## 4 Results and Discussion
### Flow Mechanism for Trains Running in the Open Air without Crosswind
As a result, to reduce the total drag over the whole high-speed train, the reduction of pressure drag should be mainly focused on. The distributions of shear force coefficients of four models along the train body are given in Figure 10b. It could be found that shear force fluctuates massively about the irregular region of the train. Shear force around the streamlined region on the head is relatively large and that around the streamlined region on the tail is rather small. Shear force around the bogies is apparently smaller than that around the regions with constant cross section. From the streamlined head to the tail, fluctuation amplitude of shear force gradually becomes smaller and reaches the lowest at the trailing nose tip. Similar shear force magnitude is measured around the constant cross-sectional regions for the four models. Among these four models, the minimum shear force around the streamlined regions could be observed on TP4. Shear force originates from the viscosity effect of the turbulent boundary layer on the train. Figure 11 shows the velocity profile within the boundary layer at different cross sections for the four models. It can be seen that the boundary layer grows thicker as the airflow runs from head to tail, exceeding as much as 1.5 m or 40% of the train height around the constant cross-sectional region on the tail. The amplitude of velocity variation is rather huge around the streamlined region on the head, because the boundary layer is not fully developed and the pressure gradient is enormous, causing shear force to oscillate significantly. Around the constant cross-sectional region on the leading car, the boundary layer gradually develops and the inner flow within the boundary layer stabilizes. As the boundary layer develops along the train body, its thickness increases gradually, meanwhile the pressure gradient near the train surface becomes smaller and smaller, leading to reduction of shear force. The pressure gradient of TP4 is the largest over the constant cross-sectional region on the leading car, resulting in the largest shear force on the corresponding regions among the four models. For the middle carriages, the pressure gradients of the four models are similar. Consequently, the shear forces of the four models tend to be similar too. Around the constant cross-sectional region on the trailing carriage, the pressure gradient of TP4 is still the most significant and naturally its shear force becomes the biggest among the models. As for the streamlined region on the trailing car, owing to the longest streamline, the flow separation location of TP4 is the furthest away from the trailing nose tip. As a result, the distance from where the boundary flow is broken to the nose tip of TP4 is also the longest. Figure 11: Velocity profile within the boundary layer at different section planes. Figure 12 shows plots of accumulated Cd on four computational models along the x axis at t = 2 s. It could be observed that Cd fluctuates severely on the head, the tail, and bogies. In the region where the cross section remains constant, Cd keeps a relatively low value but increases apparently around the bogie regions. The distribution of Cd varies from each other along the streamlined shape for the four models. For TP1 whose nose is constructed in double-arch ellipsoid, the first peak appears at the transition from the head nose to the cab window and a minimum in the middle of the cab window. After that, the second peak of Cd appears about the rear of the first bogie cabin. Built in single-arch ellipsoid, Cd of TP2 turns to be the largest compared to the other three at the leading nose tip. However, it drops rapidly afterwards until the middle of the cab window. It keeps negative in the following 4 m along the streamline until the rear of the first bogie cabin, where the first Cd peak appears. TP3 is constructed in a spindle with a cowcatcher in the front. The drag of TP3 along the streamline remains positive and also meets its peak at the rear of the first bogie cabin.