## 4 Results and Discussion
### Flow Mechanism for Trains Running in the Open Air without Crosswind
As for TP4 whose shape is a wide-flat double-arch, Cd at the nose tip is the minimum. After the stagnation around the nose tip Cd drops sharply to under zero and then unsteadily increases until it reaches the top at the rear of the first bogie cabin. However, Cd along the streamlined shape on the tail performs adversely to that on the head but its amplitude reduces apparently. Therefore, it can be seen that when the streamlined head and tail are designed symmetrically, the drag distributions along both streamlined shapes, other than only head or tail, should be considered to achieve the minimum drag of the train. However, if the streamlined head and tail could be designed differently, a recommendation could be proposed that the head can be designed in single-arch ellipsoid while the tail can take the form of a spindle with a cowcatcher in the front. Time-averaged Cd of the four models is given in Table 3. From the given data it can be seen that the whole Cd of TP1 is the highest while that of TP4 is the lowest, dropping by 4.2% compared to TP1. On the other hand, the whole Cd of TP2 and TP3 remains close to each other. Specifically, Cd of the leading car of TP2 is the smallest while that of the trailing car is the largest among the four models. For TP3, the Cd of the leading car is the largest while that of the trailing car is close to TP4. The Cd of the middle carriages for TP2 and TP3 remain close to each other, which is in accordance with the drag distribution shown in Figure 10b. The Cd of the leading car for TP4 increases by 3.2% to TP2. However, the Cd of middle carriages and the trailing car is the smallest among all the models. Although the aerodynamic drag coefficients of streamlined head and tail are almost similar for TP1 and TP3, the Cd of middle carriages for TP1 is relatively larger than TP3. It could be concluded that when performing drag reduction of a high-speed train, not only the drag of the leading and trailing streamlines should be considered, but also the streamlined variation influence on the middle carriages. In brief, the drag reduction design should aim at the drag of the whole train. Figure 12: Plots of Cd on four nose shapes along the x axis at t = 2 s.  
Since the high-speed train is running very close to the ground, ground effect makes a significant contribution to the aerodynamic performance of the bogie system [28; 32]. Drag of the bogies makes up 27% of the whole resistance [3]. For the convenience of analyzing the influence of streamlined structures on the aerodynamic performance of the bogies, each bogie as well as the corresponding cabin are divided separately from the carriage, so there are 16 bogie systems in total. Figure 13 shows the time-averaged Cd of each bogie system (with BOGIE representing the bogie and BOTTOM representing the bogie cabin) for the four models. It could be observed that Cd of BOGIE-1 is evidently larger than any other BOGIE. Cd of all BOGIEs is not so distinct except BOGIE-1, while in detail for one bogie system Cd of the cabin is far more considerable than Cd of the bogie. The drag coefficient of BOGIE-1 is close to each other for TP1 and TP3, while Cd of BOGIE-1 for TP2 is the lowest, dropping by about 26% compared to TP3. Judging from total drag of the bogie system, TP2 and TP4 own similar drag while TP1 has the most significant resistance, growing by 8.2% compared to TP2. The first bogie is the most sensitive in drag performance to the streamlined structures under the nose tip. However, because of the fully developed turbulent flow around the wake region, the last bogie of the train is not sensitive to the streamlined structures at all. The influence of the streamlined structures on the last bogie could be neglected. As mentioned above, streamlined structures influence the flow details around the first bogie region to a large degree. As the clearance \(H\) between the streamlined head and the ground varies, the flux and velocity of air flowing through this clearance to the first bogie cabin also change.