Structure evolution and demarcation of small and large bubbles in

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Thermodynamics, Transport, and Fluid Mechanics

Structure evolution and demarcation of small and large bubbles in bubble columns Chao Han, Xiaoping Guan, and Ning Yang Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 04 Jun 2018 Downloaded from http://pubs.acs.org on June 4, 2018

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Industrial & Engineering Chemistry Research

Structure evolution and demarcation of small and large bubbles in bubble columns Chao Han a,b, Xiaoping Guan b, Ning Yang b* a b

School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China

State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China *Corresponding author: [email protected]

ABSTRACT Large bubbles and small bubbles represent two competing dominant structures in bubble columns. Understanding the structure evolution is of great significance in physical modeling. Dynamic gas disengagement (DGD) and dual conductivity probe (DCP) methods were applied to demarcate large and small bubbles. While the number-based BSD only presents a single peak, the dual peaks could only be found from the volume-based BSD. The demarcation method based on the holdup ratio of the two bubble groups proves more reasonable to reflect the intrinsic nature of bubble structure. A sharp change of gas holdup was detected for the uniform distributor. The difference in gas holdup structure of coarse and uniform distributors was contributed mainly by small bubbles at homogeneous regime, yet by large bubbles at transition and heterogeneous regimes. However, the coexistence of small and large bubbles is the intrinsic nature, and the effect of gas distributor is marginal in heterogeneous regime.

Key Words: bubble column, mesoscale, bubble size distribution, gas-liquid flow, dynamic gas disengagement, dual conductivity probe.

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Plate A Coarse distributor Plate B Fine distributor

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Critical Bubble Diameter dc (cm)

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Superficial gas velocity Ug (cm/s)


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1. INTRODUCTION Bubble columns have been widely used in petrochemical, biochemical and environmental processes in view of their simple structure, easy maintenance, low operation cost and good heat and mass transfer performance1-3. Knowledge of gas holdup, bubble size distribution, flow structure and flow regime is important for understanding mixing, mass and heat transfer, and hence design, optimization and operation of bubble column reactors. Although a large amount of knowledge has been accumulated from the experimental measurements on different gas-liquid or gas-liquid-solid systems, the comprehension on dominant mechanisms governing the heterogeneous flow structure is limited. On the other hand, computational fluid dynamic (CFD) simulation is sensitive to various sub-models on drag, lift, bubble-induced turbulence or kernel functions for bubble coalescence and breakage, as the meso-scale structure and physics is hardly reflected in these sub-models or closure equations, though the behavior of single bubble or the global parameters of multiphase systems can be measured. A better understanding of the meso-scale structures and dominant mechanisms is therefore in the study of flow regime transition or development of sub-models for CFD simulation. In literature, the coexisting small bubbles and large bubbles have been corroborated as the dominant structures in bubble columns. However, it is still challenging to analyze the underlying mechanisms behind the two bubble groups. The dynamic gas disengagement (DGD) method, first proposed by Srirma and Mann4, provides a reasonable way to tell the difference of the movement tendencies of the two kinds of bubbles. When the gas-liquid flow in a bubble column reaches quasi-steady state, the gas source is suddenly shut down and the remaining gas bubbles in the column then escapes out of the column with different speeds. As large bubbles move faster than small bubbles, the gas holdup of large and small bubbles can be easily detected by recording the dynamic height of gas-liquid dispersion with time or the variation of pressure drop. There are several assumptions in the DGD method: (1) there is no bubble breakup or coalescence during gas disengagement; (2) Bubbles ACS Paragon Plus Environment

