## 1 Introduction
It was found that the VGs transfer the high momentum fluid to the near-wall region, and the variation of the velocity component direction in the boundary layer along the flow increases. In 2014, [PERSON] et al. [30] conducted numerical simulations on the FFA-W3-301 and FA-W3-360 airfoils. The calculated results were compared with wind tunnel measurements, and the variation of lift and drag with the angle of attack was obtained. Although their method was not able to capture the flow details accurately, it can be used to qualitatively compare the effects of different VG settings on airfoil aerodynamic performance. In 2015, [PERSON] and [PERSON] [31] employed passive VGs as a simple and effective method to delay or suppress airfoil flow separation, and carried out an experimental study on the optimized blades. Flow visualization of triangular VGs through three-dimensional particle image velocimetry was carried out. Overall, the results demonstrated that the maximum lift increased by 44%, while the drag increased by 0.2%. [PERSON] et al. [17] experimentally evaluated a boundary layer separation control method using miniature surface VGs. Wind tunnel tests were carried out in a low-turbulence pressure tunnel at the NASA (The National Aeronautics and Space Administration) Langley research center. The measured parameters included lift, drag, surface pressure, wake profile, and surface heat flux fluctuations. The results indicated that small VGs can effectively reduce the flow separation in the boundary layer of the flaps. [PERSON] et al. [32] performed computational fluid dynamics (CFD) simulations to study the effect of the physical characteristics and magnitudes of flow from VGs on the aerodynamic performance of the DU97-W-300 blunt-trailing-edge wing. The effect of the VG size was analyzed in terms of the trailing edge thickness and the VG length. The results demonstrated that the drag loss was more sensitive to the increase in the VG's height than lift, while an increase in the VG's length had a negative impact on both lift and drag. Analysis of the streamlines and vortices further revealed the flow field characteristics in the wake region. In 2016, [PERSON] et al. [33] experimentally studied the NACA 4415 airfoil equipped with VGs. The results showed that triangular VGs were more suitable for controlling the boundary layer separation, while micro VGs can effectively control the flow. [PERSON] et al. [34] studied the effect of VGs on the aerodynamic performance of thick blades. In particular, the effects of height and chord position of VGs and double-row VGs on airfoil aerodynamic performance were investigated. The results demonstrated that after the VGs were installed on the airfoil leading edge, the maximum lift coefficient increased. In addition, the lift coefficient of the double-row VGs could be further improved at high angles of attack due to the different installation positions and sizes. In 2017, [PERSON] et al. [12] studied the aerodynamic performance of the S809 airfoil with and without VGs using CFD simulations. The results showed that the VGs can effectively improve the aerodynamic performance of the S809 airfoil, reduce the thickness of the boundary layer, and delay stall. The double-row VG arrangement demonstrated a good performance in controlling flow separation, which further improved the aerodynamic performance of the S809 airfoil. [PERSON] et al. [35] studied the motion of micro VGs in the boundary layer of a flat plate using numerical simulations. The installation angle of the VGs was 18.5\({}^{\circ}\). The trajectory and size of the vortices on the plate were analyzed. [PERSON] et al. [36] improved airfoil aerodynamic efficiency by means of passive VGs placed on the control surface. First, the aerodynamic characteristics of the airfoil were simulated using a Reynolds-averaged Navier-Stokes solver (RANS). Then, through the parameterization study of different VG sizes, the effectiveness of the VGs under certain flow conditions were studied. In 2018, [PERSON] et al.