## 3 Prediction of the Pool Shape
### Fuel Discharge Experiment Considering Inclination Effects
#### 3.1.1 Experimental Setup  
Figure 3 illustrates the experimental setup. The experiment was conducted indoors where the discharged fuel was not affected by wind conditions. A mild steel (SS400) plate with a length and breadth of 6.0 m and 0.8 m, respectively, was selected as the substrate. One end of the plate was attached to a 30-ton overhead crane, so that the inclination angle of the plate could be adjusted through the control of the crane height. A digital inclinometer was used to measure the inclination angle. The angle of the steel plate needed to be setof combustion is the heat released when a unit quantity is oxidised completely, and the mass burning rate represents the mass loss rate caused by fuel combustion. k\(\beta\) is an empirical constant. As the fuel spill rate considerably affects the spreading behaviour, several discharge rates were examined, and every experimental scenario was conducted twice to account for reproducibility of the experiment.  
The pump was calibrated prior to the experiment to discharge the fuel at the intended rates. The outlet of the pipe connected to the pump was positioned near one of the shorter edges of the plate. This configuration allowed the discharged fuel to flow parallel to the longer edge of the inclined substrate. The discharge duration was 30 s, and after each experiment the steel plate was cleaned using oil-absorbent wool and compressed air. To ensure that no fuel remained on the plate, a 10 min break was observed between experiments. The spill shape was recorded using a camera positioned atop the steel plate.  
Table 3 summarises the experimental conditions. Temperature and humidity measurements are tabulated for each scenario. Twenty-one scenarios with different inclination angles (1-10\({}^{\circ}\)) and discharge rates (200-400 mL/min) were examined. The inclination angles were determined to emulate certain sea state conditions under which the target structure is subjected. Table 4[31] provides roll angles for conventional surface ships with varying beams under different sea state conditions. In this study, the sea states up to sea state four were considered. The examined fuel discharge rates of 200-400 mL/min were determined based on the breadth of the steel plate, as for larger discharge rates, the pool tended to reach the long edges of the plate.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **Value** & **Unit** \\ \hline Density & 810 & kg/m\({}^{3}\) \\ \hline Dynamic viscosity & 2.28 & cSt (mm\({}^{2}\)/s) \\ \hline Surface tension & 0.025 & N/m \\ \hline Contact angle & 30 & \({}^{\circ}\) \\ \hline Heat of combustion & 43.0 & MJ/kg \\ \hline Mass burning rate & 0.54 & kg/m\({}^{2}\)s \\ \hline \(k\beta\) & 1.6 & m\({}^{-1}\) \\ \hline \hline \end{tabular} Note: 1.0 \(\cSt\) = 0.01 St = 1 mm\({}^{2}\)/s.  
\end{table}
Table 2: Material properties of JP-5.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Exp. No.** & \begin{tabular}{c} **Inclination** \\ **Angle (\({}^{\circ}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Discharge Rate** \\ **(mL/min)** \\ \end{tabular} &
\begin{tabular}{c} **Temperature** \\ **(\({}^{\circ}\)C)** \\ \end{tabular} & **Humidity (\%)** \\ \hline
1-1 & & 200 & 11.2 & 53 \\ \hline
1-2 & 1 & 300 & 11.2 & 51 \\ \hline
1-3 & & 400 & 11.2 & 51 \\ \hline
2-1 & & 200 & 11.1 & 49 \\ \hline
2-2 & 2 & 300 & 11.0 & 48 \\ \hline
2-3 & & 400 & 11.0 & 48 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary of the experimental conditions.