## 5 Conclusions  
In this study, diesel spray was tested with a 3D-CFD numerical simulation. First, the 3D-CFD numbers were checked for their accuracy from the experimental data. Then, we studied the effects of various injection rate shapes on the properties of the spray and analyzed them using the 3D-CFD simulation results. The preliminary conclusions can be summarized as follows:  
1. The 3D-CFD model can predict the spray behavior's agreement with the experimental data both during the injection and after the end of the injection, covering different temperatures and injection pressure situations.
2. The injection rate shapes affect the penetration of both liquid and vapor, which in turn influence spray evaporation and spray mixing. The spray behavior can change even when the injection duration and injection mass are the same for all simulation cases.
3. Injection rates with high peak injection rates (QIGD, GIGD, and GIGD) can provide higher vapor penetration capabilities compared to injection rates with a low peak injection rate (RECT). Furthermore, injection rates with the same peak injection rates will ultimately yield the same vapor penetration.
4. Injection rates with a high initial fuel injection, such as the RECT and QIGD injection rates, will make the evaporation more rapid. When the injection rate is rapid enough, resulting in a high temperature, the high TKE and SMD decrease rapidly. For the QIGD injection rate, the TKE grows and moves to an area according to the length of the spray, which results in a longer spray penetration and a leaner equivalence ratio in the spray tip area than the other injection rates. For the RECT injection rate, the TKE grows and moves to an area according to the width of the spray due to the constant injection rate. This means that the initial injection rate shape has a significant impact on the evaporation efficiency and TKE production.
5. Injection rate shapes with good evaporation efficiency, such as the QIGD injection rates, will likely result in a shorter ignition delay, including a more rapid onset of combustion and a shorter duration of combustion. The QIGD injection rate has high rail pressure and the strongest turbulent mixing at initial injection, resulting in faster mixing. For a low initial injection rate, the GIGD injection rate shows the opposite, and CO emissions increase because the fuel injection does not have enough time to develop good air entrainment before the start of combustion. Strategies for creating high pressure in the cylinder often result in NO\({}_{\text{x}}\) emissions and high engine noise levels. This means that the initial injection rate and rail pressure have a significant impact on combustion time, emissions, and engine noise levels.  
Finally, the analysis of the numerical simulation of the effects of different fuel injection rate shapes on the diesel spray mixing process shows that the variation in the structure of the air and fuel mixture in diesel engines depends on the shape of the fuel injection rate. The injection rate influences the diesel spray mixing process both during injection and after the EOI.  
Conceptualization, L.L.; methodology, I.N.; simulation, I.N.; validation, L.L., K.N. and D.L.; formal analysis, L.L. and I.N.; data curation, I.N.; writing--original draft preparation, I.N.; writing--review and editing, L.L.; project administration, X.M. 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 number 51509051), and the International Exchange Program of Harbin Engineering University for Innovation-oriented Talent Cultivation.  
This paper was funded by the International Exchange Program of Harbin Engineering University for Innovation-oriented Talent Cultivation. The experimental data were taken from the Engine Combustion Network website that is maintained and operated by the Engine Combustion Department of Sandia National Laboratories.  
The authors declare no conflict of interest.