ARTICLE pubs.acs.org/IECR
Determination of Liquid Multiscale Circulation Structure in a Bubble Column by Tracing the Liquid Flowing Trajectory Zi-Bin Huang and Zhen-Min Cheng* State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, P. R. China ABSTRACT: To identify the liquid circulation flow structure in a bubble column, a set of multipoint tracer injection and detection device was developed for a systematic study in a bubble column of 550 cm in height and 50 cm in diameter. Tracer response profiles were measured to track the liquid flowing trajectory under various flow conditions in the column with and without draft tubes. They showed that only when the draft tube length was greater than 3 m could the tracer response exhibit obvious periodicity. To resolve the liquid circulation flow structure in the time and frequency domain, wavelet multiresolution analysis was adopted. The results showed that the liquid circulation frequency increased with superficial gas velocity, which is in agreement with the published literature. It was also found that the macroscale, mesoscale, and microscale circulation loops coexisted in the bubble column.
1. INTRODUCTION As one of the most fundamental and important fluid dynamic properties of a bubble column, liquid circulation has been considered only as a phenomenon caused by the nonuniform gas holdup radial profile. During the last 40 years, liquid circulations in bubble columns are mainly considered as a global circulation cell that comprises an upward flow in the column core and a downward flow near the wall.13 Instead of the single global circulation assumption, Joshi and Sharma4 proposed a circulation structure consisting of multiple stationary cells in the axial direction with the cell height equal to the column diameter. In their subsequent work,5,6 Joshi further assumed that the adjacent cells were interacting and pointed out that the circulation cell structure was instantaneous, which did not remain stationary in space and time. Dudukovic7 emphasized that these interacting multiple circulation cells were indeed a single circulation cell with a number of secondary cells within it. Zehner8 reported a multiple circulation cell structure as an alternative to that of Joshi and Sharma, in which stationary cylindrical eddies were layered transversely above each other. From these works, it is conceivable that these multiple circulations are essentially mesoscale loops whose size is equal to the column diameter. Different from the above viewpoints, Chen et al.9 reported that at greater liquid depths in a 2-D bubble column the multiple circulation cell structure did not appear. The pattern they observed was that of two staggered rows of circulation vortexes, which were similar to the Karman vortex street. Dudukovic and co-workers10 concluded from measurement of liquid velocities by using the computer automated radioactive particle tracking facility that only two scales of circulation loops existed in the bubble column at low gas velocities, the larger of which encompassed nearly the whole column, while the smaller one spread over the entry region. By employing an optical technique and pressure fluctuation analysis, Groen et al.11 observed the presence of one largescale overall liquid circulation rather than those distinct circulation cells in the bubble column. More detailed descriptions on the liquid circulation in a bubble column were also reported; e.g., Franz et al.12 measured r 2011 American Chemical Society
the instantaneous axial, tangential, and radial liquid velocities in a 3-D bubble column by applying hot-film anemometry and revealed the existence of a circulation structure that comprises a helical upward flow in the center and a downflow region close to the wall. From a great deal of comprehensive work, Fan and co-workers1316 observed through flow visualization and particle image velocimetry that when the global circulation flow occurs in the system, there are four distinct flow regions, namely, the central plume region, the fast bubble flow region, the vertical flow region, and the descending flow region. In fact, these four flow regions are characterized by a regular macroscale circulation loop of the liquid, in which mesoscale circulation loops on different scales are assumed to superimpose upon it. Apart from the above work, the understanding of liquid circulation structure in a bubble column has been mainly based on a liquid velocity profile,1721 although a few studies were based upon tracer response; e.g., Schweitzer and Kressmann22 measured the liquid residence time distribution using argon-41 as a radioactive tracer to characterize the hydrodynamics of a benchscale ebullated bed reactor with a liquid recycle pump. However, although several radioactive detectors were placed downstream to detect the response of a pulse injection, the tracer was only injected in the liquid inlet pipe rather than in the column; therefore, liquid circulation information about the inside of the column is not available. Since circulation means periodicity, if there is a circulation loop in the column, a liquid tracer injected into the system at any position in the column will be detected in a periodic manner. In this regard, we developed a multiple-point tracer injection and detection device that could inject the liquid tracer into the system at various positions along the wall of the column and detect the tracer response above or below the injection point, so that the liquid flow trajectory could be tracked Received: April 20, 2011 Accepted: September 19, 2011 Revised: September 14, 2011 Published: September 19, 2011 11843
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Figure 2. Bubble column (1) without a draft tube and with a draft tube of (2) 2 m, (3) 3 m, and (4) 4 m.
