# Study on Mechanism of Series-Flow of Pollutants between Consecutive Tunnels by Numerical Simulation
## 3 Results and Discussions  
### Flow Characteristic  
Figure 3 depicts the flow structure at the portals of the three-lane (\(D\) = 8.6 m) tunnels under \(u_{\text{up}}\) = \(u_{\text{down}}\) = 3 m\(\cdot\)s\({}^{-1}\). It can be seen that after pollutants are discharged from upstream tunnel exit, theycontinuously entrain surrounding air and flow downstream, resulting in a spreading jet boundary with increased air flux and lowered velocity. When they arrive at the downstream entrance, pollutants near the tunnel entrance will directly run into the downstream tunnel to form series-flow due to the jet inertia and suction of downstream tunnel entrance. The rest pollutants spread to the upward and two lateral sides of the downstream tunnel entrance due to pressure gradient. Due to the Coanda effect, the jet flow near the road surface at the entrance is unable to suck air, resulting in a high airflow velocity and low static pressure, in contrast with the upper part of the jet flow where the airflow velocity is small and static pressure is large. The pressure difference between the upper and lower parts makes the jet flow axis close to the road surface, so the influence of the inner layer can be ignored. Assume that the bottom layer thickness of the boundary is 0, so the axis of jet flow coincides with the \(x\)-axis; namely the maximum velocity \(u_{\text{max}}\) of jet flows is always on the \(x\)-axis. According to the attenuation law of \(u_{\text{max}}\), the three-dimensional wall jet can be divided into the potential core region and decay region. In the potential core region (where \(\Delta L/D\leq 7\)), the \(u_{\text{max}}\) remains constant, \(u_{\text{max}}/u_{\text{up}}=1\); in the decay region (where \(\Delta L/D>7\)), with further development of the jet-flow entrainment and mixing of fresh air, the \(u_{\text{max}}\) begins to decrease [23]. Figure 4 shows the distribution of the maximum flow velocity \(u_{\text{max}}\) in the symmetric plane of upstream exit jet for different values of \(\Delta L\). It can be seen from the figure, whether the downstream tunnel entrance is within the potential core region or the decay region, the change rule of \(u_{\text{max}}\) of the upstream tunnel exit jet basically matches that of three-dimensional wall jet. Only near the downstream tunnel entrance is \(u_{\text{max}}\) surged by the negative pressure to deviate from the \(u_{\text{max}}\) attenuation curve of three-dimensional wall jet. Figure 3: Flow structure and CO concentration distribution between the portals of consecutive tunnels under different \(\Delta L\). Figure 5 shows the flow field structure of the three-lane tunnel for \(\Delta L\) = 120 m with \(u_{\rm up}/u_{\rm down}\) being 2, 0.67, and 0.4, respectively, and Figure 6 the change rule of the maximum flow velocity \(u_{\rm max}\) in the symmetric plane of upstream exit jet at different values of \(u_{\rm up}/u_{\rm down}\). Based on Figures 5 and 6, one can conclude that the effect of the negative pressure on the upstream jet structure almost has no connection with \(u_{\rm up}\) or \(u_{\rm down}\) individually but is clearly related to \(u_{\rm up}/u_{\rm down}\). An increased \(u_{\rm up}/u_{\rm down}\) will widen the suction range of the downstream tunnel, damage the jet structure of the upstream tunnel exit more obviously, and raise the \(u_{\rm max}\) near the downstream tunnel entrance. Figure 4: Distribution of \(u_{\rm max}\) in the symmetric plane of upstream exit jet for different values of \(\Delta L\). Figure 5: Series-flow structure for different values of \(u_{\rm up}/u_{\rm down}\). Figure 6: Distribution of \(u_{\rm max}\) in the symmetric plane of upstream exit jet for different values of \(u_{\rm down}\). Therefore, the series-flow can be considered as three-dimensional wall jet diffusion of the upstream tunnel pollutants influenced by the negative pressure near the downstream tunnel entrance. Jet characteristics are mainly related to \(\Delta L\) and \(D\).