Double linearization theory for prediction of mean loading effect on cascade flutter, I: Two-dimensional subsonic cascade

Abstract

In this paper an improved mathematical formulation is given of the double linearization theory for predicting the mean loading effect upon the unsteady aerodynamic force for two-dimensional vibrating cascades in subsonic flows. The double linearization theory deals with both steady and unsteady components of disturbances on the basis of a linearized approximation on the assumption that the cascade is lightly loaded and vibrating with an infinitesimal displacement amplitude. The improvement is to take account of the effect of equivalent unsteady mass sources due to motion of blades with a steady fluid density jump between the upper and lower surfaces of blades. Unsteady aerodynamic forces on lightly loaded cascades predicted by the present theory show good agreement with predictions by numerical field methods and experimental data. The dependence of the flutter boundary upon cascade design parameters is demonstrated.