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Ind. Eng. Chem. Process Des. Dev. 1986, 25, 156-163
Heat Transfer from an Immersed Vertical Tube in a Gas-Fluidized Bed AJay Mathur, Satfsh C. Saxena,’ and Antony Chao Department of Chemical Engineering, University of Illinois at Chicago, Chicago, Illinois 60680
The totel heat-transfer CoefficIenJ, h,, is measured for vertical tubes of diameters 12.7, 28.6, and 50.8 mm immersed in beds of g4ss beads (dp = 275 and 410 pm) and silica sands (dp= 500, 665, and 803 pm) at ambient conditions as a function of fluldlzlng velocity. A general trend of the dependence of h , on the tube diameter is observed. This trend is most explicit for h, which consistently increases as the tube diameter decreases. The correlations of Nu, proposed by various investigators are found incapable of predicting Nu,, values, and, therefore, a correlation Is proposed which reproduces all the existing and present data within f25 % . The dependence of h, on tube diameter is discussed and explained in the context of distributor design, bed geometry, and hydrodynamics.
The disruptions in the international oil supplies which occurred in the past decade have led to the development of a broad-based energy industry, emphasizing the development of various alternative technologies. One of these involves the fluidized-bed combusion of coal either at atmospheric or at higher pressures. This process can utilize high-sulfur as well as high-ash coals in an environmentally acceptable manner. The design of fluidized-bed coal combustors, however, is still based on several empirical and approximate correlations due to our inadequate understanding of the various processes governing its operation. The knowledge of heat removal rates by the boiler tubes immersed in the bed is one such area, though considerable work dealing with the mechanisms of heat transfer has been done (Zabrodsky, 1966; Botterill, 1978; Saxena et al., 1978; Saxena and Gabor, 1981). A discussion of this nature pertaining to a single vertical tube and particularly relating to its diameter constitutes the subject matter of the present work. We have been engaged in a comprehensive effort to understand the mechanism of heat transfer in fluidized beds and have conduded planned experimentti to establish the dependence of h, for horizontal tubes on operating and system parameters (Grewal and Saxena, 1980,1981; Goel and Saxena, 1983),distributor design (Grewal et ai., 1979; Upadhyay et al., 1981),and surface roughness (Grewal and Saxena, 1979; Goel et al., 1984). Some preliminary work has been done with vertical tubes (Verma and Saxena, 1983,1984). The emphasis of the present work is on the nature of the dependence of h, on the vertical tube diameter. Goel and Saxena (1983) observed with horizontal tubes that h, decreased with DT for DT < 50.8 mm but increased with DT for DT 1 50.8 mm. This trend is explained on the basis of the increasing size of the trapped gas bubble of the tube as the tube diameter is increased. The air leakage from the large trapped bubbles causes better movement of the fines, resulting in increased h, values, and particularly for a relatively wide size range bed charge. By contrast, the symmetrical flow pattern around a vertical tube precludes the possibility of an angular variation of voidage around the tube circumference and hence suggests h, to be likely independent of DT at least at the first glance. Our preliminary work, Verma and Saxena *The author to whom all correspondence should be addressed. 0 196-4305/86/ 1125-0 156$0 1.50/ 0
(1983), with five different particles and three different tubes could not lead to a clear conclusion due to the limitation in the maximum fluidizing velocity of about 0.55 m/s. The present work is conducted with three silica sands, two glass beads, and three tubes over a much wider gas velocity range which has become possible due to upgrading of our experimental facility, described in the next section followed by a presentation of our data. The general dependence of h, on bed geometry (size and shape) and bed hydrodynamics in relation to distributor design is discussed in an attempt to understand the role of the heat-transfer tube diameter.
