Laser Doppler Anemometer Measurements in Bubble Column: Effect

Nov 10, 2006 - Measurements of flow pattern in a 150 mm i.d. bubble column were carried out using a laser doppler anemometer (LDA) in a forward scatte...
1 downloads 0 Views 175KB Size
Download PDF
Ind. Eng. Chem. Res. 2006, 45, 9201-9207

9201

Laser Doppler Anemometer Measurements in Bubble Column: Effect of Sparger Manish R. Bhole, Swarnendu Roy, and Jyeshtharaj B. Joshi* Institute of Chemical Technology, UniVersity of Mumbai, Matunga, Mumbai 400 019, India

Measurements of flow pattern in a 150 mm i.d. bubble column were carried out using a laser doppler anemometer (LDA) in a forward scatter mode. A superficial gas velocity of 20 mm/s was used in all the experiments. Two different spargers (perforated plate and porous plate) were employed. The liquid flow starts developing from the sparger where non-uniformities in the gas sparging exist. From z/D g 2 (z ) axial location; D ) column diameter), the fully developed axial liquid velocity profiles are seen. The radial variation of mean axial velocity shows gross liquid circulation in the column. Circulation velocities are smaller for the bubble column with porous plate sparger mainly due to the fact that the mean bubble size is small and the gas distribution is relatively uniform over the column cross-section. The difference in the hydrodynamic behavior with two different spargers is also apparent from the profiles of the turbulent kinetic energy and Reynolds stress measured from the velocity-time series. Introduction Local measurements of flow pattern in bubble columns are important to understand their complex multiphase hydrodynamics. In bubble columns, gas phase is dispersed in liquid phase, and buoyancy-driven bubbly flow is obtained. For practical considerations, the net liquid throughput is generally very small or even absent. Depending upon the gas flow rate, details of gas sparging device, and bubble size, various flow regimes can be observed like homogeneous, transition, and heterogeneous regimes. The flow field and the rates of heat and mass transfer vary considerably depending upon the operating conditions in the column. Since the bubble columns are used extensively in chemical and allied industries, there is a great interest in understanding their hydrodynamics. In this regard, the detailed measurements of local flow field by flow visualization techniques are very important. Furthermore, there is a growing interest in numerical simulation of bubble columns using computational fluid dynamics (CFD). Important information regarding interface momentum transfer, turbulence closure, as well as the validation of simulation results is provided by experimental measurements. A variety of instrumentation is available for the measurement of two phase flows. For example, various investigators have used hot film anemometer (HFA), fiber optic probes, computeraided radioactive particle tracking (CARPT), laser doppler anemometer (LDA), particle image velocimeter (PIV), and ultrasound velocity profiler (UVP) to study the hydrodynamics of bubble columns. Each of these techniques has its distinct advantages as well as limitations. LDA offers noninvasive measurements of velocity at very high data rates; hence, it can be used to investigate not only the mean but also turbulence quantities associated with the flow field. Application of LDA in bubble columns is mainly restricted to the low gas holdup. Interruption of laser beams by bubbles become very significant, and the data acquisition rate is reduced considerably at higher gas holdup. Nonetheless, LDA has been successfully used at gas holdup as high as 25% by Mudde et al.1 In a typical bubble column operating in the transition or heterogeneous regime, the radial variation of mean axial velocity shows upflow in the central region of the column and downflow * To whom correspondence should be addressed. Phone: +91-2224 14 5616. Fax: +91-22-24 14 5614. E-mail: [email protected].

