Evolution of vortex structures over flapping foils in shear flows and its impact on aerodynamic performance

The evolution of vortex structures over flapping NACA0012 foils in shear flows and the corresponding aerodynamic performance are numerically studied using a two dimensional (2D) high-order accurate spectral difference Navier-Stokes flow solver, and further analyzed using the dynamic mode decomposition (DMD) method and vortex theory. Several types of vortex structures over pitching or plunging foils are simulated and analyzed to answer the following questions: (1) how mean flow shear affects the evolution of vortex structures, including both leading and trailing edge vortices, over flapping foils; and (2) how mean flow shear affects the aerodynamic performance under different kinematics. A temporal DMD method is used to analyze vortex structures. It is found that mean flow shear does not modify the dominant temporal frequencies in flow fields, but strong mean flow shear can significantly alter the growth rate, amplitude, and spatial patterns of coherent structures. From simulation results, it is observed that mean flow shear can affect evolution as well as interaction among leading and trailing edge vortices, thus altering the direction of wakes behind flapping foils. The mechanism of shear-induced deflective wakes is explained via qualitative analysis of evolution of simplified vortex street models. Finally, the effects of mean flow shear on aerodynamic performances of flapping foils with different kinematics are studied. By comparing the practical aerodynamic performances with those predicted by the steady aerodynamic theory, it is shown that flapping motion can significantly promote unsteady lift generation in mean flow shear. Furthermore, compared with flapping foils with positive mean angles of attack in a uniform incoming flow, the lift over flapping foils in flows with negative mean flow shear is enhanced without compromising thrust generation.