## 3 Effect of Grooves Position on Aerodynamic Performance of Airfoil  
In order to improve the flight performance of MVAs, it is imperative to increase the battery capacity while concurrently reducing the energy consumption per unit time of propulsion. The former is intricately linked to the lift coefficient of the airfoil, whereas the latter is contingent upon the drag coefficient of the airfoil. The expressions for the lift coefficient and drag coefficient are delineated in Equations (7) and (8), as follows:  
\[C_{L}=\frac{L}{\frac{1}{2}\rho|V|^{2}c} \tag{7}\]  
\[C_{D}=\frac{D}{\frac{1}{2}\rho|V|^{2}c} \tag{8}\]  
In the equations, \"\(L\)\" represents lift, \"\(D\)\" denotes drag, and \"\(c\)\" stands for the characteristic length of the airfoil. The comprehensive impact of both lift and drag on aerodynamic performance is expressed through the airfoil lift-drag ratio (\(C_{L}/C_{D}\)). To contrapuntally distribute grooves over a wide range, it is significant to investigate the influence of groove placement. Consequently, we positioned grooves on both the suction and pressure surfaces corresponding to the front, middle, rear, and tail sections, as illustrated in Figure 3, to systematically explore their aerodynamic performance. The depths of the grooves are determined collectively by the local Clauser parameter (\(\beta\)), the local Reynolds number, and the drag reduction model ([PERSON] et al.) [31]. When the span is within 5 mm, we assume that the local Reynolds number and \(\beta\) remain relatively constant, and the groove depth (H) in this segment remains consistent. The specific groove depths for each segment are illustrated in Figure 7. The number of grooves is the range divided by the width (rounded off). Figure 6: Validation of computational accuracy. We placed these transverse grooves on various segments of the airfoil suction and pressure surfaces, as depicted in Figure 3. The aerodynamic performance parameters of the airfoil are presented in Figure 8. In this figure, the blue dashed line represents the data corresponding to the smooth airfoil without grooves for reference. From Figure 8a, it is evident that in most cases, the airfoil with grooves experiences a significant reduction in drag coefficient. Moreover, regardless of whether the grooves are placed on the suction or pressure surface, those positioned closer to the leading edges result in a lower drag coefficient for the airfoil. Therefore, in subsequent designs, it is advisable to place grooves close to the front portion of the airfoil. In comparison to the suction surface, grooves on the pressure surface exhibit relatively similar drag reduction capabilities across different positions, with variations occurring primarily in the rear section. In terms of drag reduction effectiveness, placing grooves on the front section of the suction surface yields the smallest drag coefficient and the highest drag reduction rate. Additionally, when grooves are positioned in the middle section of the suction surface, the drag coefficient of the airfoil is still lower than that corresponding to the pressure surface. However, when grooves are positioned in the rear section of the suction surface, their drag reduction capabilities notably diminish compared to the grooves in the same location on the suction surface. And when grooves are placed in the tail section of the suction surface, the drag reduction effect rapidly deteriorates, so much so that the drag coefficient even surpasses that of the smooth airfoil, which is detrimental to flight. This observation indicates that after placing grooves in positions characterized by significant adverse pressure gradients (as illustrated in Figure 2), the benefits of grooves in reducing viscous drag can no longer offset the increase in pressure-induced drag, leading to a rapid increase in overall drag. Consequently, this region was avoided when subsequently arranging the grooves.