## 5 Conclusions  
In this paper, a numerical study based on OpenFOAM was conducted to investigate the macrospray morphology and microdroplet behavior of iso-pentane two-phase flashing spray to simulate the accidental release due to leakage of a high-pressure hydrocarbon liquid in the form of a small hole. The effects of the initial injection pressure and temperature on iso-pentane flashing spray were examined and analyzed.  
The numerical result of the spray morphology shows good agreement with the images captured by the experiments at all spray conditions. Through the introduction of the spray angle as one of the input boundary conditions in the numerical study, which were extracted from the near-nozzle field spray images, the simulation can reasonably reflect the rapid expansion of the flashing spray in the radial direction. The radial expansion is greatly enhanced as the initial temperature is increased, while it is less affected by the injection pressure. The initial injection pressure has a more significant effect on the diffusion length of the gas phase in the axial direction. However, increasing the initial injection pressure and superheat both contribute to a decrease in the droplet penetration distance because of the better atomization and a more intense evaporation of smaller droplets.  
The gas temperature and vapor concentration profile of the spray suggest that a cold and highly concentrated area exists in the central spray area. Furthermore, droplets in the near-field of the nozzle exit (about 10 mm away from nozzle exit) evaporate intensively due to the quick release of the superheated liquid bulk, causing a rapid decline in the droplet diameter and droplet velocity. Afterward, when the droplets travel downstream, the changing rates of the droplet temperature, diameter, and velocity slow down. Both a higher overheat degree and injection pressure cause smaller droplets and a more substantial evaporation. Moreover, the study points out that a higher temperature can lead to a more homogeneous droplet diameter distribution in the spray's radial direction, while the inject pressure is the major factor that affects droplet velocity distribution in both the axial and radial directions of iso-pentane flashing spray.  
Conceptualization, Z.-F.Z. and D.-Q.Z.; methodology, D.-Q.Z., S.-Y.C. and J.-F.W.; software, D.-Q.Z. and H.-J.X.; validation, J.-F.W. and B.C.; formal analysis, Z.-F.Z. and D.-Q.Z.; investigation, D.-Q.Z., H.-J.X. and S.-Y.C.; writing--original draft preparation, D.-Q.Z.; writing--review and editing, Z.-F.Z.; visualization, J.-F.W.; supervision, Z.-F.Z. and B.C.; project administration, Z.-F.Z.; funding acquisition, Z.-F.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (52176163) and the aerospace science funding (2019 ZB070002). Thanks are also given to the Fundamental Research Funds for the Central Universities and Cyrus Tang Foundation.  
Not applicable.  
Figure 11: Effects of injection temperature and pressure on the variation of droplet velocity along spray radial direction. (**a**) Effect of \(T_{inj}\) on velocity variation under \(P_{inj}\) = 1.5 MPa; (**b**) Effect of \(P_{inj}\) on velocity variation under \(T_{inj}\) = 60 \({}^{\circ}\)C.  
Data Availability Statement: The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.