## 4 Conclusions  
In this paper, the diesel spray characteristics with elliptical and circular nozzles under a high ambient density of 65.6 kg/m\({}^{3}\) were investigated by experimental and simulation methods. The present study involved three macroscopic spray parameters, namely spray tip penetration (STP), spray cone angle (SCA), spray area (SA), and one microscopic spray parameter, namely Sauter Mean Diameter (SMD). The main conclusions are as follows:  
(1) Compared with the circular nozzle, the STP of the elliptical nozzles decreased dramatically, and the STP of elliptical nozzles with aspect ratios of 1.25 and 1.5 decreased by 19.29% and 20.96%, respectively, and STP for the elliptical nozzle with larger aspect ratio was observed to be smaller. The reasons for this were the fact that the elliptical nozzles had a larger spray surface area, which was subjected to greater aerodynamic drag, and that  
Figure 21: Weber number of particles for three nozzles. Figure 20: Sauter Mean Diameter (SMD) for circular and elliptical nozzles. the elliptical nozzles were more likely to generate stronger turbulence, resulting in faster kinetic energy dissipation. (2) In the XZ plane, the average SCA of elliptical nozzles with aspect ratios of 1.25 and 1.5 increased by 76.90% and 77.17%, respectively, compared to that of the circular nozzle, and in the YZ plane, the average SCA of elliptical nozzles with aspect ratios of 1.25 and 1.5 increased by 27.04% and 37.43%, and the average SCA of the elliptical nozzle with a larger aspect ratio was the largest in both planes. The reason was that the initial cross-section of the spray with elliptical nozzles was asymmetric, the asymmetry of the spray resulted in the instability of the spray boundary layer, and the surrounding gas volume suction effect was stronger, so the contact area of the elliptical spray and ambient gas was larger than the circular one, and the elliptical spray was subjected to greater aerodynamic drag during spraying, resulting in reduced STP and SCA becoming larger. (3) In the XZ plane, the SA of elliptical nozzles was larger, and the average SA of elliptical nozzles with aspect ratios of 1.25 and 1.5 increased by 9.39% and 13.05%, respectively, compared to that of the circular nozzle. Additionally, after the spraying process, an elliptical nozzle with a larger aspect ratio exhibited the largest SA. In the YZ plane, the average SA of elliptical nozzles with aspect ratios of 1.25 and 1.5 decreased by 17.28% and 14.38%, respectively, compared to that of the circular nozzle. For the same STP, the elliptical nozzle with a larger aspect ratio exhibited the largest SA in both planes. (4) In comparison to the circular nozzle, elliptical nozzles demonstrated a more rapid reduction in SMD, suggesting a more expeditious fragmentation of the spray. When the SMD tended to stabilize, the SMD of the circular nozzle and the elliptical nozzle with an aspect ratio of 1.25 both reached about 6.3 \(\upmu\)m, and that of the elliptical nozzle with a 1.5 aspect ratio reached 6.1 \(\upmu\)m. The reason for this was the asymmetric geometry of elliptical nozzles, which resulted in the spray being subjected to uneven shear force, which made the spray more susceptible to instability and turbulence, causing the droplets to break up faster. Conceptualization, T.S. and W.Y. ; Data curation, Q.S. ; Methodology, Q.S. ; Resources, F.L. ; Software, L.L. and H.W. ; Supervision, T.S. ; Validation, L.L. and H.W. ; Writing--original draft, Q.S. ; Writing--review and editing, R.Z. and F.L. All authors have read and agreed to the published version of the manuscript. This work was supported by the Applied Basic Research Programs of Shanxi Province in China (Grant No. 202203021222045). Not applicable. Not applicable. Informed Consent Statement: Not applicable. The data that support the findings of this study are available from both the first author and the corresponding author upon reasonable request. The data are not publicly available because relevant data need to be confidential.