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4.3 4.3-1 Introduction Turbine Blade Aerodynamics The aerodynamics of the fl ow in a turbine stage (stator/rotor) is rather complex and is still the subject of many ongoing research activities in the gas turbine community. The fl ow is inherently three dimensional due to the vane/blade passage geometry with features such as twisting of the vane/blade along the span, clearance between the blade tip and the shroud, fi lm cooling holes, and end wall contouring1. The passage fl ow is characterized by boundary layer effects, secondary fl ows generated by the passage pressure gradients, and vortical fl ow structures such as the leading edge horse-shoe vortices, tip-leakage fl ow vortices, and corner vortices2. The effects of centrifugal-buoyancy, shock- boundary layer interaction, and fl ow interactions between the stator and rotor rows complicate the passage fl ow fi eld even further. Along the end walls, the fl ow structure is strongly three- dimensional with the passage vortex and coolant injection on the hub side and the tip-leakage vortex on the tip side. In the mid- span regions located away from the passage walls and outside the viscous shear layer, the radial fl ow is almost negligible and Sumanta Acharya the fl ow is effectively two dimensional. The fl uid dynamics in this region can then be based on two dimensional planar cascade fl ow studies without any signifi cant loss of information. The three dimensional complex fl ow structures near the hub endwall region and in the blade tip-shroud clearance have been simulated in annular vane/blade passages with and without rotating blade row3. Studies of the complex end-wall fl ows have also been performed in stationary cascades with three dimensional airfoil shapes4. The qualitative features of the passage fl ows, which comprise mainly of the passage crossfl ow (fl ow from the pressure side of vane/blade to suction side of adjacent vane/blade) and vortical fl ows induced by the leading edge, the corners, and the injected coolant fl ows have been studied in detail in stationary cascades and are considered to be similar in both stationary and rotating blade rows. The primary difference in the secondary fl ow structure between the blade passage and vane passage is that the Gazi Mahmood vortical fl ows and cross fl ows in the blade passage are stronger because of higher turning of the fl ows along the blade passage. Secondary fl ows are the major source of aerodynamic losses, which account for 35%-40% of all losses5 and thermal loading in the turbine passage, and thus require special considerations by the turbine designers. The primary objectives of this chapter are to present and analyze the features of the fl ow fi eld in the turbine vane/blade passage near the hub endwall and mid-span locations of the blade. Toward this effort, reported measurements and computations of Louisiana State University pressure, velocity distributions, fl ow turning angles, turbulence CEBA 1419B, Mechanical intensity, and vorticity distributions in the cascade test section Engineering Department are presented. Recent efforts to reduce the secondary fl ows by Baton Rouge, LA 70803 structural modifi cations in the passage are discussed. In this chapter, basic fl uid dynamic principles and mathematical models phone: (225) 578-5809 of the fl ow in the passage are not discussed, and the reader is email: [email protected] referred to notes 1, 2, and 6 for additional details6. Also details on the aerodynamic design methodology for the vane/blade passage are not presented. 363 4.3-2 Flow Field in the Mid-span Region Fig. 1. Streamlines and static pressure distribution in the mid-span plane Fig. 2. Flow yaw angle (deg) contours in mid-span plane along blade passage. along blade passage. Source: See Note 56 (Acharya). Source: See Note 56 (Acharya). Figure 1 shows the streamlines and static pressure distribution along the mid-span plane of the blade passage. Flow along the blade passage at the mid-span locations turns with the passage contour and essentially follows the ideal flow behavior except very close to the blade walls. At zero degree angle of incidence, the streamline splits at the stagnation point corresponding to the blade leading edge with one leg moving along the pressure side and the other leg moving along the suction side of the blade. The pressure gradient from the pressure side to the suction side leads to the development of secondary flows. These secondary flows and the endwall boundary layer produce deviations to the nearly-inviscid mid-span streamlines shown in figure 2. The flow turning angle, known as the yaw angle relative to the axial +X direction, at the mid-span plane through the blade passage is shown in figure 2. The yaw angle is nearly uniform along a constant pitch line from the