Yang Fluidization, Solids Handling, and Processing

Heat Transfer in Fluidized Beds 175

In fast fluidized beds, the particles enter the bottom of the bed with little or no vertical velocity, gaining velocity by momentum transfer from the high speed gas as they pass upward through the bed. Since particle velocity increases with elevation in the bed, mass balance requires that the average solid volumetric concentration decrease with elevation along the length of the vertical bed. Figure 11 shows representative data obtained by Herb et al. (1989). For the operating conditions represented in this figure, it is seen that the axial height required to approach fully-developed flow conditions (i.e., constant solid concentration) can be many meters, increasing with increasing particle size. The data of Hartige, Li and Verther (1986), as shown in Fig. 12 indicate that the exact rate of axial development of solid concentration varies also with solid mass flux and with bed diameter. The figures also illustrate that in the fast fluidized regime, cross- sectional-averaged solid concentrations are typically less than 5%, in contrast to solid concentrations in a range of 30–40% for bubbling dense fluidization.

The hydrodynamic characteristic of fast fluidized beds is complicated by the existence of significant radial (horizontal) variations in solid concentration and velocity. Radial profiles of solid volume fraction, measured by Beaude and Louge (1995) are shown in Fig. 13. It is seen that for the same Froude number, there is increasing nonuniformity of solid concentration with increasing solid mass flux. At the higher mass fluxes shown in this figure, local solid volume fractions adjacent to the bed wall approach magnitude of 30%, in contrast to solid fractions of 1–3% near the bed centerline. Herb, Tuzla and Chen (1989) and Werther (1993) noted that such radial distributions can be normalized as a general similarity profile for various operating conditions by utilizing dimensionless ratio of local solid concentration to cross-sectional-averaged solid concentration.

Solid flow mass flux and velocity also vary in magnitude across the radius of fast fluidized beds. Experimental measurements obtained by Herb, Dou, Tuzla and Chen (1992) are plotted in Fig. 14. It is seen that while local solid fluxes are positive upward in the core of the bed, they can become negative downward in the region near the bed wall. The difference between core and bed regions becomes increasingly greater as total solid mass flux increases. This downward net flow of solid in the region near the bed wall has important significance for heat transfer at the wall.

Heat Transfer in Fluidized Beds 179

erosion in the fast-flowing two-phase flow. Thus the designer is concerned with effective heat transfer coefficients on vertical surfaces which are exposed to the fast-fluidized media. Operational parameters that are known to affect the magnitude of the heat transfer coefficient include: gas velocity, solids flow rate (mass flux), mean particle diameter, axial location of the heat transfer surface along height of the fluidized bed, radial location of the heat transfer surface across the bed, and physical dimension of the heat transfer surface. Some of the generic characteristics were indicated by the early data of Kiang et al. (1976), as shown in Fig. 16. General characteristics may be noted as:

•Magnitude of the heat transfer coefficient generally decreases with elevation along the bed.

•At low elevations the heat transfer coefficient generally decreases with increasing gas velocity.

•At higher elevations the heat transfer coefficient increases with increasing gas velocity.

•Magnitude of the heat transfer coefficient is higher than that for equivalent air convection, but lower than that found in dense bubbling beds.

These characteristics point to a correlation of the heat transfer coefficient with local solid concentration. As indicated in Fig. 11, solid concentrations tend to be higher in the bottom region of fast fluidized beds; hence the higher heat transfer coefficients in that region. Increasing gas velocity increases the upward acceleration of solid particles, causing a decrease of solid concentration at the bottom and increasing concentrations of solid at the top regions—with corresponding changes in the local heat transfer coefficients. Grace (1985) illustrates this correlation characteristic by plotting heat transfer coefficient versus the suspension density of the solid-gas mixture, using data of Fraley et al. (1983). As shown in Fig. 17, such a plot graphically illustrates the increasing heat transfer coefficient with increasing solid concentration. The various lines in Fig. 17 are correlations that attempt to capture this dependence, generally of the form,

Eq. (15)

h=a∙(ρsusp)b

where a = empirical function of physical properties b = empirical exponent

180 Fluidization, Solids Handling, and Processing

182 Fluidization, Solids Handling, and Processing

reaching a plateau or decreasing slowly with further increases in gas velocity. The data of Fig. 16 also illustrates a second parametric effect — that for a given gas velocity, the heat transfer coefficient generally decreases with axial elevation, the effect being strongest at relatively low superficial gas velocities.

Furchi et al. (1988) measured heat transfer coefficients at the wall of a 7.2 cm diameter fast fluidized bed, operating with glass particles of various diameters. Their results, shown in Fig. 18 indicates significant parametric effects of solid mass flux and of particle diameter. For a given size of particles, it is seen that there is a marked increase in the heat transfer coefficient as the solid mass flux (Gs /Gg) increases. This trend is most obvious for the smaller size particles (dp of 109 μm), becoming less obvious with particle diameters greater than 200 μm. For a given gas velocity and solid mass flux, the data in Fig. 18 indicate significant increases in heat transfer coefficients as diameter of the fluidized particles are reduced; at a Gs/Gg of 10, the effective heat transfer coefficient is increased by approximately 300% as the particle diameter decreased from 269 to 109 μm.

The interaction of parametric effects of solid mass flux and axial location is illustrated by the data of Dou et al. (1991), shown in Fig. 19. These authors measured the heat transfer coefficient on the surface of a vertical tube suspended within the fast fluidized bed at different elevations. The data of Fig. 19 show that for a given size particle, at a given superficial gas velocity, the heat transfer coefficient consistently decreases with elevation along the bed for any given solid mass flux Gs. At a given elevation position, the heat transfer coefficient consistently increases with increasing solid mass flux; at the highest elevation of 6.5 m, where hydrodynamic conditions are most likely to be fully developed, it is seen that the heat transfer coefficient increases by approximately 50% as Gs increased from 30 to 50 kg/m2s.

The experiments of Dou et al. (1991) also indicate that the heat transfer coefficient varied with radial position across the bed, even for a given cross- sectional-averaged suspension density. Their data, as shown in Fig. 20, clearly indicate that the heat transfer coefficient at the bed wall is significantly higher than that for vertical surfaces at the centerline of the bed, over the entire range of suspension densities tested. Almost certainly, this parametric effect can be attributed to radial variations in local solid concentration which tends to be high at the bed wall and low at the bed centerline.

Heat Transfer in Fluidized Beds 183

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184 Fluidization, Solids Handling, and Processing

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