## 3 Numerical Details  
Fire Dynamics Simulator (FDS) [32] version 6.7.0 was used for the numerical analysis of fire phenomena under experimental conditions. To minimize the error caused by boundary conditions in the numerical analysis results, including the compartment (0.6 m \(\times\) 0.9 m \(\times\) 0.6 m), the expanded calculation area had a size of 0.6 m \(\times\) 1.8 m \(\times\) 1.2 m. The physical properties of the inner walls were input with reference to the specific heat (1.088 kJ/kg\(\cdot\)K), thermal conductivity (0.058-0.17 W/m\(\cdot\)K), and density (128 kg/m\({}^{3}\)) of the insulating material used in the experiments. FDS directly analyzes the governing equations for large eddies, which are responsible for most of the energy and turbulent transport in a fire environment, and for sub-grid scale eddies, large eddy simulation (LES), which applies a model, was adopted. Therefore, the accuracy of numerical analysis using FDS is closely related to the grid size (8x). This is why it is critical to select an appropriate grid size when using FDS, and grid sensitivity analysis is performed for this. When selecting the grid size for an experimental set comprising many conditions, it is effective to perform grid sensitivity analysis on the smallest-scale experiment (HRR). The smallest-scale experiment in this study is the condition \(\phi_{\text{g}}\) = 0.2. Hence, a grid sensitivity analysis was conducted under the conditions of DW05 and \(\phi_{\text{g}}\) = 0.2. When configuring the grid system for the grid sensitivity analysis, the characteristic fire length (D\({}^{*}\)) concept [33] can be considered. The characteristic fire length is a dimensionless number that indicates the size of a fire source and is defined as in Equation (3):  
\[\text{D}^{*}=\left(\frac{\dot{\text{Q}}_{\text{max}}}{\rho_{\text{os}}\text{ C}_{\text{P}}\text{T}_{\text{os}}\sqrt{\text{g}}}\right)^{\frac{2}{3}} \tag{3}\]  
where \(\dot{\text{Q}}_{\text{max}}\) is the maximum HRR of the fire source. \(\rho_{\text{os}}\), C\({}_{\text{P}}\), T\({}_{\text{os}}\), and g indicate the density (1.2 kg/m\({}^{3}\)), specific heat (1 kJ/kg\(\cdot\)K), and temperature (293.15 K) of the surrounding air and gravitational acceleration (9.81 m/s\({}^{2}\)), respectively. Under room temperature 20\({}^{\circ}\)C and atmospheric pressure 1 atm, D\({}^{*}\) of the condition \(\phi_{\text{g}}\) = 0.2 according to Equation (1) is 0.12 m. According to previous studies [34; 35], adequate predictive performance can be expected when D\({}^{*}\)/\(\delta\)x is 4 to 20. This study considered coarse (\(\delta\)x = 0.02 m), moderate (\(\delta\)x = 0.015 m), and fine (\(\delta\)x = 0.01 m) conditions for the grid sensitivity analysis. D\({}^{*}\)/\(\delta\)x of each grid system is 6, 8, and 12, and the total cell number is 162,000, 384,000, and 1,296,000. 1 The grid sensitivity analysis using these grid systems was conducted for the ULT and chemical species concentrations (O\({}_{2}\), CO\({}_{2}\)). Figure 4 shows the grid sensitivity analysis results. In Figure 4a, in the process of increasing the temperature, the temperature measured in the experiment rises more slowly  
\begin{table}
\begin{tabular}{c c c} \hline
**Global Equivalence Ratio ( \(\phi_{\text{g}}\))** & **Fuel Flow Rate (L/min)** & **Ideal HRR (kW)** \\ \hline
0.20 & 3.9 & 5.5 \\
0.40 & 7.9 & 11.0 \\
0.60 & 11.8 & 16.6 \\
0.70 & 13.8 & 19.3 \\
0.80 & 15.8 & 22.1 \\
0.85 & 16.8 & 23.5 \\
0.90 & 17.8 & 24.8 \\
0.95 & 18.8 & 26.2 \\
1.00 & 19.7 & 27.6 \\
1.10 & 21.7 & 30.  
than the predicted temperature; this difference is attributed to the shape, diameter, and direction of the beads. However, the predicted and measured temperatures in the steady state, the focus of this study, exhibited similar trends. The temperatures predicted according to grid size showed the same values over all sections, indicating that the grid sensitivity to temperature was not large. In contrast, in Figure 4b, the decrease in O2 was overestimated for the coarse condition, unlike moderate and fine.