## 4 Computational Fluid Dynamics Modeling
### FDS Performing
#### 4.4.2 Grid Sensitivity Analysis  
The mesh resolution that constitutes an acceptable compromise between the calculation time and the accuracy of the numerical simulation results for the investigation being undertaken was identified by performing a grid sensitivity analysis. In this respect, the optimal grid size for a given problem is achieved when the ratio between the characteristic fire diameter \(D^{*}\) [m] and the nominal size of a mesh cell \(\delta_{x}\) [m] is within the range of 4-16 [25], with \(D^{*}\) calculated as follows:  
\[D^{*}=\left(\frac{Q}{\rho_{\infty}c_{p}T_{\infty}\sqrt{g}}\right)^{\frac{2}{g}}, \tag{2}\]  
where \(Q\) is the HRR (i.e., 34,000 kW for the BEB and 30,000 kW for the ICEB), \(\rho_{\infty}\) is the density of air (i.e., 1.204 kg/m\({}^{3}\)), \(c_{p}\) is the specific heat of air (i.e., 1.005 J/(kgK)), \(T_{\infty}\) is the ambient temperature (i.e., 293 K), and \(g\) is the gravity acceleration (i.e., 9.81 m/s\({}^{2}\)). For the problem under consideration, \(D^{*}\) was found to be equal to 3.93 and 3.74 for the fire scenario involving the BEB and ICEB, respectively. This means that the optimal cell size should range from 0.25 m to 0.98 for the BEB fire and from 0.23 m to 0.93 m for the burning ICEB. It is also worth noting how the FDS code only allows for the use of parallelepiped cells, better if cubic. In light of this, by assuming cubic elements with sides of 0.25, 0.4, 0.5, or 0.8 m, Figure 4 shows the predictions of temperatures and HF concentrations, as a function of the cell size, at points \(A\), \(B\), and \(C\) after a time (\(t\)) of 15 min from the start of the BEB fire (i.e., HRR\({}_{\text{max}}\) of 34 MW and HF release rate of 3 g/s), considering the scenario of longitudinal mechanical ventilation. The points \(A\), \(B\), and \(C\) have the same distance \(z\) of 2 m (i.e., about the breathing height) from the road surface, while their distance \(x\) from the wall \(\gamma\) is 0.6 m (i.e., along the sidewalk \(\alpha\) centerline), 5 m (i.e., along the tunnel centerline), and 9.4 m (i.e., along the sidewalk \(\beta\) centerline), respectively. The positions of these three points, all of which refer to the cross-section located at 10 m downstream of the fire center, were selected to highlight the effects of grid size in a sufficiently large domain on the predicted temperatures and HF concentrations. It is to be stressed that given the transverse location of the pairs of jet fans (i.e., centrally beneath the tunnel ceiling, see Figure 1), the velocity of the air flow generated by the longitudinal mechanical ventilation system was found to be higher along the tunnel centerline (i.e., point \(B\)) than in the proximity of the tunnel walls (i.e., points \(A\) and \(C\)). Since the effects of longitudinal ventilation to push the combustion products (e.g., hot gases, toxic substances, and smoke) toward Portal \(B\) increase as its velocity increases,  
Figure 3: Comparison between the HF concentrations predicted by the FDS code and those provided by [PERSON] et al. [13] in the event of a BEV fire in an enclosed garage. the peak values of the temperatures and HF concentrations along the tunnel centerline are expected to be reached farther downstream of the fire than near the tunnel walls. This explains why the values of the temperatures and HF concentrations detected at point \(B\) are lower than at points \(A\) and \(C\). Figure 4 shows that using cubic cells with side sizes smaller than 0.4 m did not lead to substantial differences in the predictions of either temperatures or HF levels. In fact, the percentage differences between the results obtained using cubic elements having sides of 0.4 m rather than 0.25 m were found to be less than 5%. It is worth pointing out that a grid sensitivity analysis was also performed for the scenario involving the BEB fire in the naturally ventilated tunnel.