Eigenmode Analysis in Unsteady Aerodynamics: Reduced Order Models

TLDR

Reduced order modeling is a conceptually novel and computationally efficient technique for computing unsteady flow about isolated airfoils, wings, and turbomachinery cascades, and this review cites 25 references. The article reviews the current status of reduced order modeling for unsteady aerodynamic systems. The method begins with a CFD analysis of unsteady flow, solves a large sparse eigenvalue problem via the Lanczos algorithm, and uses a few dominant eigenmodes to construct a reduced‑order model that is validated against classical theory, compressible and viscous flow calculations, and flutter analysis. The reduced‑order model accurately predicts unsteady aerodynamic responses across a wide frequency range, provides physical insight through eigenmode data, and is especially useful for active control of aeroelastic and aeroacoustic phenomena as well as flutter or gust analysis.

Abstract

In this article, we review the status of reduced order modeling of unsteady aerodynamic systems. Reduced order modeling is a conceptually novel and computationally efficient technique for computing unsteady flow about isolated airfoils, wings, and turbomachinery cascades. Starting with either a time domain or frequency domain computational fluid dynamics (CFD) analysis of unsteady aerodynamic or aeroacoustic flows, 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 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 flow about an isolated airfoil based on the Euler equations, and 4) reduced order calculations of unsteady viscous flows associated with cascade stall flutter, 5) flutter analysis using the Reduced Order Model. This review article includes 25 references.