Using ROMs and adjoint-ROMs to optimize the flow past pitching-plunging wings

When an arbitrary new motion trajectory is explored to improve aerodynamic performance of the flow past pitching-plunging wings, the large control space makes most optimization efforts too expensive to be feasible. In this work, an adjoint-based method is used to study and optimize the flow past a pitching-plunging NACA0012 airfoil. The advantage of an adjoint-based method is to keep the computational cost independent of the number of control parameters. However, adjoint-based optimization using direct numerical simulation (DNS) may still be expensive because the optimization process requires many iterations with DNS and adjoint-DNS computations. To further improve the optimization efficiency for potential real-time applications, this work developed approaches to build and integrate reduced-order models (ROM) and adjoint-ROMs in an optimization scheme. Three control parameters are studied: plunging amplitude, pitching amplitude, and the phase delay between pitching and plunging motions. It is shown that the adjoint approach using ROMs can drastically reduce the optimization cost while reaching the same optimal solution achieved by the adjoint approach using DNS.