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are assumed to be in a state of uniform distribution along axial direction before cutting off gas source; (3) the interactions between different bubble classes are neglected during gas disengagement4. Krishna et al.5, 6 employed the DGD method to study the large-bubble and small-bubble holdup for different column diameters, static liquid height and solid content in slurry bubble columns. They reported that the large-bubble holdup was related to liquid viscosity and solid concentration, but not influenced by column diameter and initial liquid level height. Furthermore, in the heterogeneous regime, the small-bubble holdup did not change with superficial gas velocity, but decreased with increasing solid content. Xing et al.7 analyzed the effect of liquid viscosity by using the DGD method and CFD and population balance model(PBM). They found that liquid viscosity did not affect the total, small-bubble and large-bubble holdup in low viscosity. But for high viscosity, the total and small-bubble holdup decreased with increasing viscosity. Lim et al.8 analyzed the holdup structure of different bubbles in viscous slurry bubble columns of lower surface tension. The gas was found to be composed of three kinds of bubbles, i.e., large, small and fine bubbles. The fine bubbles were detected by simultaneously employing static pressure drop and DGD methods. The size of small bubbles were usually less than 10 mm in the above DGD measurements9. Recently, Basha and Moris10 used an iterative energy balance algorithm and DGD method to give bubble size distribution and Sauter bubble diameter in a slurry bubble column. On the other hand, many hydrodynamics models were established on the basis of the two-bubbles concept. Shah et al.11 introduced a two-bubble-class model, which assumed that there were two bubble sizes in heterogeneous regime and only small bubbles in homogeneous regime. Davies et al.12 summarized the correlations of diameter and volume fraction of small bubbles. Krishna et al.13 distinguished the slurry bubble column systems into a dense phase containing the slurry phase in which small bubbles were finely dispersed, and a dilute phase containing the fast rising large bubbles. The dense phase behaved like the complete mixing flow, whereas the dilute phase behaved like plug flow. Correlations of gas holdup and rising velocities of the


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two phases were then developed. They also applied the two-bubbles concept into the three-fluid CFD simulation of slurry systems14. Jiang et al.15 analyzed the various two-bubble-classes (TBC) models in literature, and proposed further a reactor model to calculate the axial distribution of gas holdup and component in Fischer-Tropsch synthesis based on the dual-bubble-size (DBS) model. The DBS model was proposed by Yang et al.16 based on the Energy-Minimization Multi-scale (EMMS) approach17. The model was based on the compromise of two dominant mechanisms, i.e., a liquid-dominant regime in which small bubbles prevail and tends to circulate with liquid, and a gas-dominant regime in which large bubbles govern and disengage from liquid. It is mathematically formulated as a stability condition, i.e., the minimization of the sum of two energy consumptions, providing another physical constraint to the complex gas-liquid systems in addition to the conservation equations of mass and momentum. The conceptual model can capture a jump change of total gas holdup and interpret the regime transition from a more fundamental perspective. It also captured the dual effects of viscosity and surface tension on regime transition18. A drag model and a new mesoscale constraint were proposed to CFD-PBM simulation19-23. These experimental or CFD studies actually differentiate the two bubble classes in terms of movement tendencies, rather than pure geometrical sizes. Some researchers combined the DGD method with other measurement techniques to obtain more detailed bubble characteristics in bubble columns, such as local gas holdup, bubble size distribution and critical bubble size to demarcate large bubbles and small bubbles. Jin et al.24 and Hashemi et al.25 measured the local gas holdup in slurry stirred tanks or bubble columns by using electrical resistance tomography (ERT) and DGD. Fransolet et al.26 applied DGD and ERT methods to distinguish the different bubble groups in non-Newtonian fluids. Jin et al.27 employed dual-electrical resistivity probe(DRP) to measure the bubble chord length distribution, and then combined DRP with DGD method to determine the critical bubble size demarcating large and small bubbles in slurry bubble column systems. The critical size was determined based on the discriminant criterion that the gas holdup of small bubbles or large bubbles



measured by DRP should be identical to the counterparts measured by DGD. However, the critical bubble size in Jin et al.27 was obtained in terms of bubble chord length. Since different size of bubbles may be identified with the same chord length by DRP, the chord length may not represent a characteristic parameter. In addition, Jin et al.27 used the one-point data measured by DRP and the large-bubble and small-bubble holdup obtained by DGD to determine the critical size. Actually bubble size distribution may be non-uniform along radial direction. It is acknowledged that large bubbles tend to be in column center, and small bubbles distributes near walls. It is more reasonable to employ the cross-sectional area-averaged data of electrical conductive probe since the DGD method is also based on global hydrodynamics. Furthermore, it may also be important to evaluate different discriminant criteria in determining the critical bubble size.. This paper used dynamic gas disengagement (DGD) and dual conductivity probe (DCP) methods to investigate the bubbles structure in a bubble column. The bubble chord length distribution(CLD) measured by DCP was transformed into the bubble equivalent diameter distribution in seven radial positions following the method of Guan et al.28. The variation of bubble shape was considered in the transformation without the assumption of fixed bubble aspect ratio. The feasibility of this method in heterogeneous regime is relevant to the shape correlation. The shape correlation and the obtained BSD was validated in a square bubble column by high speed camera at about Ug = 0.8 cm/s in Guan et al.28. Then the cross-section area-averaged bubble diameter distribution was obtained, and finally the critical bubble diameter demarcating large and small bubbles was given. The large and small bubbles holdup, bubble size distribution and the critical bubble size under different superficial gas velocities were investigated, and the effects of gas distributor were examined. The measured data can provide benchmark for future CFD simulations.

