*4.3. Ventilation Network Verification*

In tunnel ventilation systems, network calculation can capture overall mean flow parameters, such as velocity and pressure, with a one-dimensional flow regime [29]. Two typical concepts, node and branch, will be discussed. Both tunnels and cross passages are characterized as branches, while the intersection point of branches are described as nodes. Figure 5 shows typical tunnels with a three cross passage ventilation network, which includes a main loop, ten nodes and fourteen branches.

The ventilation airflow at the *m*th node in tunnels follows the mass balance Equation (9), and the pressure balance equation for the *n*th branch can be represented as Equation (10). The on-way resistance and local resistance will meet Equations (4) and (5), respectively. In addition, fire exists as resistance in branch and its wind pressure is set at 5 Pa [25].

$$
\sum M\_m = 0\tag{9}
$$

$$
\sum p\_n = 0 \tag{10}
$$

**Figure 4***.* Velocities in both accident tunnel and service tunnel: The velocity at both ends of service tunnel is (**a**) 0.70 m/s; (**b**) 0.75 m/s; (**c**) 0.80 m/s; (**d**) 1.00 m/s; (**e**) 1.30 m/s. **Figure 4.** Velocities in both accident tunnel and service tunnel: The velocity at both ends of service tunnel is (**a**) 0.70 m/s; (**b**) 0.75 m/s; (**c**) 0.80 m/s; (**d**) 1.00 m/s; (**e**) 1.30 m/s. pressurize ventilation through three open cross passages, in order to limit smoke movement in the case of a 20 MW fire in the main tunnel. 

tion (9), and the pressure balance equation for the branch can be represented as Equation (10). The on-way resistance and local resistance will meet Equations (4) and (5), re-**Figure 5.** Calculation result of ventilation network. **Figure 5.** Calculation result of ventilation network.

Pa [25].

spectively. In addition, fire exists as resistance in branch and its wind pressure is set at 5 *M=0*(9) **5. Conclusions** In this paper, a ventilation mode with service tunnel and cross passages for auxiliary air supply and smoke control was studied using FDS simulation. The study proposed a Figure 5 represents the calculation results and data of the ventilation network. At both ends of the accident tunnel, ventilation pressure of 210 Pa is applied in the same direction, and ventilation pressure of 135 Pa with opposite direction is set in the service

ventilation and smoke exhaust scheme, and solved the problem of longitudinal ventilation

applied in the accident tunnel, and the airflow speed of 1.3 m/s will be supplied at both ends of the service tunnel, together with three cross passages open to provide airflow,

(2) A ventilation network model is established according to the design parameters of extra-long tunnels. The calculation results show that the longitudinal wind speed at the fire source reaches 4.5 m/s, exceeding the critical velocity for smoke control of 3.5 m/s, which is in accordance with the numerical simulation results. In theory, cross passage

It should be noted that the distance between cross passages, and the angle between cross passages with main tunnel, will influence ventilation efficiency. Therefore, further experiments and simulations are needed, and parameters should be extended in order to investigate the optimum ventilation scheme. In this paper, design parameters are closely related to the tunnel structure, which are not necessarily applicable to other projects. With regards to ventilation design, the methods and ideas highlighted in this paper are significant; perhaps other tunnels need similar structural models and calculation conditions.

**Author Contributions:** Conceptualization, W.Y. and J.K.; methodology, W.Y.; software, J.K.; validation, W.Y. and J.K.; formal analysis, W.Y.; investigation, W.Y.; resources, W.Y.; data curation, W.Y.; writing—original draft preparation, J.K.; writing—review and editing, J.K.; visualization, W.Y.; supervision, W.Y.; project administration, J.K.; funding acquisition, J.K. All authors have read

**Funding:** This research was funded by Philosophy and Social Science Planning of Zhejiang, grant number 20NDJC199YB; National Natural Science Foundation of Zhejiang, grant number

which can effectively control the fire smoke and improve the human evacuation.

(10)

*n*

*m*

*<sup>n</sup> p = 0*

pressurized air supply technology is proved feasible.

and agreed to the published version of the manuscript.

**Institutional Review Board Statement:** Not applicable.

GF22F030254.

tunnel. The ventilation volume of the CP.1, CP.2 and CP.3 are 29.9 m<sup>3</sup> , 36.9 m<sup>3</sup> and 45.5 m<sup>3</sup> , respectively; the average airflow velocity are 2.5 m/s, 3.1 m/s and 4.8 m/s. The fire source is located in the 10th branch, with ventilation velocity of 4.5 m/s, exceeding the longitudinal critical velocity of 3.5 m/s. The calculation results of the ventilation network agree with the numerical simulation. Therefore, it is feasible to use the service tunnel to pressurize ventilation through three open cross passages, in order to limit smoke movement in the case of a 20 MW fire in the main tunnel.