pressure side to the suction side, and also changes uniformly along the axial length of the passage. The high yaw angle near the leading edge occurs because of the stagnation region where the streamlines sharply turn around the blade suction side. Figure 3 shows the distribution of the static pressure coefficient, Cp, which is determined from the difference of blade surface pressure and reference pressure at the passage inlet normalized by the passage inlet dynamic pressure. The lowest Cp on the suction surface corresponds to the location at the passage throat area where the flow velocity is the highest. The highest Cp is the stagnation point location on the blade section at the mid-span height. The pressure distribution does not change along most of the blade span or height except near the hub or tip region. The blade loading or lift that provides work on the turbine shaft is determined based on the area circumscribed by such pressure curves as shown in figure 3. The pressure side velocity increases steadily as the Cp decreases on the pressure side from the leading edge to the trailing edge. Along the suction surface, the velocity initially increases toward the throat, but starts to decline when it encounters the adverse pressure gradients downstream of the throat in a subsonic flow. The peak velocity in figure 3 corresponds to the location of the minimum Cp on the suction surface. Due to the adverse pressure gradient on the suction surface downstream of the minimum Cp, there is the potential of boundary layer separation from the suction-side blade surface near the trailing edge and this represents a major source of profile losses in the blade passage. Boundary layer separation at the blade trailing edge can also occur due to a finite trailing-edge thickness and can lead to a distinct wake region. For blade profiles with high loading, flow separation is a major issue. With increased loading on the blade surface, suction surface pressures are reduced, and the velocity and Mach number over the suction surface increases with the local Mach number reaching supersonic values. This leads to local shocks as schematically depicted in figure 3, and creates additional aerodynamic losses such as shock losses or wave drag7. Downstream of the shock, suction surface pressure rises in the adverse pressure gradient region and 364 Sumanta Acharya boundary layer separation can occur earlier leading to increased profile losses for the highly loaded blade. Refer to notes 5 and 8 for discussion on the limiting pressure and velocity distributions on the blade surfaces and provide guidelines to limit the wake region over a very small region at the trailing edge in the blade design8. 4.3-3 Flow Field in the Endwall Region The flow field near the hub endwall region of the blade passage is dominated by the boundary layer, strong pressure gradients, and cross flow in the pitchwise direction from the pressure side to the suction side. The resulting near-wall flow field is complex and consists of strong secondary flows and vortex roll-up9. When the endwall boundary layer approaches the blade row, a vortex is formed near the junction of the blade leading edge and the endwall. This vortex is termed as the leading edge horse- shoe vortex. The horse-shoe vortex splits at the leading edge, and propagates downstream into the passage on both the pressure side and the suction side of the blade passage forming two legs of the early passage vortex flows. Corner vortices are also induced in the corner formed by the blade and the hub endwall. Fig. 3. Pressure and velocity distribution on blade surface at The streamlines slightly above the endwall in figure 4 show different spanwise locations. some distinct features of the endwall boundary layer flow. These features are identified by the separation lines in the figure. The Source: See Note 56 (Acharya). streamlines along the blade leading edge bifurcate as they approach the saddle point. The saddle point is the location on the endwall where the zero degree incidence line meets the separation line and corresponds to the lowest friction velocity. The incoming endwall boundary layer detaches along the separation line, and secondary vortical flows are formed in the regions immediately downstream and adjacent to the separation line. This is indicated by the high concentration of the streamlines adjacent to the separation line. The strong reverse flow in the vortex regions counter the boundary layer streamlines causing them to be concentrated more densely near the separation line. The leading edge horse-shoe vortex immediately downstream of the saddle point is clearly evident in figure 4. The region between the separation line and the blade suction side in figure 4 represents the suction-side leg of the horse shoe vortex10.

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