Reduced-order modeling and adjoint-based optimization of flows with fluid-structure interactions

Abstract

Fluid-structure interaction (FSI) is ubiquitous in nature, and has drawn great attention in fluid mechanics community for about a century. However, the complexity of FSI has perplexed the physical analysis and understanding on this problem. In addition, FSI often brings a huge parametric space when moving solid boundaries exist, which makes the parametric space too computationally or experimentally costly to explore thoroughly. In the present thesis, first a global proper orthogonal decomposition (POD) and Galerkin projection based reduced-order model (ROM) has been developed to represent the essential physics of a FSI system with moving solid boundaries. The ROM is able to work on both numerical and experimental two-dimensional (2D) and three-dimensional (3D) dataset, and has shown adequate accuracy in the reconstruction of flow dynamics and the prediction of key aerodynamic properties, while keeping the computational cost very low. Then an adjoint approach has been derived, based upon the ROM and the conventional adjoin approach, to achieve fast flow control and optimization of a FSI system with moving solid boundaries. Different strategies have been designed to guarantee the accuracy of ROMs during the optimization process. The adjoint-ROM has been applied to the stabilization of the flow field as well as the aerodynamic force optimization of 2D flows past oscillating cylinders and NACA0012 airfoils. The adjoint-ROM approach has been proved effective and fast, of which the computational cost saving may make a near-real-time flow control possible. Additionally, the adjoint-based approach has been leveraged to study two important yet sophisticated FSI problems: the gust mitigation problem, and the hydrofoil schooling problem. The gust mitigation has been investigated for 2D and 3D heaving-pitching wing models under low Reynolds numbers. The streamwise gust and the transverse gust have been mitigated for both models. The non-cylindrical enabled full-order model (FOM) based adjoint approach has been used for all cases, while the adjoint-ROM developed in the present work has been used for 2D weak gust mitigation only. The mitigation of gust has been realized by minimizing a well-designed objective function to recover the mean lift of the base flow, while keeping the lift profile as steady as possible. The FOM-based adjoint approach was applied to both 2D and 3D strong gusts, and was highly effective in recovering the target lift, while keeping a reasonable computational cost. The adjoint-ROM approach was used for 2D weak gusts. It was able to mitigate the gust impact with relatively lower controllability and partially recovered lift. Moreover, its online computation was fast enough for real-time control. The hydrofoil schooling problem has been studied by FOM-based adjoint approach for the first time to optimize the hydrodynamic force on trailing hydrofoils in a school. Both 2D oscillating rigid hydrofoils and undulating flexible hydrofoils have been studied at modest Reynolds numbers. It was found the adjoint approach effectively optimized the motion and the formation of the hydrofoil school to achieve huge drag reduction as well as drag-to-thrust conversion on trailing hydrofoils. The vortex-foil interaction was investigated and was found to be crucial for the optimization of hydrodynamic force.