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Ind. Eng. Chem. Res. 2009, 48, 330–340
Analysis of Hydrodynamics and Microstructure in a Bubble Column by Planar Shadow Image Velocimetry M. Sommerfeld* and D. Bro¨der† Mechanische Verfahrenstechnik, Zentrum fu¨r Ingenieurwissenschaften, Martin-Luther-UniVersita¨t Halle-Wittenberg, D-06099 Halle, Saale, Germany
The hydrodynamics and bubble behavior in a laboratory-scale bubble column (diameter 140 mm) was analyzed using planar shadow image velocimetry. Different air flow rates were considered by using capillary aerators with different capillary diameter. This implies that a gas hold-up between 1 and 5% and a bubble number mean diameter between about 2 and 4 mm was realized. The imaging system consists of a background illumination utilizing a LED-array and a single CCD-camera which records simultaneously bubble and tracer images. The demarcation of the thickness of the imaging plane was realized by using a macrolens adjusted to small depth of field. To discard out-of-focus images of bubbles and tracer particles and to discriminate between both phases different gradient filters were applied. A Sobel filter was used to evaluate the bubble contours in order to obtain the area equivalent diameter, the eccentricity, and the bubble orientation. The velocity fields of both phases and horizontal profiles along the bubble column were determined by applying PTV (particle tracking velocimetry) for the bubbles and PIV (particle imaging velocimetry) for the tracer particles. For both phases axial and radial mean velocities as well as their fluctuating components were determined by averaging a sufficient number of double images. From these results also cross-sectional averages and global averages of turbulent kinetic energy and fluctuation energy of the bubbles were determined. It was found that the bubble fluctuation in the radial direction was higher than in the axial one for bubble sizes in the range between about 2.0 and 3.8 mm which is a result of the zigzag or helical motion of the bubbles. Finally also the bubble behavior was further analyzed by determining bubble eccentricity and orientation of the bubbles in the flow. These data are especially useful for modeling bubble oscillation and tumbling motion. 1. Introduction Bubbly flows are found in a number of different types of reactors as very effective liquid-gas contacting devices. A bubble column is probably the most used apparatus to yield an efficient mixing between liquid and gas. In this configuration no net liquid flow is existent and the liquid motion is solely driven by the buoyancy of bubbles which are created at the bottom of the column. Hence, the flow structure developing in a column largely depends on gas flow rate, bubble size, and aerator design. The size of the bubbles in the column is determined by the formation process at the aerator and microscale phenomena such as bubble coalescence and break-up. The gas hold-up in the column is regulated by gas flow rate and bubble size (i.e., aerator design). For its technical importance bubble columns have been experimentally studied and analyzed for many decades with regard to the hydrodynamics developing in dependence of the operational conditions. In the early years the steady-state large-scale circulation pattern developing in the column was of major concern (see Mudde1 for a review of this work), and the development of appropriate mixing models based on this steady-state structure was attempted.2 However, in bubble columns the flow is highly unsteady involving a range of different vortical structures and scales as well as a meandering centrally rising bubble plume.3,4 After sufficiently long time averaging, however, the large scale circulation pattern with a down-flow of liquid near the wall and an up-flow in the core region becomes visible. This time-averaged flow field might nevertheless be asymmetric due to small disturbances in the aeration.5 Moreover, the flow structure in a bubble column may * To whom correspondence should be addressed. E-mail:
[email protected]. † Former doctorate student at the institute.
be separated in a homogeneous and heterogeneous regime which strongly depends on the gas flow rate, the bubble size, and hence on the average void fraction established.6 Mainly the transverse lift force and bubble coalescence are responsible for this transition. Small bubbles (smaller than about 5.5 mm for an air-water system) migrate toward the wall, while larger ones will migrate toward the core and coalesce with other bubbles owing to the higher local void fraction. Therefore, larger bubbles will be formed, rising faster in the core of the column. As a conclusion, the flow structure in a bubble column is strongly affected by the microscale phenomena associated with the bubble behavior, as for example transverse lift forces, bubble oscillation, and tumbling motion as well as coalescence and break-up. The methods to be used for an experimental analysis of such highly complex and unsteady flows strongly depend on the realized gas hold-up and the desired spatial resolution of the flow. A detailed review of available measurement techniques for bubbly flows was provided by Boyer et al.7 Experimental studies at high gas volume fraction can only be performed using tomographic methods or intrusive probes, such as optical needle probes, hot film anemometry or electro-diffusion probes. Although these techniques can provide information on velocities, bubble size, and gas volume fraction, their accuracy is rather limited and they locally disturb the flow. Optical nonintrusive measurement techniques are applicable only to rather low gas volume fractions (i.e., roughly up to about 10% for a laboratory scale facility with a diameter of about 150 mm). The information which can be extracted from these measurements depends on the technique applied. Laser-Doppleranemometry can provide velocities of both phases, but is faced with the problem of discriminating between the signal information from tracer particles and bubbles.8,9 This method has
10.1021/ie800838u CCC: $40.75 2009 American Chemical Society Published on Web 12/31/2009
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however the advantage of providing details on the temporal variation of especially the liquid velocity in a bubble column.9 Phase-Doppler-anemometry can additionally provide local bubble size distributions, but is restricted to spherical bubbles only which have a diameter of less than about 1.2 mm for an air-water system.10 Moreover, imaging techniques have been applied for studying the hydrodynamics in bubble columns. Older applications are limited to the visualization of the flow structure in bubble columns.11 By using a light sheet illumination combined with a CCD-camera for image recording and applying PIV (particle image velocimetry) or PTV (particle tracking velocimetry) methods, it is also possible to determine instantaneous velocity fields of both phases. Averaging a sufficiently large number of double images additionally mean velocity profiles can be determined. Pioneering work in applying PIV for measurements in bubble columns has been carried out in the group of L.-S. Fan (see for example refs 3, 4, and 12). In these studies the discrimination between the phases (i.e., tracer particles and bubbles) was simply done on the basis of their images size, which is not the most accurate way. Axial liquid phase velocity profiles throughout a two-dimensional bubble column have been presented by Lin et al.4 for different superficial gas velocities. For reliable measurements of velocity fields of both phases (i.e., liquid and bubbles) an appropriate discrimination between the phases is essential. The most elegant way to realize this is to employ fluorescing tracer particles whereby the scattered light includes two wavelengths, namely the illumination wavelength scattered by the bubbles and the fluorescent wavelength coming from the tracer particles. Applying now two CCD-cameras with appropriate optical band-pass filters, separate double images for bubbles and tracer particles are recorded (for details see for example ref 5). In this study a laboratory bubble column (diameter 140 mm) aerated by rather small bubbles (mean diameter about 2.0 mm) was considered. One objective of this work was in finding the limitations of the imaging technique with regard to the local gas volume fraction. It was shown that bubble velocities could be measured up to a void fraction of about 16%. However, reliable liquid phase velocity measurements were only possible to about 5% void fraction in order to ensure a sufficiently high data rate. This is associated with the growing light absorption by the bubbles for increasing gas volume fractions. Nevertheless, the PLV (pulse light velocimetry) allowed obtaining velocity fields of both phases throughout the entire bubble column for lower gas hold-up. In addition the distribution of the continuous phase turbulent kinetic energy was determined. These results were also used for validating numerical computations by applying the Euler/Lagrange approach.13 In the following section a selection of detailed measurements in bubble columns (i.e., which might be useful for validating numerical predictions) applying different instrumentation are summarized. A series of detailed measurements in a bubble column with a diameter of 290 mm were performed by Yao et al.14 using different probing techniques. The liquid velocity and its fluctuations were measured using a hot-film anemometer, the ultrasonic Doppler technique was employed for measuring two components of the bubble velocity (including mean and fluctuating components) and a five-point conductivity probe was used for obtaining bubble size and their rise velocity. The measurements were performed at different cross-sections above the aerator with the superficial gas velocity as a parameter, so that the gas hold-up was in the range between 10 and 20%. For low gas hold-up it was observed that the radial component of
the bubble fluctuation was higher than the axial one. With increasing gas hold-up, however, the bubble fluctuation became more isotropic. The axial component of the liquid velocity fluctuation was found to be remarkably higher than that of the bubbles, especially for the cases with higher gas hold-up. Degaleeson et al.15 measured the liquid phase velocity fields in bubble columns of different diameter (i.e., between 14 and 44 mm) using computer-automated radioactive particle tracking (CARPT). The superficial gas velocity was in the range between 2 and 12 cm/s yielding an averaged gas hold-up of 5 to 25%. The CARPT is rather time-consuming and provides only timeaveraged liquid phase velocities and associated Reynoldsstresses. This is realized by ensemble averaging of the velocities of the radioactive tracer particle for a long time. The presented horizontal profiles include the liquid vertical mean velocity and the different components of the Reynolds-stresses. A bubble column of square cross-section with a central aeration at the column bottom was considered by Deen et al.16 The velocity fields of both phases were determined by a planar PIV system. The discrimination between the phases was realized by using fluorescing tracer particles in connection with two CCD cameras being equipped with appropriate optical band-pass filters as described above. Profiles of axial and radial velocities of both phases at a single height in the column are presented, including mean values and mean fluctuations. The bubble size was found to be around 4 mm. The profiles of the mean velocity fluctuations of the bubbles show rather strong fluctuations indicating that the measurement time was still too short. In these studies, the bubble axial velocity fluctuation was found to be slightly higher than the radial component. The liquid velocity field in a 150 mm diameter bubble column was measured by Kulkarni et al.17 using an LDA system with extended signal processing to remove the signal information from the bubbles. Profiles at various distances above the aerator are presented for axial and tangential liquid mean velocity as well as for turbulent kinetic energy and turbulent eddy viscosity. The velocities of the bubbles could not be measured with the LDA system applied. In extension of the previous study5 where only the velocities of both phases could be measured, also local properties of the bubbles, such as bubble size, bubble shape, and bubble orientation was of interest in the present study. For this purpose, high resolution planar shadow image velocimetry was developed18 and applied to study bubble-column hydrodynamics. In the following section the test facility and the instrumentation will be described. Then a brief summary of the image acquisition and evaluation, including bubble detection and velocity measurements for bubbles and tracer particles, will be given. The results first concentrate on the global flow structure in the bubble column and in a second section the microstructure in a bubble swarm will be discussed. 2. Experiments 2.1. Test Facilities. The bubble column used in the present investigations is made of Plexiglas and has a diameter of 140 mm. The height of the water level in the column was 0.65 m (Figure 1). All experiments were conducted with water obtained from a reverse osmosis purification system. To reduce bubble coalescence effects propanol was added to the water at a volume concentration of about 0.004% in most of the experiments. For reducing refraction effects at the curved column wall, the bubble column was placed in a square vessel made of Plexiglas which was also filled with tap water (see Figure 1). The aerator consisted of 50 capillaries with an inner diameter of 0.4 or 0.6
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Figure 1. Bubble column with imaging system and data acquisition: column diameter, 140 mm; liquid level, 650 mm.
