## 4 Results and Discussion
### Hoods at Tunnel Entrance  
The mitigation mechanism for the MPW due to enlarged hoods, oblique hoods, and hoods with opening side holes are studied first. As is well known, the compression wave has three-dimensional characteristics only at the initial stage of formation, transforming into a one-dimensional plane wave after going a certain distance in the tunnel. So, only the pressure characteristics of the right monitoring point are analyzed in subsequent studies. The reference values for the geometric parameters of the hood in the calculation are as follows: \(A_{\text{h}}\) = 155 m\({}^{2}\), \(k\) = 1.25, \(n\) = 4. When a train passes through the tunnel with different types of hoods (shown in Figure 6a) entering at a speed of 400 km/h, the pressure characteristics of the RP point and the MPW at the RM point are shown in Figure 6b,c. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Mesh 1** & **Mesh 2** & **Mesh 3** & **Mesh 4** \\ \hline Grid quantity & 6.329 \(\times\) 10\({}^{6}\) & 7.354 \(\times\) 10\({}^{6}\) & 7.990 \(\times\) 10\({}^{6}\) & 8.945 \(\times\) 10\({}^{6}\) \\ \(\Delta p\) ( kPa) & 2.785 & 2.591 & 2.597 & 2.598 \\ \((\Delta p_{\text{m}})_{\text{max}}\) (Pa) & 60.17 & 59.44 & 59.39 & 59.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The pressure differential and amplitude of the MPW with different meshes. Figure 5: Comparison of pressure obtained by numerical simulation and field measurement: (**a**) Pressure at 140 m; (**b**) Pressure at 400 m.  
When an enlarged hood is installed at the entrance of the tunnel, the rising process of the compression wave is divided into three stages, corresponding to three small waves. When the train enters the hood, the surrounding air is compressed to generate the first wave (\(w_{\rm t}\)), and the air in front of the train is compressed further as the train enters the tunnel, resulting in a second compression wave (\(w_{\rm p}\)) and an expansion wave propagating to the rear. The expansion wave is reflected into a new compression wave (\(w_{\rm r}\)) at the hood entrance, causing the third increasement in pressure. The compressibility effects caused by the train entering the hood can be attenuated by an oblique entrance, leading to a decrease in the pressure gradient of \(w_{\rm t}\). The time when the pressure gradient peak appears is also delayed. When several opening holes are arranged at the side wall of the hood, a relief effect is induced to the pressure gradient of \(w_{\rm t}\), while a new compression wave \(w_{\rm h}\) is generated as the train passes through the openings, which tends to overlap with \(w_{\rm t}\). Subsequently, when the train enters the tunnel, \(w_{\rm p}\) appears at the same time as other hoods installed, but the intensity increases slightly. The time when \(w_{\rm r}\) arrives is earlier, with a decrease in the intensity due to the opening holes. The MPW at the measuring point 20 m outside the tunnel (RM point) is shown in Figure 6d. The variation of the MPW is basically the same as that of the pressure gradient, except for that the waves \(w_{\rm t}\) and \(w_{\rm h}\) superimpose into one wave (denoted as \(w_{\rm h}\)) when the hood with holes is adopted. The maximum values of the pressure gradient of the compression wave and the MPW with the mentioned four hoods are shown in Table 2. The values of \((\partial p/\partial t)_{\rm max}\) and \((\Delta p_{\rm m})_{\rm max}\) decrease by 53.97% and 51.80%, respectively, compared to that without a hood, which means that the rising process of the compression wave can be extended effectively by an oblique enlarged hood with opening holes, resulting in the mitigation of the MPW. Figure 6: Comparison of tunnel aerodynamics with different types of hoods: (**a**) Tunnel with different hoods; (**b**) Pressures at RP point; (**c**) Pressure gradient at RP point; (**d**) MPW at RM point.