Integral Analysis of Turbulent Natural Convection with Condensation in the Presence of a Noncondensable Gas

Abstract

An approximate model is presented for turbulent natural convection flow of a two-component mixture in which condensate forms along a vertical wall. The integral method is employed as the scheme for the analysis of the gas boundary layer. By incorporating empirical correlations and profiles for temperature, velocity, and density, the compressible Navier-Stokes equations are solved for boundary layer thickness and maximum velocity. Eventually, the desired physical characteristics of heat flux and condensation rate are determined. The major constraint enforced in the model is that the water within the boundary layer is either saturated vapor or slightly superheated. Local condensation away from the wall is not considered. A diverse range of mixtures were studied to examine the effects of noncondensable gas concentration on the heat transfer and condensation rates. It is shown in the results how the presence of air is a hindrance to the diffusion of vapor through the gas boundary layer. The results are compared to a previous empirical model. The results showed reasonable agreement with the previous experimental study discussed. For very large and often times more applicable temperature differences, the model predicts volumetric condensation within the gas boundary layer. A semi-empirical one-equation turbulence model was introduced, and although the turbulent impact on effective properties was determined to be small, it was included nonetheless for flexibility. Code logic and methodology are presented to automate this problem, as the solution is obtained through the iteration on both the turbulent viscosity and the interface temperature.