mm, respectively. The circular aeration area had a diameter of 100 mm. Hence, the aeration area is 51% of the bubble column cross-sectional area. The aerator was connected via a flow meter to a pressurized air supply system. The gas flow rate was varied by increasing the supply pressure to the stagnation chamber. Hence, measurements were performed for different average void fractions up to about 5%. Furthermore, different rather narrow bubble size spectra in the range between 1.0 and 5.0 mm were realized with the different capillary diameters and gas flow rates. A typical image of the bubble distribution in the column is shown in Figure 1, which was obtained by regular photography. The imaging system, namely a CCD-camera and a pulsed LED array as light source were mounted on CNC traversing systems allowing for fully automated measurements at all desired locations inside the bubble column (see Figure 1). All components of the measurement system and the CNC traverse system were controlled by the image processing PC (Intel Pentium III 700 MHz) to allow fully automated online measurements for both phases in the bubbly flow (nowadays of course faster PCs are available whereby the image processing time would be considerably reduced). The synchronization of the CCD-camera and the pulsed LED-array, as well as the pulse duration and the time delay between the pulses was performed by a timer card, which was also installed in the image processing PC. 2.2. Image Acquisition. The images of the two-phase flow were collected by a double shutter CCD-camera (type: PCO SensiCam) which allowed the acquisition of two successive images with a resolution of 1280 by 1024 pixel within a predefined time delay. The images were exposed by a background illumination using a pulsed LED-array consisting of 551 high performance LEDs with a total area of 160 mm × 100
mm. In front of the LED-array an opaque plate was installed in order to produce a diffuse illumination. The typical duration of the light pulses was 50-70 µs, while the time delay between the two successive images was adjusted to the local flow velocity in a range from 1 to 3 ms. The images were transferred in a digital way from the CCD-camera to the controlling and image processing PC.18 The online evaluation of the images and all controlling tasks were performed by an in-house developed software written in Delphi. By using the MMX (multimedia-extension) technology of the PC an online evaluation of the raw images was possible yielding liquid and bubble velocity fields as well as the bubble properties thereby avoiding the storage of a huge amount of raw data. Especially in the present application where the bubbly flow field in the entire test facility should be analyzed, fully automatic, high resolution (i.e., by resolving the bubbles) online processing is essential. For offline processing, data storage of more than 500 GB would have been necessary, and this was not available at the time of the studies. In a first image processing step the images were transformed from the camera’s 12 bit format to an 8 bit format gray value image. This step involves an automatic optimization of the contrast and a normalization of the gray scale values. The histogram of the gray values of each image was analyzed, and from this histogram a contrast optimized lookup table for the transformation was created. A perspective projection method based on a linear transformation was applied to all images collected in order to remove any distortion and to correct the magnification. The required coefficient matrix was determined by collecting an image of a defined regular grid placed at the measurement location. To allow measurements of the liquid velocity fields the flow was seeded with narrow sized polyamide tracer particles with a mean diameter of about 65 µm and a material density of 1050 kg/m3 (Fa. Hu¨ls, Vestosint). In preliminary experiments it was found that these tracer particles did not adhere to the bubble surface and hence were not floated. However, smaller tracer particles with a diameter of about 20 µm were floated and therefore not useful. Prior to the experiments 100 mL slurry of water and tracer particles was produced and then dispersed in the aerated test facility. Hence the tracer volume fraction was low enough not to affect the flow, but the number concentration was sufficiently high for the PIV. With a solids volume fraction of about 10% in the slurry, this eventually yields a tracer volume fraction of around 1.0 × 10-4 in the entire bubble column. The applied macro camera optics (Nikkor, focal length, s ) 50 mm; aperture, f ) 1.2) had a small depth of field which was the basis to discriminate between bubbles and tracer particles inside and outside of the camera’s depth of field utilizing the gradients of gray values. Sharply depicted objects in the focal plane have high gradients, while blurred objects out of focus have low gradients of gray values. Hence, the imaging plane was not produced by a light sheet, but a proper selection of the macro lens and different filter operations. Preliminary experiments with calibration objects of different size have shown that the applied optical configuration and filter operations yield a depth of field smaller than 4 mm for the bubbles in the considered size range. The discrimination between bubbles and tracer particles was performed in the evaluation procedure using a series of different digital image filters as will be described below. The data sampling and image processing was performed in the following way. At the beginning 500 double images were collected and processed to yield first bubble and continuous phase instan-
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taneous velocity fields. This number of images was sufficient to obtain statistically reliable profiles for the continuous phase mean velocities and mean fluctuating values. The measurement for the bubble phase was further continued if necessary until 30 000 validated bubbles were collected at the considered location. This procedure ensured that also statistically reliable results for the bubble mean velocity components as well as distributions of bubble size, eccentricity, and orientation angle were obtained. The processing time for filtering a double image, detecting the bubbles and performing the PTV took around 1 s, while the processing time for filtering and performing the PIV for the liquid phase took around 5 s. This yields a processing rate of about 0.1 to 0.2 double frames per second for the first measurement period and about 1 Hz for processing only the bubble phase. The typical overall measurement time for a combined measurement of both phases at five vertical measurement sections in the bubble column was therefore around 12-15 h. 2.3. Bubble Detection and Velocity Measurements. The tasks in the image processing and evaluation include the detection of bubble contours and centroids, bubble velocity determination by PTV and liquid phase velocity measurement by PIV. As mentioned above, the imaging plane was produced by shadow imaging in connection with a camera lens having a small depth of field. Hence, the images include sharply depicted bubble contours and out-of-focus bubbles as well as images of tracer particles. In order to get the different two-phase flow properties also different sets of filter operations had to be used. The first task consists in extracting the in-focus bubble contours from the images. By applying a 5 × 5 median filter small noise objects and the images of the tracer particles were removed from the image. The bubble contours were obtained by applying a 3 × 3 Sobel filter (i.e., gradient filter) whereby the gray scale distribution on the image now highlights the regions of high intensity gradients, namely, the contours of the bubbles. After applying a certain threshold level, which was optimized yielding an optimum bubble detection rate, only those contours remain which belong to in-focus bubbles. Then the bubble contours were descretized into about 42-72 segments and polynomials of third order were used as spline functions to the contour points. With these spline functions also missing parts of bubble contours, which may occur when bubbles overlap each other, could be reconstructed. For reasons of computational efficiency and accuracy only those bubble contours were reconstructed which had missing portions of 15% at most. With the contour information the bubble cross-sections are subdivided into the respective number of segments and the cross-sectional area of the planar bubble images and the centers of the bubble images are calculated as well. Since for the present operational regime the bubble shape was in the ellipsoidal regime, also the major (A) and minor (B) axes as well as the bubble orientation angles with respect to the horizontal were determined. The area equivalent bubble diameter is determined from the major and minor axis as: DA ) (AB)1/2. As a result of the tumbling motion and the application of planar imaging, the area equivalent bubble diameter will be overestimated (i.e., mainly the minor axis B will be overestimated). This error was analyzed in detail by Bro¨der and Sommerfeld.18 For an eccentricity of χ ) A/B ) 1.5 and a bubble tilting angle of 30°, which is in the upper range of measured orientation angles as will be shown below, the bubble diameter is overestimated to about 6% and for a higher eccentricity of χ ) 2.0 this error increases to about 15%. However, the highest probabilities of bubble orientation angle are in the range (20° with a maximum at zero (see Figure 18a),
Figure 2. Schematic diagram of the filter operations for phase discrimination by extracting the images of tracer particles from the pictures of the twophase flow (the images are a zoom from the full size image).