near the wall, most notably captured by Hills using a Pitot tube.2 A similar time-averaged circulation pattern using LDA has been obtained in refs 3-5. The dynamics of the flow field has also been studied by Mudde and Van den Akker6 and Kulkarni et al.7 using multiresolution analysis. The wavelet decomposition of velocity-time series in various scales has been carried out to identify the low-frequency structures related to circulation cells in the column. Kulkarni et al.5,8 have shown that it is possible to obtain liquid velocity, gas holdup, and bubble sizes from LDA measurements in bubble columns. Most of the work in the literature describes the LDA measurements at a fixed axial location in the column (in most of the cases, away from the sparger). Thus, only the radial variation of mean flow and turbulence variables are presented. The axial evolution of the flow pattern still remains to be investigated. Recently, Kulkarni et al.9 have presented comprehensive LDA measurements at various axial locations in the column (from sparger to gas disengagement zone) employing a multipoint and a single-point sparger. Their analysis shows that the radial variation of axial liquid velocity and the gas holdup are independent of spargers at z/D ≈ 4 where the flow is fully developed. The average gas holdup was the same (about 6%) with the two different spargers employed in their work. In this work, we have presented the development of flow profiles by employing two different spargers, a perforated plate (multipoint sparger) and a porous plate. However, the development of flow profiles in the two cases is distinctly different. This is basically due to different bubble sizes and the average gas holdup obtained in the two cases. At superficial gas velocity of 20 mm/s, the average gas holdup in the bubble column is about 5.5% with the perforated plate sparger and about 10% with the porous plate sparger. Visual observations indicate that the bubbles are considerably smaller with porous plate sparger and that they rise almost uniformly in the column as against the central turbulent plume of large bubbles obtained with the perforated plate sparger. These qualitative observations are also supported by the quantitative flow field information obtained using LDA. Although the bubble column operates in the transition regime and the bulk liquid circulation is present in both the cases, the hydrodynamics of bubble column with porous plate resembles more closely to the homogeneous regime. This is also apparent from the profiles of turbulent kinetic energy

10.1021/ie060745z CCC: $33.50 © 2006 American Chemical Society Published on Web 11/10/2006

9202

Ind. Eng. Chem. Res., Vol. 45, No. 26, 2006

Figure 1. Schematic of experimental setup: (1) 5 W Ar-ion laser, (2) bubble column, (3) photomultiplier tubes, (4) burst spectrum analyzer, (5) personal computer, (6) rotameter, and (7) compressor.

and the Reynolds stresses measured using LDA. Throughout the work, we have contrasted the hydrodynamics of the bubble columns with the perforated plate and the porous plate spargers.

Figure 2. Variation of average gas holdup with superficial gas velocity in the bubble column for the two gas spargers. (0) Porous plate sparger. (2) Perforated plate sparger.

Experimental Section An acrylic column of 150 mm diameter and 1 m height was employed as a bubble column. A schematic diagram for the experimental setup is shown in Figure 1. To avoid the laser beam distortion, the cylindrical column was enclosed by a square column, and the gap between the two is filled with water. An oil-free diaphragm compressor was used to sparge the air through the gas sparger. Air flow rate was monitored using a rotameter, which was precalibrated using a soap-film meter. Ordinary tap water was used as the liquid phase, and oil-free compressed air was used as the gas phase. The height of gasliquid dispersion was kept about 900 mm. The bubble column was mounted on a traverse, which allowed the accurate vertical movement so that the measurements at various axial locations in the column are possible. At a fixed axial location, the radial variation of the measurement volume was obtained by accurate movement of the laser-focusing front lens along a guided horizontal platform. The measurements were made from the center of the column up to the wall. Axisymmetry was ensured by circular symmetric sparger plate design and the perfect vertical orientation of the column. A slight departure from the vertical orientation leads to a considerable asymmetry in the flow profile. Thus, the issue of the column orientation is not trivial. In fact, in our measurements, we ensured axisymmetry by comparing the mean axial velocity at two points equidistant from the center (r ) 0). The average gas holdup in the column was measured by noting the height of liquid with and without gas dispersion. All the LDA measurements were carried out at superficial gas velocity of 20 mm/s. However, the average gas holdup was measured at various superficial gas velocities. Two different spargers were employed in this study. A multipoint sparger (perforated plate) with 2 mm hole diameter and having 25 holes was used. Another sparger was a porous plate (fine wire mesh with the pore opening about 40 µm). LDA setup consists of 5 W Ar-ion laser from Spectra Physics. To identify the flow direction, a frequency shift of 40 MHz is given to one laser beam. All the optics are from Dantec Dynamics and include the cover and retarder plates (to adjust the beam polarization), beam splitters, Bragg cell, beam expander, and 1200 mm front lens for focusing. The measurement volume is formed by three mutually perpendicular laser beams, viz., blue (λ ) 488 nm), green (λ ) 514.5 nm), and

