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Experimental analysis of bubble velocity in a rotating fluidized bed
Chemical Engineering and Processing 48 (2009) 178–186
Contents lists available at ScienceDirect
Chemical Engineering and Processing: Process Intensification journal homepage: www.elsevier.com/locate/cep
Experimental analysis of bubble velocity in a rotating fluidized bed Hideya Nakamura ∗ , Tomohiro Iwasaki, Satoru Watano Department of Chemical Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan
a r t i c l e
i n f o
Article history: Received 8 October 2007 Received in revised form 5 March 2008 Accepted 8 March 2008 Available online 16 March 2008 Keywords: Fluidization Rotating fluidized bed Bubble velocity Centrifugal force field
a b s t r a c t The bubble velocity in a two-dimensional rotating fluidized bed (RFB) was experimentally analyzed. The motion of bubbles was observed by means of a high-speed video camera, and the radial and angular components of bubble velocity were experimentally measured. The radial bubble velocity (UBr ) and angular bubble velocity (ωB ) were expressed as a function of actual centrifugal acceleration acting on the 0.5 bubble (gB ), bubble diameter (Db ), and angular velocity of the rotating vessel (v ): UBr = Kr (gB Db ) and ωB = K ωv , respectively. The effects of the operating parameters (gas velocity and centrifugal acceleration) on the bubble velocity coefficients (Kr and K ) were analyzed experimentally. The distribution of both bubble velocity coefficients could be well correlated by the log-normal distribution function. The distributions of Kr and K showed almost unchanged with the gas velocity and centrifugal acceleration, because the buoyancy force acting on a bubble under high centrifugal force field is so high, and the interaction from other bubbles can be neglected. The bubble velocity coefficients in an RFB could be empirically obtained as Kr = 0.52 and K = 0.96. The experimental mean bubble velocities at the various operating conditions were compared with the predicted ones by using the obtained bubble velocity coefficients and our proposed model for the bubble diameter [H. Nakamura, T. Iwasaki, S. Watano, Modeling and measurement of bubble size in a rotating fluidized bed, AIChE J. 53 (2007) 2795–2803]. The radial and angular bubble velocities could be predicted only by the operating parameters. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Fluidized beds have been widely used in many industries because of its desirable characteristics such as high heat and mass transfer rates between gas and particles, temperature homogeneity, easy handling and rapid mixing of particles. However, the conventional fluidized beds cannot still overcome some existing limitations: it is difficult to operate under high gas velocity since the gas–solid contact becomes poor due to the formation of large bubbles, slugs and particle entrainment; fine particles such as Geldart’s group-C particle [1] fluidize poorly, exhibiting channeling, plugging, and forming large agglomerated. Recently, a rotating fluidized bed (RFB) has gathered a special interest because it has high potential to overcome the conventional limitations. The RFBs have unique fluidization concept [2] as shown in Fig. 1. The system consists of a cylindrical gas distributor rotating around its axis of symmetry inside the stationary plenum chamber. Due to the rotational motion of the gas distributor, particles are forced to move toward the rotating vessel (gas distributor) by the centrifugal force, forming annular particle bed on the gas distributor. Fluidization gas flows inward through the distributor, and
∗ Corresponding author. Tel.: +81 72 254 9305; fax: +81 72 254 9305. E-mail address: [email protected] (H. Nakamura). 0255-2701/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2008.03.003
particles are balanced by the fluid drag force and centrifugal force, leading to fluidization of particles in a high centrifugal force field. The RFBs have such advantages as (1) the RFBs can prevent growth of large bubbles and entrainment of particles even at relatively high gas velocities by controlling the vessel rotational speed [3]; (2) the RFBs can smoothly fluidize fine cohesive particles [4] such as Geldart’s group-C particles, because it imparts high centrifugal force and drag force to the particles; (3) its space requirement is very small. The RFBs have been expected to be used as some advanced industrial processes from the advantages, such as the reactor for rocket propulsion system in micro-gravity field [5], high efficient dust filter [6], simultaneous removal process of NOx and soot from diesel engine exhaust gas [7], incinerator of sludge waste [8], granulator and coater for fine particles [2,9] and processor for handling of nano-particles [10,11]. In spite of many published studies, the reliable RFB process has not been established yet, because design and operation of the RFB processes have been conducted depending on experiences and skills without scientific justification. Therefore, in order to establish the design methodology of RFB processes, elucidation of the fundamental fluidization mechanisms is strongly required. It is well known that bubbling characteristics in gas–solid fluidized beds greatly affect the fundamental fluidization phenomenon, such as gas–solid contact, particle mixing, entrainment, and so on [12]. The bubbling characteristics thus become the critical
H. Nakamura et al. / Chemical Engineering and Processing 48 (2009) 178–186
179
rise velocity (UB ): UB = K
Fig. 1. Rotating fluidized bed (RFB) system.
parameters for design and operation of the fluidized bed processes. Therefore, in an RFB the bubbling characteristics should be elucidated. However, there has been no report anywhere with regard to the RFB. Only Chevray et al. [13] studied the bubbling characteristics and derived equations for bubble velocity and trajectory based on the Lagrangian approach. However, there was no experimental data for evaluating the validity of their model. The overall objective of this study is to analyze the bubbling characteristics in an RFB. We here focused on the bubble velocity, which is one of the most important bubbling characteristics. The motion of bubbles in an RFB was observed by means of a highspeed video camera, and the radial and angular bubble velocities were experimentally measured. The effects of the operating parameters such as gas velocity and centrifugal acceleration on the bubble velocities were investigated. Furthermore, an empirical correlation to estimate the bubble velocity was proposed using the obtained experimental data.
