## 3 Effect of Ship Motion on Hydrogen Dispersion
### Effect of Ship Motion Types  
A numerical analysis was performed by applying roll and pitch motions to the enclosed area; our results revealed the effects of vessel motion type on hydrogen diffusion behavior. Table 4 compares the effects of ship motion type on the hydrogen response time for each sensor S2-S6. The percentages, shown below the time, represent differences in the hydrogen sensor's response time in the motion compared to the steady state. Compared to the steady state, hydrogen reaches the sensor faster to S4 by approximately 63% (25 s) in pitch motion and S2 by approximately 50% (30 s) in roll motion.  
Figures 9 and 10 illustrate the hydrogen concentration values of sensors S4 and S6 located at the center of the ceiling's leak space for roll and pitch motions with a period of 60 s; they move clockwise on each positive axis. Compared to the roll and pitch motions of S4 and S6 in the steady state, hydrogen reaches the sensor faster by 10 s, 25 s, 34 s, and 64 s, respectively. These results indicate that ship motion type significantly affects hydrogen diffusion.  
Compared to the roll motion in Figure 9, the hydrogen concentration increases according to the 60-s cycle after 255 s of hydrogen leakage in the pitch motion. This trend can be explained as follows: After leaking from the hydrogen leak hole at the center of the bow's side, the hydrogen rises to the ceiling due to the buoyancy attributed to the density difference and forms a ceiling jet flow in the longitudinal direction of the leak space.  
Furthermore, it moves between the bow and stern under the effects of pitch motion, which is a longitudinal motion centered on S4; the concentration repeatedly rises and falls according to the cycle. In the case of roll motion, moving between the starboard and port compared with pitch motion, the change in position based on S4 is half, and the concentration diffusion speed is fast; therefore, the effect on the concentration value compared with pitch motion is relatively minor. This phenomenon is confirmed in Figure 10, which shows the hydrogen concentration near sensor S6. For roll motion, the hydrogen concentration rises repeatedly and falls in two cycles (30 s) during one pitch motion cycle (60 s). The hydrogen concentration ranges from 0.0634% at 75 s to 0.0374% at 120 s to 41%  
\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{2}{*}{60 s period Pitching to bow up} & 45 s & 30 s & 15 s & 30 s & 60 s \\  & (\(-\)23\%) & (\(-\)43\%) & (\(-\)63\%) & (\(-\)43\%) & (\(-\)52\%) \\ \hline \multirow{2}{*}{60 s period Rolling to port up} & 30 s & 45 s & 30 s & 45 s & 90 s \\  & (\(-\)50\%) & (\(-\)15\%) & (\(-\)25\%) & (\(-\)15\%) & (\(-\)27\%) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Time for hydrogen to reach each sensor according to the ship motion types.  
Figure 8: Plane view and ship motion period graph: (**a**) Pitching to bow down; (**b**) Rolling to port down; (**c**) Counterclockwise.  
after hydrogen leakage in the roll motion, and from 0.0664% at 90 s to 0.0318% at 135 s in the pitch motion with a drop rate of 52%. A downward trend was observed; this tendency is attributed to the rotational force generated in the opposite direction of the leakage before the leaked hydrogen diffuses to the ceiling and forms a concentration layer. The latter occurs because hydrogen moves in the port direction in the case of roll motion.