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CFD Simulation of Bubble Columns: Modeling of Nonuniform Gas Distribution at Sparger M. R. Rampure,†,‡ S. M. Mahajani,‡ and V. V. Ranade*,§ Industrial Flow Modeling Group, National Chemical Laboratory, Pune-411 008, INDIA Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai-400076, INDIA Tridiagonal Solutions PVt. Ltd., 100 NCL InnoVation Park, Pune 411008, INDIA
Most laboratory bubble columns are equipped with sieve plate spargers. The sieve plate spargers are known to lead to nonuniform gas distribution. It is important to account for such nonuniform gas distribution at the sparger in the computational model before experimental data collected from such columns are used to fit the model parameters. In this article, such an attempt is made. A detailed, 3D CFD model was developed to simulate unsteady gas-liquid flows in bubble columns with sieve plate spargers. The sensitivity of the nonuniformity of gas distribution at the sparger with sparger resistance was examined. The model predictions were compared with the experimental data. The developed model and presented results will be useful for simulating industrial bubble columns. Introduction Most of the computational fluid dynamics (CFD) simulations of bubble column reactors are based on the assumption that gas is uniformly distributed at the sparger. In most of these studies, the investigators manipulate values of lift and drag coefficients to obtain reasonable agreement between predicted overall gas hold-up and liquid circulation with experimental data (review by Joshi1 and references cited therein). The experimental data used to evaluate and fit these model parameters is usually obtained with a sieve plate sparger. The sieve plate spargers are known to lead to nonuniform gas distribution. Only a fraction of the total numbers of holes of such a sieve plate sparger are active at any instant and this leads to nonuniform distribution of gas. The active region of the sparger varies with time leading to complex unsteady flow. Typical dynamic flow behavior on the sparger plate for the air water system is shown in Figure 1. It is obvious that it is essential to capture nonuniform distribution of gas at the sparger for realistic simulations of gas-liquid flow in bubble columns. Such an attempt is made here.
acquired wall pressure fluctuations data was analyzed using an in-house software called AnTS (Utikar et al.2). A typical power spectrum obtained from acquired wall pressure fluctuations (part a of Figure 3), showed three major peaks at frequency ranges of 0.2-0.3 Hz, 3-5 Hz, and 18-25 Hz signifying bubble swarm oscillations, large bubble formation near sparger, and movement
Figure 1. Bubble swarms oscillating on the sparger plate at superficial gas velocity of 0.05 cm/s.
Experimental Section In this work, a bubble column (air-water system) of 0.2 m diameter and 2 m height with the uniform-hole sparger (hole diameter 1.2 mm and open area of 1.13%) was used. The dispersed height to diameter ratio of 5 was maintained with the superficial gas velocities ranging from 0.05-0.40 m/s. Various experimental techniques such as conductivity meter, dual-tip conductivity probe, and wall pressure fluctuations were used by wall mounting the sensors at various axial locations (as shown in Figure 2). The wall pressure fluctuations were measured using dynamic pressure transducers (PCB Piezotronics Inc., USA) located at different axial locations from the sparger. The pressure signal was sampled at the rate of 400 Hz for a period of 1400 s and low-pass filtered (cutoff frequency was set to 50 Hz). The * To whom correspondence should be addressed. Tel/Fax: +91-2064015548. E-mail:
[email protected]. † National Chemical Laboratory. ‡ Indian Institute of Technology. § Tridiagonal Solutions Pvt. Ltd.
Figure 2. Experimental setup.
