Experimental Study and Numerical Simulation of Bubbling Fluidized

Article pubs.acs.org/IECR

Experimental Study and Numerical Simulation of Bubbling Fluidized Beds with Fine Particles in Two and Three Dimensions Zheng Zou,†,‡ Hongzhong Li,*,† Qingshan Zhu,† and Yingce Wang†,‡ †

State Key Laboratory of Multi-phase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, P.O. Box 353, Beijing 100190, P.R. China ‡ Graduate School of Chinese Academy of Science, Beijing 100049, P.R. China S Supporting Information *

ABSTRACT: The present study provides a deeply analysis of the flow behavior of bubbling fluidized beds with fine particles in two- (2D) and three-dimensional (3D) conditions, and computational fluid dynamics (CFD) simulations of agglomerates fluidization are carried out coupled with the modified agglomerate-force balance model, correspondingly. The experimental results indicate that the fluidized bed can be divided into bottom unfluidized, middle ascending fluidized, and upper descending back-mixing sections. The local solids volume fraction value ranges from 0.11 to 0.30, which depends on the interaction between bubble phase (εs = 0−0.04) and emulsion phase (εs = 0.26−0.30). The wall effect appears to be weakened, and the cohesive particles fluidize more uniformly in 3D fluidized beds. The simulations are in reasonable agreement with the experimental findings. However, at the top region of the bed the predicted solids holdup slightly deviates from experimental measurement. The vector plots of computed agglomerates velocity support the central and wall falling down-both sides rising up flow pattern of solids, two core-annular flows exist in the bed, which can be also observed experimentally. numerical simulations of gas and solids flows based on the modified agglomerate-force balance model by using CFD.

1. INTRODUCTION As is known, fine particles often have many intrinsic properties that make them attractive for various industrial applications,1,2 and cohesive powders can be normally fluidized at agglomerates.3 It is significant to analyze and predict the fluidization behavior of cohesive particles for better design and operation of the fluidized beds, which is much more complex but has rarely been reported in the related literature.4,5 The solids volume fraction is always considered as the main parameter for characterizing two-phase flow structures, and a thorough investigation of it would helpful to understand the fluidized bed hydrodynamics and mixing behaviors.6 Compared with the other traditional measurements, optical fiber probe has shown to be more effective on measuring the local solids holdup by a number of studies.7−9 Theoretically, the CFD method is also able to simulate the fluidization behavior of fine particles.10 In view of the fact that the solids move mainly in the form of agglomerates which considerably affects flow patterns, the models developed for noncohesive particles do not have the capability of describing flow behavior for cohesive particle systems. Nevertheless, several models for predicting the agglomerates size either based on the force11,12 or energy balance principle13 have been reported in the literature so far. The one proposed and utilized here is developed by Zhou and Li,11 which has shown good agreement with the experimental data and has been adopted by most other researchers.14−16 It is convenient to combine the agglomerate-force balance model with CFD calculation to numerically investigate the bubbling fluidized beds with fine particles. This study provides a comprehensive experimental work about the flow structure characteristics of bubbling fluidized beds with fine particles in 2D and 3D conditions and then performs the © 2013 American Chemical Society

2. EXPERIMENTS 2.1. Materials. Fine alumina particles were used as the bed material in this experiment, as described in Table 1. These Table 1. Physical Properties of the Experimental Material parameter

value

mean diameter, dp (μm) particle density, ρp (kg/m3) bulk density, ρb (kg/m3) Hausner ratio, ρbt/ρb

10 3940 859 1.61

were group C particles within the Geldart’s classification.17 The powder size was determined by using a laser diffraction particle size analyzer (LS13320, Beckman Coulter) and a scanning electron microscope (6700F, JSM). The particle size distribution (PSD) of alumina particles is shown in Figure 1, the mean and median sizes are 10 and 6 μm, and the second peak corresponding to 55 μm is induced by the self-agglomeration of fine particles. Figure 2 shows the typical SEM image. The particle size is in the range of 1− 10 μm, which is in accord with the PSD result. The value of umb is experimentally determined and found to be equal to 0.14 m/s, Special Issue: Multiscale Structures and Systems in Process Engineering Received: Revised: Accepted: Published: 11302

November 11, 2012 December 26, 2012 January 4, 2013 January 4, 2013 dx.doi.org/10.1021/ie303105v | Ind. Eng. Chem. Res. 2013, 52, 11302−11312

Industrial & Engineering Chemistry Research

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Figure 4. The lateral locations of measurement at cross-section.

