Modified heat transfer correction function for modeling multiphase condensing flows in transonic regime

Water droplet formation and growth in the nucleation process are crucial aspects of steam condensation in moist air flow, and they are accompanied by intensive heat exchange between phases. This study proposes a mathematical model for predicting heat transfer coefficients in the condensation process, which is applicable for single-phase and multiphase flows. The proposed model based on the correction function forms a continuous model for the low Knudsen number regime, and in the region of large Knudsen numbers, it employs a simplified droplet growth model based on Hertz and Knudsen's approach derived from the kinetic theorem. The proposed model was compared with existing models based on the continuous approach, that is, models derived by Gyarmathy, Fuchs-Sutigin, and Young, as well as models based on the kinetic theorem. Furthermore, the proposed model was implemented into a numerical CFD tool, and numerical studies were conducted for two representative cases of single-species and multispecies flows, that is, steam and humid-air expansion in a converging-diverging nozzle. For steam studies, the proposed model showed a similar convergence with the experiment as Young's model however, its agreement with the experimental results for multispecies condensation flow was better. The proposed model is promising for the study of condensation when there is rapid droplet growth, which occurs in multispecies flows, even if further study is needed to find a correlation between the condensation coefficient and fluid properties.