10.1021/ie8018593 CCC: $40.75 2009 American Chemical Society Published on Web 05/08/2009
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Figure 3. Wall pressure fluctuations.
of smaller bubbles, respectively (experimental study made by Diaz et al.3). The obtained data was analyzed using a variety of methods to gain a better understanding of prevailing flow regimes. For example, the power associated with these peaks when plotted against superficial gas velocity showed that the power associated with a peak at 0.2-0.3 Hz reduces after 0.1 m/s. This may be interpreted as a reduction in coherent bubble plume oscillations and generation of more chaotic flow. The rate of variation of power associated with the peak at 18-25 Hz also changes after 0.1 m/s possibly due to the cluster formation of small bubbles (part b of Figure 3). The variation of the ratio of standard deviation to the mean of the pressure fluctuation series with respect to superficial gas velocity showed a change in slope at the superficial gas velocity of about 0.02 m/s denoting the transition flow regime (part c of Figure 3). The overall gas volume fraction was measured visually for all superficial gas velocities. The dispersed height in bubble column is measured by visual observation of the fluctuating
height (average of fluctuating boundary of the dispersed height). The dispersed height of the gas-liquid system is compared with the static liquid height to estimate the amount of gas dispersion in the bubble column. In all of the experiments, the dispersed height of gas-liquid system was kept the same so that the computational domain for the CFD model can be fixed the same for all gas velocities studied. Single-tip and dual-tip conductivity probes were used to measure the local time-averaged gas hold-up, axial bubble velocity, and bubble size distribution at two different axial locations. At each axial location, radial profiles at nine different locations along the column diameter were measured. The voidage fluctuation signal was acquired using a 5 kHz sampling frequency for 200 s. Details of the probe and the signal analysis can be found in Rampure et al.4 Conductivity cell was used for the measurement of the liquidphase mixing time. NaCl solution was used as the tracer. Time history of the conductivity signal was recorded immediately at
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the addition of tracer (35 mL of 1 M NaCl solution) until the homogeneity is attained.4 The signal showed large fluctuations ((20%) even after attaining homogeneity. This occurred due to the presence of a large number of bubbles dispersed in the liquid at higher gas velocities (>0.1m/s). Therefore, the mixing time definition was restricted to 75% homogeneity in this work, where the study was done for superficial gas velocities ranging form 0.05-0.4 m/s. All of the experimental measurements were conducted at least three times. The experimental database was used to evaluate the CFD model. CFD Model Extensive work has been done on developing CFD models to simulate gas-liquid flow in bubble columns.1,4-6 In most of these attempts, different drag correlations and lift coefficients have been used to obtain reasonable agreement with the experimental data. As gas superficial velocity increases, most of the simulations tend to overpredict gas hold-up. More often, this is interpreted as effective drag coefficient and is lower than that proposed in the correlations and usually further correction is introduced to the drag coefficient. For example, the drag coefficient is multiplied by the fourth power of the liquid volume fraction to mimic effective reduction of drag coefficient at higher superficial gas velocities. It is however important to point out that it is essential to understand the possible influence of nonuniformities at the sparger before such corrections are introduced. More often than not, sieve plate spargers are used in laboratory bubble columns. As mentioned in the introduction, sieve plate spargers lead to nonuniform sparging, which may significantly affect gas distribution and hold-up in the column. Despite the common visual observation on nonuniformities of gas at the sieve plate sparger, not many attempts have been made to include these in the CFD model. More than a decade ago, Ranade7 had attempted to account for nonuniform distribution of gas at the sparger. However, the model considered axissymmetric 2D flow in a bubble column and was a steady-state model. In this work, we have developed a comprehensive, 3D, unsteady CFD model to simulate gas-liquid flow in bubble columns after accounting for nonuniform distribution of gas at the sparger. CFD model was developed using the Eulerian approach for the two-phase system. The standard k-ε mixture turbulence model was used to incorporate the effect of turbulence. Many corrections are available in the literature to take into account the presence of the neighboring bubbles while estimating the drag coefficient. Ishii and Zuber’s8 correlation, which uses correction factor of εL2 (where εL is liquid holdup), was used to estimate the effective drag coefficient in this work. Both the plenum section and the sparger plate above were considered in the solution domain for the first time (Figure 4). The uniform gas velocity was set as the inlet to the bottom of the plenum section. The outlet boundary conditions were specified based on the assumption that bubbles escape the dispersion with bubble rise velocity. More details of the CFD model are discussed by Rampure et al.4 Sparger was modeled as a porous zone (resistance in flow is added through the source term). The source term comprising the viscous and the inertial resistance is given in eq 1. Si ) -
( Rµ V + C 21 F|V|V ) i
2
i
(1)
Figure 4. Computational domain.
