## 1 Introduction  
In recent years, there has been increasing interest in developing technologies that utilize hydrogen--an environmentally friendly energy source that has the advantage of controllable carbon dioxide emissions and low environmental pollutant emissions--to move towards a carbon-neutral society [1, 2, 3]. In particular, since hydrogen fuel-cell vehicles use electricity generated by the reaction of hydrogen and oxygen in the gaseous state as an energy source, it is necessary to develop technologies for the efficient production,storage, and transport of hydrogen. In general, hydrogen is currently stored by compressing gaseous hydrogen under high pressure in order to increase the range of hydrogen fuel-cell vehicles and make hydrogen storage more economical and efficient [4; 5; 6; 7]. Hydrogen storage systems are regulated by the SAE J2601 Hydrogen Charging Protocol, which specifies the maximum storage pressure and temperature range of hydrogen. Depending on the class of hydrogen tank, hydrogen is stored at high pressure, such as 35 MPa or 70 MPa [8], and in order to utilize hydrogen in the gaseous state at high pressure, it is essential to decompress it to a certain pressure, but the safety of this process is being improved for the commercialization of hydrogen energy [9; 10]. As a safety component of hydrogen storage systems, the check valve directly affects the safety of the hydrogen storage system by preventing depressurization and reverse flow during the hydrogen storage process and by blocking the inflow of hydrogen under abnormal pressure conditions through flow, temperature and pressure control. In particular, during this process, performance degradation occurs due to energy loss from flow resistance caused by changes in the state of the hydrogen entering the check valve and internal geometry, which directly affects the performance of the hydrogen storage system [11]. Therefore, research on check valves that directly affect the supply and shut-off of hydrogen is necessary to ensure the safety and reliability of hydrogen storage systems. This need has led to the following studies for hydrogen energy utilization. [PERSON] et al. [12] parameterized the control elements of a conical hydrogen control pressure-reducing valve and analyzed the correlation between hydrogen decompression performance, cone angle, and pressure difference when the flow is stable and constant. This results showed that the flow characteristics along the surface change from a free jet to a parallel flow when the cone angle is less than 45 degrees, confirming that the optimization of the cone structure has a significant effect on the flow pattern and hydrogen decompression performance at the surface. [PERSON] et al. [13] analyzed the energy loss and exergy loss within the valve by analyzing the number of stages and pressure ratio between the inlet and outlet of the valve for a multi-stage hydrogen decompression valve. The results show that the Mach number and exergy losses increase as the pressure ratio increases, but the opposite is true as the number of valve stages decreases. [PERSON] et al. [14] analyzed the effect of the spool head angle of the check valve on the performance and transient hydrogen flow characteristics based on the moving mesh technique. They found that the time to reach the maximum spool displacement decreased as the spool head angle increased from 10 degrees to 50 degrees. [PERSON] et al. [15] analyzed the flow and noise generation characteristics inside a solenoid check valve during rapid hydrogen charging by numerical analysis. As a result, the number and area of the outlets were changed to reduce the intensity of the strong turbulence at the bottom of the valve, which resulted in a reduction in noise generation. Previous studies have analyzed decompression and flow characteristics in response to changes in valve geometry conditions but have not analyzed the impact of energy losses due to pressure and temperature changes within the valve on valve performance.