characteristics have been measured by means of the CARPT-technique. The measurement technique is discussed in detail by Devanathan et al. (1990), Moslemian et al. (1992) and Yang et al. (1993); hence we only briefly mention the aspects that are of importance in this paper. CARPT is a particle tracking technique, in which the position of an essentially neutrally buoyant tiny particle suspended in the two-phase gas-liquid flow is pin-pointed by a set of detectors properly arranged around the bubble column. The particle used is a small fully wettable pill, containing a scandium-46 sample transmitting 7-radiation with an activity of about 300/zCi. The 16 detectors used are NaI-based scintillation counters. Since it is possible to determine the particle's position with a high sampling rate, its path through the column can be determined and recorded. In the experiment reported the sampling frequency was 33 Hz. Flow simulations For the experimental setup described, a numerical threedimensional dynamic flow simulation was performed based on the Euler-Lagrange representation of the two-phase flow as described by Lapin and Lfibbert (1994a, b). Hence, it will be described only very briefly.
2661
Shorter Communications
2662
On the column scale, the flow of the two-phase gas-liquid dispersion is simulated as a single phase flow using the Navier-Stokes equations. The linear mesh size in such numerical calculations are large as compared with the mean bubble diameter. It is thus not possible to resolve the bubbles on that scale. Consequently, it is assumed that the dispersion is a single phase flow with spatially varying density. At the lower gas holdups considered the effective viscosity is nearly equal to the liquid viscosity. Within the control volumes of the column scale representation, individual bubbles or bubble clusters are described by spatial density distributions. Due to buoyancy effects they are travelling through the dispersion. Their paths are calculated on the basis of force balances. In this Lagrangian way, more than 100,000 bubbles or bubble clusters can simultaneously be tracked on their way through the column. The motion of both phases are coupled in the following way: for a single time step the paths of the gas-phase elements lead to a pattern of cluster positions. They can be converted into density distributions on the column scale. This density field is used in the Navier-Stokes equations. Then the velocity and pressure fields which result as solutions of these equations are used to update the cluster positions. This cycle is repeated until convergence is obtained, i.e. until the error in all equations is lower than a predefined value. The spatial resolution of the simulation is high enough to obtain the chaotic motion of the two-phase flow shown in the figures without any artificial assumption about fluid turbulence; all flow structures are an immediate result of the Navier-Stokes equation system.
RESULTS
Flow patterns Velocities were calculated on a three-dimensional numerical grid of 34 × 34 x 100 nodes. Figure 1 depicts a typical velocity pattern of the two-phase gas-liquid flow in the bubble column. Velocity vectors taken at points on two perpendicular planes (x-y plane and x-z plane) through the column axis (x-axis) are shown. The arrows are projections of the three-dimensional velocity vectors onto the two planes. The velocity scale is shown as an arrow at the lower left side of the left graph. The velocity pattern depicted in Fig. 1 represents the flow computed for a particular instant in time. It shows a typical situation which appears after the system had sufficient time to reach a quasi-stationary state. However, the structure of the flow pattern is by no means stationary but is continuously changing in a chaotic way, although the assumed superficial gas velocity, Wsg = 2 cm/s, is rather low. At the time the result shown in Fig. 1 was obtained, 135,518 bubbles represented by spatial density distributions of roughly 3 mm width were within the system, they led to a gas holdup of about 10%. Figure 2 depicts a momentary situation of the bubble cluster locations within a thin slide parallel to the x-y plane and the corresponding density distribution of the dispersion. Of course, this cluster position pattern is also changing considerably with time. Similar structures can be observed by visual inspection of a laboratory bubble column in operation (e.g. Denk and Stern, 1979). Since the motion is chaotic, it is difficult to compare images calculated for different times. Quantitative comparisons of the flow patterns are possible on a statistical basis only. The easiest way is time averaging over many characteristic time-constants of the hydrodynamic motion, i.e. over periods which are long enough to average out all stochastically appearing flow structures. Such an averaged velocity pattern is shown in Fig. 3. A fairly (but not exactly!) symmetric flow profile appears after averaging. This profile is the type of flow patterns usually discussed in literature. It was
obtained after averaging over a period of 4 min only. Only in small columns like the one investigated, such short averaging times lead to reproducible patterns.
Motion of typical liquid fluid elements In order to see what a representative fluid element travelling through the two-phase gas-liquid flow in bubble columns will experience, measurements and simulations of the path of a neutrally buoyant flow follower were performed. The experiments were performed with the 7-activated particle tracked on its course through the column with the CARPT-technique described. In the simulations a single (artificial!) particle of neutral buoyancy was tracked. A typical result is shown in Fig. 4. Both results shown in Fig. 4 are paths of the fluid element taking about 5 min real time. Obviously, it is not possible to directly compare two concrete paths of a particle within a chaotic flow. However, it can easily be seen by visual inspection that the gross structure of both paths shown in Fig. 3 are obviously not regular. In order to quantify the behavior of the flow follower by a measure which is meaningful in terms of chemical engineering, we determined the mean distance R(~) the particle travels within a given time interval of length T. R(z) = (Ix(t) - x(t + ~)1) where x(t) is the 3D-position of the particle at time t. The averaging is taken over all times t available in a data set. Hence, R(z) is a measure of how far the particle can move away from an arbitrarily chosen origin within a time span z. In Fig. 5 a comparison is made of the measured and the simulated distances R(z) as a function of the travelling time r based on the paths depicted in Fig. 4. The averaging time was about 4 min. The asymptotic behavior of the curves reflects that the size of the local flow structures is limited by the finite column dimension. The experimental path is slightly more irregular. At small time spans T, the distances R(z) are a little bit larger for the real particle since it makes additional stochastical motions on the smaller scale which cannot be resolved in the simulation. However, it can be seen that both functions have very much the same character. This confirms the similarity between the experimental and the theoretical results.
