Correcting for tube curvature effects on condensation in the presence of a noncondensable gas in laminar regimes

Abstract

Filmwise vapor condensation in the presence of noncondensable gases (NCG) continues to attract interest due to its widespread range of applications. In studies of NCG effects on condensation over external surfaces, experimentalists and analysts alike usually employ correction factors to transfer tube condensation rates to flat plate equivalents or vice-versa. For laminar flows over vertical cylinders, these factors are estimated from pure convection correlations as a function of the Grashof number and tube curvature only. We show that this procedure is not rigorous and leads to significant errors, especially at low NCG fractions and small tube radii. Indeed, the usual way of correcting for curvature is strictly valid only in the limit where the NCG fraction is so large that convection heat transfer dominates condensation. On the other hand, as the NCG fraction becomes vanishingly small, the vapor condensation rates should tend to values predicted by the Nusselt film theory, and no enhancement due to tube curvature is to be expected.This paper focuses on vapor condensation as the gas mixture moves along a vertical tube in the laminar free convection regime. The gas and liquid film boundary layer equations are coupled at the gas/film interface and a marching solution procedure using local non-similarity is adopted. The methodology is first verified for near pure free convection flows as well as previous analyses of condensation over a flat surface. The model is subsequently validated against data on steam condensation on a square plate in the presence of air. Finally, a correlation is deduced from the parametric numerical results to allow a proper correction for curvature effects when vapor condenses in the presence of a NCG. The proposed correction spans the whole range of NCG fractions, and displays the expected behavior at the extremes of this range.