# Experimental and Numerical Investigation on Ballast Flight from Perspective of Individual Particles
## 3 Results and Discussions
### Simulation Results
#### 3.2.2 Flow Characteristic around Ballast Particle  
The four ballast particles with the number of 15 in different shapes (A15, B15, C15, D15) were selected, and the different windward surfaces of the ellipsoid ballast and prolate ballast were considered (B15_1, B15_2, D15_1, D15_2). The simulation of ballast samples mentioned above was conducted based on the model in Figure 6. For the sake of comparing and analyzing, Figure 15 is the schematic diagram of the ballast samples, which shows the six numerical models from different views. The distance between particles in the simulation experiment was same with that of the wind tunnel experiment.  
Based on the model in Figure 15, the airflow around the ballast particle was calculated at a wind speed of 30m/s. The pressure contour and the streamline of the ballast are shown in Figures 16 and 17, respectively. It can be seen from Figure 16 that the pressure on the windward surface is positive, and that on the top, side, and back of the ballast is negative. The maximum positive pressure generates at the apex of the convex region on the windward surface of the ballast, and its magnitude is mainly affected by the local angular features of the particles. The maximum positive pressure increases with the sharpness of the ballast apex. Meanwhile, the maximum negative pressure generates at the common edge of the two adjacent surfaces on the top, side, or back of the ballast, and its magnitude is mainly affected by the angle formed by the two sides of the particle. The maximum negative pressure gets higher with the decrease of the ballast angle. Since the angle of the ballast samples is approximate, the maximum positive pressure of each ballast in Figure 16 is similar, and it is all about 530 Pa. However, the maximum negative pressure of each ballast is noticeably different. The maximum  
Figure 15: The numerical model in different views.  
negative pressure of B15_1 is the highest (\(-\)781 Pa), which exists on its side. Therefore, the ellipsoid ballast (B15_1) has the largest pressure difference (1312 Pa) when its long side faces the wind, and it is the most likely to fly under the condition of the same mass.  
Figure 17 shows the streamline around the ballast, and the airflow is blocked by the ballast to induce a disturbing flow when the wind blows parallel to the test bench. The airflow deflects upward and laterally, causing the streamline bending and forming a flow separation at the boundary of the ballast. Both the side and the top of the ballast are in the domain of flow separation, where the air pressure is negative, and the maximum negative pressure is just at the point of the flow separation.  
The shape and placement direction of the ballast also have an effect on its streamline distribution. In Figure 17, a wide (from top view) and high (from side view) airflow generates behind the ballast particles with the shape of ellipsoid and spherical after the flow separation stage. The vortex formed by the flow separation sheds into the airflow on the top, side, and rear of the ballast, which increases the wind suction acting on the particle and enlarges the negative pressure further. On the contrary, the flow around the oblate ballast and the prolate ballast is along their contours. It generates less flow separation and wake flow, and it is less prone to occur ballast flight. Compared with the ballast that had its long side facing the wind, the ballast that had its short side facing the wind had a large depth in its downwind direction. The incoming airflow produces a flow separation at the corner of the windward side and then attaches to somewhere on the long axis of the particle. Finally, the airflow separates again at the end of the ballast and forms a narrow turbulent wake flow, which reduces the negative pressure and wind suction acting on the ballast surface. Therefore, the ballast of the long side facing the wind is more likely to fly, and it is consistent with the conclusion from the wind tunnel experiment.