Influence of Aspect Ratio and Superficial Gas Velocity on the Evolution

Ind. Eng. Chem. Res. 2006, 45, 7301-7312

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Influence of Aspect Ratio and Superficial Gas Velocity on the Evolution of Unsteady Flow Structures and Flow Transitions in a Rectangular Two-Dimensional Bubble Column M. Elena Dı´az, Francisco J. Montes,* and Miguel A. Gala´ n Departamento de Ingenierı´a Quı´mica y Textil, UniVersity of Salamanca, Plaza de los Caı´dos 1-5, 37008, Salamanca, Spain

In this paper, the flow regimes developed in a centrally aerated two-dimensional (2D) bubble column are studied by means of visual observations and the measurement of wall pressure fluctuations. The combined effect of the aspect ratio (H/W) and superficial gas velocity (UG) on the hydrodynamics of the bubble column is investigated. Moreover, the time-averaged and time-dependent flow behavior are analyzed together. The results reveal the importance of H/W and UG on the developed flow regimes and the significance of the steadiness or unsteadiness of the flow on the resulting time-averaged flow regimes. A detailed description of the flow patterns based on H/W and UG is presented. As UG is increased, at H/W ) 1.25, two pseudo-steadystate flow regimes (characterized by one or two circulation cells) are observed. At H/W ) 2.25, only unsteady bubble plumes of decreasing oscillation period are obtained. At H/W ) 1.50, 1.75, and 2.00, unsteady flow structures occur, at increasing values of UG. 1. Introduction Bubble columns are multiphase equipment that is frequently used in the chemical, biological, and petrochemical industries. The preference of this equipment over other multiphase reactors is based on distinctive advantages: simple and inexpensive construction, low operation costs, and satisfactory mass- and heat-transfer capacity.1 These advantages have made bubble columns the preferred equipment used for bringing gas and liquid phases into contact with each other. Gas, which constitutes the dispersed phase, is distributed at the bottom of the column and rises as bubbles through the liquid, which constitutes the continuous phase. Despite the extended industrial application of bubble columns, there are still some unanswered questions regarding their design and scaleup, basically because of the partial knowledge of the fluid dynamics of the gas-liquid flow. Many efforts have been made in the past decades that have been directed at improving the state of the art; however, the complex hydrodynamic characteristics and the inherent unsteadiness of the flow have slowed the resolution of the main problems that are encountered when designing and operating bubble columns. One of the main objectives of the design and operation of this multiphase reactor is to maximize its performance, that is, the calculation of the optimum conditions for mass and heat transfer. Transfer phenomena that occur across the gas/liquid interface are strongly dependent on the mixing efficiency and, therefore, also on the existing flow regimes inside the bubble column. Consequently, the correct design of bubble columns requires the accurate identification of all particular flow patterns given under different experimental conditions, because this identification is key in the selection of appropriate models for mass and heat transfer. There are two flow regimes commonly observed in bubble columns:1-10 the dispersed bubble and coalesced bubble flow regimes. The coalesced bubble flow regime can be subdivided into the vortical and turbulent flow regimes. The particular * To whom correspondence should be addressed. Tel.: +34-923294479. Fax: 34-923-294574. E-mail address: [email protected].

values of the superficial gas velocity (UG), together with the properties of the phases, the gas distributor design, and the column dimensions constitute the experimental variables determining the existence of a particular flow regime.2,4,11 At low values of UG, the dispersed bubble regime can be obtained with monodispersed bubbles uniformly injected through the sparger that rise approximately vertically throughout the column. Both the time-averaged gas holdup and velocity profiles are flat in the radial direction.3 No large-scale liquid circulations occur. As UG increases, the dispersed bubble regime becomes unstable and a transition to the coalesced bubble regime is observed.12,13 The transition flow regime (vortical flow6,10) presents four different flow regions (descending, vortical, fast bubble, and central plume). The four-region flow can evolve at increasing values of UG to a three-region flow that consists of one central fast bubble region together with the vortical and descending flow regions.8 Furthermore, the four-region flow is not observed for bubble columns with a width of less than ∼20 cm.8 The fast bubble flow region shows a wavelike motion in 2D bubble columns that becomes a spiral motion in three-dimensional (3D) bubble columns.6 As the turbulent flow regime gets established, the coalescence and break-up processes are of great importance, giving, as a result, bubbles of different sizes. Macroscale liquid circulations are generated and time-averaged parabolic velocity and gas holdup profiles are developed.3 It is possible that only the vortical or turbulent flow regimes are obtained for all values of UG.2,11,14,15 Particularly, the fact that the injection of gas into the liquid is not always uniform has been noted as one factor that determines the existence of only one type of flow regime for all values of UG.7,11,14,16 Together with the effect of the nonuniformity of aeration of the gas distributors on the type of flow regime, the use of partially aerated plates generates bubble plumes.6-8,17-26 These bubble plumes show an oscillatory movement that creates ascending and descending liquid circulation structures, which is something that is typically observed in industrial-size bubble columns.25 This is an important factor, because the existence of moving circulation cells favors movement of the liquid and, therefore, the mixing, increasing the rate of the transfer

