Investigation into Bubble Size Distribution and Transient Evolution in

May 18, 2009 - Republic of China, and Department of Chemistry and Chemical Engineering, Weifang UniVersity,. Weifang 261061, People's Republic of Chin...
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Ind. Eng. Chem. Res. 2009, 48, 5824–5832

GENERAL RESEARCH Investigation into Bubble Size Distribution and Transient Evolution in the Sparger Region of Gas-Liquid External Loop Airlift Reactors Changqing Cao,*,† Liangliang Zhao,† Dongyan Xu,† Qijin Geng,†,‡ and Qingjie Guo† College of Chemical Engineering, Qingdao UniVersity of Science and Technology, Qingdao 266042, People’s Republic of China, and Department of Chemistry and Chemical Engineering, Weifang UniVersity, Weifang 261061, People’s Republic of China

It is well-known that the gas sparger can play an important role on the transient evolution of bubbles and bubble size distribution (BSD) in gas-liquid external loop airlift reactors (EL-ALRs). Therefore, the main subject of the present work was to study the influence of sparger design and process parameters on the transient evolution of bubbles and bubble size distribution (BSD) in the sparger region of the considered EL-ALRs. For this purpose, both detailed measurements and prediction of the size of bubbles produced at the sparger were carried out in EL-ALRs with different size and sparger structure parameters. The unique set of BSD curves were obtained by analyzing a large amount of bubbles with a measurement based on an image analysis technique. Additionally, Colella’s model of BSD evolution in bubble columns was further developed by implementing a detailed physical model for predicting the initial BSD at the sparger applied to gas-liquid EL-ALRs where the model input is only based on design/process parameters. A validation of the model was carried out using data from gas-liquid EL-ALRs with different size and sparger design parameters. In order to provide more deep insight for transient evolution of bubbles at the local scale in the sparger region, the computational fluid dynamics (CFD) code Fluent 6.2 was used. The transient evolution of bubbles was simulated in the sparger region of gas-liquid EL-ALR. The simulating results of bubble size are in good agreement at the lower gas velocity with the experimental data in the sparger regions of TU-A and TU-B. With increasing gas flow rate, the difference between simulations and experimental values for bubble size increases. The simulations underestimate bubble size at high gas flow rate. Introduction In chemical engineering operations and practice, gas-liquid contactors are widely used for carrying out reactions and mass transfer operations such as stripping, absorption, and biochemical and petrochemical industrial processes. The presence of a gas phase dispersed in a continuous liquid is the reason why such reactors can provide high interfacial area for mass and heat exchange, good mixing, and high thermal stability. The dispersion of the gas into the column is a critical aspect determining the performance of gas-liquid systems. Small bubbles and a uniform distribution over the cross section of the equipment are desired to maximize the interfacial area and improve transport phenomena. The interfacial mechanisms focusing on coalescence and breakage in three bubble columns (with different L/DR and geometry) were investigated analyzing more than 500 bubbles for each bubble size distribution (BSD) by Colella et al.1 One of the main conclusions of that investigation was that the global hydrodynamics of the three columns is strongly dependent on the gas distributor. Therefore, a correct estimation of the influence of sparger design and process parameters on BSD, which is the subject of the present work, is essential. The formation of bubbles at orifices submerged in a liquid has been the subject of many theoretical and experimental works. The main review publications in this field were presented in * To whom correspondence should be addressed. Tel.: 0086-53284022506. E-mail: [email protected]. † Qingdao University of Science and Technology. ‡ Weifang University.

refs 2-4. In the above cited publications, the research was mainly focused on the bubble formation at a single orifice. As a consequence, the interaction between the neighboring bubbles was hardly investigated. However, Miyahara et al.5 studied experimentally the influence of the distance between the holes and of the number of holes on the bubble diameter in the perforated plates measuring bubbles at 25 and 45 cm from the sparger in a column 70 cm high. They concluded that the volume of the gas chamber does not influence the bubble diameter when the number of holes of the perforated plate is above ∼15. For conditions in which the gas chamber volume has no effect, decreasing the pitch increases the bubble diameter due to coalescence when the ratio of the pitch to the hole diameter (P/dH) is less than ∼8. The added value of the present work in comparison to the literature is the detailed measurement of bubble sizes close to the sparger (from 0 to 0.32 m) using 800 bubbles for each distribution. The experiments were carried out in different external loop airlift reactors (EL-ALRs) using different perforated ring and perforated plate spargers. The evolution of BSD is investigated as function of height, gas superficial velocity, sparger design (i.e., number of holes, holes’ diameter and pitch), and process parameters (i.e., gas flow rate). From the modeling point of view, Colella’s model of BSD evolution in bubble columns was further developed by implementing a detailed physical model for predicting the initial BSD at the sparger where the model input is only based on design/ process parameters. A validation of the model was carried out using data from EL-ALRs with different size and sparger

