## 3 Results and Discussion
### Analysis of the CFD Calculation Results
Figure 9 shows the \(Q\) isosurfaces colored according to the velocity in the flow field (\(Q=1\times 10^{5}\)). Many disordered vortices were observed in the turbulent flow field without VGs. However, typical turbulent coherent structures could be distinguished. In the initial flow stage, under the fluid viscosity and shear stress, the vortices were rolled up near the wall (as indicated by A). Due to self-rotation of the vortices, the radius of the vortex cores increased gradually downstream. At the same time, disturbed by the three-dimensional flow field, the vortices fluctuated extensively, twisted, and protruded upward along the normal direction. The protrusion was induced by the self-rotation of the spanning vortices, which intensified the protrusion height (as indicated by B). Under the action of a shear flow, the vortices continued to stretch and lift, and gradually developed into closed upper end hairpin vortices with an opening at the lower end (as indicated by C). Moving backwards, the legs of the vortices extended and the head of the hairpin vortices became larger, forming a local high-shear layer. Under the action of the mainstream fluid, the vortex was stretched along the flow direction into a tube (as indicated by D). This indicated that in turbulent flows, the average length of the vortex tube was generally increased. The energy transport process from larger to smaller vortices and the viscous dissipation into heat is called the cascade principle. Figure 10 shows \(Q\) isosurfaces colored according to the velocity in the flow field (\(Q=1\times 10^{5}\)) as a result of the VG control. First, by comparing Figures 9 and 10, it can be found that without the VG control, many irregular vortices were generated downstream of the computational domain, while this number was reduced when the flow was controlled by VGs. By comparing the vortices under different VG spacings, it can be found that with the increase of the VG spacing, the height of the vortices increased. As it can be seen in Figure 10b, the presence of VGs created longitudinal vortices, and this fact organized the local vortex structure and further hindered the development and movement of the spanwise vortices. The vortices generated between two VGs rotated in opposite directions, thus the outward vortices of the VGs were \"suppressed.\" On the other hand, the upward forces at the inner side of the VGs were toward the center. Under the action of the two concentrated vortices, the inner extended vortices were \"raised\" to form hairpin-like vortices, and as the flow developed downstream, the concentrated vortices gradually merged with the leg of the hairpin-like vortices. The legs of the concentrated and hairpin-like vortices played an important role in the exchange of kinetic energy and energy dissipation near the wall. When \(\lambda/H=3\), the centralized vortices generated by the two VGs were so close to each other that the spanning vortices inside the VGs were not \"raised,\" but instead were fused together at a downstream location under a reverse pressure gradient, forming hairpin-like vortices. When \(\lambda/H=5\), the outer spreading vortices of the VGs were \"suppressed,\" while the inner spreading vortices were \"raised,\" forming regular hairpin-like vortices that moved downstream. When  
Figure 9: \(Q\) isosurfaces (\(Q=1\times 10^{5}\)) colored according velocity without VGs: (**a**) computational domain and (**b**) inlet section. \(\lambda/H=7\) and \(\lambda/H=9\), no regular hairpin-like vortices were developed on the inner side due to the large VG spacing. Such disordered turbulent structures were not conducive to the energy exchange in the near-wall region, which became prone to flow separation. Figure 11 shows vorticity isolines and spatial streamlines at five cross-sectional locations downstream of the VGs. First, as it can be seen in Figure 11a, the concentrated vortices generated by the VGs scrolled around the vortex core center and rotated in spirals.