Figure 1. Schematic diagram of the experimental setup: (1) N2 cylinder, (2) KCl tracer container, (3) electromagnetic valve, (4) liquid inlet, (5a5f) tracer injection positions, (6A6D) tracer sampling ports, (7) gas distributor, (8) gas inlet, (9) liquid turbine flow meter, (10) liquid pump, (11) gas turbine flow meter, (12) data acquisition system, (13) computer, and (14) liquid outlet.
2. EXPERIMENTAL SECTION The experimental work was conducted in a Plexiglas column of 50 cm in diameter and 550 cm in height, as shown in Figure 1. The gas distributor was placed at the bottom of the column, which consisting of 85 stainless steel bubble cap tubes of 4 mm in diameter. Both the air and water were flowing upward through the gas distributor to the bottom of the column after being metered with turbine flow meters. The superficial liquid velocity was fixed at 0.75 cm s1 while the superficial gas velocity was varied from 1.5 to 13.6 cm s1, which covers the flow regime of uniform bubbling flow and churn turbulent flow. In view of the large volume of the system and the high static water pressure at the bottom of the column, 2500 mL of aqueous potassium chloride tracer solution of 20 wt % in concentration was contained in a small tracer container, which was pressurized. When the system had reached steady state, the tracer solution was injected into the system as an impulse within 3 s by highpressure nitrogen of 1.0 MPa through the switch of an electromagnetic valve. As depicted in Figure 1, six pulse injections for the tracer were provided, where two of them were located at the bottom (5a) and at the top (5f), while the other four were located at 0.9, 1.8, 3.0, 3.9 m above the gas distributor, denoted as 5b, 5c, 5d and 5e, respectively. Correspondingly, one of the response sensors was placed at the outlet (6D) of the column, while the other three probes were located 0.3 m (6A), 2.2 m (6B), and 3.6 m (6C) from the gas distributor, respectively. Once the liquid tracer was injected into the column, four sets of conductivity probes and corresponding conductivity meters would be simultaneously employed to monitor the electrical
conductivity values of the potassium chloride tracer upstream or downstream of some injection point. To avoid problems of conductivity measurement due to air bubbles, liquid samples were withdrawn continuously at each detecting point from the column to a small gasliquid separator, where the entrained gas bubbles were disengaged from the liquid, which then flowed over the probe tips.23 The response signals of all sensors were then amplified and transmitted to a computer by a data acquisition system that would be converted into corresponding concentration signals of the liquid tracer.24,25 In order to eliminate small-scale circulation loops from the large ones, draft tubes with different lengths were installed coaxially into the column. Since the axial liquid velocity profile has an inversion point at a dimensionless radius of 0.7,2628 we chose this ratio, which is 35 cm, as the diameter of the draft tubes to minimize the impact of the internal on the liquid axial flow pattern in the column. The validity of our choice on draft tube diameter has been verified by the literature report. For instance, Freedman and Davidson29 found the draft tube did not influence the gas holdup data in a bubble column with the same distributor. Bernemann30 used an anemometer technique and found, although, that the average flow pattern of the liquid phase in a bubble column was different with and without internals. However, the inversion point (static liquid flow) between the positive and negative liquid velocities in the radial profile was maintained at about the same dimensionless radius of 0.7.31 The draft tube positions and the sampling probe locations in the column are shown in Figure 2. Table 1 summarizes the operating conditions of the total 27 tracer experiments with and without draft tubes in the present work.