10.1021/ie801700s CCC: $40.75  2009 American Chemical Society Published on Web 05/18/2009

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structure parameters. Additionally, in order to provide more deep insight for transient evolution of BSD at the local scale in the sparger region, the transient evolution of BSD was also simulated using computational fluid dynamics (CFD) code Fluent 6.2 in the sparger region of gas-liquid EL-ALR. The simulating results of transient evolution of BSD agreed well with the experimental data. As Gg increases, the difference between simulations and experimental values for bubble size increases. Consequently, the simulations underestimate bubble size at a high gas flow rate. Numerical Models The simulation of the gas-liquid EL-ALRs was performed using the Eulerian-granular model. This approach describes both phases as interpenetrating continua where the local instantaneous equations are averaged in a suitable way to allow coarser grids and longer time-steps being used in numerical simulations. Because of its obvious computational advantage, the Eulerian two-fluid modeling approach has been applied instead of the Euler-Lagrangian approach on the assumption that the gas-liquid flow system has laminar, unsteady flow patterns. 6 Model Establishment. The calculations of BSD were carried out by turbulence of the standard -ε model. It is a two-equation turbulence model based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (ε). The turbulence kinetic energy, k, and its rate of dissipation, ε, are obtained from the following transport equations: k equation µt ∂κ ∂ ∂ ∂ (Fκ) + (Fκui) ) µ+ + G k + Gb ∂t ∂xi ∂xj σκ ∂xj Fε - YM + Sk

[(

) ]

(1)

ε equation µt ∂ε ∂ ∂ ∂ (Fε) + (Fεui) ) µ+ + ∂t ∂xi ∂xj σε ∂xj ε ε2 G1ε (Gk + C3εGb) - C2εF + Sε (2) k k

[(

) ]

where Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients. Gb is the generation of turbulence kinetic energy due to buoyancy. YM represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. C1ε ) 1.44, C2ε ) 1.92, C3ε ) 0.09, σk ) 1.0, and σε ) 1.3. The gas-liquid system consists of a set of continuity and momentum equations for each phase under the Eulerian multiphase model. The continuity equation for gas-liquid phases is ∂ (R F ) + ∇ · (RqFqb V q) ) 0 ∂t q q

P ) p + p' where Ui, ui, and u′i denote instantaneous velocity, time-averaged velocity and fluctuating velocity, respectively. P, p, and p′ are instantaneous pressure, time-averaged pressure, and fluctuating pressure, respectively. Numerical Methods. A commercial CFD code FLUENT 6.2 is used to simulate the local flow properties in EL-ALRs. In order to numerically solve the system of partial and ordinary differential equations presented above, discretion of the equations has been carried out using a finite volume scheme with an algebraic multigrid solver (AMG) as implemented in the CFD code CFX-4.3. The coupling between pressure and velocity is dealt with the SIMPLEC method. The second discretion method is performed to solve each phase velocity weight, local phase hold-up, and turbulent weight. The momentum equation coefficient has been implemented by means of the weighting method. Variables in the cell nodal point are simulated using second wind interpolation. Variables are stored with the center point method. Due to the large dimensions of the flow domain under consideration, the need is for transient and two-dimensional calculations as well as limited computational resources. A very coarse numerical grid had to be implemented with a total number of 36 334 cells. The time step length is chosen as 0.5 s. A typical solver running over 10 s of computed time takes about 100 h to complete on a supercomputer. Calculations always assume fully fluidized state as an initial condition. Convergence is good in all computations presented here, reaching the desired accuracy in 30 or less iterations. The ultimate convergent standard for all equations is no change of the volume fraction in the flow field. Boundary Conditions. In this study, the sparger region (from 0 to 0.32 m) of EL-ALR is taken as the computational domain. The divided network cells are carried out mostly by using heterocomplex rectangular body structure. The surface of inlet gas orifice of gas distributor is using triangle grid, and each surface of orifice is divided 18 grids. In order to divide grid conveniently, the outlet gas orifice is located at 0.01 m. The meshes of three dimension computational model and the gas distributor with orifices are yielded by using GAMBIT software. Due to presence bend phenomenon intensively in EL-ALRs, the wall surface is dealt with nonequilibrium wall function. Boundary conditions in inlet have been adopted by entrance gas superficial velocity (the value is directly transferred on the basis of gas flux). Initial superficial gas velocities (UG0) from 0.08 to 5.10 cm/s are given for the whole simulation. The inlet turbulent kinetic energy (k0) is defined as k0 ) 1.5(uI)2, where u ) uz, I ) 0.16(ReDt)-1/8, and the turbulent kinetic energy dispersed rate (ε0) is defined as ε0 )

