## 4 Effect of Surface Grooves on Aerodynamic Characteristics of Airfoil  
In this section, the NACA0012 airfoil is selected for research, as shown in Figure 8. The triangular concave grooves are arranged on the suction side of the NACA0012 airfoil and the same grooves are arranged on the pressure side. The aerodynamic characteristics are calculated and compared with the NACA0012 airfoil without grooves. The chord lengths of the three airfoils are all 1 m, and the numerical calculation is performed under the conditions of an incoming flow speed of 0.5 Ma and Reynolds number of \(1.17\times 10^{7}\). The calculation area of the three airfoils adopts a circular calculation area, with the leading-edge point of the airfoil as the center of the circle, and the diameter is twenty times the chord length. Figure 7: Streamlines of various plates at 0.5 Ma. (**a**) The triangular concave grooves, (**b**) the triangular protrusions, (**c**) the trapezoidal concave grooves, (**d**) the trapezoidal protrusions, and (**e**) the circular concave grooves. For the NACA0012 airfoil with triangular concave grooves on the suction and pressure sides and the standard NACA0012 airfoil, numerical simulation calculations are used. For the choice of turbulence model, the three airfoils are the same, where a standardized \(k\)-\(\varepsilon\) model was selected for calculation, because the model is suitable for complex geometry external flow problems and satisfying the calculation accuracy. The Coupled algorithm was selected as the solving algorithm. The Coupled algorithm is an implicit coupling algorithm for uniformly solving momentum and pressure-based continuous equations. It is solved by the discrete pressure gradient term and dissipation term in the momentum equation. For three types of airfoils, the calculation is started from \(-8^{\circ}\) angles of attack with an interval of \(2^{\circ}\) angles of attack, and until the three types of airfoils have reached the stall angle of attack. After obtaining the approximate range of the stall angle of attack of the three airfoils, the transient calculation was used to analyze the changes in the flow conditions around the airfoils when the three types of airfoils stall. As can be seen from Figures 9-11, the introduction of triangular concave grooves on the suction side of the standard NACA0012 airfoil reduces the airfoil's lift coefficient and lift-to-drag ratio, but it increases the stall angle of attack of the airfoil. The stall angle of attack of standard NACA0012 airfoil is promoted from 14-16 to 18-20, and in the case of a larger angle of attack, the drag coefficient of the NACA0012 airfoil with triangular concave grooves on the suction side is smaller than the standard NACA0012 airfoil. For the introduction of a triangular concave groove on the pressure side of the standard NACA0012 airfoil, the lift is increased but the drag is also increased, and the lift-drag ratio is increased compared to the airfoil with grooves on the suction side, but it is still lower than the standard airfoil, and the stall angle of attack also decreases. In general, when the angle of attack is small, the aerodynamic performance of the standard NACA0012 airfoil is better, but when the angle of attack is increased to a certain extent, the aerodynamic performance of the NACA0012 airfoil with triangular concave grooves on the suction side is more prominent. The NACA0012 airfoil with triangular concave grooves on the pressure side reduces the aerodynamic performance of the original NACA0012 airfoil. To compare their aerodynamic parameters at small angles of attack, an angle of attack of \(4^{\circ}\) is selected.