## 4 Conclusions  
Hydrogen leakage diffusion under various ship motion conditions was simulated numerically in our study using the CFD code FLUENT for the enclosed area. Furthermore,  
\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
15 s period Pitching to bow up & 68 s & 49 s & 23 s & 49 s & 60 s \\  & (+13\%) & (\(-\)8\%) & (\(-\)43\%) & (\(-\)8\%) & (\(-\)52\%) \\ \hline
60 s period Pitching to bow up & 45 s & 30 s & 15 s & 30 s & 60 s \\  & (\(-\)23\%) & (\(-\)43\%) & (\(-\)63\%) & (\(-\)43\%) & (\(-\)52\%) \\ \hline
120 s period Pitching to bow up & 60 s & 60 s & 40 s & 60 s & 60 s \\  & (0\%) & (+13\%) & (0\%) & (+13\%) & (\(-\)52\%) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Time for hydrogen to reach each sensor according to ship motion periods.  
Figure 14: Hydrogen concentration by roll and pitch motion at S6.  
Figure 15: Hydrogen concentration by pitch motion at S4: (a) 15 s period; (b) 60 s period; (c) 120 s period.  
we analyzed the hydrogen concentration distribution within the enclosed area and drew the following conclusions:  
1. When the hydrogen leakage is located in the lateral direction, it reaches the sensors approximately 63% (15 s) faster during pitch (lateral) motion than in the steady state. On the other hand, in the case of longitudinal motion, it reaches the sensor approximately 50% (30 s) faster. When the direction of rotation is the same based on the hydrogen leak's location, the effect on the hydrogen concentration distribution and diffusion is significant;
2. We confirmed that the difference in time required by hydrogen to reach the sensor depends on the direction of motion and location of the hydrogen leak. When moving in the same direction as the hydrogen leakage, it reaches the sensor 52% (64 s) faster than in the steady state due to updraft formation; however, in the opposite case, the time required to reach the sensor compared to the steady state increases by 50% (20 s);
3. By comparing the results of hydrogen concentration, we confirmed that the difference in time elapsed to reach the sensor, dependent on the motion period of the vessel, is smaller compared to the steady-state; the longer the cycle, the weaker the effect of the cycle period on hydrogen diffusion.  
In summary, motion conditions must be considered to understand the leakage and diffusion characteristics of the hydrogen vessel and install a hydrogen sensor because hydrogen's diffusion behavior varies according to the vessel's motion characteristics. However, it is also necessary to evaluate the effects of hydrogen concentration diffusion by applying scenarios that combine the roll and pitch motions of a ship and various periods and amplitudes. These considerations can help overcome limitations in the future, such as analysis targets, leakage, and ship motion conditions.  
Conceptualization, B.K. and K.-I.H.; methodology, B.K.; software, B.K.; validation B.K.; formal analysis, B.K. and K.-I.H.; investigation, B.K.; data curation, B.K.; writing--original draft preparation, B.K.; writing--review and editing, B.K.; visualization, B.K.; supervision, K.-I.H.; project administration, K.-I.H.; funding acquisition, K.-I.H. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the \"Development of guidance for prevent of leak and mitigation of consequence in hydrogen ships\", funded by the Ministry of Oceans and Fisheries, Korea; and the BK21 Four program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education of Korea (Center for Creative Leaders in Maritime Convergence).  
The authors declare no conflict of interest.