A Method for Transonic Inverse Cascade Design With a Stream Function Equation

Abstract

A new profile design method is developed on the basis of [1–3] for transonic flow. The rotational dynamic stream function equation, which is expressed in functional form using calculated coordinates, is deduced. This method can be used for the calculation of cascade and S1 stream surface of a transonic flow with a local shock wave on the blade suction surface. This method consists of two parts: an inverse method with a given velocity distribution along the suction surface and a given thickness distribution; and an inverse method with given velocity distributions on suction and pressure surfaces. Using this method it is easy to obtain a blade profile with prescribed velocity and thickness distributions. The design of optimal profile may then be done with the calculated optimal velocity distribution on the blade surface. The rotational condition is satisfied when the stream function equation is adopted with the entropy term. If the compatibility condition can be fulfilled between the S1 and S2 equations, the iterative calculations of two kinds of stream surfaces in three-dimensional flow will be convergent. In this paper a unique value of density can be determined from the known stream function value. The computational program is written with this method and several transonic examples have been calculated. These results are quite good.