## 2 Methodology
### Scenario Description  
In this study, explosion simulation scenarios were designed under the assumption of ammonia gas leakage followed by ignition inside the FPR. The interior was initially filled with 100% ammonia gas at ambient pressure and temperature (101,325 Pa; 288.15 K; equivalent to 15 \({}^{\circ}\)C). The flammable gas cloud was defined as a rectangular volume measuring 10 m \(\times\) 15 m \(\times\) 5 m, yielding an equivalent gas volume of 750 m\({}^{3}\) under stoichiometric conditions (ER = 1). This setting represents a conservative worst-case scenario commonly adopted in explosion risk assessments. All the computational domain boundaries (XLO, XHI, YLO, YHI, ZLO, and ZHI) were assigned as Euler-type open boundaries to allow for unrestricted gas expansion. The complete sets of initial and boundary conditions are summarized in Table 2.  
To investigate the effects of the ignition location, multiple simulation scenarios were constructed in which the ignition positions were varied. In most cases, the Z-coordinate was fixed at 0.1 m to reflect floor-level ignition conditions where key equipment and piping are commonly installed. The ignition time was uniformly set at 0.1 s across all scenarios, enabling consistent comparisons and simulations of near-immediate ignition following leakage. The spatial configurations for each ignition case are listed in Table 3. \begin{table}
\begin{tabular}{c c} \hline \hline  & **Boundary Condition** \\ \hline XLO & Euler \\ XLO & Euler \\ YLO & Euler \\ YHI & Euler \\ ZLO & Euler \\ ZHI & Euler \\ \hline \multicolumn{3}{c}{**Initial Condition**} \\ \hline Ambient pressure [Pa] & 101325 \\ Environment temperature [K] & 288.15 \\ Gas composition ratio & Ammonia 100\% \\ Gas cloud volume & Equivalent volume(ER = 1) \\ Shape of cloud volume & \(10\times 15\times 5\) cube \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Initial and boundary conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Case**} & **Ignition Position** & **Ignition Position** & **Ignition Position** \\  & **X Axis (m)** & **Y Axis (m)** & **Z Axis (m)** \\ \hline
1. & 0.1 & 5.5 & 0.1 \\
2. & 2.1 & 5.5 & 0.1 \\
3. & 4.1 & 5.5 & 0.1 \\
4. & 6.1 & 5.5 & 0.1 \\
5. & 8.1 & 5.5 & 0.1 \\
6. & 9.9 & 5.5 & 0.1 \\
7. & 5.1 & 5.5 & 0.1 \\
8. & 5.1 & 7.5 & 0.1 \\
9. & 5.1 & 8.5 & 0.1 \\
10. & 5.1 & 9.5 & 0.1 \\
11. & 5.1 & 11.5 & 0.1 \\
12. & 5.1 & 13.5 & 0.1 \\
13. & 5.1 & 14.9 & 0.1 \\
14. & 5.1 & 5.5 & 0.1 \\
15. & 5.1 & 5.5 & 1.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The coordination position of ignition points in FPR. This study employed the equivalent gas method to represent the gas cloud, which is a widely adopted approach in industrial explosion modelling. This simplified the simulation process by eliminating the need to explicitly model gas dispersion and ignition separately. Instead, a predefined equivalent volume under stoichiometric conditions was used to represent the realistic and flammable gas accumulation. This method enhanced the computational efficiency while preserving accuracy and scenario consistency [35]. Using this methodology, the explosion risks in an ammonia FPR were quantitatively evaluated based on the ignition location, with specific attention given to pressure distribution and structural impacts. The adopted approach supports a systematic hazard assessment across various ignition scenarios. One of the critical parameters in explosion simulations is the flammable gas volume. In this study, a stoichiometric equivalent gas volume of 750 m\({}^{3}\) was used, which corresponds to the amount of ammonia gas that would participate in complete combustion at an ER of 1. Typically, this equivalent volume is approximately half to one-third of the actual leaked volume, depending on the mixing conditions. This approach, which is widely adopted in industrial explosion analysis, enables the simulation to bypass separate dispersion modelling and instead assume an immediately ignitable cloud.