10.1021/ie060466b CCC: $33.50 © 2006 American Chemical Society Published on Web 09/12/2006

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Ind. Eng. Chem. Res., Vol. 45, No. 21, 2006

Figure 1. Schematic representation of different types of flow patterns in bubble columns: (a) snapshots ((left) partial aeration resulting in a jet of bubbles, (middle) partial aeration resulting in an oscillating bubble plume; and (right) uniform aeration); and (b) resulting time-averaged flow regime common to all flows shown in panel a.

processes.18,23 The resulting instantaneous flow pattern differs considerably from the time-averaged flow regime.6,19 However, as it is schematically sketched in Figure 1, several snapshots of different flow patterns (Figure 1a) can lead to the same time-averaged flow regime (Figure 1b). In these cases, classifying the flow based on time-averaged variables may lead to erroneous conclusions about important parameters of the process, such as the liquid velocity distributions and mixing times.6,18 The gas-liquid flow dynamics in bubble columns is essentially time-dependent, consisting of a high-frequency component that accounts for bubble-scale phenomena and a lowfrequency component that is caused by the periodic motion of macroscopic flow structures. Considering the possible existence of the low-frequency motion of the liquid, the flow regimes can be considered as pseudo-steady state, if no oscillating bubble plume is observed, or unsteady if, in contrast, it is detected. From this point of view, the dispersed and turbulent flow regimes could be considered to be pseudo-steady state while the vortical flow regime is considered to be time-dependent. Despite the steadiness or unsteadiness of the flow inside bubble columns, the characterization of the different flow regimes is usually based on time-averaged variables and, therefore, on timeaveraged flow regimes. This approach is a very valuable tool for characterizing the hydrodynamics in the bubble column but, sometimes, additional information is required. The remarkable differences between the unsteady and time-averaged structures evidence the need of a detailed analysis of the different nonstationary flow patterns to have the hydrodynamics of the bubble column entirely identified. This analysis should be made taking into account that different experimental conditions lead to different flow structures. Thus, the use of partially aerated plates does not lead to the same type of flow pattern for different aspect ratios (liquid height to column width, H/W). It has been reported that different values of H/W result in the existence/nonexistence of unsteady structures and the generation of different numbers of them. In this way, when H/W ) 1, several authors21,24 have reported that

