Wakes forming bubbles

The bubble phase formed by gas in excess of that required for the onset of fluidization. The bubble is usually surrounded by a cloud of gas-soM mixture and is characterized by an indentation caused by suction due to the upward movement of the bubble. The solids that flU up this region are called the wake. The bubbles are usually large and move faster than the surrounding emulsion gas flowing at u p thus giving rise to the cloud. This behavior is usually characteristic of Geldart A and B particles (see Section 11.4.2.2). 

Each bubble drags a wake of solid particles up with it (Rowe and Partridge, 1965). This forms an additional region, and the movement creates recirculation of particles in the bed upward behind the bubbles and downward elsewhere in the emulsion region. 

The ratio of wake volume to bubble volume is difficult to assess, and is given by Kunii and Levenspiel (1991, p. 124) in the form of graphical correlations with particle size for various types of particles. From this, we assume that the bed fraction in the wakes1 is ... 

Note that the continuity equations for product B reflect the fact that B, formed in the cloud + wake and emulsion regions, transfers to the bubble region. This is in contrast to reactant A, which transfers from the bubble region to the other regions. 

At low Re, wakes behind large bubbles and drops are closed (B3, H5, S5, W2, W6), whereas at high Re open turbulent wakes are formed (F15, Ml, W6). The value of Re for transition between these two types of wake has been determined as 110 + 2 (B3) for skirtless bubbles. There is some evidence (H5) that the transition Reynolds number may be increased if skirts are present. 

Bhaga (B3) determined the fluid motion in wakes using hydrogen bubble tracers. Closed wakes were shown to contain a toroidal vortex with its core in the horizontal plane where the wake has its widest cross section. The core diameter is about 70% of the maximum wake diameter, similar to a Hill s spherical vortex. When the base of the fluid particle is indented, the toroidal motion extends into the indentation. Liquid within the closed wake moves considerably more slowly relative to the drop or bubble than the terminal velocity Uj, If a skirt forms, the basic toroidal motion in the wake is still present (see Fig. 8.5), but the strength of the vortex is reduced. Momentum considerations require that there be a velocity defect behind closed wakes and this accounts for the tail observed by some workers (S5). Crabtree and Bridgwater (C8) and Bhaga (B3) measured the velocity decay and drift in the far wake region. 

Focusing on the bubbles, it should be mentioned that they are not exactly spherical. They contain very small amounts of solids and have an approximately hemispherical top and a pushed-in bottom. Each bubble of gas has a wake that contains a significant amount of solids. These characteristics are illustrated in Figure 3.58. Consequently, during their journey in the reactor, the bubbles carry an amount of solids. The net flow of the solids in the emulsion phase must therefore be downward. The gas within a particular bubble remains largely within that bubble and only a small part of it penetrates a short distance into the surrounding emulsion phase, forming the so-called cloud. 

Particles are ejected into the freeboard via two basic modes (1) ejection of particles from the bubble roof and (2) ejection of particles from the bubble wake, as illustrated in Fig. 9.19. The roof ejection occurs when the bubble approaches the surface of the bed, and a dome forms on the surface. As the bubble further approaches the bed surface, particles between the bubble roof and surface of the dome thin out [Peters et al., 1983]. At a certain dome thickness, eruption of bubbles with pressure higher than the surface pressure takes place, ejecting the particles present on top of the bubble roof to the freeboard. In wake ejection, as the bubble erupts on the surface, the inertia effect of the wake particles traveling at the same velocity as the bubble promptly ejects these particles to the freeboard. The gas leaving the bed surface then entrains these ejected particles to the freeboard. 

When a spherical-cap bubble rises through a uniform swarm of smaller bubbles in water, velocity enhancement of the cap bubble is observed, the enhancement being associated with a change in its shape to an axially elongated form (HIO, Fig. 4). In this case the wake will probably be reduced considerably in volume. 

The gas-filled voids (bubbles) rise in the fluidized bed due to an inflow of solids from their perimeter. Because free flowing and/or incipiently fluidized bulk solids have small angles of repose, they cannot stand at 90° angles and, therefore, the solids slide down along the bubble s walls into the bottom area where all peripheral streams converge to form a so-called wake, as illustrated in Figure 170. 

As the Reynolds number increases, a wake is formed behind the fluid sphere or ellipsoid [22, 45]. The formation of a wake behind a fluid particle is delayed compared to a solid sphere due to the internal circulation of the gas. The recirculating wake may be completely detached from the fluid sphere. A secondary internal vortex will then not be formed. For smaller particle Reynolds numbers the wake is symmetrical, but as the Reynolds number increases further the vortex sheet breaks down to vortex rings. Further increase of the Re molds number cause the vortex rings to shed asymmetrically, and the drop or bubble will show a rocking motion. This is one of the two types of secondary motion defined. The other is oscillations (shape dilations), and is also thought to be due to the vortex shedding. 

The acceleration of the liquid in the wake of the bubbles can be taken into account through the added mass force given by (5.112), whereas the Eulerian lift force acting on the dispersed phase is normally expressed on the form (5.65). 

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... 

One may imagine that just above the distributor solid is entrained by the rising bubbles to form the bubble wake. This solid is carried up the bed with the bubbles at velocity Ub and is continually exchanged with fresh emulsion solid. At the top of the bed the wake solids rejoin the emulsion to move down the bed at velocity Ug. The upward velocity of gas flowing through the emulsion is thus ... 

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