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Ind. Eng. Chem. Res. 1996, 35, 3822-3823
CORRELATIONS A Correlation for the Suspension-to-Wall Heat-Transfer Coefficient in Circulating Fluidized Beds Xiao S. Wang* and Bernard M. Gibbs Department of Fuel and Energy, Leeds University, Leeds LS2 9JT, England
Martin J. Rhodes Department of Chemical Engineering, Monash University, Victoria 3168, Australia
Derek Geldart Department of Chemical Engineering, Bradford University, Bradford BD7 1DP, England
The Zadbrodsky correlation for heat transfer in bubbling fluidized beds is modified for use in circulating fluidized beds. The modified correlation is demonstrated to be capable of providing reasonable predictions of the suspension-to-wall heat-transfer coefficient in circulating fluidized beds for a range of particle sizes and riser diameters. Introduction In recent years circulating fluidized beds (CFBs) have been extensively used for coal combustion and gas-solid reactions. In the design of CFB boilers or reactors it is important that the heat-transfer coefficient be estimated with reasonable accuracy. While a considerable amount of research has been carried out, prediction of heattransfer coefficients in a CFB has met with only limited success. Although a number of models are now available in the literature, their application often involves complicated computation. In addition, the required input parameters such as the contact time and velocity distributions of particle packets on the heat-transfer surface are difficult to determine. Development of a simple expression for heat transfer in a CFB is therefore of practical significance. Since the basic mechanism of heat transfer in a CFB resembles that in a bubbling fluidized bed (BFB) (in both cases particle packets play an important role in suspension-to-wall heat transfer), it would be worthwhile to see if correlations developed under BFB conditions are still valid for a CFB. In this work the well-known Zadbrodsky correlation has been modified and compared with measurements of the suspension-to-wall heat-transfer coefficient in CFBs made by a number of researchers.
Adaptation of Zadbrodsky Correlation for CFB Conditions Equation 1 can be rewritten as
h ) 35.8[Fp(1 - w)]0.2kg0.6dp-0.36/(1 - w)0.2
Zadbrodsky (1966) proposed the following correlation for the maximum bed-to-surface heat-transfer coefficient (neglecting radiation effects) in a BFB:
(1)
where Fp, kg, and dp are particle density, gas thermal conductivity, and particle diameter, respectively. This dimensional correlation was determined based on measurements using small spherical calorimetric heat probes. * To whom correspondence should be addressed. Telephone: (44) 113 233 2491. Fax: (44) 113 244 0572. Email:
[email protected].
S0888-5885(96)00164-9 CCC: $12.00
(2)
to include the term Fp(1 - w), the bulk density of the bed (or suspension) at the wall. For a BFB w is about 0.6, so (1 - w)0.2 is approximately 0.83. It should be emphasized that we are dealing with the voidage giving rise to the maximum heat-transfer coefficient and that (1 - w)0.2 is quite insensitive to the actual value of voidage of the BFB used. Therefore, eq 2 may be expressed as
h ) 43.1[Fp(1 - w)]0.2kg0.6dp-0.36
(3)
According to Rhodes et al. (1992), voidage at the wall (w) may be approximately correlated to the crosssectional mean voidage () of a CFB by
(1 - w)/(1 - ) ) 2
Zadbrodsky Correlation
h ) 35.8Fp0.2kg0.6dp-0.36
The validity of the correlation for powders of Geldart’s group B in BFBs has been widely demonstrated (Botterill, 1986).
(4)
Hence, eq 3 can be expressed as
h ) 49.5[Fp(1 - )]0.2kg0.6dp-0.36
(5)
This modified Zadbrodsky correlation (eq 5) has been used to predict the variations in the bed-to-surface heat-transfer coefficient in a CFB with suspension density Fp(1 - ). Results and Discussion Comparisons of predictions using eq 5 with measurements made by a number of researchers (Zhou, 1992; Wu et al., 1989; Basu and Nag, 1987) are shown in Figures 1-4, which include variations in particles, © 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3823
Figure 1. Variation in the suspension-to-wall heat-transfer coefficient with suspension density for a 75 µm alumina powder in a 0.305 m i.d. riser (Zhou, 1992) and prediction of eq 5.
Figure 4. Variation in the suspension-to-wall heat-transfer coefficient with suspension density for 227 µm silica sand in a 0.102 m i.d. riser (Basu and Nag, 1987) and prediction of eq 5.
solids flux that independently affects the heat-transfer coefficient. It should be emphasized that eq 5 may represent the upper limit of the heat-transfer coefficient and is therefore suitable for predicting heat-transfer coefficients for small heat-transfer surfaces. For larger heat-transfer surfaces the variations of suspension density and gas thermal conductivity along the heat-transfer surface must be carefully considered. In addition, the radiation effect needs to be taken into account when the operating temperature is above 600 °C. Acknowledgment
Figure 2. Variation in the suspension-to-wall heat-transfer coefficient with suspension density for a 75 µm alumina powder in a 0.152 m i.d. riser (Zhou, 1992) and prediction of eq 5.
The research work reported here was carried out with the financial support of the EPSRC. Nomenclature dp ) particle diameter (m) h ) bed-to-surface heat-transfer coefficient (W/m2 K) kg ) gas thermal conductivity (W/m K) Greek Letters ) cross-sectional mean voidage w ) voidage at the wall Fp ) particle density (kg/m3)
Literature Cited
Figure 3. Variation in the suspension-to-wall heat-transfer coefficient with suspension density for 171 µm silica sand in a 0.152 m i.d. riser (Wu et al., 1989) and prediction of eq 5.
particle sizes, and riser diameters. In most cases the agreement between measurements and predictions is encouraging, suggesting that mechanisms of heat transfer are similar in both bubbling and circulating beds. This is because in both systems heat transfer is due to the renewing contact of particle packets on the heattransfer surface. Equation 5 implies that, for a given particle size and operating temperature, the heattransfer coefficient is a function only of the suspension density. This agrees with the observation of some researchers (e.g., Zhou, 1992) that it is the suspension density rather than the superficial gas velocity or the
Basu, P.; Nag, P. K. An Investigation into Heat Transfer in Circulating Fluidized Bed. Int. J. Heat Mass Transfer 1987, 30, 2399. Botterill, J. S. M. Fluid Bed Heat Transfer. In Gas Fluidization Technology; Geldart, D., Ed.; John Wiley & Sons Ltd.: New York, 1986; p 219. Rhodes, M.; Zhou, S.; Benkreira, H. Flow of Dilute Gas-Particle Suspensions. AIChE J. 1992, 38, 1913. Wu, R. L.; Lim, C. J.; Grace, J. R. The Measurement of Instantaneous Local Heat Transfer Coefficient in Circulating Fluidized Bed. Can. J. Chem. Eng. 1989, 67, 301. Zadbrodsky, S. S. Hydrodynamics and Heat Transfer in Fluidized Beds; MIT Press: Cambridge, MA, 1966. Zhou, S. Fluid Dynamics and Heat Transfer in Circulating Fluidized Beds. Ph.D. Dissertation, University of Bradford, Bradford, U.K., 1992.
Received for review March 20, 1996 Revised manuscript received May 24, 1996 Accepted May 24, 1996X IE960164H
X Abstract published in Advance ACS Abstracts, August 15, 1996.
