Aeroelastic design optimization for laminar and turbulent flows

The design of flexible structures undergoing aeroelastic deformations is a challenging task, in particular if the prediction of the fluid loads and the evaluation of the aerodynamic performance criteria require accounting for laminar and turbulent effects. This paper presents a general optimization methodology for fluid-structure interaction problems based on turbulent flow models. The structure is modeled via a geometrically nonlinear finite element method. The flow field is computed by solving a finite volume approximation of the Navier–Stokes equations on moving grids augmented by turbulence models. The global design sensitivity equations are presented and solution methods for computing the numerically consistent and approximated design sensitivities are introduced. The accuracy of the sensitivity analysis methods are studied by numerical examples for three-dimensional problems. The potential of the overall optimization methodology is illustrated by the shape and thickness optimization of a realistic wing. The numerical examples suggest that the derivatives of the turbulence variables can be neglected in the sensitivity analysis without noticeable errors. Comparing the optimization results for Euler and Navier–Stokes flow models shows the importance of accounting for viscous laminar and turbulent effects for fine-tuning the design and obtaining reliable optimization results.