## 2 Research Methods and Content
### Model Validation  
Regarding the model validation method for engine numerical research, one common way is using a real engine. In addition, constant-volume combustion vessels are also widely used in engine numerical research, mainly due to the advantage of an easily controlled environment, which helps us to better understand the effects of fuel spray and mixture process. Similar methods using a constant-volume combustion vessel can be found in many engine studies [33; 34; 35], although a few elements are not exactly the same as those occurring in the cylinder of the real engine during operations.  
This study utilized a constant-volume combustion vessel and the Schlieren technique to compare the measured hydrogen injection process with the simulated one. The Schlieren experimental setup primarily consists of a constant-volume combustion vessel, injection system, injection control system, high-speed camera, and optical Schlieren system, as shown in Figure 3.  
A single-hole electromagnetically controlled valve nozzle with a hole diameter of 0.35 mm was used in the experiment. The hydrogen injection pressure was 6 MPa, and the high-precision resolution of injection was 0.1 MPa. The pressure and temperature of the background gas (nitrogen) were 1 MPa and 300 K, respectively. The injection pulse width was set to 2 ms. During the experiment, a high-speed camera (NAC Memrecam GX-8), with a maximum speed of 600,000 frames per second, was employed to record the spray evolution process. The experimental case was repeated twenty times to ensure accuracy and minimize errors. Afterwards, MATLAB software was used to process, analyze, and  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Initial Region** & **Temperature (K)** & **Pressure (MPa)** \\ \hline Cylinder & 938 & 0.158 \\ Intake port & 320 & 0.099 \\ Exhaust port & 886 & 0.143 \\ Hydrogen injector volume & 300 & 2.4 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Initial conditions.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Boundary Region** & **Temperature (K)** & **Pressure (MPa)** \\ \hline Piston & 520 & NA \\ Cylinder & 450 & NA \\ Air inlet & 300 & 0.1 \\ Intake port & 350 & NA \\ Exhaust outlet & 480 & 0.1 \\ Exhaust port & 420 & NA \\ Hydrogen inlet & 300 & 2.4 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Boundary conditions.  
calculate the recorded spray images. A numerical model was established under the same conditions as the experiment, and the turbulence model used the RNG k-\(\epsilon\) model.  
Table 5 presents a comparison of spray shapes between the experiment and simulation images. On the whole, the simulation results closely match the experimental observations. Furthermore, the experimental and simulated hydrogen jet penetration length and cone angle are shown in Figure 4. The jet penetration length is defined as the distance from the nozzle to the point where the vertical line through the nozzle intersects the leading edge of the jet. The jet cone angle is defined as the angle formed by the external boundary of the jet. It can be found that given that the simulation model simplified the needle valve structure, disregarding needle valve motion and variations in flow cross-sectional area, the initial stage's simulated hydrogen flow rate exceeded that of the experimental value. Consequently, this resulted in a slightly larger penetration length for the simulated jet compared with its experimental counterpart. Nevertheless, this discrepancy is deemed acceptable, leading to the conclusion that our simulation setup ensured reliable simulation accuracy.  
Figure 3: Schematic of the experimental setup.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Time (ms)** & **0.2** & **0.4** & **0.6** & **0.8** & **1.0** & **1.2** & **1.4** & **1.6** & **1.8** & **2.0** \\ \hline Experiment & & & & & & & & & & \\ Simulation & & & & & & & & & & \\ \hline \end{tabular}
\end{table}
Table 5: Comparison of experiment and simulation spray images.