2. EXPERIMENTS


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2.1 Experimental setups The schematic drawing of the experimental apparatus is illustrated in Figure 1. The bubble column made of Plexiglas was 15 cm in diameter and 200 cm in height, and operated in a semi-batch mode. Fresh tap water was used as liquid phase, and air as gas phase. All experiment runs were performed at superficial gas velocities ranging from 1 cm/s to 25 cm/s with two different perforated plate gas distributors. Plate A (a coarse distributor) has 76 holes of 1.5 mm diameter. The triangular pitch distance was 15 mm and the open area was 0.73%. Plate B (a fine distributor) has 206 holes of 0.5 mm diameter and open area 0.23%, distributed along seven circular rings of 10 mm apart.

1-reactor, 2- dual-tip conductivity probe (DCP), 3-measuring instrument, 4-computer, 5-computer, 6- differential pressure gauge, 7-flange, 8-flow meter, 9-buffer tank, 10-air compressor, 11-gas distributor, 12-silicone soft tube

Figure 1. Experimental setups Bubble size was measured by means of a dual-tip conductivity probe (DCP) 29-31. The axial distance between the two tips was about 1.55 mm. The probe was positioned at a distance 0.8 m above the gas distributor, and radially mounted at r/R=0, ±0.27, ±0.58 or ±0.8. The sampling frequency was 20 kHz and the sampling time was 100 s. The DGD method was applied to measure the holdup of large and small bubbles



under the same superficial gas velocities. The pressure drop variation during gas disengagement were measured by a differential pressure transducer,and the distance between the two pressure taps 80 cm. The data were recorded in a period of 30 s with the sampling frequency 100 Hz. Figure 2 illustrates the image of DGD process taken by a high-speed camera. Clearly observed is the separation of the slow-rising smaller bubbles and fast-rising larger bubbles. When almost all the fast-rising larger bubbles just rushed out of liquid, the small bubbles started to rise slowly. At lower superficial gas velocity (Ug=5 cm/s), the group of slow-rising bubbles contains only spherical smaller bubbles. For higher superficial gas velocity (Ug= 23 cm/s, the slow-rising bubbles group contains not only spherical small bubbles, but some larger ellipsoid bubbles.

Faster rising bubble group

Slower rising bubble group (a)

Faster rising bubble group

Slower rising bubble group (b)

Figure 2. Image of DGD process for Plate B (a): Ug = 5cm/s, (b) Ug = 23 cm/s 2.2 Gas holdup measurement Figure 3 depicts the gas holdup disengagement curve for Plate A at Ug=6 cm/s. The original experimental data shown in Figure 3(a) fluctuated greatly even at lower ACS Paragon Plus Environment

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superficial gas velocity when liquid turbulence was not very intense. Both the Butterwoth filter and the average filter were applied to reduce the data noise, as shown in Figure 3(b). The time series of the two filters was quite similar. Since the average filter may smooth out some useful and important signals such as the inflection point of disengagement curve demarcating small and large bubbles, the Butterworth filter was used for all the data treatment. The large-bubbles and small-bubbles holdups were then calculated by analyzing the different tendencies of curve slope change. 0.30 (a) 0.25

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Figure 3. Gas holdup disengagement curve for Plate A at Ug = 6 cm/s: (a) original data, (b) filtered data 2.3 Bubble size measurement The rise velocity of individual bubble: ACS Paragon Plus Environment


Ubi =

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s t 0i

(1)

where s is the axial distance between the two tips, t0i is the time lag of each bubble passing through the distance. The chord length li for each bubble is: li = Ubi * tchord

(2)

where tchord denotes the time while a bubble contacts with the probe. More details about the bubble size measurement can be referred to Guan et al.28. We compared the data of single-point (r/R = 0.58) and cross-sectional area to acquire the critical bubble chord length. It can be determined by comparing the DGD measurement of different bubble groups with the counterparts obtained from the bubble size distribution of DCP measurement. There are three discriminant conditions in terms of small-bubbles holdup, large-bubbles holdup or the holdup ratio of small-bubbles to large-bubbles:

fS, DCP = fS, DGD

(3)

fL, DCP = fL, DGD

(4)

fS, DCP fS, DGD = fL, DCP fS, DGD

(5)

where fS,DGD and fL,DGD denote the holdup of small bubbles or large bubbles obtained from DGD. The local gas holdup of DCP was the ratio of the total time while the probe contacted with bubbles to the total sampling time: ∞

∑t fDCP =

chord

0

ttotal

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where ttotal is the total sampling time. fS,DCP and fL,DCP can then be calculated by artificially specifying a trial value of the critical time tc,chord, and summarizing the time smaller or larger than tc,chord.