Figure 1. Size distribution of fine alumina particles.

Figure 5. Calibration curves of solids volume fraction.

2.2. Apparatus. Experiments were carried out in 2D and 3D fluidized beds, shown in Figure 3. The main bed dimensions were 1000 (height) × 200 (width) × 20 (depth) mm and 1000 (height) × 140 (i.d.) mm, respectively. For each fluidized bed, a sintered plate whose thickness being equal to 3 mm was placed at the bed bottom to produce a uniform distribution of gas. Below the distributor a wind box filled with glass beads allowed to equalize the gas flow. There was a cyclone separator for gas−solid separation, whereafter, a further separation was carried out in a bag filter. The separated particles were eventually recycled into the bed bottom, so the total amount of bed material could keep constant even at higher gas velocity. Air was used as fluidizing gas, and the flow rate was accurately measured through a flowmeter, covering the range of 0−417 L/min. A dehumidifier and an oil filter were also assembled online on the gas feed. 2.3. Measurements. The flow dynamics of cohesive particles in 2D and 3D fluidized beds were investigated based on the axial and radial solids volume fraction acquired by the optical fiber probe (model PC-6M, produced by our institute), under four superficial gas velocities of 0.21, 0.28, 0.35, and 0.42 m/s. When experiments were conducted, the probe was inserted into the fluidized beds at different elevations. At each level, the radial solids holdup was recorded at intervals of 10 mm from axial to wall, and two measurement ports (P1 and P2) were installed in vertical directions to obtain the data especially for the 3D fluidized bed, as shown in Figure 4. To ensure the validity and repeatability of sampled signal, the sampling time was 60 s with a frequency of 1000 Hz. In order to prevent particles adhering on the top of the tip and blind zone, a glass cover was placed over the probe tip.

Figure 2. SEM image of fine alumina particles.

Figure 3. Experimental set-ups.

which is a little less than 0.16 m/s measured for the 3.87 μm alumina particles by Zhou.18 Before each experiment, the powders were dried completely. 11303

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Figure 6. The snapshots of fluidization behavior of cohesive particles under four gas velocities. (a) Initial bed, (b) ug = 0.21 m/s, (c) ug = 0.28 m/s, (d) ug = 0.35 m/s, and (e) ug = 0.42 m/s.

Figure 7. Radial profiles of solids holdup at different bed heights. (a) ug = 0.21 m/s, (b) ug = 0.28 m/s, (c) ug = 0.35 m/s, and (d) ug = 0.42 m/s.

Table 2. Experimental Conditions parameter

2D

bed cross-section area, At (m2) weight of solids, m (kg) static bed height, H0 (m) superficial gas velocity, ug (m/s)

0.2 × 0.02 0.88

Table 3. Fluidized Bed Height and Expansion Rate under Four Gas Velocities

3D

(π × 0.142)/4 3.4 0.18 0.21, 0.28, 0.35, 0.42

NO.

ug (m/s)

H0 (mm)

H (mm)

Hunfl (mm)

H/H0

b c d e

0.21 0.28 0.35 0.42

180 180 180 180

235 250 270 295

70 50 30 25

1.31 1.39 1.50 1.64

Corresponding to the same voltage, the solids holdup of alumina is lower than that of FCC;19 this can be attributed to the fact that with the same light reflectivity, the cluster bulk density of fine particles is lower than that of A or B type powders.

According to the calibration between the local voltage measured by the probe and the solids holdup computed from the pressure drop, the relationship between the voltage signal output and the solids volume fraction is built and shown in Figure 5. 11304



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Figure 8. The influences of superficial gas velocity and bed elevation on the radial solids volume fraction distribution. (a) h = 100 mm, (b) h = 150 mm, (c) h = 200 mm, and (d) h = 250 mm.

