# Study on Fire Smoke Distribution Characteristics in Mountain Spiral Highway Tunnels
## 2 Materials and Methods
### Grid Size  
Previous research indicates that the accuracy of the simulation results is greatly affected by the size of the grid, and the mesh size is closely related to the fire characteristic diameter \(D^{\star}\). When the fire characteristic diameter \(D^{\star}\) is between 4 and 16 times the grid size, the simulation results can reflect the real situation more accurately [26]. Equation (6) is used to calculate \(D^{\star}\):  
\[D^{\star}=\left(\hat{Q}/\rho_{\infty}c_{p}T_{\infty}\sqrt{g}\right)^{\
icefrac{{ 2}}{{5}}}, \tag{6}\]  
where \(D^{\star}\) is the fire characteristic diameter, \(\hat{Q}\) is the HRR, \(\rho_{\infty}\) is the air density, \(c_{p}\) is the specific heat capacity of air, \(T_{\infty}\) is the ambient temperature, and \(g\) is the gravity acceleration. As shown in Equation (1), the fire characteristic diameter will increase when the ambient pressure decreases. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Details** \\ \hline Materials of sidewalls, floor, and ceiling & Concrete \\ Type of model portal & Open \\ Combustion model and its type & N-heptane fuel [30] and Simple Chemistry [31] \\ Yield of CO and soot & 0.01 g/g and 0.037 g/g \\ Height of fire source & 2.6 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Details of the model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & **Altitude, m** & **Ambient** & **Ambient** & **Air Density,** & **Radius of** & \\
**Pressure, kPa** & **Temperature, \({}^{\circ}\)C** & **kg/m\({}^{3}\)** & **Curvature, m** & **Slope Gradient, \%** \\ \hline
1–9 & 0 & 101.325 & 26.0 & 1.267 & 600, 800, 1000 & 20, 25, 30 \\
10–18 & 2000 & 79.501 & 22.2 & 1.007 & 600, 800, 1000 & 20, 25, 30 \\
19–27 & 3000 & 70.121 & 18.3 & 0.900 & 600, 800, 1000 & 20, 25, 30 \\
28–36 & 4000 & 61.66 & 16.8 & 0.795 & 600, 800, 1000 & 20, 25, 30 \\
37–45 & 5000 & 54.048 & 15.0 & 0.702 & 600, 800, 1000 & 20, 25, 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of all tests. The calculation results indicate that the suitable grid size for the 30 MW fire varies between 0.233 m and 0.94 m. Figure 2 shows the comparison of simulation results with grid sizes of 0.25 m, 0.3 m, 0.5 m, 0.6 m, and 0.9 m for the case of 0 m altitude; a radius of curvature of 800 m; and slope gradient of 15% at 300 s. It can be seen from Figure 2 that with the decrease in grid size, the discrepancy of temperature at different vertical heights with different grid sizes becomes negligible except for the grid size of 0.6 m and 0.9 m. At a height of 5 m, the temperature obtained from grid sizes of 0.25 m and 0.5 m is consistent, 437.4 \({}^{\circ}\)C. At this point, the results obtained from grid sizes of 0.3 m and 0.4 m are 421.0 \({}^{\circ}\)C and 398.8 \({}^{\circ}\)C, respectively. The calculated results have an error of 6.0% and 8.59% compared to the calculated result at grid size of 0.25 m. When the grid size is over 0.5 m, the mesh is not fine enough that the error would be more than 10%. Nevertheless, as the grid size is further diminished, the computational time required escalates exponentially. For this example used to determine the appropriate grid size, it takes 265 min to calculate for 300 s with a grid size of 0.5 m. However, with a grid size of 0.25 m, it takes 2268 min to calculate for 300 s on a computing device with 64 G of memory and an AMD Ryzen 9 7950X processor. This means that when the grid size is 0.25 m, the computing time for the model will be 8.55 times that of when the grid size is 0.5 m. This means that when the grid size is no greater than 0.5 m, further refining the grid size cannot significantly improve the simulation accuracy, and more simulation time is required. Following the requirements of the FDS for grid size, to ensure that the calculations in the encrypted area can be performed normally, the grid size in the non-refined area should be an integer multiple of the grid size in the refined area.