The incorporation of nature-inspired techniques to control or reduce boundary layer separation, to bring about performance enhancements on air/water vehicles, has been an active research area for many years. In this paper, a baseline NACA0012 airfoil is modified using a short flap on its upper surface at a Reynolds number of Re = 1000. The impact of the flap configuration—described by length, attachment position, deployment angle, and material properties, on the aerodynamic performance of the airfoil—quantified by mean and fluctuating forces, is investigated, and the flow field is analyzed. Inspired by the observation of pop-up feathers on a bird’s wing, the flap is first set to be rigid for a range of location, size, and inclination angles. After the optimal location of a rigid flap has been established, the flap is then allowed to be flexible, its motion is coupled to the encircling flow field, and it is tested for a range of mass ratios and bending stiffness values. The fluid motion is obtained by solving the lattice Boltzmann equation, while the dynamics of the flexible flap are calculated using the finite element method and the coupling between the flow and flap handled by the immersed boundary method. For the flexible flap, two flapping patterns are observed and the mechanism of separation control via rigid/flexible flap is explained. Compared to the flapless NACA0012 airfoil case, in the case with a flap of optimal configuration, the mean lift coefficient is improved by 13.51%, the mean drag coefficient is decreased by 3.67%, the mean lift-drag ratio is improved by 17.84%, the maximum lift fluctuation is decreased by 40.90%, and the maximum drag fluctuation is decreased by 56.90%.

Reduced-order models such as dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) have been extensively utilized to model unsteady flow. Although the major flow patterns can be captured by DMD and POD, due to the linear assumption, the modeling accuracy is low for complex and strongly nonlinear flow structures such as shock wave and vortex. To improve the accuracy and robustness of predicting unsteady flow, this work proposes a novel modeling method based on a hybrid reduced-order model. Since the flow can be regarded as a fusion of the main flow and the residual flow from a modeling perspective, the hybrid reduced-order model is constructed by DMD and POD, which are, respectively, used to obtain different flow properties. First, DMD is applied in describing the main flow, which contains the dominant modes determining most properties of the flow. Then, POD combining the long short-term memory is conceived to model the residual flow that the DMD cannot capture, to further enhance the modeling accuracy. The proposed method is validated by modeling two unsteady flows, which are the flow past a two-dimensional circular cylinder at Reynolds number 100 and the forced oscillation of an airfoil at transonic speed. The results indicate that the proposed method with proper modeling efficiency gains better accuracy and robustness than the existing methods. In particular, this approach has better forecasting accuracy of shock wave and vortex.