gDB
(1)
where K, g, and DB are the bubble velocity coefficient, gravitational acceleration, and bubble diameter, respectively. This has been recognized as the fundamental equation for giving the bubble rise velocity. The value of K depends on a depth of particle bed, and determined as 0.71 for a three-dimensional bubble [14] and 0.5 for a two-dimensional bubble [15]. The bubble rise velocity in a bubble swarm is generally higher than the rise velocity of a single bubble due to the acceleration effects caused by the bubble–bubble interaction and the overall circulation of particles [16]. Many researches have proposed several equations to estimate a bubble swarm rise velocity by modifying Eq. (1) [16–19], and empirically derived many types of additional or multiplication correction terms in order to take into account the wall effect and the acceleration effects. In RFBs, the bubbles mainly move in the two directions, i.e., radial and angular directions. The radial bubble velocity (UBr ) and angular bubble velocity (ωB ) were thus analyzed in this study. It was assumed that the radial bubble velocity (UBr ) could be expressed as the following equation, which is similar to Eq. (1): UBr = Kr
gB DB
(2)
gB
where is the actual centrifugal acceleration acting on the bubble, and Kr is the radial bubble velocity coefficient. In RFBs, bubbles move along the rotating vessel without any significant random motions. The angular bubble velocity (ωB ) was thus assumed as the following correlation: ωB = K ωv
(3)
where ωv is the angular velocity of the rotating vessel (gas distributor), and K is the angular bubble velocity coefficient. In this study, the effects of operating parameters (gas velocity and centrifugal acceleration) on the bubble velocity coefficients (Kr and K ) were experimentally analyzed.
2. Bubble velocity in gas–solid fluidized beds
3. Experimental
So far, many researchers have studied the bubble rising velocity in conventional gas–solid fluidized beds. Davis and Taylor [14] theoretically derived the following equation expressing a single bubble
Fig. 2 shows the experimental set-up for visualization of bubbling behaviors in the RFB. A thin porous cylindrical plate (i.d. 250 mm × D. 5 mm), which was made of stainless sintered mesh
Fig. 2. Experimental set-up.
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H. Nakamura et al. / Chemical Engineering and Processing 48 (2009) 178–186
Fig. 3. Size distribution of model particle.
with 20 m openings, was used as the rotating gas distributor. The covers of the chamber and rotating vessel are both made of transparent acrylic plastic that allows observation of bubbling behavior at various circumferential locations. Spherical glass beads (FUJISTONE GB-01, Fuji-rika industrial Co., Ltd.) were used as experimental model particles and their median diameter and density were 136 m and 2520 kg/m3 , respectively. The size distribution of the particles measured by a sieve analysis is indicated in Fig. 3. The model particle had relatively narrow size distribution, and 94% of the particles existed within 106–180 m. The particles of 170.0 g were charged into the vessel of which the initial bed height was 31 mm. The bubbling behaviors were observed by means of a stationary located high-speed video camera (FASTCAM MAX, Photoron Co., Ltd.). The recording frame rate and shutter speed were set at 2000 frames/s and 0.14 ms, respectively. A metal halide lamp was used as light source. Recording of the bubbling behaviors was carried out under the backlight condition. Fig. 4 shows the representative recorded images of the bubbling behavior. In this study, two-dimensional bubbles were observed. The digitized recorded images consisted of 1024 × 512 picture elements (pixel), and the whole visualized area was 16 cm × 8 cm. An image analysis technique was utilized for the measurement of bubble velocity. First, the binarization processing for segmen-
Fig. 5. Bubble motion over time interval t between two consecutive images.
tation of a bubble from its background (emulsion phase) was conducted. These two phases were distinguished by an optimum threshold value which was determined based on a discriminant analysis method [20]. The binarization processing was individually applied to the measured bubbles. Subsequently, the position of center of gravity of the binarized bubble image in a cylindrical coordinate system was determined individually. The instantaneous radial and angular bubble velocities (UBri and ωBi ) were then obtained from displacement of the center of gravity over a time interval t between two consecutive recorded images as shown in Fig. 5: UBri =
ri,t+t − ri,t t
(4)
ωBi =
i,t+t − i,t t
(5)
In this experiment, the radial direction from the surface of gas distributor to the rotational axis of vessel and the counterclockwise direction in the recorded images were defined as the positive direction of UBr and ωB , respectively. The radial and angular bubble velocity coefficients (Kri and Ki ) were then determined using the following equations: UBri
Kri =
Ki =
ωBi ωv
(6)
ri ωBi 2 DBi (7)
where r¯ i and DBi ,which were the mean radial position and mean bubble diameter between the consecutive recorded images, were obtained using the following equations:
Fig. 4. Recorded bubbling behavior.
ri = 0.5(ri,t+t + ri,t )
(8)
DBi = 0.5(DBi,t+t + DBi,t )
(9)
The bubble diameter was defined as an equivalent diameter of sphere, which was calculated as a product of the bubble phase area and the vessel depth [21]. The total number of measured bubbles was approximately 1500 in each operating condition. We also defined the restrictive conditions for tracking of the bubble motion in order to eliminate the unreliable experimental
H. Nakamura et al. / Chemical Engineering and Processing 48 (2009) 178–186
data; the bubbles which satisfied the following three equations were selected as the measurable ones: ri,t+t ≥ ri,t
(10)
i,t+t ≥ i,t 0.95 <
DBi,t+t < 1.05 DBi,t
Fig. 6. Log-normal distributions of radial bubble velocity coefficient at various operating conditions.