3. WAVELET ANALYSIS OF RESPONSE SIGNALS As a newly developed timefrequency analysis method, the wavelet transform has been shown to be a powerful tool in signal analysis and processing. Compared with the traditional Fourier transform, the wavelet transform is well-suited for treatment of data involving transient or nonstationary processes owing to its localization properties in both the time and frequency domains.32 According to the theory of multiresolution analysis,33,34 it is possible to decompose any probe response signal x(t) into an 11844
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Table 1. Operating Conditions for the Tracer Experiment experiment no.
uL
uG
tracer injection
length of
(cm s1) (cm s1) position (see Figure 1) draft tube (m)
1
0.75
1.5
5f
0
2
0.75
4.5
5f
0
3
0.75
7.5
5f
0
4
0.75
13.6
5f
0
5
0.75
1.5
5d
0
6
0.75
4.5
5d
0
7 8
0.75 0.75
7.5 13.6
5d 5d
0 0
9
0.75
1.5
5a
0
10
0.75
4.5
5a
0
11
0.75
7.5
5a
0
12
0.75
13.6
5a
0
13
0.75
7.5
5b
0
14
0.75
7.5
5c
0
15 16
0.75 0.75
7.5 1.5
5e 5f
0 2
17
0.75
4.5
5f
2
18
0.75
7.5
5f
2
19
0.75
13.6
5f
2
20
0.75
1.5
5f
3
21
0.75
4.5
5f
3
22
0.75
7.5
5f
3
23 24
0.75 0.75
13.6 1.5
5f 5f
3 4
25
0.75
4.5
5f
4
26
0.75
7.5
5f
4
27
0.75
13.6
5f
4
∑ Dj ðtÞ
j¼1
ð7Þ
ð8Þ j ¼ 1, 2, :::, J
ð9Þ
where fs is the sampling frequency. On the basis of the above analysis, the fourth-order Daubechies’ wavelet (db4) was used as the wavelet function to carry out multiresolution analysis on the probe response signals. In this study, five detailed subsignals and five approximated subsignals were obtained from each tracer concentration signal under different flow conditions, which help to explore the liquid multiscale circulation structure in the time and frequency domains.
4. RESULTS AND DISCUSSION 4.1. Tracer Study on Liquid Circulation Flow without a Draft Tube. 4.1.1. Tracer Injection at the Top of the Column.
ð1Þ
AJ ðtÞ ¼
∑k aJ, kϕJ, k ðtÞ
ð2Þ
Dj ðtÞ ¼
∑k dj, k ψj, kðtÞ
ð3Þ
where aJ,k and dj,k are the approximate and detail coefficients, respectively, which are expressed as Z xðtÞ ϕJ, k ðtÞ dt ð4Þ aJ, k ¼ ÆxðtÞ, ϕJ, k ðtÞæ ¼ Z xðtÞ ψj, k ðtÞ dt
ψj, k ðtÞ ¼ 2j=2 ψð2j t kÞ
Dj ðtÞ : ½2ðj þ 1Þ f s, 2j f s
where J is the maximum level of wavelet transform. The approximation subsignal AJ(t) and the detail subsignal Dj(t) are written as
dj, k ¼ ÆxðtÞ, ψj, k ðtÞæ ¼
ð6Þ
Aj ðtÞ : ½0, 2ðj þ 1Þ f s
xðtÞ≈A1 ðtÞ þ D1 ðtÞ ¼ A2 ðtÞ þ D2 ðtÞ þ D1 ðtÞ J
ϕj, k ðtÞ ¼ 2j=2 ϕð2j t kÞ
where the time translation parameter k = 1, 2, ..., N/2j and the scaling parameter j = 1, 2, ..., J. It should be noted that Aj+1(t) is smoother than Aj(t), since the finer feature Dj+1(t) in Aj(t) is subtracted in order to get Aj+1(t). At each level j, the approximated and detailed components lying with a frequency band is given by
ordered set of orthogonal signal components at different scales. Namely, the original discrete tracer response signal x(t) (t = 1, 2, ..., N) can be expressed approximately as the summation of the approximations and the details in a multistep manner
¼ ::: ¼ AJ ðtÞ þ
The base functions ϕj,k(t) and ψj,k(t) are produced by dilations and translations of the orthogonal father wavelet function ϕ(t) and mother wavelet function ψ(t) as follows
ð5Þ
Figure 3 shows that the liquid tracer was first detected by probe D because it was located at the outlet of the system, which was closest to the tracer injection point. Afterward, the probes C and B monitored the liquid tracer in sequence. While probe A, despite being located at the bottom of the column, still detected the tracer concentration signal in a short time. In all the cases, the tracer was detected in less than 20 s, as shown in Table 2. From the respond time of probe A and the distance (5.2 m) between the tracer injection and detection position, we can calculate that the moving velocity of the tracer was from 0.29 to 0.61 m s1. According to diffusion theory, we know that it is impossible for the tracer to move upstream at such a large velocity only by molecular diffusion; therefore, the tracer could only be carried downward by an actual large-scale recirculation flow in the column. In other words, there exists a liquid macroscale circulation loop that can span the entire column. Surprisingly, it was found, even under uniform bubbling flow condition, that probe A located at the bottom