*2.1. Longitudinal Ventilation Critical Velocity*

If a fire occurred in a tunnel under longitudinal ventilation, the critical velocity is defined as the minimum longitudinal airflow velocity, which can limit smoke flow to one side of the fire source. Li et al. [8] carried out a model experiment of tunnel fire to investigate the movement and control of smoke, based on previous research [24]. A set of modified formulas for critical longitudinal velocity can be expressed as:

$$V\_{\mathbb{C}} = V\_{\mathbb{C}}^{\*} \sqrt{\mathbb{g}H} \tag{1}$$

$$V\_c^\* = \begin{cases} 0.81 Q^{\*1/3} & \text{ $Q^\*$ } \le 0.15\\ 0.43 & \text{ $\!/\!Q^\*$ } > 0.15 \end{cases} \tag{2}$$

$$Q^\* = \frac{Q}{\rho\_0 c\_p T\_0 g^{1/2} H^{5/2}}\tag{3}$$

where *V<sup>c</sup>* is critical velocity, (m/s); *V* ∗ *c* is dimensionless critical velocity; *Q* is heat release rate, (kW); *Q*∗ is dimensionless heat release rate; *g* is gravitational acceleration, (m/s<sup>2</sup> ); *H* is tunnel height, (m); *ρ*<sup>0</sup> is ambient density, (kg/m<sup>3</sup> ); *c<sup>p</sup>* is thermal capacity of air, (kJ/kg K); *T*<sup>0</sup> is ambient temperature, (K).
