## 3 Results
### CO\({}_{2}\) Emissions  
The CO\({}_{2}\) emissions in all simulations are presented in Figure 13. The results showed a considerable reduction in CO\({}_{2}\) emissions in the DF mode, in comparison to the diesel mode. The DF mode reduced CO\({}_{2}\) emissions by approximately 20%, compared to the diesel mode. As is globally known, carbon dioxide (CO\({}_{2}\)) is a carbon-based emission. Its formation is directly dependent on the number of C (carbon) atoms contained in hydrocarbon fuels. Moreover, its formation is strongly influenced by the combustion quality in the engine cylinder. CO\({}_{2}\) is the final product of the complete combustion of hydrocarbon fuels. In the combustion process of ICEs, hydrocarbon fuel is firstly oxidized by O\({}_{2}\) contained in the charge air to form CO. CO is then oxidized to form CO\({}_{2}\) sequentially by the residual O under high-temperature conditions in the engine cylinder. The higher the O\({}_{2}\) concentration and temperature, the greater the CO is oxidized. In this study, the reduction in CO\({}_{2}\) emissions in the DF mode was related to two reasons: (1) compared to the diesel mode, the DF mode produced a better fuel-air mixing quality inside the engine cylinder that led to a better combustion quality; and (2) the cleaner characteristics and fewer C atoms of NG, compared to the diesel oil. Figure 12: Foot emission in all simulation cases. Figure 13: CO\({}_{2}\) emissions in all simulation cases. Chemically, assuming that in the ideal conditions, diesel oil (C\({}_{13}\)H\({}_{23}\)) and CH\({}_{4}\) are completely burnt. The chemical reactions for the combustion of the fuels are expressed as:  
\[\mathrm{C}_{13}\mathrm{H}_{23}+\frac{75}{4}\mathrm{O}_{2} \to 13\mathrm{CO}_{2}+\frac{23}{2}\mathrm{H}_{2}\mathrm{O} \tag{3}\] \[\mathrm{CH}_{4}+2\mathrm{O}_{2} \to\mathrm{CO}_{2}+2\mathrm{H}_{2}\mathrm{O} \tag{4}\]  
Based on Equations (3) and (4), it is calculated that 16 g CH\({}_{4}\) produces 44 g CO\({}_{2}\), while 16 g C\({}_{13}\)H\({}_{23}\) produces 51 g CO\({}_{2}\) if the fuels are completely burnt. In this study, the fuel dosage supplied to the engine in the diesel and DF modes were 0.0020667 g C\({}_{13}\)H\({}_{23}\) and 0.001782 g (including 0.001682 g C\({}_{13}\)H\({}_{23}\) and 0.0001 g CH\({}_{4}\)) per cycle, respectively. It is very easy to calculate that, in the case of complete combsions, the diesel mode produces approximately 0.00658 g CO\({}_{2}\), while the DF mode produces only approximately 0.0049 g CO\({}_{2}\). The reduction in the CO\({}_{2}\) emissions when running in the DF mode, compared to the diesel mode, will thus be around 25%. However, due to the fact that the combustion of fuel inside the cylinder of actual ICEs will not be complete. As a result, the actual reduction in CO\({}_{2}\) when using CH\({}_{4}\), instead of diesel in real life will be a little different depending on the combustion efficiency of the engine. Compared to a reduced level of 20% in CO\({}_{2}\) emissions when running the engine in the DF mode instead of the diesel mode in this study, it can be concluded that the simulation results are reasonable. The reduction tendencies of the CO\({}_{2}\) emissions in the DF mode when using NG as the primary fuel, compared to the diesel mode, had also been reported in many previous studies [8; 9]. 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 the engine to reduce CO\({}_{2}\) emissions. It helped to reduce 0.77% and 0.31% CO\({}_{2}\) emissions in the diesel and DF modes, respectively. Through the results presented in Sections 3.4 and 3.5, it is very interesting to note that, in both diesel and DF modes, the injector with a SA of 150\({}^{\circ}\) produced the lowest soot and CO\({}_{2}\) emissions. This is related to the wall-wetting phenomena mentioned above.