# Aerodynamic Characteristics When Trains Pass Each Other in High-Speed Railway Shield Tunnel
## 4 Results and Discussion
### Aerodynamic Load on Surface of Train  
When the high-speed train entered the shield tunnel, the pneumatic load acting on the train carriage expanded in the X-, Y-, and Z-directions, corresponding to the aerodynamic resistance of the train, the aerodynamic side force, and the aerodynamic lift, respectively. Each train carriage was divided into several segments along the direction of travel, the averages of the static pressure data over time were computed at the bottom surface, top surface, leeward side, and windward side for each segment in each operating condition. When the two trains intersected in the tunnel, the impact on the pneumatic lift was small, and the torque was calculated based on the pneumatic side force. The pneumatic resistance and pneumatic side force mainly depend on the speed, lining structure, and intersection position. The formulae used to calculate the aerodynamic resistance \(F_{x}\) and the aerodynamic lateral force \(F_{y}\) on a single carriage of the train are as follows:  
\[F_{x}=0.5\rho v_{t}{}^{2}C_{d}A_{tr1}, \tag{13}\]  
\[F_{y}=0.5\rho v_{t}{}^{2}C_{s}A^{\prime}_{tr}, \tag{14}\]  
where \(\rho\) is the air density (kg/m\({}^{3}\)), \(v_{t}\) is the train speed, \(A^{\prime}_{tr}\) is the area of the side of the train and \(A_{tr1}\) is the cross-sectional area of the train. When high-speed trains meet in a tunnel, due to the space limitations in the tunnel, the transient amplitude of the aerodynamic load will significantly affect the safety of the train operation. Figure 16 shows a time history curve of aerodynamic drag at different train speeds. Table 3 shows the maximum aerodynamic resistance of the train surface under different working conditions. Figure 16 and Table 3 show that as the train speed increased,  
Figure 15: Pressure curves of the micro-pressure wave outside the tunnel exit when the trains met at different positions from the tunnel entrance: (**a**) 100 m, (**b**) 200 m, (**c**) 300 m, and (**d**) 400 m.  
the aerodynamic drag on the train surface gradually increased. The aerodynamic drag generated at a train speed of 400 km/h in the shield tunnel was 80.3% higher than that at a train speed of 300 km/h. At the same speed (350 km/h), the maximum aerodynamic drag and the minimum aerodynamic drag generated by trains in the lining/shield tunnels were \(29.7/30.1\) kN and \(-32.8/-32.3\) kN, respectively. Thus, the maximum aerodynamic drag difference of the lining and shield tunnels was about 1.35%, and that of the minimum aerodynamic drag was 1.52%. The aerodynamic drag was greatly affected by the train speed. Under the same blocking ratio, the influences of the two different tunnel lining structures on the aerodynamic drag were almost negligible. Figure 17 shows the aerodynamic lateral force of the train surface. As shown in Figure 17a, there was a slight difference between the maximum positive and negative lateral forces when two trains met in the shield tunnel and the molded lining tunnel. The maximum positive and negative side pressures of the train head in the lining/shield tunnels were \(25.2/25.3\) kN and \(-20/-21.4\) kN, respectively. Thus, the maximum positive side pressure difference of the train head in the lining and shield tunnels was about 1.35%, and that of the minimum positive side pressure was 1.52%. The maximum positive and maximum negative side pressures of the middle train in the lining/shield tunnels were \(13.1/13.2\) kN and \(-13.6/-13.7\) kN, respectively. Thus, the maximum positive side pressure difference of the difference of the middle train in the lining and shield tunnels was about 0.8%, and that of the minimum positive side pressure was 0.7%. As shown in Figure 17b, as the train speed increased, the maximum lateral force on the head of the train increased more than it did for the middle and trailing trains. This showed that, compared with different tunnel lining structures, the influence of the train speed on the aerodynamic lateral force on the surface of the train was slightly greater.