# Effects of the Ventilation System by Using Jet Fans during a Fire in Road Tunnels
## 2 Effects of the Ventilation System in a One-Way Road Tunnel during a Fire Using Analytical Methods  
The use of jet fans (Figure 2) in longitudinal ventilation of one-way tunnels enables the control of fumes upstream of the fire, keeping them contained to a small distance from it (back-layering distance), and allowing the escape and rescue of the tunnel occupants towards the upstream entrance. When the high temperatures of the fire engage fans downstream and render them inoperable, the ventilation system may experience a crisis. It would be possible to guarantee limited control of the fumes at least during the first evolutionary phase (fire growth) by restricting the operation of the fans to the upstream zone (possibly also downstream but at a certain distance from the fire). This would allow a slow propagation of the effects of the fire toward the upstream entrance. Figure 2: Example of a pair of jet fans anchored to the tunnel roof, used in the longitudinal ventilation of a one-way road tunnel, with airflow in the same direction as the vehicular flow. Back-layering phenomenon happens when the air velocity is lower than the critical velocity (\(v_{c}\)) [17; 18; 19; 20]. Typically, critical velocities are estimated in the range of 2.5-3.0 m/s [17; 18; 19; 21]. According to NFPA 502-Annex D [10], \(v_{c}\) can be evaluated by the following equations:  
\[v_{c}=K_{Fr}\cdot K_{g}\cdot\sqrt[3]{\frac{g\cdot H\cdot HRR}{\rho\cdot C_{p} \cdot A\cdot T_{f}}} \tag{4}\]  
where:  
\(K_{Fr}\) is the Froude number factor, which can be expressed as a function of \(HRR\) in kW by the following expression:  
\(K_{Fr}\cong 3.7136\cdot HRR^{-0.157}\) when \(HRR\) is between 10,000 and 100,000 kW  
\(K_{Fr}=0.870\) when \(HRR\leq 10\),000 kW; \(K_{Fr}=0.606\) when \(HRR\geq 100\),000 kW;  
\(K_{g}\) is the grade factor (1 for horizontal tunnels);  
\(g\) is the gravity acceleration (9.81 m/s\({}^{2}\));  
\(H\) is the tunnel height (m);  
\(\rho\) is the air-specific mass upstream of the fire (kg/m\({}^{3}\)), depending on the temperature and atmospheric pressure (1225 kg/m\({}^{3}\) in standard conditions);  
\(C_{p}\) is the air average specific heat (kJ/(kg\cdot K)); generally, is adopted 1.009 kJ/(kg\(\cdot K\)) for standard conditions;  
\(A\) is the tunnel cross section (m\({}^{2}\));  
\(T_{f}\) is the average temperature of the fire gas (K), defined by the following equation:  
\[T_{f}=\frac{HRR}{\rho\cdot C_{p}\cdot A\cdot v}+T \tag{5}\]  
\(T\) and \(v\) are the air temperature and velocity upstream of the fire, respectively. The critical speed \(v_{c}\) is obtained putting \(v=v_{c}\) in Equation (5) and then adopting an iterative process using Equations (4) and (5) until finding the convergence of the values of \(v_{c}\) and \(T_{f}\), starting from nil initial values for both [10]. [PERSON] and [PERSON] [21] proposed another interesting equation for \(v_{c}\), subsequently modified by [PERSON] et al. [20], based on laboratory and in situ experiments, as follows:  
\[v_{c}=0.81\cdot\sqrt[3]{\frac{g\cdot HRR}{\rho\cdot C_{p}\cdot T\cdot H}}\text { if }HRR\leq 0.15\cdot\rho\cdot C_{p}\cdot T\cdot\sqrt{g\cdot H^{5}} \tag{6}\]  
\[v_{c}=0.43\cdot\sqrt{g\cdot H}\text{ if }HRR>0.15\cdot\rho\cdot C_{p}\cdot T \cdot\sqrt{g\cdot H^{5}} \tag{7}\]  
If the air velocity is lower than the critical one (\(v<v_{c}\)), it is possible to determine the distance \(L_{b}\) from the fire reached by the fumes in the upstream section of the tunnel (Figure 3) [18; 22]:  
\[L_{bl}\cong k\cdot\sqrt[3]{\frac{g\cdot H^{2}\cdot HRR}{\rho\cdot C_{p}\cdot T \cdot v^{3}}} \tag{8}\]  
where:  
\(k\) is a dimensionless constant experimentally evaluated between 0.6 and 2.2 [17; 23; 24; 25];  
The other quantities expressed in congruent units. [PERSON] et al.