## 3 Results
### Soot Formation  
The soot mass fraction and specific soot in all simulation cases are shown in Figures 14b and 15a, respectively. The simulation showed that the soot mass fraction tended to increase when the IP increased from 0.01 to 0.02 m at each SA in both diesel and DF modes. Meanwhile, at each IP, when the SA increased from 40 to 45 and 50 degrees, the soot mass fraction tended to increase in the diesel mode; it, however, tended to increase and then slightly decreased in the DF mode. These trends may be related to two main factors: (1) the intensity of turbulence inside the engine combustion chamber affected the local fuel-air equivalence ratio [6; 47], and (2) the fuel films formed on the piston surface due to impinging sprays [6; 48]. Under high fuel-air equivalence ratio (fuel-rich) conditions, which are typically found in the diffusion combustion of direct-injection CIEs, hydrocarbon fuels have a strong tendency to form carbonaceous particles, i.e., soot [49]. Meanwhile, the increase in fuel films formed on the piston surface increases soot formation.  
Figure 14: NO emissions in all simulation cases: (**a**) NO mass fraction, (**b**) specific NO emissions.  
In this study, soot formation tended to increase when the IP increased at each SA. This is due to the increase in fuel films formed on the piston surface caused by the target injection region of the fuel being shifted closer to the piston surface when the IP increased. This tendency can be observed in Figure 7 in Section 3.1 or Figure 11 in Section 3.3. [PERSON] et al. also reported in [31] that the increase in the deposition of fuel film on the piston wall led to higher soot formation. The CFD simulation results obtained by [PERSON] and [PERSON] [33] also showed higher soot formation due to injected fuel impingement onto the combustion chamber walls. Meanwhile, the increase in soot formation as the SA increased from 40 to 50 degrees at each IP may be related to higher local fuel-air equivalence ratios inside the engine combustion chamber. At each IP, the reductions in TKEs when the SA increased (Figure 8) reduced the mixing quality between the fuel and air. This led to increases in the local fuel-air equivalence ratio and thus increased soot formation.  
Compared to the diesel modes, the DF modes produced significantly lower soot. This is because the mixing quality between the injected fuel and air in the DF modes (using gaseous fuel) was higher than that in the diesel mode (using liquid fuel). Higher fuel-air mixing quality resulted in significant reductions in the local fuel-air equivalence ratio in the DF modes. This helped to reduce soot formation in the DF mode. In addition, because CH\({}_{4}\) does not contain C-C bonds, and it contains no aromatics and sulfur, NG tends to minimally produce soot compared to other hydrocarbon fuels [1; 50]. The reduction tendencies in soot formation in DF modes using CH\({}_{4}\) compared to the diesel mode using only diesel oil had also been reported in previous studies [10; 11; 12].  
Considering engine power, when expressing the amount of soot emitted in terms of specific values, the simulation result showed a different trend, as can be seen in Figure 15b. It can be seen from the figure that the IP of 0.01 m with an SA of 40 degrees produced the lowest specific soot emission in both diesel and DF modes. This set of injection parameters decreased the specific soot emissions of the engine by 23.35% and 16.81% compared to when using the original set of injection parameters (IP = 0.01/SA = 45) in the diesel and DF mode, respectively. It is thus considered to be the optimal parameter that should be set for the fuel injector to reduce soot emissions in both diesel and DF modes.