# Aerodynamic Analysis of the Opening Hood Structures at Exits of High-Speed Railway Tunnels
## 5 Results and Discussion
### Analysis of the Impact of Exit Hood Opening Ratio
The effective solid angle is a parameter that quantifies the influence of tunnel exit topography on the radiation area of MPWs, as shown in Figure 5c. When assessing the influence of the surrounding topography on the MPWs within the spherical range of radiation, it can be achieved by calculating the effective solid angle (\(\Phi\)) at each measurement point. The effective solid angle (\(\Phi\)) in Equation (10) is closely related to the maximum pressure gradient at the tunnel exit and the maximum value of  
Figure 10: Comparison of the pressure contours at different times: (**a**) t = 2.2 s in Case 1; (**b**) t = 2.2 s in Case 2; (**c**) t = 2.3 s in Case 1; (**d**) t = 2.3 s in Case 2; (**e**) t = 2.4 s in Case 1; (**f**) t = 2.4 s in Case 2; (**g**) t = 2.5 s in Case 1; (**h**) t = 2.5 s in Case 2; (**i**) t = 2.6 s in Case 1; and (**j**) t = 2.6 s in Case 2. (Unit: Pa). MPWs. Based on the calculation results, the representative wavelength of the compression wave is approximately 45 m. Therefore, the maximum pressure gradient of the compression wave within a range of 50 m from the tunnel exit is selected for further analysis. To describe the relationship between different hoods and an infinite plane, we introduce a correction coefficient denoted as \(k=\Phi/2\pi\). This correction coefficient represents the ratio between the effective solid angle with a hood and the radiation solid angle under the assumption of an infinite plane. In the case of an infinite plane, the radiation solid angle is \(2\pi\). \[\Phi=(1+\frac{\ell}{r}\cos\theta)\frac{2S}{[P_{MW}]_{\max}cr_{p}}[\frac{ \partial p}{\partial t}]_{\max} \tag{10}\]  
where \(t\) is time, \(P_{MW}\) is the micro-pressure wave, \(p\) is the pressure of the compression wave, \(r_{p}\) is the distance from the center of the hood outlet to the monitor point, \(\Omega\) is the spatial solid angle, \(S\) is the cross-sectional area at the tunnel exit, \(c\) is the speed of sound, \(\theta\) is the angle between the monitor point and the centerline of the tunnel exit, \(\ell\) is the end correction factor, and the coefficient \(\ell\cos\theta/r\) is used to represent the directional correction of the dipole effect in Equation (10). Figure 11 shows the spatial distribution pattern of MPWs near the exit. According to the results in Figure 11a, for the MPW radiating with a radius of 20 m, the maximum amplitude is observed at the F1 monitor point in Case 1. Simultaneously, the MPW amplitude at measurement points located in front of the exit plane of the hood (\(\alpha\),\(\beta<\) 90\({}^{\circ}\)) shows a decreasing trend as the azimuth angle increases. Conversely, for measurement points located behind the exit plane (\(\alpha\),\(\beta>\) 90\({}^{\circ}\)), the MPW amplitude increased with the increment of the azimuth angle. This phenomenon is primarily attributed to the dominant role of MPW reflection near the mountainous terrain [27]. Due to the influence of opening the hood, in Cases 2-4, the MPW amplitudes on the side plane (Plane _zox_) and the top plane (Plane _zoy_) increased with the azimuth angle. However, the recorded MPW amplitudes at points in front of the hood exit plane are smaller than those in Case 1. Except for the T3 measurement point, the MPW amplitudes at all measurement points show a decreasing trend with the increase in opening ratio. Behind the hood exit plane, the MPW amplitudes on the side and top of Cases 2-4 are greater than in Case 1. Additionally, the MPW amplitude at the top of the hood structure was significantly higher than that on the side. This phenomenon is attributed to the proximity of the measurement points behind the hood to the opening. The compression wave directly released a portion of the pressure at the opening, and simultaneously, the MPW experienced reflection near the mountain. These combined effects resulted in significantly higher MPW amplitudes in the top area of the hood compared to other areas.