whereby the average error in bubble sizing is much lower. More details on the bubble detection algorithm and the resulting accuracy are provided by Bro¨der and Sommerfeld.18 Additionally, the volume equivalent diameter may be estimated assuming the bubble shape can be approximated by an oblate spheroid which yields: DV ) (A2B)1/3. Owing to the assumptions involved in the determination of the volume equivalent diameter and the associated errors this value has been only used to allow a comparison of the present results with literature data. Once the centroids of the bubbles on subsequent images are known, also the instantaneous bubble velocity can be determined. Corresponding bubble pairs on both images were found by the criteria of overlapping bubble contours and the closest neighbor in the estimated direction of bubble motion. This was achieved by adjusting the time delay between successive images in such a way that the distance between the two centroids was around one-half of the bubble area equivalent diameter. Moreover, the diameter of the bubbles on the two images should not defer more than 5% in order to ensure that the same bubble is considered. Eventually, the bubble velocity is calculated from the determined translation of the centroids and the time delay between the double images. The information on the bubble geometry, the translations, and the velocities were also stored for later data analysis and the determination of bubble velocity profiles. The evaluation of the liquid velocity field from the raw double images (image A in Figure 2) is somewhat more sophisticated (for details see ref 18). First the so-called LOG (Laplacian of Gaussian) edge filter is applied with a standard deviation corresponding to the image size of the tracer particles. This operation yields an enhancement of the image edges and also removes the images of out-of-focus tracer particles (i.e., from those tracer particles which are outside the focal plane). The resulting image B now includes the in-focus tracer images as well as images from the sharply depicted bubbles. Applying now a 3 × 3 median filter an image was created which only includes bubble contours (image C in Figure 2). Finally, image C was subtracted from image B to yield image D which only includes in-focus tracer images. Although the applied tracer particles did not show a tendency to be floated by the bubbles, in some cases still tracer were detected close to the bubble interface. Since however the interface velocity is close to the liquid velocity directly at the interface this effect will not yield any erroneous liquid velocity measurements. Now a PIV algorithm incorporating a successive refinement of the interrogation area is applied to the double images of the
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3. Results
Figure 3. Instantaneous flow field of the continuous phase in the bubble column overlapped onto the original image containing bubble and tracer. Mean velocities of the vector field have been subtracted to visualize the fluctuations (gas volume fraction 0.9%, bubble diameter about 2.1 mm)
tracer particles. The determination of the displacement vectors is based on a combination of the MAD (minimum absolute difference) and the MQD (minimum quadratic difference) methods. The first two evaluations with an interrogation area of 128 × 128 pixels and 64 × 64 pixels were performed with the faster but less accurate MAD method and the final step with an interrogation area of 40 × 40 pixels was done with the more accurate but slower MQD method. The accuracy of the PIV and the enhancement of the processing speed are discussed in detail by Bro¨der and Sommerfeld.18 A typical image of the original bubble and tracer distribution and the resulting vector field of the continuous phase in the bubble swarm are shown in Figure 3 for a local gas volume fraction of 0.9%. It is obvious that in regions with in-focus bubbles no continuous phase velocities are available. However, at the locations of blurred bubble images tracer particles still can be detected due to the applied filter operations.
