A Rational Analysis of Periodic Flow Perturbation in Supersonic Two-Dimensional Cascade

An analytical formulation which can be applied to obtain unsteady aerodynamic solutions for a cascade of flat plate blades oscillating in subsonic or supersonic flow with either subsonic or supersonic axial velocity component is presented. In the analysis, the flow is assumed to be two-dimensional and isentropic and the blades are undergoing small amplitude harmonic oscillations. The method of superposition of basic wave solutions of the linearized unsteady flow equation is used to construct the flow field induced by the harmonic motion of blades in cascade. This method leads to an integral equation from which the unsteady loading on a blade can be determined. Since the equation applied to both subsonic and supersonic inlet conditions, the present approach provides a unified basis for analyzing and understanding the complex physical phenomena associated with flow past vibrating cascades. The technique used to determine a solution for an unsteady supersonic cascade is also described and the results obtained are shown to agree with those from previous solution.