of the column could also detect the tracer signal in a short time, as shown in Figure 3(1) and Table 2, which should be impossible since the liquid is thought to be in plug flow. It means that under the uniform liquid flowing condition there also exists a macroscale liquid circulation loop in the column. Such an observation is just on the contrary to the results reported in a number of studies3537 but is consistent with the findings of Hills38 and other workers.39,40 This may be due low gas flow rates; although the flow is uniform, the rising gas bubbles may move upward not in a straight line but in a spiral manner41 or in a meandering way,42,43 which will also carry liquid upward in their wakes, thus inducing the convective circulation flow of liquid. It should be noted that the motion of 11845
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Figure 3. Tracer response curves without a draft tube for injection at the top of the column.
Table 2. Response Time of the Four Probes at Various Superficial Gas Velocities for the Tracer Injected at the Top of the Column without a Draft Tube (time unit s) uG (cm s1)
probe A
probe B
1.5
18.1
10.7
7.6
3.2
4.5
15.7
8.3
6.3
3.2
7.5 13.6
10.5 8.5
7.2 6.3
6 5.3
3.1 3.1
probe C
probe D
liquid circulation flow under this condition is not vigorous and the liquid circulation velocity is much slower compared with that under the churn turbulent flow regime. 4.1.2. Tracer Injection at the Middle of the Column. As shown in Figure 4, it is clear that both probes A and D could detect the tracer in a short time, which further confirms that there is a liquid macroscale circulation loop in the bubble column under both bubbly and churn turbulent flow regimes. It can be seen from Figure 4 that the liquid tracer is monitored by probes B, C, and D in nearly the same time but is always detected later by probe A. Moreover, the response signal at position D has a lower concentration peak value in comparison with that in Figure 3. When the tracer was added into the column, a part of tracer would be carried downward along the column wall by the descending liquid, whereas others entrained in the column core region from the action of mesoscale circulation loops would be carried upward by rising gas bubbles. Naturally, the tracer will be diluted due to mixing when it reaches the exit of the column. In addition, the liquid circulation rising velocity in the column core region is
higher than the liquid descending velocity near the wall under the same operating condition, so the tracer is always detected last by probe A. 4.1.3. Tracer Injection at the Bottom of the Column. Figure 5 shows that the liquid tracer is first monitored by probe A and is detected subsequently by probes BD under both bubbly and churn turbulent flow regimes. It is apparent that the response signal detected by probe A exhibits a pronounced perturbation compared with the other cases, which could be explained from the very complicated flow field in the column bottom caused by the changing of the liquid flowing direction from vertical to transversal. By comparing Figures 35, it is clear that each response curve demonstrates the obvious long tail phenomenon under both bubbly and churn turbulent flow conditions, which implies the liquid flow pattern in the bubble column is analogues to backmixing flow. 4.2. Tracer Study on Liquid Circulation Flow with Draft Tubes. In the following section, the liquid tracer was injected only at the top of the column. 4.2.1. Tracer Experiments with Draft Tubes of 2 and 3 m. Compared with the empty bubble column, it is observed from Figure 6 that when a draft tube with a length of 2 m was installed in the upper part of the column, the tracer response profile at position D shows an obvious oscillating characteristic, while the oscillations at other positions are less pronounced. The two distinctive peaks at position D means the tracer was detected to pass this position at two subsequent times. The first time is at the beginning of tracer input, when the tracer was carried to the liquid outlet position D; the second time is at a period afterward when the tracer was recycled back around the draft 11846
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Figure 4. Tracer response curves without a draft tube for injection at the middle of the column.
