Wakes volume

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 ... 

Predicted and observed wake lengths and wake volumes agree closely for Re = 100 (Figs. 5.7 and 5.8). For Re > 100, the excess pressure over the leading surface of the sphere approaches that for an ideal fluid, but there is little recovery in the wake. As Re increases, the importance of skin friction decreases relative to form drag. 

The formation of an attached wake and the subsequent onset of wake shedding tend to be promoted by increasing oblateness (see Chapter 6) and by the tendency of surface-active contaminants to damp out internal circulation (see Chapter 5). Experiments have been conducted with dyes added to enable attached wakes and shedding phenomena to be visualized (H8, Ml, M2, S2) and wake volumes to be measured (H8, Y4) for drops and bubbles. Since dyes tend to be surface active, the results of these experiments are probably relevant... 

Closed wakes have been modeled as completing the sphere or spheroid of which the particle forms the cap [e.g. (C5, P2)]. However, the wake is smaller than that required to complete a spheroid for Re < 5 and greater for larger Re (B3). The wake becomes more nearly spherical as Re 100, but is still somewhat egg-shaped (B3, H5). Wake volumes, normalized with respect to the volume of the fluid particle, are shown in Fig. 8.6 for Re up to 110. Note the close agreement with results (Kl) for solid spherical caps of the same aspect ratio. This is not surprising since separation necessarily occurs at the rim of the... 

Fig. 8.6 Dimensionless wake volumes for ellipsoidal-cap and spherical-cap bubbles and drops, compared with solid spherical-caps.

Wall Effect on Wake Volume for Large Bubbles in Viscous Liquids (Bl)"... 

Stewart129 derived a relation between the gas and liquidholdups assuming the flux of liquid in the wakes of bubbles to be kUoa, where k is the mean value of liquid-wake volume/bubble volume. He used the principle of continuity and assumed thal if this system is particulately fluidized (i.e., in the case of zero gas flow rate), a relation proposed by Richardson and Zaki.114 namely,... 

If is the fractional wake volume, the hquid phase mass balance gives... 

The ratio of wake volume to gas bubble volume is given by... 

It was assumed that the wake volume to bubble volume ratio, a, is a known constant and Vs can be determined if the bubble size is specified. It was further assumed that Vsup, a, m, and Vs are fixed. (This assumption is tantamount to the assumption of starting with liquid-fluidized bed at t = 0, or with a bed of specified properties and degree of expansion.) With these assumptions, Eqs. (197) and (198) were simplified to... 

Equation (207) reveals that a high ratio of wake volume to bubble volume favors bed contraction. 

Darton and Harrison (1975) derived a criterion for the point of transition to predict whether a solid-liquid fluidized bed will expand or contract when the gas is first introduced. The definition of Pa used by Darton and Harrison was the ratio of upper clear (particle-free) wake volume to the bubble volume. But since they did not consider the circulation of sohds associated with the lower nonclear portion of the wake, their Pa was effectively the same as that of Bhatia and Epstein (1974). The use of the Wallis drift flux approach by Darton and Harrison (1975) also represents no real difference from the relative velocity approach taken by Bhatia and Epstein (1974), since the two methods are rigorously interrelated. It is therefore not surprising that the final criteria of Bhatia and Epstein (1974) and Darton and Harrison (1975) are identical. 

Ratio of wake volume to bubble volume Constant in pressure drop-velocity relationship, Eq. (101) Constant in pressure drop-velocity relationship, Eq. (102) Constant in pressure drop-velocity relationship, Eq. (101) Constant in pressure drop-velocity relationship, Eq. (102) Proportionality constant in Eq. (31)... 

The wake volume Vyj is defined as the volume occupied by the wake within the sphere that circumscribes the bubble. 

Volume of solid in bubble, cloud, emulsion, or wake/volume of bubble phase. 

Vertical and horizontal line segments marked on the column test section made it possible to scale down the prints and their analysis gave values of wake length 1, wake volume v, slug length L and slug volume V. The data obtained are shown in Figures 3 and 4. 

Figure 3. Dependence of wake volume on slug length for 19 mm i.d. column.

The fraction wake volume/bubble volume has been experimentally determined in fluidized beds to have values in the following range ... 

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