## 3 Effect of Grooves Position on Aerodynamic Performance of Airfoil
Figure 8: Effect of grooves at different positions on aerodynamic parameters of airfoils: (a) \(C_{D^{\prime}}\); (b) \(C_{L^{\prime}}\) and (c) \(C_{L}/C_{D}\). Figure 7: Depth of grooves at different positions on the airfoil surface. From the perspective of lift coefficient (Figure 8b), when grooves are placed on the pressure surface, the change in the airfoil lift coefficient is little, with variations not exceeding 1% in magnitude compared to the smooth airfoil. However, when grooves are positioned on the pressure surface, there is a more pronounced alteration in the lift coefficient. When grooves are located on the front section of the suction surface, there is a substantial increase in the airfoil lift coefficient. In contrast, when grooves are situated in the middle section, although the lift coefficient remains higher than that of the smooth airfoil, the increment is less than half of that observed in the front section. Furthermore, when grooves are placed in the rear or tail section of the suction surface, the aerodynamic performance of the airfoil deteriorates rapidly, causing the lift coefficient to drop below that of the smooth airfoil. Due to the relatively stable lift coefficient and drag coefficient, as depicted in Figure 8c, there is little variation in the lift-drag ratio when grooves are placed at different locations on the pressure surface. These results exhibit higher lift-drag ratios greater that of the smooth airfoil, and indicate that the aerodynamic performance of the airfoil can experience a modest improvement when appropriately sized grooves are placed on any segment of the pressure surface. For grooves on the suction surface, owing to the smaller drag coefficient and larger lift coefficient, the airfoil lift-drag ratio can be significantly enhanced when grooves are positioned in the front and middle segments. The effects of placing grooves on the rear and tail segments of the suction surface, conversely, lead to a rapid deterioration in the airfoil aerodynamic performance, especially in the tail section. On the whole, the variations in the drag coefficient largely align with the trends observed in groove-induced drag reduction under adverse pressure gradients [37; 38], where groove drag reduction rate becomes greater under mild adverse pressure gradients (Figure 2, Front and Middle sections of the suction surface), but deteriorates as the adverse pressure gradient approaches a strong magnitude (\(\beta=2\)) (Figure 2, Rear and Tail sections of the suction surface). Due to the absence of significant pressure gradients on the pressure surface, the drag reduction effects observed in various segments are similar. In order to investigate the reasons behind the impact of grooves at different locations on the suction surface on the lift coefficient, Figure 9 compares the pressure distributions near the suction surface. Figure 9: Pressure distribution of airfoils (suction surface grooves): (**a**) Pressure on suction surfaces; (**b**) smooth airfoil; (**c**) front section; (**d**) middle section; (**e**) rear section; and (**f**) tail section. The pressure contours in Figure 9b-f show that the grooves on the suction surface have almost no effect on the pressure distribution near the pressure surface. As illustrated in Figure 9a, when grooves are positioned in the front or middle section of the airfoil, the pressure distribution on the suction surface closely resembles that of the smooth airfoil, with pressure values reduced only in the vicinity of the grooves and their downstream regions. This is evident in Figure 9c,d as an expansion of the deep blue region (pressure below \(-80\) Pa) compared to the smooth airfoil (Figure 9b). The source of this pressure drop is the stable rotating vortex in the groove. The high-energy vortex in the groove injects momentum into the low-energy fluid near it, causing an increase in radial velocity and pressure drop [46; 47]. So, this phenomenon only occurs in the grooves and their downstream vicinity.