3.1. Experimental Results in 2D Fluidized Bed. 3.1.1. Fluidization Behavior. Two-dimensional fluidized beds are considered as an effective way of viewing the flow patterns in a rectangular cross-section, from which the fluidization behavior of material can be observed clearly. Also as is known, the fluidization of fine powders is characterized by that they fluidized at agglomerates and there always exists a fixed bed of large agglomerates at the bottom of bed, which can be detected from Figure 6, the snapshots of fluidization behavior of cohesive particles under different superficial gas velocities. The solids suspension is discovered to be dilute with particles flowing up at both sides of the bed but dense with aggregations falling down in the central and near-wall regions. Table 3 summarizes the bed height and expansion rate at four conditions; the height of the unfluidized part is also indicated. As is shown, with the superficial gas velocity rising, both the bed height and expansion rate increase, whereas the unfluidized part diminishes. 3.1.2. Radial Profiles of Solids Holdup. Figure 7a−d shows the radial profiles of solids volume fraction at different elevations above the distributor under four gas velocities. It should be mentioned here that the profiles of concentration are assumed to be axisymmetric, and the data points of the right half are mirror to the left ones in this study. It can be seen that the local solids volume concentration value ranges from 0.11 to 0.30. Besides toward the wall, the solids holdup also increase a bit at the center of bed at certain elevations. The radial profiles exhibit U- or W-type on the whole. Combined with the fluidization behavior described in Figure 6, it is validated that two uniform

Figure 9. The axial solids volume fraction distribution.

3. EXPERIMENTAL RESULTS The flow dynamics of the cohesive particles in 2D and 3D fluidized beds were investigated under four superficial gas velocities. The experimental conditions are given in Table 2. 11305



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Figure 10. The PDD curves of local solids holdup at different elevations and radial positions under four gas velocities.

core-annular flows form around the radial position of r/R = ± 0.5; this is consistent with the result reported in our previous work,20 which was conducted by analyzing the bubbling behavior of fluidized beds with the same material. Generally, the annular flow structure is mainly related to bed geometry, which has been reported by Gidaspow21 and Lim et al.22 When a broad bed is not tall enough, the solids return to the bottom of bed not only at the walls but also through the center of the bed.23 The influences of superficial gas velocity and bed elevation on the radial solids volume fraction distribution are displayed in Figure 8a−d. With the increase of gas velocity, the solids holdup reduces successively. It is also indicated that in the wall region, due to the wall effect or wall friction, the boundary of particle aggregation area expands from r/R = −0.9 to r/R = −0.7 with the elevation above the distributor rising. 3.1.3. Axial Profiles of Solids Holdup. According to the axial solids distribution displayed in Figure 9, the fluidized bed can be divided into bottom unfluidized, middle ascending fluidized, and upper descending back-mixing sections. Along the bed height, the cross-sectional average solids holdup decreases gradually in the ascending fluidized section, while it increases in the descending back-mixing part. Such a trend has been reported by Wang et al.24 as well, and this phenomenon can be interpreted as follows: the particles moving directions reverse in the top region of the fluidized bed, which results in the increase of residence time, and the solids volume fraction rises, accordingly. 3.1.4. Probability Density Distribution (PDD) of Local Solids Holdup. To further explore the relationship among the

variation of solids holdup, gas velocity, and radial position, the PDD curves of local solids holdup are plotted in Figure 10. Evaluation were taken at three elevations and four radial positions (r/R = −1, −0.7, −0.3, 0) under different gas velocities. Two obvious peaks can be found in PDD curves, the one located at low solids volume fraction of 0−0.04 represents the bubble phase and the one of 0.26−0.30 corresponds to the emulsion phase. It is inferred that the local solids volume fraction value ranging from 0.11 to 0.30 depends on the interaction between the bubble phase and the emulsion phase within the fluidized beds. 3.2. Experimental Results in 3D Fluidized Bed. The radial profiles (filled mark) of the average solids holdup obtained from the two measurement ports in 3D fluidized bed are plotted in Figure 11. With the superficial gas velocity rising, the solids volume fraction at the same elevation decreases. Compared with the radial profiles (empty mark) of solids holdup acquired in 2D bed, the profiles in 3D exhibit more smoothly, the wall effect appears to be weakened, and the cohesive particles fluidize more uniformly.

