Computation of unsteady two-dimensional inviscid flow in turbomachinery cascades

A numerical technique has been developed to solve the governing equations of motion for unsteady two-dimensional inviscid flow in turbomachinery cascades. The technique has been applied to the analysis of steady transonic flows in turbine cascades with the steady state solution computed as the asymptotic limit in time of the unsteady solution. The physical plane was transformed to a computational plane to eliminate nonuniform mesh intervals and to simplify the application of the boundary conditions. The full method of characteristics was employed for the boundaries in the leading edge region; the reference plane characteristics method was employed for all other boundaries; MacCormack's method was employed for all interior points. Two cases of turbine cascade flows were solved. The first case involved subsonic flow through the cascade. The second case involved subsonic inlet and discharge flows, but with transonic flow over a portion of the cascade passage. In both cases, the computed results are compared with cascade experimental data. The computed results for the cascade analysis are in good agreement with the experimental data.