## 4 Results and Discussion
### Evolution Mechanism of Flow Field  
#### 4.3.1 Macroscopic Flow Field  
Figures 15 and 16 depict the plane and three-dimensional flow field within the tunnel at key moments, considering both the scenarios of a single train and trains crossing at a speed of 300 km/h. For this analysis, only a specific moment during the single train operation (\(t_{2}\)\({}^{\prime}\) = 1.93) is considered, while two distinct moments are chosen for the scenario of two trains passing in the tunnel (\(t_{1}\)\({}^{\prime}\) = 0, \(t_{2}\)\({}^{\prime}\) = 1.93). In the figures, the \(XY\) plane and the three-dimensional flow field are color-coded to represent the \(X\) direction wind speed, whereas the \(XZ\) plane flow field is shaded to illustrate the \(Z\) direction wind speed. Under the conditions of a single train, a complex three-dimensional flow field is observed as the train moves through the tunnel. The train moves forward in the \(XZ\) plane, causing rapid displacement of air in front of the train, resulting in a high wind speed region near the train's frontal section. Simultaneously, air from the rear of the train quickly fills the space behind, creating another high wind speed area near the rear. The pressure difference prompts the air around the train body to flow from the front to the rear, leading to a flight trajectory of falling debris in the \(XZ\) plane that opposes the direction of the train's movement. Figure 14: Moment coefficient of falling debris: (**a1–a3**) single train; (**b1–b3**) trains crossing. In the \(YZ\) plane, air around the train's head (C1 section) diverges, with the highest wind speed occurring at the nose tip. Due to air viscosity, turbulence intensifies near the train body (C2, C3, and C4 sections), giving rise to variously sized vortex structures. Concurrently, the air velocity within the tunnel is notably lower than at the front of the train. Influenced by the wake vortex, the air flow direction in the rear of the train (C5 section) experiences reversal. In the \(YZ\) plane, the predominant air flow direction near the falling debris is in the -\(Z\) direction, causing all falling debris from the vault to move uniformly in the -\(Z\) direction. Under the conditions of trains crossing, the wind speed induced by train operation is heightened, leading to a more intricate flow field within the tunnel. In the \(XZ\) plane, the airflow direction in the proximity of the train's front, body, and rear remains consistent with  
Figure 16: Macroscopic flow field in tunnel under trains-crossing conditions: (**a**) \(Y=1.5\) m plane; (**b**) cross section; (**c**) three-dimensional view. Figure 15: Macroscopic flow field in tunnel under single train condition: (**a**) \(Y\)=1.5 m plane; (**b**) cross section; (**c**) three-dimensional view. that observed under single train conditions. Prior to the train intersection (\(t_{1}\)\({}^{\prime}\) moment), the flow field characteristics near the train closely resemble those during single train operation. Taking time \(t_{2}\)\({}^{\prime}\) as an example, when two trains converge within the tunnel, the wind speed in the train intersection section (from C1 to C3) is comparatively reduced. However, owing to the confined space for airflow, the wind speed in the non-intersection sections is notably higher than that near the body during single-train travel. In the YZ plane, at \(t_{1}\)\({}^{\prime}\) moment, the air near the nose (C2 section) flows in all directions with the tip of the nose as the source point, resulting in a strongly symmetrical wind speed distribution in the tunnel. Apart from the vicinity of the train head, the flow field distribution at other locations in the tunnel mirrors that of single-train conditions. At \(t_{2}\)\({}^{\prime}\) moment, the air in proximity to the nose (C1 and C3 sections) is predominantly influenced by the nose tip, resulting in divergent motion. The flow field in the train intersection area (C2 section) demonstrates a roughly symmetrical distribution.