181
(11) (12)
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The number fractions of bubbles satisfying the above conditions were more than 98% of the total number in each operating condition. 4. Results and discussion 4.1. Distributions of bubble velocity coefficients In this study, a log-normal distribution was used as the distribution function for bubble velocity coefficients, because Kr and K were well correlated by a log-normal distribution function among others. Fig. 6 shows log-normal distributions of radial bubble velocity coefficient (Kr ) at various gas velocities and centrifugal accelerations. The solid curves indicate the approximated log-normal distribution functions. The geometric mean and geometric standard deviation of Kr were expressed as Kr50 and gr , respectively. G0 is the dimensionless centrifugal factor which is defined as the ratio of centrifugal acceleration at the surface of gas distributor to the gravitational acceleration. The range of Kr varied from 0.2 to 2.0 in each operating parameter. In conventional fluidized beds, the bubble velocity coefficient strongly depends on the bubbling intensity [15–19]; the bubble velocity coefficient increases with an increase in the gas velocity due to the acceleration effect caused by the bubble–bubble interaction. In the RFB, however, the distributions of Kr almost unchanged with the gas velocity and centrifugal acceleration, although the differences of bubbling intensity were clearly observed. In RFBs, the buoyancy force acting on a bubble, which is the driving force of bubble movement, is much larger than that in conventional fluidized beds due to the high centrifugal acceleration. Therefore, the bubble–bubble interaction can be neglected as compared with the huge buoyancy force, resulting in the constant Kr at various operating conditions. The experimental data of Kr for all operating conditions were also approximated by the log-normal distribution function as shown in Fig. 7. As a result, the mean value of Kr could be empirically determined as 0.52. In conventional fluidized beds, value of the bubble velocity coefficient for a two-dimensional single bubble,
which can be recognized as the bubble velocity coefficient without the bubble–bubble interaction, was reported as approximately 0.5 [15,17]. It should be noted that the value of Kr in an RFB was close to the value of the bubble velocity coefficient for a two-dimensional single bubble in conventional fluidized beds. This result means that in the centrifugal force field the bubble–bubble interaction can be neglected as compared with the huge buoyancy force acting on a bubble. Therefore, we believe that value of the bubble velocity coefficient for a three-dimensional single bubble in conventional fluidized beds, which was reported as 0.71 [14], can be adapted as the value of Kr for a three-dimensional bubble in RFBs. Fig. 8 shows log-normal distributions of the angular bubble velocity coefficient (K ) at various operating conditions. The distributions of K could also be expressed by the log-normal distribution function and were almost constant regardless of the operating conditions. Fig. 9 indicates the distribution of K for all the operating conditions. From approximation of K by the log-normal distribution function, the mean value of K could be determined empirically as 0.96. This result means that the averaged angular bubble velocity is slightly smaller than angular velocity of the rotating gas distributor because of slipping between the fluidized particle bed and the rotating gas distributor. In conclusion, the both of bubble velocity coefficients (Kr and K ) could be obtained as the constant value under various conditions of gas velocity and centrifugal acceleration. We believe this simple result becomes great advantage from the viewpoint of design and control of RFBs. 4.2. Prediction of bubble velocities By using the obtained empirical coefficients of Kr = 0.52 and K = 0.96, the radial and angular bubble velocities were estimated solely by the operating parameters. The radial and angular bubble velocities can be expressed as UBr = Kr
gB DB ,
ωB = K ωv , where gB =
gB
Kr = 0.52
K = 0.96
(13) (14)
is the actual centrifugal acceleration acting on a bubble:
2
K G0 g ˇ
(15)
ˇ is the dimensionless radius defined as ˇ=
RV RV − L
(16)
where RV and L are the vessel radius and radial distance from the surface of gas distributor, respectively. The bubble diameter DB in the Eq. (13) can be estimated using our proposed bubble growth model for RFBs [21]. This model is briefly described as follow: we noticed the big differences of fluidization condition between conventional fluidized beds and RFBs, and modified the staged bubble coalescence model proposed by Darton et al. [22] according to the following two concepts: (i) the centrifugal acceleration and excess gas velocity are considered to be expressed as a function of radial distance L from the surface gas distributor, and (ii) the bubble volume flow rate passing through the particle bed with forming the bubbles increases with an increase in L. According to Darton et al. [22], the bubble coalescence is assumed to occur in several steps as shown in Fig. 10. The distance LN from the surface of the gas distributor at the Nth stage of coalescence can be expressed as the following equation: Fig. 7. Log-normal distributions of radial bubble velocity coefficient for all operating conditions.
LN = Dc0 + Dc1 + · · · + Dc(N−1)
(17)
H. Nakamura et al. / Chemical Engineering and Processing 48 (2009) 178–186
183
Fig. 8. Log-normal distributions of angular bubble velocity coefficient at various operating conditions.
where Dc is the circle diameter of distributor per hole. indicates the bubble coalescence constant which was preliminary determined as 0.77. The value of N is chosen depending on the particle bed height. The correlation between the Dc and DB at the Nth stage of coalescence can be defined by using the correlation of Miwa
et al. [23]:
DcN = 0.75
gN 0.25 DBN 1.25 (u − umf )N 0.5
(18)
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The volume balance of bubble in each coalescence stage can be expressed as follows:
⎫
3 = 2D3 + 2D3 DB1 ⎪ B0 BG,1 ⎪ ⎪ 3 = 2D3 + 2D3 ⎪ DB2 ⎪ B1 BG,2 ⎬ 3 3 3 DB3 = 2DB2 + 2DBG,3 ⎪ .. ⎪ ⎪ . ⎪ ⎪ 3 3 3 DB(N−1) = 2DB(N−2) + 2DBG,(N−1) ⎭
(21)
where, DBG,N is defined as the “gained bubble diameter” at Nth coalescence stage. The gained bubble originates from the increased bubble volume flow rate with an increase in L. The equation of DBG,N is derived based on the correlation of Miwa et al. [23] as follows:
DBG,N = 1.38
Fig. 9. Log-normal distributions of angular bubble velocity coefficient for all operating conditions.
where gN and (u − umf )N are the local centrifugal acceleration and local excess gas velocity at the Nth stage of coalescence, respectively. They are defined as a function of L [24]. gN =
G0 g ˇN
(19)
(u − umf )N = ˇN u0 −
×
1 ˇN f dp 2
33.7 + 0.0408
f (p − f )dp3 G0 g
0.5
2 ˇN
− 33.7
(u − umf )N − (u − umf )N−1 0.5 gN−1
0.4 Ac(N−1)
Finally, the correlation between the bubble diameter and the dimensionless radius can be obtained by numerically solving the Eqs. (17)–(22). The validity of this model has already been confirmed [21]. Fig. 11 shows the estimation and experimental results of radial bubble velocity as a function of dimensionless radius ˇ. The experimental bubble velocities indicate the geometric mean velocity obtained by the fitting of log-normal distribution function in the range of a certain ˇ to ˇ + ˇ. The each curve is predicted value by the Eq. (13). The values of sequential number N used for estimation by the proposed bubble growth model are also presented in Fig. 11. The radial bubble velocities increased with an increase in ˇ due to the bubble growth. With further increase in ˇ, the increasing rate of radial bubble velocity gradually decreased, because the actual centrifugal acceleration gB became smaller. The radial bubble velocity also increased with an increase in G0 ; this means that the bubble velocity in RFBs is higher than that in conventional fluidized beds when the bubble sizes are the same. Fig. 12 shows comparison of the estimation results of radial bubble velocity with the experimental results at various operating conditions. Since the estimated bubble size using the proposed bubble growth model showed high
(20)
Fig. 10. Schematic illustration of bubble growth model.
