Bubble columns transition

This admits periodic solutions for each value of A, and in general A = m. This indicates multiple cells in the horizontal direction. We restrict ourselves to just one horizontal cell, i.e., n = 1. The value of n = 1 corresponds to one horizontal cell, and all the values of n that are greater than 1 correspond to multiple cells in the horizontal direction. In bubble column transitions, the multiple cells in horizontal direction have been observed only in shallow bubble columns in which the height-to-diameter ratio is less than 1. In the present case, we have considered HID > 1. Therefore, the transition to the heterogeneous regime is characterized by one cell in the horizontal direction. Thus, the first transition appears to correspond to a single cell in the horizontal direction ... 

Figure 3.28 Transition region in two-phase water-air bubble columns (Koide, 1996).

The addition of solids has been found to increase or even decrease the gas holdup, depending on the experimental conditions. When the solids addition promotes bubble break up, the average bubble size is smaller, the bubble rising velocity is reduced, and the gas holdup increases (DOE, 1985). The following correlation of Koide et al. (1963) is used in slurry bubble columns and for the heterogeneous and transition regimes (Koide et al., 1984 Koide, 1996) ... 

Figure 17 Physical explanation of regime transition in bubble columns (Yang et ah, 2007, 2010).

The transition from homogeneous to heterogeneous regime in case of bubble columns was qualitatively described in the introduction. At a certain critical superficial gas velocity, a small disturbance in the hold-up profile sets in liquid circulation, which in turn magnifies the hold-up disturbance. In this way, the disturbance grows, and finally an approximately parabolic gas hold-up profile and intense liquid circulation develop, which are the characteristics of the heterogeneous regime. 

In the present work, we have analyzed only one transition for all the multiphase systems. For bubble columns, we have considered the transition from region III to region II (point Q). In region I, gas hold-up is typically... 

Equation (61) is the transition criterion provided the conditions given by equation (52) are satisfied. From Table I it can be seen that these conditions are satisfied only in the case of gas-solid fluidized beds and in some cases of solid-liquid fluidized beds where ps Pl- Therefore, for other multiphase dispersions [such as gas-liquid (bubble columns) and solid-liquid fluidized beds (where pl is not negligible)] the comparison of dynamic wave velocity with continuity wave velocity is not valid for deciding the bed stability. Further, the above analysis holds for transition from region I to II (point P in Fig. 1) and not for III to II (point Q). Therefore, the criterion does not hold for bubble columns and dilute dispersions. 

As discussed earlier, transition in bubble columns occurs in most cases because the denominator in Eq. (24) becomes zero, i.e.. 

Fig. 24. Effect of bubble diameter-terminal rise velocity on transitions bubble columns [oi = 0.5, Cv = 1.0, m = 1.9].

Fig. 25. Effect of virtual mass coefficient on transition gas hold-up bubble columns [a = 0.5, m = 1.9, dB-VBoo Clift et al relation].

The transition in bubble columns has been the subject of interest for the past 30 years. Table V summarizes the previous work. The value of Vboo has been estimated from the corresponding Vsup-SQ data on the basis of initial slope. Using this value of Uboo and the physical properties, the bubble diameter was estimated using the correlation of Clift et al (1978). The value of m was estimated using Usup- G data. 

In the previous section, it was pointed out that the critical gas hold-up is very sensitive to the d -v oo relationship and the values of m, Cy, and a. It was thought desirable to calculate the value of a for all the experimental points shown in Table V. For each point, four values of m (1, 1.4, 1.9 and 2.4) and three levels of Cy were considered. The values of a are given in Table VI. The average value works out to be 3.14. Table V also gives the comparison between the experimental critical gas hold-up and the critical gas hold-up predicted using the transition criterion [Eq. (25)] with dispersion coefficient equal to 3. The comparison between predicted and experimental gas hold-up for bubble columns is shown in Fig. 30. It can be seen... 

A unified approach has been developed for the prediction of transition in multiphase reactors such as gas-hquid bubble columns, liquid-liquid spray columns, solid-liquid fluidized beds, gas-solid fluidized beds, and three-phase fluidized beds. 

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