The viscous resistance and the inertial resistance for the perforated plate were estimated using the correlation suggested by Smith and Van-Winkle.9 2 1 (Ap /Af) - 1 (2) t C2 It should be noted that the sparger model is a function of fractional open area. For shallow bubble columns and for noncoalescing liquids, hole diameter and pitch may also influence flow in bubble columns. However, for tall bubble columns with coalescing liquids like water, it is not necessary to include hole area and pitch in the sparger model. The sparger model was implemented in the commercial CFD code, FLUENT 6.3 (Ansys-Fluent Inc., USA) for carrying out simulations of gas-liquid flow in bubble columns. On the basis of preliminary numerical simulations with different grid sizes, 58 000 computational cells (including plenum section) were used for this study. Higher-order discretization scheme, QUICK, was used for the numerical solution of model equations (FLUENT 6.3 Documentation for more details on QUICK). Buwa and Ranade10 carried out flow visualization using CCD camera for gas velocity of 0.10 m/s in a rectangular bubble column. They report an average bubble size of 5 mm. Therefore, this value was used as the bubble size in all of the simulations discussed here. Simulations were carried out using the time step of 0.01 s until the unsteady flow was established. Time averaging was started after discarding the initial transients (quasi-steady state attained). The thickness of the plate used in the experiments was 2 mm. To reduce demands on the number of computational cells, it was decided to use a thicker sparger without changing the effective resistance of the sparger. Simulations were carried out to examine the effect of such pseudothick sparger over the range of 1-5 cm thickness. The value of the thickness was not found to have any significant impact on predicted results. Therefore, for all of the subsequent simulations a 1 cm thick porous region was used. The results are discussed in the following section.
C2 )
Results and Discussion Typical snapshots of the unsteady CFD simulations are shown in parts a and b of Figure 5. It can be seen that the results show significant unsteady motion and instantaneous flow is far from symmetric. This has already been established by various experimental and numerical studies. The gas-liquid flow in
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Figure 5. CFD simulations.
Figure 6. CFD results predicted for uniform and nonuniform gas distribution at the sparger.
bubble column was found to be inherently unsteady even if the gas is sparged uniformly at the sparger. The key difference in prior studies and the present one is that this is the first time where transient nonuniformity of gas distribution at the sparger is accounted for. The results clearly show that only a portion of sparger is active at any point of time and the active region of sparger varies with time. Details of this are discussed later in this section. Before discussing the nonuniform distribution at the sparger, it will be worthwhile to compare results predicted with uniform and nonuniform distribution at the sparger. Comparison of these results is shown in Figure 6. One of the key global parameter
of interest in bubble columns is overall gas hold-up. Various attempts have been made to match predicted results with the experimental data. Most of these attempts were focused on introducing corrections to drag coefficient. Ishii and Zuber8 have proposed a correction term as (1 - εG)p where p is equal to 2 (this value is conditional to bubble shape and a detailed discussion may be seen in Joshi et al.,11). Olmos et al.6 had carried out simulations with different values of p in the range of 1 to 4. They recommend higher values of p as superficial gas velocity increases. Recently Behzadi et al.12 have proposed a different empirical correction factor comprising of a combination of exponential and power law. However, it was observed
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Figure 7. Time-averaged gas hold-up.
that power law-type corrections proposed by Ishii and Zuber8 represent the observed trends fairly well. Following the recommendations of Olmos et al.,6 previously we have used corrections terms as εL2 for superficial gas velocities of 0.05, 0.10, and 0.20 m/s and as εL4 for higher superficial gas velocities of 0.40 m/s with uniform gas hold-up at the inlet.4 It was observed that the overall gas hold-up followed similar trend with the experimental data. The overall gas volume fraction predicted higher values compared to experimental data and also had convergence difficulties for the drag correction of εL2 while simulating for uniform sparger at Ug ) 0.4 m/s; hence correction of εL4 was used when uniform gas distribution was specified at the sparger. When nonuniform gas distribution was simulated by including plenum in the solution domain, it was found that it was not necessary to use the correction of εL4. In the present study of nonuniform sparger drag correction of εL2 was used for all gas velocities (including 0.4 m/s). The predicted results are shown
Figure 8. Time-averaged axial liquid velocity.
