# Experimental and Numerical Investigation on Ballast Flight from Perspective of Individual Particles
## 2 Materials and Methods
### Computational Fluid Dynamics Simulation
#### 2.3.1 Model Formulation  
The shape and size of the test bench in the numerical simulations were consistent with those in the wind tunnel experiment. The height from the test bench to the top of the computational boundary was 0.419 m, which was same as the height from the ballast bed surface to the train underbody [6]. The size of the calculation domain was 4 m \(\times\) 2 m \(\times\) 0.419 m, as shown in Figure 6.  
Figure 5: Ballast samples with different windward directions. (**a**) Long side faces the wind; (**b**) Short side faces the wind. Figure 6: Calculation domain of the numerical simulation. The approximate simulation method [29] was used in some numerical studies to reconstruct the simulation model of the ballast particles, which could only represent the ballast size roughly and ignored the local features of the ballast particles. In this paper, a refined numerical simulation model of ballast particles was developed based on the 3D scanning results. The principle and method were as follows. The STL file of ballast features obtained by the 3D scanning system was a geometric model, which could represent the ballast contour by a set of triangles, and the simulation precision could be adjusted by controlling the number of triangles. The information in each triangle contained only the 3D coordinates of vertices and the normal vector of the plane. That was, the ballast model obtained by scanning only recorded the geometric position information of the ballast surface, but not the topological information of the relationship between the geometries. Therefore, it was necessary to decompose and reconstruct the regular geometric voxels from the ballast contour information, rebuild the topological relationship based on the position information, and establish the whole body model of the ballast particles. In addition, the validity and closure of the geometric voxels of the ballast model should be checked to repair the geometric defects such as the cracks and isolated edges. The \"body\" was created to determine the generated scale of mesh after reconstructing the ballast model in the calculation domain. The computational space was divided by the tetrahedral unstructured mesh because the geometric shape of the ballast was extremely complicated. In order to analyze the flow around the ballast particles, a boundary layer mesh was generated on the surface of the ballast model with an initial height of 0.2 mm, a growth rate of 1.2, and a mesh level of 3. Figure 7 shows the surface mesh and the spatial mesh of the numerical model. The mesh near the contour of the ballast was refined by building a density box to improve the accuracy of calculation. In order to improve the computational efficiency and convergence, the mesh size changed smoothly from the density box to the computational boundary with a growth rate of 1.2. Figure 8 shows the final numerical simulation model with approximate 5.74 million mesh elements. Figure 8: The refined model of the computational fluid dynamics (CFD) simulation. Figure 7: Mesh model of a ballast particle with accurate features. (**a**) Surface mesh; (**b**) Spatial mesh. The \(k-\varepsilon\) two-equation turbulence model of the incompressible fluid was used as the mathematical model because the Mach number of the flow was less than 0.3 [37]. The governing equations of the flow field were established to solve the airflow according to the conservation law.