Vapor-film region

For plain media, the film evaporation adjacent to a heated vertical surface is similar to the film condensation. In porous media, we also expect some similarity between these two processes. For the reasons given in the last section, we do not discuss the cases where 8gld — 1, where 8g is the vapor-film region thickness. When 8gld 1 and because the liquid flows (due to capillarity) toward the surface located at y = 8g, we also expect a large two-phase region, that is, ld 1. Then a local volume-averaged treatment can be applied. 

A One-Dimensional Analysis for Bo 1. Figure 9.22 depicts the one-dimensional model for evaporation in porous media with heat addition q from the impermeable lower bounding surface maintained at T0> Ts, where T, is the saturation temperature. The vapor-film region has a thickness 8g, and the two-phase region has a length 8g(. 

FIGURE 9.22 Evaporation due to the heat addition from below at temperatures above the saturation. The vapor-film region, the two-phase region, and the liquid region, as well as the evaporation and condensation zones are shown. Also shown are the distributions of temperature and saturation within these regions. 

Vapor-Film Region. The one-dimensional heat conduction for the stagnant vapor-film region is given by... 

We note that these heat fluxes are lower bounds, because 8 is actually occupied by the vapor-film region, evaporation zone, as well as the two-phase region. For the porous layer to contain both of the layers, we need heat fluxes much larger than those given by Eq. 9.145, that is,... 

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 general features of two-dimensional flow with evaporating liquid-vapor meniscus in a capillary slot were studied by Khrustalev and Faghri (1996). Following this work we present the main results mentioned in their research. The model of flow in a narrow slot is presented in Fig. 10.16. Within a capillary slot two characteristic regions can be selected, where two-dimensional or quasi-one-dimensional flow occurs. Two-dimensional flow is realized in the major part of the liquid domain, whereas the quasi-one-dimensional flow is observed in the micro-film region, located near the wall. 

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. 

Figure 1. Morphological evolution of unstressed thin-film regions, made ofinitially fourmonolayers, through thermal fluctuations. The early stages of islanding are examined on the left side, while the final equilibrium shapes are shown on the right for three different cases of substrate-vapor surface energy, y ...

Young s equation can also be used to determine wetting. The derivation of this venerable expression is based upon a consideration of the three-phase equilibrium that exists at a partially wet surface. The three equilibria present are chosen to be liquid droplets (or regions of thick film) in equilibrium with the vapor (/v), regions of thin adsorption in equilibrium with the solid si, because the thin layer is adsorbed on the solid), and regions of thick film in equilibrium with the solid (sv). 

Let us now turn our attention to a more detailed discussion of transitions that occur between different types of films, and in particular to the way in which these transitions are influenced by the temperature, the structure of surfactant molecules and the composition of the medium. The direct transition from gaseous and vapor films to liquid and solid condensed ones is a two-dimensional first-order phase transition that is quite similar to a three-dimensional vapor condensation. A decrease in the area per molecule in the adsorption layer in the region of gaseous films causes a gradual increase in pressure up to the level that corresponds to the condensation pressure of a saturated two-dimensional vapor, 7rc, at an area per molecule equal to sc (see Fig. 11-21). The subsequent compression of film is not accompanied by an increase in the two-dimensional pressure the two-dimensional vapor transforms into the two-dimensional condensed state, which can be either liquid expanded, liquid condensed, or solid, depending on the nature of the... 

Stratified-Wavy. At high vapor velocities, the flow deviates from the idealized situation just described. First of all, heat transfer in the stratified liquid pool at the bottom of the tube may not be negligible. Secondly, axial interfacial vapor shear may influence the motion and heat transfer in the thin film region around the top part of the tube. Dobson [144] studied this more complex situation and reported that stratified-wavy flow exists when G < 500 kg/m2s and Frm < 20, where Frm is a modified Froude number given by ... 

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