Subcooled, boiling

As the bulk temperature of the liquid some distance away from the heating surface is decreased, the characteristics of the bubbles growing at the surface undergo a marked change. The bubbles become smaller and of higher fre- 

Symmetrical growth and collapse curves of the sort pictured herein are difficult to obtain by a laminar-flow heat-convection model. This is because the heat equation is not symmetric with respect to time reversal. On the other hand, such symmetry is observed in the growth and collapse of cavitation bubbles, and indeed, is implied by the extended Rayleigh equation (Bll)  

If experimental growth and collapse bubble radius data are employed, this equation can be numerically integrated to obtain Ap, the difference between the pressure at the bubble wall and in the surroundings, as a function of time (P3). If Ap can be assumed to be nearly constant, the first integral of this equation is readily obtained. 

Bankoff and Mikesell showed that this equation could be fairly well 

Note that at this point no recourse need be made to any theory of energy transport, since the only equation necessary to describe the motion of the fluid is the pressure equation. The calculated pressure difference as a function of subcooling is shown in Fig. 20 from the data of Gunther and Kreith (GIO) at a heat flux of 2.75 Btu/(sq in.)(sec) and a superficial liquid velocity of 10 ft/sec past the heating strip. One interpretation of these results is that the liquid surrounding the bubble has been given an initial supply of kinetic 

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Sato T, Matsumura H (1964) On the conditions of incipient subcooled-boiling with forced convection. Bull Jpn Soc Mech Eng 7 392-398... 

To predict the detached voidage in region II, the experimental work of Thom et al. (1966), as modified by Tong (1967a), is recommended. Thom et al. measured the local void fraction in subcooled boiling water flows in a 1.52-m (5-ft)-long tube... 

Figure 3.25 Void fraction in various (subcooled) boiling regions.

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... 

Figure 3.26 Velocity and temperature distribution in a subcooled boiling flow (bubble boundary-layer concept). (From Larson and Tong, 1969. Copyright 1969 by American Society of Mechanical Engineers, New York. Reprinted with permission.)...

So far the pressure drop in two-phase flow in pipes and rod bundles has often been predicted by empirical correlations, despite the development of analytical models as described in the previous sections. Thus, in the highly subcooled boiling region,... 

The relationship between the wall temperature and the coolant temperature can be seen in Figure 4.5. The wall temperature starts to bend at the incipience of subcooled boiling, where the coolant temperature is defined as Tm. The wall temperature follows a curve of partial boiling and then reaches an approximately constant value at a fully developed nucleate boiling where the coolant temperature... 

Figure 4.10 Thermocapillarity mechanism of subcooled boiling. (From Brown, 1967. Reprinted with permission of Massachusetts Institute of Technology, Cambridge, M A.)...

When the boiling crisis occurs, the surface temperature rises. Because of the fairly good transfer coefficient of a fast-moving vapor core in an annular flow, the wall temperature rise after a dryout in the high-quality region is usually smaller than that in a subcooled boiling crisis. It is even possible to establish steady-state conditions at moderate wall temperatures, so that physical burnout may not occur immediately. Thus dryout is also described as slow burnout. 

For convenience of application, a simplification of subcooled boiling length dnb is suggested to be measured from the inlet rather than from the inception of local boiling. This simplification has two justifications. First, the empirical expres-... 

Compound dynamic instabilities as secondary phenomena. Pressure-drop oscillations are triggered by a static instability phenomenon. They occur in systems that have a compressible volume upsteam of, or within, the heated section. Maul-betsch and Griffith (1965, 1967), in their study of instabilities in subcooled boiling water, found that the instability was associated with operation on the negative-sloping portion of the pressure drop-versus-flow curve. Pressure drop oscillations were predicted by an analysis (discussed in the next section), but because of the... 

Cumo, M., and A. Palmieri, 1967, The Influence of Geometry on Critical Heat Flux in Subcooled Boiling, AIChE Preprint 18, 9th Natl. Heat Transfer Conf., Seattle, WA. (5)... 

Griffith, P., J. A. Clark, and W. M. Rohsenow, 1958, Void Volumes in Subcooled Boiling Systems, ASME Paper 58-HT-19, ASME, New York. (3)... 

Ivey, H. J., and D. J. Morris, 1962, On the Relevance of the Vapor Liquid Exchange Mechanism for Subcooled Boiling Heat Transfer at Higher Pressure, Rep. AEEW-R-137, UK Atomic Energy Authority, Winfrith, England. (2)... 

Jeglic, F. A., and T. M. Grace, 1965, Onset of Flow Oscillations in Forced Flow Subcooled Boiling, NASA-TN-D 2821, NASA Lewis Res. Ctr., Cleveland, OH. (6)... 

Levy, S., 1966, Forced Convection Subcooled Boiling—Prediction of Vapor Volumetric Fraction, Rep. 

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