## 4 Conclusions  
In this study, pressure and flow results were compared for the conditions of differential pressure between the inlet and outlet and hydrogen-inlet temperature change for the purpose of analyzing the change of turbulence characteristics and energy loss of the check valve for high-pressure hydrogen charging. The exergy destruction results were compared for the purpose of analyzing the effect of the flow-separation phenomenon on the energy loss, and the following conclusions were obtained.  
1. In the case of a differential pressure (\(\Delta\)P) of 10 MPa and a hydrogen-inlet temperature (T\({}_{\rm in}\)) of 363 K at the point X = 90.7 mm in the L-shaped curved tube area of the check valve, the flow rate at the point Y = 2.3 mm at the top of the valve decreases by up to approximately 60%, and it is found that the flow rate decreases and the pressure increases due to the viscosity of the wall surface, forming a separation point.
2. The flow separation that occurs in an L-shaped curved tube causes a wake and reverse flow to form in the downstream region, which affects the delay in pressure recovery at the boundary layer and the occurrence of a recirculation area, and it reduces the flow area of the main flow, resulting in a bias towards the bottom of the check valve.
3. The pressure coefficient (C\({}_{\rm P}\)) analysis shows that the pressure coefficient increases by up to 98% at the X = 91.7 mm measurement position in the (T\({}_{\rm in}\)) 233 K condition compared to the (T\({}_{\rm in}\)) 363 K condition. This is believed to be due to the fact that the increase in hydrogen-inlet temperature promotes flow reattachment within the boundary layer of the flow-separation region, which reduces the pressure change.
4. In the L-shaped curved tube region of the core part, the turbulent dissipation rate (TDR) at the X = 95 mm point increased by up to about 3000% compared to the \(X\) = 90 mm point, and the temperature results also increased by up to about 4.5 K compared to the inlet temperature. This is due to the conversion of the dissipated turbulent kinetic energy into heat energy, which is the major contributor to the temperature rise and energy loss of hydrogen.
5. The exergy destruction results show a 74% decrease in the discharging part compared to the core part for the (T\({}_{\rm in}\)) 233 K condition, and the differential pressure (\(\Delta\)P) increases by up to 14.6% for the 233 K condition compared to the (T\({}_{\rm in}\)) 363 K hydrogen-inlet temperature condition under the same conditions. This is believed to be due to the higher density at T\({}_{\rm in}\) of 233 K, which increases the viscosity dissipation within the boundary layer of the flow-separation zone and increases the temperature-rise rate and energy-dissipation rate, resulting in increased exergy destruction.  
Conceptualization, S.-H.O., S.-M.J. and H.-K.S.; methodology, S.-H.O. and H.-K.S.; software, S.-H.O. and S.-M.J.; validation, S.-H.O. and H.-K.S.; formal analysis, H.-K.S.; investigation, S.-H.O.; resources, S.-H.O.; data curation, S.-H.O. and S.-M.J.; writing--original draft preparation, S.-H.O.; writing--review and editing, H.-K.S.; visualization, H.-K.S.; supervision, H.-K.S.; project administration, H.-K.S.; funding acquisition, H.-K.S. All authors have read and agreed to the published version of the manuscript.  
This study was conducted with the support of Korea Energy Technology Evaluation and planning funded by the Ministry of Trade, Industry and Energy (202303004020C, Develop technology to for parts of hydrogen storage tank system).  
Not applicable.  
The data presented in this study are available on request from the corresponding author due to (Their use in ongoing business collaborations).  
The authors declare no conflicts of interest.