Eigenmode Analysis of Unsteady Flows about Airfoils

Abstract

We present a reduced-order modelling technique for analyzing the unsteady subsonic aerodynamic flow about isolated airfoils. To start, we model the flow using the time-linearized full potential equation. The linearized potential equation is discretized on a computational mesh composed of quadrilateral elements using a variational finite element technique. The resulting discretized equations are linear in the unknown potential, but quadratic in the reduced frequency of vibration. We compute the dominant (low frequency) eigenfrequencies and mode shapes of the unsteady fluid motion using a nonsymmetric Lanczos algorithm, and then we use these eigenmodes to construct a low degree-of-freedom reduced-order model of the unsteady flow field. A static correction technique is used to account for the high-frequency eigenmodes not retained in the model. We show that the unsteady flow can be modelled accurately using a relatively small number of eigenmodes.