2

∑R

q

)1

(4)

q)1

The momentum balance becomes in general formulation

(

Ui ) ui + ui′

(3)

where

)

[(

)

]

∂uk ∂ui ∂ui ∂ui ∂P ∂ + Uk )+ µ + - Fui′u′k + F ∂t ∂xk ∂xi ∂xk ∂xk ∂xi FFi (5)

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Cµ0.75k01.5 0.075Dt

Boundary conditions in the outlet have been used as the pressure outlet. As the outlet position is free interface, the meter pressure (Pm) is assumed to be 0. Experimental Procedure The experiments were carried out in different reactors located in Taishan Mountain Scholar Lab (briefly indicated in the following with the acronym TMSL) and in Tianjin University

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Figure 1. Schematic representation of the experimental airlift reactor: (1) manometer; (2) rotameter; (3) valve; (4) gas sparger; (5) conductivity-meter; (6) A/D converter; (7) computer; (8) riser; (9) downcomer disengagement zone; (10) riser disengagement zone; (11) downcomer; (12) measuring electrodes; (13) tracer injection; (14) conductive probe; (15) junction zone; (16) camera. Table 1. Summary of the Main Experimental Conditions for the Three Different G/L Systems Analyzeda

b

reactor

H (cm)

DR (cm)

h (cm)

Ug (cm/s)

Gg (cm3/s)

TMSL

180 (170)b

15.5 (6.2)b

2.30 2.08

430 62.7

TMSL

378 (353)b

54.5 (17.5)b

0.43 2.82

998 678

TU

250 (250)b

27 (18.5)b

0 4.5 16 0 8 18 0 16 32

0.33 4.90

567 1320

a Operating conditions: ambient temperature, tap water, and air. Refer to the dimensions of the downcomer.

(TU) using different spargers. Figure 1 shows a schematic diagram of the EL-ALR used in this study. The measurements include the evolution of BSD as a function of sparger design (i.e., hole’s diameter, number of holes, distance between the holes) and process parameters (i.e., gas flow rate) and also as a function of height and gas superficial velocity in the sparger region. All the main features of the experiments performed are reported in Table 1. Table 1 summarizes the geometry of the columns, the values of gas flow rate, gas superficial velocity, and the distance from the sparger where the measurements were taken. The gas-liquid system investigated in all these EL-ALRs was air bubbles in tap water. The main features of used spargers and operating conditions for the EL-ALRs are given in Table 2. To determine the regime of bubble formation, the Reynolds number through the hole (Reth) was calculated by means of the average value of the gas velocity through each single orifice

