Aerodynamic Shape Optimization of unsteady flapping wings

This study introduces a new approach for building surrogate models, in the form of Reduced Order Models (ROMs), for PDE-constrained optimization. A physics-constrained data-driven framework is developed to transform large-scale non-linear optimization problems into ROM-constrained optimization problems. Unlike conventional methods, which suffer from instability of the forward sensitivity function, the proposed approach projects optimization problems to system dynamics optimization problems in Hilbert space to increase stability, diminish memory requirements, and lower computational cost. The present approach is applied to shape optimization of a 2D flapping wing section at $Re=2,400$, where the non-linear interaction of the wing with fluid includes chaotic flow structures. It is shown that the proposed approach can significantly enhance the time-averaged thrust force and propulsive efficiency by 37\% and 40\%, respectively. We also tested this approach for a 3D flapping wing and the results reveal the potential of the proposed approach for more complex optimal designs in the aerospace industry.