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tc , chord

fBS, DCP =

∑t

chord

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ttotal

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∞

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∑t

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ttotal

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Then the corresponding trial value of critical chord length was calculated from

lc = tc, chord × Ub

(9)

where Ub is the average bubble rise velocity and can be calculated from the ratio of superficial gas velocity and total gas holdup obtained from the DCP measurement. Finally, the critical bubble chord length was determined by comparing the DGD and DCP data for small-bubbles holdup or large-bubbles holdup, and herein the three different discriminant conditions were applied:

dc = d ( fS, DCP = dc = d ( fL , DCP =

dc = d ( ffLS,DCP ,DCP

fS, DGD )

fL , DGD )

=

fS,DGD ) fL ,DGD

(10) (11) (12)

Theoretically the critical size determined by the small-bubbles holdup should be the same with that of the large-bubbles holdup. But the total gas holdup measured by DGD might be different from the local gas holdup of DCP. We then compare the critical chord length in the following sections. Moreover, since the bubble diameter is more representative of bubble size than the chord length, the chord length by DCP was transformed into an equivalent bubble diameter distribution at each radial position28 in this work, and the area-averaged bubble diameter distribution P(d) was then obtained. Hence, the ratio of small-bubble holdup to total gas holdup can be calculated from:



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dc

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3. Results and discussion 3.1 Demarcating small and large bubbles by DGD method Figure 4(a) shows the total gas holdup, small-bubbles holdup and large-bubbles holdup obtained by DGD for the bubble column with the coarse gas distributor Plate A. The flow regime can be classified into three zones in terms of the increasing tendency of total gas holdup as a function of superficial gas velocity: homogeneous regime(0-5 cm/s), transition regime(5-11 cm/s) and heterogeneous regime (>11 cm/s) 32

. In the homogeneous regime, the total gas holdup increases linearly and the

two-phase flow was dominated by small bubbles. The proportion of large bubbles was very small. In the transitional flow, the increase of total gas holdup slows down due to bubble coalescence. The large-bubble holdup increases rapidly with superficial gas velocity, and the small-bubbles holdup slightly decreases. In the heterogeneous flow, the increase rate of total gas holdup and large-bubbles holdup slowed down, and the holdup of small bubbles was almost constant. Similar regime demarcation has been reported in previous researchers 18,32-36. Figure 4(b) shows the total gas holdup, small-bubbles holdup and large-bubbles holdup obtained by DGD for the bubble column with the fine distributor Plate B . At the homogeneous regime, there was no separation of large and small bubbles. The flow was dominated by small bubbles, and the flow dominated by single bubbles could be kept to a higher superficial gas velocity 6 cm/s with higher gas holdup. Beyond the homogeneous regime, there was a sharp change in the total, small-bubbles and large-bubbles gas holdup. This sharp change has been predicted by the DBS model of Yang et al.16,18 based on the EMMS approach. In the DBS model, the sharp change of total gas holdup


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corresponded to the jump change of the point of global minimum of the sum of two energy consumptions (stability condition) within the space of structure model parameters. The model therefore provided a physical interpretation of the macroscale regime transition from a mesoscale perspective. The DBS model was only a conceptual model without considering the effects of boundary conditions and gas distributors. However, the jump change of gas holdup is usually dampened to a gradual or smooth variation when using some non-uniform gas distributors. In this sense, the model may reflect some intrinsic nature of the gas-liquid systems. As illustrated in Figure 4(a)-4(b), the significant difference between the two plates was the abrupt variation for the coarse distributor (Plate A) and the gradual transition for the fine distributor (Plate B). Although the total gas holdup increased gradually, there was significant difference in the small-bubbles and the large-bubbles holdup. Figure 4(b) showed a sharp decrease in small-bubbles holdup and a sharp increase in large-bubbles holdup. Similar sharp change was reported by Guo et al

37

for nitrogen-ethanol solutions. There was also a sharp change at the end of homogeneous regime, and the higher the ethanol concentration, the more obvious the peak was. The addition of ethanol strongly inhibited bubble coalescence and the system was dominated by small bubbles in homogeneous regime. With increasing the gas flow rate, the excess gas tended to exist in the form of more and more small bubbles. At a critical state, the single bubbles-dominated state was broken. In this study, as the hole diameter of Plate B(0.5 mm) was much smaller than that of Plate A(1.5 mm) and the hole number (200) of Plate B was much greater, this homogenous gas distributor could also be regarded as an inhibitor for bubble coalescence. Mudde et al.38 reported also the sharp change when using needle spargers and contaminated water.



