Reduced order models in unsteady aerodynamics

Abstract

A review of the status of reduced order modeling of unsteady aerodynamic systems is presented. Reduced order modeling is a conceptually novel and computationally efficient technique for computing unsteady flow about isolated airfoils, wings, and turbomachinery cascades. For example, starting with either a time domain or frequency domain computational fluid dynamics (CFD) analysis of unsteady aerodynamic 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 aeroelastic analysis of active control for flutter or gust response. As an alternative to the use of eigenmodes, Proper Orthogonal Decomposition (POD) is also explored and discussed. In general POD is an attractive alternative and/or complement to the use of eigenmodes in terms of computational cost and convenience. Balanced modes, a concept widely used in control engineering, are also briefly discussed, as are input/output models. Numerical results presented include a discussion of the effects of discretization and a finite computational domain in the CFD model on the eigenvalue distribution, the effects of the Mach number and viscosity on reduced order models and representative results from linear and nonlinear aeroelastic analysis. Recent results for transonic flows with shock waves including viscous and nonlinear effects are emphasized.

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