Figure 3. Typical velocity-time series in the bubble column with perforated plate sparger obtained from LDA at z/D ) 4 and r/R ) 0.

cyan (combination of blue and green) beams. The scattered laser light from the measurement volume is captured by photomultiplier tubes in a forward scatter mode. The simultaneous measurements of two orthogonal velocity components were made. Since the tap water naturally contains seeding for the scattering of light, the flow was not artificially seeded. Data validation and signal processing (online fast Fourier transform) were performed by the burst spectrum analyzer (62N40 BSA, F60 processor) from Dantec Dynamics, which consists of two velocity channels. The entire operation of data acquisition including the high voltage to photomultiplier tubes and the record length selection for the burst detection were controlled by a personal computer using BSA Flow software version 4.0. To maximize the data rate, the photomultiplier tube is placed almost collinear with the front lens and measurement volume. This is because the intensity of scattered laser light (in the forward scatter mode) is highest at the receiving angle of 0°. Data acquisition in bubbly flows is relatively difficult compared to the single phase flows. Laser beams are blocked by bubbles rising through their path; hence, the data rate gets reduced substantially. Various modes of bubble-beam interactions are elucidated by Kulkarni et al.5 In the center of the column, the lowest data rate is observed. This is mainly due to the fact that the laser beams have to travel a larger distance through the bubbly fluid and the frequency of beam interruption by the bubbles increases. Furthermore, the gas holdup is also higher in the center of a typical bubble column. Bubbles also pose an important difficulty due to multiple reflections of the laser light from their surfaces. In our work, we have obtained the data rate as high as 1000 Hz near the wall and about 100 Hz at the

Ind. Eng. Chem. Res., Vol. 45, No. 26, 2006 9203

high, and the photomultiplier anode current must not exceed a certain value in order to keep the noise level in the acquired data to a minimum level. Although, the mean velocities may not get affected, the RMS velocities increase considerably if the data validation is poor and/or photomultiplier anode current is high. Thus, a judicious optimization between the data rate, data validity and photomultiplier anode current must be carried out to obtain a good signal from the LDA. In this work, we have maintained the data validity of more than 90%. Typically, the data acquisition at a particular location is carried out for a period of 300 s to ensure that the mean velocity is not affected by the total measurement time. LDA measurements were carried out at four axial locations in the column (viz., z/D ) 1, 2, 3, and 4). At each axial location, the measurements were made from the center up to the wall with 5 mm gap between the successive points. Due to extreme curvature effects, the LDA measurements very close to the wall are not possible. In our column of 150 mm diameter, the measurement point closest to the wall is about 3-4 mm away from the wall. This corresponds to the dimensionless radial distance (r/R) of about 0.95. Results and Discussion

Figure 4. Histogram of axial velocity obtained from LDA at r/R ) 0 and z/D ) 4. (A) Perforated plate sparger. (B) Porous plate sparger.

center. To study the turbulence quantities such as power spectra and Reynolds shear stresses, a higher data rate is preferable. However, it must be noted that the data validity must also be

Average Gas Holdup. Before presenting the detailed LDA measurements, it is instructive to study the variation of the average gas holdup (∈ j G) with the superficial gas velocity (VG) as shown in the Figure 2. At VG ) 20 mm/s, the gas holdup with the porous plate sparger is almost double that of the perforated plate sparger. The porous plate produces small bubbles that travel relatively slowly in the column. Thus the gas holdup is higher in this case. The lines in the Figure 2 are shown to indicate the trends in the gas holdup curve. The ∈ jG VG relationship for the bubble column has been proposed by Joshi et al.10 as follows:

∈ j G ∼ V nG

(1)

Figure 5. Radial variation of axial liquid velocity in the bubble column: (A) z/D ) 1, (B) z/D ) 2, (C) z/D ) 3, (D) z/D ) 4. (0) Porous plate sparger. (2) Perforated plate sparger.

