Single Bubble in a Fluidized Bed

In the experimental study of single-bubble behavior, the gas-solid fluidized bed to which a single bubble is introduced is usually maintained at the minimum fluidization condition. Characteristics of a single gas bubble in a gas-solid fluidized bed are similar to those in a liquid medium [Clift and Grace, 1985 Fan and Tsuchiya, 1990 Krishna, 1993]. 

Most bubbles in gas-solid fluidized beds are of spherical cap or ellipsoidal cap shape. Configurations of two basic types of bubbles, fast bubble (clouded bubble) and slow bubble (cloudless bubble), are schematically depicted in Fig. 9.7. The cloud is the region established 

The wake angle 0W defined in Fig. 9.7 is closely related to the shape of a bubble. A smaller 6W represents a flatter bubble, whereas a large 0W represents a more rounded one. A large wake angle 0W yields a smaller wake fraction /w which is defined as the volume ratio of wake to bubble. As shown in Fig. 9.9,0W is related to particle diameter dp. An increase in 

In gas-solid fluidized beds wake shedding has also been observed. The shed wake fragments are banana-shaped and the shedding may occur at fairly regular intervals [Rowe and Partridge, 1965 Rowe, 1971], 

To describe the particle and gas flows around the bubble in fluidized beds, the pioneering model of Davidson and Harrison (1963) is particularly noteworthy because of its fundamental importance and relative simplicity. On the basis of some salient features of this model, a number of other models were developed [e.g., Collins, 1965 Stewart, 1968 Jackson, 1971]. The material introduced later follows Davidson and Harrison s approach. 

---

Bubble velocity and diameter In the context of the bubbling bed theory, the rise velocity of a single bubble in a fluidized bed is given by (Wen, 1984)... 

Derive the cloud thickness and volume ratio of cloud to bubble for a single bubble in a fluidized bed in terms of the Davidson-Harrison (1963) model. Since the cloud is the region established by the gas circulating in a closed loop between the bubble and its surrounding, the following assumptions can be employed (1) zero radial gas velocity outside the surface of the cloud sphere (r = Rc) (2) uniform gas velocity at far distance from the bubble, i.e., Uboo... 

It was observed that like a single bubble in liquid, a rising bubble in a fluidized bed drags a wake of material consisting of a gas-solid mixture up the bed behinds it. Close to the bottom of the bed, just above the gas distributor, solids are entrained by the rising bubbles to form the bubble wake. There is... 

Eqs. (47) and (48) describe, for the conditions considered by Kim et al. [49], (uq = 2.0-50.0 cm/s) the significant effect of uq on and d. Iforeover, the same equations also show the relatively small and more complex dependence of d y and on V and a parameters. The bubble velocity observed by Kim et al. [49] was about 50-60% higher than the velocities that could be predicted using eq. (44) for the same bubble sizes.lt was claimed that this difference resulted from the fact that bubble clouds rise considerably faster than a single isolated bubble in a fluidized bed. 

The phenomenon of a gas bubble rising in a fluidized bed is similar to that of a gas bubble rising in a liquid bubbles rise through the bed at a constant velocity for a given size, this velocity being proportional to bubble diameter. The general relationship for a single bubble is of the... 

Consider a bubble rising in a fluidized bed. It is assumed that the bubble is solids-free, is spherical, and has a constant internal pressure. Moreover, the emulsion phase is assumed to be a pseudocontinuum, incompressible, and inviscid single fluid with an apparent density of pp(l — amf) + pamf. It should be noted that the assumption of incompressibility of the mixture is not strictly valid as voidage in the vicinity of the bubble is higher than that in the emulsion phase [Jackson, 1963 Yates et al., 1994]. With these assumptions, the velocity and pressure distributions of the fluid in a uniform potential flow field around a bubble, as portrayed by Fig. 9.10, can be given as [Davidson and Harrison, 1963]... 

Tuot, J. and Clift, R. (1973). Heat Transfer Around Single Bubbles in a Two-Dimensional Fluidized Bed. Chem. Eng. Prog. Symp. Ser., 69(128), 78. 

Fig. 16. Computer-generated solidity distribution showing the single bubble in a 2D gas fluidized bed. Physical properties of density, 2660 kg/m. Bed dimensions width, 0.58 m height, 1.0 m.

If the bubbles in case a of Fig. 42 do not interfere with each other (D3), then the velocity of the bubbles should equal the free-fise velocity so of a single bubble in a cross-sectional area of liquid large enough for the liquid phase to have no net vertical velocity. This has been indicated by TUrner (T28) in regard to the fluidized bed, for which he modified Eq. (5-1) to the form... 

This expression and the arguments for its use were first presented by Nicklin ]102] for gas-liquid systems determining the rise velocity of a single bubble in a cloud of gas bubbles rising through a stagnant liquid, and later used by Davidson and Harrison [29] (p 28) for bubbles in fluidized beds. 

Bubble formation in liquids with the presence of particles, as in slurry bubble columns and three-phase fluidized bed systems, is different from that in pure liquids. The experimental data of Massimilla et al. (1961) in an air-water ass beads three-phase fluidized bed revealed that the bubbles formed from a single nozzle in the fluidized bed are larger than those in water, and the initial bubble size inereases with the solids concentration. Yoo et al. (1997) investigated bubble formation in pressurized liquid solid suspensions. They used aqueous glyeerol solution and 0.1 mm polystyrene beads as the liquid and solid phases, respectively. The densities of the liquid and the particles were identical, and thus the partieles were neutrally buoyant in the liquid. The results indicated that initial bubble size deereases inversely with pressure under otherwise eonstant eonditions, that is, gas flow rate, temperature, solids eoneentration, orifiee diameter, and gas chamber volume. Their results also showed that the particle effect on the initial bubble size is insignificant. The difference in the finding regarding the particle effect on the initial bubble size between Massimilla et al. (1961) and Yoo et al. (1997) is possibly due to the difference in particle density. 

Measurements in large fluidized beds of fine particles indicate that bubble coalescence often ceases within a short distance above the gas distributor plate. Indications from density measurements or single bubble velocities are that bubble velocity Ug and diameter often reach maximum stable values, which are invariant with height or fluidizing gas velocity. 

Darton and Harrison20 studied the hydrodynamics of a single gas bubble with equivalent diameters in the range 5 through 25 mm in water-fluidized beds of 500-/imand l-mmsand particles in a 22.9-cm-diameter column. The rising velocity of spherical cap bubbles was correlated by a relation... 

---