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Sumanta Acharya vortex. The vortex is confined in a region which is smaller than one boundary layer thickness from the endwall21. The endwall location where the reverse flow in the horse-shoe vortex meets the incoming boundary layer flow is termed as the saddle point which is generally located along the line corresponding to the zero degree incidence-angle as shown in figure 4. The center of the horse-shoe vortex is located in between the saddle point and the blade leading edge. The exact locations of the saddle point and horse-shoe vortex center depends on the radius of curvature of the blade leading edge and the oncoming boundary layer thickness. The flow visualization in figure 8 shows the typical formation of an instantaneous horse-shoe vortex at the blade leading edge in a linear cascade22. In the figure, the roll-up of the vortex is in the counter-clockwise direction. Periodically, a pair of horse-shoe vortices form that have the same relative size and the same sense of rotation. The time-averaged structure of the horse-shoe vortex obtained from a numerical simulation at the same blade leading edge is also shown in figure 8. The vortex structure is similar to the leading edge horse-shoe vortex in front of a cylinder23. The vortex center in figure 8 is located at the point of the maximum kinetic energy. At the corner of the leading edge, a small counter rotating vortex is induced by the large horse-shoe vortex. This clockwise rotating vortex is known as the leading edge corner vortex. Pressure side leg and suction side leg vortices: The path of the leading edge horse-shoe vortex is along the separation line shown in figure 4, and is driven by the endwall region pressure gradient and cross flow. The horse-shoe vortex essentially splits near the leading edge with one leg moving along the pressure side and the other leg moving along the suction side. These two primary legs of the horse-shoe vortex represent the origin of the major secondary flow system that develops in the blade passage. The two legs rotate opposite to each other. The pressure side leg of the horse-shoe vortex is driven along the separation line across the passage from the leading edge to the adjacent blade suction side. The suction side vortex leg wraps around the suction side from the leading edge along the separation line in figure 4. The vortices are termed as the right side clockwise and left side counter-clockwise vortices, respectively, in the flow visualization images in figure 924. The vortices in the figure are being viewed in the flow direction in pitchwise planes at different axial locations. The pressure side and suction side of the blade passage in the study are located on the right and left hand side, respectively, in the images. At location A, which represents the pitchwise plane going through the leading edge, a pair of vortex structures appears along both the pressure side leg and suction side leg of the vortex system. As with the leading edge horse- shoe vortex pair, these pairs form periodically from a single pressure side and suction side leg vortex. The vortices are very close to the passage pressure side and suction side at plane A. As the vortex legs advect to farther downstream locations at planes B, C, and D in the passage in figure 9, the endwall cross flow and pressure gradient from the pressure side to the suction side sweeps the pressure side leg of the vortex toward the suction side of the passage. As a result, the pressure side vortex approaches closer to the suction side leg vortex from the adjacent blade at the downstream locations. Nearly half way down the passage at Fig. 8. Typical horse-shoe vortex and corner vortex at a blade lead- ing edge. HS=horse-shoe, LE=leading edge, and Tke=turbulent kinetic energy. Source: See Notes 22, 56 (Acharya). Fig. 9. Flow visualization of pressure side leg and suction side leg vortices from. Vph= pressure side leg vortex and Vsh=suction side leg vortex. Source: See Note 9. 369 location D, the two vortex legs merge to form a single structurePDF Image | Turbine Blade Aerodynamics
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