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Figure 4. Gas holdup data obtained by DGD (a):Plate A, (b):Plate B Figure 5 compares the total, large-bubbles and small-bubbles holdup of the two gas distributors. The total gas holdup of Plate B was greater than that of Plate A for all superficial gas velocities. Camarasa et al39 and Zahradnik et al40 reported that in homogeneous flow, uniform gas distributors cause less bubble coalescence. As large bubbles moved faster than small bubbles, the holdup of Plate B was larger than that of Plate A. It should be noted that, the difference of total gas holdup between the two distributors was contributed by small bubbles in the homogeneous regime, and large bubbles beyond the homogeneous regime. Furthermore, the gas holdup of total, small and large bubbles tended to be constant in the heterogeneous regime, suggesting that the liquid capacity for accommodating gas or the “solubility” attains its saturating state. After reaching that state at higher superficial gas velocity, this intrinsic nature of two-bubble-group structure would not be affected by gas distributors. 0.4

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Figure 5. Effect of gas distributor on gas holdup:(a) total gas holdup,(b) small-bubbles holdup, (c) large-bubbles holdup Figure 6 compares the ratio of small-bubbles or large-bubbles holdup to the total gas holdup. For Plate A, the small-bubbles ratio increased with superficial gas velocity in homogeneous regime. The rooms for large bubbles were rather limited, and most of the excess gas exists in the form of small bubbles when increasing gas flow rate. While in the transition regime, the ratio of large bubbles increased and more large-bubbles could be accommodated. For Plate B, all the bubbles exist in the form of small bubbles in homogeneous regime. In transition regime, as the system has “dissolved” more small bubbles than it could bear, the system was not stable. The “over-saturated” small bubbles suddenly coalesce into large bubbles at a critical flow rate. In heterogeneous regime, the structure of two groups of bubbles tends to be stable for both the gas distributors. In this sense, the coexisting of large and small bubbles should be the intrinsic property of gas-liquid two-phase flow systems, and the distributors (boundary conditions) may serve as external factors. The ratio of smallbubble holdup to the total gas holdup can be correlated as:

fS, DGD = 0.651 + 0.074*Ug fDGD

(14)

for the coarse distributor Plate A and superficial gas velocity lower than 5 cm/s, and

fS, DGD = 1.445 − 0.106*Ug + 0.510*Ug 2 − 0.882*Ug 3 fDGD

(15)

for the coarse distributor Plate A and superficial gas velocity larger than 5 cm/s, and fS, DGD =1 fDGD


(16)


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for the fine distributor Plate B and superficial gas velocity lower than 5 cm/s, and

fS, DGD = 0.913 − 0.043*Ug + 0.285*Ug 2 − 0.707 *Ug 3 fDGD

(17)

for the fine distributor Plate B and superficial gas velocity larger than 5 cm/s. fs,DGD/fDGD fL,DGD/fDGD

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Figure 6. Ratio of small-bubbles or large-bubbles holdup to total gas holdup obtained by DGD measurement: (a)Plate A, (b)Plate B

3.2 Bubble size distribution obtained by DCP Figure 7 compares the BSD of bubble columns when using the two different distributors. The BSD for the two distributors was remarkably different at the homogeneous regime. In contrast to the prevalence of small bubbles for Plate B, the bubble distribution for Plate A was wider. With further increasing superficial gas velocity, the two BSD curves became closer, and finally merged together in heterogeneous regime. The BSD would not be affected by gas distributors. At lower superficial gas velocities, the gas holdup was smaller and bubbles have less probability to interactive with each other, and the coalescence frequency of two small bubbles is also lower. In this case, the structure of bubbles of different size was strongly affected by gas distributors. With the increase of superficial gas velocity, more and more bubbles tend to interactive with each other through breakage or coalescence, and the effect of gas distributors becomes marginal.


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3.0

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Figure 7. Number-based bubble size distribution (a)Ug = 1 cm/s (b) Ug= 6 cm/s (c) Ug = 10 cm/s (d) Ug = 14 cm/s However, it is still difficult to demarcate the large or small bubbles through the continuous variation of the BSD curves in Figure 7 and reveal the dominant mechanisms relevant to two representative groups of bubbles. Figure 8 depicts the bubble size distribution based on bubble volume fraction for Plate A and Plate B in various flow regimes. Two peaks appear for almost all the cases except the homogeneous flow of Plate B in which small bubbles dominated. Hence the volume-based BSD is more of significance in the study of two-bubbles structure.



