## 3 Results and Discussion
### Effect of Wake on the Integrated LPT-GV
Because of the wake dissipation and the interaction between the roll-up vortex induced by wake vortices [34] and the boundary layer, the boundary layer loss coefficient was high in the wake sweeping cycle, especially after the wake-induced transition (Line T), as shown in the green and red color blocks between Line A and Line B in the lower row of Figure 14. Comparing the different cases, with increasing \(d/s\), the enhanced wake promoted the early transition of the boundary layer, and the wet area of the turbulent boundary layer with a high boundary layer loss coefficient (the red block behind Line T) expanded in the lower row of Figure 14. For example, when \(d/s\) = 0.122, the front point of the boundary layer transition was 0.065C\({}_{x}\) earlier than that of the \(d/s\) = 0.078 case. Overall, wakes could not only reduce the losses by suppressing separation bubbles but also increase viscosity loss due to the increasing wet area of the turbulent boundary layer, which indicated that a comprehensive balance of these two factors was the key to the effective use of sweeping wakes. Before discussing the influence of the upstream wake on vortices, its origin and distribution in the integrated LPT-GV passage must be briefly introduced. Figure 15 shows the vortex distribution in the LPT-GV passage when \(d/s\) = 0.078. The upstream boundary  
Figure 14: Space-time diagram of the boundary layer shape factor and loss coefficient when \(d/s\) = 0.078, 0.10 and 0.122.  
layer rolled up at the leading edge of the LPT-GV and moved downstream along the blade, resulting in a horseshoe vortex in the upper and lower regions. This vortex with a small scale was generally confined in the boundary layer of the hub or shroud. In the upper-end region of LPT-GV, the pressure surface branch of the horseshoe vortex moved toward the suction surface under the circumferential pressure gradient, continuously entrained the low momentum fluid in the end region, and then developed into a passage vortex. After reaching the suction surface, because of the radial secondary flow from the shroud to the hub at the rear of the LPT-GV, this passage vortex moved down radially and finally split into two vortices: one of the vortices moved down radially, as shown by PV3 in Figure 15; the other vortex continued to move downstream along the blade root and then split into two vortices again by the pull of radial secondary flow when it grew large enough, as shown by PV1 and PV2 in Figure 15. Because of the weakening radial pressure gradient, this passage vortex only split once when \(d/s\geq 0.10\), resulting in PV1 and PV3 vortices in Figure 15. A small-scale corner vortex was near the shroud. In the lower end region, there was also a passage vortex based on the same formation mechanism mentioned above. Under the radial pressure gradient at the rear of the LPT-GV, this passage vortex did not grow upward radially but concentrated around the blade root. There were also two small-scale vortices--the counter vortex and the corner vortex--as shown in Figure 10:0 For the interaction and mixing process between different vortices, the readers can refer to [32; 39; 41]. Figure 16 shows the total pressure coefficient contour of five streamwise sections in the LPT-GV channel when \(d/s=0.078\), \(0.10\) and \(0.122\). When \(d/s\leq 0.10\), due to the abovementioned radial upward secondary flow, the low-energy fluid was enriched near the shroud (as shown in Figure 11b,c), resulting in a thick boundary layer on the shroud, as shown by 'TBL' in Sections C1 and C2 in Figure 10:1 In contrast, when \(d/s>0.10\), because the radial pressure gradient was weakened by the stronger sweeping wake, the boundary layer of the shroud (as shown by 'BL' in Sections C1 and C2 in Figure 16) was thinner than that of the case with a small \(d/s\), but the total pressure coefficient near the shroud (h/H = 0.7\(\sim\)1.0) still decreased because of the dissipation of strong wakes.