the bubble plume does not oscillate, constituting a simply stationary bubble jet that either rises vertically, forming two liquid circulation cells24 (see Figure 1a), or moves laterally, forming a single liquid circulation cell21 (not depicted here). For H/W > 1.5,21 1.8,23 2.0,24 and 2.25,19 the development of unsteady structures has been reported. In addition, as the aspect ratio is further increased, the number of unsteady vortices increases from two at H/W ) 1.5 to three at H/W ) 2 and four at H/W ) 3.21 Therefore, the aspect ratio has been proven to be a very important experimental variable when studying nonstationary structures. Furthermore, it is an essential parameter in scale-up operations.4 Despite the information on unsteady structures as a function of the aspect ratio, there is not a systematic study of the gradual evolution of the flow patterns from bubble jets to the bubble plume as a function of the aspect ratio H/W and UG in partially aerated bubble columns. Moreover, an analysis of the developing structures that considers both the time-averaged and the nonstationary approaches is lacking, even though both approaches are needed to have a complete description of the flow inside the bubble column. In this paper, the development of unsteady flow structures in a symmetrically aerated 2D bubble column is studied as a function of UG and H/W. The use of 2D bubble columns allows visual observations of flow regions and bubble shapes and sizes. Furthermore, the simplification that implies the consideration of only two dimensions facilitates the development and validation of dynamic flow and computational models. Nevertheless, care should be taken when extrapolating the 2D bubble column results to the 3D cases. Similarities on the flow structure between the two geometries have been observed,6 and important qualitative information can be obtained. However, there are limitations8,10,26,27 regarding parameters such as experimental transition velocities between flow regimes or dynamic behavior of the bubble plumes. The quantitative analysis of the flow regimes is based on the measurements of wall pressure fluctuations, whereas qualitative description of the type of flow is obtained by image analysis. Both methods provide in situ and nonintrusive measurements. Furthermore, the measurement of wall pressure fluctuations presents numerous advantages over other techniques28 and can be used in situations in which no visual observations of the flow are possible, such as in industrial-scale bubble columns, at high operating pressures or at high values of UG. The quantitative analysis is performed considering both time-averaged and nonstationary approaches. The analysis of existing time-averaged flow patterns for given experimental conditions is based on the representation of the global gas holdup (G) versus UG and on the drift flux analysis.29 The shape of the resulting curves, as well as possible changes in their slope, are indicative of a particular type of flow regime.2,3,30 The study of nonstationary structures is based on the spectral analysis that considers the Fourier transform of the resulting pressure time series. This method provides information of the oscillation frequency of the bubble plume,17 as well as information on the different physical phenomena that are occurring in the bubble column,11,17,19,28,31-34 through the resulting spectra and the mean and characteristic frequencies. In short, the main objectives of this work are as follows: (1) Identification of the particular aspect ratio at which the transition from a jet of bubbles to a bubble plume occurs and its variation with UG. (2) Experimental characterization of the flow when a jet of bubbles occurs, and identification of the time-averaged flow type as a function of UG.

Ind. Eng. Chem. Res., Vol. 45, No. 21, 2006 7303

provided by Keller. The pressure signals are directly stored in a personal computer (PC). Appropriate software is used to control the data acquisition. After the pressure time series are recorded, calculations are performed using custom-made routines in Matlab. 3. Experimental Results and Discussion

Figure 2. Schematic representation of the experimental setup.

(3) Experimental characterization of the flow with bubble plumes, identification of the time-averaged flow type as a function of UG, and analysis of the variation of the frequency of oscillation relative to UG and H/W. (4) Variation of gas holdup and period of oscillation of the bubble plume with H/W. 2. Experimental Section: Setup and Procedure A schematic representation of the experimental setup is shown in Figure 2. A 2D transparent bubble column constitutes the central part of this setup. The bubble column, which is composed of Plexiglas, is 0.2 m wide, 1.8 m high, and 0.04 m deep; this is a geometry that is similar to that presented by other authors.17,26,35 Water at room temperature and atmospheric pressure constitutes the liquid phase in all the experiments. Air is fed from the gas chamber through an aluminum sparger (eight centered holes 1 mm in diameter with a pitch of 6 mm) and constitutes the gas phase for all runs as well. UG is varied over a range of 2.4-21.3 mm/s by means of the appropriate combination of volumetric flow meters. The aspect ratio is varied over a range of 1.25-2.25, in increments of 0.25, and the entire range of UG is studied for each value of the aspect ratio. The modification of the aspect ratio is based on the variation of the liquid height, with the column width being kept constant. A high-speed digital video system is used for flow visualization. The system consists of a high-speed digital camera (Redlake MotionScope PCI 1000s), which was used to obtain images at 500 fps (frames per second), and a 500 W halogen lamp, which provided the necessary light. The images are analyzed and processed using commercial image analysis software. The pressure time series are obtained by means of two piezoresistive sensors (Keller PR35X, 0-200 mbar and 0-500 mbar with and a resolution of 0.002% of the full scale) flush mounted on the sidewall of the column. The pressures taps used in this work are placed at positions of 3.8, 21.3, 26.3, 31.3, 36.3, and 41.3 cm above the sparger. The location of the different pressure sensors is denoted with the subscript x, with x ) 1 corresponding to the sensor positioned closer to the distributor (3.8 cm). The interface converter from RS485 to USB (Keller K104-B) is powered by a supply unit that was also

