The characteristics of laminar film condensation of pure vapor flow in a vertical tube

In this study, we investigate the characteristics of laminar film condensation of pure vapor flow in a vertical tube, taking into account (i) the vapor flow rate reduction owing to condensation, (ii) the finiteness of the vapor boundary-layer thickness, (iii) the curvature of the vapor layer, and (iv) the pressure variation. An approximate integral two-phase boundary-layer equation model is derived, and a condition that pressure recovery occurs is determined from the asymptotic analysis around the tube inlet. Furthermore, the present model is further simplified to obtain an analytical solution if the degree of subcooling is sufficiently large. The asymptotic solution for sufficiently large degrees of subcooling gives a good approximation to the numerical solution. The tube length of complete condensation is estimated. Comparison with vertical plane condensation demonstrates that the film thickness and the Nusselt number increased and decreased, respectively, by the vapor flow reduction for large degrees of subcooling.