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4.3-2 Flow Field in the Mid-span Region Fig. 1. Streamlines and static pressure distribution in the mid-span plane along blade passage. Source: See Note 56 (Acharya). Fig. 2. Flow yaw angle (deg) contours in mid-span plane along blade passage. 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 364PDF Image | Turbine Blade Aerodynamics
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