3.1. Visualization of the Flow. The variation of H/W and UG leads to very different pictures of the flow inside bubble columns. Figure 3 shows video snapshots of the resulting flow patterns at three different values of UG for the five different H/W values studied in this work. When H/W is set to 1.25, no oscillating bubble plume is observed and the flow presents a pseudo-steady-state behavior (Figure 3a). For small superficial gas velocities (UG e 9 mm/s), a single circulation cell that has the width of the column is observed. As UG is increased, two symmetrical vortices develop. A basically symmetrical flow pattern is observed, with the liquid phase moving upward, following the column’s centerline, and moving downward along the sidewalls. These observations agree with those presented by Borchers et al.,21 who also reported the existence of a single vortex for an aspect ratio of H/W ) 1 and low values of UG. Chen et al.36 experimentally and Delnoij et al.24 computationally, on the other hand, reported two symmetrical vortices for an aspect ratio of H/W ) 1 and higher values of UG. These observations also agree with our experimental results. Therefore, both flow patterns are possible for aspect ratios up to 1.25, and the results presented here unify previous observations that did not study the effect of UG on the resulting flow regime. As the aspect ratio is increased to H/W ) 1.50 (Figure 3b), an oscillatory bubble plume is observed at low values of UG (UG e 8 mm/s). The resulting unsteady flow consists of two vortices moving periodically with very small amplitude and high period. As the superficial gas velocity is increased, the flow becomes steady and the flow regime characterized by the two symmetrical circulation cells is recovered. Similar results were obtained for aspect ratios of H/W ) 1.75 and 2.00 (Figures 3c and 3d, respectively); however, the transition from the unsteady flow pattern to the steady-state regime occurs at increasing values of the superficial gas velocity (UG ≈ 10.0 mm/s). Finally, with an aspect ratio of H/W ) 2.25 (Figure 3e), the flow is unsteady for all values of UG studied in this work and three transient circulation cells can be clearly recognized. The bubble plume moves alternately from right to left, with decreasing period and increasing amplitude, as UG increases. Several authors19,21,23,24 have reported the existence of the oscillating bubble plume for aspect ratios of H/W > 1.25. However, none of them reported the transition from unsteady flow structures to a pseudo-steadystate type of flow for increasing values of UG. An overview of the resulting flow patterns for different aspect ratios and UG is presented in Figure 4. As a result of the type of aeration used, the dispersed bubble regime, as described in the Introduction, is not observed, even at the lowest superficial velocities studied in this work. As it can be clearly observed, low values of H/W and high values of UG favor the pseudosteady-state flow patterns, whereas the unsteady flow structures prevail as UG decreases and H/W increases. In this way, at low values of UG, there is a transition from the pseudo-steady-state flow regime, which consists of a single circulation cell (single cell bubbly flow (SCBF)) that occurs with H/W ) 1.25 to the unsteady flow structures generated by the oscillation of the bubble plume at higher H/W values (vortical flow, VF). As UG increases, the symmetrical two-vortex turbulent flow (doublecell turbulent flow, DCTF) that occurs when H/W ) 1.25

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Figure 4. Qualitative description of the existing flow regimes, as a function of the superficial gas velocity (UG) and aspect ratio (H/W), based on experimental observations. Legend: SCBF, single-cell bubbly flow; DCTF, double-cell turbulent flow; and VF, vortical flow.

Figure 3. Snapshots of the gas-liquid flow in the bubble column at different superficial gas velocities (UG) and aspect ratios (H/W): (a) H/W ) 1.25, (b) H/W ) 1.50, (c) H/W ) 1.75, (d) H/W ) 2.00, and (e) H/W ) 2.25. For each panel, the left image was for UG ) 2.4 mm/s, the middle image was for UG ) 12.0 mm/s, and right image was for UG ) 21.3 mm/s.

evolves to the nonstationary vortical flow pattern as H/W is increased to higher values. The velocity of the transition

