Aerodynamic Indicial Response and Stability Derivatives of a Rotor Annulus

Abstract

The key to finding the aerodynamic forces acting on a rotor in arbitrary rigid-body motion is its response to indicial input of its individual degrees of freedom. A theory is developed to find such indicial responses for an unloaded rotor annulus moving in its own plane. New rational approximations in the complex-frequency domain are used to find the corresponding transient cascade forces for incompressible flow. The indicial response consists of an initial impulse and an oscillatory decaying part for force components parallel and perpendicular to the applied motion. The harmonic response is also found and is expressed in terms of complex “rotor-stability-derivatives,” which are essentially the direct-and cross-coupled frequency dependent damping or stiffness force coefficients. Both responses are obtained explicitly in terms of the unsteady cascade characteristics and reduced frequency or time. Parametric studies indicate lowered damping, aerodynamic spring-softening and cross-stiffness whirling forces dependent on the upstream dynamic pressure for perturbation frequencies near the rotor speed.