## 5 Conclusions  
In this paper, the influence of platform sinking shape on aerodynamic drag and noise of high-speed pantograph is studied by numerical simulation. The flow and acoustic fields are predicted by the IDDES method and the FW-H equation. The difference of aerodynamic  
Figure 19: Sound pressure levels at side receiver position.  
Figure 18: Diagram of the position of the receiver.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parts**} & \multicolumn{2}{c}{**Aerodynamic Drag (N)**} & \multicolumn{2}{c}{**Far-Field Noise (dBA)**} \\ \cline{2-5}  & **Original** & **Optimized** & **Original** & **Optimized** \\ \hline Cavity & — & 754.2 & — & 79.77 \\ Panhead & 911.2 & 916.9 & 86.48 & 84.74 \\ Upper frame system & 356.6 & 347.1 & 83.65 & 82.73 \\ Lower frame system & 253.7 & 204.8 & 79.24 & 77.66 \\ Base & 1144.4 & 634.2 & 84.97 & 82.15 \\ Insulators & 546.6 & 187.5 & 78.22 & 71.14 \\ Pantograph & 3212.5 & 2290.5 & 90.57 & 88.58 \\ Total (Pantograph + cavity) & 3212.5 & 3044.7 & 90.57 & 89.11 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of Aerodynamic Drag and Noise.  
performance of pantograph with or without platform sinking is compared and discussed. The conclusions are as follows:  
(1) The highly unstable shear layer airflow is separated from the upstream surface of the cavity and hits the bottom and downstream surface of the cavity, forming a recirculation zone. The key position of aerodynamic noise generation is downstream of the cavity with a highly turbulent kinetic energy region. In addition, the cavity has a larger downstream windward surface, which will form a local high-pressure zone and generate additional cavity resistance. The flow separation of the cavity with rounded or sloped edges is weakened and the recirculation area is reduced.  
(2) With the increase of the sloping angle of the cavity edges, the aerodynamic drag of the cavity gradually decreases. Too-large, sloping angles will significantly reduce the shielding effect of the cavity, which is not conducive to the drag reduction of the whole system. With the increase of the roundness of the cavity edges, the aerodynamic drag of the cavity reaches the minimum when \(R/D\) is about 0.8. Continuing to increase the roundness will lead to a recirculation zone. Compared with the unmodified rectangular cavity, the sloped and rounded cavities reduce the noise by 8.04 dB and 10.13 dB, respectively.  
(3) The bottom structure of the pantograph without platform sinking is exposed to high-speed airflow, resulting in excessive aerodynamic drag. However, the cavity formed by the sinking of the installation platform reduces the velocity of the airflow, weakens the airflow impact on the bottom structure of the pantograph, and reduces the turbulent energy around the pantograph. The optimized cavity structure reduces the aerodynamic drag and noise of the pantograph by 28.7% and 1.99 dBA, respectively. However, the cavity must also be considered as an additional aerodynamic drag and noise source. Overall, the total drag and radiated noise of the entire pantograph system are reduced by 5.22% and 1.45 dBA, respectively.  
Methodology, T.D.; Investigation, T.L.; Writing--original draft, T.D. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available from the corresponding author, upon reasonable request. The data are not publicly available due to privacy.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.