increases as H/W is increased from 1.25 to 2.00. For H/W ) 2.25, no transition is observed and the unsteady flow pattern prevails for all values of UG. In addition to the liquid flow patterns inside the bubble column, the bubble size distribution and gas holdup profile are important variables when characterizing the flow. At low values of UG, the existence of either a jet of bubbles with one circulation cell or a bubble plume with periodic movement generates marked gas holdup profiles, producing partial aeration in the entire bubble column. There is a narrow bubble size distribution, although, as UG increases, bubble clusters are observed. Depending on H/W, increasing the UG values can lead to a transition to the upward flow jet of bubbles along the centerline. If this transition is not observed, the oscillating bubble plume persists. In both cases, the processes of coalescence and breakup begin to be important, generating bubbles of different sizes. The frequency of occurrence and the diameter of the large bubbles increase as UG increases. When the bubble plume occurs, the spreading of the bubbles as they ascend is apparent. Thus, in the higher section of the bubble column, total aeration is observed, although the central oscillating bubble plume persists. In the case of the symmetrical, two-circulation-cells type of flow, the liquid carried up by the central bubble jet returns down along the side walls of the bubble column, dragging along small bubbles. As a result, total aeration is observed in the higher sections of the column, even though the central bubble jet that contains large bubbles persists. In view of Figure 3, it is also noticeable that the resulting flow patterns for higher values of H/W seem to favor the mixing. This statement is based on the observations of the moving liquid circulation cells that, for high values of H/W, create high turbulence along the width and the height of the bubble column, which consequently enhance the mixing processes. In the case of the two symmetrical circulation cells, the generated liquid velocities are lower and, therefore, the mixing does not seem to be so efficient. These experimental observations agree well with the experimental results on mixing times performed by Buwa et al.,18 which confirm the fact that the existence of unsteady flow structures favor the mixing processes. Looking at Figure 3, the apparent increase on the voidage as H/W


between two pressure sensors, is used.11,13,30,32 After simplification of the momentum balance equation, the consideration of a negligible gas density leads to32

G ) 1 -

(pj1 - pjx)aerated (pj1 - pjx)non-aerated

( {

2, if H/W ) 1.25 3, if H/W ) 1.50 for x ) l 6, if H/W ) 2.25

})

(1)

Figure 5. Schematic representation of the global gas holdup versus the superficial gas velocity typically found in bubble columns; the solid line represents dispersed bubble, transition, and turbulent regimes, whereas the dashed line represents a coalesced bubble regime.

increases is also noticeable. In any case, this is just a visual remark. The numerical calculations performed later in this paper provide the quantitative information needed to confirm this analysis. The visual characterization of the flow provides important qualitative and approximate information regarding the hydrodynamic characteristics of the existing flow patterns. However, to characterize the type of flow inside the bubble column quantitatively, and to obtain the experimental conditions under which the transitions occur, wall pressure time series are analyzed in the following sections. 3.2. Time-Averaged Description of the Flow. The identification of the particular type of time-averaged flow regime under any given experimental conditions has been classically performed by studying the evolution of the global gas holdup (G) with UG.2,3,11,30,34 As discussed in the Introduction, for some particular experimental conditions, the three regimes observed in bubble columns can occur. In such a case, according to the results presented by several authors,3,11,34 the plot of G vs UG presents three characteristic regions (Figure 5). At low values of UG, the dispersed bubble flow regime prevails. According to Ruzicka et al.,3 during this regime, the value of G increases as the value of UG increases, and the resulting curve is convex (G ≈ UG2). At a given value of UG, the curve deviates from this behavior, leading to the beginning of the transition (vortical) regime. Other authors11,34 have identified the beginning of the transition (vortical) regime as the point at which the G-UG plot deviates from the straight line that represents the dispersed bubble flow regime. In either case, during the transition regime, as the value of UG is increased, the value of G initially increases, reaches a local maximum, and then starts to decrease. Finally, as the value of UG is increased further, the curve reaches a local minimum, which is a point that determines the beginning of the turbulent flow regime. This regime is now differentiated by the concavity of the G-UG plot.3 Under different experimental conditions, it is also possible that only the coalesced bubble (vortical or turbulent) flow regime is obtained for all values of UG. In such a case, the G-UG curve does not exhibit any maximums or minimums. Furthermore, G increases continuously with UG, following a concave curve (Figure 5). To calculate the global gas holdup, the well-known manometric method, which is based on the static pressure difference

