# Impact of Different Nose Lengths on Flow-Field Structure around a High-Speed Train
## 4 Results and Analysis
### Flow-Field Visualization
#### 4.4.2 Wake Flows  
Figure 19 shows time-averaged velocity vectors of vertical planes 1 \(H\), 2 \(H\), 3 \(H\), 4 \(H\), 5 \(H\), and 6 \(H\) from the tail of the train. It can be seen from the figure that with increasing distance from the tail car the time-averaged velocity vectors of vertical planes with different nose lengths also show the law of continuous downward and outward development, and the radius of the vortex increases. However, the nose length has a great influence on the time-averaged velocity vector of the tail. At the same position from the tail car, when the nose length of the train is 4 m, the vortex radius is obviously larger than that of the other nose lengths, and the vortex center is higher from the ground and closer to the trackside position and the platform position. As a result, the time-averaged \(U\) with a nose length of 4 m is larger in the near-wake region. With increasing distance from the tail car, the time-averaged \(x\)-vorticity (\(\overline{w_{x}}\)) decreases with increasing nose length. However, at the same location, \(\overline{w_{x}}\) for a nose length of 4 m is significantly larger than that of other nose lengths.  
Figure 18: Time-averaged pressure at a height of 1.6 m from TOR (from top to bottom: 4, 7, 9, and 12 m).  
In the wake of the train, there are two vortices with opposite rotation direction that continue to develop downward and outward, and the appearance of the peak value of \(U\) is related to the two wake vortices [17]. At present, a large number of scholars use the Q criterion to study the development and separation of wake structures along HSTs [34; 35; 36; 37]. The iso-surface of the second invariant of the velocity gradient tensor Q is defined as follows [36]:  
\[\mathrm{Q}=\frac{1}{2}(\|\mathbf{\Omega}\|^{2}+\|\mathbf{S}\|^{2}), \tag{9}\]  
where \(\mathbf{\Omega}\) is the rate-of-rotation tensor and \(\mathbf{S}\) is the rate-of-strain tensor. Figure 20 shows a Q (Q = 5000) iso-surface with the time-averaged \(U\) colored according to the flow of different nose lengths at the wake. It can be seen from the figure that there are two vortices with opposite rotation direction in the wake of the four nose lengths, and the \(U\) value near the nose tip of the tail car is relatively large. The black line distance COT is 3 m. It can be seen from the figure that the nose length increases from 4 to 12 m, and the fluctuation of the wake vortex narrows in the lateral direction. In particular, when the  
Figure 19: Time-averaged velocity vectors of vertical planes 1 \(H\), 2 \(H\), 3 \(H\), 4 \(H\), 5 \(H\), and 6 \(H\) from tail of train, colored by time-averaged x-vorticity (hollow pink square: platform position; hollow pink circle: trackside position).  
nose length is 4 m it can be seen that the fluctuation of the vortex structure in the lateral direction is obviously wider and more intense. This may be the reason why the \(U\) value of a HST with a nose length of 4 m in the near-wake region is larger than that of other nose lengths. At the same time, in the longitudinal direction the nose length is longer and the wake vortex shedding distance is farther, and the wake vortex with nose lengths of 9 and 12 m is obviously longer than that with a nose length of 4 m. This may cause the \(U\) value of a nose length of 4 m to be smaller than those of nose lengths of 7, 9, and 12 m in the far-wake region, as can also be seen in Figure 9. In the vertical direction, with increasing nose length, the height of the vortex near the nose tip of the tail car is lower.