Unsteady blade rows in high-speed flow

Abstract : This report covers analytic investigations toward defining the instability boundaries of low incidence supersonic compressor flutter. A closed form expression was developed for the unsteady pressure distribution for a flat plate cascade in supersonic flow which is valid for a frequency range of practical interest. The work was extended to symmetric parabolic arc airfoils in cascade. Finite thickness was shown to have a first order effect on the flow field. Coupling the flow analysis with blade vibration modes indicates a bending instability in the frequency range of conventional design in general agreement with experimental data. An expression for the frequency of the unsteady pressure along the stationary rotor casing due to a vibrating blade row was derived. It indicates casing treatment tuned approximately to blade passing frequency and its harmonics should be effective in absorbing this unsteady flow energy.