## 3 Results and Discussion
### Influence on Flow Mechanism of Integrated LPT-GV  
On the basis of the above conclusion on the wake propagation in various \(f\) cases, the influence of the residual wakes on the unsteady flow mechanism of the integrated LPT-GV such as flow separation, vortex dynamics, and loss mechanism is analyzed below. Figure 6: Radial distribution and contour of the \(\mathrm{Cp_{0}}\) in Section B6. Figure 7 compares the instantaneous limiting streamline on the integrated LPT-GVs' suction surface in the cases with \(f\) = 0.71, 0.90, and 1.61. At t = 0.2 T and t = 0.4 T, before the wake center reaches the separation bubble, upon comparing the limiting streamline in the cases with different \(f\), the size of the separation bubble (between the red separation Line S and orange reattach Line R in Figure 7) at the same moment decreases with the increasing \(f\), which means that the separation bubble of the LPT-GV can be suppressed in advance by increasing the reduced frequency. This is because the turbulence intensity in the interval between the adjacent wakes (as shown in Section B6 of Figure 6) is promoted as the wake diffusion is accelerated with increasing \(f\). As the wake center reaches the separation bubble of the LPT-GV (such as t = 0.6 T and t = 0.8 T in Figure 7), the wake can completely inhibit the separation bubble in all cases studied in this paper, but the radial range of the suppression (marked by \"W\" in Figure 7) decreases with increasing \(f\). This is because the width of the wake vortex band is narrowed by its enhanced elongating effect in the high \(f\) cases. After the sweeping wakes pass (t = 1.0 T), the separation bubble size recovers to its original level. The separation bubble of the LPT-GV in the case of \(f\) = 1.61 is smaller than that in the other two cases, which is related to the enhanced turbulence intensity between adjacent wakes in the high \(f\) cases. Figure 8 shows the space-time diagrams of the loss coefficient (\(\xi\)) and shape factor (H\({}_{12}\)) at the integrated LPT-GVs' midspan in the cases of \(f\) = 0.71, 0.90, and 1.61. Based on the empirical criterion [24], the wakes' leading edge (A)/trailing edge (B)/centerline (L), the transition location (T) and the calm zone bounds (C) are also marked in Figure 8. The H\({}_{12}\) is defined as the ratio of the displacement thickness to the momentum thickness: a smaller H\({}_{12}\) generally indicates the boundary layer velocity profile is fuller; on the contrary, a larger H\({}_{12}\) tends to mean a concave velocity profile, which usually suggests that the boundary layer separation has occurred [29]. Based on the experimentally verified conclusions, the boundary layer of LPT has been separated when H\({}_{12}\) > 3.5 [26]. Compared with the spatiotemporal range of the separation bubble identified by the isoline of H\({}_{12}\) = 3.5 in the cases of \(f\) = 0.71, 0.90, and 1.61, the maximum axial dimensions of the separation bubble are 0.119C\({}_{x}\), 0.116C\({}_{x}\), and 0.101C\({}_{x}\), respectively, while the peak values of H\({}_{12}\) characterizing the separation bubble thickness are 6.5, 6.45, and 5.75, respecti  
Figure 7: The instantaneous limited streamline on the integrated LPT-GVs’ suction surfaces (red dashed line: leading edge of separation bubble; orange dotted line: reattachment line; PV@H: passage vortex near the hub; PV@C: passage vortex near the casing; W: the radial range of the wake suppression). separation bubble length and thickness decrease with the increasing \(f\). This is because the separation bubble size recovered after the wake passes, though is suppressed to a certain extent by the enhanced turbulence intensity in the interval between adjacent wakes (as shown in Section B6 of Figure 6) in cases with high \(f\). However, with increasing \(f\), the duration of the recovered separation bubble increases: in the case of \(f\) = 0.71, 0.90, and 1.61, the maximum existence times of the recovered separation bubble were 0.48 T, 0.50 T, and 0.58 T, respectively.