Unsteady aerodynamic force modeling via proper orthogonal decomposition rom

A method for constructing reduced-order models (ROMs) of unsteady flows is presentedusing mode-based method. The mode vectors, developed from correlation matrix formed with thesnapshots in full-order system, are used for a Galerkin projection. Singular Values Decomposition(SVD) is then used for system proper realization. Results are obtained for reduction of three highorder systems: (1) an arbitrary state-space system with order (n = 406), allowing some insightsinto the performance of the method, (2) two-dimensional airfoilaeroelastic system with order (n =4800), and (3) AGARD 445.6 wingaeroelastic system with order (n = 239400). In the second case,basis procedure for Mode-based ROM is presented in detail. First, Linearized unsteady EULERmodels are derived to obtain snapshots either in time domain or frequency domain. Then modevectors are computed, allowing that reduced subspace project on full order system to derivemode-based ROM. The reduced order model obtained by the method captured the full ordersystem dynamics and is especially efficient in frequency domain. Finally, the method was appliedfor a practical wing system-AGARD 445.6. Flutter boundary of the wing was identified withROM, and the result agrees well with CFD/CSD direct coupling. All the results indicate thatmode-based ROM is efficient and accurate enough to provide a powerful tool for aeroelasticsystem analysis.