DISCUSSION AND CONCLUSIONS The two-phase gas-liquid flow in bubble columns appears to be, as shown in Fig. 1, a chaotic flow. Nevertheless, it contains local flow structures of different sizes. The largest and most prominent of them have characteristic length scales in the order of the column diameter. Detailed simulations showed that the vortex-like structures may accumulate gas. Then their density decreases relative to their surrounding. Consequently, they rise within the column. The structures are thus not stable neither with respect to their location nor to their form and size. The results shown clearly demonstrate that the flow in bubble column reactors is transient and chaotic even if the reactor is operated at low superficial gas velocities. Obviously, this influences the mixing properties of these columns. It is to be expected that larger industrial bubble columns are even more susceptible to flow instabilities since the same superficial velocities then lead to much higher Reynolds numbers. An example was shown by Lapin and Liibbert (1994b) for the case of a production-scale beer fermenter. At the current state of the simulation technique, it is not possible to resolve the detailed flow of liquid around individual bubbles. Hence, the transport of the flow follower in bubbles wakes could not be considered. However, the gross motion of the flow particle is reproduced rather well as was demonstrated in Figs 4 and 5.
Shorter Communications
2663
10 [cm/s]: A
X-Y-Plane
X-Z-Plane
Velocity Pattern in an A i r / W a t e r C o l u m n (D = 8 in, wsg : 2 cm/s) Fig. 1. Typical instantaneous flow structure of the dispersion in the bubble column. Two mutually perpendicular cuts through the axis of the bubble column are shown. The scale at the lower left marks the velocity of 10 cm/s. Since the arrow length is not easy to see, the velocity is additionally represented by the size of the triangle which marks the position of the origin of the arrow. Blue color indicates that the vectors have a component coming out of the plane, red arrows are directed into the plane, black ones fairly remain within the plane. The graph above the two figures depicts the velocities within the cross section of the column's top.
2664
Shorter Communications
Transient Density Pattern
Transient Cluster Positions
Pattern of the Gas-Phase Distribution (D = 8 in, w~8 = 2 cm/s) Fig. 2. Momentary density pattern of the dispersion corresponding to the velocity pattern on left-hand side of Fig. 1. The corresponding bubble cluster position pattern is shown in the right part of the figure. The different densities are marked by colors. Ten classes have been distinguished: white corresponds to the smallest density, black to the highest.
Shorter Communications
,.:...... ~:-".
2665
i ...... ~._'--~-", ', ', ', ',",,'-.,:"-,.~.-"-.-.:7
:?!\
1/.
[,,~l111~lflllltllllllttll,.
I
r "'~lllIllllllllllltlltlltt'
l
t.,~llIllll
l
i
I
lllllttlttt~,,
i.,~ll~lllllllllfltlttllt~,.l
,~1111I[llllllllllltltt "1 ,~11t111111fllllttttll~,, ,~1111111111ttlttttt,,[
,,tlTllllllllltlllltIIt ,,i
,, IIIIllllllllllllIIrr,,, ,, Illtllllllltllllr r,, ,, TI11IIIIIIIIIIIIITTr ,, ,, tltttTtlTtllllllll , ,,,ttrttrTtllttltttltttlf, .,ftt~IIIlltttltttttttl~,
,,~rrtttttlltltliltlttt,, ,, ttt/lt/tttttttttttl ,, _.,z~.:,i/Z/i/lltll!~\\\\\\,. i
Fig. 3. Left: velocity pattern in one of the planes depicted in Fig. 1, but averaged over a time period of about 4 min. The upper part shows the velocity pattern in the top surface of the column. Right: in order to make the result more transparent, typical velocity profiles across the column diameter are additionally shown. The scale, 10 cm/s, is shown in form of the arrow at the lower left side of the graph. This graph was made from the data shown on the left part of the figure.
2666
Shorter Communications
Measured
Simulated
Fig. 4. Typical path of a neutrally buoyant particle moving through the two-phase gas-liquid flow in bubble columns. On the left the experimental result, on the right the simulated result is shown.
20
N
Simulation
R ( f ) = (I-2(t) - Y.(t + z')l)
o
lo
~~
Travelling Time [s]
3'0 ,~ go Travelling Time [s]
. . . . .
Fig. 5. Average distance R(,) the neutrally buoyant particle travels within a time interval of length ~. The inserted plot depicts the expanded part of R(z) at smaller travelling times.
Shorter Communications The "particles" suspended in the two-phase gas-liquid flow in bubble columns, whether they are liquid fluid elements, inorganic catalyst particles or microbial cells, do see the transient flow structures only and not the averaged ones primarily discussed in literature. This immediately becomes clear from the experiments and the simulations of the particle paths. Thus, there is no physical base for the assumption of a plug flow of the liquid through the bubble column reactor superimposed by a diffusional process as often assumed in chemical engineering discussions. Hence, the essential message which can be extracted from the investigation described here is that the flow in bubble column reactors must be regarded as a transient chaotic flow instead of a simply structured one. Acknowledgement--The financial support of the Deutsche Forschungsgemeinschaft is gratefully acknowledged. N. DEVANATHAN M.P. DUDUKOVIC
Department of Chemical Engineering Washington University St. Louis, MO 63130, U.S.A. A. LAPIN A. LOBBERT* Institut ffir Technische Chemie Universitat Hannover D-30167 Hannover Germany REFERENCES
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