tube. The clear distinction of the two peaks is due to the introduction of the draft tube, which has suppressed the mesoscale radial flow of liquid in the draft-tube region. Therefore, when the tracer was injected into the system from the topmost of the column, it could only flow downward along the annulus between the draft tube and the wall. Accordingly, the tracer responses at positions B and A, where there is no draft tube at the bottom, have no periodic behavior. To further study the filtering effect of the draft tube on small scale loops, a longer draft tube of 3 m in length was introduced into the system. As shown in Figure 7, the tracer responses measured at positions D, C, and B exhibited obvious oscillating behavior, unlike that for the one at position A. This could be explained by their locations in the column. It is known that positions C and B are in the draft tube region; therefore, the mesoscale circulation loops at the two positions could be blocked. At position A, where it is beyond the length of the draft tube, the liquid flow contains different scales of loops and will have relatively unclear oscillation performance. 4.2.2. Liquid Flowing Trajectory with Draft Tube of 4 m. When the draft tube was extended to 4 m, it could occupy a major length of the column. As shown in Figure 8(1), the tracer profiles have shown apparent perturbations even in the homogeneous regime; however, the order of the tracer being detected by probes A and B is different from that in Figure 3(1) in the empty bubble column. This is probably because the liquid radial flow in the column has been restricted to a much larger degree in the presence of a draft tube as long as 4 m. In addition, pronounced periodic wave peaks were observed in Figure 8(3) and 8(4) compared with that in Figures 6 and 7 in the heterogeneous flow
regime. It can also be seen that the magnitude of the first peak is always larger than the second for probe D, which is located at the outlet of the bubble column. However, such a situation is not always true for the other three probes (probes AC), which are located at the bottom and middle of the column. By comparing tracer response signals of the four probes with and without draft tubes, it clearly appears that the periodic response signals are getting more and more obvious with the length of introduced draft tube. On the other hand, these periodic signals are only limited to the first 120 s of the sampling data. This means that the introduction of a draft tube does restrict liquid mesoscale circulation loops to some extent; however, it cannot restrict all meso- and microscale circulation loops completely, especially for those within the draft tube and at the top and bottom region of the column. In addition, the motion of the tracer circulation flow is not vigorous due to the lower gas velocity under bubbly flow and transient flow regime. Therefore, the strictly single macroscale recirculation flow does not exist in the system. Even in the case with draft tube of 4 m, the micro- and mesoscale circulation loops may coexist in the bubble column. Consequently, not all the tracer injected into the system will circulate along the draft tube, and the magnitude of the first peak is not always larger than the second for probes AC, whose sampling locations are within the bubble column. 4.3. Wavelet Analysis and Discussion. 4.3.1. Wavelet Transform on Response Signals. For the sake of comparison, the sampling data in the first 120 s was used in wavelet transformation, and each subsignal is plotted on the same scale of coordinates as the original response signal. From Figure 9 it can be seen that the shape of each low-frequency level is similar to the original signal 11847
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Figure 5. Tracer response curves without a draft tube for injection at the bottom of the column.
Figure 6. Tracer responses with the draft tube of 2 m for injection at the top of the column.
Figure 7. Tracer responses with the draft tube of 3 m for injection at the top of the column.
S, and there is almost no evident sudden changes in the detail coefficients, which means that no obvious periodic waves were observed in the original response signal. However, it is evident from Figure 10 that more than one peak appear in the original tracer response signal S when the 4 m draft tube is inserted into the column. Through comparison of approximation coefficients and detail coefficients in Figure 10, it is seen that the multiple-peak characteristics in the original signal S are mainly decomposed into the levels 5 and 4 of high-frequency components from the corresponding low-frequency components a4 and a3. The low-frequency subsignal of level 5 a5 in Figure 10
nearly has no apparent local periodic peaks and is basically similar with that in Figure 9 under no draft tube condition. By comparing Figures 9 and 10, it clearly appears that no obvious periodic phenomenon is observed in the original response signals under the situation of no internal draft tubes in the bubble column, and no evident sudden changes occur in the lowand high-frequency components of the corresponding wavelet decomposition. When the draft tubes are introduced, liquid circulation flow phenomena in the column begin to appear, apparently due to the liquid radial flow being suppressed, especially in the case of the longest draft tube of 4 m. 11848
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Figure 8. Tracer responses with the draft tube of 4 m for injection at the top of the column.
