Departure diameter

Staniszewski (1959) conducted experiments on bubble departure sites for boiling water and alcohol under various pressures and found the bubble departure diameter to be linearly proportional to the bubble growth rate at the last stage. 

Substituting the bubble departure diameter from Eq. (2-59) and identifying Vb with the liquid velocity in Eq. (2-79), it becomes... 

Hence, Ub is a function of UbL, Db, and fluid properties. The equivalent diameter of the vapor blanket, Db, can be obtained from the correlation for the bubble departure diameter (Cole and Rohsenow, 1969). To calculate the liquid velocity, UbL,... 

Cole, R., and W. R. Rohsenow, 1969, Correlation of Bubble Departure Diameters for Boiling of Saturated Liquids, AIChE Chem. Eng. Prog. Symp. Ser. 6J(92) 211. (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)... 

The bubble growth history for two fluids with different eontact angles (water and PF5060) is shown in Fig. 6. In general, the lower the contact angle, the smaller is the bubble departure diameter and... 

Figure 6 Comparison of bubble departure diameter and bubble growth time for water and PF5060.

Figure 10 Comparison of experimental data with numerical prediction for various gravity levels (a) bubble departure diameter and (b) bubble growth time.

It was supposed, that for a high vapor velocity and a thin liquid film the influence of gravity is small and the correlation for up flow was used. Total boiling suppression occurs when mass quality more than 0.3 for a film thickness less than 60 pm. That value is close to the bubble departure diameter observed for flow boiling in a film. When the film thickness is smaller than the critical one, the forced convection occurs with a small heat transfer coefficient. The crisis of the heat transfer was observed for a complete liquid evaporation on a heated wall. While the mass quality less than 0.3, we have the cell or slug flow mode, so boiling is not suppressed. 

Equations for the calculation of the frequency f of vapour bubbles of departure diameter dA, originally started with the assumption that fdA = const, where the constants for water and carbon tetrachloride were found to be lOOmm/s [4.60]. The constants were later expressed in terms of the physical properties of the boiling liquid,... 

As can be seen in (4.86), for large departure diameters, the second term in the square brackets is small, then we have fd1/2 = const. If, however the departure diameter is sufficiently small the second sum in the square brackets will be large, giving /dA = const. In a middle region of the departure diameter the expression in the square brackets is independent of the departure diameter, and with that fdA = const. The equations contain the relationships, ascertained by different authors, between the frequency and the departure diameter. 

The quantities with relate to the saturated boiling liquid, and those with " relate to the saturated vapour. The Nusselt number is defined by Nu = adA/A. The departure diameter dA is given by (4.85), in which gL = g and gG = g" have to be substituted. For the contact angle j30 in water 7t/4 rad = 45°, in cryogenic liquids 0.01745 rad = 1° and for other liquids 0.61 lrad = 35° have to be used. 

Bubble Departure Diameter. At a certain point in the bubble growth process, the bubble detaches from the surface and the cycle begins again. Clearly the release diameter of the bubble is an important factor in understanding nucleate boiling. For pool boiling, Carey [4] gives... 

For the boiling of binary mixtures, Thome [62] suggests that the reduction in bubble departure diameter for binary mixtures can be calculated using the relationship... 

In forced convective systems, the bubble departure diameter can be critically affected by the presence of a velocity field. Studies of bubble departure diameters in forced convection include those of Al-Hayes and Winterton [66], Winterton [67], Kandlikar et al. [68], and Klausner et al. [69]. The results obtained by Klausner et al. for the probability density function of departure diameter as a function of mass flux and heat flux, respectively, are shown in Figs. 15.28 and 15.29. The most probable departure diameter decreases strongly with increasing flow rate and decreases (less strongly) with decreasing heat flux at a fixed flow rate. It is clear that these velocity effects have to be taken into account in predicting forced convective boiling systems. 

FIGURE 15.28 Probability density function of bubble departure diameter in flow boiling as a function of mass flux for a constant heat flux (from Klausner et al. [69], with permission of Elsevier Science). 

For multicomponent mixtures, the mechanisms are even more complex, involving mass transfer in both liquid and vapor phases. Detailed measurements of bubble frequency (/), bubble departure diameter (dd), and number of active nucleation sites ((V ) are reported by Bier and Schmidt [127] for the propane/n-butane mixtures studied, the bubble departure diameter initially increases (relative to its value for n-butane) with increasing mole fraction of propane and then decreases to a value less than that for pure propane before increasing rapidly with concentration and propane mole fractions greater than about 0.9. Ilie bubble frequency shows the opposite trends. The number of active sites (Na) passes through a minimum as the mole fraction of propane is increased, the maximum reduction being around a factor of 3. It is clear, therefore, that the effects of having a multicom-... 

FIGURE 15.109 Typical departure diameters and burst diameters for bubbles formed in nucleate boiling in annular flow (from Sun et al. [272], with permission from Taylor Francis, Washington, DC. All rights reserved). 

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