Eigenmode analysis in unsteady aerodynamics: Reduced-order models

A conceptually novel and computationally efficient technique for computing unsteady flow about isolated airfoils, wings, and turbomachinery cascades is presented. Starting with either a time-domain or frequency-domain computational fluid dynamics analysis of unsteady aerodynamic or aeroacoustic hows, a large, sparse eigenvalue problem is solved using the Lanczos algorithm. Then, using just a few of the resulting eigenmodes, a reduced-order model of the unsteady flow is constructed. With this model, one can rapidly and accurately predict the unsteady aerodynamic response of the system over a wide range of reduced frequencies. Moreover, the eigenmode information provides important insights into the physics of unsteady flows. Finally, the method is particularly well suited for use in the active control of aeroelastic and aeroacoustic phenomena, as well as in standard aeroelastic analysis for flutter or gust response. Numerical results to be presented include 1) comparison of the reduced order model to classical unsteady incompressible aerodynamic theory, 2) reduced-order calculations of compressible unsteady aerodynamics based on the full potential equation, 3) reduced-order calculations of unsteady how about an isolated airfoil based on the Euler equations, and 4) flutter analysis using the reduced-order model.