9204

Ind. Eng. Chem. Res., Vol. 45, No. 26, 2006

Figure 6. Variation of centerline axial liquid velocity in the bubble column. (0) Porous plate sparger. (2) Perforated plate sparger.

The value of n signifies the regime prevailing in the bubble column. For the homogeneous regime, n is greater than or equal to 1 whereas for the heterogeneous regime it lies in the range of 0.4-0.8. For the transition regime, the value of n continuously decreases from a higher value corresponding to the homogeneous regime to a lower value corresponding to the heterogeneous regime. In case of bubble column with porous plate sparger, the value of n was found to be 1.6 in the range of VG ) 5-15 mm/s and about 1 above this range, which signifies that the regime of operation is changing from the homogeneous to the transition with the increase in the superficial gas velocity. In contrast, the bubble column with perforated plate sparger operates in the transition regime (n ) 0.9) for the entire range of superficial gas velocity considered. Velocity-Time Series. Typical velocity-time series at z/D ) 4 and r/R ) 0 for the perforated plate sparger is shown in Figure 3. Large time gaps between the data points are apparent. These time gaps generally correspond to the beam interruption by bubbles. Furthermore, the arrival times of seeding particle in the measurement volume are random and are described by Poisson distribution.11 Velocity-time series is essentially unequispaced.

Velocity Histogram. The histograms of the instantaneous axial velocity in the bubble column at r/R ) 0 and z/D ) 4 for both spargers are shown in Figure 4. The spread in the instantaneous velocities is wider with perforated plate sparger. This also manifests itself in the higher turbulent kinetic energy as seen later. In bubble columns, the turbulence is due to liquidphase motion (shear-induced turbulence) as well as bubble wakes (bubble-induced turbulence). Due to buoyancy, the bubbles travel faster than the local liquid. If the motion in the bulk liquid and that in the bubble wakes have different velocity scales, they would manifest themselves in the velocity histogram and the two distinct peaks would be observed. However, the unimodal distribution is seen with the experiments indicating that there is a considerable overlap between the velocity scales of the bulk liquid and the bubble wakes. Axial Velocity. The radial variation of the mean axial liquid velocity (uj) at various axial locations in the column is shown in Figure 5. Typical upflow in the central region and the downflow near the wall region is well-captured by LDA. The location of zero mean axial velocity point is close to r/R ) 0.7 as observed in the literature.2-5 The liquid-phase mass balance requires that the net throughput of the liquid over the crosssection of the column must be zero at any axial location. This constraint can be written as follows:

∫oR 2πr ∈Luj dr ) 0

(2)

Equation 2 has been amply verified for all the experimental data of mean axial velocity in the column. It assumes axisymmetry and any substantial deviation of the net liquid flow from the zero indicates the lack of axisymmetry. The profiles of mean axial velocity are seen to be well-defined for z/D ) 2, 3, and 4. However at z/D ) 1, the time-dependent non-uniformities in the gas sparging creates bubble plume oscillations; hence, the profiles are not well-defined. Thus, the constraint given by eq 2 is difficult to verify in the sparger zone. The axial velocity profile is seen to be developed (independent of z/D) at z/D ∼ 2 itself for the case of perforated plate sparger. This is evident

Figure 7. Radial variation of the turbulent kinetic energy in the bubble column: (A) z/D ) 1, (B) z/D ) 2, (C) z/D ) 3, (D) z/D ) 4. (0) Porous plate sparger. (2) Perforated plate sparger.

