## 4 Fire Consequences of Pool Fires on Inclined Substrates
### Pool Fire Simulation Considering Substrate Inclination  
The pool shapes for the fire scenarios without and with inclination are tabulated in Table 6. The formula proposed by [PERSON] et al. (2018) was used to predict the pool radius of spilled fuel for the case without inclination, while the formulae proposed in this study were used for the inclined case. The conditions of the experimental case 3-3 in Table 3 (i.e., inclination angle and spill rate of \(3^{\circ}\) and \(400\) mL/min, respectively) were used for calculating the pool dimensions of the two scenarios. It was assumed that JP-5 was spilled on a steel surface and flowed in the positive x-direction with a uniform thickness across the surface area. As large compartments are known to have drain holes along the edges, the pool thickness was assumed to be uniform. Furthermore, the spillage was assumed to occur in a large compartment without any wind interference. Once the pool surface areas were estimated, the HRR and duration of the pool fires could be calculated. The HRR was calculated using Equation (4), as explained above. The material properties in Table 2 were substituted into the equation. The estimated HRR and fire duration values for the scenarios without and with inclination are presented in Table 7. The HRR estimated using the proposed empirical formula was 36.0% higher than the estimation obtained using the formula proposed by [PERSON] et al. (2018). The increase in HRR for pool fires on an inclined substrate was due to the larger pool area, which also resulted in a shorter fire duration, as the same amount of fuel was spilled for all of the scenarios. The mesh resolution for the computational model was determined using Equation (5). According to [PERSON] et al. (2014), the recommended mesh sizes for the fire scenarios without \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{3}{c}{**Without Inclination**} & \multicolumn{4}{c}{**With Inclination**} \\ \hline
**Radius (mm)** & **Area (mm\({}^{2}\))** & **Thickness (mm)** & **Length (mm)** & **Breadth (mm)** & **Area (mm\({}^{2}\))** & **Thickness (mm)** \\ \hline
258.6 & 210,096 & 0.9519 & 1552.5 & 312.3 & 277,260 & 0.7213 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Predicted pool dimensions for pool fires without and with inclination. Figure 10: Comparison of the experimental data and simulation results: (**a**) heat flux, (**b**) heat dose. and with substrate inclination are 0.036-0.143 m and 0.041-0.165 m, respectively. In this study, a mesh size of 0.03 m was used for both scenarios, which corresponds to the plume resolution indices of 19.1 and 22.0 for the scenarios without and with substrate inclination, respectively. The number of meshes was approximately 1,300,000. Figure 11 shows the model used in the pool fire analyses. The dimensions of the computational domain were determined such that the fire was not affected by the exterior boundaries, which were set to behave as passive openings to the outside. Moreover, no objects other than the floor were modelled. These settings ensured that only the effects of substrate inclination were observed. Figure 11b shows the pool and locations of the measuring devices. Because all objects inside the computational domain were forced to conform with the mesh in a rectilinear manner, the pool was modelled as shown in the figure. The fire analysis results are presented in Figures 12-14. The HRR of each pool fire with respect to time is shown in Figure 12. While the HRR for the pool fire with inclination was approximately 36% higher than that of the fire without inclination, it decreased more rapidly. The estimated HRR for each pool fire, shown in Table 7, is also marked in the figure. Excluding the stages where the HRR rises or falls, the HRR estimation was reasonably well reproduced by the simulations. Figure 11: Numerical model for pool fire analysis: (**a**) computational domain, (**b**) pool and locations of measuring devices.