Experimental Facility Many of the details of our experimental facility are given in earlier publications (Goel et al., 1984; Verma and Saxena, 1983), and therefore here only the major relevant features and modifications are briefly described. Air is supplied by two 18.65-kW air-cooled compressors, capable of delivering a total of 0.1 m3/s of air at 377 kPa. The compressed air is dried, filtered to remove oil and water vapors, and metered on rotameters before entering the fluidized-bed system. The fluidization column has a square cross section, 0.305 m to a side, and consists of a plenum chamber, bubble-cap distributor plate, and test and freeboard sections. The column is made from 9-mm sheet metal (all joints are welded to ensure no air leakage) and is sturdy to handle air velocities up to several meters/ second. The test section is 0.61 m t alland is provided with Plexiglas windows for visual observations. Steel mounting supports for the vertical heat-transfer probes are provided at 0.54 m above the distributor plate. A typical design of the heat-transfer probe is shown in Figure 1 and these are provided with 12.7” Cahod heaters. These heaters are powered by a regulated Hewlett-Packard 6274B power supply, and power input is measured by a calibrated voltmeter and ammeter, having an accuracy of 1% . The tube surface temperature is measured by thermocouples, three to eight in number, mounted flush on the surface. The end losses are minimized by providing Teflon caps at both the ends of the tubes. The conical Teflon cap at the lower end of the tube minimizes the perturbations to flow around the tube. The upper end of the tube is force-fitted into a Teflon tube. The vertical stem of a T-shaped mount is forced-fit into the other end of the Teflon tube. This mount is fabricated from two stainless steel tubes welded together to form a T. The two horizontal arms of the T 0 1985 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 1, 1986
157
Table I. Sieve Analysis of the Bed Charges and Their Mean Diameters wt fraction of sample retained between sieves, x i
sieve openings, pm >1400 1180-1400 1000-1180 850-1000 600-850 500-600 425-500 355-425 300-355 250-300 212-250 180-212 150-180 Solids flow direction Gas flow direction
Figure 9. Bubble and solids flow patterns in tall beds, (H/D,) > 2.
wall (Werther and Molerus, 1973). The pattern of bubble flow and associated solids movement in fluidized beds is also given in a recent continuing effort by Chen et al. (1983) and Lin et al. (in press). Unlike the above-mentioned workers, these investigators measured the solids velocity profile and inferred the bubble flow pattern therefrom. The measurements were taken in two 14 cm diameter beds of glass beads of average diameters ranging between 420 and 800 bm. The solids velocity profiles were obtained by tracking the instantaneous position of a radioactive tracer particle by 16 strategically located scintillation counters connected to a minicomputer for real-time analysis. The flow pattern in the bed changed with the fluidizing velocity. They found at low velocities an ascending wall descending center (AWDC) vortex, which implied that the bubbles existed predominantly near the bed walls and moved very little toward the vessel centerline during their rise in the bed. As a result, solids were observed to rise near the walls and descend in the central region of the bed. As the fluidizing velocity was increased, a second countervortex, ascending center descending wall (ACDW) was observed in the upper region of the bed near the walls. This implied that the bubbles moved more toward the vessel centerline and solids descended both in the central region of the bed and along the bed walls in the upper region of the bed, and these are carried upward by the rising bubbles, leading to the formation of the ACDW vortex. Further increases in the fluidizing velocity caused the ACDW vortex to increase
its size in the bed at the expense of the AWDC vortex. At sufficiently high velocities ( U / U,, > -4.6), the AWDC vortex disappeared completely. From the above discussion, it is clear that the change in the bubble flow profile with the aspect ratio and the fluidizing velocity has a pronounced effect on the nature of the descending solids stream and hence on the nature of the solids mixing pattern in the bed. It will, therefore, appear that the value of h, for an immersed surface will characteristically depend upon its location in the bed, upon its size, and upon its size relative to the bed diameter. We discuss these dependencies in the following. However, in passing, we may mention that Werther and co-workers (1973, 1974, 1975), Chen et al. (1983), and Lin et al. (in press) used porous plate distributors, while Whitehead and co-workers (1967a, 1967b, 1967, 1970) employed multituy5re distributors which are similar in hydrodynamic behavior to commonly used bubble-cap distributors. To the extent that the qualitative patterns of solids and bubble movement found by these groups of workers are similar,we conclude that these results are valid, in general, for beds equipped with porous, mitltiorifice, or bubble-cap distributors. In the case of shallow beds, the heat-transfer surface located in the