Vapor films

Interfacial Forces. Neighboring bubbles in a foam interact through a variety of forces which depend on the composition and thickness of Hquid between them, and on the physical chemistry of their Hquid—vapor interfaces. For a foam to be relatively stable, the net interaction must be sufficiently repulsive at short distances to maintain a significant layer of Hquid in between neighboring bubbles. Otherwise two bubbles could approach so closely as to expel all the Hquid and fuse into one larger bubble. Repulsive interactions typically become important only for bubble separations smaller than a few hundredths of a micrometer, a length small in comparison with typical bubble sizes. Thus attention can be restricted to the vapor—Hquid—vapor film stmcture formed between neighboring bubbles, and this stmcture can be considered essentially flat. 

Pressure can also be controlled by variable heat transfer coefficient in the condenser. In this type of control, the condenser must have excess surface. This excess surface becomes part of the control system. One example of this is a total condenser with the accumulator running full and the level up in the condenser. If the pressure is too high, the level is lowered to provide additional cooling, and vice versa. This works on the principle of a slow moving liquid film having poorer heat transfer than a condensing vapor film. Sometimes it is necessary to put a partially flooded condenser at a steep angle rather than horizontal for proper control response. 

Figure 8 shows that increasing the heat flux at constant mass velocity causes the peak in wall temperature to increase and to move towards lower enthalpy or steam quality values. The increase in peak temperature is thus due not only to a higher heat flux, which demands a higher temperature difference across the vapor film at the wall, but to a lower flow velocity in the tube as the peaks move into regions of reduced quality. The latter effect of lower flow velocity is probably the dominant factor in giving fast burn-out its characteristically rapid and often destructive temperature rise, for, as stated earlier, fast burn-out is usually observed at conditions of subcooled or low quality boiling. 

The spheroidal modulus (So) is defined as the ratio of conduction heat flux through the vapor film to the evaporation heat flux ... 

Figure 2.39 Schematic drawing of the growth of the vapor film in film boiling on a vertical surface. (From Dwyer, 1976. Copyright 1976 by American Nuclear Society, LaGrange Park, IL. Reprinted with permission.)...

Annular flow. In annular flow there is a continuous liquid in an annulus along the wall and a continuous gas/vapor phase in the core. The gas core may contain entrained droplets—dispersed mist—while the discontinuous gas phase appears as bubbles in the annulus. This flow pattern occurs at high void fractions and high flow velocities. A special case of annular flow is that where there is a gas/vapor film along the wall and a liquid core in the center. This type is called inverse annular flow and appears only in subcooled stable film boiling (see Sec. 3.4.6.3)... 

Transition Zone III is of utmost importance, since the formation of dry spots is accompanied by a dramatic change in the heat transfer mechanism. In such units as gas-fired boilers, the dry spots may cause the tube wall temperature to approach the temperature of the heating gas. However, before the tube wall temperature reaches a steady-state value, the tensile strength of the tube wall is reduced, and rupture may occur. This phenomenon, called burn-out, may also occur at any point along the tube wall if the wall heat flux qmt is large enough so that a vapor film forms between the tube wall and the liquid surface. 

Macbeth (M5) has recently written a detailed review on the subject of burn-out. The review contains a number of correlations for predicting the maximum heat flux before burn-out occurs. These correlations include a dependence upon the tube geometry, the fluid being heated, the liquid velocity, and numerous other properties, as well as the method of heating. Sil-vestri (S6) has reviewed the fluid mechanics and heat transfer of two-phase annular dispersed flows with particular emphasis on the critical heat flux that leads to burn-out. Silvestri has stated that phenomena responsible for burn-out, due to the formation of a vapor film between the wall and the liquid, are believed to be substantially different from phenomena causing burn-out due to the formation of dry spots that produce the liquid-deficient heat transfer region. It is known that the value of the liquid holdup at which dry spots first appear is dependent on the heat flux qmi. The correlations presented by Silvestri and Macbeth (S6, M5) can be used to estimate the burn-out conditions. 

The superheated liquid concept, in any case, may only supply a local trigger to initiate the RPT. Other ways to trigger such events are possible, e.g., detonation of small explosive charges can sometimes be employed. To produce large-scale, coherent RPTs, the trigger may cause collapse of vapor films in adjacent masses of volatile liquid and lead to the escalation of the small triggering event. 

Some effort has been expended in obtaining RPTs from methane-rich LNG by impacting water on a cryogen surface. The rationale for such tests is to eliminate the vapor film and cause direct liquid-liquid contact. Little success has, however, been achieved for any LNG, but one can... 

The pressure wave propagating through the premixed LNG and water collapses the vapor film surrounding the LNG. Intimate liquid-liquid contact occurs and, since the interface temperature is above T i, rapid heat transfer and vaporization occur. The time scale of the vaporization is comparable to that of the trigger step. Propagation and escalation then result. 

Yet methane could have an RPT with water if there were some way to collapse the protective vapor film, perhaps by impaction upon the water surface at high velocity. Liquid nitrogen will even show an RPT if so impacted on water (Anderson and Armstrong, 1972). Extremely violent and immediate RPTs are also obtained when liquid ethane is impacted on water. In all these cases, good liquid-liquid contact is assured and, if the hot fluid temperature is greater than T, RPTs are possible. 

