## 4 Results  
### Spray Morphology  
Firstly, the simulation result of spray morphology (left half) near the nozzle field within 20 mm under four initial injection pressures (\(P_{inj}\)) and four initial injection temperatures (\(T_{inj}\)) is presented in Figure 4. To further validate the simulation result, the experimental result of the spray images (right half) obtained by a high-speed camera (Fastcam SA-Z, Photron) with a backlit illumination method is also presented for comparison. As can be seen from Figure 4, the simulative and experimental results agree with each other reasonably under all 16 experimental conditions. The spray angle and expansion area toward the lateral direction both increase with the increment of initial injection pressure and temperature. However, the initial temperature has a more significant effect on the spray morphology compared with the injection pressure. That is, increasing the initial temperature from 50 \({}^{\circ}\)C to 80 \({}^{\circ}\)C leads to an obvious increase in the spray angle and expansion width at all injection pressures, while the increase in the spray angle and expansion width is far weaker if one changes the injection pressure. This can be explained by the fact that increasing the initial temperature enhances the superheat degree of the flashing spray, while increasing the injection pressure only enhances the discharging rate and initial velocity. As we know, the governing factor of flashing spray is the nonequilibrium thermodynamics due to a rapid release of unstable energy of superheat liquid through the explosive atomization. As a result, a higher superheat degree produces a more violent flashing atomization, accompanied by a larger spray angle and expansion width near the nozzle field. Lastly, it should be mentioned that the initial spray expansion of the simulated results in the radial direction was realized through the introduction of the spray angle extracted from the near-nozzle field spray images recorded by the high-speed camera. Figure 5 shows the overall spray morphology combining both liquid droplets and diffusion gas mixture, mainly to examine the initial injection pressure and temperature on the penetration distance of iso-pentane flashing spray (0.05 s after injection). The results indicate that a higher injection pressure causes a larger penetration distance of the gas phase, while the injection temperature has less influence on it. To better illustrate this, Figure 6 plots the variation of the penetration distance of the gas and liquid (droplet) phases under different conditions. The droplet penetration distance is the distance that 95% of the droplets' total mass traveled. In addition, the gas diffusion length is defined  
Figure 3: Comparison of droplet diameter distribution between experiment and simulation. (**a**) Droplet diameter distribution of spray 5 mm away from the nozzle exit; (**b**) Droplet diameter distribution of spray 80 mm away from the nozzle exit. as the distance where the iso-pentane gas concentration is reduced to 5% in the spray axial direction. Figure 6a shows that the gas diffusion length nearly presents a linear increase with the injection pressure. This is because a higher injection pressure could induce a larger discharging velocity of spray at the nozzle exit, which makes the total spray have more energy to fly further in the axial direction. However, increasing the initial injection temperature mainly exerts an influence on the spray angle and radial width due to the more violent release of superheat energy, while having much less influence on the spray axial penetration distance. In Figure 6b, a dimensionless number \(\Delta T^{*}/\left(P_{inj}/P_{b}\right)\) is introduced to present the relation between the liquid penetration distance and different operating conditions.