Bubble wake

Studies of individual bubbles rising in a two-dimensional gas—Hquid—soHd reactor provide detailed representations of bubble-wake interactions and projections of their impact on performance (Fig. 9). The details of flow, in this case bubble shapes, associated wake stmctures, and resultant bubble rise velocities and wake dynamics are important in characteri2ing reactor performance (26). 

Fig. 9. Bubble-wake interactions in a gas—Hquid-soHd reactor (a) soHds concentration profile within bubble-wake domain, where A—A and B—B represent planes through the bubble, vortex, and wake (b) projected impact of interactions on reaction rate as function of particle si2e and Hquid velocity, where (—)...

L. S. Fan and K. Tsuchiya, Bubble Wake Dynamics In Tiquids andTiquid—SolidSuspensions Butterworth-Heinemaim, Boston, Mass., 1990. 

Solid circulation Entrainment in bubble wake Elutriation by bursting of bubbles... 

Tsutsumi, A., Nieh, J.Y. and Fan, L.S., 1991. Role of the bubble wake in fine particle production of calcium carbonate in bubble column systems. Industrial and Engineering Chemistry Research, 30, 2328-2333. 

From the assumption that liquid volume elements travel as bubble wakes at velocities higher than the average liquid velocity, it follows that the bubble movement must influence the residence-time distribution of the liquid phase. However, no work on this subject has come to the author s attention. 

Fan, L. S., Gas-Liquid-Solids Fluidization Engineering . Butterworths, Stoneham, MA (1989). Fan, L. -S., and Tsuchiya, K., Bubble Wake Dynamics in Liquid and Liquid-Solid Suspensions . Butterworth-Heinemann, Stoneham, MA (1990). 

Based upon observations of fhe rise of parficles in the bubble wake and spout (see Chapter 1, p 18), Rowe (1977) showed that the average particle circulation time t around a bed was inversely proportional to the excess gas velocity... 

The classic mechanism of particles being lifted up through the bed in the bubble wake and in the spout behind a bubble (see Chapter 1, p 18) still operates when the bed is composed of two distinct layers jetsam at the bottom and flotsam above. However, Rowe, Nienow and co-workers also showed that bubbles are responsible for segregation... 

If viscous interactions between bubbles and drops are considered, Reay s model predicts that drops can be trapped hydrodynamically in the wake behind the rising bubbles, especially for very small or negative values of G (e.g., small oil drops). In fact, the relative vacuum in the bubble wake can trap oil drops regardless of oil drop surface chemistry. Since hydrodynamic collection can be accomplished by both collision and direct-wake capture, the calculated and observed rate constants should agree when collection occurs by collision, whereas the calculated rate constants should be greater than predicted when direct-wake capture also occurs. The contribution of dircct-wake capture to total collection decreases as oil drop size increases. 

Figure 9.8. (a) An NO2 bubble rising in a two-dimensional ballotini bed showing the cloud region of the bubble (b) A two-dimensional bubble rising through a layer of black particles showing the bubble wake in a gas-solid fluidized bed (from Rowe, 1971 reproduced with permission). 

Figure 9.19. Two main mechanisms of solids injection into the freeboard (from Kunii and Levenspiel, 1991) (a) From the bubble roof (b) From the bubble wake.

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. 

Fan, L.-S. and Tsuchiya, K. (1990). Bubble Wake Dynamics in Liquids and Liquid-Solid Suspensions. Boston Butterworths. 

Particle mixing is caused by the bubbles, partly be shear displacement or drift but also by the bulk transport of particles in the bubble wake. Bubbles may also cause segregation if there are different kinds of particles present. Unlike other kinds of mixers, segregation is insensitive to particle size difference but particularly sensitive to density difference. In a binary system of particles segregation increases approximately as particle density ratio to the power 5/2 but with particle size ratio only to the power 1/5 (11). This can cause problems in, for example, coal combustion where char has a markedly lower density than ash and also in some ore reduction processes using coke. 

