## 4 Effect of Grooves Range on Aerodynamic Performance of Airfoil
For instance, when grooves are arranged on the front-middle section (Figure 12b) or front-middle-rear section (Figure 12c) of the suction surface, wavy, low-speed regions (depicted in blue) appear in proximity to the grooves. In the enlarged local images, it is evident that there are obvious shedding vortices near the grooves. In the case of the front-middle section, this tendency is less conspicuous; however, when grooves are positioned in the front-middle-rear section, this separation phenomenon extensively occurs near the rear portion of the suction surface. Moreover, the wake region exhibits heightened instability, characterized by the expansion of the blue low-speed region at the trailing edge and the rapid curvature of streamlines. When grooves are exclusively placed in the front section of the suction surface (Figure 12a), almost no such phenomenon is observed. This elucidates why, when  
Figure 11: Drag coefficient changes with the number of iterations. grooves are arranged on the front-middle-rear section of the suction surface, the drag coefficient exhibits significant fluctuations with iteration steps. Furthermore, a comparison between Figure 12d,e reveals that when grooves are positioned on the front-middle section of the pressure surface, the blue low-speed region near the rear part of the pressure surface enlarges. This implies an increase in boundary layer thickness near the rear, resulting in elevated drag, aligning with the trends observed in the black dots of Figure 8a. This phenomenon also increases the static pressure on the pressure surface, resulting in an increase in the overall lift coefficient of the airfoil, as shown in Figure 10b. In contrast, when grooves are placed on the front-middle-rear-tail section of the pressure surface, not only does the boundary layer near the tail thicken, but the wake also exhibits mild instability, with minor deviations observed in streamlines near the trailing edge. From Figure 13, the vorticity near the grooves increases to varying degrees, indicated by the proliferation of regions with strong vorticity (depicted in red). When grooves are only placed in the front section of the suction surface, the change in vorticity distribution is slight. However, when grooves are positioned in the front-middle section of the suction surface, mild fluctuations in vorticity distribution are observed in the vicinity of the airfoil midsection (Figure 13c), but the duration is not long, indicating the onset of weaker flow separation. When grooves are arranged in the front-middle-rear section of the suction surface, a series of detached, bubble-like structures form near the rear part of the suction surface (Figure 13c). This demonstrates the evolution and rupture of separation bubbles, causing highly unstable flow. In Figure 13e,f, when grooves are extensively placed on the pressure surface, the vorticity intensity on the pressure surface increases, particularly near the trailing edge. This signifies an augmented turbulence level. Because the diffusion rate of turbulent vortices greatly exceeds that of viscous vortex diffusion, the boundary layer thickness increases, leading to an elevation in the drag coefficient. To mitigate the impact of increased turbulence levels, the possibility of discontinuously placing grooves on the airfoil surface was explored. Figure 14 provides a comparative analysis of the variation in aerodynamic parameters of airfoils when grooves are positioned in the front-middle-rear-tail section, front-middle-tail section, and middle-rear section of the suction surface, and the middle-rear section of the pressure surface. It can be observed that when grooves are absent on the rear section or front-tail section of the pressure surface, the drag coefficient is lower than that of the grooves placed in the front-middle-rear-tail section of the pressure surface.