## 3 Results and Discussion
### Influence on Flow Mechanism of Integrated LPT-GV
This is because the significantly narrowed wakes band shortens the time for the inhibition of separation bubbles in cases with high \(f\). Reduction of the separation bubble length and thickness is beneficial to reduce the loss of the integrated LPT-GV, but the increased separation bubble duration will raise its loss. This indicates that adjusting the wakes' reduced frequency to balance the above two effects is the key to reducing the profile loss of the integrated LPT-GV. The loss coefficient characterizes the magnitude of the viscous loss in the boundary layer. As the separation loss is non-viscous loss, the _xi_ in the region corresponding to the separation bubble is small in Figure 8. Along with increasing \(f\), the separation bubble duration increases, resulting in the increasing width of the green color block (representing the low _xi_) and the decreasing _xi_. Within the sweeping interval of the wakes (Line A-B), _xi_ increases significantly with the wake-induced boundary layer transition. In the case of \(f\) = 1.61, the transition Line T is obviously behind that in the other two cases in Figure 8, and the yellow and red blocks representing the high _xi_, in the high \(f\) cases are located downstream of that in the low \(f\) cases, which indicates that _xi_, is obviously decreased in the high \(f\) cases. The leading edges of the isoline of _xi_ = 0.014 are located at 0.590C\({}_{x}\), 0.591C\({}_{x}\), and 0.604C\({}_{x}\) for the three cases shown in Figure 8, respectively. Therefore, the above two aspects indicate that the total boundary layer loss coefficient (i.e., viscosity loss) decreases with increasing \(f\). Figure 8: Space-time diagrams of the H\({}_{12}\) and _xi_ for various cases of \(f\) (Line A: right boundary of wake; Line B: left boundary of wake; Line C: bound of calm region; Line L: wake center trace; Line T: transition line). Figure 9 shows the time-averaged Cp\({}_{0}\) contour of Sections C1-C5 and the limiting streamlines on the LPT-GVs suction surfaces (marked by \"SS\") in the cases of \(f=0.71\), 0.90, and 1.61. In the upper area of LPT-GV channel, the low-momentum fluid migrates faster radially in the lower \(f\) cases (such as \(f=0.71\)) and accumulates on the shroud, which makes the boundary layer (the yellow blocks TBL in Section C1) on shroud significantly thicker than that in the higher \(f\) cases (such as \(f=0.90\)). The thicker boundary layer on the shroud is conducive to promoting the pressure surface (PS) branch of the horseshoe vortex at the leading edge of the LPT-GV to develop into a large-scale passage vortex (PV). As shown in Section C2, the PV size in the case of \(f=0.71\) is significantly larger than that in the case of \(f=0.90\). However, in the case with higher \(f\) (i.e., \(f=1.61\)), the PS branch of the horseshoe vortex entrains the residual wake vortices near the shroud (as shown by RWV in Section C1 for the case with \(f=1.61\)) and then develops into a large-scale passage vortex, as shown in PV in Section C2. Under the radial downward pressure gradient, some of those passage vortices detach from the shroud and continue to move radially downward along the suction surface, as shown by PV2 in Section C3-C5. Compared with the lower \(f\) cases, the passage vortex (PV2) has a larger scale in the case of \(f=1.61\). The sweeping wake can completely eliminate the flow separation in the middle of the LPT-GV, as shown by the smooth time-averaged limiting streamline. However, as mentioned above, the separation bubble recovered after the wake passes has a smaller axial dimension and thickness in the high \(f\) cases (such as \(f=1.61\)), so the time-averaged thickness of the boundary layer is thinner than that in the lower \(f\) cases. Near the hub, with increasing \(f\), the initial boundary layer becomes thicker and the passage vortices (PV3) seem to become stronger, but there was not much difference among the passages vortices. Figure 9: _Cont._  
Figure 10 compares the pitchwise mass-averaged \(\rm Cp_{0}\) in Section B9 for the three typical cases.