## 3 Simulation Results and Discussion  
This study investigates the impact of the nozzle hole number, injection direction, combustion chamber geometry, and injection timing on the concentration distribution of the mixture under rated conditions with an injection pressure of 2.4 MPa and an excess air coefficient of 1.8. When studying the influence of a certain factor on the concentration distribution of a mixture, other factors are selected as fixed values, and the fixed values are gradually replaced with an optimal value.  
To investigate the influence of the nozzle hole number and injection direction on the mixture formation and concentration distribution, four schemes were implemented at a hydrogen injection timing of \(-\)140 \({}^{\circ}\)CA. Scheme P1, as shown in Figure 5A, employed a multi-hole nozzle with a diameter of 6 \(\times\) 0.8 mm. The nozzle featured a hole spacing ranging from 2.23 to 3.15 mm and a hole angle from 10\({}^{\circ}\) to 13\({}^{\circ}\). Scheme P2 utilizes a single-hole nozzle (6 mm diameter) with an injection direction towards the center of the combustion chamber, as shown in Figure 5B (a). Scheme P3 utilized a single-hole nozzle (6 mm in diameter), and the injection direction was rotated 45\({}^{\circ}\) clockwise based on scheme P2, as shown in Figure 5B (b). Scheme P4 utilized a single-hole nozzle (6 mm diameter), and the injection direction was rotated 30\({}^{\circ}\) counterclockwise based on scheme P2, as illustrated in Figure 5B (c). As shown in Figure 6, the hydrogen nozzle is equipped with a guide cap based on the outer open ring type. Therefore, this paper simulates the mass flow rate at the injector valve through the detailed internal structure of the injector and takes it as the boundary condition for subsequent simulation to ensure that the global equivalent ratio under different injector holes is the same and the injection pulse width is 46 \({}^{\circ}\)CA.  
For hydrogen direct-injection engines, the injection timing invariably influences the jet behavior and in-cylinder mixture formation. Owing to the changes in the thermodynamic parameters inside the cylinder, the changes in the hydrogen injection timing will change the relative time and the position where the jet impinges on the wall. This, in turn, affects both the jet behavior and the mixing process with air. Hence, at the early stage of the compression stroke, five different timings were selected to investigate the impact of the hydrogen injection timing on mixture formation. These timings are \(-\)144 \({}^{\circ}\)CA, \(-\)142 \({}^{\circ}\)CA, \(-\)140 \({}^{\circ}\)CA, \(-\)138 \({}^{\circ}\)CA, and \(-\)136 \({}^{\circ}\)CA.  
Figure 4: Comparison of experimental and simulation results.  
The geometry of the combustion chamber plays a pivotal role in the mixture formation and combustion processes in hydrogen direct-injection engines. Different combustion chamber geometries yielded different in-cylinder flows, leading to different mixture concentration distributions and combustion characteristics. To study the impact of combustion chamber geometry on in-cylinder mixture formation, two configurations were chosen, (a) a flat-bottom combustion chamber and (b) a sloping combustion chamber, as shown in Figure 7.  
Figure 5: Schematic diagram of the injection direction of multi-hole and single-hole nozzles. (**A**) Illustration of nozzle hole arrangement. (**B**) Different injection directions of single-hole nozzle.  
Figure 6: Nozzle structure diagram.  
Figure 7: Different combustion chamber sizes.