(i.e., overall gas flow rate divided by the number of holes and by the holes area). From the values of Reth reported in Table 2, the bubble formations in TMSL reactors were all in the intermediate regime. And for the TU-B, the bubble formation was also in the intermediate regime except for the TU-B at the highest gas flow rate that was in the jetting regime.7 However, the bubble formations for the TU-A were all in the jetting regime. The images were recorded by a Hitachi camera on an S-VHS cassette and converted into an AVI format file using Adobe Photo Shop. All the details about the image acquiring and the image analysis techniques are reported in the works of Colella et al.1 and Vinci.9 For the purpose of analyzing the growing bubble at the sparger level, the focal plane for the ring spargers was taken on the surface characterized by the sparger itself whereas for the perforated plates the camera was focused on the column vertical axis. For more details about experimental procedure, see the work of Di Stanislao.8 For TMSL and TU airlift reactors, the third dimension of the bubbles was calculated with the assumption that the bubbles are symmetric around the minor axes (i.e., assuming the oblate spheroid shape). Subsequently, the diameter of the sphere with the same volume of the measured ellipsoid and the subdivision into bubble classes were computed as described by Colella et al.1 and Vinci.9 In the case of TU airlift reactors, from the analysis of the pictures, it was observed that the big bubbles, generated from the ring sparger with 1.2 mm hole diameter, were not an oblate spheroid but presented a concave lower surface as illustrated by the pictures of Mattia et al.10 This effect was also observed by Rabiger et al.11 and Schwarzer et al.,12 who used a highspeed camera to analyze the bubble detachment by the sparger. This effect has not been seen in the bubbles generated from the other gas distributors because of their smaller size. Hence, a different hypothesis on the third dimension only for the bubbles produced by the sparger of the airlift reactor was required. It was then supposed that the bubbles had a bell shape. The detailed subdivision into classes is summarized in Table 3. Table 3 shows the range values for each class and experimental apparatus. Results and Discussion Experimental Investigation of Bubble Size at the Sparger. In this section, the main experimental trends as a function of the experimental conditions and apparatus are analyzed in terms of the arithmetic average bubble size. That value gives us a useful compact way to describe the main experimental features. Accordingly, in all the following tables, we will refer only to that value. In particular, the whole picture of the experiments is summarized in Table 4, where for each apparatus and operating condition that average value is reported. From the analysis of the experimental data, the following is concluded. Experimental bubble size distribution is well-

Table 2. Main Features of Used Spargers and Operating Conditions for the Examined EL-ALRs sparger

type

TMSL-A TMSL-B TMSL-C TMSL-D TU-A

perforated perforated perforated perforated perforated

plate plate plate plate ring

TU-B

perforated ring

N

dH (mm)

pitch (mm)

Gg (cm3/s)

Ug (cm/s)

Reth

jε (%)

run

57 43 43 43 86

0.8 0.4 0.4 0.4 0.3

16 24 16 8 9

32

1.2

29

998 430 430 430 567 1320 567 1320

0.43 2.30 2.30 2.30 0.33 4.90 0.33 4.90

606 394 394 394 1385 3224 129 1739

1.0 13 13 13 4.0 9.2 8.4 19.6

1 2 3 4 5 6 7 8

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Table 3. Sketch of the Adopted Discretization of BSD into Bubble Classes (cm) sparger TMSL-A, B, C, D

sparger TU-A

W1 W2 W3 W4 W5 W6 W7 W8 W9

0.00-0.46 0.46-0.62 0.62-0.77 0.77-0.93 0.93-1.08 1.08-1.24 1.24-1.39 1.39-1.55 1.55-1.71

X1 X2 X3 X4 X5 X6 X7 X8 X9

0.00-0.38 0.38-0.52 0.52-0.65 0.65-0.79 0.79-0.92 0.92-1.06 1.06-1.19 1.19-1.33 1.33-1.46

Table 4. Comparison Between Experimental and Calculated Average Bubble Diameter for the Three Different G/L Systems sparger TMSL-A TMSL-B TMSL-C TMSL-D TU-A TU-B

Gg Ug GH dExp dCal (cm3/s) (cm/s) (cm3/s) (cm) (cm) 998 430 430 430 567 1320 567 1320

0.43 2.3 2.3 2.3 0.33 4.9 0.33 4.9

17.5 10 10 10 6.59 15.3 17.7 41.25

0.68 0.81 0.75 0.70 0.49 0.51 0.99 1.11

0.55 0.64 0.64 0.64 0.40 0.42 0.83 0.93

sparger TU-B

∆%

σD

run

18.78 20.70 14.66 8.22 17.59 18.11 16.20 16.05

0.11 0.11 0.12 0.17 6.89 × 10-2 6.78 × 10-2 0.19 0.25

1 2 3 4 5 6 7 8

represented by a log-normal distribution function.13 This description is in agreement with the findings of many other authors.5,14,15 It can be found from Figures 2-4 and Table 4 that gas flow rate and the hole diameter have the same effect on the BSD: the increase of the values of these parameters leads to a shift of the BSD toward larger bubble sizes. In Table 4, calculations were performed using a developed model based on the Geary and Rice model.16 It is proved that the gas

Figure 2. Bubble size distribution measured in TU-A as a function of inlet gas flow rate.

Figure 3. Influence of hole diameter on bubble size distribution at constant gas superficial velocity.

Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9

0.00-0.64 0.64-0.88 0.88-1.12 1.12-1.36 1.36-1.60 1.60-1.83 1.83-2.07 2.07-2.31 2.31-2.55

momentum term is highly significant in gas-liquid systems.16 The normally dominating forces of coalescence and breakup define the bubble size, hence formation dynamics would control ulteriorly. Also, it is shown that the intermediate drag law is more appropriate than Stokes for forming bubbles.16 It can also be seen from Figure 5 and Table 4 for runs 1 and 2 that increasing the number of holes, which results to be the same as decreasing the gas flow rate through the hole, shifts the BSD to smaller classes. The lines in Figure 5 represent spargers A, B, C, and D. Furthermore, from Figure 5 and Table 4 for runs 2-4, when the pitch (distance between the holes) is on the order of magnitude of the bubble diameter, the BSD is clearly sensitive to pitch variations: i.e., as the pitch decreases, the BSD shifts to smaller values. The influences of the pitch and number of holes on the BSD interact. But, the influence of the pitch is prevails when compared to the influence of the number of holes. Figure 6 gives a dimensionless correlation of volumetric mean diameter of bubbles. For values of dimensionless velocity (Nw) less than 14, the dimensionless bubble diameters (dw) are well-

Figure 4. Influence of hole diameter on bubble size distribution at constant gas flow rate through the sparger hole.

Figure 5. Influence of the number of holes and the pitch on bubble size distribution at constant gas superficial velocity in EL-ALRs of TMSL.

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Figure 6. Dimensionless correlation of volumetric mean diameter of bubbles.

Figure 8. Dimensionless correlation of volumetric mean diameter of bubbles.

Figure 9. Comparison between experimental and predicted volumetric mean diameter. Figure 7. Evolution of the bubble size distribution in EL-ALR of TU-A.

estimated with the dimensionless correlation.5 For Nw > 14, it was not possible to consider dw as a constant anymore and then a new dimensionless correlation was carried out to fit the experimental values. As suggested by Miyahara et al.,5 an exponential correlation was used. dw ) 17522Nw0.362

(6)

It is possible to conclude that for a value of Nw > 14 the mean bubble size diameter is well-estimated by correlation 6 as shown in Figure 5. Such a correlation estimates the experimental points with an average error of ∼12%. Figure 7 shows the evolution of the bubble size bubble distribution in TU-A EL-ALRs during run 6 of Table 4. In the sparger region (h/DR ) 0.5), by increasing the distance from the gas distributor at constant gas superficial velocity, the BSD shifts to smaller bubble sizes. When h/DR is greater than 0.8, the bubble diameter decreases rapidly. This trend is the same that was observed far from the sparger by Colella et al.1 It can be found from Figure 8 that the bubble average diameter tends to reach a stable bubble mean diameter of roughly 0.75 cm along the logarithmic distance from the sparger in the air-water system. However, the result of Fair et al.7 in air-water system was roughly 0.5 cm. The breakage rate is faster on increasing gas velocity due to enhancement of bubble-bubble interactions.5 In fact, when increasing the gas superficial velocity, larger bubbles are produced at the sparger but, after a certain distance from the sparger, smaller bubbles can be observed. The influence of the distributor is prevailing up to a distance from the sparger of the order of magnitude of the reactor diameter. Prediction of Bubble Size at the Sparger. A population balance equation model, which computes BSD evolution in

Figure 10. Sensitivity analysis with respect to the parameters of the Geary and Rice model.

bubble columns, was already developed for the airlift reactor by Colella et al.1 However, the input distribution of this model is obtained from measured BSD. Therefore, the main aim of this part of the investigation is exploring the possibilities to simulate an initial size distribution at the sparger for the prediction of BSD evolution in EL-ALRs. As a first step to obtain a description of the evolution of BSD in EL-ALRs without experimental BSD input, a detailed physical model was tested for the prediction of bubble size at the sparger, whose input is based only on design/process parameters. After a review of the main study, both experimental and modeling, for bubble size prediction published in the literature,2,4,5,11,16-19 the Geary and Rice model was chosen and implemented in Fortran code.16 The main reasons for the choice of this model were the following:

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Table 5. Standard Values Adopted for the Sensitivity Analysis Simulations parameter

standard value

unit

R FL µL σ FG Gg dH N

11/16 1000 1.005 × 10-3 72.52 1.21 5.67 × 10-4 1.2 × 10-3 32

(s) (kg/m3) (Pa s) (mN/m) (kg/m3) (m3/s) (m) (s)

Table 6. Discretization into Bubble Classes Adopted for the Simulations with Colella’s Model sparger