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1.5

Ug = 1 cm/s 0.4

Ug = 6 cm/s

0.2

1.0

Ug = 6 cm/s 0.5

0.1

0.0

0.0 0

2

4

0

6

2

4

0.6

0.6

(c)

Plate B Transition flow

(d)

Plate A Transition flow

0.5

0.5

Ug = 7 cm/s

Ug = 7 cm/s 0.4

0.4

Ug = 9 cm/s

0.3

Ug = 9 cm/s Ug = 11 cm/s

-1

PDF (cm )

Ug = 11 cm/s

-1

PDF (cm )

6

d (cm)

d (cm)

0.2 0.1

0.3 0.2 0.1

0.0

0.0 0

2

4

6

0

2

4

d (cm) 0.6

(e)

6

d (cm) 0.6

Plate A Heterogeneous flow

0.5

Plate B Heterogeneous flow

(f) 0.5

Ug = 14 cm/s

Ug = 14 cm/s

Ug = 19 cm/s

0.4

PDF (cm )

Ug = 23 cm/s

-1

0.3

Ug = 19 cm/s

0.4

Ug = 23 cm/s

-1

PDF (cm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.2 0.1

0.3 0.2 0.1

0.0

0.0

0

2

4

6

0

d (cm)

2

4

6

d (cm)

Figure. 8 Volume-based bubble size distribution of Plate A and Plate B Figure 9 presents the Sauter mean bubble diameter (d32) obtained by the DCP measurement. This figure indicates that for Plate A, d32 was almost stable in homogeneous and transition regimes (about 1.7 cm), and then decreased a little at heterogeneous regime. For Plate B, d32 increased rapidly to 1.7 cm in homogeneous flow, and kept almost unchanged after that. Schafer et al41 pointed out that the increase in superficial gas velocity enlarges the bubble collision frequency, leading to a higher coalescence rate and thereby increasing Sauter mean diameter. In this study, we found that the more-uniform gas distributor (Plate B) did influence the Sauter


Page 19 of 31

diameter. In this case, it looks like that the coalescence tendency or the so-called coalescence potential was accumulated while the coalescence of smaller bubbles did not occur at homogeneous regime, despite the increase in superficial gas velocity. At heterogeneous regime, the breakage and coalescence events may occur more frequently and randomly, but the coalescence potential may not be large. This implies that some thermodynamic constraint may be required in the modeling of kernel functions of bubble breakage or coalescence. Recently we developed an EMMS-based PBM16,42, using the stability condition to provide a closure for population balance equations. 2.0

Plate A Plate B

Sauter Mean Diameter d32 (cm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.5

1.0

0.5 0

5

10

15

20

25


Figure 9. Effect of gas distributors on Sauter mean diameter d32 3.3 Critical Bubble Size Jin et al27 calculated the critical bubble chord length by comparing the large-bubbles and small-bubbles holdup obtained from DRP and DGD measurements. The DRP measurement was performed for the point at r/R = 0.5, and either small-bubbles holdup or large-bubbles holdup was calculated from the BSD curves by specifying a trial value of the critical bubble size. In this pater, we compared the three kinds of demarcating methods, as shown in Equations (10)-(12). The DCP measurements was performed for seven points along radial directions to obtain the cross-sectional average holdup. Figure 10(a) compares the critical bubble chord length of Plate A obtained from



the three demarcating methods. At superficial gas velocities ranging from 1 cm/s to 8 cm/s, the critical chord lengths demarcated by the large-bubbles holdup and the ratio are quite similar. There are no data points for the demarcation using small-bubble holdup at lower Ug as the small-bubbles holdup obtained from DGD measurement was always larger than that of DCP for all the trial value of critical bubble size, as shown in Figure 10(b). Beyond Ug = 8 cm/s the difference of the three methods becomes larger. This is due to the difference of the total gas holdup obtained by the pressure drop in DGD and the local gas holdup measured by DCP, as shown in Figure 10(b). Figure 10(c) compares the critical chord length and the critical diameter for the ratio method. The variation tendency of the two parameters was similar. The critical chord length was smaller than the critical diameter at the homogeneous regime. Beyond that regime, the two parameters were similar. Since the total gas holdup measured by the two methods (pressure drop and DCP) could hardly be the same, the ratio-demarcation method should be more suitable and eliminate this difference. 5.0