(22)
Fig. 11. Radial bubble velocity as a function of dimensionless radius.
H. Nakamura et al. / Chemical Engineering and Processing 48 (2009) 178–186
185
5. Conclusions
Fig. 12. Comparison of estimation results of radial bubble velocities with experimental results at various operating conditions.
accuracy [21], the estimated radial bubble velocities showed good agreement with the experimental results, and the calculation errors were within approximately 30%. Fig. 13 indicates the estimation and experimental results of angular bubble velocity as a function of ˇ. The angular bubble velocities were constant with a change in ˇ at G0 = 10–30. However, it slightly increased with an increase in ˇ at G0 = 40. This is because the effect of the Coriolis force acting on a bubble becomes higher than that under lower centrifugal acceleration.
Fig. 13. Angular bubble velocity as a function of dimensionless radius.
The bubble velocity in a rotating fluidized bed (RFB) was experimentally analyzed. The two components of bubble velocity in the radial and angular directions were measured. The radial bubble velocity was expressed using the similar type of equation for the bubble rise velocity in conventional fluidized beds, and the angular bubble velocity was described using the linear relationship with the angular velocity of vessel. The coefficients of radial and angular bubble velocities (Kr and K ) were then evaluated under various conditions of gas velocity and centrifugal acceleration. The distributions of Kr and K could be expressed by the log-normal distribution function. It should be noted that the distributions of Kr and K were constant regardless of operating conditions, because the buoyancy force acting on the bubble was much higher than the bubble–bubble interaction force. The bubble velocity coefficients could be empirically obtained as Kr = 0.52 and K = 0.96. The correlation to estimate the bubble velocity in RFBs was then proposed empirically. The proposed empirical correlation could estimate the radial and angular bubble velocities within approximately 30% and 5% of estimation error, respectively. Consequently, the radial and angular bubble velocities could be predicted only by the operating parameters. It was also confirmed that the bubble velocity in an RFB is generally higher than that in a conventional fluidized bed if the bubble sizes are the same, because in high centrifugal force field the buoyancy force acting on a bubble which is the driving force of bubble movement is much larger than that under gravitational field. Acknowledgement Authors acknowledge the financial support by the Grant-in-Aids for JSPS Research Fellow from the Ministry of Education, Science, Sports and Culture of Japan. Appendix A. Nomenclature Ac dp DB DBG Dc g g gB G0 Kr K L r Rv t u umf u0 UB UBr
area of distributor per hole (m2 ) particle diameter (m) bubble diameter (m) gained bubble diameter (m) circle equivalent diameter of Ac (m) gravity acceleration (m s−2 ) local centrifugal acceleration (m s−2 ) actual centrifugal acceleration acting on a bubble (m s−2 ) dimensionless centrifugal factor radial bubble velocity coefficient angular bubble velocity coefficient radial distance from surface of gas distributor (m) radius of cylindrical coordinate (m) radius of vessel (m) time interval between consecutive two images (s) superficial gas velocity (m s−1 ) minimum fluidization velocity (m s−1 ) superficial gas velocity at gas inlet (m s−1 ) rise velocity of single bubble (m s−1 ) radial bubble velocity (m s−1 )
Greek letters ˇ dimensionless radius -coordinate in cylindrical coordinate system (rad) constant in Eq. (17) gas viscosity (Pa s) f gas density (kg m−3 )
186
p g ωB ωv
H. Nakamura et al. / Chemical Engineering and Processing 48 (2009) 178–186
particle density (kg m−3 ) geometric standard deviation angular bubble velocity (rad s−1 ) angular velocity of vessel (rad s−1 )
Subscripts i a certain tracked bubble N sequential number of bubble coalescence r radial component angular component 50 geometric mean value References [1] D. Geldart, Types of gas fluidization, Powder Technol. 7 (1973) 285–292. [2] S. Watano, Y. Imada, K. Hamada, Y. Wakamatsu, Y. Tanabe, R.N. Dave, R. Pfeffer, Microgranulation of fine powders by a novel rotating fluidized bed granulator, Powder Technol. 131 (2003) 250–255. [3] H. Nakamura, S. Watano, Numerical simulation of particle fluidization behaviors in a rotating fluidized bed, Stud. Surf. Sci. Catal. 159 (2006) 505–508. ´ [4] G.H. Qian, I. Bagyi, I.W. Burdick, R. Pfeffer, H. Shaw, J.G. Stevens, Gas–solid fluidization in a centrifugal field, AIChE J. 47 (2001) 1022–1034. [5] H. Ludewig, A.J. Manning, C.J. Raseman, Feasibility of rotating fluidized bed reactor for rocket propulsion, J. Spacecraft 11 (1974) 65–71. [6] G.H. Qian, I.W. Burdick, R. Pfeffer, H. Shaw, J.G. Stevens, Soot removal from diesel engine exhaust using a rotating fluidized bed filter, Adv. Environ. Res. 8 (2004) 387–395. [7] A. Tsutsumi, W. Ju, K. Yoshida, Reduction of NO in diesel exhaust by soot using a centrifugal fluidized bed, AIChE Symp. Ser. 92 (1996) 86–90. [8] W.Y. Wong, Y. Lu, V.S. Nasserzadeh, J. Swithenbank, T. Shaw, M. Madden, Experimental investigation into the incineration of wool scouring sludges in a novel rotating fluidized bed, J. Hazard. Mater. B73 (2000) 143–160.
