## 4 Conclusions  
When VGs are used for the flow control of wind turbine blades, they are always installed under a certain arrangement. In this paper, the LES method was used to simulate the boundary layer separation flow with and without VGs in an adverse pressure gradient environment. The large-scale coherent structure of the boundary layer separation caused by the adverse pressure gradient and its evolution process in the turbulent flow field were analyzed. The effect of different VG spacings on the suppression of the boundary layer separation were compared through the distance between vortex cores, the kinetic energy of the fluid in the boundary layer, and the pressure loss coefficient. Subsequently, the effect of VG spacings on the lift-drag characteristics, airfoil surface pressure distribution, and airfoil pressure loss were investigated in a wind tunnel using the DU93-W-210 airfoil as the research object.  
According to the relationship between the vortex core radius and the distance between the vortex cores, when the VG spacing was \(\lambda/H=3\), the distance between the vortex cores \(\Delta z/2\) was smaller than the vortex core radius \(r\) in most positions along the flow direction. Therefore, this spacing inhibited the development of vortices. When \(\lambda/H=7\) and 9, \(\Delta z/2\) was always larger than \(r\). When \(\lambda/H=5\), at \(x/H\) = 10, the \(\Delta z/2\) and the \(r\) were approximately equal. Thus, the \(\lambda/H=5\) spacing was more suitable for flow control. The increase in fluid kinetic energy in the boundary layer was inversely proportional to the VG spacing. However, when the VG spacing was \(\lambda/H=3\), the distance between vortices was small and the vortex core was far from the wall, resulting in the high-energy fluid in the downstream boundary layer being higher from the wall. In the near-wall region, the kinetic energy of the fluid was the largest when \(\lambda/H=5\), especially at the \(x/H=35\) cross-section. When \(\lambda/H=5\), the \(C_{\Delta P}\) between the inlet and outlet of the computational domain was the smallest, which was by 30.95% lower than that in the computational domain without VGs.  
In the wind tunnel experimental results, it was found that the stall AoA of the airfoil with VGs was increased by \(10^{\circ}\) compared to that of the clean airfoil. When \(\lambda/H=5\), the maximum lift coefficient of the airfoil with VGs increased by 48.77%, which was the largest increase. Furthermore, at an AoA of \(18^{\circ}\), when \(\lambda/H=5\), the drag coefficient decreased by 83.28%, which was the largest reduction. At an AoA of \(18^{\circ}\), the lift-drag ratio of the airfoil increased by 741.03% when \(\lambda/H=3\), 821.86% when  
Figure 19: Distribution of total pressure coefficient at the wake rake.  
\(\lambda/H=5\), 612.06% when \(\lambda/H=7\), and 55.06% when \(\lambda/H=9\). Consequently, it can be deduced that, when the VG spacing was \(\lambda/H=5\), the comprehensive effect of airfoil flow control was the best. The optimization of the VG spacing was essentially the optimization of vortex scale and vortex core spacing. The vortex scale and vortex core spacing were related to the VGs installation angle, geometric height, and arrangement spacing.  
[PERSON]-k.L., [PERSON], [PERSON]-j.Z., and [PERSON]-m.W. conceived the research idea. [PERSON]-k.L. and [PERSON]-d.W. performed the numerical simulation. [PERSON]-m.W. and [PERSON]-j.Z. analyzed data and numerical results. All authors contributed to the writing, editing, and revising of this manuscript.  
This work was jointly supported by the National Natural Science Foundation of China (no. 51806221) and the Development Plan of Key Scientific and Technological Projects of China Huadian Engineering Co., LTD (CHEC) (no. CHECKJ 19-02-03).  
The authors declare