Critical Bubble Chord Length lc (cm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 31

fS,DCP=fS,DGD

4.5

(a)

fL,DCP=fL,DGD

4.0

fs,DCP/fL,DCP=fs,DGD/fL,DGD

3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

5

10

15

20



25

Page 21 of 31

0.35

(b) Local gas holudup using DCP Global gas holdup using pressure drop

0.30

Gas Holdup

0.25 0.20 0.15 0.10 0.05 0.00 0

5

10

15

20

25

Superficial gas velocity Ug (cm/s) 5.0

(c)

4.5

Critical Bubble Size (cm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


lc fs,DCP/fL,DCP=fs,DGD/fL,DGD dc fs,DCP/fL,DCP=fs,DGD/fL,DGD

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

5

10

15

20

25


Figure 10. Demarcating small and large bubbles for Plate A (one point DCP measurement): (a) Critical bubble chord length (b) Gas holdup (c) Critical bubble size in chord length or diameter Figure 11(a) compares the critical bubble chord length calculated from the three demarcation methods for Plate B. The differences in critical chord length were also caused by the difference in global and local gas holdups, as shown in Figure 11(b). Figure 11(c) compares the critical bubble chord length and the critical bubble diameter by using the ratio-based method. The critical diameter was larger than the critical chord length at transition flow, and the two parameters were basically the same at heterogeneous regime. There were no data points for superficial gas velocity



less than 6 cm/s as the small-bubbles or large-bubbles holdup measured from DGD and DCP could not be identical. The variation of critical bubble diameter was much smaller, in contrast to the larger variation of the critical chord length of Plate B. Both the two parameters vary a lot for the coarse distributor (Plate A), as shown in Figure 10(c). Since the effect of gas distributor is almost eliminated in the uniform distributor, the critical bubble diameter is more reasonable to demarcate the small bubbles and large bubbles, reflecting the intrinsic nature of two-phase flow.


5.0

(a)

4.5

fS,DCP=fS,DGD

4.0

fL,DCP=fL,DGD

3.5


3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

5

10

15

20

25

Superficial gas velocityUg (cm/s) 0.35

(b)

Local gas holudup using DCP Global gas holdup using pressure drop

0.30 0.25

Gas Holdup

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 31

0.20 0.15 0.10 0.05 0.00 0

5

10

15

20



25

Page 23 of 31

5.0

lc fs,DCP/fL,DCP=fs,DGD/fL,DGD

(c)

4.5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


dc fs,DCP/fL,DCP=fs,DGD/fL,DGD

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

5

10

15

20

25


Figure 11. Demarcating small and large bubbles for Plate B (one point DCP measurement): (a) Critical bubble chord length (b) Gas holdup (c) Critical bubble size in chord length or diameter To reduce the difference in gas holdup, we then used the gas holdup of cross-sectional area averaged from the measurement at seven radial locations r/R=0, ±0.27, ±0.58 and ±0.8. Figure 12(a) compares the critical bubble chord length of Plate A using the three methods. Now the difference of the three methods becomes smaller except for the data at 8 cm/s, which is also due to the difference of global and local gas holdup shown in Figure 12(b). Figure 12(c) indicated that the critical bubble diameter was larger than the critical bubble chord length at homogeneous and transition regimes, and the trend reversed at heterogeneous regime.




5.0

fS,DCP=fS,DGD

(a)

4.5

fL,DCP=fL,DGD

4.0


3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

5

10

15

20

25

Superficial gas velocityUg (cm/s) 0.35

(b) Cross-sectional average gas holdup using DCP Global gas holdup using pressure drop

0.30

Gas Holdup

0.25 0.20 0.15 0.10 0.05 0.00 0

5

10

15

20

25


(c)

4.5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 31


4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

5

10

15

20

25


Figure 12. Demarcating small and large bubbles for Plate A (cross-sectional area averaged DCP measurement): (a) Critical bubble chord length (b) Gas holdup (c) Critical bubble size in chord length or diameter


Page 25 of 31

Figure 13(a) compares the

critical chord length of Plate B using the three

demarcating methods mentioned above. The critical chord length under the same superficial gas velocities is similar except for Ug = 14 cm/s. The difference in the global gas holdup of DGD and the cross-section area holdup of DCP was larger, as shown in Figure 13(b). Figure 13(c) indicated that the critical bubble diameter was larger than the critical bubble chord length at homogeneous and transition regimes, and the two parameters become closer at heterogeneous regime. The difference of the critical chord length and the critical diameter is remarkable for homogeneous and transition regimes. The critical diameter varies little and may therefore be used to demarcate the large bubbles and small bubbles more reasonably, and revealing the intrinsic nature of the flow structure composed of two types of dominant bubbles.


