Shear, interfacial, condensation

Heat transfer coefficients for condensation processes depend on the condensation models involved, condensation rate, flow pattern, heat transfer surface geometry, and surface orientation. The behavior of condensate is controlled by inertia, gravity, vapor-liquid film interfacial shear, and surface tension forces. Two major condensation mechanisms in film condensation are gravity-controlled and shear-controlled (forced convective) condensation in passages where the surface tension effect is negligible. At high vapor shear, the condensate film may became turbulent. 

An interfacial shear may be very important in so-called shear-controlled condensation because downward interfacial shear reduces the critical Re number for onset of turbulence. In such situations, the correlations must include interfacial shear stress, and the determination of the heat transfer coefficient follows the Nusselt-type analysis for zero interfacial shear [76], According to Butterworth [81], data and analyses involving interfacial shear stress are scarce and not comprehensive enough to cover all important circumstances. The calculations should be performed for the local heat transfer coefficient, thus involving step-by-step procedures in any condenser design. The correlations for local heat transfer coefficients are presented in [81] for cases where interfacial shear swamps any gravitational forces in the film or where both vapor shear and gravity are important. 

The basic Nusselt analysis ignores inertial effects in the condensed film and subcooling effects. Approximate methods of accounting for subcooling were discussed above. A method of accounting for both effects is discussed in this section. To illustrate the method, condensation on an isothermal vertical plate is again considered [52] to [54]. Interfacial shear stress effects will be neglected. 

The Reynolds and Prandtl numbers are related to the condensing coefficient in Fig. 7.17. However, that figure is based on Ad = 0, which assumes no interfacial shear. The following factors can be used to evaluate the effects of any interfacial shear (h = coefficient with interfacial shear h0 = coefficient with no interfacial shear) ... 

For liquid metals, on the other hand, the rate of condensation is high, and the interfacial shear stress causes a noticeable decrease in the Nusselt number as the parameter Ja/Pr increases. For this case, the integral balance of momentum is... 

In real situations, the vapor velocity varies with position along the plate, and the interfacial shear stress is not constant since mass is removed due to condensation. The variation in vapor velocity depends upon the condensation rate and any changes in the vapor cross sectional flow area. For moderate condensation rates, the interfacial shear stress may be approximated by ... 

For practical values of H and Prf, Eq. 14.33 was found to be near unity, indicating that acceleration and convection effects are negligible. Chen [34] included the effect of vapor drag on the condensate motion by using an approximate expression for the interfacial shear stress. He was able to neglect the vapor boundary layer in the process and obtained the results shown in Fig. 14.8. The influence of interfacial shear stress is negligible at Prandtl numbers of ordinary liquids (nonliquid metals, Pr< > 1). Chen [34] was able to represent his numerical results by the approximate (within 1 percent) expression ... 

Koh et al. [35] solved the boundary layer equations of both the condensate and the vapor using a more accurate representation for the interfacial shear stress. They found a dependence on an additional parameter... 

During upflow of vapor, interfacial shear will retard the drainage of condensate, thicken the condensate film, and decrease heat transfer. Care must be exercised to avoid vapor veloc-... 

For the interfacial shear-controlled flows, annular film flow pattern is established, and the tube orientation is irrelevant. Consequently, the correlations for annular condensation in horizontal tubes can be applied for vertical internal downward flows as well—see Table 17.25. 

However, even at relatively low film Reynolds numbers, the assumption that the condensate layer is in laminar flow is open to some question. Experiments have shown that the surface of the film exhibits considerable waviness (turbulence). This waviness causes increased heat transfer rates. Better heat transfer correlations for vertical condensation were presented by Dukler in 1960. He obtained velocity distributions in the liquid film as a function of the interfacial shear (due to the vapor velocity) and film thickness. From the integration of the velocity and temperature profiles, liquid film thickness and point heat-transfer coefficients were computed. According to the Dukler development, there is no... 

Figure 7-4 presents the heat transfer data for values of Aj = 0, no interfacial shear. Figure 7-5 can be used to predict condensing heat transfer when interfacial shear is not negligible. 

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