4. NUMERICAL MODEL To simulate the hydrodynamics of bubbling fluidized beds with fine particles based on the agglomerate-force balance model by using CFD, gas and particle agglomerates were treated as separated continuum phases, and the two-fluid model with the simplified kinetic theory of granular flow (KTGF) for particulate phase stresses was used here.21 The complete model equations are summarized in Table S1 in the Supporting Information. It is worth 11306



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Figure 11. Radial profiles of solids holdup measured in 3D fluidized bed.

Table 4. Parameters Setting for the Simulation value description

2D

3D

diameter of particle, dp (μm) particle density, ρp (kg/m3) agglomerate density, ρa (kg/m3) gas density, ρg (kg/m3) grid interval spacing, Δz (mm) initial solid packing height, H0 (m) initial solid fraction, εi (-) Hamaker constant, A (J) distance between agglomerates, δ (m) time interval, Δt (s) bed dimension, (m3) superficial gas velocity, ug (m/s)

10 3940 988 1.225 5 0.18 0.31 1.169 × 10−19 4 × 10−10 1 × 10−4 0.2 × 0.02 × 1 0.28, 0.42

0.14 (i.d.) × 1 0.21, 0.35

Drag force (Fd) + Collision force (Fcf ) = (Gravitational force‐buoyancy force) (Fg) + Cohesive force (Fv)

(1)

The further expression of agglomerates diameter is described as below

Figure 12. The computational domains with the boundary conditions of 2D and 3D fluidized beds.

noting that the particle diameter (dp) used in the original formulation of kinetic theory is replaced by the agglomerate size (da) here. On the other hand, the balance equation of forces acting on the agglomerates at equilibrium condition can be given by

(ρa −

ρg )gda2

=0 11307

⎡ 6 3 1/5⎤ 0.996 ⎛⎜ πV a ρa ⎟⎞ ⎥ A ⎢ 2 −4.8 − ⎢0.33ρg ug εg + × ⎜ 2 ⎟ ⎥da + 2 π πδ k 4 ⎝ ⎠ ⎦ ⎣

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Figure 13. Comparison of radial profiles of solids holdup between simulation and experiment under (a-c) ug = 0.28 m/s and (e-f) ug = 0.42 m/s.

CFD modeling was performed using FLUENT 6.3. Corresponding to the experiments conducted in 2D and 3D fluidized beds, numerations were also executed in both conditions. The current simulations were carried out only for the main bed sections, and the enlarged parts above were ignored. The computational domains with the boundary conditions are schematically displayed in Figure 12, and the relevant computational parameters are listed in Table 4. The time mean average was calculated on the real-time simulation interval of 10−30 s to ensure that the statistical steady state behavior inside the bed was attained. Note that, to keep the total amount of bed material constant during the simulation, the solids leaving from the top outlet circulated into the sidewall inlet which is located at the elevation of 100 mm above the distributor, as displayed in Figure 12.

Figure 14. The distribution of agglomerates diameter along the bed height.

5. SIMULATION RESULTS 5.1. Simulation Results in 2D Case. 5.1.1. Comparison of Radial Profiles of Solids Holdup between Simulation and Experiment. The computed fluidization behaviors for 2D case were studied under ug = 0.28 m/s and ug = 0.42 m/s, respectively. The comparison of radial profiles of solids volume fraction between simulation and experiment is shown in Figure 13. It can be seen that the simulation based on the modified agglomerate-force balance model gives a close result to the experimental data. On the other hand, it is indicated that with the elevation increasing, the calculated concentration is slightly smaller than the measured data. This discrepancy can be explained as follows: the solids holdup is experimentally found to increase at the top of the bed for the back-mixing of particles, but the computed concentration decreases along the bed height regularly. It implies that the present model has not considered the effect of back-mixing properly, which should be further improved for a better computation. As reflected in Figure 13d, the computed solids volume fraction in the right wall region is higher than the left value at

where A is the Hamaker constant, J; δ is the distance between agglomerates, m; and Va is the relative velocity between agglomerates, m/s. As an important parameter in determining the agglomerates size, the relative velocity Va estimated by Zhou and Li11 and Iwadate and Horio12 is represented as follows 0.5 Va = (1.5Ps,n ̅ D bgεg)

(3)