The bubble motion will also determine the solid circulation in the bed, as a consequence of the entrainment of solids in the bubble wake. For an assumed ratio of wake to bubble volume, the volumetric circulation rate of solids per unit cross-sectional area of bed is equal to (uQ-umf)a. The solid circulation time is then equal to h/(uo-um )a. For the values uq = 2m/s, = 0.4m/s,... 

A height of three to four meters above the bed is required to allow solids entrained by the bubble wakes into the freeboard to return to the bed surface. The initial velocity of the solids that splash into the freeboard is 4 to 8 times the bubble rise velocity (100) and the freeboard height is determined by the kinetic energy of the larger particles for which drag forces are relatively unimportant. For a bubble rise velocity of 3.2 m/s (estimated from + 0.71 /gd (29) and a bubble diameter of... 

Large-diameter solid particles in a three-phase fluidized-bed system cause bubbles to be small, whereas, in a fine particle slurry, the bubbles can become large. Henriksen and Ostergaard40 showed that the large bubbles in the latter case can break as a result of Taylor instability at the root of the bubble. The wake properties of bubbles in a three-phase fluidized-bed system have been studied by Rigby and Capes.115 They showed that bubble wakes in a three-phase system consist not only of a stable portion carried with the bubbles but also of vortices shed by the bubbles. 

The structure of wakes behind the gas bubbles affects several aspects (such as holdup, gas-liquid mass transfer, etc.) of three-phase fluidized-bed behavior. The magnitude and composition of such wakes are still not known with any certainty. Wake holdups have been estimated from experimental measurements of gas and solid holdups. It is commonly assumed that the bed can be divided into three regions a liquid fluidized region, a gas-bubble region, and a bubble-wake region and that the bubbles and their wakes travel at the same velocity. Different investigators have, however, assumed different values of hws the ratio of solids holdup in the wake to the solids holdup in the liquid fluidized region. Different methods have been used to calculate wake holdups from the experimental... 

Another model worth considering is to assume all the deadwater resides in the stagnant pockets in bubble wakes. Here, a moving coordinate system would be used, taking the bubble swarm velocity to be U. For this model, equation (13) is replaced by the distributed parameter equation ... 

Sharma ( ) who deduct the energy dissipated in bubble wakes to obtain... 

Ranade and Joshi (1987) have developed a criterion for small bubbles. The small bubbles rise upward without any oscillations. The liquid carried upward in the bubble wakes is released at the top liquid surface, which then flows downward in the bubble-free region. The downward liquid flow hinders the bubble rise. It was proposed that the transition will occur when the bubble rise velocity equals the downward liquid velocity. Under this condition, the bubble rise velocity with respect to the column wall is zero and the gas phase accumulates in the column, leading to transition. 

Stewart and Davidson (1964) and Ostergaard (1965) proposed similar mechanisms to explain the contraction phenomenon. They offered qualitative and semiquantitative explanations based on the assumption that gas bubbles in the bed are followed by wakes. The wakes travel at velocities equal to the bubble velocities and thus considerably higher than the average superficial liquid velocity in the bed. Therefore, it follows from the continuity equation that the velocity in the bed outside the bubble wakes is lower than the average superficial velocity, and thus the expansion of this part of the bed must be correspondingly reduced. 

Ratio of solid hold-up in bubble wakes to that in liquid fluidization, in equation (208)... 

Figure 19 shows, as an example, the evolution and propagation of bubbles in a 2D gas-fluidized bed with a heated wall. The bubbles originate from an orifice near the heated right wall (air injection velocity through the orifice s 5.25 m/s, which corresponds to 2 Uj. The instantaneous axial profile of the wall-to-bed heat transfer coefficient is included in Fig. 19. From this figure the role of the developing bubble wake and the associated bed material refreshment along the heated wall, and its consequences for the local instantaneous heat transfer coefficient, can be clearly seen. In this study it became clear that CFD based models can be used as a tool (i.e., a learning model) to gain insight into complex system behavior.

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