Aerodynamic shape optimization using a time spectral coupled adjoint for nonlinear aeroelastic problems

Abstract

In this work, prediction of flutter and Limit Cycle Oscillations (LCO) for the aircraft wing has been carried out using a coupled, time spectral computational fluid dynamics (CFD) and computational structural dynamics (CSD) method. Flutter related shape design has also been carried out using a coupled, adjoint based sensitivity analysis framework. A discrete adjoint solver was developed in time-spectral form to calculate coupled sensitivity of the dynamic aeroelastic motion. The total structural energy was constrained at different levels to determine the flutter onset conditions or different LCO solutions. Compared to the time-marching approach, the time-spectral method not only enables faster convergence for unsteady problems, but also leads to significant improvement in implementation of adjoint based sensitivity analysis. Unlike the time-marching approach, there is no high memory requirement for time-spectral approach. The proposed method was applied to a pitch-plunge airfoil section at transonic flight conditions. The flutter and LCO results showed great agreements with time-marching results. The adjoint based sensitivity values were validated by finite difference based results, showing great agreement with errors less than 2%. Finally, aerodynamic shape optimization was carried out with the design objective of maximizing the flutter velocity, with and without constraint on the drag coefficient, respectively. Significant increase in flutter boundary velocity was observed in both cases.