2.2.3. Grid Independence Verification and Model Validation Grid Independence Verification

Grid independence verification was performed to evaluate the dependency of fire simulation results pertaining to the size and number of grids. Appropriate grid size can be accessed by the dimensionless expression *D*∗/*δ<sup>x</sup>* [22], where *δ<sup>x</sup>* is the grid size (m), and *D*∗ is the characteristic diameter of the fire source (m), as shown in Equation (1). For accurate simulation results to be obtained, it is recommended that *D*∗/*δ<sup>x</sup>* be between 4 and 16.

$$D^\* = (\frac{\stackrel{\bullet}{Q}}{\rho\_{\infty}c\_p T\_{\infty}\sqrt{g}})^{\frac{\frac{2}{3}}{2}} \tag{1}$$

Here, • *Q* is the peak heat release rate of fire (kW); *ρ*<sup>∞</sup> is the ambient air density (kg/m<sup>3</sup> ); *c<sup>p</sup>* is the ambient air specific heat (kJ/(kg·K)); *T*<sup>∞</sup> is the ambient air temperature (K); and *g* is the gravity acceleration (m/s<sup>2</sup> ).

*D*∗ of the 50 MW fire was calculated to be 4.6 m, so the grid size should be between 0.3 m and 1.1 m. The results of independent verification for different grid sizes are compared in Table 8. The absolute percentage errors (APE) of temperature values on both sides of the fire source were calculated, with the temperature detection points set at positions of 7.5 m height from the road and along the central axis in the Y direction. The APE was less than 1.8% between the 0.4 m grid and the 0.3 m grid. There was no significant difference in temperature distributions if the grid size was less than 0.4 m, so it was acceptable to use a 0.4 m grid size for the model of the tunnel fire in Section 3.1. In addition, it could be found that a more accurate description of the fire plume can be obtained by using a smaller grid size near the fire source, such as 0.2 m, and a significantly increased computation time. Considering that its effect on the smoke parameters in the entire tunnel is very small, for the purpose of this work, did not use dense grids near the fire source.


**Table 8.** Independent verification of grid size.
