Parameter Adaptation of Reduced Order Models for Three-Dimensional Flutter Analysis

Abstract

The accurate prediction of flutter for large 3-D structures in the transonic flight regime requires the construction of high-fidelity models of the fluid system in order to represent the complex flow characteristics present in this nonlinear regime. The computational expense can be quite considerable when the model is large (many degrees of freedom) and/or long integration times are required to determine the stability properties of the flow. The computational expense of this type of flutter analysis on large systems makes it impractical for use as a tool in applications such as aircraft design, flight testing, or controller design. Recently, the proper orthogonal decomposition (POD) method has been used to construct reduced order models (ROMs) of the fluid system in order to reduce the computational expense of the flutter analysis. The POD method constructs a reduced basis by using either experimental or simulation data at a particular flight condition. The full fluid system is then projected onto this reduced basis in order to form the ROM which is used for the flutter analysis. Here, we investigate the robustness of the POD-based ROM constructed in the time domain in terms of its accuracy when used for flight conditions that are dierent from those at which the ROM was created. We construct a ROM of the fluid system and use it along with a modal representation of the three dimensional structure to perform time domain aeroelastic analyses at dierent freestream Mach numbers, pressures, and densities to define the flutter boundary. We compare these results to experimental data as well as full order nonlinear simulation data. The POD-based ROM is applicable to a very wide range of freestream pressures and densities mostly owing to the fact that the pressure and density only appear as a constant factor in computing the aerodynamic lift force. Thus, a single ROM constructed at a given Mach number can be used to perform aeroelastic analyses over a large range of pressures and densities which increases its application potential in a design process. However, as expected, the POD-based ROM does exhibit sensitivity to the Mach number. We present two interpolation methods for adapting the POD basis vectors to varying Mach numbers. The first approach uses a simple and conventional Lagrange interpolation. The second approach is based on interpolating the angles between the ROM subspaces. We demonstrate these approaches on the AGARD Wing 445.6