pj represents the mean pressure and x the pressure sensor position. To calculate G, pressure signals are recorded at a frequency of 15 Hz for 3 min. Figure 6 presents data of G obtained at different values of UG and H/W. As can be readily observed in this figure, there is a clear evolution of the G-UG plot as H/W increases. For H/W ) 1.25 and 1.50, the G-UG curve approximately follows the typical flow regime diagram described previously in this section. When H/W ) 1.25, at low values of UG, a steep increase of G is observed. After reaching a local maximum, at ∼9 mm/s, G decreases sharply until reaching a local minimum at 12.8 mm/s. Similar results were obtained for H/W ) 1.50, regarding the existence of a minimum value of the gas holdup at 13.8 mm/s. However, the low superficial gas velocity region does not show an increase that is as steep as that in the aforementioned case and an initial convex curve that ends at ∼6.2 mm/s is observed before reaching any maximum value. When the aspect ratio is increased to H/W ) 1.75, the GUG plot undergoes a clear change, with respect to the results obtained for lower H/W values. No maximums or minimums are obtained, even though a change of slope is observed when UG is ∼8.1 mm/s. The resulting G-UG plots for the aspect ratios of H/W ) 2.00 and 2.25 are equivalent. There is no evident change in the slope of any of the curves; G increases continuously and a concave line represents both of the variations well. There are neither maximums nor minimums. The analysis of the evolution of G with UG has been shown to be inaccurate for some experimental conditions.2,11 Therefore, additional studies must be performed. Also, based on the measurement of G, the drift flux method29 can provide a more accurate description of the flow regime limits.9,11,13,34 This analysis is based on the study of the drift flux (j), which, for a negligible superficial liquid velocity, can be calculated as

j ) (1 - G)UG

(2)

The identification of the transition points between flow regimes results from the study of the variation of j with G. In this way, if a change in the slope of the j-G curve is observed, the transition point between the dispersed bubble flow and the coalesced bubble flow regimes can be calculated.37 Figure 7 shows the resulting values of j vs G for the same conditions as those given in Figure 6. No variation in the slope of the curves is observed for the higher aspect ratios (H/W ) 2.00 and 2.25) whereas the corresponding plots at lower aspect ratios (H/W ) 1.25 and 1.50) show appreciable changes. The identification of the points of change of slope for H/W ) 1.25 and 1.50 leads to similar results to those obtained by means of the G-UG plot analysis. In the case of H/W ) 1.75, the j-UG curve shows a clear change of slope when UG is ∼8.1 mm/s, which is a value that is in complete agreement with the result obtained by means of the G-UG plot analysis. The results obtained and shown in Figures 6 and 7 reveal the influence of UG and H/W on the resulting values of the

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Figure 6. Evolution of the global gas holdup (G), relative to the superficial gas velocity (UG), at different aspect ratios (H/W); the identification of the flow regimes is based on changes in the slope of the curve.

Figure 7. Effect of the aspect ratio (H/W) on the variation of the drift flux (j), relative to the superficial gas velocity (UG).

averaged gas holdup (G) and drift flux (j). These two methods provide a global and time-averaged characterization of the flow regimes that are occurring inside the bubble column. In view of Figures 7 and 8, it can be stated that transitions between flow regimes are only detected for H/W values up to 1.75. Considering the visual observations presented previously in this work, together with Figure 7, at H/W ) 1.25, the convex fraction of the curve that ends at a local maximum of the gas holdup at UG ) 9 mm/s represents the pseudo-steady-state SCBF that occurs at low superficial gas velocities. The beginning of the bubble coalescence results in a decrease of the gas holdup, reaching a minimum at UG) 12.8 mm/s, which is a velocity

that delimits the existence of the pseudo-steady-state DCTF. Similar shape of the G-UG curve is obtained at H/W ) 1.50 with transition velocities of 6.2 and 13.8 mm/s. In this case, the transition is from VF to DCTF. At H/W ) 1.75, just one transition velocity is noticeable, at UG) 8.1 mm/s, and, again, it delimits the existence of VF and DCTF. The transition velocities obtained from the drift flux analysis (Figure 8) are equivalent to those obtained in Figure 7. When H/W ) 2.00 and 2.25, no transitions can be detected and the curve shows a concave form. As discussed previously in this section, this feature of the curve indicates the existence of the coalesced flow regime for all values of UG. These results agree very well with


Figure 8. Variation of the power spectral density, relative to the superficial gas velocity (UG), at different aspect ratios (H/W): (‚ ‚ ‚) UG ) 2.4 mm/s, (- - -) UG ) 6.2 mm/s, and (s) UG ) 21.3 mm/s.

