## 3 Results and Discussion  
### Analysis of the CFD Calculation Results  
Figure 7 shows time-averaged axial velocity contours on the symmetrical plane of the computational domain. As it can be observed, the channel expanded between 0-35\(H\), which led to an adverse pressure gradient (APG), and a continuous decrease in fluid velocity. Under the action of the APG and wall viscosity, flow separation occurred at the lower wall, and a low-velocity zone appeared. The flow separation position was approximately at \(x_{1}\approx 20H\). Since the free-slip wall boundary condition was adopted on the upper wall of the computational domain, no flow separation occurred. In the 35-135\(H\) section, there was a zero pressure gradient (ZPG), and flow reattachment occurred at \(x_{2}\approx 60H\). The axial velocity contours with VGs revealed that the VGs inhibited flow separation in all four cases. When the VG spacing was \(\lambda/H=7\), a small low-speed region appeared at \(x\approx 30H\). When the VGs spacing was \(\lambda/H=9\), the area of the low-speed region at the same location increased. This showed that when \(\lambda/H=9\), the effectiveness of the concentrated vortices at this location became weak, while the hydrodynamic energy was already low under the inverse pressure gradient due to the large spacing between VGs. No low-velocity zone appeared at the other two installations with a smaller spacing. Figure 8 shows the distribution of the pressure coefficient (\(C_{p}\)) on the bottom wall of the computational domain. In the no VG case, the inflection point of \(C_{p}\) appeared at \(x\approx 20H\), and the slope of the \(C_{p}\) change decreased. In the cases where the boundary layer flow was controlled by the VGs, the \(C_{p}\) on the wall increased in the APG section. Since no flow separation occurred, no alteration in the slope of \(C_{p}\) change in the APG section was observed. The \(C_{p}\) in most positions of the ZPG segment was basically 0. The difference between different VG spacings was primarily reflected in the turning position of the \(C_{p}\) curve. In particular, the larger the VG spacing, the smaller the slope of the wall pressure drop and the worse the flow control effect. After the fluid passed through the expansion section, the \(C_{p}\) increased. According to Figure 7, the flow separation occurred at \(x\approx 20H\). After the flow separation, the slope of the \(C_{p}\) drop decreased, while after the flow reattachment, no significant changes in \(C_{p}\) were observed in the ZPG section. Figure 6: Comparison of experiments: (**a**) lift coefficient and (**b**) drag coefficient. Although in some simple flows, the existence of vortices can be determined by intuition and visualization, in three-dimensional viscous flows, especially in complex flows, a large number of experimental or numerical simulation data are required to show the structure, evolution, and interaction of vortices. Therefore, it is necessary to give an objective discrimination of the vortices' criteria. At present, the \(Q\) criterion is more commonly used, where the region of \(Q>0\) is defined as a vortex, that is \(\left\|\Omega\right\|^{2}>\left\|\left|\mathrm{E}\right|\right|^{2}\). Its physical meaning is that the fluid rotation in the region of the vortex plays a leading role in comparing the strain rate. The specific formula is as follows:  
\[Q=\frac{1}{2}(\left\|\Omega\right\|^{2}-\left\|\mathrm{E}\right\|^{2}) \tag{6}\]  
Figure 8: Distribution of \(C_{p}\) on the bottom wall of the computational domain. Figure 7: Spanwise mean velocity contours on the plane of symmetry of the computational domain. where \(\left\|\mathbf{E}\right\|^{2}=e_{i}e_{ji}\) and \(\left\|\mathbf{\Omega}\right\|^{2}=\Omega_{ij}\Omega_{ji}=\frac{1}{2}|\omega|^{2}\), \(e_{ij}\), \(\Omega_{ij}\) are the strain rate tensor and the vorticity tensor, respectively. In this study, the \(Q\) criterion was used to identify the three-dimensional vortices in the flow field.