Ind. Eng. Chem. Res., Vol. 45, No. 26, 2006 9205

Figure 8. Radial variation of the Reynolds stresses in the bubble column with perforated plate sparger at z/D ) 4. ([) Axial normal stress (u′u′). (×) Radial normal stress (V′V′). (2) Axial-radial shear stress (u′V′).

from the axial profile of centerline axial liquid velocity shown in Figure 6. For the porous plate sparger, the distinct region of flow development from the sparger cannot be seen. The fully developed profiles indicate that the centerline velocities are more than double with perforated plate sparger as compared to the porous plate sparger. The circulation is suppressed in case of porous plate sparger due to presence of small bubbles and the relative radial uniformity of the gas distribution as well as bubble sizes and bubble velocities. Turbulent Kinetic Energy. The extent of fluctuating (eddy) motion is characterized by the turbulent kinetic energy and is defined as follows:

k)

1

N

∑

N i)1

[

]

(u′i)2 + (V′i)2 + (w′i)2 2

(3)

Figure 7 shows the turbulent kinetic energy profile in the

column. Like, the mean axial velocity, the turbulent kinetic energy profile is also seen to be well-defined away from the sparger (z/D g 2). Furthermore, the turbulent kinetic energy is higher in case of bubble column with the perforated plate sparger (except z/D ) 1), indicating the high level of turbulence in this case. The profiles of turbulent kinetic energy do not show any peak near the wall as generally observed in case of turbulent pipe flows.12,13 In our work, the access to the near wall region was limited up to r/R ≈ 0.95 due to extreme curvature effects. However, the experimental observations from the literature also indicate that the turbulent kinetic energy does not show any peak near the wall.9,14 Obviously, the pipe flow and bubble column are two different hydrodynamic systems. The sharp velocity gradients due to no-slip boundary condition near the wall are responsible for the generation of turbulence in case of pipe flows. The presence of bubbles creates a large number of points of no-slip everywhere in the column; hence, the turbulent kinetic energy production occurs relatively uniform in the column. For bubble column with perforated plate sparger, the turbulent kinetic energy is lower at z/D ) 1 whereas the reverse is true for the porous plate sparger. For both the spargers, the nonuniformity in gas distribution exists near the sparger region. However there is an important difference in the two cases. In case of perforated plate sparger, the flow develops heterogeneity beyond z/D ) 1, which causes an increase in turbulent kinetic energy. Whereas in case of porous plate sparger, the nonuniformity of flow decays with an increase in z/D and the flow tends to become more homogeneous, which causes a reduction in turbulent kinetic energy beyond z/D ) 1. Reynolds Stresses. Reynolds stresses are important to characterize the turbulence in the bubble column. The normal Reynolds stresses (u′2, V′2, w′2) contribute to the turbulent kinetic energy. The axial-radial Reynolds shear stress (u′V′) is responsible for maintaining the circulation in the bubble column. The calculation of Reynolds shear stress requires coincident LDA data of two velocity components. It is possible to acquire

Figure 9. Radial variation of Reynolds shear stress (u′V′) in the bubble column: (A) z/D ) 1, (B) z/D ) 2, (C) z/D ) 3, (D) z/D ) 4. (0) Porous plate sparger. (2) Perforated plate sparger.

9206

Ind. Eng. Chem. Res., Vol. 45, No. 26, 2006

Figure 10. Radial variation of gas holdup in the bubble column: (A) z/D ) 1, (B) z/D ) 2, (C) z/D ) 3, (D) z/D ) 4. (0) Porous plate sparger. (2) Perforated plate sparger.

the coincident LDA data directly from the measurement volume based on the hardware coincidence. In our experiments, we have found that a reasonable data rate is obtained with hardware coincidence. But the data validity is low (below 70%); hence, the software coincidence was selected to obtain the coincident LDA data. In this case, velocity-time data is obtained simultaneously but independently in the two channels, and the velocity points in the two channels for which arrival time difference is smaller than a certain threshold (called record interval window) are selected as coincident points for the calculation of crossmoments. The recommended value of record length window is the measurement volume diameter divided by the maximum velocity expected in the flow.15 A smaller value of the record interval window is preferable to capture truly coincident data points. However, very small values can lead to statistically insufficient sample size for the calculation of cross-moments. In our experiments, the record interval window of 200 ms was found to be satisfactory. Axial-radial Reynolds shear stress is calculated from the coincident data as follows:

u′V′ )

