## 3 Prediction of the Pool Shape
### Fuel Discharge Experiment Considering Inclination Effects
#### 3.1.2 Experimental Results  
To correctly assess the fire-affected area in large compartments under motion, defining the spreading extent of the spilled fuel is vital. The spreading extent can be quantitatively \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sea State** & **Roll Angle (\({}^{\circ}\))** & **Ship Beam (m)** & **Wave Height (m)** & **Characteristics** \\ \hline \multirow{4}{*}{0–3} & \multirow{2}{*}{Less than 5} & Less than 15 & \multirow{4}{*}{0.00–1.25} & \multirow{4}{*}{0.00–1.25} & Calm \\  & & 15–23 & & (glassy)–slight \\  & & 23–32 & & \\  & & Greater than 32 & & \\ \hline \multirow{4}{*}{4} & 7 & Less than 15 & \multirow{4}{*}{1.25–2.5} & \multirow{4}{*}{ Moderate} \\  & 6 & 15–23 & & \\  & 6 & 23–32 & & \\  & 5 & Greater than 32 & & \\ \hline \multirow{4}{*}{5} & 12 & Less than 15 & \multirow{4}{*}{2.5–4.0} & Rough \\  & 10 & 23–32 & & \\  & 9 & Greater than 32 & & \\ \hline \multirow{4}{*}{6} & 19 & Less than 15 & \multirow{4}{*}{4.0–6.0} & \multirow{4}{*}{Very rough} \\  & 16 & 15–23 & & \\  & 15 & 23–32 & & \\  & 13 & Greater than 32 & & \\ \hline \multirow{4}{*}{7} & 28 & Less than 15 & \multirow{4}{*}{6.0–9.0} & \multirow{4}{*}{High} \\  & 24 & 15–23 & & \\ \cline{1-1}  & 22 & 23–32 & & \\ \cline{1-1}  & 20 & Greater than 32 & & \\ \hline \multirow{4}{*}{8} & 42 & Less than 15 & \multirow{4}{*}{9.0–14.0} & \multirow{4}{*}{Very high} \\  & 37 & 15–23 & & \\ \cline{1-1}  & 34 & 23–32 & & \\ \cline{1-1}  & 31 & Greater than 32 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Roll motion for conventional surface ships. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Exp. No. ** & **Inclination Angle (\({}^{\circ}\))** & **Discharge Rate (mL/min)** & **Temperature (\({}^{\circ}\)C)** & **Humidity (\%)** \\ \hline
3-1 & & 200 & 11.0 & 48 \\ \hline
3-2 & 3 & 300 & 11.0 & 47 \\ \hline
3-3 & & 400 & 10.8 & 47 \\ \hline
4-1 & & 200 & 12.0 & 60 \\ \hline
4-2 & 4 & 300 & 12.0 & 59 \\ \hline
4-3 & & 400 & 12.1 & 59 \\ \hline
5-1 & & 200 & 11.5 & 60 \\ \hline
5-2 & 5 & 300 & 11.8 & 60 \\ \hline
5 represented in terms of the distance, direction, and area of the spilled pool. The pool length and breadth determine the direction and distance in which the spilled pool spreads. The pool length was defined as the spreading distance of the pool along the inclination direction of the substrate, while the breadth is defined as the maximum distance perpendicular to the pool length. The area represents the surface area of the spilled pool, which affects the HRR of pool fires. The pool shape definitions above have been widely adopted in the literature [21,22]. Figure 4a shows the pool shape with an inclination angle of 3\({}^{\circ}\) and discharge rate of 300 mL/min. The discharged fuel flowed from the left to the right of the figure due to the inclination of the steel plate. The pool dimensions are not easily discernible in the original form and thus were processed as shown in Figure 4b. Figure 5 shows the outlines of the experimentally measured pools 30 s after the start of fuel discharge for each experiment. The pool spread from left to right, with the fuel discharge point as the origin. Figure 5a displays the outline of the spilled pool on a 1\({}^{\circ}\)-inclined substrate. Higher discharge rates resulted in a larger pool length, breadth, and area. The maximum pool length and breadth were 691.7 mm and 351.4 mm, respectively. Figure 5b shows the pool shapes on the 5\({}^{\circ}\)-inclined substrate. For each discharge rate, the pool lengths were longer and the breadths shorter than those of the 1\({}^{\circ}\) inclination case (see Figure 5a). Figure 5c shows the pool outlines for the 10\({}^{\circ}\)-inclined substrate. Similarly, higher discharge rates resulted in larger pools in terms of length, breadth, and area. Furthermore, longer pool lengths and shorter breadths were measured compared with the cases with lower inclination angles. Figure 4: Experimental result: (**a**) recorded pool shape, (**b**) processed pool shape.