Figure 9. Wavelet decomposition of signal at probe B without a draft tube (uL = 0.75 cm s1, uG = 7.5 cm s1).
4.3.2. Liquid Circulation Loop Frequency. According to the sampling frequency of 2 Hz in this paper, the magnitude of the approximate frequency band of Aj(t) and Dj(t) is summarized in Table 3.
On the basis of the experimental results and wavelet analysis of response signals, the liquid circulation frequency associated with draft tube of different lengths could be calculated, as illustrated in Figure 11. It shows that the liquid circulation frequency increases 11849
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Figure 10. Wavelet decomposition of signal at probe B when the 4 m draft tube is installed (uL = 0.75 cm s1, uG = 7.5 cm s1).
Table 3. Frequency Bands of Subband Signals at Various Levels approximation
A1(t)
A2(t)
A3(t)
A4(t)
A5(t)
frequency band (Hz)
00.5
00.25
00.125
00.0625
00.03125
detail
D1(t)
D2(t)
D3(t)
D4(t)
D5(t)
frequency band (Hz)
0.51
0.250.5
0.1250.25
0.06250.125
0.031250.0625
Figure 11. Effect of superficial gas velocity on circulation loop frequency.
with the superficial gas velocity, which is in agreement with the finding of Buwa and Ranade.44 On the other hand, the liquid circulation frequency tends to increase with a decrease of the length of the draft tube. It is also found that the macroscale circulation loop frequency is about 0.07 Hz, corresponding to the case in which the tracer
was injected from the top of the column with the draft tube of 4 m. This value agrees well with the result of wavelet multiscale decomposition shown in Figure 10 and Table 3. In Figure 10, the periodic features of the original tracer response signals were mainly decomposed into the high-frequency components on levels 4 and 5, which correspond to a frequency band of 0.0625 0.125 and of 0.031250.0625 Hz, respectively. Similar results were obtained for other cases under different operating conditions in our experiments. It should be pointed out that the liquid circulation frequency may be changed with the variation of column dimensions, since the maximum size of the macroscale circulation loop depends on the column diameter and column height. Low-frequency oscillations corresponding to liquid local circulation flow were reported with frequencies less than 1.0 Hz by Buwa and Ranade.44 However, these values were calculated using a power spectral density function from wall pressure fluctuation measurements, which was different from our experimental technique and analytical method. 4.4. The Liquid Multiscale Circulation Structure in the Bubble Column. From the above experimental investigation and analysis, we can see that if the macroscale circulation loop does not exist in the column, the tracer injected into the system from the topmost of the column will not be detected by the probe A, which is located at the bottom of the column. However, this hypothesis conflicts with the experimental results under both bubbly and churn turbulent flow conditions in this work. If there 11850
dx.doi.org/10.1021/ie200859q |Ind. Eng. Chem. Res. 2011, 50, 11843–11852
Industrial & Engineering Chemistry Research is only the macroscale circulation loop in the column but there are no mesoscale circulation loops with different sizes, similar results for experiments with and without draft tubes of different lengths should be achieved. Nevertheless, a clear difference among response signals in various operating conditions was observed. If only the macroscale and the mesoscale circulation loops with low cycle frequency exist in the column but the microscale circulation does not exist, the obviously periodic characteristic of response signals should not be only focused on the first 100 s after the tracer was injected into the system under different operating conditions. However, this assumption contradicts the experimental observation. Therefore, we can draw the conclusion that liquid multiscale circulation loops exist in the bubble column. The system is superposed by three parts, viz., the macroscale regular circulation loop which encompasses the entire column, the microscale fluctuation circulation loops where liquid phase mixing occurs on the microscopic level, and the mesoscale irregular circulation loops whose size is between the above two. Furthermore, the countless microscale fluctuation loops and the irregular mesoscale circulation loops are dynamically superimposed on the macroscale regular circulation loop structure. The large scale circulation loops contain small scale circulation loops that also include smaller scale loops, and there are interactions between these circulation loops of different scales, which make the gas liquid flow structure in the bubble column rather complex.
