# Effects of Bogies on the Wake Flow of a High-Speed Train
## 5 Results and Discussions
### Time-Averaged Flow Field  
#### 5.2.1 Slipstream  
The train is kept stationary in the current simulations and the velocities of the freestream and moving ground are set equal to the train running speed (\(V\) = 300 km/h) but in opposite directions. Therefore, when analyzing the slipstream, the stationary ground should be used as the reference frame and the slipstream velocity is defined as:  
\[u_{w}=\sqrt{\left(u-V\right)^{2}+v^{2}+w^{2}}, \tag{15}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Standard Deviation of** & **Standard Deviation of** & **Standard Deviation of** \\  & **Drag Coefficient** & **Lift Coefficient** & **Side Force Coefficient** \\ \hline Real Model & \(1.19\times 10^{-2}\) & \(2.57\times 10^{-2}\) & \(2.22\times 10^{-2}\) \\ Semi-simplified Model & \(0.93\times 10^{-2}\) & \(1.35\times 10^{-2}\) & \(0.94\times 10^{-2}\) \\ Simplified Model & \(0.03\times 10^{-2}\) & \(0.15\times 10^{-2}\) & \(0.15\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Standard deviations of the aerodynamic forces of the trailing car of the three high-speed train models. Figure 12: Time history curves of the aerodynamic coefficients of the trailing cars of three models. where \(u\), \(v\), and \(w\) are the time-averaged velocity components in the streamwise, spanwise, and vertical directions. The distributions of the slipstream velocity at (\(y\), \(z\)) = (3, 0.2) m and (3, 1.4) m are shown in Figure 13. The position of \(z\) = 0.2 m is very close to the upper surface of the rail and is greatly influenced by the underbody flow and ground effect. The position of \(z\) = 1.4 m is about half the train height and is also at the same level as the height of a human body; this is important with regard to safety. As shown in Figure 13, the slipstream velocity peaks occur at positions corresponding to the noses of the head and trailing cars. This occurs because when the train moves forward, the airflow in front of the nose of the head car is pushed forward and sideward. The airflow changes dramatically in the streamlined region of the head car where the cross-sectional area exhibits significant changes; this results in the velocity peak of the slipstream. The slipstream distributions of the three train models are similar near the noses of the head cars. Similarly, the cross-sectional area in the streamlined region of the trailing car varies and, therefore, a significant change occurs in the airflow, resulting in another velocity peak of the slipstream. Moreover, the slipstream near the nose of the trailing car is also affected by separation and recirculation regions and shedding vortices. A comparison of the three curves in Figure 13a shows that the airflows change little in the middle of the simplified and semi-simplified train models due to their constant cross-sectional shapes, which results in an approximately zero slipstream velocity. However, in the real model, a strong slipstream occurs in the middle of the train and becomes larger at the end of and far away from the train. This result is in agreement with the research results of [PERSON] et al. [13; 14]. The differences between the real model and the simplified and semi-simplified models are the different configurations of the bogie in the middle of the train models. The bogie has a significant influence on the external flow field of the train and increases the nearby flow and hence the slipstream. At \(z\) = 1.4 m, as shown in Figure 13b, the effect of the bogie on the flow field is smaller, which results in the similar distributions  
Figure 13: Distributions of the slipstream velocity of the three train models at \(y\) = 3 m and (a) z = 0.2 m and (b) z = 1.4 m.  
of the slipstream velocity (close to zero) in the middle of the three models. It can be concluded that bogies have large effects on the flow field of high-speed trains, especially on the underbody flow field.