# Effects of Bogies on the Wake Flow of a High-Speed Train
## 5 Results and Discussions
### Instantaneous Wake Flow  
In this section, the effects of the bogies on the generation and the evolution of the flow structures of the wake vortices are analyzed by comparing the pressure, velocity, and vorticity distributions of the three models. The instantaneous structures of the wake vortex of the three models are shown in Figure 16 as iso-surfaces of the second invariant of the velocity gradient \(Q\), which is defined as:  
\[Q=-\frac{1}{2}\frac{\partial u_{i}}{\partial x_{j}}\frac{\partial u_{j}}{ \partial x_{i}}. \tag{17}\]  
In Figure 16a, a pair of large streamwise vortices characterized by alternating generation and shedding is observed in the wake of the real model; these vortices have a large influence range in the spanwise direction. Not coincidentally, a pair of slightly smaller streamwise vortices also appears in the semi-simplified model wake but with slightly weaker alternating generation and shedding and a slightly smaller influence range, as shown in Figure 16b. However, as shown in Figure 16c, the wake of the simplified model is clearly characterized by two layers of vortex structures, which are quite different from those in the other two models and result in the two TKE peaks in the vertical direction; the influence range in the spanwise direction is rather small in the wake of the simplified model (Figure 15). A comparison of the structures of the wake vortex of the three models for the same \(Q\) value demonstrates that the wake vortices are larger in the real model than the semi-simplified model and both are significantly larger those in the simplified model. However, due to the small size of the wake vortex in the simplified model, the exact differences cannot be easily determined and further analysis is required. It is also observed in Figure 16c that the lower pair of vortices in the simplified model originates from the cowcatcher, whereas the upper pair of vortices originates from the nose of the trailing car; this is illustrated in more detail in Figure 17. At \(x=37\) m, a pair of internally rotating vortices (A and A) occurs on both edges of the cowcatcher. As shown in Figure 18, the pressure on the cowcatcher is lower than the pressure on the bottom of the trailing car, which results in the air flowing over the edge of the cowcatcher L1 (as shown in Figure 19) from the bottom of the trailing car due to pressure gradients. This vortex generation mechanism is quite similar to that of wing-tip vortices in airplanes. Then, at \(x=38\) m, the size and strength of the lower pair of vortices gradually increase. At \(x=38.9\) m, the other two pairs of vortices (B-B' and C-C') begin to detach from the nose of the trailing car. The rotating directions of these two pairs of vortices are opposite to each other. The detailed generating mechanism of these two pairs of vortices has been described in several studies [6; 9; 27]. The downstream airflow at the end of the trailing car can be divided into three parts: the flow on the top of the streamlined surface, the flow on the lateral surfaces, and the flow beneath the streamlined surface. The flow velocity on the top of the streamlined surface decreases rapidly, whereas the flows on the lateral surfaces maintain their velocity, resulting in strong velocity shear layers and formations of vortex structures. One difference between the model simulated in this study and those in previous studies is that the cross-section of the nose is elliptical and the nose geometry is transversely zygomorphic with a small curvature, as shown in Figure 19; this configuration results in the same velocity gradients on L2 and L3, induces rotating airflow, and ultimately generates two pairs of vortices. However, the strength of the upper pairs of vortices decreases rapidly. At \(x=44.5\) m, the vortex pair C and C' disappears and, at \(x=55\) m, another upper pair of vortices (B and B') disappears, whereas the lower pair of vortices is still clearly visible but the vortices are spaced further apart.