Numerical analysis of mixed-convection laminar film condensation from high air mass fraction steam–air mixtures in vertical tubes

A numerical analysis is performed for condensing downward flow from steam–air mixtures in vertical tubes with constant wall temperature. The focus of this study is on the case of high inlet non-condensing gas (air) mass fractions (greater than 0.80). The parabolic governing equations are solved for steady, axisymmetric, laminar flow in the liquid film and in the vapour–gas mixture. A complete two-phase model, based on the conservation of mass, momentum, and energy in each phase, is presented. Detailed results are presented in both the film and mixture regions. Those results include radial-direction profiles of axial velocity, temperature, and air mass fraction, as well as axial variation of film thickness, Nusselt number, interface and bulk temperatures, interface and bulk air mass fraction, and proportion of latent heat transfer. In all the cases studied the interface temperature is very close to the wall temperature and the condensation rates are small due to high interface air mass fractions.The inlet relative humidity is varied from 30% to 100% and the inlet temperature is varied from 25 °C to 90 °C. These conditions cover the range of inlet air mass fraction approximately in the range from 0.865 to 0.995 for an inlet pressure of 1 bar. In addition, the effects of varying the inlet Reynolds number (500 to 2000), the wall temperature (5 °C and 15 °C), and the tube radius (2.5 mm to 10.0 mm) are examined. It was found that decreasing the inlet relative humidity reduced the heat transfer rate and that the condensate film thickness increased with an increase in the inlet Reynolds number, inlet-to-wall temperature difference, and inlet relative humidity. Due to high air mass fraction, in some cases only 40% or less of the total heat transfer to the tube wall was due to condensation. For a fixed Reynolds number, decreasing the tube radius increased the condensation rate.