## 4 Conclusions and Discussion  
This study numerically researched the effect of the injector spray angle on the combustion and emissions of a 4-stroke NG-diesel DF marine engine. The ultimate target of the study is to find out the optimal spray angle of the injector for the engine, in order to reduce exhaust gas emissions without using any post-treatment devices.  
The major results of the study are listed as follows:  
1. The in-cylinder peak temperature in the DF mode was lower than that in the diesel mode, due to the more uniform temperature distribution within the engine combustion chamber.
2. The DF mode reduced the NO emissions by up to 71%, compared to the diesel mode. The injector SA of 145\({}^{\circ}\) is the optimal value for reducing the NO emissions in both diesel and DF modes.
3. The DF mode significantly reduced the soot emissions, in comparison to the diesel mode. The soot emissions in the DF mode was almost zero. In both diesel and DF modes, the injector SA of 150\({}^{\circ}\) produced the lowest soot emissions. This is thus the recommended SA for the injector of this engine to reduce soot emissions. It helped to reduce 56% and 17% of soot in the diesel and DF modes, respectively.  
A considerable reduction in the CO\({}_{2}\) emissions in the DF mode, compared to the diesel mode was observed. The DF mode reduced the CO\({}_{2}\) emissions by approximately 20%, compared to the diesel mode. In both diesel and DF modes, the injector SA of 150\({}^{\circ}\) produced the lowest CO\({}_{2}\) emissions. This is thus the recommended SA for the injector of this engine to reduce CO\({}_{2}\) emissions.
5. It is important to note that this study investigated the effects of the injector SA on the combustion and emissions of the engine, without considering the effects of the piston bowl geometry. Actually, the mixing quality of the fuel-air mixture which strongly influences the combustion quality of the engine depends not only on the injector SA but also on the piston surface shape. Therefore, the optimal SA for the injector in this study is applicable to the engines with a \(\omega\)-type piston surface shape only. For engines with other types of piston surface shapes, such as a U-type or re-entrant types, the optimal SA for the fuel injectors might be different.  
Based on the above conclusions, it is highly recommended to use a SA of 145\({}^{\circ}\) or 150\({}^{\circ}\) for the fuel injector of \(\omega\)-type-piston engines, to reduce the NO or soot and CO\({}_{2}\) emissions, respectively, depending on which emission regulations need to be met while retaining the engine power.  
Conceptualization, V.C.P., W.-J.L. and J.-H.C.; Methodology, V.C.P., V.V.L. and J.-H.C.; Software, V.C.P. and W.-J.L.; Validation, V.V.L. and J.-H.C.; Formal analysis, V.C.P., S.Y. and J.-H.C.; Data curation, V.C.P., S.Y. and V.V.L.; Writing--original draft preparation, V.C.P.; Writing--review and editing, V.C.P. and W.-J.L.; Project administration, J.-H.C.; Funding acquisition, W.-J.L. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Korea Institute of Marine Science & Technology Promotion (KIMST) funded by the Ministry of Oceans and Fisheries (20220603, 20220568).  
Not applicable.  
The authors declare no conflict of interest.