D b = 0.652[A t (ug − umf )]2/5

(4)

where P̅s,n is the dimensionless average particle pressure, (P̅s,n ≈ 0.77); εg is the local bed voidage; and Db is the bubble diameter, m. Since eq 4 is derived from the fluidization of A or B type particles,25 for a more accurate numeration, the formula of Db is replaced by Db = 0.21(ug − umb)0.49 (h + 4(A0)1/2)0.48/g0.2 in this study, which is developed for the bubble diameter of the bed with cohesive particles reported in our previous paper.20 11308



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Figure 15. The snapshots of solids volume fraction contour under (a) ug = 0.28 m/s and (b) ug = 0.42 m/s.

of the bed and eventually recycled into the bed bottom after the time of 10 s. 5.2. Simulation Results in 3D Case. In the 3D fluidized bed, the radial experimental data were measured along two radial directions (P1 and P2) as shown in Figure 4, and the following simulation results of solids volume fraction and solids vertical velocity were obtained through two monitoring radial lines (L1 and L2) perpendicular to each other created in the simulation software, correspondingly. 5.2.1. Comparison of Radial Profiles of Solids Holdup between Simulation and Experiment. Figure 16a-c, d-f shows the comparison of radial profiles of solids volume fraction between the experimental and simulated results for the superficial gas velocity of 0.21 and 0.35 m/s, respectively. It is indicated that the predicted profiles are also in reasonable agreement with experimental results for the 3D case, except for the comparatively little underestimate of solids holdup at the elevation of 200 mm, where the deviation is also due to not taking into account the back-mixing effect, as discussed above. From the cross-sectional time-averaged contours of solids holdup also shown in Figure 16, it is revealed that the solids volume fraction is dense not only near the wall but also in the center of the bed, which is consistent with the experimental phenomenon that the aggregation of solids forms at the above two regions shown in Figure 6. In addition, by comparing the

the elevation of 100 mm; this is mainly attributed to the fact that a large amount of small particles blown out of the bed circulated into the sidewall inlet there, and this phenomenon will be more prominent under higher gas velocity. 5.1.2. Distribution of Agglomerates Diameter along the Bed Height. The axial profiles of cross-sectional averaged agglomerates diameter under the superficial gas velocity of 0.28 and 0.42 m/s are plotted in Figure 14. As it reflects, the higher the elevation or the gas velocity is, the smaller the predicated agglomerate is. The computed size of small agglomerates fluidized at the upper bed varies from 100 to 200 μm, and this is closed to the diameter of 164 μm measured by Zhou experimentally,18 which is conducted in the bubbling fluidized beds with alumina (dp = 3.87 μm) at the superficial gas velocity of 0.32 m/s. 5.1.3. Snapshots of Computed Solids Volume Fraction Contours. Figure 15 shows the instantaneous distribution of particles volume fraction during the time period of 0−30 s. The dense region at the bed bottom is due to the existence of large agglomerates. Comparing Figure 15a with b, it can be found that with the superficial gas velocity increasing from 0.28 to 0.42 m/s, the bed height expands while the dense region diminishes, which matches the general experimental finding. Besides, as exhibited in Figure 15b, the particles were blown out 11309



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Figure 16. Comparison of solids volume fraction between the experimental and simulated results under different gas velocities: (a-c) ug = 0.21 m/s and (d-f) ug = 0.35 m/s.

Figure 17. Computed solids vertical velocity under different gas velocities: (a-c) ug = 0.21 m/s and (d-f) ug = 0.35 m/s.

contours located at the same elevation under different superficial gas velocities, the time-averaged solids holdup is reflected to

decrease with the gas velocity increasing, also providing a good qualitative agreement with the experimental result. 11310



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In the second part of the work, the 2D and 3D simulations of gas and solids flows based on the modified agglomerate-force balance model were performed using CFD. A general comparison of the results with experimental data shows reasonable agreement, while a few discrepancies existing at the top of the bed are aroused from that the present model has not taken into account the back-mixing effect. According to the vector plots of computed agglomerates velocity, it is supported that the central and wall falling down-both sides rising up flow pattern of solids, two core-annular flows exist in the bed, which can be also observed experimentally.

■

ASSOCIATED CONTENT

S Supporting Information *

The governing equations are summarized in Table S1. This material is available free of charge via the Internet at http:// pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Phone: +86 10 62556951. Fax: +86 10 62536108. E-mail: [email protected]. Notes

Figure 18. Vector plots of solids velocity.

