## 3 Simulation Results and Discussion
### Effect of Hydrogen Injection Timing on the In-Cylinder Mixture Formation  
Figure 14 shows the distribution of the mixture inside the cylinder at TDC in both radial and circumferential sections for different hydrogen injection timings. From the radial section, it can be observed that the mixture is uniformly distributed at TDC for different hydrogen injection timings, resulting in good mass distribution of the mixture. In the circumferential section at hydrogen injection timings of \(-144\ ^{\circ}\)CA and \(-142\ ^{\circ}\)CA, a  
Figure 12: The mass fraction of the mixture with different equivalent ratios inside the cylinder at \(-5\ ^{\circ}\)CA, TDC and \(5\ ^{\circ}\)CA.  
Figure 13: Variations in NSD and mass fraction of mixtures with different equivalent ratios at TDC for the four schemes.  
lean mixture is observed near the exhaust valve. This characteristic assists in mitigating pre-ignition to a certain degree. However, for hydrogen injection timings of \(-136\)\({}^{\circ}\)CA, \(-138\)\({}^{\circ}\)CA, and \(-140\)\({}^{\circ}\)CA, a rich mixture area exists in the vicinity of the exhaust valve, thereby increasing the likelihood of pre-ignition. The main reason for this difference lies in the variation of hydrogen injection timing, which leads to differences in the distance and position of the jet impinging on the top surface of the piston. As shown in Figure 15, as the hydrogen injection timing is delayed, the distance at which the hydrogen jet impinges on the wall decreases, and the position of impinging on the wall shifts to the left. When the hydrogen injection timing is \(-136\)\({}^{\circ}\)CA, \(-138\)\({}^{\circ}\)CA, and \(-140\)\({}^{\circ}\)CA, respectively, the impinging distance on the wall is shorter, resulting in a larger jet momentum at the moment of impingement and a larger wall-attached jet momentum. Therefore, after the wall-attached jet detaches from the wall, a smaller counterclockwise vortex structure forms on the right side, restricting the mixing of the jet with air. This leads to a higher concentration of the mixture near the exhaust valve at the TDC.  
Figure 16 presents the distribution of the equivalence ratio of the mixture and the NSD at TDC at various hydrogen injection timings. It is discernible that, irrespective of the injection timing, the distribution of the equivalence ratio of the mixture almost tends towards a normal distribution. When hydrogen injection timing is at \(-144\)\({}^{\circ}\)CA, the peak value of the mixture mass fraction curve appears near the equivalence ratio of 0.7, while other hydrogen injection timings have peak values around 0.6. Interestingly, NSD seems to exhibit minimal sensitivity to changes in hydrogen injection timing, which may be attributed to overall early injection and longer mixing time, enhanc  
Figure 14: In-cylinder mixture distribution at TDC for different hydrogen injection timings.  
Figure 15: Qualitative schematic diagram of jet–wall collision position for different hydrogen injection timings.  
quality. In summary, the uniformity of the mixture in the cylinder is the best at \(-144^{\circ}\), and it has a higher equivalent ratio near the spark plug, which is conducive to ignition.