## 3 Effect of Ship Motion on Hydrogen Dispersion
### Effect of Ship Motion Directions  
The numerical analysis was performed by applying roll and pitch motions, which move clockwise and counterclockwise on each axis, to the enclosed area for understanding the effect of the ship's motion direction on hydrogen diffusion behavior. The hydrogen response time for each sensor, S2-S6, is listed in Table 5 to compare the effects of motion direction. Compared to the steady state, hydrogen reaches the S6 sensor faster by approximately 52% (64 s) during pitch motion and 30% (37 s) during roll motion. Figure 11 shows the central longitudinal cross-section of hydrogen concentration distribution contour based on the time required to reach sensor S6. As shown in Figures 11 and 12, the distribution of hydrogen differs according to the direction of roll and pitch motion.  
Figure 10: Hydrogen concentration by roll or pitch motion at S6.  
Figure 9: Hydrogen concentration by roll or pitch motion at S4.  
For pitch motion with a period of 15 s, simulations were performed by dividing motions into clockwise and counterclockwise directions. S2 was close to the leak hole, and sensor S6 was located near the ceiling opening of the enclosed area. Hydrogen concentration values are illustrated in Figures 13 and 14. The leakage port in the center of the stern is located higher than the existing position when moving in the same direction as the hydrogen leakage direction (clockwise). The hydrogen leakage attributed to the updraft reaches the ceiling faster. When S6 was located near the opening, the sensor detected the hydrogen concentration at 75 s for pitching to bow; however, in the opposite case, it was detected at 120 s, and a verifiable difference of approximately 45 s occurred. For S2 located near the hydrogen leak hole, the hydrogen concentration was detected at 64 s when moving in the same direction (clockwise) as the hydrogen leak direction; however, in the opposite case, it was detected at 8 s. For the roll motion shown in Figures 13 and 14, lateral motion is less affected by the hydrogen leak hole located in the longitudinal direction than pitch motion, and the lateral motion is less affected by the hydrogen leak hole located in the longitudinal direction than pitch motion.  
Figure 11: Central longitudinal cross-section of hydrogen distribution: (**a**) Steady state; (**b**) Pitching to bow up; (**c**) Pitching to bow down.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **S2** & **S3** & **S4** & **S5** & **S6** \\ \hline Steady state & 60 s & 53 s & 40 s & 53 s & 124 s \\ \hline \multirow{4}{*}{Pitch motion 15 s period} & \multirow{2}{*}{Bow up} & 68 s & 49 s & 23 s & 49 s & 60 s \\  & & (+13\%) & (\(-\)8\%) & (\(-\)43\%) & (\(-\)8\%) & (\(-\)52\%) \\ \cline{3-6}  & & 53 s & 79 s & 60 s & 79 s & 101 s \\  & & (\(-\)12\%) & (+49\%) & (+50\%) & (+49\%) & (\(-\)19\%) \\ \hline \multirow{4}{*}{Roll motion 15 s period} & \multirow{2}{*}{Port up} & 45 s & 41 s & 65 s & 64 s & 87 s \\  & & (\(-\)25\%) & (\(-\)23\%) & (+63\%) & (+21\%) & (\(-\)30\%) \\ \cline{3-6}  & & 45 s & 64 s & 65 s & 41 s & 87 s \\ \cline{1-1}  & & (\(-\)25\%) & (+21\%) & (+63\%) & (\(-\)23\%) & (\(-\)30\%) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Time for hydrogen to reach each sensor according to the ship motion directions.  
and there is no difference in time to reach the sensor; however, the motion cycle remains affected. According to the 15-s cycle, the concentration repeatedly rises and falls, and the overall hydrogen concentration increases. These results suggest that the ship's motion characteristics must be considered in selecting the sensor location because the detection time for each sensor location varies depending on the location of the hydrogen leakage and the direction of motion.  
Figure 12: Central transversal cross-section of the hydrogen distribution: (**a**) Steady state; (**b**) Rolling to port up; (**c**) Rolling to port down.  
Figure 13: Hydrogen concentration by roll and pitch motion at S2.