## 4 Results and Discussion
### Flow Mechanism for Trains Running in the Open Air without Crosswind
At z = 1.44 m, the behavior of the train-induced wind velocity is in accordance with the situation at z = 0.2 m around the streamlined region on the head. After passing by the head, the wind accelerates gradually but drops suddenly at the trailing nose tip. Then the velocity of the train wind climbs up again and eventually arrives at the maximum in the wake flow field about 50 m away from the trailing nose tip. The maximum train-induced wind velocity of TP1 and TP2 are 4.7 m/s while those of TP3 and TP4 are 6.8 m/s. Figure 14: Velocity contour of the longitudinal section at the first bogie region and pressure contour of the first bogie region. Since the high-speed train is symmetrical along the y axis, the side force on the leading car and middle carriages can be ignored. Due to the vortex shedding in the wake flow, strong asymmetric characteristics could be observed in the wake flow, and strong fluctuation of side force could be found on the trailing car [2; 6], which affects severely the amenity of the train. Figure 16 shows the time histories of coefficients of the side force (Cs) of the four models. It is clear that the side force on tails of four models vibrates about zero and the time-averaged value approaches zero in spite of large amplitude. The smallest amplitude of Cs on TP2 is about 0.072 while the largest amplitude of Cs on the TP4 is about 0.1. The amplitude of TP1 and of TP4 are 0.085 and 0.075, respectively. For a high-speed train with eight carriages, the length of the train is 60 times larger than its height, indicating that the flow has already been fully turbulent when the boundary layer develops as far as to the trailing car. Prominent flow separation could be found on the streamlined trailing, resulting in complicated vortex shedding in the wake. Figure 17 exhibits the contour of vorticity at a particular cross section (\(X=95\) m) around the last bogie in the trailing car at different timesteps for the four models. As shown in Figure 17, the train body is surrounded by vortices with distinct sizes and intensity. Moreover, the vortices at both sides of the train are asymmetrical. As time changes, the sizes and intensity of vortices alter continuously, exhibiting apparent unsteady features. Specifically, TP2 owns the shortest nose and this section does change too much from the constant cross section of the main body. As a result, flow separation for TP2 is not that drastic so the sizes of vortices are rather small. On the contrary, TP4 which has the longest nose generates the strongest and largest vortices, since its streamlined shape changes so dramatically at this section that the flow separation magnifies. TP1 and TP3 both have the  
Figure 16: Time histories of coefficients of the side force (Cs) for the four models. Figure 7:0 Curves of time-averaged velocity of the train-induced wind at standard positions: (a) \(z=0.2\) m; (b) \(z=1.44\) m.  
same length of nose. The section of the former is nearly elliptical, making large vortices mainly scatter at both sides of the train. However, the section of the latter is almost wide-flat, leading to the emergence of large vortices on top of the train. These phenomena also explain why the side force vibration movement of TP1 is greater than that of TP3. Figure 18 shows surface streamlines on the trailing car at different timesteps. Two distinct separation lines can be found on the streamlined nose region and their positions develop as time flows by, showing remarkable unsteady characteristics for the generation and detachment of vortices. Since the vortices at both sides of the trailing nose repeatedly generate and detach from the surface, the separation lines sway about the central axis. Taking TP3 as an example, as Figures 17 and 18 show, at t = 1 s S2 is far from the central line while S1 is closer to the center, generating a peak for the side force of the trailing car. Afterwards when it comes to t = 1.5 s, the situation is quite the other way around as compared to t = 1 s, leaving the side force of the trailing car down in the trough.