The authors declare no competing financial interest.

■

5.2.2. Computed Solids Vertical Velocity. The computed radial profiles and time-averaged contours of solids vertical velocity for the superficial gas velocity of 0.21 and 0.35 m/s are displayed in Figure 17. It reveals that the vertical velocity is negative near the wall, almost zero in the center, and positive at both sides of the bed. And the downward velocity of solids near the wall decreases with the elevation rising. Through contrasting the contours shown in Figures 17 and 16, it is found that the cross-sectional distributions of solids axial velocity and solids holdup are just contrary to each other, the higher the solids vertical velocity is, the lower the solids holdup is. 5.2.3. Simulated Vector Plots of Solids Velocity with Vertical Slice. In the end, the vector plots of solids velocity with vertical slice are illustrated in Figure 18. For the length of the vector tail is proportional to the size of velocity, it is indicated that the solids velocity in the upper bed region is higher than that in the lower part, and the solids at the bottom of the bed are almost static for large agglomerates forming there. The time-averaged velocity magnitude of solids is in the range of 0− 0.25 m/s. The arrows representing the agglomerates moving directions also support the central and wall falling down-both sides rising up flow pattern of solids, two core-annular flows exist in the bed.

ACKNOWLEDGMENTS The authors are grateful to the State Key Development Program for Basic Research of China (973 Program) under Grant No. 2009CB219904, the National Natural Science Foundation of China under Grant No. 20736004, and the National Science and Technology Support Program of China under Grant No. 2012BAB14B03.

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NOTATION

Latin letters

A0 = distributor area per orifice, m2 At = bed cross-section area, m2 Cd = drag coefficient dp = mean particle diameter, μm Db = bubble diameter, m e = coefficient of restitution for particle collisions g = gravitational acceleration constant, m/s−2 g0 = radial distribution function h = height above air distributor, m H = fluidized bed height, m H0 = static bed height, m Hunfl = unfluidized bed height, m I2D = second invariant of the deviatoric stress tensor k = function of Poisson’s ratio and Young’s modulus (k = 3.0 × 10−6), Pa−1 m = weight of solids, kg p = pressure, Pa Re = Reynolds number ua = agglomerates velocity, m/s ug = superficial gas velocity, m/s umb = minimum bubbling velocity, m/s Δt = time interval, s

6. CONCLUSIONS The work presented here consists of two major parts. The first part involves a comprehensive experimental investigation on the flow structure characteristics of bubbling fluidized beds with fine particles in 2D and 3D conditions. As result of this study, the fluidized bed can be divided into bottom unfluidized, middle ascending fluidized, and upper descending back-mixing sections according to the axial solids holdup distribution; the local solids volume concentration value ranges from 0.11 to 0.30, which depends on the interaction between the bubble phase (εs = 0− 0.04) and the emulsion phase (εs = 0.26−0.30) within the bed; compared with the 2D bed, the radial profiles of solids volume fraction in 3D exhibit more smoothly, the wall effect appears to be weakened, and the cohesive particles fluidize more uniformly.

Greek letters

ε = volume fraction Θ = granular temperature, m2/s2 τ = stress−strain tensor, Pa ρp = solid density, kg/m3

11311



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ρb = solid bulk density, kg/m3 ρbt = tapped bulk density, kg/m3 λ = bulk viscosity, kg/(m s) μ = shear viscosity, kg/(m s) ϕ = angle of internal friction (◦)

(20) Zou, Z.; Li, H. Z.; Zhu, Q. S. The bubbling behavior of cohesive particles in the 2D fluidized beds. Powder Technol. 2011, 212, 258. (21) Gidaspow, D. Multiphase Flow and Fluidization Continuum and Kinetic Theory Descriptions; Academic Press: San Diego, CA, 1994. (22) Lim, C. N.; Gilbertson, M. A.; Harrison, A. J. L. Bubble distribution and behaviour in bubbling fluidised beds. Chem. Eng. Sci. 2007, 62, 56. (23) Merry, J.; Davidson, J. Gulf stream circulation in shallow fluidised bed. Trans. Inst. Chem. Eng. 1973, 51, 361. (24) Wang, D. W.; Lu, C. X. Radial distribution and axial development of solids hold-up in the riser coupled with fluidized bed. Chin. J. Process. Eng. 2008, 8, 217. (25) Mori, S.; Wen, C. Y. Estimation of bubble diameter in gaseous fluidized beds. AIChE J. 1975, 21, 109.

