## 2 CFD Simulation Method
### Grid System  
In this paper, an O-type mesh is selected as the blade body-fitted structured mesh. The two-dimensional section of the blades is distributed along the radial direction in an H shape, and finally an O-H blade body-fitted structured grid is formed, as shown in Figure 2. The advantage of using the H-shaped distribution is that the blade body-fitted structured grid has a high grid quality, and it is not easy to produce grid distortion. At the same time, this type of grid has high computational efficiency. In order to simulate the separation of the blade tip shock wave and the airflow separation near the blade root, the mesh of the blade tip has been refined in the radial direction. The body-fitted structured grid surrounding the blade belongs to the foreground grid in the nested grid system and meets the requirements of forming a nested relationship with the background grid.  
Since the upper and lower rotors of the coaxial double rotor are very close, generally less than 0.1D, the lower rotor is in the downwash flow field of the upper rotor, and the aerodynamic interference between the upper and lower rotors is very strong. The body-fitted structured foreground grid of the upper and lower rotor blades cannot pass through each other's blade surface, so the outer boundary of the foreground grid of the upper and lower rotor blades is smaller than 0.1R. The foreground grid area and the background grid area are divided into smaller grid sizes to ensure an effective nesting relationship between the foreground and background grids. The background grid area corresponding to the middle region of the coaxial double rotor is locally clustered. The coaxial dual-rotor structure motion nested grid system is shown in Figure 3.  
In this paper, a polyhedron nested grid method is used for the simulations. The foreground grid includes propeller region mesh and paddle area mesh, which is moving with time; the background grid is a fluid domain grid containing the entire composite coaxial helicopter structure, which is always stationary.  
Since there are many irregularities in the background grid area, it is not suitable for the use of structured grids. Therefore, the entire flow field of a compound coaxial helicopter was generated by commercial software to produce a Cartesian grid system which is similar to the structured grid. Region, swept by the foreground grid, is partly clustered to ensure the background mesh and the foreground mesh boundary size equal, which achieve the  
Figure 3: Coaxial dual-rotor structure motion nested grid system.  
Figure 2: The O type mesh.  
foreground grid and background grid nested. The fuselage, the landing gear, the wing and the tail field boundary is made with a grid refinement process to ensure higher computing accuracy. Compound coaxial helicopter motion nested mesh system assembly diagram is shown in Figure 4.  
The basic dimensions of the background grid, the blade grid, and the propeller grid are 0.25 m, 0.01 m, and 0.005 m, respectively. The rest of the grids are refined on the basic dimensions to generate a reference grid. In addition to the reference grid (grid C) with 13,659,192 cells, two coarser grids were constructed, consisting of 6,819,093 (grid B) and 3,402,798 cells (grid A). The grids were obtained by coarsening the reference(fine) grid with twice about a factor of 2. The results of the rotor thrust coefficients calculated with the three grids are shown in Figure 5. The results show that the reference (fine) grid is suitable. The difference in the rotor thrust coefficients is about 0.5% between the fine grid and grid B, while it is 7.5% between the reference fine grid and grid A.