Model Order Reduction for Aeroelastic Analysis of Very Flexible Aircraft

With increasing requirements for lower emissions and costs, next-generation transport aircraft are poised to deal with high-aspect-ratio wings. Long light-weight structures are naturally flexible, and this fact brings new challenges to the aeroelastic analysis. Time-domain simulation of these nonlinear systems is desirable to analyze their aeroelastic behavior over the flight envelope. In the structural end, while simplified methods exist to model slender wings with equivalent nonlinear beams, essential details can only be captured with built-up finite element models. Unfortunately, these models are expensive and non-robust for extensive dynamic simulations. This dissertation builds upon previous efforts to develop nonlinear modal reduced-order models (ROMs). Through a series of nonlinear static solutions with large displacements as training data, stiffness terms and higher-order displacements are identified as functions of the modal degrees of freedom. A combination of linear modes and supplementary shapes called dual modes can accurately represent large displacements. A static condensation process allows the inclusion of dual modes in the equations of motion, keeping only the original degrees of freedom associated with the linear modes. Accounting for the inertia forces related to the dual modes is a significant contribution of this thesis to allow accurate simulations under large displacements. The developed nonlinear modal ROMs based on the newly-introduced Enhanced Implicit Condensation and Expansion (EnICE) process achieves computational time savings of orders of magnitude relative to the original 3D built-up finite element simulations. The EnICE approach was integrated into the computational fluid dynamics code CFL3D for high-fidelity aeroelastic analyses. This environment is later used as a source of reference data to build an aerodynamic ROM. This is based on (linear) convolution corrected by a (nonlinear) correction factor obtained from steady aerodynamic solutions. To reduce the number of steady aerodynamic solutions and speed up the process, the correction factors are obtained from the Method of Segments (MoS). Finally, the MoS evaluation process was modified from using local geometric angles of attack to local induced angles of attack, which improved the correlation of the aerodynamic ROM and the reference CFD solution particularly in transonic regime. Among the contributions of this dissertation, the integration of the CFL3D code with a nonlinear modal solution represents a significant step towards the development of cost-effective high-fidelity analysis for geometrically nonlinear, very flexible structures. Due to the capability of the modeling approach to handle arbitrarily complex structural representations, it allows one to model realistic aircraft structures. Moreover, the modal-like nature of the nonlinear structural representation allows a direct modification of existing CFD-based aeroelastic analysis codes by enhancing its coupled structural model and creating a new enhanced framework for high-fidelity nonlinear analysis. The aeroelastic solution arising from the two reduced-order models is capable of large displacement simulations, taking into account structural and aerodynamic nonlinearities. Employing a correction factor on top of a linear convolution from step responses proved to be a good strategy for the case of incompressible flow analyzed with large displacements and angles of attack. However, the errors were higher for a transonic case. At the end, significant reductions in simulation time were achieved by using the reduced order aeroelastic model when compared to the high-fidelity one. Accuracy may be increased in future investigations by adjusting the reference condition around which the correction factors are evaluated.