Research on the Condensation Process of Gaseous Water and Water/Ethanol Mixture in the Laval Nozzle
Authors: Bian Jiang , Cao Xuewen 
Published: November 2019

Abstract
Condensation phenomenon has been studied actively for decades because of its extensive and significant applications in various fields of technology and engineering. The condensation phenomenon of condensable component in supersonic flows is still not understood very well as a result of the complex nucleation and droplet growth process, especially the condensation characteristic of gas mixture. In this paper, the Laval nozzle was designed based on the bi-cubic curve, state equation of real gas, arc plus straight line and viscous correction of boundary layer. The physical and mathematical models were developed to predict the condensation process in the supersonic air flows based on the nucleation and droplet growth theories, surface tension model and gas-liquid governing equations. The condensation processes of gaseous water/air binary (single condensable) gas and water/ethanol/air ternary (double condensable) gas mixture in the designed nozzle were simulated, and the reliability of the established models was verified by the experimental data. By comparing the condensation process of water/air binary gas with water/ethanol ternary gas, the influence of the second condensable component on the condensation process was analyzed. The results show that in the condensation process of gaseous water, as the pressure and temperature of water vapor decrease in the nozzle, spontaneous condensation occurs further downstream the nozzle throat. The nucleation rate grows rapidly from 0 to peak in a very short distance. With the consumption of water vapor, due to the decrease of the degree of supercooling, the nucleation environment is destroyed, and the nucleation rate quickly decreases to 0. The nucleation process is rapid in time and space, while the droplet growth process could maintain longer. The droplet number and mass fraction increase continuously till the nozzle outlet. There is a weak condensation in the nozzle due to the release of latent heat, but it is not obvious because the air acts as a heat container and absorbs the latent heat released by condensation.
In the water/ethanol/air ternary system, the ethanol nucleates prior to water vapor. With the increase of supercooling, water vapor also begins to nucleate. In essence, there are two kinds of condensation nuclei (water nuclei and ethanol nuclei), and both the water and ethanol vapor can aggregate on these two kinds of condensation nuclei. Compared with the condensation process of water, the Wilson point of condensation is closer to the throat and the outlet mass fraction of liquid phase is greater in the condensation process of water/ethanol mixture, which shows that the water and ethanol can affect and promote each other. The maximum nucleation rate, droplet growth rate, droplet radius and outlet mass fraction of liquid phase of water/air binary and water/ethanol/air ternary mixture are about 9.46 × 1026 m−3s−1 and 2.57 × 1027 m−3s−1, 1.65 × 10−5 m/s and 1.02 × 10−5m/s, 1.32 × 10−7m and 1.63 × 10−7m, 0.19% and 1.34%, respectively.