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) α-Re parameter space, where α is the angle of attack and Re is the Reynolds number. The angle of attack is varied in the range of -5°≤ α≤ 10°, 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 α, 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 α, being characterised by a different frequency and a distinct triggering mechanism. The critical Re decreases as |α| increases, and scales as a power law for large positive/negative α. At intermediate Re, different limit cycles arise depending on α, each one characterised by a distinctive vortex interaction, leading thus to secondary instabilities of different nature. For intermediate positive/negative α, 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 α, of a 2-D Neimark-Sacker bifurcation for small negative α, of a 3-D pitchfork bifurcation for small positive α and of a 3-D subharmonic bifurcation for large positive α. The aerodynamic performance of the dragonfly-inspired airfoil is discussed in relation to the different flow regimes emerging in the α-Re space of parameters.