5. CONCLUSIONS In contrast to most previous studies, which were based on liquid velocity profiles, the present paper provided an experimental demonstration on liquid circulation flow structure in a pilot plant scale bubble column by tracing and monitoring the liquid flowing trajectory. First, the existence of a liquid macroscale circulation loop under turbulent flow regime was confirmed experimentally by tracking the trajectory of liquid flow in the column. In addition, the work supplied an experimental proof that the liquid also has a macroscale circulation flow behavior in the bubble column, even in the bubbly flow regime. For further illustration of liquid circulation flow structure in an effort to purify the tracer response so that the small scales of liquid circulation could be separated from the large ones, three draft tubes with different lengths were introduced into the column. It was found that the periodic features of liquid circulation flow in the bubble column were reflected from the response signal in the presence of the draft tube. Besides, the longer the draft tube, the more obvious the periodic feature of the response signal, which means a more significant periodicity of the liquid flow, which implies the removal of the various mesoscale circulation loops with a wide distribution in the column. Finally, in view of the transient, nonstationary characteristics of response signals obtained in the experiments, wavelet multiresolution analysis was adopted to help understand the liquid circulation flow structure from time and frequency domains. The results indicate that there exist not only macroscale regular circulation loops, which encompass the whole column, but also various mesoscale circulation loops with a wide size distribution and countless microscale ones in the column. In addition, the microscale fluctuation loops and the mesoscale irregular circulation loops are dynamically superimposed on the macroscale regular circulation loop structure.
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’ ACKNOWLEDGMENT This work was carried out under support from Natural Science Foundation of China through Grant No.20876043 and No. 21076072. ’ SYMBOLS aJ,k = approximate coefficient of level J Aj(t) = approximation subsignal of level j dj,k = detail coefficient of level j Dj(t) = detail subsignal of level j db4 = the fourth-order Daubechies’ wavelet function E(t) = E-curves (s1) fs = sampling frequency (Hz) N = number of data points S = original signal in Figures 9 and 10 t = time (s) uG = superficial gas velocity (cm s1) uL = superficial liquid velocity (cm s1) x(t) = original discrete tracer response signal ’ GREEK LETTERS ϕ(t) = father wavelet function ϕj,k(t) = dilated father wavelet function ψ(t) = mother wavelet function ψj,k(t) = dilated mother wavelet function ’ SUBSCRIPTS G = gas phase j = multiresolution level J = the maximum level of wavelet transform k = time translation parameter L = liquid phase ’ REFERENCES (1) De Nevers, N. Bubble driven fluid circulations. AIChE J. 1968, 14, 222–226. (2) Rice, R. G.; Geary, N. W. Prediction of liquid circulation in viscous bubble columns. AIChE J. 1990, 36, 1339–1348. (3) Joshi, J. B. Computational flow modelling and design of bubble column reactors. Chem. Eng. Sci. 2001, 56, 5893–5933. (4) Joshi, J. B.; Sharma, M. M. A circulation cell model for bubble columns. Trans. Inst. Chem. Eng. 1979, 57, 244–251. (5) Joshi, J. B. Axial mixing in multiphase contactors-a unified correlation. Trans. Inst. Chem. Eng. 1980, 58, 155–165. (6) Joshi, J. B. Comments on flow mapping in bubble columns using CARPT. Chem. Eng. Sci. 1992, 47, 508–509. (7) Dudukovic, M. P.; Devanathan, N; Moslemian, D. Authors’ reply to comments by J. B. Joshi. Chem. Eng. Sci. 1992, 47, 509–510. (8) Zehner, P. Momentum, mass and heat transfer in bubble columns. Int. Chem. Eng. 1986, 26, 22–35. (9) Chen, J. J. J.; Jamialahmadi, M; Li, S. M. Effect of liquid depth on circulation in bubble columns: A visual study. Trans. Inst. Chem. Eng. 1989, 67, 203–207. (10) Devanathan, N; Moslemian, D; Dudukovic, M. P. Flow mapping in bubble columns using CARPT. Chem. Eng. Sci. 1990, 45, 2285– 2291. 11851
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