## 3 Validation of Numerical Simulation Method
### Validation of Aerodynamic Force
In this paper, the numerical simulation is implemented with an unsteady method, but the figures such as the streamline diagram, turbulent kinetic energy diagram, pressure distribution diagram, friction drag diagram and so on, deal with a time-averaged method. All numerical data are the time-averaged results of 50 time steps after convergence. Figure 6 shows the comparison of pressure distribution of the airfoil at different turbulence intensities and angles of attack. The pressure distribution shows that: there are few differences in pressure distributions at \(\alpha=5^{\circ}\), and the overall trend of pressure distribution is relatively approximate (Figure 6a). As for the pressure distribution at \(Tu=0.6\%\), the upper and lower surface pressure coefficients tend to be consistent about 50%c, resulting in the loss of lift contribution from this position to the trailing edge. However, there are significant differences in pressure distributions between \(Tu=6\%\) and \(Tu=0.6\%\) at \(\alpha=10^{\circ}\) and \(\alpha=15^{\circ}\) (Figure 6b,c). At \(Tu=6\%\), the pressure distribution changes sharply for the both angles of attack. A pressure bulge is generated at about 20%c and 10%c respectively, which is similar to that of the classical separation bubble, and is quite different from that of the flow separation at high angle of attack. At \(Tu=0.6\%\), the premature separation of the flow results in a rapid attenuation of the suction peak near the leading edge of the airfoil, and the pressure coefficient near 5%c keeps almost constant until the trailing edge, which indicates that the high turbulence intensity has a certain inhibitory effect on the flow separation. A further comparison of turbulent kinetic energy and streamline around the airfoil corresponding to \(Tu=6\%\) and \(Tu=0.6\%\) is conducted in the following figures (Figures 7 and 8). The streamlines in the figures clearly reflect the aerodynamic characteristics of the flow field. Figure 5: Comparison of numerical calculation and experiment results. (**a**) \(C_{L}\)_vs_\(\alpha\); (**b**) \(C_{D}\)_vs_\(\alpha\). Figure 6: Airfoil pressure distribution affected by different turbulence intensities at three angles of attack. (**a**) \(\alpha=5^{\circ}\); (**b**) \(\alpha=10^{\circ}\); (**c**) \(\alpha=15^{\circ}\). It can be seen that: At \(\alpha=5^{\circ}\)and \(Tu=6\%\), the flow separation only occurs near the trailing edge of the airfoil, and the streamline adheres well at other positions; At \(\alpha=10^{\circ}\), the separation begins near 20%c of the upper surface of the airfoil and reaches to the trailing edge. The topology of the separation vortex is more similar to the characteristics of the classical laminar separation bubble (LSB) separation as mentioned earlier. With the increase of the angle of attack, the scale of the separation vortex becomes larger and the separation point is advanced, but the center of the separation vortex is still within the chord range of the airfoil. When the turbulence intensity is 0.6%, the flow separation region expands as the angle of attack increases. At \(\alpha=5^{\circ}\), the flow separation occurs near 45%c of its upper surface. At \(\alpha=15^{\circ}\), the streamline begins to separate near 5%c of the upper surface, and there is no reattachment after the flow separation. The center of the separation vortex is located outside the chord of the airfoil, forming a typical high-attack-angle separation. The magnitude of turbulent kinetic energy represents the intensity of turbulence. When transition occurs in the boundary layer, the turbulent kinetic energy would increase sharply. Comparing the streamline and turbulent kinetic energy under two turbulence intensities, it can be found that when the airfoil is at the same angle of attack, the flow corresponding to the large turbulence intensity is more stable, and the flow separation area is smaller.