3.1. Hydrodynamics in the Bubble Column. In the bubble column, the vertical and horizontal velocities of both phases (i.e., bubbles and liquid) were measured for five vertical sections above the aerator in the vertical midplane of the bubble column. To guarantee a good spatial resolution of the bubbles, the horizontal width of an image was 60 mm, whereas the vertical height for each measurement plane was limited to 40 mm. Hence, the measurement of the velocity fields over the entire cross-sectional width of the column was realized by collecting three series of overlapping images in the horizontal direction. Mean and fluctuating velocity fields were evaluated from 500 double images for the continuous phase and sampling at least 30 000 bubbles in each measurement area to obtain bubble velocity statistics. The collection of 500 double images was found to be sufficient to obtain reliable values of the liquid phase mean and fluctuating velocities. The horizontal and vertical movement of the entire imaging system was realized by the CNC-controlled traversing system so that the measurements were fully automated. For each of the two capillary aerators three sets of measurements with different air flow rate and hence gas hold-up were performed. In addition to the variation of bubble size by using aerators with different capillary diameter, the bubble size increased also with increasing gas flow rate. The operational conditions of all experiments, that is, gas flow rate and gas holdup, are summarized in Table 1. The number-averaged bubble size was obtained from the measured size distribution. The average bubble number density was estimated with the number mean bubble diameter, which was also used to estimate an average bubble Reynolds number in connection with the measured average slip velocity. The distributions of the determined area equivalent bubble diameters for the A-cases with the 0.4 mm capillaries are shown in Figure 4. These results were obtained 75 mm above the aerator where the formation process of the bubbles was completed. The size distributions were evaluated in the core region of the bubble column in a sample area of 50 mm × 40 mm (horizontal × vertical dimension). With increasing gas flow rate, the number mean diameter increases and the size distribution is slightly broadened. The evolution of the bubble area equivalent diameter along the bubble column is shown in Figure 5 for case B3. Even for this rather high gas volume fraction the size distribution does not change very strongly except from the first to the second vertical location. For all distributions a slight reduction in the bubble size along the column is observed which is most likely associated with bubble break-up. Any effects of bubble coalescence are not observable in the development of the size distribution. The profiles of the mean and fluctuating velocities for both phases along the bubble column are shown in Figures 6 and 7 for case A2. The profiles of the absolute bubble-rise velocity along the bubble column are almost symmetric and have a parabolic shape (Figure 6). The maximum value slightly decreases from a value of about 0.35 m/s just above the aerator to about 0.25 m/s 75 mm from the surface of the column (i.e., last profile at z ) 575 mm). Close to the walls where the liquid is flowing downward the bubble rise velocity is lower, namely around 0.2 m/s. Comparing the two components of the bubble mean fluctuating velocities reveals an anisotropic character. Namely, the mean horizontal fluctuation of the bubbles is considerably higher than the vertical component. This phenomenon has been also found in the studies of Yao et al.14 for lower gas hold-up and is a result of the zigzag or helical motion of
Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 335 Table 1. Summary of Measurements in the Bubble Column for Different Operational Conditionsa case
capillary diameter (mm)
gas flow rate (l/h)
global gas hold-up (%)
bubble number density (1/m3)
number-averaged bubble size (mm)
bubble Eo¨tvo¨s number
bubble Reynolds number
A1 A2 A3 B1 B2 B3
0.4 0.4 0.4 0.6 0.6 0.6
80 160 320 160 320 480
0.90 1.26 4.70 1.4 2.7 5.1
5.02 × 106 2.94 × 106 2.35 × 106 1.70 × 106 1.41 × 106 1.32 × 106
1.95 2.55 2.85 3.35 3.68 3.81
0.50 0.86 1.08 1.49 1.79 1.92
527 663 713 804 868 895
a The bubble number density was calculated with the number-averaged bubble size. The bubble Reynolds number was calculated with the number-averaged bubble size and the slip velocity obtained from the measurements.
Figure 5. Number-weighted bubble size distribution of the area equivalent bubble diameter measured along the bubble column for case B3 (Table 1).
Figure 4. Number-weighted bubble size distribution of the estimated area equivalent bubble diameter measured 75 mm above the aerator for the three A cases (Table 1).
ellipsoidal bubbles in the present size range, that is, between 2.0 and 3.5 mm. A similar result was also found from measurements in a loop facility.18 A further discussion on the anisotropic bubble fluctuation behavior will be provided below. The vertical mean velocity profiles of the liquid show the expected behavior for a bubble column, namely an upward flow in the core region and a down-flow near the walls (Figure 7). Please note that the kinks in the profiles result from the overlapping of three images, necessary to collect profiles over the entire column cross-section. Moreover, it seems that the upper profiles show a too strong downward liquid motion, which was also confirmed by a mass balance. This is most likely the result of a nonsymmetric flow structure within the column implying that the region of strongest upward flow is shifted out of the core region of the bubble column as already observed in previous studies.5 Such an asymmetry might be caused by small disturbances in the aeration and the highly unstable nature of the flow in a bubble column. To avoid such an error, it would be necessary to measure the liquid velocity fields in several
circumferential vertical planes and from that determine an averaged profile. This would however be very time-consuming. The two components of the mean fluctuating velocity of the liquid phase are also not identical with the vertical component being about twice as large as the horizontal one. Hence, the turbulence in the bubble column is highly anisotropic. The higher vertical component is of course the result of the flow being mainly driven by the dominant vertical bubble rise due to buoyancy. The mean fluctuating values of the liquid are however considerably lower than the bubble fluctuating velocities and the vertical component decreases from about 0.04 m/s near the aerator to about 0.02 m/s near the liquid surface of the column. Similar observations were made for the other cases with different air flow rates and also in a previous study with smaller bubbles.5 The averaged turbulent kinetic energy kav of the continuous phase along the bubble column was calculated from the profiles of the mean fluctuating components (vertical, u′L, horizontal, V′L) in the following way: n
kav )
∑
1 0.5(u′L2 + 2V′L2)i∆Ai A i)1
(1)
where ∆Ai is the local annular cross-sectional area and A the total cross-sectional area of the column. The calculation of the turbulent kinetic energy in this way relies on the assumption that the two horizontal fluctuating components of the liquid are almost identical, which is justified for the flow in a bubble column with circular cross-section. For most of the considered cases, the average turbulent kinetic energy first increases from the aerator to a maximum at about one-third of the column height and then continuously decreases toward the surface of the bubble column (Figure 8). The maximum is the result of the strong mixing between bubble
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Figure 7. Profiles of the vertical and horizontal mean velocity and the vertical and horizontal mean fluctuation for liquid, case A2, Vgas ) 160 L/h (data are available on request). Figure 6. Profiles of the vertical and horizontal mean velocity and the vertical and horizontal mean fluctuation for bubbles, case A2, Vgas ) 160 L/h (data are available on request).
