Analytical method for subsonic cascade profile

A method of subsonic cascade design for axial-flow compressor is provided as follows. The equations of continuity and quasi-irrotationality are transformed into the potential-stream function coordinates. Then a Laplace equation can be deduced for an aerodynamic parameter 'Q'. The boundary conditions thereby are given as the distributions of velocity coefficients on the stagnation streamlines of both suction and pressure sides of a flow channel. The flow field is obtained from the analytical solution of the Laplace equation. Subsequently the field is turned back into the physical plane by differentiation and integration. Then the blade profile coordinates and the geometry of the cascade result from this analysis. The method has an advantage over other inverse methods in the fact that the flow field parameter 'Q' can be easily obtained from the analytical solution of the Laplace equation instead of the numerical solution of a complex differential equation. So the method is easy to be programmed and to save computing time. To illustrate the validity of the design method, two compressor stator blade profile with subsonic inlet Mach number were designed and compared with the method presented in ref. [3]. The good agreement between the two methods show the applicability of this method.