## 3 Aerodynamic Drag and Noise of Cavities with Different Shapes
### Aerodynamic Drag and Noise  
Figure 10 shows the results of the aerodynamic drag coefficient (\(C_{d}\)) of the modified cavity, and the corresponding values are listed in Table 2. The windward cross-sectional area of the cavity is selected as the reference area. With the increase of the sloping angle, the \(C_{d}\) of the cavity increases first and then decreases. When the sloping angle is greater than \(30^{\circ}\), the cavity achieves drag reduction. When the sloping angle is \(75^{\circ}\), the aerodynamic drag of the cavity is reduced by \(44.3\%\). For all cavities with rounded edges, the aerodynamic drag of the modified cavity is smaller than that of the rectangular cavity. The aerodynamic drag of the modified cavity corresponding to \(R/D=0.8\) is reduced by \(35.18\%\). The roundness of the cavity with rounded edges is not the greater, the smaller the resistance. When the roundness of the cavity edges is large enough (\(R/D>0.8\)), new recirculation zones form within the cavity, creating additional drag sources and leading to further increases in aerodynamic drag. Therefore, in the rounded edge cases, an appropriate roundness is necessary to achieve lower aerodynamic drag of the cavity. The flow recirculation zone formed by separating the airflow from the leading or trailing edge of the cavity is one of the main sources of aerodynamic drag. Another main source of aerodynamic drag is the high positive pressure region formed by the impact of high-speed airflow on the downstream surface of the cavity. When the sloping angle of  
Figure 8: Distribution of turbulent kinetic energy around the modified cavity with different sloping angles. (**a**) \(\theta=0^{\circ}\) (**b**) \(\theta=15^{\circ}\) (**c**) \(\theta=30^{\circ}\) (**d**) \(\theta=60^{\circ}\). Figure 9: Distribution of turbulent kinetic energy around the modified cavity with different rounded. (**a**) \(R/D=0\) (**b**) \(R/D=0.4\) (**c**) \(R/D=0.6\) (**d**) \(R/D=0.8\). the cavity edge is small, the recirculation region in the cavity changes little, but the high positive pressure region formed on the downstream surface increases, which will lead to the increase of the aerodynamic drag of the cavity. As the sloping angle of the cavity edge increases, the recirculation region significantly decreases, and the decrease in the velocity of shearing airflow also reduces the impact of the airflow on the downstream surface of the cavity, thereby reducing the positive pressure on the trailing edge of the cavity, resulting in a reduction in aerodynamic drag. For all cavities with rounded edges, similar physical mechanisms are involved. The difference is that the pressure change on the downstream surface of the cavity with a small, rounded edge is also small. However, the rounded edges can significantly improve the airflow separation at the leading edge of the cavity, reducing the separation zone and causing a decrease in aerodynamic drag. Overall, the aerodynamic drag is smaller when the cavity has a larger slopped edge or a rounded edge with appropriate roundness. However, the cavity with a too-large, sloped edge will expose the bottom structure of the pantograph to high-speed airflow, which is not conducive to the aerodynamic drag reduction of the pantograph. Therefore, the rounded edge (\(R/D=0.8\)) can be selected for cavity optimization. An acoustic receiver 25 m away from the cavity and located on the side is used to evaluate the cavity noise. The results of the overall sound pressure level (OASPL) are listed in Table 3. Compared with the unmodified rectangular cavity, the two modification methods of the cavity achieve different degrees of noise reduction. The noise is reduced by 8.04 dB when the sloping angle of the cavity is 75\({}^{\circ}\). Meanwhile, for the cavity with \(R/D=0.8\) rounded edges, the noise is reduced by 10.13 dB.