Bubble departure

Klausner JF, Mei R, Bernard D, Zeng L (1993) Vapor bubble departure in forced convection boiling. Int J Heat Mass Transfer 36 651-661... 

The following phenomena pertaining to bubble departure from a heated surface are discussed in this section bubble size at departure, departure frequency, boiling sound, and heat transfer effects by departing bubbles. 

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. 

In a detailed study of bubble departure, Hatton and Hall (1966) concluded that bubble departure is relatively independent of heat flux but strongly dependent on cavity size Dc and pressure. They presented a bubble departure criterion including the effect of cavity size ... 

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

Note that the local boiling void calculated this way is independent of channel length. The prediction of the point of bubble departure (void detachment) is, however, important in predicting the subcooled boiling void. Rouhani (1967) assumed... 

The flow friction of a channel having subcooled local boiling behaves in a manner similar to the flow friction of a channel having a rough surface. From air-water data obtained at low void fractions (Malnes, 1966), the two-phase flow friction factor without bubble departure was found (Tong, 1968b Thorgerson, 1969)to be... 

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)... 

Koumoutsos, N., R. Moissis, and A. Spyridonos, 1967, A Study of Bubble Departure in Forced Convection Boiling, ASME Paper 67-HT-13, National Heat Transfer Conf. (3)... 

Both the bubble departure frequency / and the number of nucleation centers n are difficult to evaluate. These quantities are known to be dependent on the magnitude of the heat flux, material of construction of the tube, roughness of the inside wall, liquid velocity, and degree of superheat in the liquid elements closest to the tube wall. Koumoutsos et al. (K2) have studied bubble departure in forced-convection boiling, and have formulated an equation for calculating bubble departure size as a function of liquid velocity. 

At present, Eq. (68) only provides a simple estimate of the mass and energy transfer processes in forced-flow nucleation. The methods for evaluating the parameters must be improved by further detailed research on forced-flow nucleation. In particular, the calculation of the rate of nucleation n and of the bubble departure frequency / are the weakest points in the analysis of this heat-transfer region. Obviously, accurate prediction of the pressure drop and holdups are also needed. 

Interfacial area of entrained / Bubble departure frequency... 

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.

When nucleate boiling occurs in narrow channel the flow regime could be different from it s in conventional tube. In conventional tube the bubble departure size is typically less that the tube diameter, so bubble flow pattern and nucleate boiling are preferable in wide range of vapor content. In case of narrow channel the bubble departure size could be comparable with the channel size, it causes strong interaction between bubbles and change both the flow pattern and heat transfer rate. 

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. 

The detachment of the bubble occurs if the condition FB = Fc is satisfied. It follows that the mean bubble departure radius (Rd) is well defined for a given electrode—electrolyte configuration (typical values are around 50 pm [115]). It may be expected that the mean bubble departure radius is mainly a property of the electrode (the electrode surface roughness which influences D), the electrode wettability (through the contact angle i9), and the electrolyte (density and surface tension of the electrolyte), but not of the current density j. However, the question is whether a cavity (nucleation site) is active or non-active. The current density may influence the activation of the nucleation sites. 

Several authors have studied the dependence of the mean bubble departure radius (Rd) on the current density. Venczel [109] found that for small current densities (typically j < 2 kA/m2) the radius decreases with decreasing current density. It seems to become independent of the current density for higher values, while the number of growing bubbles increases. Vogt [115] observed a similar behaviour for small current densities. Other authors [18,38,42] found that the mean departure radius increases with the current density j according to the following empirical power law ... 

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. 

Models for bubble departure in flow boiling are given by Klausner et al. [69] and Al-Hayes and Winterton [66]. The Al-Hayes and Winterton model was developed for gas bubble detachment from a surface but has been extended to the case of vapor bubble detachment (in boiling) by Winterton [67], When inertial forces are negligible, the stability of a bubble on the surface is governed by a balance between three forces on the bubble, resolved parallel to solid surface, namely the buoyancy force Fb, the drag force Fd, and a surface tension force Fs. Al-Hayes and Winterton give the buoyancy force as... 

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). 

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