central region of the bed is continuously exposed to a descending stream of solids. The extent of bubbles reaching it would be minimal, unless the tube diameter is large compared to the bed diameter. One would, therefore, expect that the heat-transfer coefficient will show a weak dependence on the tube diameter for a wide range of DT values provided the bed diameter is sufficiently wide in comparison to DT. The experimental results of Antmishin (1966),Chen and Withers (1974), Verma and Saxena (1983), and the present work indicate that the dependence of h, on DT is quite small for small values of DT, but this dependence becomes more pronounced as DT increases. On the other hand, if the bed height is sufficiently greater then 201, based on Werther's (1974) observation, the heat-transfer tube located in the central region of the bed will be exposed to a continuously rising stream of bubbles. In case the tube diameter is quite large as compared to the bed diameter, so that the annulus, (Db D T ) / ~is, narrow, the radial intermixing between the solids in the rising bubble and the descending solids streams and the enhanced turbulence will reduce the solids residence time on the heat-transfer surface. A dependence of h, on DT would, therefore, be observed, with h, being larger for tubes having larger values of DT. This has been observed by Baskakov et al. (1973) who measured the solids residence time on tubes of 15- and 30-mm diameter in beds of 92- and 98-mm diameter. They found the dependence of the solids residence time on the tube diameter to vary as D T ~ , " ~White . et al. (in press) have also observed a similar trend in a cylindrical fluidized bed of 0.152-m diameter for tubes of 25.4- and 60.3-mm diameter. We found the h, values for the wider tube to be greater than those for the narrower tube over the entire range of fluidizing velocities in six different beds with an aspect ratio of 4.5 f 0.2. The width of the annulus in the two cases is 63.3 and 45.9 mm. An approximate quantitative criteria for the annulus width to be characteristically narrow or wide can be developed by its analogy with heat-transfer measurements using tube bundles immersed in a fluidized bed. The analogue of the annulus width will be the pitch of the tube bundle, the latter being defined as the distance between the centers of the two adjacent tubes. Borodulya et al. (1983) found that the character-
Ind. Eng. Chem. Process
istics of heat transfer from a single tube in a bundle are not influenced by the presence of other tubes in the bundle as long as the relative pitch is greater than three. The relative pitch is defined as the ratio of pitch to the tube diameter. This will suggest that as long as the annulus is less than twice the tube diameter, probably good mixing between the wake solids and solids in the descending stream may be expected. Pending the availability of more elaborate experimental data, this qualitative rule may be helpful in design work. We must, however, emphasize that the bubble flow is perturbed by the presence of the heat-transfer tube in the central region of the bed. Rowe and Everett (1972) found that for slender tubes (DT < 7 mm), the bubble motion remained undisturbed, unless a bubble was directly beneath the tube. On the other hand, Rowe and Mason (1981) observed that tubes with diameters ranging between 10 and 50 mm tended to elongate and accelerate the bubbles. This would obviously decrease the solids residence time and thus increase the value of h,, the increase being larger for wider tubes. This experimental observation is in confirmity with our measurements and reinforces the qualitative picture of bed hydrodynamics elucidated above for beds of varying heights, with an immersed vertical tube having different values of diameter. Acknowledgment This work is supported in part by a grant from the National Science Foundation. Nomenclature Ar = Archimedes number = gd 3pg(pa- p,)/pz, dimensionless C,-C4 = constants in eq 7 a n d & dimensionless C = specific heat of fluidizing gas, J/(kg K) = specific heat of the bed particles, J/(kg K) d , = harmonic mean diameter of bed particles, m dPi= average diameter of particles retained between ith and (i + 11th sieves, m Db = bed diameter, m DT = diameter of heat-transfer tube immersed in bed, m DT(=12.7mm) = heat-transfer tube 12.7 mm in diameter, m g = acceleration due to gravity, m/sz h, = heat-transfer coefficient between the bed and an immersed tube, m h , , , = maximum heat-transfer coefficient between the bed and an immersed tube, m H = bed height, m k = thermal conductivity of_fluidizing gas, W/(m K) d u = Nusselt number = h,d,/k,, dimensionless Nu, = Nusselt number Corresponding to hw,, = hw,,dp/kg, dimensionless NU,,,^,, = experimental value of Nu,, dimensionless NU,,,^^,,^^^ = value of Nu,, predicted by a correlation, dimensionless R e = Reynolds number = d p p g U / p ,dimensionlets Re, = Reynolds number corresponding to Uopt= dppgUopt/p, dimensionless U = superficial fluidizing velocity, m/s Ud = superficial fluidizing velocity at minimum fluidization, m/s U,,, = superficial fluidizing velocity at which h,,,,, occurs, m/s xi = fraction of bed sample retained between ith and (i + 1)th sieves, dimensionless
