## 3 Results and Discussion
### Explosion of Hydrogen Vapor Clouds  
In this section, we investigated the explosion characteristics in cases where the vapor cloud, generated from the leaked liquid hydrogen, was ignited even though no ignition was introduced in the experiment. The ignition source was applied at a location where the equivalence ratio was approximately 0.8 to initiate the vapor cloud explosion since the hydrogen concentration was excessively high near the leak source of liquid hydrogen. For both hydrogen leakage flow conditions of m = 0.225 and 0.73 kg/s, the ignition source was introduced 20 s after the liquid hydrogen began to leak. Figure 12 shows the overpressure distribution within a cross section of Z = 0.4 m during the explosion of a hydrogen vapor cloud, for a case of \(\dot{\mathrm{m}}\) = 0.225 kg/s. In the figure, the coordinates (X, Y) with a position of (0 m, 0 m) represent the origin of the leak. For this condition, the ignition source was located at coordinates (4.0 m, 2.0 m) at the cross section of Z = 0.2 m. The highest overpressure was observed in the cross section of Z = 0.4 m, despite the ignition source being positioned at Z = 0.2 m. High overpressure began to generate near the ignition source and propagated in all directions, forming a maximum overpressure region near the leak source at approximately 20.119 s. At this time, the maximum overpressure recorded was 38.3 kPa, which was lower than that for a case of m = 0.73 kg/s with a larger leakage mass flow rate. After the maximum overpressure was reached, it rapidly propagated in all directions and dissipated. Figure 13 shows the overpressure distribution in a cross section of Z = 0.2 m. The highest overpressure was recorded in this section when the vapor cloud, resulting from a leak in liquid hydrogen, exploded for the case of \(\dot{\mathrm{m}}\) = 0.73 kg/s. Similar to Figure 12, the coordinates (X, Y) with a position of (0 m, 0 m) represent the origin of the leak, while the coordinates (6.5 m, 4.2 m) denote the position of the ignition source. Following ignition, the explosion rapidly progressed, and at approximately 20.493 s after the onset of leakage,  
Figure 12: Computed overpressure distributions at the cross section of Z = 0.4 m, for a case of \(\dot{\mathrm{m}}\) = 0.225 kg/s. the maximum overpressure region was identified near the leak source, reaching a peak overpressure of 428 kPa. Subsequently, the overpressure rapidly propagated in all directions for a brief duration and gradually decreased. Figure 14 shows the overpressure-impulse diagram and damage thresholds for human by explosion [28]. The overpressures and impulses were recorded at the locations of the maximum overpressure point and ignition point to assess the hazards to humans resulting from the explosions for the cases of m = 0.225 and 0.73 kg/s. When an explosion occurs under the condition of a larger leaked mass flow rate, m = 0.73 kg/s, the impact of the explosion is not severe enough to cause significant injuries near the ignition source. However, humans can still be strongly affected by the maximum overpressure and impulse, potentially resulting in fatal outcomes. Furthermore, in the case of a smaller leaked mass flow rate, m = 0.225 kg/s, injuries can occur near the ignition source, and at the point of maximum overpressure, the damage can be severe enough to rupture the eardrum. As confirmed by the results, it is important to note that the damage caused by the explosion varies depending on the mass flow rate of the leaked liquid hydrogen. However, the magnitude and distribution of the explosion overpressure may vary depending on the location of the ignition source. In this study, the hydrogen vapor cloud was ignited 20 s after the liquid hydrogen began to leak, inducing the explosion. However, if the duration of the liquid hydrogen leakage is longer before ignition, resulting in a larger amount of leaked hydrogen, it is estimated that the overpressure caused by the explosion would increase further.