Regimes of Filmwise Condensation

From Thermal-FluidsPedia

As in the case of external heterogeneous dropwise condensation, filmwise condensation occurs when a cold wall surface is in contact with a vapor near saturation conditions. Filmwise condensation on a vertical surface occurs when the liquid phase fully wets the surface, whereas in dropwise condensation the liquid incompletely wets the solid surface.

The condensation process begins with vapor condensing directly on the wall surface. However, in contrast with dropwise condensation, after the wall is initially wetted it remains covered by a thin film of condensate. After that point, condensation occurs only at the liquid-vapor interface. Therefore, the condensation rate is directly a function of the rate at which heat is transported across the liquid film from the liquid-vapor interface to the wall.

The figure on the right shows three distinct regimes of filmwise condensation on a vertical wall. These regimes are proceeding in order from the top of the wall (x = 0): laminar, wavy, and turbulent. The Reynolds number is defined as Re_δ = 4Γ / μ_l, where Γ is mass flow rate of condensate per unit width. At the top of the wall, where the film is thinnest, the laminar regime exists. As the condensation process proceeds, more and more condensation appears on the surface and the liquid condensate is pulled downward by gravity. As the condensate moves downward, the film becomes thicker. The first sign of transition to a non-laminar regime appears as a series of regular ripples or waves of condensate. This regime is called the wavy regime and is considered neither laminar nor turbulent. It is characterized by consistent, regular series of waves in time. Finally, if the wall is long enough, the film thickness becomes so great that irregular ripples in both time and space will appear which is identified as turbulent flow regime.

The laminar regime was first rigorously analyzed by Nusselt (1916). Because many simplifying assumptions were made, this analysis provided a closed-form solution. This classical analysis was a very good building block for later studies that gradually chipped away at the assumptions made by Nusselt by employing numerical methods. The classical laminar flow condensation analysis will be presented in this section, followed by some of the later studies that improved Nusselt’s model. The improvements presented here will include the consideration of noncondensable vapors in the condensation process and the effect of vapor flow (Nusselt assumed a stagnant vapor reservoir). The wavy and turbulent regimes are obviously much more difficult to solve than the laminar, and numerical methods are required to obtain an acceptable solution. However, the reasoning behind these regimes will be presented because the overall heat transfer rate from the vapor reservoir to the cooled wall is dominated by contributions from the wavy and turbulent sections. In fact, most industrial applications require that the walls in surface condensers are of a sufficient length and have the surface modified in order to guarantee wavy and turbulent.

References

Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA

Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.

Nusselt, W., 1916, “Die Oberflächenkondensation des Wasserdampfes,” Z. Vereins deutscher Ininuere, Vol. 60, pp. 541-575.