For the smelt-water case. Nelson suggested the water in contact with the very hot smelt was, initially, separated by a thin vapor film. Either because the smelt cooled—or because of some outside disturbance— there was a collapse of the vapor film to allow direct liquid-liquid contact. The water was then heated to the superheat-limit temperature and underwent homogeneous nucleation with an explosive formation of vapor. The localized shocks either led to other superheat-limit explosions elsewhere in the smelt-water mass or caused intense local mixing of the smelt and water to allow steam formation by normal heat transfer modes. 

While the mechanism proposed by Nelson explained many of the characteristics of a smelt-water explosion, it had one very serious drawback, i.e., the smelt temperature was significantly higher than the expected superheat-limit temperature of water (1100-1200 K compared to 577 K). For LNG-water, it was shown earlier in Section III that if the water temperature were much higher than the superheat-limit temperature of the LNG, explosions were then rarely noted. For such cases, the filmboiling mode was too stable and collapse of this vapor film was unlikely. 

Hygroscopicity Tests. Hygroscopicity is the affinity of a substance for water vapor. It is a complex phenomenon which is controlled by the rate of diffusion of water across the vapor-liquid interface. This rate depends on temperature, surface area, liquid depth, and liquid and vapor film coefficients. Inasmuch as it is impractical to measure the effect of all these variables, simplified empirical tests have been... 

This process can be nuclear or film type. In nuclear boiling, bubbles detach themselves quickly from the heat transfer surface. In film boiling the rate of heat transfer is retarded by an adherent vapor film through which heat supply must be by conduction. Either mode... 

Numerous investigations have been conducted of mass transfer coefficients in vessels with a variety of kinds of packings. Many of the mote acceptable results are cited in recent books on mass transfer, for instance, those of Sherwood et al. (Mass Transfer, McGraw-Hill, New York, 1975), Cussler (Diffusion, Cambridge, 1984), and Hines and Maddox (1985). A convenient correlation of mass transfer coefficients in granular beds covering both liquid and vapor films is that of Dwivedi and Upadhyay [Ind. Eng. Chem. Process Des. Dev. 16, 157 (1977)], namely,... 

Figure 13.44. Factors in Eqs. (13.239) and (13.240) for HTUs of liquid and vapor films and slopes m and m" of the combining Eqs. (13.235) and (13.236) [Bolles and Fair, Inst. Chem. Eng. Symp. Ser. 56(2), 3.3/3.S, (1979)]. (a) Definitions of slopes m and m" in Eqs. (13.235) and (13.236) for combining liquid and gas film HTUs / = 1 for equimolal counter diffusion / = (jtB)mean for diffusion through a stagnant film, (b) Factor (j> of the liquid phase Eq. (13.239). (c) Factor C of the liquid phase, Eq. (13.239). (d) Factor ip of the gas phase, Eq. (13.240), for metal pall rings.

D. Growth of a Vapor Film on a Rapidly Heated Plane Surface. 102... 

An interesting class of exact self-similar solutions (H2) can be deduced for the case where the newly formed phase density is a function of temperature only. The method involves a transformation to Lagrangian coordinates, based upon the principle of conservation of mass within the new phase. A similarity variable akin to that employed by Zener (Z2) is then introduced which immobilizes the moving boundary in the transformed space. A particular case which has been studied in detail is that of a column of liquid, initially at the saturation temperature T , in contact with a flat, horizontal plate whose temperature is suddenly increased to a large value, Tw T . Suppose that the density of nucleation sites is so great that individual bubbles coalesce immediately upon formation into a continuous vapor film of uniform thickness, which increases with time. Eventually the liquid-vapor interface becomes severely distorted, in part due to Taylor instability but the vapor film growth, before such effects become important, can be treated as a one-dimensional problem. This problem is closely related to reactor safety problems associated with fast power transients. The assumptions made are ... 

The principal physical error is probably geometrical. Compared to this, the above assumptions are not unduly restrictive, although extremely fast high-power excursions at low pressures are ruled out by assumptions (2) and (3). Assumption (2) is more nearly fulfilled at high pressures with low liquid heads. Assumption (3) is acceptable in the vapor-film problem even when the radiative flux from the solid surface is appreciable, provided that the liquid (and, of course, vapor) is nearly transparent. 

Fig. 5. Dimensionless heat flux versus plate temperature in the growth of a vapor film at the surface of a suddenly heated plate in contact with liquid (H2). Reproduced by permission of Pergamon Press.

Maximum and minimum bounds for the growth of the vapor film at the surface of a rapidly heated plate in contact with a semi-infinite body of liquid initially at the saturation temperature have been deduced in a similar manner for arbitrary monotonic surface temperature or heat flux, following the method of Section II, D (H3). 

The peak heat flux for nucleate pool boiling is indicated as point a in Fig. 9-3 and by a dashed line in Fig. 9-8. Zuber [7] has developed an analytical expression for the peak heat flux in nucleate boiling by considering the stability requirements of the interface between the vapor film and liquid. This relation... 

There are upper and lower limits of applicability of the equation above. The lower limit results because natural-convection heat transfer governs at low temperature differences between the surface and the fluid. The upper limit results because a transition to film boiling occurs at high temperature differences. In film boiling, a layer of vapor blankets the heat-transfer surface and no liquid reaches the surface. Heat transfer occurs as a result of conduction across the vapor film as well as by radiation. Film-boiling heat-transfer coefficients are much less than those for nucleate boiling. For further discussion of boiling heat transfer, see Refs. 5 and 6. 

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