1

N

∑ (ui - uj)(Vi - Vj)

N i)1

(4)

Reynolds normal and shear stresses at z/D ) 4 for the perforated plate sparger are shown in Figure 8. It can be seen that the normal stresses are much higher than the shear stresses as also observed by Lee et al.16 and Kulkarni et al.9 However, the axial-radial Reynolds shear stress (u′V′) is important to generate the liquid circulation in the column.17,18 Hence, we have given the radial profiles for the same in Figure 9. For the porous plate sparger, Reynolds shear stress is typically much small (except near the sparger), indicating that the circulation is not as strong as in case of perforated plate sparger. Gas Holdup and Mean Bubble Size Profiles. LDA has been successfully used to measure the gas holdup profile in bubble columns.5 The basic idea is to identify the events in the time

Figure 11. Radial variation of the mean bubble size in the bubble column at z/D ) 4. (0) Porous plate sparger. (2) Perforated plate sparger.

series that mark the bubble passage through the measurement volume. Multi-resolution analysis can be used to study the local intermittency in the wavelet spectrum of velocity-time series. Based on the threshold of local intermittency index and the arrival time gap criterion, the local gas holdup can be estimated; hence, the radial gas holdup profile can be obtained as shown in Figure 10. The details of the methodology can be found in Kulkarni et al.5 The values of the gas holdup are obviously higher in the case of porous plate sparger. Further, due to nonuniformities in the gas sparging for the porous plate sparger, the holdup profile is still developing at z/D ) 1 and 2 and is steep. On the other hand, at higher z/D ) 3 and 4, the flow tends to be homogeneous, which results in a relatively uniform holdup profile. The bubble size distribution can be obtained from the chord length distribution measured by LDA. The bubble events identified using multi-resolution analysis also give an idea of

Ind. Eng. Chem. Res., Vol. 45, No. 26, 2006 9207

slip velocity distribution in the column from which an estimate of bubble size distribution can be obtained using appropriate rise velocity correlation. The two techniques have been compared by Kulkarni et al.8 In our work, we have followed the later approach to obtain an idea of bubble sizes in the column. Figure 11 shows an estimate of the average bubble diameter at various radial locations in the column at z/D ) 4. Clearly, the bubble sizes are smaller in the case of porous plate sparger. Conclusion The hydrodynamics of bubble column with two different gas spargers was studied using LDA. The porous plate sparger and the perforated plate sparger showed different hydrodynamics. With the porous plate sparger, smaller bubbles and higher gas holdup were obtained. The gas holdup profile was relatively uniform at z/D ) 3 and 4. The liquid circulation in the column was small. On the other hand, with the perforated plate sparger, a relatively higher bubble size and low gas holdup were obtained. A central plume of large-sized bubbles was seen to create turbulent motion in the column with well-defined liquid circulation patterns. All these observations are captured by quantitative measurements using LDA. The radial profiles of mean axial velocity, turbulent kinetic energy, and the Reynolds shear stresses in the two cases are distinctly different. For both spargers, at z/D ) 1 and 2, the time-dependent non-uniformities of the gas distribution create chaotic flow. Bubble plume oscillations are seen. Thus, the well-defined profiles of mean velocity and turbulence variables such Reynolds stress and turbulent kinetic energy cannot be obtained near the sparger. However, the flow gets quickly developed at about z/D ) 2. The work essentially highlights the ability of LDA to capture the hydrodynamics of bubble columns. Nomenclature D ) diameter of bubble column (m) k ) turbulent kinetic energy of liquid phase (m2/s2) N ) number of data points in velocity-time series (-) r ) radial location in the column (m) R ) radius of the bubble column (m) u, uj, u′ ) instantaneous, mean, and fluctuating axial liquid velocities (m/s) V, Vj, V′ ) instantaneous, mean, and fluctuating radial liquid velocities (m/s) w, w j , w′ ) instantaneous, mean, and fluctuating tangential liquid velocities (m/s) VG ) superficial gas velocity (m/s) z ) axial location in the column with respect to the sparger (m)

