Inﬂuence of pantograph ﬁxing position on aerodynamic characteristics of high-speed trains

To study the inﬂuence of the pantograph ﬁxing position on aerodynamic characteristics of high-speed trains, the aerodynamic models of high-speed trains with eight cars were established based on the theory of computational ﬂuid dynamics, and eight cases with pantographs ﬁxed on different positions and in different operational orientations were considered. The pantographs were ﬁxed on the front or the rear end of the ﬁrst middle car or ﬁxed on the front or the rear end of the last middle car. The external ﬂow ﬁelds of the high-speed trains were numerically simulated using the software STAR-CCM ? . The results show that the pantograph ﬁxing position has little effect on the aerodynamic drag force of the head car and has a large effect on the aerodynamic drag force of the tail car. The inﬂuences of the pantograph ﬁxing position on the aerodynamic lift forces of the head car, tail car and pantographs are obvious. Among the eight cases, considering the total aerodynamic drag force of the train and the aerodynamic lift force of the lifted pantograph, when the pantographs are ﬁxed on the rear end of the last middle car and the lifted pantograph is in the knuckle-upstream orientation, the aerodynamic performance of the high-speed train is the best.


Introduction
With the increase in the train speed, the interaction between the train and the air becomes more severe, and it leads to a series of aerodynamic problems, such as aerodynamic drag force, lift force, aerodynamic noise [1]. The aerodynamic drag force is proportional to the square of the train speed. When the train speed reaches 200-300 km/h, the aerodynamic drag accounts for 70% to 85% of the total drag of the train [1,2]. The aerodynamic drag of pantographs accounts for 8% to 14% of the total aerodynamic drag, and the aerodynamic lift of pantographs is proportional to the square of the train speed [3]. Thus, the increase in the train speed would lead to a stronger interaction of pantograph-catenary [4,5].
A great deal of research has been carried out to investigate the aerodynamic characteristics of pantographs of high-speed trains. Zhang et al. [6] studied the influence of the fairing and windshield on the aerodynamic drag of pantographs through wind tunnel tests. Guo et al. [7] studied the unsteady aerodynamic characteristics of pantographs of high-speed trains with and without crosswind conditions using the detached eddy simulation method. Li et al. [8] analyzed the aerodynamic forces of pantographs with knuckle-downstream and knuckle-upstream orientation through a numerical simulation based on the threedimensional (3D) steady Reynolds Average Navier-Stokes (RANS) method, and the simulation results were basically consistent with the experimental results. Fu et al. [9] studied the aerodynamic forces of pantographs and the vibration characteristics induced by winds through wind tunnel tests. Pombo et al. [10] analyzed the influence of the aerodynamic forces on the pantograph-catenary system for high-speed trains under crosswinds using numerical simulations and experiments. Lee et al. [11] performed wind tunnel tests of pantographs with different arms and optimized the panhead shape. Du et al. [12] numerically calculated the flow field around a pantograph and analyzed the aeroacoustic characteristics of the pantograph.
However, the research about the aerodynamic characteristics of pantographs in the above literature mainly focused on the pantograph itself and neglected the influence of the train body on the aerodynamic characteristics of pantographs. As the thickness of the boundary layer increases along the opposite running direction of the train, the pantograph fixing position would have significant influences on the aerodynamic characteristics of the pantographs and the train body [13]. In the present paper, aerodynamic models of high-speed trains with pantographs fixed on different positions are established based on the theory of computational fluid dynamics (CFD). The external flow fields of the high-speed trains are numerically simulated using the software STAR-CCM?. In addition, influences of the pantograph fixing position on the aerodynamic characteristics of the high-speed train and pantographs are analyzed.

Computational model 2.1 Geometric model
Based on a new-type high-speed train, a train model with eight cars (including a head car, six middle cars and a tail car) is established. The total length of the train is 200 m. Figure 1 shows a simplified model of the head car and the whole train. The CX-PG pantograph is used for this study, which is a widely used pantograph in China Railway High-Speed 380. The main components of the pantograph are reserved, and the cables and bolts are ignored. There are two pantographs in each position: One is lifted, and the other is folded. The model of the pantograph and the pantograph region is shown in Fig. 2.