plume and surrounding liquid yielding a strong shear flow. The decrease of turbulent kinetic energy toward the surface is a consequence of the fact that the bubbles are dispersed over the entire cross-section of the bubble column, yielding locally a smaller momentum transfer from the bubble to the liquid. This observation is in agreement with previous studies for smaller bubbles.5 With increasing gas flow rate the level of turbulence in the column considerably increases as expected due to the increasing agitation by the bubbles. Increasing gas flow rate also implies an increasing bubble size and hence bubble Reynolds number. Thereby the agitation by the bubble is further enhanced. For the cases with the larger bubbles (i.e., cases B1-B3) the turbulent kinetic energy is remarkably higher compared to the cases with smaller bubble size (i.e., cases A1-A3). The turbulence level in the entire column was calculated as the mean value of the cross-sectional averages and plotted versus the gas volume fraction (Figure 9). For the same volume fraction the cases with larger mean bubble diameter (i.e., cases B1-B3) have a considerably higher overall turbulence level, although the bubble number density is lower (Table 1). Hence, the higher bubble-induced turbulence for the B-cases is mainly caused by the larger values of the bubble Reynolds numbers (Table 1). Moreover, the fluctuation energy of the bubble phase was evaluated along the bubble column (Figure 10). As mentioned before, the bubble fluctuations are considerably higher than those of the continuous phase. The cross-sectional averages of the bubble fluctuation energy continuously decrease from the aerator to the surface for all cases. An increase of gas flow rate results in higher levels of bubble fluctuation energy. Hence, there exists
Figure 8. Cross-sectional average of the liquid phase turbulent kinetic energy along the bubble column for the different operational conditions.
a dependence on both bubble size and gas hold-up. The fluctuation ratio (i.e., stream-wise versus radial component) of the bubbles averaged over the entire bubble column shows a clear dependence on the bubble size (Figure 11). For bubbles in the size range between 2 and 3.8 mm the horizontal fluctuation is larger than the vertical component. This is associated with a zigzag or helical motion of the bubbles in this size range. For bubbles smaller than 2 mm a tumbling motion is less pronounced and hence the fluctuation is almost isotropic. The tumbling motion of bubbles larger than 3.8 mm is hindered due to interactions between the bubbles at this higher gas volume fraction of 5.1%. It should be noted that the interbubble spacing for a regular cubic arrangement is about 2 bubble diameters in this case only. A similar result was also found for experiments in the up-comer of a loop facility.18 To allow the observation of bubbles for a longer period the bubble behavior was also recorded in the down-comer of the loop
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Figure 9. Mean value of the liquid phase turbulent kinetic energy in the entire bubble column in dependence of the gas hold-up.
Figure 10. Cross-sectional average of the bubble phase fluctuation energy along the bubble column for the different operational conditions.
Figure 11. Ratio of the bubble fluctuating components in axial and radial direction averaged over the entire bubble column and plotted versus average area equivalent bubble diameter. (Note, the gas hold-up is also different in the six considered cases.)
facility using a high-speed CCD-camera. The measured horizontal and vertical velocity components are shown in Figure 12 for a bubble size of 3.5 mm. Also in this situation the horizontal component of the bubble velocity shows much stronger fluctuations than the vertical component because of their tumbling motion. 3.2. Microstructure in Bubbly Flows. In the following, the bubble behavior in the column is analyzed in more detail using the bubble identification algorithm described above. Important
Figure 12. Time series of the vertical and horizontal bubble velocity in a counterflow situation recorded in the down-comer of a loop facility: bubble area equivalent diameter, 3.5 mm; gas volume fraction, about 1%.
Figure 13. Contour diagram of the eccentricity in dependence of the area equivalent bubble diameter obtained from all the cobble column experiments (see Table 1).
properties considered are the eccentricity and the orientation of the bubbles in the flow (i.e., with respect to the horizontal axis). The determination of the major and minor axis of the bubbles, assuming oblate ellipsoids of revolution, was described by Bro¨der and Sommerfeld.18 The eccentricity of the bubbles was calculated as the ratio of major to minor axis, χ ) A/B, and was evaluated by considering all bubble images collected throughout the bubble column, which were typically around 80 000 individual bubble images. Since for the different operational conditions also different bubble size distributions were obtained, the correlation of the distribution of eccentricity as a function of bubble size was put together from these different operational conditions (see Table 1). For this purpose the bubble size range was subdivided in 0.2 mm classes. The result is shown in Figure 13 as a contour plot in dependence of the estimated area equivalent bubble diameter. It is clear, that both the mean value and the standard deviation of the eccentricity χ are strongly depending on bubble size. The mean value of χ increases of course with bubble size and reaches a kind of plateau for bubble sizes between 1.7 and 3 mm with a value of around 1.8. A further increase of bubble size is associated with a decreasing eccentricity approaching a value of about χ ) 1.6 (see also Figure 15). PDF values of the eccentricity extracted from Figure 13 for different bubble size classes are compared in Figure 14. It is obvious, that these PDF values can be approximated with reasonable accuracy by a normal distribution function. The PDF
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Figure 14. Probability density distribution (PDF) of bubble eccentricity for different bubble size classes (width 0.2 mm) obtained from the bubble column experiments.