Greek Symbols ∈G ) gas holdup at a location in the column (-) ∈ j G ) average gas holdup for the whole column (-) ∈L ) liquid holdup at a location in the column (-) Literature Cited (1) Mudde, R. F.; Groen, J. S.; Van den Akker, H. E. A. Application of LDA to bubbly flows. Nucl. Eng. Des. 1998, 184, 329. (2) Hills, J. H. Radial nonuniformity of velocity and voidage in a bubble column. Trans. Inst. Chem. Eng. 1974, 52, 1. (3) Mudde, R. F.; Groen, J. S.; Van den Akker, H. E. A. Liquid velocity field in a bubble column: LDA experiments. Chem. Eng. Sci. 1997, 52, 4217. (4) Vial, Ch.; Laine, R.; Poncin, S.; Midoux, N.; Wild, G. Influence of gas distribution and regime transitions on liquid velocity and turbulence in a 3-D bubble column. Chem. Eng. Sci. 2001, 56, 1085. (5) Kulkarni, A. A.; Joshi, J. B.; Ravi Kumar, V.; Kulkarni, B. D. Application of multiresolution analysis for simultaneous measurement of gas and liquid velocities and fractional gas hold-up in bubble column using LDA. Chem. Eng. Sci. 2001, 56, 5037. (6) Mudde, R. F.; Van den Akker, H. E. A. Dynamic behavior of the flow field of a bubble column at low to moderate gas fractions, Chem. Eng. Sci. 1999, 54, 4921. (7) Kulkarni, A. A.; Joshi, J. B.; Ravi Kumar, V.; Kulkarni, B. D. Wavelet transform of velocity-time data for the analysis of turbulent structures in a bubble column. Chem. Eng. Sci. 2001, 56, 5305. (8) Kulkarni, A. A.; Joshi, J. B.; Ramkrishna, D. Determination of bubble size distributions in bubble columns using LDA. AIChE J. 2004, 58, 3068. (9) Kulkarni, A. A.; Ekambara, K.; Joshi, J. B. On the development of flow pattern in a bubble column reactor: experiments and CFD. Chem. Eng. Sci. In press. (10) Joshi, J. B.; U. Parasu Veera; Prasad, Ch. V.; Phanikumar, D. V.; Deshpande, N. S.; Thakare, S. S.; Thorat, B. N. Gas hold-up structure in bubble column reactors. Proc. Indian Natl. Sci. Acad. 1998, 64A (4), 441. (11) Adrian, R. J.; Yao, C. S. Power spectra of fluid velocities measured by laser Doppler anemometry. Exp. Fluids 1987, 5, 17. (12) Hrenya, C. M.; Bolio, E. J.; Chakrabarti, D.; Sinclair J. L. Comparison of low Reynolds number k- turbulence models in predicting fully developed pipe flow. Chem. Eng. Sci. 1995, 50, 1923. (13) Thakre, S. S.; Joshi, J. B. Momentum, mass and heat transfer in single phase turbulent flow. ReV. Chem. Eng. 2001, 18, 83. (14) Olmos, E.; Gentric, C.; Midoux, N. Numerical description of flow regime transition in bubble column reactors by a multiple gas-phase model. Chem. Eng. Sci. 2003, 58, 2113. (15) Dantec Dynamics. BSA Flow software Version 4, Installation & User’s Guide; 2005. (16) Lee, D. J.; McLain, B. K.; Cui, Z.; Fan, L. S. Pressure effect on the flow field and the Reynolds stresses in a bubble column. Ind. Eng. Chem. Res. 2001, 40, 1442. (17) Burns, L. F.; Rice, R. G. Circulation in bubble columns. AIChE J. 1997, 43, 1390. (18) Liu, H.; Zhang, Z.; Qiu, C. Buoyancy-driven circulation in bubble columns: Alternative analysis. AIChE J. 1998, 44, 2561.

ReceiVed for reView June 12, 2006 ReVised manuscript receiVed August 30, 2006 Accepted September 28, 2006 IE060745Z