## 3 Prediction of the Pool Shape
### Fuel Discharge Experiment Considering Inclination Effects
#### 3.1.2 Experimental Results
The parameters defining the spill shape were tracked with respect to dimensionless time, calculated as the ratio of the time at which the parameters were measured \(t_{m}\) (i.e., the duration from the start of the discharge to the moment at which the parameter was measured) to the total discharge duration \(t_{d}\), which was 30 s for all experiments. To obtain the pool shape variation trend over time, the parameters were measured at nine time points with equal intervals. Figure 6 displays the pool length with respect to dimensionless time. In the left part of the figure, experimental measurements of the pool length for lower substrate inclination angles are shown, whereas the measurements for higher inclination angles is shown on the right side. The length was proportional to both the discharge rate and inclination angle, with the inclination angle exerting a stronger influence. Furthermore, the measured pool lengths increased almost linearly with respect to time for every experimental case. Figure 6 shows the breadth of the spilled pool as a function of dimensionless time. The breadth was proportional to the discharge rate while inversely proportional to the inclination angle. Moreover, the breadth increases rapidly at the start of the experiments, with the rate of change decreasing over time. A clear relationship between the inclination angle, discharge rate, and the measured pool breadth, as seen in Figure 6, was not found. Figure 6 presents the experimentally measured spilled pool area as a function of dimensionless time. The area increased almost linearly with time for each scenario. Moreover, the area was proportional to the inclination angle and discharge rate, with the discharge rate having a stronger effect. Figure 5: Pool shapes of spilled fuel after 30 s with the inclination angles of (**a**) \(1^{\circ}\), (**b**) \(5^{\circ}\), and (**c**) \(10^{\circ}\). Figure 7 illustrates the effects of the inclination angle and discharge rate on the pool shape using the experimental measurements at \(t_{m}/t_{d}=1.00\). Figure 7a,b show the influence of the substrate inclination angle and discharge rate on the pool length, respectively. Near-linear relationships between the pool length and both the inclination angle and discharge  
Figure 6: Experimentally measured pool dimensions: (**a**) length, (**b**) breadth, (**c**) area. rate was found. Furthermore, as already seen in Figure 6, the pool length was more affected by the inclination angle. Similarly, the pool breadth is plotted in Figure 7c,d. The breadth decreases with larger inclination angle and increases for higher discharge rates, except for the inclination angle of \(7^{\circ}\). It is thought that the condition of the surface affected the measurements. Furthermore, the experimental results were inconsistent with the findings of [PERSON] and [PERSON] [21], in that in this study, the pool breadth was dependent on the discharge rate and the inclination angle. This inconsistency is due to the fundamental difference in the experimental setups. [PERSON] and [PERSON] [21] investigated the spilled pool shape in narrow tunnels, where the spilled fuel was spilled until it reached drainage gutters at the roadside. In contrast, the present study considered large compartments which do not physically confine the spilled pool, and the pool breadth was measured as it spread. The difference in the pool breadth definition caused disagreement between the results. Figure 7e,f show the relationship between the pool area, inclination angle, and discharge rate. The pool area increased in a predictable manner until the \(4^{\circ}\)-inclined cases, with the cases under larger inclination angles displaying a lower increment in area. Furthermore, higher discharge rates resulted in larger pool areas, and with a few exceptions higher inclination angles resulted in larger areas, regardless of the discharge rate. The experimental measurements of each case are summarised in Table 5, with only one of the repetitions displayed.