Development of Design Method for Supersonic Turbine Aerofoils Near the Tip of Long Blades in Steam Turbines: Part 2 — Configuration Details and Validation

Both inflow and outflow velocities near the blade tip become supersonic when the blade length exceeds a threshold limit. The aerofoil near the tip of such a long blade has four features that demand an original supersonic turbine aerofoil design: supersonic flow in the entire field, high reaction, large stagger angle, and large pitch-to-chord ratio. This paper describes design method development for the supersonic turbine aerofoil. First, the aerofoil shape is defined using a curve with continuity in the gradient of the curvature. Second, six loss generation mechanisms are clarified by turbulent flow analysis. Third, an allowable design space between the pitch-to-chord ratio, the stagger angle and the axial-chord-to-pitch ratio is clarified by formulating three geometrical constraints to accelerate supersonic flow smoothly. When there is no solution in the theoretically allowable design space because of the large pitch-to-chord ratio, methods to reduce shock wave losses are proposed. Increasing the outlet metal angle of the pressure surface by around 10 deg from the theoretical outlet flow angle reduces the loss caused by the trailing shock wave. The physical mechanism for this is as follows: the increased outlet metal angle increases the outlet flow passage area so that the overexpansion is suppressed downstream from the flow passage. Fourth, both a cusped leading edge and an upstream pressure surface which has both an angle corresponding to the inflow angle and near-zero curvature can reduce the loss caused by the leading shock wave and satisfy the unique incidence relation. Finally, the aerodynamic performance of the supersonic turbine cascade and the design method are validated by supersonic cascade wind tunnel tests.