## 5 Experimental Validation  
### Experimental Setup  
We constructed an experimental system to quantitatively evaluate the performance of ultra-high-pressure hydrogen solenoid valves across the operating range from 0 MPa to 87.5 MPa. The testing apparatus enabled comparative assessment between conventional rectangular contact geometry and optimized concave contact geometry through systematic experimental methodology, as illustrated in Figure 13.  
The experimental setup for ultra-high-pressure valve testing with an integrated data acquisition system is shown in Figure 14. The apparatus comprises a pressure regulator, manual isolation valves, precision pressure sensors positioned at both inlet and outlet sections, and the test valve specimen. The system incorporates a high-resolution camera for synchronized visual observation of bubble formation in leak detection fluid. The specifications of key equipment components utilized in this investigation are summarized in Table 11.  
Figure 13: Flowchart of experimental procedure for sealing performance evaluation. Data acquisition was conducted through a LabVIEW 2020-based system with pressure measurements recorded at 100 ms intervals using National Instruments hardware [22]. The system provides 16-bit resolution with \(\pm\)0.02% accuracy across the \(\pm\)20 mA input range for precise measurement of pressure variations during testing. The experimental procedure for determining sealing pressure involved installing the test valve in the apparatus and gradually increasing inlet pressure from 0 MPa at a constant rate of 0.5 MPa/min while continuously monitoring both inlet and outlet pressures. The sealing pressure threshold was identified when outlet pressure began to rise above 0.5 MPa, indicating the onset of leakage. Considering the pressure sensor accuracy of \(\pm\)0.25% F.S (\(\pm\)0.25 MPa), this threshold was selected to ensure measurement reliability. To provide additional verification of the pressure sensor measurements, leak detection fluid was applied to the valve outlet region. This method utilizes the principle of bubble formation when pressurized gas escapes through microscopic leakage paths, creating visible bubbles in the detection fluid [23]. The formation and cessation of bubbles serve  
Figure 14: Experimental setup for ultra-high-pressure hydrogen valve testing with integrated data acquisition system. \begin{table}
\begin{tabular}{c c c} \hline
**Equipment** & **Parameter** & **Value** \\ \hline Pressure Regulator & Operating Range & 0–100 MPa \\ (Tescom 26-1000, Tescom Corporation, Elk River, MN, USA) & Control Precision & \(\pm\)0.5\% F.S \\ \hline Pressure Sensor & Measuring Range & 0–100 MPa \\ (KELLER PA-21Y, KELLER AG, Winterthur, Switzerland) & Accuracy & \(\pm\)0.25\% F.S \\  & Response Time & \textless{1 ms} \\ \hline Pressure Booster & Max Output & \\ (Haskel AGT-62152, Haskel International, Burbank, CA, USA) & Pressure & 100 MPa \\ \hline Data Acquisition System & Resolution & 16-bit \\ (NI cDAQ-9174, National Instruments, Austin, TX, USA) & Max Sampling Rate & 100 KS/s \\ \hline Analog Input Module & Input Range & \(\pm\)20 mA \\ (NI 9203, National Instruments, Austin, TX, USA) & Accuracy & \(\pm\)0.02\% Range \\  & Resolution & 16-bit \\ \hline Camera & Resolution & 1920 \(\times\) 1080 \\ (FFF-WCAM8M, FFF SMART LIFE CONNECTED Co., Ltd., Ayase, Japan) & Frame rate & 30 fps \\ \hline \end{tabular}
\end{table} 
Table 11: Experimental equipment specifications. as a visual indicator that directly corresponds to leakage onset and sealing achievement, respectively. Synchronized camera recording captured bubble formation throughout the pressure ramping process, enabling post-experimental correlation between pressure sensor data and visual bubble detection for enhanced measurement accuracy. All experiments were conducted at room temperature (23 \(\pm\) 2 \({}^{\circ}\)C) using nitrogen gas as the test medium.