TU-B

sparger

TMSL-D

Y1a Y1b Y1c Y1d Y2 Y3 Y4 Y5

0.00-0.24 0.24-0.36 0.36-0.48 0.48-0.64 0.64-0.88 0.88-1.12 1.12-1.36 1.36-1.60

W1a W1b W1c W1d W2 W3 W4 W5 W6 W7

0.00-0.12 0.12-0.24 0.24-0.34 0.34-0.46 0.46-0.62 0.62-0.77 0.77-0.93 0.93-1.08 1.08-1.24 1.24-1.39

• It is one of the most recent models based on the physics of bubble formation. • It is simple and can be easily solved numerically. • It was validated by the authors using independent experimental data.2,20 • It contains no adjustable parameters. Furthermore, the following hypotheses were applied for the simulation of perforated distributors using a model for bubble formation at a single orifice to predict the mean size of the bubbles produced at the sparger: • All the holes are equivalent. • All the holes are independent; i.e., the interaction between the neighbors is neglected. This hypothesis is natural when the distance between the holes is larger than the order of magnitude of the bubble diameter. This is the case for many industrial reactors. • Each hole is bubbling; i.e., the weeping phenomenon is absent. • The gas flow rate through each hole is the same. From the validation of the model, the following is concluded. It can be found from Figure 9 and Table 4 that a detailed comparison between the bubble diameter at the sparger level predicted by the model and experimental data, for all the ELALRs with all the different spargers, shows that the model is reliable since the agreement between experimental and calculated values is always within ∼20%. In Figure 10, from the sensitivity analysis, made with reference values summarized in Table 5, it is found that the model is sensitive to variations of the gas flow rate, the number of holes, the hole diameter, and the gas density. The response of the model to variation of all these parameters is consistent with experimental findings both in the present work and in the literature.2,17,18 The model is not sensitive to the liquid density, the coefficient of virtual mass, the surface tension, and the liquid viscosity in a wide range of variation, as expected from the literature in the studied range of gas flow rates. It is important to notice from Figure 10 that the bubble diameter increases ∼28% with a variation of the gas flow rate. However, the experimental increase from Figure 9 is ∼32%. This can be one of the reasons why the model always underestimates the bubble size at the sparger, as it is evidenced by the data summarized in Table 4. Another reason

Figure 11. Comparison calculated and experimental BSD for TU-B airlift reactor at a certain distance from the sparger and constant gas superficial velocity.

Figure 12. Comparison calculated and experimental BSD for TU-B airlift reactor at a certain distance from the sparger and constant gas superficial velocity.

Figure 13. Comparison calculated and experimental BSD for TMSL-D airlift reactor at a certain distance from the sparger and constant gas superficial velocity.

to explain this underestimation could be the hypothesis that all the holes of the sparger are bubbling at the same time with the same gas flow rate. If this assumption is rigorous only in the average, the actual instantaneous gas flow through the hole could be higher and consequently the bubble size could be bigger.17,18 At this point, the possibility of calculating the BSD using as initial data a physically based model was tested (i.e., no BSD measurements as an input). It was carried out using the Colella model in combination with the Geary and Rice model. BSD is computed/validated using experimental data from the TMSL-D

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Figure 14. Contours of bubble formation.

Figure 15. Comparison of CFD calculated and the experimental technique for estimation of bubble size.

EL-ALR (at the height of 0 cm from the sparger) and the TU-B EL-ALR (at the heights of 16 and 32 cm from the sparger). The experimental data of TMSL EL-ALRs were taken from the work of Colella et al.1 As an initial distribution for the Colella model, an impulse function was used which is based on the mean diameter predicted by the implemented Geary and Rice physical model. The subdivision into bubble classes here considered is reported in Table 6 for both reactors. The comparison between the computed BSD and the measurements for the different spargers is presented in Figures 11-13 where the relative frequency is plotted versus the bubble classes. The results show good agreement with the measurements, which give the possibility of future computation of BSD (study of interfacial