the visual observations at H/W ) 2.25, which is the aspect ratio at which only VF was observed. However, at H/W ) 2.00, a transition from VF and DCTF was apparent when visual results were analyzed. The fact is that, at H/W ) 1.50, a bubble plume that oscillates with very low amplitude (see Figure 3) and frequency is observed at low values of UG, whereas, at higher H/W, the unsteady flow structures increase progressively in number and in velocity of movement also at low values of UG. Therefore, the G-UG plot and drift flux analyses are unable to determine transitions between flow regimes when highly unsteady flow structures exist. Special care should be taken when analyzing the flow transitions that are occurring at partially aerated bubble columns by means of these two methods. According to the description of the characteristic shape of the G-UG plot described previously, the conclusions that can be obtained in view of Figure 7 could be erroneous if visual

observations are not considered, because the dispersed bubble flow regime is not visually observed, although the initial portion of the G-UG plot can lead one to consider otherwise. In addition to the flow regimes identified through the analysis of the G-UG curves, the effect of the aspect ratio on the global gas holdup can be analyzed. According to our results, and as observed visually, as the coalesced bubble flow regime (as VF or DCTF) is established for all aspect ratios (UG g 14.7 mm/ s), increasing H/W produces an increase in the values of G. These experimental results are in agreement with previously published results that report changes on G with H/W in the coalesced bubble flow region for values of H and W lower than a minimum value (see Ruzicka et al.4 for a review). However, most of these reports show an increase in G with increasing values of the column diameter, height, and aspect ratio in the coalesced bubble flow regime, although the opposite tendency

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has also been observed for narrow bubble columns.4 This discrepancy can be related to the fact that changes in H/W imply, in this work, changes in the instantaneous flow structures. Thus, according to our results, the existence of several moving circulation cells (VF) favors the holdup of the gas phase, whereas the existence of two symmetrical pseudo-steady-state vortices (DCTF) enhances the acceleration of the central high voidage region to the top of the liquid surface. The increase of G with H/W when the bubble column is operating in the coalesced bubble flow regime is not so clearly observed for lower values of UG, as a result of the different shapes of the curves obtained for different aspect ratios. However, for H/W ) 1.25 and 1.50, it seems clear that the gas holdup that corresponds to the SCBF and transition regions is higher than the values obtained for higher H/W operating under coalesced bubble flow conditions. This means that the existence of SCBF and VF results in higher values of the gas holdup (G). The variation of G with UG and the drift flux analysis do not provide information on the unsteady structures. Therefore, to confirm the previously presented results, and to obtain quantitative information on the unsteady flow structures, further analyses are needed. 3.3. Spectral Analysis. The use of the spectral analysis to characterize gas-liquid flows inside bubble columns provides a very useful way of determining the existence of a particular flow regime,11,28,31,32,34 as well as the presence of physical phenomena that occur periodically.17,20,24 This method consists of the transformation of the pressure time series from the time domain to the frequency domain. The analysis of the resulting spectra and related parameters can lead to the determination of peak frequencies that are characteristic of a particular flow pattern. The transformation of the pressure time series to the frequency domain is based on the calculation of the discrete Fourier transform (DFT), which is defined as

DFTx(f) )

(

1 N-1

∑ px(tn)e(-i2πft /N) n

N n)0

{

2, if H/W ) 1.25 3, if H/W ) 1.50 for n ) 0, ..., N - 1, x ) l 6, if H/W ) 2.25

)

(3)

where f is the frequency, N the number of elements of the pressure time series, and t the time. The power spectral density function (PSDF), from which information about the peaks can be obtained, is calculated as

PSDFx(f) )

1 (DFTx(f))(DFT*x(f)) Fs

( {


)

(4)

where Fs is the sample frequency and DFT* is the complex conjugate of DFT. According to Drahosˇ et al.,28 the peaks of interest in bubble columns are those situated at frequencies up to 20 Hz. Thus, pressure time series are taken at a frequency of 50 Hz filtered with a low pass filter, at a cut-off frequency of 20 Hz. Each pressure time series contains 30 000 points, which is an adequate number to maintain a low statistical error.17 The

average frequency of the resulting spectra can provide valuable information on the flow patterns in a bubble column.32,34 Its calculation is based on the integration of the first- and zeroorder moments of the PSDF from 0 Hz to 20 Hz:

( {


∫020 f × PSDFx(f) df (fh) ) ∫020 PSDFx(f) df x

)

(5) Among the characteristic peaks situated between 0 Hz and 20 Hz, in this work, the peak situated at frequencies of

Influence of Aspect Ratio and Superficial Gas Velocity on the Evolution

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