## 4 Results and Discussion
### Hoods at Tunnel Entrance
Figure 9: The peak values of pressure gradient and MPW of the three stages with different hood areas: (**a**) Pressure gradient at RP point; (**b**) MPW at RM point. The pressure gradient caused by the train entering the hood can be weakened by an oblique entrance. The pressure gradient at the RP point when different oblique rates of the hood entrance adopted is shown in Figure 10a. The effective area and the length of the hood entrance increase with the oblique rate, resulting in a decrease of \(w_{\text{t}}\)--which is caused by the compressibility effect when a train enters the hood--while the intensity of \(w_{\text{h}}\) increases gradually. The pressure gradient of \(w_{\text{t}}\) is about the same as that of \(w_{\text{h}}\) when \(k=0.5\), which corresponds to the minimum pressure gradient. At the same time, the waveform of the MPW is changed due to the superposition effect during the propagation of the compression wave, leading to a decrease in the MPW with the increasing oblique rate, as shown in Figure 10b. In addition, when the slope of the entrance hood changes, the micro pressure wave (\(w_{\text{p}}\)) caused by the train entering the tunnel and the micro pressure wave (\(w_{\text{r}}\)) caused by the reflected compression wave basically do not change with the slope. The micro pressure wave (\(w_{\text{h}}\)) caused by the complete entry of the train into the tunnel hood dominates, and its peak value decreases with the increase of the slope, which can be approximated as:  
\[\left(\Delta p_{\text{m}}\right)_{\text{max}}=12.796\text{e}^{-k/0.494}+61.737 \tag{9}\]  
Actually, the intensity of the MPW remains basically unchanged when \(k>1\), so \(k=1.25\) is taken. The influences of the number of holes on the formation and evolution of the compression waves are also studied. When the number of holes ranges from 0 to 24, the pressure gradients of the RP point is shown in Figure 11a. The wave \(w_{\text{h}}\) appears obviously in the waveform and begins to play a dominant role when \(n>4\). Due to the influence of \(w_{\text{t}}\), the wave \(w_{\text{h}}\) increases with the increasing number of holes. As the end of the opening moves away from the hood entrance (\(n>8\)), the wave \(w_{\text{h}}\) decreases as the number of holes increases due to the weakened influence of \(w_{\text{t}}\). At the same time, the wave \(w_{\text{h}}\) increases with the increasing holes number again due to the influence of \(w_{\text{p}}\), as the end of the opening is closed to the tunnel entrance (\(n>12\)). When the number of holes exceeds 20, \(w_{\text{h}}\) and \(w_{\text{p}}\) are superimposed into a single wave, leading to a rapid increase of the pressure gradient. The MPW exhibits the same variation compared with the pressure gradients as shown in Figure 11b; however, the superposition between \(w_{\text{h}}\) and \(w_{\text{t}}\) is more obvious due to the influence of the inertia effect. The distinction between \(w_{\text{h}}\) and \(w_{\text{t}}\) is inconspicuous when \(n>8\), while \(w_{\text{h}}\) and \(w_{\text{p}}\) are completely superimposed together for cases where \(n>18\). Figure 10: The effects of oblique hood entrance on tunnel aerodynamics: (**a**) Pressure gradient at RP point; (**b**) MPW at RM point. Actually, the intensity of \(w_{\rm t}\) is acceptable when \(n=6\), while the amplitude of \(w_{\rm h}\) increases significantly due to its influence. The superposition effect of \(w_{\rm t}\) and \(w_{\rm h}\) can be weakened by moving the holes at the third row forwards (towards tunnel entrance). Figure 12 shows the pressure gradient and the MPW when the position of the holes at the third row changes, where \(i\) represents the position of the holes located at the third row originally. As the holes move forward, \(w_{\rm h}\) is divided into two small waves, denoted as \(w_{\rm h1}\) and \(w_{\rm h2}\). The pressure gradient amplitude of \(w_{\rm h1}\) is about the same as that of \(w_{\rm h2}\) when \(i=5\), which has the best alleviation effect on the MPW.