Unsteady supersonic cascade theory including nonlinear thickness effects

Abstract

Several problems are treated which arise in the study of generalized airforces in unsteady supersonic cascades having subsonic axial velocity. The finite cascade of oscillating wedges is first solved numerically. When the thickness is very small, the general nonlinear solution agrees with results based on the linear theory of characteristics, while for the single wedge oscillating near shock detachment it agrees closely with Carrier's exact solution. There is some indication that thickness effects are reduced by cascading. Next, the finite cascade of oscillating flat plates is solved analytically, to the third power of oscillation frequency. The generalized surface pressure is shown to agree with exact numerical results for moderate blade index, but diverges in the far field of the cascade. For comparison with the finite cascade, there is presented finally an elementary periodic solution for the infinite cascade. A simple relationship between the two basic cascade models is developed. The investigation is presently restricted to flow regions upstream of Mach wave reflections in the blade passages.