# Flow-Induced Vibration Analysis by Simulating a High-Speed Train Pantograph
## 2 Aerodynamic Simulation and Analysis of Pantograph
### Geometric Modeling and Computational Setup for Pantograph  
In this article, a simplified model of a certain high-speed train consisting of three cars is utilized, with the train model having a height (H) of 3.1 m, a width (W) of 3.2 m, the length (L) of the lead and tail cars being 25.8 m, and the length (L) of the middle car being 24.9 m. The established high-speed train model is depicted in Figure 2.  
Focusing on a specific type of pantograph as the research subject, a simplified model of the pantograph was established. The pantograph principally consists of the bow head, upper arm, balancing rod, lower arm, upper and lower pull rods, base frame, and insulators. The structure is illustrated in Figure 3.  
In this article, the tunnel model is 255 m in length, designed as a single-track tunnel. According to the National 8 th Five-Year Plan Scientific and Technological Project--\"Research Report on the Selection of Design Parameters for High-Speed Railway Line Bridges and  
Figure 3: Geometric model of pantograph.  
Figure 2: Geometric model of train.  
Tunnels\"--the cross-sectional area of the tunnel can be adopted as 100 m\({}^{2}\). The tunnel model and its cross-sectional area are depicted in Figure 4.  
The calculations were performed using the commercial software Fluent for the simulation of the airflow around a train set operating within a tunnel. The computational domain is illustrated in Figure 5, with the train positioned such that the nose tip of the lead car is 50 m away from the tunnel entrance. A pressure outlet boundary condition is defined, with buffer zones of 310 m set up at both the tunnel entrance and exit to accommodate the acceleration and deceleration phases of the train. The study assumes the gas to be an ideal gas, requiring the definition of a pressure far-field boundary at the exit. The sides of the buffer zone are set as symmetric walls, located 10H away from the train's symmetry line, where H represents the height of the train. The top surface of the buffer zone is also designated as a symmetric wall, positioned 15H above the ground. The tunnel entrance and exit wall surfaces are defined as stationary walls. To simulate the ground effect during the train's operation, the tunnel ground is set as a stationary wall, while the ground in the train operating domain is defined as a slip wall.  
The global mesh size for the train body surface is set to 60 mm. In this study, a finer mesh resolution of 20 mm is applied in the vicinity of the pantograph to enhance the mesh density in that area. Additionally, boundary layers are established on the surfaces of both the train and the pantograph, with the first layer of the boundary near the pantograph wall being 0.1 mm in height. The sliding mesh method is employed for the simulation, with the mesh count for the sliding block being approximately 11.58 million and the mesh count for the stationary domain being about 3.16 million, totaling a mesh count of 14.74 million. Figure 6 presents a simulation and analysis diagram of the mesh.  
In this article, 10.55 million, 14.74 million, and 16.87 million grids, are used to compare the calculation results of 10.55 million, 14.74 million, and 16.87 million grids, 10.55 million  
Figure 4: Tunnel geometric model and cross-section.  
Figure 5: Boundary condition settings.  
Figure 6: Computational domain.  
grids and two other quantity grids, 16.87 million and 5-10%, considering the influence of grid quantity within the acceptable range. Then, 14.74 million grids are selected in the final project to ensure the calculation cost.