Figure 15. Dependence of the mean eccentricity measured in the bubble column for all cases on the bubble Weber number including comparison with the theory of Moore19 and the data of Celata et al.20
for the smallest bubble size class (i.e., 1.5 mm) is considerably narrower than for the larger bubble sizes. For all the bubble sizes, the eccentricity roughly scatters between 1.0 and 3.0. The mean eccentricity as a function of the bubble Weber number obtained from the present experiments is also compared with correlations and data from literature (Figure 15). The analytical correlation proposed by Moore19 was derived for bubbles which do not markedly deviate from spherical shape, assuming that the flow around the bubble is inviscid. This implies that the result is only valid for higher bubble Reynolds numbers (in this case ReB > 200), where the bubbles shape is not strongly influenced by viscous effects. It should be noted that the average bubble Reynolds number in the present experiment was between 500 and 900. The derived relation between Weber number and eccentricity is given by19 We )
4(χ3 + χ - 2)[χ2 sec-1 χ - (χ2 - 1)1 ⁄ 2]2 χ4⁄3(χ2 - 1)3
(2)
with |FF - FB|DVVB
2
We )
(3) σ Here DV is the volume equivalent bubble diameter, VB is the bubble terminal rise or slip velocity, FF and FB are the liquid and gas density, and σ is the surface tension. The present measurements in the bubble column, where the Weber number was also calculated with the volume equivalent diameter, show about 15% larger eccentricity values up to WeB ) 2.5 compared to the result from the Moore-correlation. The experiments of Celata et al.20 where a bubble chain rising in quiescent refrigerant (i.e., FC 72) was considered, yielded even lower eccentricity values than the analytical result of Moore.19 In the refrigerant which can be regarded as a very “clean” fluid, a continuous increase of the eccentricity up to WeB ≈ 3.2 is observed (Figure 15). For higher Weber numbers and hence larger bubbles a larger scatter in the eccentricity may be identified with an almost constant value around χ ) 2.0. The experiments of Okawa et al.21 for single bubble rise in distilled water provided eccentricity values as a function of bubble Weber number which are more or less scattered around the correlation of Moore.19 The differences between the present experiment and theory as well as other experiments can be first explained with the effect of gas volume fraction which was between 1 and 5% in the present case whereas the other studies were performed for
Figure 16. Measured rms-value of the eccentricity as a function of the volume equivalent bubble diameter.
single bubbles. Hence the interaction between the bubbles will affect bubble oscillation and accordingly eccentricity. Moreover, the higher liquid turbulence level (i.e., bubble induced turbulence) in the present study is supposed to cause an enhancement of bubble oscillation yielding higher eccentricities. Therefore, further studies are required to analyze the effect of turbulence and gas volume fraction on bubble oscillation in more detail. The standard deviation of χ initially increases with bubble size and reaches a maximum for bubbles with DV between 3.0 and 3.5 mm (Figure 16). In accordance with the decrease of the mean value of χ, also the standard deviation decreases when the bubbles grow further. For a volume equivalent diameter of about 4 mm a limiting value is reached (i.e., χrms ≈ 0.34). The scatter of the data for bubbles smaller than 1.5 mm and larger than 4 mm is caused by the lower number of samples collected for these size regions. In the following, the bubble orientation angel (β) and the direction of bubble motion (γ) are evaluated from the bubble column experiments (see Figure 17 for definition). For both properties, averaged PDFs are determined for the cases A1-A3 and B1-B3. In the considered bubble sizes and gas hold-ups (see Table 1), the distributions of the orientation angle were found to be almost identical (Figure 18a). The standard deviation of β is about 19°. The PDFs of the direction of bubble motion (angle γ) also exhibit, as expected, a normal distribution function (Figure 18b). However, there are slightly larger differences between the experiments with different gas-hold-up and bubble
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Figure 17. Sketch for the motion of a spheroidal bubble, indication of bubble orientation, and motion angle.
Figure 19. Correlation between the bubble orientation angle β and the motion angle γ obtained from all the measurements in the bubble column (see Table 1).
Figure 20. Bubble eccentricity as a function of orientation angle β for different bubble size ranges, the data were obtained from all the measurements in the bubble column (see Table 1).
Figure 18. Probability density functions of bubble orientation angle β (a) and motion angle γ (b) obtained from all the measurements in the bubble column (see Table 1).
size (here between cases A and B). The results for the orientation angle β and the direction of motion γ suggest that they might be highly correlated. Hence, the data were evaluated in this respect and the correlation function Rβ,γ was calculated as Rβ,γ )
2βiγi
(4) (π ⁄ 2)2 The result in Figure 19 indeed shows a strong correlation between β and γ, which implies that the probability that the direction of bubble motion is most probably perpendicular to the major axis of the bubble is very high. Moreover, the correlation between eccentricity and orientation angle of the bubbles was determined for the six conditions of the bubble column experiments (Table 1). These data clearly reveal that two different fractions of bubbles with a different behavior can be identified (Figure 20). Bubbles with an area equivalent diameter between 3 and 4 mm most likely move vertically (i.e., are horizontally aligned) with a maximum in the eccentricity. Such behavior was also found by Tomiyama et al.,22 namely, the eccentricity has a maximum if the vertical component of the bubble velocity also has the highest values.
However, there is a small delay between both curves, resulting from the action of the added mass. The distribution of the eccentricity as a function of orientation has almost a parabolic shape for these larger bubbles. For bubbles between 1 and 2.5 mm the eccentricity still has a maximum when the orientation angle is around zero. However, two side maxima appear around an orientation angle of about (35°. For a zigzag bubble rise pattern with a sinusoidal trajectory these side maxima are associated with the point of inflection. The larger orientation angles for bubbles with smaller eccentricity are most likely resulting from small bubbles which rise in a random way due to the interaction with turbulent structures. It should be noted, however, that the number of detected bubbles is relatively small whereby the statistics for orientation angles larger than 40° is less good. 4. Conclusions Planar shadow imaging velocimetry was applied for a detailed analysis of the hydrodynamics in a laboratory bubble column for six different cases with increasing gas flow rate and hence gas hold-up and bubble size. The resolution of the imaging technique was high enough for also resolving the bubble contours. Hence, in addition to the velocities of both phases (i.e., bubbles and tracer particles), the bubble behavior could also be studied in more detail. From the planar images of the bubbles their area equivalent diameter, the eccentricity, and the bubble orientation in the flow were also determined.
