Interfacial vapor shear

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 ... 

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. 

T Solid-vapor interfacial energy dyn/cm dyn/cm z Pow der shear stress kg/cm psf... 

When a co-current vapor flow is present, the basic nature of this flow does not change, but the details differ because of the thinning of the liquid film by interfacial shear stress. Dropping the convective terms we can write the Navier-Stokes equations for steady film flow as follows ... 

In this work, we show that small amounts of water vapor dramatically lower the lateral force required to fiacture the salt-glass bond as the SFM tip is drawn across the particle. We model this decrease in terms of the effect of water vapor on tiie interfticial surfiice energy. Particle size also affects the interfticial shear strength, presumably due to variations in the size of interfacial flaws relative to the total interftice area. 

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-... 

Developing a description of the vapor film, modeling both the interfacial shear stress (affected by the bulk flow) and the wall shear stress. 

In the preceding section, the case of evaporation of thin films in annular flow was discussed. In this case, the vapor had a dominant role in determining the flow of the film through its influence on the interfacial shear stress. However, there are many situations of industrial importance in which a liquid film is present that falls down the heat transfer surface under the influence of gravity. Here, we can distinguish two cases ... 

T Ti Stefan-Boltzmann constant (5.669 x 10"8), W/m2K4 t/tc (Fig. 15.24) hovering period of vapor mushrooms, s dimensionless time (Eq. 15.151) interfacial shear stress, N/m2... 

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... 

The interfacial shear stress is influenced by both the interface velocity and the mixture side velocity. Moreover, the entrainment from a liquid film is associated with the onset of disturbance waves at the interface and, in general, depends on both the vapor and the liquid flow rates. In fully turbulent flow, above a film Reynolds number of 3000 the condition for the onset of entrainment depend mainly upon the vapor velocity [5]. For this reason, the fothers in Equation (2) is correlated as. 

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