## 5 Conclusions  
In this paper, we studied the plates with triangular concave grooves, triangular protrusion riblets, trapezoidal concave grooves, trapezoidal protrusion grooves, and arc concave grooves, and compared them with the flat plate. The influences of the grooves and riblets for the flow parameters of the two-dimensional flow area were analyzed. After studying the plates with grooves and riblets, the triangular concave grooves were combined with the standard NACA0012 airfoil to analyze the influence of the triangular concave grooves on the aerodynamic characteristics. After a series of calculations and analyses, the following research results were obtained:  
The lateral riblets and grooves had a significant effect on reducing frictional resistance, and the trapezoidal concave grooves had the best effect on reducing frictional resistance. Frictional resistance was mainly generated on the windward side of the riblets and grooves, and vortices were generated inside the grooves. On the one hand, these vortices change the flow direction of the airflow in the grooves, resulting in negative shear stress in the grooves, which reduced the total frictional. On the other hand, the vortices play an \"air bearing\" effect, which converts sliding friction into rolling friction to reduce frictional resistance. The groove and riblet structure also had a certain effect on the boundary layer. Due to the riblet and groove structure, the thickness of the boundary layer increased, the average speed gradient was reduced, and the frictional resistance was reduced. Besides, the lateral riblets and grooves caused additional pressure resistance. Geometry and speed had a great influence on pressure resistance. Due to the geometric shape of the circular groove, a large pressure resistance will be generated, and when the speed reaches the transonic speed, the pressure resistance of the trapezoidal protrusion will increase greatly. Therefore, in the future, the factors that affect the additional pressure resistance will be deeply explored to achieve the purpose of reducing the total resistance.  
After the triangular concave groove is introduced on the suction side, the aerodynamic characteristics of the airfoil at a small angle of attack will be weakened, but the aerodynamic characteristics at a large angle of attack will be improved, because of the addition of stall angle of attack. Comparing it with the standard NACA0012 airfoil, the vortex was attached to the entire suction side before stalling. The introduction of triangular concave grooves changed the situation, and ensured that some gas can flow normally. It increased the stall angle of attack and the aerodynamic characteristics at large angles of attack. The introduction of triangular concave grooves on the pressure side weakened the aerodynamic characteristics of the standard NACA0012 airfoil, but it can increase the lift slightly.  
[PERSON] and [PERSON] designed and performed the simulations; [PERSON] and [PERSON] analyzed the data; [PERSON] and [PERSON] wrote the paper. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China, grant number 11532013.  
Figure 26: t = 0.1 s, velocity distribution of NACA0012 airfoil with grooves on the pressure side at a 10 angle of attack.  
**Acknowledgments:** The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China, Grant No. 11532013. and the support of China Scholarship Council.  
**Conflicts of Interest:** The authors declare no conflict of interest.