## 5 Conclusions  
This study focused on the low-speed NACA2412 airfoil as the research subject, employing numerical simulation techniques to investigate the feasibility of implementing transverse grooves as a drag-reduction structure on the airfoil of the MAV. Additionally, it conducted an analysis of the physical mechanisms underlying the influence of various groove placement schemes at low Reynolds numbers on the lift-drag ratio of the airfoil. Based on the rules, we have designed a grooved airfoil with a high lift-drag ratio and proposed preliminary design criteria for grooved MAV airfoils that have a certain guiding significance for subsequent research. The specific research findings are as follows:  
1. The grooves near the leading edge of the airfoil exhibit lower drag, with the lowest drag coefficient decreasing from 0.0179 to 0.0167 compared to the smooth airfoil. As the groove position moves backwards, the unfavorable pressure gradient will reduce the drag-reduction effect of the grooves. The grooves on the pressure surface have a slight impact on the lift coefficient of the airfoil, whereas the grooves on the suction surface cause a significant change in the lift coefficient. At the front, the ability of the grooves themselves to reduce static pressure will reduce the static pressure on the suction surface and increase lift. As the groove position moves back, the thickening of the boundary layer causes an increase in static pressure on the suction surface, resulting in a decrease in the lift coefficient from 0.380 to 0.332 (smooth airfoil: 0.370). Therefore, the relationship between the lift-drag ratio and groove position is similar to the lift coefficient.
2. When grooves are widely deployed on the suction surface of the airfoil, grooves positioned in the front-middle section yield the best aerodynamic performance (low \(\beta\)). In contrast, excessive grooves on the suction surface can cause airflow separation, and the degree of separation is positively correlated with the range and the local adverse pressure gradient. When significant separation occurs, it results in a series of separated bubbles causing disorder flow, which will be detrimental to the flight of MAV. On the pressure surface, widespread grooves will thicken the boundary layer, ultimately leading to increased drag and lift. Intermittently placing groove on the airfoil can reduce mutual interference between grooves, reducing this impact.
3. Simultaneously introducing grooves in both the front-middle section of the suction surface and the front-middle-tail section of the pressure surface of the airfoil has yielded the optimal aerodynamic performance, a 33.747% increase in lift-to-drag ratio. This result confirms the effectiveness of the application of transverse grooves on MAVs, and we have also given preliminary design criteria: do not arrange grooves in high adverse pressure gradient areas (\(\beta>0.5\)), and under low adverse pressure gradients, discontinuous arrangements of large-scale grooves should be adopted at the rear of the airfoil.  
Conceptualization, Z.L., Y.Z., H.Z. and L.H.; Data curation, Y.Z.; Formal analysis, Z.L., Y.Z. and H.Z.; Funding acquisition, Z.L., P.Z.; Investigation, Y.Z.; Methodology, Y.Z. and H.Z.; Project administration, Z.L.; Software, Y.Z.; Supervision, Z.L., P.Z. and H.Z.; Validation, Y.Z.; Writing--original draft, Y.Z.; Writing--review & editing, H.Z., P.Z., L.H., E.S., Y.L. and L.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundation of China (No. 52176032), National Science and Technology Major Project (2017-\(\parallel\)-0005-0016), Natural Science Foundation of Tianjin Municipal Science and Technology Commission (Youth Program No. 22)CQNJC00050).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data are contained within the article.  
**Conflicts of Interest:** The authors declare no conflict of interest.