Bubble departure frequency

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... 

Values of the average bubble departure frequency per nucleation site , i.e., the area under the distribution curves, are given on each plot for pure water and the two different polymer solutions. Compared to pure water ( = 223 bubbles per second), the average bubble departure frequency per nucleation site increased slightly in the polyacrylamide ( = 249 bubbles per second) and hydroxethyl cellulose ( = 243 bubbles per second) solutions. 

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. 

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-... 

In addition to the boiling curve measurements, the bubble dynamics have been photographed along the entire heated surface of the platinum wire at a saturated boiling heat flux of 0.358 + 0.006 W.mm for the Natrosol 250 HHR and Separan AP-30 solutions. Both polymer solutions have been tested only at a relative viscosity of 1.08. Slow motion films of the bubble dynamics have been analyzed to determine the average number density of active nucleation sites, and the frequency distribution of bubble departure diameters. 

Figures 2(b) and 2(c) show the frequency distributions of bubble departure diameters for the polyacrylamide and the hydroxyethyl cellulose solutions, respectively. In both cases, the polymer solution s average bubble departure diameters ( = 1.19 mm for the polyacrylamide and = 1.13 mm for the...

Fig.2. The frequency distributions of bubble departure diameters for (a) pure water boiling at...

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)... 

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,... 

Cole, R. Bubble frequencies and departure volumes at subatmospheric pressures. Am. Inst. Chem. Eng. J. 13 (1967) 779-783... 

Where v is the volumetric growth rate of the bubble (calculable from the heat flux). The time required for the formation of a new macrolayer with its associated vapor mushroom was very short and the frequency of vapor mushroom departure is therefore f 1/x. 

The pendulum is a means of appreciating the departure from linearity. Equation 25 describes an undamped oscillator. Dissipation of energy tends to damp the motion. In order to sustain the latter, another oscillator can deliver some energy at each cycle of frequency (f) to the pendulum (of length 1) during a period (t). Under resonance oscillator and pendulum oscillate synchronously. If length 1 is reduced by a factor of two (i.e., frequency increases by a factor of two), the energy of the external oscillator will be delivered two times less frequently and the amplitude of pendulum motion will reduce. Bubbles behave similarly, at least qualitatively. 

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