## 3 Numerical Simulation Results and Discussions
### Variation Characteristics of Circulating Air Mixing Ratio
#### 3.2.2 The Relationship between Circulating Air Mixing Ratio and Tunnel Structure Parameters  
Figure 12 shows the change rule of circulating air mixing ratio \(\varphi_{\rm c}\) with lateral distance \(d\). With the increase of \(d\), \(\varphi_{\rm c}\) under each type of staggered distance \(\Delta l\) decreased nearly exponentially. The smaller the \(\Delta l\) is, the smaller the \(\varphi_{\rm c}\) will be. For example, when \(d=10\) m, \(\varphi_{\rm c}\) falls below 3% under the conditions of \(\Delta l=0\) m and \(\Delta l=-10\) m, while \(\varphi_{\rm c}\) is still up to 25.0% and 37.4% under the conditions of \(\Delta l=30\) m and \(\Delta l=50\) m, respectively.  
Figure 13 shows the change rule of \(\varphi_{\rm c}\) with \(\Delta l/D\) for a two-lane tunnel and a three-lane tunnel. It can be observed that there is no direct relationship between \(\varphi_{\rm c}\) and the tunnel portal hydraulic diameter \(D\), but \(\varphi_{\rm c}\) varies with the increase of \(\Delta l/D\).  
Figure 11: Impacts of velocity ratio \(u_{\rm in}/u_{\rm out}\) on circulating air mixing ratio \(\varphi_{\rm c}\).  
Figure 12: Impacts of lateral distance \(d\) on circulating air mixing ratio \(\varphi_{\rm c}\).  
When \(\Delta l\leq 0\), the bigger the \(\Delta l\) is, the more intense the impacts of the negative-pressure zone at the tunnel inlet on the jet flow at the tunnel outlet will be and the faster the \(u_{\rm max}\) will be attenuated (Figure 8a). Therefore, \(\varphi_{\rm c}\) rises with the increase of \(\Delta l/D\). Take the curve \(d=5\) m in Figure 13b as an example. At \(\Delta l/D=-1.2\), the inlet is placed behind the outlet, and combined with Figure 9a, it can be found that the influence of the negative-pressure zone at the inlet on the jet structure at the outlet is very limited, and the jet flow fully develops. At this time, a negligible amount of polluted air permeates into the inlet and \(\varphi_{\rm c}\) is only \(5.1\%\). With the increase of \(\Delta l/D\), the influence of the negative-pressure zone at the inlet on the jet structure at the outlet is gradually enhanced and \(\varphi_{\rm c}\) increases linearly. When \(\Delta l/D=0\), the outlet and the inlet are aligned and the negative-pressure zone at the inlet causes obvious damage to the jet structure at the outlet, but the jet flow still develops to some extent. At this instant, the polluted air partially permeates into the inlet and the \(\varphi_{\rm c}\) is \(19.3\%\).  
When \(\Delta l>0\), the decay rate of \(u_{\rm max}\) increases firstly with increasing \(\Delta l\) before witnessing a decrease afterwards (Figure 8b). So \(\varphi_{\rm c}\) also rises firstly and then declines with increasing \(\Delta l/D\). When \(d=5\) m, \(\varphi_{\rm c}\) will reach the maximum at \(\Delta l/D=14.6\), and the bigger \(u_{\rm in}/u_{\rm out}\) is, the greater the variation of \(\varphi_{\rm c}\) and \(\varphi_{\rm c}\) at unit \(\Delta l/D\) will be, as shown in Figure 13a. With the gradual increase of d, \(\Delta l/D\) also rises gradually when \(\varphi_{\rm c}\) reaches the maximum. For example, when \(d=10\) m, \(\varphi_{\rm c}\) will be the maximum at \(\Delta l/D=26.3\), as shown in Figure 13b.