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The fluctuation velocities of the continuous phase were found to be anisotropic with the stream-wise component being higher than the radial one. This is mainly the result of the flow being driven by the buoyancy of the bubbles and the resulting turbulence production. For all considered cases with a gas holdup between 1 and 5% the fluctuation energy of the continuous phase was considerably lower than that of the bubble phase. For bubble mean diameters between 2 and 3.8 mm it was found that their radial fluctuation was remarkably higher than the vertical component. This is originated in the tumbling motion of the bubbles (i.e., zigzag or helical) in this size range. For the largest bubbles considered, the fluctuation was close to isotropic. This is a result of the hindrance of bubble tumbling motion in this situation where the gas hold-up was about 5%. The analysis of the microstructure in the bubble swarm showed that the eccentricity in the present study deviates from literature data which were mostly obtained for single bubbles or bubble chains. Hence, the bubble oscillation behavior and the resulting eccentricity distributions seem to be strongly affected by interactions between bubble (i.e., at the cases with higher gas volume fraction) and flow turbulence. Further studies are needed to quantify these effects on bubble oscillation behavior. The bubble orientation angle in the flow and their angle of motion were almost normal distributed and found to be almost independent of bubble size in the considered range (i.e., between 2 and 4 mm). The highest eccentricity values are found for bubbles which move vertically upward. This is in accordance with single bubble studies which exhibit a zigzag motion. Acknowledgment The financial support of the present studies by the Deutsche Forschungsgemeinschaft (DFG) under contract number SO 204/ 19 is gratefully acknowledged. Literature Cited (1) Mudde, R. F. Gravity-driven bubbly flows. Annu. ReV. Fluid Mech. 2005, 37, 393. (2) Joshi, J. B.; Shah, Y. T. Hydrodynamic and mixing models for bubble column reactors. Chem. Eng. Commun. 1981, 11, 165. (3) Chen, R. C.; Reese, J.; Fan, L.-S. Flow structure in a threedimensional bubble column and three-phase fluidised bed. AIChE J. 1994, 40, 1093. (4) Lin, T.-J.; Reese, J.; Hong, T.; Fan, L.-S. Quantitative analysis and computation of two-dimensional bubble columns. AIChE J. 1996, 42, 301. (5) Bro¨der, D.; Sommerfeld, M. An advanced LIF-PLV system for analysing the hydrodynamics in a laboratory bubble column at higher void fraction. Exp. Fluids 2002, 33, 826.
(6) Ruzicka, M. C.; Zahradnik, J.; Drahos, J.; Thomas, N. H. Homogeneous-heterogeneous regime transition in bubble columns. Chem. Eng. Sci. 2001, 56, 4609. (7) Boyer, C.; Duquenne, A.-M.; Wild, G. Measuring techniques in gasliquid and gas-liquid-solid reactors. Chem. Eng. Sci. 2002, 57, 3185. (8) 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. (9) Kulkarni, A. A.; Joshi, J. B.; Kumar, V. R.; 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. (10) Bro¨der, D. and Sommerfeld, M. Simultaneous Measurements of Continuous and Dispersed Phase in Bubble Columns by PDA. Proceedings Ninth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 1998, Vol. 2, Paper 27.2, 1998. (11) Chen, J. J. J.; Jamialahmadi, M.; Li, S. M. Effect of liquid depth on circulation in bubble columns: A visual study. Chem. Eng. Res. Des. 1989, 67, 203. (12) Chen, R. C.; Fan, L.-S. Particle image velocimetry for characterising the flow structure in three-dimensional gas-liquid-solid fluidised beds. Chem. Eng. Sci. 1992, 47, 3615. (13) Lain, S.; Bro¨der, D.; Sommerfeld, M.; Go¨z, M. F. Modelling hydrodynamics and turbulence in a bubble column using the Euler-Lagrange procedure. Int. J. Multiphase Flows 2002, 28, 1381. (14) Yao, B. P.; Zheng, C.; Gasche, H. E.; Hofmann, H. Bubble behaviour and flow structure of bubble columns. Chem. Eng. Process 1991, 29, 65. (15) Degaleesan, S.; Dudukovic, M.; Pan, Y. Experimental study of gasinduced liquid-flow structures in bubble columns. AIChE J. 2001, 47, 1913. (16) Deen, N. G.; Solberg, T.; Hjertager, B. H. Large eddy simulation of the gas-liquid flow in a square cross-sectioned bubble column. Chem. Eng. Sci. 2001, 56, 6341. (17) 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. 2007, 62, 1049. (18) Bro¨der, D.; Sommerfeld, M. Planar shadow image velocimetry for the analysis of the hydrodynamics in bubbly flows. Meas. Sci. Technol. 2007, 18, 2513. (19) Moore, D. W. The rise of a gas bubble in a viscous liquid. J. Fluid Mech. 1959, 6, 113. (20) Celata, G. P., Cumo, M., D’Annibale, F., DiMarco, P., Tomiyama, A. and Zovini, C., Effect of Gas Injection Mode and Purity of Liquid on Bubble Rising in Two-Component Systems. 5th International Conference on Multiphase Flow, ICMF’04, Yokohama, Japan, May 30-June 4, 2004, Paper No. 477, 2004. (21) Okawa, T.; Tanaka, T.; Kataoka, I.; Mori, M. Temperature effect on single bubble rise characteristics in stagnant distilled water. Int. J. Heat Mass Transfer 2003, 46, 903. (22) Tomiyama, A.; Celata, G. P.; Hosokawa, S.; Yoshida, S. Terminal velocity of single bubbles in surface tension force dominant regime. Int. J. Multiphase Flow 2002, 28, 1497.
ReceiVed for reView May 26, 2008 ReVised manuscript receiVed October 22, 2008 Accepted October 23, 2008 IE800838U
