Eigenanalysis of unsteady flows about airfoils, cascades, and wings

TLDR

A general technique for constructing reduced‑order models of unsteady aerodynamic flows about two‑dimensional airfoils, cascades, and three‑dimensional wings is developed. The method starts from a time‑domain small‑disturbance flow model, computes eigenmodes of an unsteady vortex‑lattice system, retains only the dominant modes, approximates the remainder with a static correction, and builds a reduced‑order model that can be embedded in aeroelastic flutter analyses. Once eigenmode data are available, the method enables inexpensive construction of reduced‑order models for any number of airfoil motion modes, and numerical examples confirm its accuracy and computational efficiency.

Abstract

A general technique for constructing reduced order models of unsteady aerodynamic flows about twodimensional isolated airfoils, cascades of airfoils, and three-dimensional wings is developed. The starting point is a time domain computational model of the unsteady small disturbance flow. For illustration purposes, we apply the technique to an unsteady incompressible vortex lattice model. The eigenmodes of the system, which may be thought of as aerodynamic states, are computed and subsequently used to construct computationally efficient, reduced order models of the unsteady flowfield. Only a handful of the most dominant eigenmodes are retained in the reduced order model. The effect of the remaining eigenmodes is included approximately using a static correction technique. An important advantage of the present method is that once the eigenmode information has been computed, reduced order models can be constructed for any number of arbitrary modes of airfoil motion very inexpensively. Numerical examples are presented that demonstrate the accuracy and computational efficiency of the present method. Finally, we show how the reduced order model may be incorporated into an aeroelastic flutter model.