# Aerodynamic Simulation of Helicopter Based on Polyhedron Nested Grid Technology
## 3 Validation of CFD Simulation Method  
### C-T Rotor in Hover  
In this section, the test model of the C-T rotor [23] is taken as an example to verify the accuracy of numerical simulation in the hovering state. The detailed parameters of the C-T rotor are shown in Table 1.  
In order to verify the accuracy of the CFD method proposed in this paper, four working conditions with comprehensive test data were selected from the test report. They are: (1) \(M_{tip}~{}=~{}0.433\), \(\theta_{c}~{}=~{}5^{\circ}\), \(\Omega~{}=~{}1250\) RPM, \(C_{T}~{}=~{}0.00213\); (2) \(M_{tip}~{}=~{}0.612\), \(\theta_{c}~{}=~{}8^{\circ}\), \(\Omega~{}=~{}1750\) RPM, \(C_{T}~{}=~{}0.00455\); (3) \(M_{tip}~{}=~{}0.877\), \(\theta_{c}~{}=~{}8^{\circ}\), \(\Omega~{}=~{}2500\) RPM, \(C_{T}~{}=~{}0.00473\); (4) \(M_{tip}~{}=~{}0.612\), \(\theta_{c}~{}=~{}12^{\circ}\), \(\Omega~{}=~{}1750\) RPM, \(C_{T}~{}=~{}0.00807\). Where, \(M_{tip}\) is the Mach number at the blade tip, \(\theta_{c}\) is the total pitch, \(\Omega\) is the rotation speed, and \(C_{T}\) is the thrust coefficient of the rotor. Figure 3 shows the pressure contours of a blade surface in working condition 3, and Figure 4 shows the vorticity contours of the flow field in working condition 3. It can be seen from Figure 3 that there are significant shock waves near the blade tip. Figure 5 shows the comparison between the pressure coefficient at 0.96R obtained by CFD simulation and the test data. It can be seen from this figure that the pressure coefficient distribution at 0.96R on the blade surface obtained by CFD simulation fits well with the test data. \begin{table}
\begin{tabular}{c c} \hline
**Number of Blades** & **2** \\ \hline Blade radius R & 1.143 m \\ Plane shape of blade & Rectangle \\ Airfoil & NACA0012 \\ Chord length \(c\) & 0.1905 m \\ Undercut \(R_{cut}\) & 0.243 R \\ Torsion angle & \(0^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Detailed parameters of C-T rotor. Figure 3: Pressure contours of a blade in working condition 3. Figure 5 shows that the pressure coefficient distribution at 0.96R on the blade surface obtained by CFD simulation fits well with the test data. To further verify the accuracy of the simulation, the thrust coefficient obtained by the simulation was compared with the test data, as shown in Figure 6:  
Figure 4: Vorticity contours of flow field in condition 3. In Figure 6, the simple moving average (SMA) is used to smooth the thrust coefficient curve. When new data are available, old data will be deleted, resulting in a curve of the average moving with the time axis. This is mainly due to the fluctuation of the monitoring results in the CFD method with the passage of physical time, which requires smoothing processing. The SMA formula is as follows:  
\[\text{SMA}\ =\ \frac{x_{M}+x_{M-1}+x_{M-2}+\cdots+x_{M-(n-1)}}{n} \tag{7}\]  
In this case, \(n\) is 60. Figure 6 clearly shows that as the CFD simulation goes on, the thrust coefficient of the rotor in hover tends to be stable gradually, and the stable thrust coefficient fits well with the test data, which is conducive to verifying the high accuracy of the CFD method presented in this paper. It should be pointed out that the test thrust coefficient is a constant in the test report, and for the convenience of comparison, the data points that remain unchanged over time are used for representation. In addition, polyhedral mesh and tetrahedral mesh are used to divide the fluid domain in the simulation. The same control scale is used in the division of the two types of grids. For the background area, the global size is 0.4 m and the size surrounding the foreground area is 0.02 m, with a smooth transition between the two dimensions. For the foreground area, the global size is 0.02 m, the blade surface size is 0.005 m, and the leading and trailing edges of the blade are encrypted with a size of 0.002 m. When polyhedral grids are used, there are about 650,000 cells in a foreground region and 1.15 million cells in a background region, totaling about 2.45 million cells.