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Recirculating and Jetting Fluidized Beds 265

gas goes through a fairly large nozzle. Because of the dominant effect of this jetting action provided by the large nozzle, this type of fluidized bed can be more appropriately called a jetting fluidized bed, especially when the jet does not penetrate through the bed like that in a spouted bed. Jetting, bubbling dynamics, and solid circulation are important hydrodynamic phenomena governing the performance and operation of large-scale jetting fluidized beds. They are the focus of our discussion in this section.

3.1Jet Penetration and Bubble Dynamics

Gas jets in fluidized beds were reviewed by Massimilla (1985). A more recent review is by Roach (1993) who also developed models to differentiate three jet flow regimes: jetting, bubbling and the transition. However, most of the data were from jets smaller than 25 mm. The discussion here will emphasize primarily large jets, up to 0.4 m in diameter, and operation at high temperatures and high pressures. The gas jets can also carry solids and are referred to as gas-solid two-phase jets in this discussion.

Momentum Dissipation of a Gas-Solid Two-Phase Jet. Gas velocity profiles in a gas-solid two-phase jet inside a fluidized bed were determined at five different horizontal planes perpendicular to jet direction using a pitot tube (Yang and Keairns, 1980). The velocity profiles were integrated graphically, and gas entrainment into a jet was found to occur primarily at the base of the jet.

The measured impact pressures and static pressures were converted to gas velocities using the following equation:

The coefficient C was assumed to be 1. The typical velocity profiles are shown in Figs. 13–15 for a nominal jet velocity of 62.5 m/s and solid loadings (weight of solids/weight of gas) of 0–1.52. Note that at 1.7 cm from the jet nozzle, the velocity profile is independent of solid loadings (Fig. 13). The jet at 1.7 cm from the nozzle is still in the potential core region. At greater distances from the jet nozzle, the velocity profiles become dependent on the solid loadings (Figs. 14–15), with jets of higher solid loadings penetrating deeper into the bed, as expected.

Recirculating and Jetting Fluidized Beds 271

Figure 19. Definition of jet penetration depth and jet half angle.

In the absence of (Ucf)p and (Ucf)atm, (Umf)p and (Umf)atm can be employed.

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The limiting form of Eq. (24) at atmospheric pressure (101 kPa), where the correction factor Rcf = 1, approaches the correlation originally proposed for atmospheric condition, as shown in Eq. (25):

Equation (25) now is only a special case of the general correlation expressed in Eq. (23).

For concentric jets and gas-solid two-phase jets, the jet momentum flux term ρf Uj2 can be evaluated as follows, as suggested by Yang et al. (1984b):

The solids particle velocity in the gas-solid two-phase jet can be calculated as shown in Eq. (27), assuming that the slip velocity between the gas and the solid particles equals the terminal velocity of a single particle. It should be noted that calculation of jet momentum flux by Eq. (26) for concentric jets and for gas-solid two-phase jets is only an approximation. It involves an implicit assumption that the momentum transfer between the concentric jets is very fast, essentially complete at the jet nozzle. This assumption seems to work out fine. No further refinement is necessary at this time. For a high velocity ratio between the concentric jets, some modification may be necessary.

The good agreement obtained for all data using the modified Froude number signifies the physical significance of the parameter. In fact, the dependence of jet penetration on the two-phase Froude number can be derived theoretically from the buoyancy theory following that of Turner (1973).

The momentum flux at the orifice, M, is given by

Recirculating and Jetting Fluidized Beds 273

The buoyancy flux at the orifice, B, can be expressed as

The characteristic length scale, Lj, taken here to be the jet penetration depth is shown by Turner (1973) for a buoyancy jet to be

Equation (30) is essentially similar to Eq. (25).

The experimental data included in the correlation, however, are mostly from jets of less than 6 cm in diameter. The question often asked is whether the developed correlation is applicable for scaleup to a much larger jet nozzle. The size effect will have to be verified with operational data from a jet nozzle considerably larger. Jet penetration data were obtained for a 0.4 m diameter compound jet in a 3-m diameter cold model. The experimental jet penetration data were compared with four existing correlations (Yang et al., 1995). These correlations were selected because they are all dimensionless in form and are often quoted in the literature. They were usually derived through either dimensionless analysis or semitheoretical argument. Pure empirical but dimensional correlations are not included because the dimensional empirical correlations based on small jet nozzle data base have no value for scaleup purpose. Correlations by Merry (1975), Wen et al. (1982), and Hirsan et al. (1980) predicted substantially higher jet penetration depth than that observed, probably because they included a dimensionless factor, do /dp. Inclusion of this dimensionless group can exaggerate the jet penetration depth when the jet nozzle diameter, do , is large. Better agreement was obtained by using the correlation proposed by Yang (1981), i.e., Eq. (23).

Jet Half Angle. Determination of jet half-angle is shown also in Fig. 19. The jet half-angle can thus be calculated from the experimentally measured bubble size and jet penetration depth as follows:

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Experimentally observed jet half-angle range from 8° to 12° for the experimental data mentioned above. These compare to 10° suggested by Anagbo (1980) for a bubbling jet in liquid.

Bubble Dynamics. To adequately describe the jet, the bubble size generated by the jet needs to be studied. A substantial amount of gas leaks from the bubble, to the emulsion phase during bubble formation stage, particularly when the bed is less than minimally fluidized. A model developed on the basis of this mechanism predicted the experimental bubble diameter well when the experimental bubble frequency was used as an input. The experimentally observed bubble frequency is smaller by a factor of 3 to 5 than that calculated from the Davidson and Harrison model (1963), which assumed no net gas interchange between the bubble and the emulsion phase. This discrepancy is due primarily to the extensive bubble coalescence above the jet nozzle and the assumption that no gas leaks from the bubble phase.

High speed movies were used to document the phenomena above a 0.4 m diameter jet in a 3-meter diameter transparent semicircular jetting fluidized bed (Yang et al., 1984b). The movies were then analyzed frame by frame to extract information on bubble frequency, bubble diameter, and jet penetration depth. The process of bubble formation is very similar to that described in Kececioglu et al. (1984), but it was much more irregular in the large 3-m bed. Because of this irregularity, it was difficult to count accurately the “bubbles” between the constrictions immediately above the jet nozzles. The initial bubble formation at the top of the jet was assumed complete when the gaseous tail with entrained solids disappeared into the gas bubbles. The largest horizontal dimension of the bubble was reported to be the bubble size; the distance between the top of the jet nozzle and the bottom of the gas bubble, the jet penetration depth.

The Davidson and Harrison (1963) model assumed there was no net exchange of gas between the bubble and the emulsion phase. The validity of this assumption was later questioned by Botterill et al. (1966), Rowe and Matsuno (1971), Nguyen and Leung (1972), and Barreto et al. (1983). The predicted bubble volume, if assumed no net gas exchange, was considerably larger than the actual bubble volume experimentally observed.

A model was developed to describe this phenomenon by assuming that the gas leaks out through the bubble boundary at a superficial velocity equivalent to the superficial minimum fluidization velocity. For a hemispherical bubble in a semicircular bed, the rate of change of bubble volume can be expressed as: