## Secondary flows and tip leakage vortex

At zero tip clearance in fig. 3.11, the passage vortex Vv develops soon after the flow enters the blade passage at X/Cx = 0.15 with a clockwise sense of rotation when looking in the direction of flow in fig. 3.11(b)-(e). The suction leg of the horseshoe vortex Vsh can also be detected from the same figures. Though weak, it lies close to the suction surface but is lifted off from the endwall, with an opposite sense of rotation to the passage vortex. On the plane at x/C = 0.45 in fig. 3.11(g)-(j), the vortex system is complex - a series of vortices integrates to form one strong passage vortex (Vp). The distinction between the passage vortex and the suction leg of the horseshoe vortex is difficult to tell, probably due to the fact that the suction leg of the horseshoe vortex revolves around the passage vortex and could be considered as part of the larger passage vortex, as suggested by Wang et al. (1997). At position X/Cx = 0.90 in fig. 3.11(l)-(o), we can see the large passage vortex Vp emerging from the blade passage near the trailing edge is strong and rotates in the counter-clock direction when looking upstream from the trailing edge.

At tip clearance level of 0.86%C in fig. 3.12(b)-(e), the passage vortex Vp is still very strong near the leading edge (X/Cx = 0.15) and the suction leg of the horseshoe vortex Vsh can also be detected, while the leakage flow is difficult to see in the pictures. At the middle blade positions of X/Cx = 0.45 and x/C = 0.45 in fig. 3.12(f)-(o), the large passage vortex (Vp) rotating in the clockwise direction can be clearly identified, although the tip leakage vortex Vti is rather weak, some fluids emerging from the tip clearance at the suction side is appears to be incorporated into the passage vortex in the pictures.

For tip clearance level of r/C = 1.72%, we can find the passage vortex Vv coexists with the small amount of tip leakage vortex (Vu) emerging from the suction side of the tip clearance at X/Cx = 0.15 in fig. 3.13(b)-(e). The leakage vortex has the same sense of rotation as the suction leg of the horseshoe vortex Vsh, and perhaps combines with the horseshoe vortex during the development, while the passage vortex remains strong and rotates in the opposite direction. In fig. 3.13(g)-(j) at X/Cx = 0.45, a relatively strong passage vortex still can be observed. Similar to that observed by Yamamoto (1988), the weak leakage vortex Vti from the suction side of the tip clearance is drawn into the large passage vortex, which eventually develops into one large passage vortex Vp in pictures at position x/C = 0.45 in fig. 3.13(l)-(o).

At a higher tip clearance level of r/C = 3.45% in fig. 3.14(b)-(d), the passage vortex Vp is not well developed at X/Cx = 0.15. In fig. 3.14(f)-(h), the passage vortex is much simpler and in a pattern quite different from those with small tip clearance at position X/Cx = 0.45. We can also observe that the tip leakage vortex Vti becomes stronger and bends down in an opposite sense of rotation to that of the passage vortex, pushing the passage vortex away from the suction surface. At X/Cx = 0.90 in fig. 3.14(j)-(l), the much smaller passage vortex rotates under the tip leakage vortex coming out of the tip clearance with a different sense of rotation is displayed.

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