[9] S. Watano, H. Nakamura, K. Hamada, Y. Wakamatsu, Y. Tanabe, R.N. Dave, R. Pfeffer, Fine particle coating by a novel rotating fluidized bed coater, Powder Technol. 141 (2004) 172–176. [10] S. Matsuda, H. Hatano, K. Kuramoto, A. Tsutsumi, Modeling for size reduction of agglomerates in nanoparticle fluidization, AIChE J. 50 (2004) 2763–2771. [11] J. Quevedo, R. Pfeffer, Y. Shen, R. Dave, H. Nakamura, S. Watano, Fluidization of nano agglomerates in a rotating fluidized bed, AIChE J. 52 (2006) 2401–2412. [12] D. Kunii, O. Levenspiel, Fluidization Engineering, 2nd ed., ButterworthHeinemann, Boston, 1991, pp.137–164. [13] R. Chevray, Y.N.I. Chan, F.B. Hill, Dynamics of bubbles and entrained particles in the rotating fluidized bed, AIChE J. 26 (1980) 390–398. [14] R.M. Davies, G. Taylor, The mechanics of large bubbles rising through extended liquids and through liquids in tubes, P. R. Soc. Lond. A: Mater. 200 (1950) 375–390. [15] K.S. Lim, P.K. Agarwal, Bubble velocity in fluidized beds; the effect of nonvertical bubble rise on its measurement using submersible probes and its relationship with bubble size, Powder Technol. 69 (1992) 239–248. [16] A.S. Hull, Z. Chen, J.W. Fritz, P.K. Agarwal, Influence of horizontal tube banks on the behavior of bubbling fluidized beds. 1. Bubble hydrodynamics, Powder Technol. 103 (1999) 230–242. [17] J.F. Davidson, D. Harrison, Fluidized Particles, Cambridge Univ. Press, New York, 1963, pp. 29–42. [18] J. Werther, J. Wein, Expansion behavior of gas fluidized beds in the turbulent regime, AIChE Symp. Ser. 90 (1994) 31–44. [19] R. Krishna, J.M. van Baten, Using CFD for scaling up gas-solid bubbling fluidised bed reactors with Geldart A powders, Chem. Eng. J. 82 (2001) 242–257. [20] S. Watano, K. Miyanami, Image processing for on-line monitoring of granule size distribution and shape in fluidized bed granulation, Powder Technol. 83 (1995) 55–60. [21] H. Nakamura, T. Iwasaki, S. Watano, Modeling and measurement of bubble size in a rotating fluidized bed, AIChE J. 53 (2007) 2795–2803. [22] R.C. Darton, R.D. Lanauze, J.F. Davidson, D. Harrison, Bubble growth due to coalescence in fluidized bed, Trans. Inst. Chem. Eng. 55 (1977) 274–280. [23] T. Miwa, S. Mori, T. Kato, I. Muchi, Behavior of bubbles in gaseous fluidized bed, Kagaku Kougaku 35 (1971) 770–776. [24] J. Kao, R. Pfeffer, G.I. Tardos, On partial fluidization in a rotating fluidized bed, AIChE J. 33 (1987) 858–861.
Contents lists available at ScienceDirect
Chemical Engineering and Processing: Process Intensification journal homepage: www.elsevier.com/locate/cep
Experimental analysis of bubble velocity in a rotating fluidized bed Hideya Nakamura ∗ , Tomohiro Iwasaki, Satoru Watano Department of Chemical Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan
a r t i c l e
i n f o
Article history: Received 8 October 2007 Received in revised form 5 March 2008 Accepted 8 March 2008 Available online 16 March 2008 Keywords: Fluidization Rotating fluidized bed Bubble velocity Centrifugal force field
a b s t r a c t The bubble velocity in a two-dimensional rotating fluidized bed (RFB) was experimentally analyzed. The motion of bubbles was observed by means of a high-speed video camera, and the radial and angular components of bubble velocity were experimentally measured. The radial bubble velocity (UBr ) and angular bubble velocity (ωB ) were expressed as a function of actual centrifugal acceleration acting on the 0.5 bubble (gB ), bubble diameter (Db ), and angular velocity of the rotating vessel (v ): UBr = Kr (gB Db ) and ωB = K ωv , respectively. The effects of the operating parameters (gas velocity and centrifugal acceleration) on the bubble velocity coefficients (Kr and K ) were analyzed experimentally. The distribution of both bubble velocity coefficients could be well correlated by the log-normal distribution function. The distributions of Kr and K showed almost unchanged with the gas velocity and centrifugal acceleration, because the buoyancy force acting on a bubble under high centrifugal force field is so high, and the interaction from other bubbles can be neglected. The bubble velocity coefficients in an RFB could be empirically obtained as Kr = 0.52 and K = 0.96. The experimental mean bubble velocities at the various operating conditions were compared with the predicted ones by using the obtained bubble velocity coefficients and our proposed model for the bubble diameter [H. Nakamura, T. Iwasaki, S. Watano, Modeling and measurement of bubble size in a rotating fluidized bed, AIChE J. 53 (2007) 2795–2803]. The radial and angular bubble velocities could be predicted only by the operating parameters. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Fluidized beds have been widely used in many industries because of its desirable characteristics such as high heat and mass transfer rates between gas and particles, temperature homogeneity, easy handling and rapid mixing of particles. However, the conventional fluidized beds cannot still overcome some existing limitations: it is difficult to operate under high gas velocity since the gas–solid contact becomes poor due to the formation of large bubbles, slugs and particle entrainment; fine particles such as Geldart’s group-C particle [1] fluidize poorly, exhibiting channeling, plugging, and forming large agglomerated. Recently, a rotating fluidized bed (RFB) has gathered a special interest because it has high potential to overcome the conventional limitations. The RFBs have unique fluidization concept [2] as shown in Fig. 1. The system consists of a cylindrical gas distributor rotating around its axis of symmetry inside the stationary plenum chamber. Due to the rotational motion of the gas distributor, particles are forced to move toward the rotating vessel (gas distributor) by the centrifugal force, forming annular particle bed on the gas distributor. Fluidization gas flows inward through the distributor, and
∗ Corresponding author. Tel.: +81 72 254 9305; fax: +81 72 254 9305. E-mail address: [email protected] (H. Nakamura). 0255-2701/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2008.03.003
particles are balanced by the fluid drag force and centrifugal force, leading to fluidization of particles in a high centrifugal force field. The RFBs have such advantages as (1) the RFBs can prevent growth of large bubbles and entrainment of particles even at relatively high gas velocities by controlling the vessel rotational speed [3]; (2) the RFBs can smoothly fluidize fine cohesive particles [4] such as Geldart’s group-C particles, because it imparts high centrifugal force and drag force to the particles; (3) its space requirement is very small. The RFBs have been expected to be used as some advanced industrial processes from the advantages, such as the reactor for rocket propulsion system in micro-gravity field [5], high efficient dust filter [6], simultaneous removal process of NOx and soot from diesel engine exhaust gas [7], incinerator of sludge waste [8], granulator and coater for fine particles [2,9] and processor for handling of nano-particles [10,11]. In spite of many published studies, the reliable RFB process has not been established yet, because design and operation of the RFB processes have been conducted depending on experiences and skills without scientific justification. Therefore, in order to establish the design methodology of RFB processes, elucidation of the fundamental fluidization mechanisms is strongly required. It is well known that bubbling characteristics in gas–solid fluidized beds greatly affect the fundamental fluidization phenomenon, such as gas–solid contact, particle mixing, entrainment, and so on [12]. The bubbling characteristics thus become the critical
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179
rise velocity (UB ): UB = K
Fig. 1. Rotating fluidized bed (RFB) system.
