## 5 Conclusions  
This work presents the numerical study of the aerodynamic noise characteristics induced by a pantograph over a simplified train geometry with the different configurations of the installation base using the large eddy simulation (LES) with finite element method (FEM). The numerical results are carried out in terms of the flow field around the pantograph and its installation base, the spatial distribution and spectrum characteristics, and the noise directivity in near and far fields under the up and down conditions at the train speed of 350 km/h. Through the discussion, the following interesting phenomena are drawn:  
(1) The complex shape of the pantograph is the main reason for its induced aerodynamic noise. A series of vortices detaches from the leeward side of each rod and they interact with each other and with downstream solid structures. The aerodynamic pressure fluctuation is generated on the rods induces aerodynamic noise. The main aerodynamic noise sources are located on the downstream base frame and on the double skateboard bow, at the connection between the upper and lower arms. The aerodynamic noise sources over the pantograph surfaces are different at 200 Hz and at 1 kHz. (2) For the spatial distributions, along the direction of the flow velocity, the aerodynamic pressure fluctuation amplitude in the front regions of the pantograph is lower than that in the rear regions of the pantograph. These distributions are more uniform at 1 kHz than at 200 Hz. In addition, the amplitude of the noise is lower at the higher frequency. (3) In the far-field regions along the x and y directions, for all x and y positions under the pantograph shape and opening direction selected in this paper, the down-pantograph with the flush configuration provides the highest OASPL. The up-pantograph with the sunken configuration produces the lowest OASPL. In addition, the OASPL caused by the up-pantograph with the flush base is higher than that by the down-pantograph with the sunken base. Thus, the pantograph with sunken configuration is a better choice in a practical engineering application. (4) On the directivity, the noise induced by the pantograph with the sunken surface is of lower amplitude than that with the flush surface, especially in the down-pantograph. For up-pantograph, the amplitude of the noise from the sunken surface configuration is close to that from the flush surface configuration in Y-Z plane and in the X-Z plane. In the X-Z plane, the results even show noise amplitude from the sunken surface configuration is predicted to be higher than that from the flush configurations at some angles in some angles. However, this still does not affect the fact that the sunken installation is conducive to a quieter noise environment on both sides of the road. It should be noted that effects of noise transmission to the exterior and interior of high-speed train need to be further studied, especially in the case of the pantograph with the sunken configuration. The present study considers only the aerodynamic noise generated by the wall fluctuating pressure of the pantograph in the exterior noise transmission to the environment. In fact, there are strong vortices in the regions near the pantograph and spatial distribution of near-field, such as Y = 0 m, may obtain a more accurate result. These are the quadrupole noise sources that contribute to aerodynamic noise. Since the operating speed is not too high (Ma = 0.278), the proportion of noise generated by the quadrupole source, which scales by u\({}^{8}\)[34], is smaller than that from dipole sources, which scales as u\({}^{6}\)[35], where u is the train velocity. Thus, the induced noise by the quadrupole source is not included in this study. Conceptualization, Z.S. and G.Y. ; Data curation, Y.Y. ; Formal analysis, Y.Y. ; Funding acquisition, Z.S. and G.Y. ; Investigation, Y.Y. and Z.S. ; Methodology, Y.Y. and W.L. ; Project administration, Z.S. and G.Y. ; Resources, Z.S. and G.Y. ; Software, Y.Y. and W.L. ; Supervision, Z.S. and G.Y. ; Validation, Y.Y. and Z.S.