Role of flexibility in determining vortex interactions and wake dynamics of flapping flexible foil

Our experiments on a foil with a flexible filament attached to its trailing edge (flexible foil), pitching in a flowing soap film, investigate how flexibility alters the wake transitions and vortex interactions for flexible foils, which are closer to the natural flapping foils in fish, birds, and insects. <span style="box-sizing:border-box; margin:0px; padding:0px">We explore a wide parameter space by varying the flexural rigidity (EI) of the filament and the Strouhal number (St); we also study an extreme case of EI → ∞. Introducing flexibility to foil results in shedding several small secondary vortices (SVs) along with big primary vortices (PVs), unlike only PVs for rigid foil. SVs are shed continuously, and their number decreases with increasing EI. The vortex structures change with St and, importantly, with filament EI. This change is bound to the interactions between vortices as they travel over a continuously deforming flexible filament and their shedding pattern. Advection time of boundary layer vortices (BLVs) varied with St and EI. Variations in vortex advection time affected the interactions of BLV and TEV (trailing edge vortex), their shedding pattern, post-shedding interaction in the near-wake, and eventually their evolution into PVs and SVs. Extensive analysis of these parameters revealed five vortex interaction mechanisms (VIMs). Several parameters simultaneously govern the interaction of the flexible structure with the fluid, thus influencing the VIMs and wake patterns. We devise a non-dimensional parameter (ϒ) to include their effects. While the type of VIMs is determined by BLV advection time, the number of VIMs is controlled by ϒ; one order increase in ϒ reduces the VIMs by one. By spanning flexural rigidity over three orders, we provide phenomenology for VIMs and construct the 𝑆𝑡–𝐸𝐼 phase maps for wake transitions and newly identified VIMs, for the first time. Understanding vortex interactions and wake transitions for flapping flexible foils is crucial because of their increased usage in bioinspired aquatic and aerial robotic propulsors.