## 4 Effect of Grooves Range on Aerodynamic Performance of Airfoil  
Purposefully arranging appropriately sized grooves on the front or middle section of the suction surface, as well as on the front, middle, rear, or tail section of the pressure surface, can enhance the aerodynamic performance of the airfoil. However, the mere simultaneous placement of these grooves on the same airfoil does not guarantee the attainment of maximum aerodynamic benefits at low Reynolds numbers. It remains uncertain whether grooves situated on the rear section contribute to the aerodynamic performance of the airfoil due to the interactions among the grooves when the range of groove placement on the suction surface is extensive. To address these issues and ultimately design an airfoil with the highest lift-drag ratio, an investigation into the impact of widely placed grooves on the airfoil surface is imperative. Because of the severe deterioration of airfoil aerodynamics resulting from the tail section grooves on the suction surface, we restricted the large-range grooves to the front-middle and front-middle-rear sections of the suction surface. Grooves on the pressure surface can be continuously positioned in the front-middle, front-middle-rear, and front-middle-rear-tail sections. After arranging these grooves, the aerodynamic parameters of the airfoil were as depicted in Figure 10.  
Figure 10: Effect of grooves at different ranges (continuous) on aerodynamic parameters of airfoils: (a) \(C_{D}\); (b) \(C_{L}\); and (c) \(C_{L}/C_{D}\). Comparing with Figure 8, in most cases, the lift-drag ratios of the airfoils were dramatically improved with the large-range of grooves (Figure 10c). For instance, when grooves are placed in the front-middle section of the suction surface, the drag coefficient decreased to 0.016 and the lift coefficient increased to 0.381, resulting in an increased lift-drag ratio of the airfoil to 23.635 (smooth airfoil: 20.733). From both a drag reduction and lift enhancement perspective, this project is markedly superior to the sole placement of grooves in one segment of the suction surface. Analyzing the trends of the black dots in Figure 10c, it can be observed that when large-range grooves are positioned on the pressure surface, airfoil with grooves placed in the front-middle section and front-middle-rear-tail section exhibit higher lift coefficients compared to only one section. The lift coefficient increases from around 21.5 to 22. However, for the grooves in the front-middle-rear section on the pressure surface, although their lift-drag ratios show improvement compared to the smooth airfoil, they remain lower than the grooves placed solely in the front section of the pressure surface. This phenomenon is attributed to the unexpected fact that as the number of grooves increases on the airfoil, the drag coefficient actually rises (in the front-middle-rear-tail section project, the increase in lift-to-drag ratio is mainly owed to an increase in the lift coefficient). To understand why a large number of grooves can weaken the overall drag reduction effect, an exploration of the underlying reasons is imperative. Moreover, it is noteworthy that Figure 10 lacks data for the scenario where grooves are placed in the front-middle-rear section on the suction surface. This omission is due to the emergence of strong non-steady-state phenomena during calculations. As depicted in Figure 11, the overall drag coefficient is elevated and exhibits continuous fluctuations, rendering the calculation results challenging to analyze comprehensively. In order to investigate the reasons for the increase in drag coefficient and why the above non-steady-state phenomena occured, we analyzed the velocity and vorticity contours of the flow. Comparing Figure 12a-c, it becomes evident that when grooves are extensively placed on the suction surface, certain separation structures manifest near the grooves that are unlikely to appear at high Reynolds numbers and low angles of attack.