in parts a and b of Figure 6. Local time-averaged gas hold-up for nonuniform gas distribution at the sparger showed good agreement with the experimental data in comparison with uniform gas hold-up at gas inlet boundary, especially at a higher gas velocity of 0.40 m/s where the additional correction (εL4) to the drag coefficient was avoided (part b of Figure 6). It is also important to study the predictions of the CFD models with the plenum section on the local level. Therefore, the radial profiles of the time-averaged profiles of the gas hold-up, axial
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Figure 9. Time-averaged axial gas velocity.
velocities were compared with the experimental data. Figure 7 shows the radial profiles for time-averaged local gas hold-up for three different gas velocities (0.05, 0.10, and 0.20 m/s) and at two different axial locations (0.17 and 0.66 m). The profiles are compared with the time-averaged local gas hold-up measurements done using a single-tip conductivity probe. A large amount of gas moving from the center causes the downward movement of the bubble near the wall due to liquid circulations. This phenomenon is predicted resulting in higher values of the gas hold-up along the column axis. The results predicted by the CFD model with the plenum section showed good agreement with the experimental data as compared to those without the plenum section (i.e., uniform gas distribution at the sparger). The radial profiles of time-averaged axial liquid velocity obtained from the CFD simulations are shown in parts a-c of Figure 8. The CFD simulations showed good comparison with the experimental data of Sanyal et al.13 (using the CARPT technique) at superficial gas velocity of 0.10 m/s (part b of Figure 8). For a gas velocity of 0.40 m/s, a 25% difference at the center line was observed in the values of time-averaged axial velocity profile for the predictions done at two axial locations with plenum section, whereas the difference was less than 1% for the prediction without plenum section (part c of Figure 8). This may because use of the additional drag-correction (εL4) while simulating without the plenum section (uniform gas sparging). Time-averaged gas velocity profiles were also evaluated and compared with the experimental data. The measured and simulated radial profiles of time-averaged axial gas velocity are shown in Figure 9. CFD simulations showed good agreement with the mean bubble velocity measured using the dual-tip conductivity probe (parts a-d of Figure 9). The comparison for higher superficial gas velocity however showed noticeable
discrepancy (part d of Figure 9) in the experimental values. One of the reasons for this discrepancy may be the increased possibility of bubbles not cutting both of the probe tips at higher gas velocity during experiments. This poses a difficulty in finding the pair of signals arising from the same bubble. Therefore, only qualitative comparison can be made at higher gas velocity (parts c and d of Figure 9). After evaluating the model for the local phase properties, the influence of sparger resistance on predicted flow characteristics was numerically investigated. An almost uniform distribution of gas hold-up on the sparger plate was observed for lower gas velocity compared to that at higher gas velocity of 0.2 m/s. The dynamic nature for flow on the sparger was more predominant for higher gas velocity. An increase in sparger resistance (leading to more uniformity in gas distribution) for lower gas velocity leads to an increase in the predicted gas hold-up. A sample of predicted results for two different gas velocities (0.05 and 0.2 Table 1. Dynamic Gas Distribution on the Sparger
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Acknowledgment One of the authors (M.R.R.) is grateful to CSIR, New Delhi for providing research fellowship. Notations R ) permeability, m2 Af ) free area or the total area of holes, m2 Ap ) area of plate (solid and holes), m2 C ) coefficient based on Reynolds number through sparger hole (0.98 current work) C2 ) inertial resistance factor, 1/m Si ) source term for ith (x, y, or z) momentum equation T ) plate thickness, m
Literature Cited Figure 10. Effect of sparger resistance on liquid-phase mixing time.