mechanism) for industrial gas-liquid columns where only the sparger design and the process parameters are used in input. Simulation Results for the Transient Evolution of Bubbles. It can be seen obviously from Figure 14 that the border bubbles will coalesce after leaving the orifice and move to the center region of the bed as simulation time is more than 0.4 s. The local circulation motion of the liquid occurrs in the sparger region. The bubbles are disengaged over a certain distance from the spargers and then, driving the liquid, move downward along the wall. It can also be seen from Figure 14 that the bubble region area increased with increasing simulation time. The size of the bubble at 0.45 s is larger than that at 0.35 and 0.40 s. It was considered in this paper that the velocity of the largersized, coalesced bubbles is larger than the initial smaller bubble coalescing velocity. In other words, the driving force for the liquid motion is enhanced. With increasing the distance from the sparger, the bubble breakup and coalescence are concomitant. The larger bubbles can be observed in the certain region from sparger with increasing simulation time. Comparison of Simulation and Experimental Values for Bubble Size. There is a good agreement at the lower gas velocity between the experimental technique for estimation and CFD simulation bubble size in the sparger regions of TU-A and TU-B. As Gg increases, the difference between simulations and experimental values for bubble size increases. Consequently, the simulations underestimate bubble size at high gas flow rate. On the contrary, larger discrepancies appear at the local scale. This may be that local liquid velocity, local gas velocity, and local bubble size predicted with the CFD model are expected

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to be different for a fine grid, while the high density of salt tracers is usually associated with significant deviations of residence and circulation time measurements. In Figure 15, comparisons between the experimental and simulation bubble size values in the sparger region of TU-A and TU-B are reported. These results show that the experimental and CFD computation bubble size agree only at lower gas flow rates, which is in agreement with most of the works that applied CFD to bubble columns up to now. The discrepancies in Figure 15 are considered to be the effect of tracer density and the coarse mesh of the sparger as probably for higher superficial gas velocities. It can be found from Figure 15 that there is a good agreement at the lower gas velocity (smaller than 600 cm3/s) between the experimental technique for estimation and CFD simulation bubble size in the sparger region. The reason for this is that a definite quantity of liquid was contained in the bubble phase for a lower gas flow rate. The two phases of gas and liquid were taken as a continuous medium and take up the same space. This is in accordance with the basic hypothesis of the double fluid model. As gas flow rate is increased, the difference between simulations and experimental values for bubble size increases. Consequently, the simulations underestimate bubble size at high gas flow rate. The reasons are the following: (i) The turbulence formulations are influenced by the accuracy of the CFD. In turbulence formulations, a strongly anisotropic bubble-induced turbulence has been shown to prevail. The k values from CFD computations are probably underestimated. As a consequence, pressure drop is underestimated, which leads to the underestimation of the bubble size at a higher gas flow rate. (ii) The computation results are affected by coarse grids. In this work, a very coarse numerical grid had to be implemented with a total number of 36 334 cells. Time step length is chosen as 0.5 s. (iii) The underevaluation of bubble size is considered the effect of the directional incoherence between grid direction and fluid flow direction for higher superficial gas velocities. (iv) The underevaluation of bubble size is considered to be the effect of tracer density and the coarse mesh of the sparger as probably for higher superficial gas velocities. It also can also be found from Figure 15 that the bubble size is a function of the gas flow rate using different sparger structure parameters. As gas flow rates are smaller than 600 cm3/s, the effect of gas flow rates on bubble size is unconspicuous. Then, a decrease in gradient is noted. As the gas flow rate is increased further, the bubble size increases, with an increasing rate with respect to gas flow rate, suggesting an approach to unbounded runaway growth. At higher gas flow rates, the intermediate decrease in gradient is less apparent. An open question is the influence of turbulence formulations on CFD accuracy, as a homogeneous single-phase turbulence is assumed and a strongly anisotropic bubble-induced turbulence has been shown to prevail. This is a critical point, as pressure drop, and consequently overall liquid circulation, is estimated from the k value. In the same way, local bubble size profiles depend directly on k estimation. As a consequence, a good prediction of turbulent parameters can be achieved only if k from the k-ε model and from the analytical model of Reynolds shear stress agree. The results show that k values from CFD computations are probably underestimated because bubbleinduced turbulence in the normal directions is not taken into account. As a consequence, pressure drop is underestimated, which leads to the underestimation of the bubble size at higher gas flow rates. These results are also demonstrated that

