Wake transition and aerodynamics of a dragonfly-inspired airfoil

We investigate the dynamics and the stability of the incompressible flow past a corrugated dragonfly-inspired airfoil in the two-dimensional (2-D) $\alpha {-}Re$ parameter space, where $\alpha$ is the angle of attack and $Re$ is the Reynolds number. The angle of attack is varied in the range of $-5^{\circ } \leqslant \alpha \leqslant 10^{\circ }$ , and $Re$ (based on the free stream velocity and the airfoil chord) is increased up to $Re=6000$ . The study relies on linear stability analyses and three-dimensional (3-D) nonlinear direct numerical simulations. For all $\alpha$ , the primary instability consists of a Hopf bifurcation towards a periodic regime. The linear stability analysis reveals that two distinct modes drive the flow bifurcation for positive and negative $\alpha$ , being characterised by a different frequency and a distinct triggering mechanism. The critical $Re$ decreases as $|\alpha |$ increases, and scales as a power law for large positive/negative $\alpha$ . At intermediate $Re$ , different limit cycles arise depending on $\alpha$ , each one characterised by a distinctive vortex interaction, leading thus to secondary instabilities of different nature. For intermediate positive/negative $\alpha$ , vortices are shed from both the top/bottom leading- and trailing-edge shear layers, and the two phenomena are frequency locked. By means of Floquet stability analysis, we show that the secondary instability consists of a 2-D subharmonic bifurcation for large negative $\alpha$ , of a 2-D Neimark–Sacker bifurcation for small negative $\alpha$ , of a 3-D pitchfork bifurcation for small positive $\alpha$ and of a 3-D subharmonic bifurcation for large positive $\alpha$ . The aerodynamic performance of the dragonfly-inspired airfoil is discussed in relation to the different flow regimes emerging in the $\alpha {-}Re$ space of parameters.