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4.3 Turbine Blade Aerodynamics vortex clearly appears much weaker and smaller than the passage vortex at this location in the vane passage. However, the relative arrangement of the passage vortex and suction side leg vortex at SS-3 in figure 16 is different than that observed at plane H in figure 12. The evolution of the passage vortex structure along a linear vane cascade and downstream of a linear vane passage show qualitative similarity with those found in figures 12, 13, and 1639. 4.3-7 Aerodynamics of 3-D Cascade A three-dimensional cascade is usually formed when the linear or twisted blade or vane profiles are stacked in an annular passage. Thus, the flow area in the cascade passage increases from the hub side to the tip side of the adjacent blades. Because of this passage structure, a radial pressure gradient is added to the flow everywhere in the annular passage40. This radial pressure gradient directing towards the hub neutralize the radially outward centrifugal force experienced by the free-stream fluid which is in equilibrium across the annular passage. The radial pressure gradient increases from the pressure side to suction side41. The data in figure 17, adopted from Sieverding et al., show the static pressure coefficients and secondary velocity vectors across an axial plane slightly upstream of the passage exit of an annular vane cascade. In the figure, the difference in static pressure coefficient between the hub and casing is higher on the suction side than on the pressure side. The effects of such pressure gradients are greater at the passage exit than within the passage. The vectors show the formation of the passage vortex near the hub and casing side. The radial displacement of the vortex centers are mostly the consequence of the pitchwise cross flow rather than the radial pressures as observed in a linear cascade. The total pressure losses near the hub and casing walls due to the two passage vortex structures are also nearly identical. However, in the same study, the total pressure losses at the passage exit are found to be asymmetric with respect to the spanwise meridian unlike that observed across a linear cascade. The total pressure losses downstream of the cascade are considerably higher near the hub wall than those near the casing42. This is attributed to the influence of the radial pressure gradient. Near the endwall in the passage, the streamwise velocity decreases in the boundary layer and the secondary flow region. As a consequence the centrifugal force generated from the circumferential component of the streamwise velocity decreases near the endwalls. But, the radial pressure gradient remains unchanged. Thus, the non-equilibrium behavior near the casing results in the reduced total pressure loss there. *The original version of this material was published by the Advisory Group for Aerospace Research and Development, North Atlantic Treaty Organization (AGARD/NATO) in AGARD Conference Proceedings CP- 469 ”Secondary Flows in Turbomachines” in 1990. Fig. 18. Total pressure loss coefficients at exit plane of a linear and an annular cascade. Source: See Note 13.* (Moustapha) Fig. 19. Spanwise distribution of pitchwise averaged total pressure loss coefficient for linear and annular cascades in Fig. 18. Source: See Note 13.* (Moustapha) 374PDF Image | Turbine Blade Aerodynamics
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