Gradient based optimization using spectral formulation-based FSI and coupled sensitivity analysis

Abstract

In this study, gradient based optimization using efficient computational methods for fluid-structure interaction and corresponding coupled sensitivity analysis. Considering that many dynamic aeroelatic problems are periodic in nature, a spectral based formulation has been used to solve them. A harmonic balance method (HBM) is used for computational fluid dynamics and finite element method (FEM) is employed for computational structural dynamics. One of the advantages of the spectral based formulation is the computational efficiency obtained by eliminating transient flow solutions to reach a periodic steady state, through the solution approximation of a discrete Fourier series. Hence, dynamic aeroelastic problems are solved by the solution methods for the static aeroelastic problems. The biggest advantage is the availability of the steady form of the adjoint sensitivity analysis for the dynamically coupled system as computational time and memory requirement for the unsteady adjoint sensitivity analysis are avoided in the current study by directly using the steady adjoint formulation. Using the sensitivity information obtained from the adjoint analysis, shape optimization of the AGARD 445.6 wing has been carried out to minimize the Lift to Drag ratio. The wing surface has been parameterized using the amplitude of Hicks-Henne functions on the wing surface as the design parameters.