# Study on Mechanism of Series-Flow of Pollutants between Consecutive Tunnels by Numerical Simulation
## 3 Results and Discussions
### Validation  
Two consecutive tunnels were selected for field measurement of series-flow effect on a windless day, and no vehicles entered the tunnel with the assistance of the local Traffic Management Bureau. Table 1 shows the structural parameters of these tunnels. The \(\Delta L\)/\(D\) values of #1 tunnel and #2 tunnel are 5.9 and 12.6, respectively, representing that the inlets of the downstream tunnels are in the potential core region and decay region, respectively. CO\({}_{2}\) was used in the test instead of toxic CO. The pollutant-releasing device mainly consist of a vortex flow meter (DN200, CERTEON, Shanghai, China), a CO\({}_{2}\) gas canister, and two-stage pressure-reducing valve. In order to ensure its well mixing at outlet section, CO\({}_{2}\) was released at 100 m away from the outlet into the upstream tunnel during the test. Figure 11a shows the distribution of CO\({}_{2}\) concentration measurement points on the tunnel cross-section. In the figure, \(H\) stands for the height of the concentration measuring point from the ground while \(X\) stands for the half the width of the tunnel bottom. The values of \(H\) for #1 tunnel and #2 tunnel are 0.9 m and 1.4 m respectively, and the values of \(X\) are 5.1 m and 6.6 m, respectively. CO\({}_{2}\) concentration was measured at the measurement points by concentration transmitters (AR8200, SMART, Guangdong, China). The accuracy of the transmitters is \(\pm\)(30 ppm + 5% readings). Arithmetic mean value of concentration of the tunnel cross-section is calculated with these measurement points. All the sensors have been calibrated. The jet fans in the tunnels were adjusted to get various values of \(u_{\text{up}}\) and \(u_{\text{down}}\). Figure 11b shows the distribution of 14 air velocity measurement points on the tunnel cross-section. A Testo 425 thermal anemometer (Testo AG, Baden-Wurttemberg, Germany) was used to measure the air velocity. The accuracy of the anemometer is \(\pm\)(0.03 m/s \(\pm\) 5%readings). The mean air velocity of the tunnel cross-section was calculated as an area-weighted value as \(u=\left(\sum_{i=1}^{14}u_{i}\Delta S_{i}\right)/S\), where \(u_{i}\) is the air velocity at the measuring point within the region \(i\) of area \(\Delta S_{i}\), and \(S\) is the total area of the tunnel entrance. In each case, the test procedure is as follows: (1) First, adjust the speed of jet fan to change the air velocity inside the tunnel; (2) Second, wait a few minutes to ensure that the speed of airflow in the tunnel is stable. (3) Then, release CO\({}_{2}\) and wait for another minute or so to make the concentration of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Upstream/downstream** & **Cross-Sectional** & \multirow{2}{*}{_D_ **(m)**} & \multirow{2}{*}{\(\Delta L\) **(m)**} & \multirow{2}{*}{\(\Delta L\)**/D**} \\  & **tunnel length \(L\) (m)** & & & & \\ \hline \#1 & 4823/4230 & 50.0 & 7.1 & 42 & 5.9 \\ \#2 & 4052/3850 & 86.9 & 9.5 & 120 & 12.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test condition of the consecutive tunnels. Figure 10: Comparison of calculated \(\varphi_{s}\) with simulated results. CO\({}_{2}\) no longer change significantly; (4) Finally, collect the concentration (velocity) data for one minute and take the mean value of the data as the measured concentration (velocity). The series-flow ratio \(\varphi_{\mathrm{s}}\) can be calculated by using the measured air velocity and CO\({}_{2}\) concentration, the formula is as follows:  
\[\varphi_{\mathrm{s}}=\frac{c_{\mathrm{down}}-c_{0}}{c_{\mathrm{up}}-c_{0}} \cdot\frac{u_{\mathrm{down}}}{u_{\mathrm{up}}} \tag{17}\]  
where \(c_{\mathrm{up}}\) and \(c_{\mathrm{down}}\) refers to CO\({}_{2}\) concentration of the cross-section in the upstream tunnel and downstream tunnel, respectively; \(u_{\mathrm{up}}\) and \(u_{\mathrm{down}}\) is the measured mean air velocity of the upstream tunnel and downstream tunnel, respectively; \(c_{0}\) stands for the local concentration of CO\({}_{2}\).