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inadequate turbulent information is mainly responsible for the poor predictive ability of CFD code at a higher gas flow rate. Conclusions (1) To understand the interfacial mechanisms in the sparger region of EL-ALRs, which play an important role in reactor hydrodynamics, detailed sets of data of BSD measurements were investigated using a photographic technique. The BSD measurements were carried out in different EL-ALRs (TMSL and TU) using different spargers. To obtain the BSD curves, about 800 bubbles for each distribution were analyzed. (2) The influence of sparger design and process parameters on BSD was investigated. The evolution of BSD in the reactor height and the influence of the gas superficial velocity were pointed out. As reactor heights of TU-A are between 0 and 8 cm, the bubble mean size is about 1.25 cm. But at a reactor height of 18 cm, the bubble mean size is about 0.71 cm. (3) Furthermore, a model has been implemented which describes bubble formation at an orifice to obtain a reliable evaluation of the size of bubble produced at the sparger. This model is used in combination with the population balance equation model developed by Colella to compute the evolution of BSD in EL-ALRs without experimental BSD input. First calculations of BSD using this model for different size ELALRs show good agreement with experimental measurements. (4) All the experimental data have been compared with simulations obtained using a classical CFD approach. A reasonable agreement is achieved in the low gas flow rate (less than 600 cm3/s). The inaccuracy of simulations at high gas flow rates is shown to be due to the poor estimation of the turbulent parameters. The difference between simulations and experimental values for bubble size is increased. Consequently, the CFD simulations underestimate bubble size at high gas flow rates. Acknowledgment The financial support of this research by the Taishan Mountain Scholar Constructive Engineering Foundation of China (Js200510036), National Natural Science Foundation of China (20676064), and Young Scientist Awarding Foundation of Shandong Province (2006BS08002) is gratefully acknowledged. Nomenclature C1ε ) constant in k-ε model in eq 2 C2ε ) constant in k-ε model in eq 2 C3ε ) constant in k-ε model in eq 2 Cµ ) constant in k-ε model in eq 2 dCal ) calculated average diameter of bubble (cm) dB ) diameter of bubble (cm) dExp ) experimental mean diameter of bubble (cm) dH ) hole diameter (mm) dMC ) mean diameter of classes (cm) DR ) column diameter (cm) dw ) 〈dExp〉{gFL/dHσ}1/3 ) mean diameter (dimensionless) fr ) relative frequency (dimensionless) Fr ) Uth2/(gdH) ) Froude number (dimensionless) g ) gravitational acceleration (m/s2) Gb ) turbulent kinetic energy produced terms by average velocity grads (kg/(m s3)) Gg ) gas flow rate (cm3/s) GH ) gas flow rate through the orifice (cm3/s) Gk ) turbulent kinetic energy produced terms by buoyancy (kg/ (m s3))

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h ) height from the sparger (cm) H ) height of reactor (cm) HLS ) logarithm the distance from the sparger (cm) k ) turbulent kinetic energy (m2/s2) k0 ) initial turbulent kinetic energy (m2/s2) N ) number of holes (dimensionless) Nw ) We/Fr1/2 ) dimensionless velocity (dimensionless) P ) distance between the holes (pitch) (mm) or pressure (Pa) p ) instantaneous pressure (Pa) p′ ) fluctuating pressure (Pa) Pm ) meter pressure (Pa) Reth ) FGUthdH/µG ) Reynolds number through the hole (dimensionless) Sk ) turbulent kinetic energy added term (kg/(m s3)) Sε ) turbulent kinetic energy dissipation rate added term (kg/ (m s4)) t ) time (s) UG ) superficial gas velocity (cm/s) Ui ) instantaneous velocity (cm/s) U0 ) initial superficial gas velocity (cm/s) ui ) time-averaged velocity (cm/s) ui′ ) pulsating velocity (cm/s) Uth ) gas velocity through the hole (cm/s) We ) dHUth2FL/σ ) Weber number (dimensionless) YM ) turbulent kinetic energy dissipation term produced by volume expansion (kg/(m s3)) R ) virtual mass coefficient (dimensionless) Rq ) qth phase holdup (dimensionless) ε ) turbulent kinetic energy dissipation rate (m2/s3) FG ) gas density (kg/m3) FL ) liquid density (kg/m3) σ ) surface tension (N/m) θ ) contact angle (rad) µG ) gas viscosity (Pa s) µL ) liquid viscosity (Pa s) µt ) turbulent viscosity (Pa s) AbbreViations BCs ) bubble classes BSD ) bubble size distribution CFD ) computational fluid dynamics EL-ALR ) external loop airlift reactor RTD ) residence time distribution TMSL ) Taishan Mountain Scholar Lab TU ) Tianjin University

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ReceiVed for reView November 7, 2008 ReVised manuscript receiVed April 16, 2009 Accepted April 21, 2009 IE801700S