parameters for design and operation of the fluidized bed processes. Therefore, in an RFB the bubbling characteristics should be elucidated. However, there has been no report anywhere with regard to the RFB. Only Chevray et al. [13] studied the bubbling characteristics and derived equations for bubble velocity and trajectory based on the Lagrangian approach. However, there was no experimental data for evaluating the validity of their model. The overall objective of this study is to analyze the bubbling characteristics in an RFB. We here focused on the bubble velocity, which is one of the most important bubbling characteristics. The motion of bubbles in an RFB was observed by means of a highspeed video camera, and the radial and angular bubble velocities were experimentally measured. The effects of the operating parameters such as gas velocity and centrifugal acceleration on the bubble velocities were investigated. Furthermore, an empirical correlation to estimate the bubble velocity was proposed using the obtained experimental data.
gDB
(1)
where K, g, and DB are the bubble velocity coefficient, gravitational acceleration, and bubble diameter, respectively. This has been recognized as the fundamental equation for giving the bubble rise velocity. The value of K depends on a depth of particle bed, and determined as 0.71 for a three-dimensional bubble [14] and 0.5 for a two-dimensional bubble [15]. The bubble rise velocity in a bubble swarm is generally higher than the rise velocity of a single bubble due to the acceleration effects caused by the bubble–bubble interaction and the overall circulation of particles [16]. Many researches have proposed several equations to estimate a bubble swarm rise velocity by modifying Eq. (1) [16–19], and empirically derived many types of additional or multiplication correction terms in order to take into account the wall effect and the acceleration effects. In RFBs, the bubbles mainly move in the two directions, i.e., radial and angular directions. The radial bubble velocity (UBr ) and angular bubble velocity (ωB ) were thus analyzed in this study. It was assumed that the radial bubble velocity (UBr ) could be expressed as the following equation, which is similar to Eq. (1): UBr = Kr
gB DB
(2)
gB
where is the actual centrifugal acceleration acting on the bubble, and Kr is the radial bubble velocity coefficient. In RFBs, bubbles move along the rotating vessel without any significant random motions. The angular bubble velocity (ωB ) was thus assumed as the following correlation: ωB = K ωv
(3)
where ωv is the angular velocity of the rotating vessel (gas distributor), and K is the angular bubble velocity coefficient. In this study, the effects of operating parameters (gas velocity and centrifugal acceleration) on the bubble velocity coefficients (Kr and K ) were experimentally analyzed.
2. Bubble velocity in gas–solid fluidized beds
3. Experimental
So far, many researchers have studied the bubble rising velocity in conventional gas–solid fluidized beds. Davis and Taylor [14] theoretically derived the following equation expressing a single bubble
Fig. 2 shows the experimental set-up for visualization of bubbling behaviors in the RFB. A thin porous cylindrical plate (i.d. 250 mm × D. 5 mm), which was made of stainless sintered mesh
Fig. 2. Experimental set-up.
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Fig. 3. Size distribution of model particle.
with 20 m openings, was used as the rotating gas distributor. The covers of the chamber and rotating vessel are both made of transparent acrylic plastic that allows observation of bubbling behavior at various circumferential locations. Spherical glass beads (FUJISTONE GB-01, Fuji-rika industrial Co., Ltd.) were used as experimental model particles and their median diameter and density were 136 m and 2520 kg/m3 , respectively. The size distribution of the particles measured by a sieve analysis is indicated in Fig. 3. The model particle had relatively narrow size distribution, and 94% of the particles existed within 106–180 m. The particles of 170.0 g were charged into the vessel of which the initial bed height was 31 mm. The bubbling behaviors were observed by means of a stationary located high-speed video camera (FASTCAM MAX, Photoron Co., Ltd.). The recording frame rate and shutter speed were set at 2000 frames/s and 0.14 ms, respectively. A metal halide lamp was used as light source. Recording of the bubbling behaviors was carried out under the backlight condition. Fig. 4 shows the representative recorded images of the bubbling behavior. In this study, two-dimensional bubbles were observed. The digitized recorded images consisted of 1024 × 512 picture elements (pixel), and the whole visualized area was 16 cm × 8 cm. An image analysis technique was utilized for the measurement of bubble velocity. First, the binarization processing for segmen-
Fig. 5. Bubble motion over time interval t between two consecutive images.
tation of a bubble from its background (emulsion phase) was conducted. These two phases were distinguished by an optimum threshold value which was determined based on a discriminant analysis method [20]. The binarization processing was individually applied to the measured bubbles. Subsequently, the position of center of gravity of the binarized bubble image in a cylindrical coordinate system was determined individually. The instantaneous radial and angular bubble velocities (UBri and ωBi ) were then obtained from displacement of the center of gravity over a time interval t between two consecutive recorded images as shown in Fig. 5: UBri =
ri,t+t − ri,t t
(4)
ωBi =
i,t+t − i,t t
(5)
In this experiment, the radial direction from the surface of gas distributor to the rotational axis of vessel and the counterclockwise direction in the recorded images were defined as the positive direction of UBr and ωB , respectively. The radial and angular bubble velocity coefficients (Kri and Ki ) were then determined using the following equations: UBri
Kri =
Ki =
ωBi ωv
(6)
ri ωBi 2 DBi (7)
where r¯ i and DBi ,which were the mean radial position and mean bubble diameter between the consecutive recorded images, were obtained using the following equations:
Fig. 4. Recorded bubbling behavior.