5.0

fS,DCP=fS,DGD

(a)

4.5

fL,DCP=fL,DGD

4.0


3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

5

10

15

20

25


(b) Cross-sectional average gas holdup using DRP Global gas holdup using pressure drop

0.30 0.25

Gas Holdup

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.20 0.15 0.10 0.05 0.00 0

5

10

15

20



25


5.0

(c)


4.5


4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

5

10

15

20

25


Figure 13. Demarcating small and large bubbles for Plate B(cross-sectional area averaged DCP measurement): (a) Critical bubble chord length (b) Gas holdup (c) Critical bubble size in chord length or diameter The critical bubble diameter of the two plates is finally depicted in Figure 14. The critical bubble diameter of Plate A increases rapidly from 2 cm to 4 cm in homogeneous regime. It decreases sharply in the transition regime.and finally approaches 2 cm, in heterogeneous regime, at which the difference between Plate A and Plate B disappears. 5.0

Plate A Plate B

4.5

Critical Bubble Diameter dc (cm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 31

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

5

10

15

20

25


Figure 14. Critical bubble diameter for two gas distributors


Page 27 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4. CONCLUSION By using DGD, a sharp change is detected for uniform gas distributor (Plate B) for the total gas holdup, small-bubbles holdup and large-bubbles holdup when increasing superficial gas velocity, whereas the change of flow structure is gradual for the coarse distributor (Plate A). This sharp change has been theoretically predicted by the Dual-Bubble-Size (DBS) model based on the EMMS approach in our previous work. The uniform gas distributor may serve as an inhibitor for bubble coalescence at homogeneous regime to maintain the small bubbles-dominant state, but the coalescence tendency or potential may be accumulated even though the coalescence frequency is small, implying the missing mechanisms in current model developments on kernel functions of coalescence and breakage in population balance modeling. Coalescence occurs when reaching the critical state and large bubbles start to intervene the flow. However, the coexistence of small bubbles and large bubbles is the intrinsic nature of the gas-liquid flow in bubble columns, and the gas distributor affects the structure at homogeneous and transition regimes, and the effect is marginal in heterogeneous regime. The difference of total gas holdup between the two distributors was contributed primarily by small bubbles in homogeneous flow, yet by large bubbles in transition and heterogeneous regimes. By using DCP, the bubble size distribution is detected. The number-based BSD only presents a single peak, whereas the dual peaks relevant to the two bubble groups could only be found from the volume-based bubble size distribution. The ratio-based method is recommended to identify the critical bubble size as it eliminates the measurement difference of DGD and DCP. Compared with the critical bubble chord length, the critical bubble diameter can more reasonably demarcate the large bubbles and small bubbles, revealing the intrinsic nature of the flow structure composed of two types of dominant bubbles.



ACKNOWLEDGMENT Financial support from National Key Research and Development Program of China (2017YFB0602500) and National Natural Science Foundation of China (Grant No. 91634203) and Chinese Academy of Sciences (Grant No. 122111KYSB20150003) are acknowledged.

NOMENCLATURE d

bubble diameter [ cm ]

d32

Sauter mean diameter [ cm ]

dc

critical bubble diameter [ cm ]

f

total gas holdup [ - ]

fL,DGD

large bubble gas holdup obtained by DGD method [ - ]

fL,DCP

large bubble gas holdup obtained by DCP method [ - ]

fS,DGD

small bubble gas holdup obtained by DGD method [ - ]

fS,DCP

small bubble gas holdup obtained by DCP method [ - ]

l

bubble chord length [ cm ]

lc

critical bubble chord length [ cm ]

P(d)

area-averaged bubble diameter distribution [ cm-1 ]

tchord

bubble pass through the probe time [ s ]

ttotal

total sampling time [ s ]

Ub

average bubble rise velocity [ cm/s ]

Ug

superficial gas velocity [ cm/s ]

SUBSCRIPTS


Page 28 of 31

Page 29 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


b

bubble phase

g

gas phase

L,DGD

large bubble of DGD method

L,DCP

small bubble of DCP method

S,DGD

small bubble of DGD method

S,DCP

small bubble of DCP method

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Structure evolution and demarcation of small and large bubbles in

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