## 4 Effect of Grooves Range on Aerodynamic Performance of Airfoil
When grooves are positioned on the  
Figure 12: Velocity contours of airfoils with grooves arranged in different ranges (suction surface grooves: (**a**,**b**), pressure surface grooves: (**d**-**f**): (**a**) front section; (**b**) front-middle section; (**c**) front-middle-rear section; (**d**) smooth airfoil; (**e**) front-middle-rear section; and (**f**) front-middle-rear-tail section. middle-rear section of the suction surface, the airfoil drag coefficient is lower than that of the smooth airfoil but remains higher than the grooves placed in the front-middle section of the suction surface. From the perspective of lift coefficient, the intermittent placement of grooves leads to an overall reduction in the lift coefficient. However, due to a more significant reduction in drag coefficient, grooves in the front-middle-tail section of the pressure surface yield the highest lift-drag ratio. From the velocity contours near the airfoil in Figure 15, it can be observed that when grooves are intermittently placed on the front-middle-tail section of the pressure surface, the overall velocity distribution of the airfoil is similar to that of a smooth airfoil without grooves. Due to the reduced interaction between grooves, the wake becomes significantly more stable (as evidenced by the reduced streamline deflection in Figure 15c). In the locally enlarged image of Figure 15f, the distribution of vortices near the pressure surface is more uniform than when the grooves are continuously placed in the front-middle-rear-tail section of the pressure surface (Figure 15e), resulting in a thinner boundary layer and greater stability in the wake region. Consequently, there is a substantial reduction in the drag coefficient. But at the same time, the thinner boundary layer highlights the ability of the grooves themselves to reduce static pressure, resulting in a decrease in static pressure on the pressure surface and a decrease in lift coefficient. From the perspective  
Figure 14: Effect of grooves at different ranges (discontinuous) on aerodynamic parameters of airfoils: (a) \(C_{D}\); (b) \(C_{L}\); and (c) \(C_{L}/C_{D}\). Figure 13: Vorticity contours of airfoils with grooves arranged in different ranges (suction surface grooves: (a,b), pressure surface grooves: (d-f): (a) front section; (b) front-middle section; (c) front-middle-rear section; (d) smooth airfoil; (e) front-middle-rear section; and (f) front-middle-rear-tail section. of comprehensive aerodynamic performance, arranging grooves in the front-middle-tail section of the pressure surface will still increase the lift-drag ratio. Based on the analysis above, it is evident that by introducing grooves in the front-middle section of the suction surface and the front-middle-tail section of the pressure surface, one can achieve their respective maximum lift-drag ratios. Therefore, the ultimate choice was made to simultaneously incorporate appropriately sized grooves in both the front-middle section of the suction surface and the front-middle-tail section of the pressure surface and then compare their aerodynamic performance with airfoils that have grooves solely on the suction or pressure surface. As depicted in Figure 16, when grooves are simultaneously incorporated in both the front-middle section of the suction surface and the front-middle-tail section of the pressure surface of the airfoil, there is a substantial reduction in the overall drag coefficient of the airfoil. Furthermore, the lift coefficient is extremely higher compared to airfoils with grooves on only one surface. The combination of lower drag coefficient and higher lift coefficient results in a remarkable enhancement of the lift-drag ratio, increasing from 20.733 for the smooth airfoil to 27.730. This represents an approximately 33.75% improvement in aerodynamic performance, which can greatly improve the endurance of MAVs.