m/s) and different sparger resistances is shown in Table 1. The instantaneous snapshots of the nonuniform gas hold-up on the sparger plate can be seen in Table 1. A comparative study of liquid-phase mixing time was done for different sparger resistances to capture dynamics of the flow influenced by sparger. Simulations of flow and mixing for different sparger resistances were carried out for gas velocity of 0.05 m/s. These results are shown in Figure 10. The increase in sparger resistance (C2 value of 4 × 108 1/m) leads to prediction of a more uniform distribution of gas at the sparger and therefore lowers local liquid velocities. This results in a longer mixing time compared to that predicted at the lower sparger resistance. This means the developed computational model is able to capture differences in flow characteristics of low-resistance sparger (like a sieve plate with a larger open area) and of highresistance sparger (like a sintered plate). Conclusions A CFD simulation of a bubble column reactor considering the plenum section was considered for the first time. Timeaveraged hydrodynamic properties such as gas hold-up, axial liquid/gas velocity showed good agreement with experimental data. Incorporation of nonuniform gas distribution at the sparger using the approach developed here avoids the need for introducing additional correction factors to the interphase drag coefficient. The approach, models, and results presented in this work will be useful for understanding the influence of the sparger on gas-liquid flow in bubble columns and will lead to morereliable CFD models and parameters for further work.
(1) Joshi, J. B. Computational flow modeling and design of bubble column reactors. Chem. Eng. Sci. 2001, 55, 5893. (2) Utikar, R. P.; Sunthakar, A. A.; Ranade, V. V. Characterizing unsteady fluid dynamics of bubble column using non-linear analysis of wall pressure fluctuations. Indian Chem. Eng. 2001, 43, 16. (3) Diaz, M.; Montes, F. J.; Galan, M. A. Experimental study of the transition between unsteady flow regimes in partially aerated two dimensional bubble column. Chem. Eng. Process. 2008, 47, 1867. (4) Rampure, M. R.; Kulkarni, A. A.; Ranade, V. V. Hydrodynamics of bubble column reactors at high gas velocity: Experiments and CFD simulations. Ind. Eng. Chem. Res. 2007, 46, 8431. (5) Ranade, V. V. Computational Flow Modeling for Chemical Reactor Engineering; Academic Press: London, 2002. (6) Olmos, E.; Gentric, C.; Midoux, N. Numerical description of flow regime transitions in bubble column reactors by a multiple gas phase model. Chem. Eng. Sci. 2003, 58, 2113. (7) Ranade, V. V. Numerical simulation of turbulent flow in bubble column reactors. AIChE symposium series No.293 1993, 89, 61. (8) Ishii, M.; Zuber, N. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE J. 1979, 25, 843. (9) Smith, P. L.; Van Winkle, M. Discharge coefficients through perforated plates at Reynolds number of 400 to 3000. AIChE J. 1958, 266. (10) Buwa, V. V.; Ranade, V. V. Dynamics of gas-liquid flow in rectangular bubble columns: Experiments and single/multi-group simulations. Chem. Eng. Sci. 2002, 57, 4715. (11) Joshi, J. B.; Veera, U. P.; Prasad, C. V.; Phanikumar, D. V.; Deshphande, N. S.; Thakre, S. S.; Thorat, B. N. Gas hold-up structure in bubble column reactors. Proceedings of Indian National Science Academy 1998, 64, 441. (12) Behzadi, A.; Issa, R. I.; Rusche, H. Modelling of dispersed bubble and droplet flow at high phase fractions. Chem. Eng. Sci. 2004, 59, 759. (13) Sanyal, J.; Sergio, V.; Roy, S.; Dudukovic, M. P. Numerical simulation of gas-liquid dynamics in cylindrical bubble column reactors. Chem. Eng. Sci. 1999, 54, 5071.
ReceiVed for reView December 3, 2008 ReVised manuscript receiVed April 6, 2009 Accepted April 7, 2009 IE8018593
