## 5 Conclusions  
In this paper, the effects of the throat radius, divergent section expansion angle and divergent section length of a nozzle on the spontaneous condensation of steam were numerically investigated. The irreversibility flow in the nozzle was also analyzed by identifying the proportion of entropy generation that could be attributed to three mechanisms (viscous dissipation, heat transport and phase change) and the distributions of the total entropy generation rate under different nozzles' geometric structures. In addition, the nozzle's performance was studied by comparing the mass flow rate, total entropy production and liquid mass fraction. The detailed findings are as follows:  
* The increase in the nozzle throat radius enhanced the intensity of the condensation shock and increased the mass flow rate and the pressure at the nozzle outlet. The total entropy production in the nozzle decreased from 11.73 to 10.56 W/K as the throat radius increased from 0.025 to 0.05 m. Therefore, increasing the nozzle throat radius can not only improve the nozzle's performance, but also reduce the waste of energy. In addition, the reduction in liquid mass fraction and phase change entropy generation indicates that the spontaneous condensation behavior of wet steam can be suppressed by increasing the throat radius. * When the expansion angle of the nozzle's divergent section changed from 0 to 11\({}^{\circ}\), the nozzle's outlet Mach number increased, but the nozzle outlet pressure decreased and the intensity of the condensation shock was weakened. Moreover, there was an increase in the liquid mass fraction, which caused an increase in phase change entropy generation. Therefore, reducing the nozzle's expansion angle inhibited the wet steam's spontaneous condensation behavior, to a certain extent. In particular, the steam's spontaneous condensation behavior disappeared at an expansion angle of 0\({}^{\circ}\). * Lengthening the nozzle's divergent section did not change the condensation shock's intensity and its position in the nozzle, which resulted in a complete overlap of the curves of the liquid mass fraction, saturation ratio, droplets' nucleation rate and droplets per unit volume in the steam condensation shock region. As the divergent section's length was increased from 0.2 to 0.7 m, the three identified types of entropy generation, total entropy production, and liquid mass fraction all increased, while the mass flow rate remained constant at 3.997 kg/s. Consequently, lengthening the nozzle's divergent section did not improve the nozzle's performance, but it did cause an increase in the humidity in the nozzle's outlet and the wastage of energy. Figure 17: The mass flow rate, total entropy production and liquid mass fraction under different lengths of the nozzle’s divergent section. No matter how the nozzle's geometric structure changed, the largest proportion of entropy generation was still accounted for by phase changes, followed by viscous dissipation and then heat transport. This indicates that steam's condensation behavior creates a large amount of irreversible energy, resulting in energy waste and reducing the nozzle's performance. Consequently, the spontaneous condensation behavior of wet steam should be suppressed in order to alleviate the performance deterioration that is caused by this behavior when a steam eject is running. Conceptualization, H.L. and X.W. ; methodology, H.L. and J.N. ; software, H.L. and H.H. ; validation, J.N. and H.H. ; formal analysis, H.L. and J.N. ; investigation, H.L., J.N. ; resources, X.W. ; data curation, H.L. and H.H. ; writing--original draft preparation, H.L. ; writing--review and editing, H.L. and H.H. ; visualization, H.L. ; supervision, X.W. ; project administration, X.W. and J.T. ; funding acquisition, X.W. and J.T. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (grant no. 51775098) and the Australian Research Council (DP160101953). Not applicable.