Numerical method and boundary conditions
In this work, the train running speed is 97.22 m/s (350 km/h), and the Mach number is 0.286, which is lower than 0.3. Therefore, the air compressibility can be ignored. The external flow fields around high-speed trains are simulated using 3D steady incompressible RANS equations. The Roe's FDS scheme and the lower-upper symmetric Gauss-Seidel (LU-SGS) method are selected for convective flux and temporal discretization, respectively. The k-x SST (shear stress transport) model is adopted as the turbulent model. The standard wall functions are used near the wall to ensure the accuracy of the CFD results with a limited amount of mesh. The governing equation of the incompressible flow can be expressed as follows [14]: where q is the air density, u is the velocity vector, u is the flow flux, U is the diffusion coefficient, and S is the source item.
The boundary conditions of the computational domain are described below. The inlet is set as a velocity inlet boundary and the velocity magnitude is equal to the train running speed. The outlet is set as a pressure-outlet boundary and the gauge pressure on the outlet is 0 Pa. The top and two sides of the domain are set as symmetry boundaries. The train body and pantographs are non-slip wall boundaries. In order to simulate the ground effect, the   Figure 7 shows the comparison of the aerodynamic drag forces of high-speed trains in various cases, where the drag force of pantographs is the sum of the drag forces of the lifted pantograph and folded pantograph. It can be seen that the pantograph fixing position has little effect on the drag force of the head car, but has a large effect on the drag force of the tail car. The aerodynamic drag forces of the pantographs fixed on the last middle car are evidently smaller than those fixed on the first middle car. The main reason is that the thickness of the boundary layer around the last middle car is much larger than that around the first middle car, and the pantographs fixed on the last middle car are almost submerged in the boundary layer. Among the eight cases, the total aerodynamic drag force of the high-speed train in case 8 is the smallest and in case 4 is the largest. Figure 8 shows the velocity contour around the pantographs in case 4 and case 8. It can be seen that the velocity of the air flow around the pantographs in case 4 is larger than that in case 8. As a result, the aerodynamic drag force of the pantographs in case 4 is larger than that in case 8.

Results and discussion
The comparison of the aerodynamic lift forces of highspeed trains in various cases is shown in Fig. 9. It can be   The aerodynamic lift force of the lifted pantograph directly influences the contact force between pantograph and catenary, and the contact state of the pantographcatenary system has a significant effect on the powercollecting capability of the pantograph. A too large contact force would lead to an abrasion increase in the pantograph and catenary. In contrast, a too small contact force would lead to an increase in the contact resistance between pantograph and catenary, resulting in heat generation, pantograph off-line, arc discharge, etc. As the sliding plate of the lifted pantograph contacts with the catenary directly, it is more reasonable to analyze the lift force of the sliding plate when considering the interaction between pantograph and catenary. Figure 10 shows the aerodynamic lift forces acting on the sliding plates of the lifted pantographs in various cases. It can be seen that the pantograph fixing position has a considerable influence on the lift force of sliding plates. The lift force of the sliding plate of the lifted pantograph in case 1 is the maximum and in case 4 is the minimum. However, the total aerodynamic drag force of the train in case 4 is the maximum (Fig. 7). The lift forces of the sliding plates of the lifted pantographs fixed on the last middle car (i.e., cases 5-8) are relatively small, and their differences between each other are within 15 N. From the above analysis, it can be concluded that considering the total aerodynamic drag force of the train and the aerodynamic lift force of the lifted pantograph, when the pantographs are fixed on the rear end of the last middle car and the lifted pantograph is in the knuckle-upstream orientation, the aerodynamic performance of the highspeed train is the best.

Conclusions
In this paper, the aerodynamic performances of high-speed trains with pantographs fixed on different positions are calculated based on the theory of CFD. The following conclusions can be drawn: (1) The pantograph fixing position has little effect on the aerodynamic drag force of the head car and has a large effect on the aerodynamic drag force of the tail car. (2) When pantographs are fixed on the rear end of the last middle car and the lifted pantograph is in the knuckleupstream orientation, the total aerodynamic drag force of the high-speed train is the minimum.