ri = 0.5(ri,t+t + ri,t )
(8)
DBi = 0.5(DBi,t+t + DBi,t )
(9)
The bubble diameter was defined as an equivalent diameter of sphere, which was calculated as a product of the bubble phase area and the vessel depth [21]. The total number of measured bubbles was approximately 1500 in each operating condition. We also defined the restrictive conditions for tracking of the bubble motion in order to eliminate the unreliable experimental
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data; the bubbles which satisfied the following three equations were selected as the measurable ones: ri,t+t ≥ ri,t
(10)
i,t+t ≥ i,t 0.95 <
DBi,t+t < 1.05 DBi,t
Fig. 6. Log-normal distributions of radial bubble velocity coefficient at various operating conditions.
181
(11) (12)
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The number fractions of bubbles satisfying the above conditions were more than 98% of the total number in each operating condition. 4. Results and discussion 4.1. Distributions of bubble velocity coefficients In this study, a log-normal distribution was used as the distribution function for bubble velocity coefficients, because Kr and K were well correlated by a log-normal distribution function among others. Fig. 6 shows log-normal distributions of radial bubble velocity coefficient (Kr ) at various gas velocities and centrifugal accelerations. The solid curves indicate the approximated log-normal distribution functions. The geometric mean and geometric standard deviation of Kr were expressed as Kr50 and gr , respectively. G0 is the dimensionless centrifugal factor which is defined as the ratio of centrifugal acceleration at the surface of gas distributor to the gravitational acceleration. The range of Kr varied from 0.2 to 2.0 in each operating parameter. In conventional fluidized beds, the bubble velocity coefficient strongly depends on the bubbling intensity [15–19]; the bubble velocity coefficient increases with an increase in the gas velocity due to the acceleration effect caused by the bubble–bubble interaction. In the RFB, however, the distributions of Kr almost unchanged with the gas velocity and centrifugal acceleration, although the differences of bubbling intensity were clearly observed. In RFBs, the buoyancy force acting on a bubble, which is the driving force of bubble movement, is much larger than that in conventional fluidized beds due to the high centrifugal acceleration. Therefore, the bubble–bubble interaction can be neglected as compared with the huge buoyancy force, resulting in the constant Kr at various operating conditions. The experimental data of Kr for all operating conditions were also approximated by the log-normal distribution function as shown in Fig. 7. As a result, the mean value of Kr could be empirically determined as 0.52. In conventional fluidized beds, value of the bubble velocity coefficient for a two-dimensional single bubble,
which can be recognized as the bubble velocity coefficient without the bubble–bubble interaction, was reported as approximately 0.5 [15,17]. It should be noted that the value of Kr in an RFB was close to the value of the bubble velocity coefficient for a two-dimensional single bubble in conventional fluidized beds. This result means that in the centrifugal force field the bubble–bubble interaction can be neglected as compared with the huge buoyancy force acting on a bubble. Therefore, we believe that value of the bubble velocity coefficient for a three-dimensional single bubble in conventional fluidized beds, which was reported as 0.71 [14], can be adapted as the value of Kr for a three-dimensional bubble in RFBs. Fig. 8 shows log-normal distributions of the angular bubble velocity coefficient (K ) at various operating conditions. The distributions of K could also be expressed by the log-normal distribution function and were almost constant regardless of the operating conditions. Fig. 9 indicates the distribution of K for all the operating conditions. From approximation of K by the log-normal distribution function, the mean value of K could be determined empirically as 0.96. This result means that the averaged angular bubble velocity is slightly smaller than angular velocity of the rotating gas distributor because of slipping between the fluidized particle bed and the rotating gas distributor. In conclusion, the both of bubble velocity coefficients (Kr and K ) could be obtained as the constant value under various conditions of gas velocity and centrifugal acceleration. We believe this simple result becomes great advantage from the viewpoint of design and control of RFBs. 4.2. Prediction of bubble velocities By using the obtained empirical coefficients of Kr = 0.52 and K = 0.96, the radial and angular bubble velocities were estimated solely by the operating parameters. The radial and angular bubble velocities can be expressed as UBr = Kr
gB DB ,
ωB = K ωv , where gB =
gB
Kr = 0.52
K = 0.96
(13) (14)
is the actual centrifugal acceleration acting on a bubble:
2
K G0 g ˇ
(15)
ˇ is the dimensionless radius defined as ˇ=
RV RV − L
(16)
where RV and L are the vessel radius and radial distance from the surface of gas distributor, respectively. The bubble diameter DB in the Eq. (13) can be estimated using our proposed bubble growth model for RFBs [21]. This model is briefly described as follow: we noticed the big differences of fluidization condition between conventional fluidized beds and RFBs, and modified the staged bubble coalescence model proposed by Darton et al. [22] according to the following two concepts: (i) the centrifugal acceleration and excess gas velocity are considered to be expressed as a function of radial distance L from the surface gas distributor, and (ii) the bubble volume flow rate passing through the particle bed with forming the bubbles increases with an increase in L. According to Darton et al. [22], the bubble coalescence is assumed to occur in several steps as shown in Fig. 10. The distance LN from the surface of the gas distributor at the Nth stage of coalescence can be expressed as the following equation: Fig. 7. Log-normal distributions of radial bubble velocity coefficient for all operating conditions.
