Transonic Cascade Flow Solved by Separate Supersonic and Subsonic Computations With Shock Fitting

Abstract

A new method to solve the transonic flow past a plane cascade with inlet bow wave and a passage shock extending from the leading edge all the way across the flow channel is presented. In this method, different algorithms are used for supersonic and subsonic flow regions, respectively, and the aerothermodynamic relations of a connecting passage shock are satisfied. Within the supersonic region, the method of characteristics is used. For calculation of the subsonic flow, the stream function equation expressed with respect to nonorthogonal curvilinear coordinates and nonorthogonal velocity components is solved with a matrix method. By the use of Rankine-Hugoniot relations, the passage shock can be accurately determined and a definite jump of the aerothermodynamic quantities across the passage shock is obtained. All calculations involved are programmed and incorporated into a single code. The computational procedure is straightforward and simple, and the computational time is short. Some results of typical applications of this method are given in this paper. Agreement of the numerical results with the experimental data, including the location and shape of the passage shock wave, is very good.