EULER-BASED INVERSE METHOD FOR TURBOMACHINE BLADES .1. 2-DIMENSIONAL CASCADES

A three dimensional inverse method for the aerodynamic design of turbomachine blades using robust time-marching algorithms for the numerical solutions of the Euler equations is proposed. In this inverse method, the circumferential mass-averaged tangential velocity (or the blade loading) is the primary specified flow quantity, and the corresponding blade geometry is sought after. The presence of the blades Is represented by a periodic array of discrete body forces which is included in the equations of motion. A four-stage Runge-Kutta time-stepping scheme is used to march a finite volume formulation of the unsteady Euler equations to a steady-state solution. Modification of the blade geometry during this time-marching process is achieved using the flow-tangency conditions along the blade surfaces. In this paper, the method is demonstrated for the design of two-dimensional infinitely thin cascaded blades ranging from the subsonic to the supersonic flow regimes, including cases with rotational hows and complex shock structures in the flow passage.