Bubble frequency

Bubbly/slug flow. Bubbles both longer and shorter than the channel diameter (Fig. 2.30b). The bubble frequencies increase rapidly with the heat flux in the evaporator, reached a peak 900 Hz and then decreased due to coalescence. 

Variation of bubble size, bubble frequency, and the standard deviation of -APbed with variation of Ug in the conical fluidized beds with a uniform gas distributor (Fopen = 3.87 %) is shown in Fig. 7. As can be seen, the standard deviation of - APbed and the bubble size increase with increasing Ug in the fully fluidized region. However, bubble frequency remains unchanged with variation of Ug that may imply the bubble size will increase as much as the volumetric gas flow increases. As shown, the bubble size dramatically increases with increasing Ug. Also, it is confirmed that the increase of standard deviation of -APbed is closely related to bubble size. 

Fig. 7. Variation of bubble size, bubble frequency and the standard deviation of -...

Note that high superheats, large liquid thermal conductivities, low pressures, and low bubble frequencies, all of which are more typical of liquid metals, tend to give bubble dynamics that approach the inertia-controlled case as the bubble growth rates are high. On the other hand, low superheats, low conductivities, high... 

Cole, R., 1967, Bubble Frequencies and Departure Volumes at Subatmospheric Pressures, AIChE J. /3(4) 779-783. (2)... 

Ivey, H. J., 1967, Relationships between Bubble Frequency, Departure Diameter, and Rise Velocity in Nucleate Boiling, Int. J. Heat Mass Transfer 70 1023. (2)... 

Figure 30. Comparison of non-dimensional bubble frequencies from two cold scaled models. (Newby and Keairns, 1986.)...

Workers generally report that bubble frequency increases with temperature (Mii et al., 1973 Otake et al., 1975 Yoshida et al., 1974). There is an initial rapid increase in frequency with temperature near ambient, which then tapers off at higher temperatures. 

Pressure also appears to cause bubble frequency to increase. This has been reported by both Rowe et al., (1984) and Chan et al., (1987). Rowe et al., (1984) also reported that bubbles were flatter at elevated pressures. 

Bubble Dynamics. To adequately describe the jet, the bubble size generated by the jet needs to be studied. A substantial amount of gas leaks from the bubble, to the emulsion phase during bubble formation stage, particularly when the bed is less than minimally fluidized. A model developed on the basis of this mechanism predicted the experimental bubble diameter well when the experimental bubble frequency was used as an input. The experimentally observed bubble frequency is smaller by a factor of 3 to 5 than that calculated from the Davidson and Harrison model (1963), which assumed no net gas interchange between the bubble and the emulsion phase. This discrepancy is due primarily to the extensive bubble coalescence above the jet nozzle and the assumption that no gas leaks from the bubble phase. 

Equation (34) and the experimental bubble frequency, n = 1 It, were used to predict the expected bubble diameter. The predicted bubble diameters are very close to those actually observed. Theoretically, Eqs. (34) and (36) can be solved to obtain both the bubble frequency and the bubble diameter if the... 

The bubbling frequencies measured in this study are much smaller than the 5- 8 Hz measured by Rowe et al. (1979) and the 20 Hz measured by Hsiung and Grace (1978). The difference may be due to the dominant effect of the much larger initial bed heights and jet nozzle sizes in this study. 

The solids circulation patterns were investigated with a force probe developed in-house. Typical force probe responses are presented in Figs. 43 and 44 for a probe located at 0.13 m from the jet nozzle and with different penetrations into the bed for an air tube velocity of 45.7 m/s. Sincetheforce probe is directional, the upward solids movement will produce a positive response from the probe and vice versa, the magnitude of the response being an indication of the magnitude of solids circulation rate. The number of major peaks per unit time is closely related to the actual bubble frequency in the bed. 

If the bubble frequency, bubble diameter, and bubble velocity are known, the solids mixing rate can be calculated. 

The solids mixing study by injection of tracer particles indicated that the axial mixing of solids in the bubble street is apparently very fast. Radial mixing flux depends primarily on the bubble size, bubble velocity, and bubble frequency, which in turn depend on the size of the jet nozzle employed and the operating jet velocity. 

The authors (B5) report that for flow rates between 50 and 250 cm3/sec, the bubble frequency remains essentially constant at 22 bubbles per second, whereas at lower flow rates, the frequency shows a marked tendency to rise. 

The bubble frequency is independent of the main fluidizing velocity. 

We will discuss the relative influence of the following parameters on the average bubbling frequency (i) the concenbation Cl of C02-dissolved molecules, (ii) the liquid temperature 6, and (iii) the ambient pressure P. 

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