GUST RESPONSE ANALYSIS FOR CASCADES OPERATING IN NONUNIFORM MEAN FLOWS

The unsteady aerodynamic response of a subsonic cascade subjected to entropic, vortical, and acoustic gusts is analyzed. Field equations for the first-order unsteady perturbation are obtained by linearizing the time-dependent mass, momentum, and energy conservation equations about a nonlinear, isentropic, and irrotational mean or steady flow. A splitting technique is then used to decompose the unsteady velocity into irrotational and rotational parts leading to field equations for the unsteady entropy, rotational velocity, and irrotational velocity fluctuations that are coupled only sequentially. The entropic and rotational velocity fluctuations can be described in closed form in terms of the mean-flow drift and stream functions that can be computed numerically. The irrotational unsteady velocity is described by an inhomogeneous linearized potential equation that contains a source term that depends on the rotational velocity field. This equation is solved via a finite-difference technique. Results are presented to indicate the status of the numerical solution procedure and to demonstrate the impact of blade geometry and mean blade loading on the aerodynamic response of cascades to vortical gust excitations. The analysis described herein leads to very efficient predictions of cascade unsteady aerodynamic phenomena, making it useful for turbomachinery aeroelastic and aeroacoustic design applications.