Subscripts

a = agglomerate b = bubble phase g = gas phase k = parameter k p = particle phase s = solid phase

■

Abbreviations

NOTE ADDED AFTER ASAP PUBLICATION After this paper was published online January 16, 2013, a correction was made to Figure 11. The corrected version was reposted January 25, 2013.

PSD = particle size distribution PDD = probability density distribution KTGF = kinetic theory of granular flow

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REFERENCES

(1) Li, H. Z. Important relationship between meso-scale structure and transfer coefficients in fluidized beds. Particuology 2010, 8, 631. (2) Yang, Y. R.; Yang, J. Q.; Chen, W.; Rong, S. X. Instability analysis of the fluidized bed for ethylene polymerization with condensed mode operation. Ind. Eng. Chem. Res. 2002, 41, 2579. (3) Wang, Z. L.; Kwauk, M.; Li, H. Z. Fluidization of fine particles. Chem. Eng. Sci. 1998, 53, 377. (4) Iyer, S. R.; Drzal, L. T. Behavior of cohesive powders in narrowdiameter fluidized beds. Powder Technol. 1989, 57, 127. (5) Kono, H. O.; Chiba, S.; Ells, T.; Suzuki, M. Characterization of the emulsion phase in fine particle fluidized beds. Powder Technol. 1986, 48, 51. (6) Bai, D.; Issangya, A. S.; Grace, J. R. Characteristics of gas-fluidized beds in different flow regimes. Ind. Eng. Chem. Res. 1999, 38, 803. (7) Ellis, N.; Bi, H. T.; Lim, C. J.; Grace, J. R. Hydrodynamics of turbulent fluidized beds of different diameters. Powder Technol. 2004, 141, 124. (8) Cui, H. P.; Mostoufi, N.; Chaouki, J. Characterization of dynamic gas−solid distribution in fluidized beds. Chem. Eng. J 2000, 79, 133. (9) Johnsson, H.; Johnsson, F. Measurements of local solids volumefraction in fluidized bed boilers. Powder Technol. 2001, 115, 13. (10) Gelderbloom, S. J.; Gidaspow, D.; Lyczkowski, R. W. CFD simulations of bubbling/collapsing fluidized beds for three Geldart groups. AIChE J. 2003, 49, 844. (11) Zhou, T.; Li, H. Z. Estimation of agglomerate size for cohesive particles during fluidization. Powder Technol. 1999, 101, 57. (12) Iwadate, Y.; Horio, M. Prediction of agglomerate sizes in bubbling fluidized beds of group C powders. Powder Technol. 1998, 100, 223. (13) Xu, C. B.; Zhu, J. Experimental and theoretical study on the agglomeration arising from fluidization of cohesive particles-effects of mechanical vibration. Chem. Eng. Sci. 2005, 60, 6529. (14) Matsuda, S.; Hatano, H.; Muramoto, T.; Tsutsumi, A. Modeling for size reduction of agglomerates in nanoparticle fluidization. AIChE J. 2004, 50, 2763. (15) See, C. H.; Harris, A. T. CaCO3 supported Co-Fe catalysts for carbon nanotube synthesis in fluidized bed reactors. AIChE J. 2008, 54, 657. (16) Valverde, J. M.; Castellanos, A. Fluidization, bubbling and jamming of nanoparticle agglomerates. Chem. Eng. Sci. 2007, 62, 6947. (17) Geldart, D. Types of gas fluidization. Powder Technol. 1973, 7, 285. (18) Zhou, T. Experimental and theoretical studies on agglomerate fluidization of cohesive particles. Ph.D. Thesis, Institute of Chemical Metallurgy, China, 1998. (19) Yan, C. Y.; Lu, C. X.; Liu, Y. S.; Cao, R.; Shi, M. X. Hydrodynamics in air lift loop section of petroleum coke combustor. Powder Technol. 2009, 192, 143. 11312


Experimental Study and Numerical Simulation of Bubbling Fluidized

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