3.1 The influence of fixed wall on calculation
In the computational domain, the tube wall is very close to the train, so setting the tube wall to a fixed wall may affect the calculation results. It is necessary to make a simple discussion on whether the fixed wall has an influence on the calculation results. In this part, the boundary condition of the tube wall is set as the moving wall with no slip and the fixed wall with no slip respectively. The air pressure in the tube is 0.5 atm. The tangential velocity of the moving wall is equal to the airflow velocity. The initial ambient temperature in the tube is 293 K. The number of mesh is about 18.8 million, and the Lmin=0.05 m (approximately 0.0156H).
In this section, the drag coefficient (Cd) and pressure coefficient (CP) are defined as follows:

where Fd and P are the aerodynamic drag and the pressure measured in the flow field, respectively. And the pressure (P) in this paper represents the difference between absolute pressure and reference pressure. ρ0 is the initial density of air in the flow field. When air pressure is 0.5 atm and the ambient temperature is 293 K, the air density is about 0.602 kg/m3. v is the train speed (1000 km/h), and Strain is the maximum cross-section area of the train, which here is about 9.637 m2.
Table 1 shows the aerodynamic drag coefficients of the train calculated by using a moving wall and a fixed wall, respectively. The difference of aerodynamic drag coefficient (Cd) between the moving wall and the fixed wall is great.
Table 1 Drag coefficient
Item
|
Moving wall
|
Fixed wall
|
Cd
|
2.2776
|
0.4743
|
Fig. 5 shows the distribution of temperature and CP on the intersection line between the train upper surface and the xy plane, respectively. Here, the surface above the train stagnation point is defined as the upper surface, and the surface below the train stagnation point is the lower surface. It can be seen from Fig. 5 that when the boundary condition of the tube wall is the fixed wall, the distribution of temperature and CP is quite different from that of the moving wall. The reason for this difference should be that the distance from the tube wall to the train is very short, and the boundary conditions have great interference in solving the flow field around the train.
Therefore, when the wind tunnel model is adopted to calculate the flow field of the tube train, it is more reasonable to set the boundary condition of the tube to the moving wall, so that the train moves relative to the tube, which is more consistent with the actual situation. Based on this result, in the following calculations, the tube wall is all set as the moving wall.
3.2 The influence of prism layer stretching ratio on calculation
In this paper, the first prism layer is little thin, about 0.01 mm. In order to ensure a good transition from prism mesh to trim mesh, and avoid the excessive prism layers resulting in a large number of meshes, the stretching ratio of prism layer is set to 1.4. In this section, a brief comparison will be made between the calculation result of the stretching ratio 1.4 and 1.2, so as to explain the rationality of setting the stretching ratio to 1.4. The initial conditions in this section are the same as in Section 3.1.
Table 2 shows the train drag coefficient calculated from different stretching ratios. The drag coefficient is 2.2776 calculated by stretching ratio 1.4, and the error is only 0.33% compared with the drag coefficient 2.2701 calculated by stretching ratio 1.2.
Table 2 Drag coefficient calculated from different stretching ratios
Items
|
Stretching ratio 1.4
|
Stretching ratio 1.2
|
Cd
|
2.2776
|
2.2701
|
Fig. 6 shows the temperature and pressure coefficient distribution on the train surface at different stretching ratios. The temperature of stretching ratio 1.2 is slightly higher than that of stretching ratio 1.4, and the temperature difference at the same position of train surface is less than 1 K. In addition, the distribution of pressure coefficient on the train surface at different stretching ratios is almost the same.
According to the above, it is reasonable to set the prism layer stretching ratio at 1.4. Moreover, the total number of mesh is approximately 32% higher at stretching ratio 1.2 than at 1.4. Therefore, taking into account the limited computing resources, the prism layer stretching ratio in this paper is set to 1.4.
3.3 Mesh independence verification
In order to ensure the rationality of the calculation, three different sizes of the mesh were generated to observe the influence of the number of mesh on the calculation results. Table 3 shows the details of the mesh, including the minimum size of the trim mesh Lmin and the total number of the mesh. The initial conditions in this section are the same as in Section 3.1.
Table 3 Details of the three types of the mesh
Items
|
Coarse mesh
|
Medium mesh
|
Fine mesh
|
Lmin
|
0.0188H
|
0.0156H
|
0.0125H
|
Total number of mesh (million)
|
10.4
|
18.8
|
29.1
|
Table 4 shows the Cd calculated from the coarse, medium and fine mesh, respectively. The difference of the Cd between coarse mesh and fine mesh is 0.33%; the Cd of the medium mesh is closer to that of the fine mesh, and the difference is only 0.05%.
Table 4 Drag coefficients (Cd) for different meshes
Items
|
Coarse mesh
|
Medium mesh
|
Fine mesh
|
Error (relative to fine mesh)
|
Cd
|
2.2689
|
2.2776
|
2.2764
|
0.33% and 0.05%
|
Fig. 7 shows the distribution of temperature and CP on the intersection line between the train upper surface and the xy plane under the three types of the mesh. It can be found that both the temperature and CP of coarse and medium meshes are comparable to those of fine mesh, and the temperature and CP of medium mesh are closer to that of fine mesh. In addition, the temperature and CP curves of the coarse mesh fluctuate at the shoulder of the tail car, while those of the medium and the fine mesh are relatively gentler. Overall, the calculation results of medium and fine mesh are more reasonable. Considering that the fine mesh will spend more time and computing resource, it is a good choice to use medium mesh to achieve reasonable calculation results.
3.4 Numerical method verification
In this section, the ONERA M6 wing, a CFD validation case, is used to verify the numerical method adopted in this paper. The numerical method is adopted to calculate the pressure coefficient of airfoil surface, and the pressure coefficient results are compared with the experimental values of Schmitt and Charpin[33]. The numerical simulations use the flow field conditions of the ONERA M6 wing in Reference [33], as shown in Table 5.
Table 5 Flow conditions of the ONERA M6 wing in Ref. [33]
Mach
|
Reynolds number
|
Attack angle
|
Sideslip angle
|
0.8395
|
11.72×106
|
3.06°
|
0°
|
Fig. 8 shows the pressure coefficient at several wing span locations, and the numerical results of the pressure coefficient were compared to the experimental values. It can be seen from Fig. 8 that the numerical results of the pressure coefficient on each section of the wing are approximately consistent with the experimental results. Consequently, the numerical method adopted in this paper is reasonable.