## 3 Simulation Results and Discussion
### Effect of Nozzle Hole Number and Injection Direction on the In-Cylinder Mixture Formation  
First, the interaction between the jets of a multi-hole nozzle was analyzed. Figure 8 presents the concentration distribution of the mixture at various sections for scheme P1 at \(-127\)\({}^{\circ}\)CA (\(13\)\({}^{\circ}\)CA ASOI) with a section spacing of \(5\) mm. It can be observed that in the middle and downstream regions, the jets fully merge owing to the Coanda effect between the adjacent nozzle holes. As shown in Figure 9, when the hydrogen injection timing is \(-140\)\({}^{\circ}\)CA, a radial section at different times displays the in-cylinder mixture formation process. The radial section intersecting the nozzle axis and perpendicular to the cylinder head divides the hydrogen jet into two symmetrical components. At \(-137\)\({}^{\circ}\)CA, the free jet front experiences a slight distortion owing to the upward airflow within the combustion chamber. It is worth noting that for scheme P1, the jet curls upwards on both sides, forming two gas vortices. At \(-127\)\({}^{\circ}\)CA, the hydrogen jet for scheme P1 is aggregated into a single stream owing to the influence of vortices on both sides and the Coanda effect. The front end of the jet rolls up under the effect of environmental resistance and preliminarily forms a vortex center as shown in Figure 9 by the black circle. At this time, in the single-hole scheme, the jet contacted the wall, and the jet cone angle was smaller than that of the porous nozzle. At \(-112\)\({}^{\circ}\)CA, it can be observed that the area where the jet hits the wall forms a local fuel-rich area. After the free jet collides with the wall, a front wall-attached jet is formed at the front end of the free jet, which is denoted as \"a\". Simultaneously, a reverse wall-attached jet was formed at the back of the free jet, denoted as \"b\". All four schemes showed a vortex structure at \(-102\)\({}^{\circ}\)C, as indicated by the black circle in the radial section. By observing the development of the mixture in the cylinder at \(-112\)\({}^{\circ}\)CA--\(72\)\({}^{\circ}\)CA, it can be found that the diffusion speed of the rich mixture moving along the wall is slow. If the size of the vortex structure is large, the mixing speed of the rich mixture can be increased after separation from the wall, and the hydrogen diffusion speed is faster. Figure 10 shows the mass fraction curves of mixtures with different equivalent ratios for the four schemes at \(-112\)\({}^{\circ}\)CA, \(-92\)\({}^{\circ}\)CA, and \(-72\)\({}^{\circ}\)CA, respectively. At \(-112\)\({}^{\circ}\)CA, the injection has not ended, and most of the area in the cylinder is still pure air, so the mass fraction of the mixture with an equivalent ratio of less than \(0.1\) is the largest. At \(-92\)\({}^{\circ}\)CA, hydrogen is mixed in the cylinder for a period of time, and the mixture with an equivalent ratio of less than \(0.1\) in the cylinder is significantly reduced. At \(-72\)\({}^{\circ}\)CA, scheme P2 has a better mixing effect, and the mass fraction of the target equivalent ratio is the largest. This improvement could be attributed to two factors. First, compared with scheme P1, the vortex structure formed by scheme P2 is larger, and the mixture diffuses faster. Second, compared with schemes P3 and P4, scheme P2 uses the combustion chamber as the center of the injection direction, so that the jet is away from the wall, thus improving the mixing efficiency. Figure 8: Multi-hole jet development. From \(-5\,^{\circ}\)CA to \(5\,^{\circ}\)CA, the mixture distribution of the four schemes did not change significantly with time. At TDC, compared with the other three schemes, the mixture on the right side of the radial section is richer in scheme P1. Through the radial section at \(-72\,^{\circ}\)C in scheme P1, the wall-attached jet 'a' forms smaller vortex structures owing to the in-cylinder squeezing effect, which hinders mass diffusion.