The purpose of this paper is development of the design method for supersonic turbine aerofoils. In particular, a design method is established for four fundamental parameters which determine the overall configuration of the aerofoils: inlet angle, outlet angle, pitch-to-chord ratio, and stagger angle.
The developed design method is constructed as follows. Three parameters of a velocity triangle, the inlet flow angle, inflow Mach number and pressure ratio, are selected as predetermined design parameters. The inlet angle is coincident with the inlet flow angle. The outlet angle is formulated as a function of the three design parameters using aerodynamic theory. An allowable design space between the pitch-to-chord ratio and the stagger angle is clarified by formulating three geometrical constraints to accelerate supersonic flow smoothly. The three geometrical constraints are the inlet and outlet flow passage areas derived from the design parameters and the no-inflection-point condition on the aerofoil surface. Good performance of supersonic turbine aerofoils designed by the developed method is confirmed using computational fluid dynamics. There is no strong shock wave.
When there is no solution in the theoretical allowable design space because of the large pitch-to-chord ratio required for low centrifugal stress, the following two methods enable the feasible design space to be enlarged without a large increase in the energy loss. One is to ease the restriction of the outlet flow passage area. The other is to increase the outlet flow angle of the pressure surface by about 10 deg in the axial direction from the theoretical angle. Their effectiveness is also validated by computational fluid dynamics.