LN = Dc0 + Dc1 + · · · + Dc(N−1)
(17)
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183
Fig. 8. Log-normal distributions of angular bubble velocity coefficient at various operating conditions.
where Dc is the circle diameter of distributor per hole. indicates the bubble coalescence constant which was preliminary determined as 0.77. The value of N is chosen depending on the particle bed height. The correlation between the Dc and DB at the Nth stage of coalescence can be defined by using the correlation of Miwa
et al. [23]:
DcN = 0.75
gN 0.25 DBN 1.25 (u − umf )N 0.5
(18)
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The volume balance of bubble in each coalescence stage can be expressed as follows:
⎫
3 = 2D3 + 2D3 DB1 ⎪ B0 BG,1 ⎪ ⎪ 3 = 2D3 + 2D3 ⎪ DB2 ⎪ B1 BG,2 ⎬ 3 3 3 DB3 = 2DB2 + 2DBG,3 ⎪ .. ⎪ ⎪ . ⎪ ⎪ 3 3 3 DB(N−1) = 2DB(N−2) + 2DBG,(N−1) ⎭
(21)
where, DBG,N is defined as the “gained bubble diameter” at Nth coalescence stage. The gained bubble originates from the increased bubble volume flow rate with an increase in L. The equation of DBG,N is derived based on the correlation of Miwa et al. [23] as follows:
DBG,N = 1.38
Fig. 9. Log-normal distributions of angular bubble velocity coefficient for all operating conditions.
where gN and (u − umf )N are the local centrifugal acceleration and local excess gas velocity at the Nth stage of coalescence, respectively. They are defined as a function of L [24]. gN =
G0 g ˇN
(19)
(u − umf )N = ˇN u0 −
×
1 ˇN f dp 2
33.7 + 0.0408
f (p − f )dp3 G0 g
0.5
2 ˇN
− 33.7
(u − umf )N − (u − umf )N−1 0.5 gN−1
0.4 Ac(N−1)
Finally, the correlation between the bubble diameter and the dimensionless radius can be obtained by numerically solving the Eqs. (17)–(22). The validity of this model has already been confirmed [21]. Fig. 11 shows the estimation and experimental results of radial bubble velocity as a function of dimensionless radius ˇ. The experimental bubble velocities indicate the geometric mean velocity obtained by the fitting of log-normal distribution function in the range of a certain ˇ to ˇ + ˇ. The each curve is predicted value by the Eq. (13). The values of sequential number N used for estimation by the proposed bubble growth model are also presented in Fig. 11. The radial bubble velocities increased with an increase in ˇ due to the bubble growth. With further increase in ˇ, the increasing rate of radial bubble velocity gradually decreased, because the actual centrifugal acceleration gB became smaller. The radial bubble velocity also increased with an increase in G0 ; this means that the bubble velocity in RFBs is higher than that in conventional fluidized beds when the bubble sizes are the same. Fig. 12 shows comparison of the estimation results of radial bubble velocity with the experimental results at various operating conditions. Since the estimated bubble size using the proposed bubble growth model showed high
(20)
Fig. 10. Schematic illustration of bubble growth model.
(22)
Fig. 11. Radial bubble velocity as a function of dimensionless radius.
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5. Conclusions
Fig. 12. Comparison of estimation results of radial bubble velocities with experimental results at various operating conditions.
accuracy [21], the estimated radial bubble velocities showed good agreement with the experimental results, and the calculation errors were within approximately 30%. Fig. 13 indicates the estimation and experimental results of angular bubble velocity as a function of ˇ. The angular bubble velocities were constant with a change in ˇ at G0 = 10–30. However, it slightly increased with an increase in ˇ at G0 = 40. This is because the effect of the Coriolis force acting on a bubble becomes higher than that under lower centrifugal acceleration.
Fig. 13. Angular bubble velocity as a function of dimensionless radius.
The bubble velocity in a rotating fluidized bed (RFB) was experimentally analyzed. The two components of bubble velocity in the radial and angular directions were measured. The radial bubble velocity was expressed using the similar type of equation for the bubble rise velocity in conventional fluidized beds, and the angular bubble velocity was described using the linear relationship with the angular velocity of vessel. The coefficients of radial and angular bubble velocities (Kr and K ) were then evaluated under various conditions of gas velocity and centrifugal acceleration. The distributions of Kr and K could be expressed by the log-normal distribution function. It should be noted that the distributions of Kr and K were constant regardless of operating conditions, because the buoyancy force acting on the bubble was much higher than the bubble–bubble interaction force. The bubble velocity coefficients could be empirically obtained as Kr = 0.52 and K = 0.96. The correlation to estimate the bubble velocity in RFBs was then proposed empirically. The proposed empirical correlation could estimate the radial and angular bubble velocities within approximately 30% and 5% of estimation error, respectively. Consequently, the radial and angular bubble velocities could be predicted only by the operating parameters. It was also confirmed that the bubble velocity in an RFB is generally higher than that in a conventional fluidized bed if the bubble sizes are the same, because in high centrifugal force field the buoyancy force acting on a bubble which is the driving force of bubble movement is much larger than that under gravitational field. Acknowledgement Authors acknowledge the financial support by the Grant-in-Aids for JSPS Research Fellow from the Ministry of Education, Science, Sports and Culture of Japan. Appendix A. Nomenclature Ac dp DB DBG Dc g g gB G0 Kr K L r Rv t u umf u0 UB UBr
area of distributor per hole (m2 ) particle diameter (m) bubble diameter (m) gained bubble diameter (m) circle equivalent diameter of Ac (m) gravity acceleration (m s−2 ) local centrifugal acceleration (m s−2 ) actual centrifugal acceleration acting on a bubble (m s−2 ) dimensionless centrifugal factor radial bubble velocity coefficient angular bubble velocity coefficient radial distance from surface of gas distributor (m) radius of cylindrical coordinate (m) radius of vessel (m) time interval between consecutive two images (s) superficial gas velocity (m s−1 ) minimum fluidization velocity (m s−1 ) superficial gas velocity at gas inlet (m s−1 ) rise velocity of single bubble (m s−1 ) radial bubble velocity (m s−1 )
Greek letters ˇ dimensionless radius -coordinate in cylindrical coordinate system (rad) constant in Eq. (17) gas viscosity (Pa s) f gas density (kg m−3 )
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particle density (kg m−3 ) geometric standard deviation angular bubble velocity (rad s−1 ) angular velocity of vessel (rad s−1 )
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