On the role of wake-capture and resonance in spanwise-flexible flapping wings in tandem

Numerical simulations of the flow around spanwise-flexible flapping wings in tandem are reported, focusing on a thrust-generating configuration. Wings of aspect ratio 2 and 4 in forward flight undergo heaving and pitching motion following optimal 2D kinematics. The Reynolds number of the simulations is $Re=1000$. The effect of flexibility is explored by varying the effective stiffness of the wings, while the effective inertia is kept constant. The aerodynamic performance of the tandem system results from a combination of unsteady aerodynamics mechanisms, fluid–structure resonance, vortex–wing interactions (denoted wake capture in this study) and aerodynamic tailoring. It is found that the aerodynamic performance and structural behavior of forewings are dominated by a fluid–structural resonance. The maximum mean thrust for the forewings is obtained when the driving frequency approaches the first natural frequency of the structure, ${\omega }_{n,f}/\omega \approx 1$, similarly to what is observed in isolated wings undergoing the same kinematics. On the other hand, hindwings show optimal performance in a broad region near ${\omega }_{n,f}/\omega \approx 2$, and their aerodynamic performance seems to be dominated by wake–capture and aerodynamic–tailoring effects. The aerodynamic performance of the hindwings is dependent on the flexibility of the forewing, which impacts the intensity of the vortices shed into the wake and the resulting effective angle of attack (i.e., wake capture). The timing between the effective angle of attack and the pitching motion of the hindwing controls the generation of thrust (or drag) of each spanwise section of the hindwing (i.e., aerodynamic tayloring). A proof of concept study on the aerodynamic performance of systems made of wings with different flexibility suggests that they could outperform tandem systems with equally flexible wings. Thus, the optimal mixed–flexibility tandem system is composed by a resonant forewing, which maximizes the thrust generation of the forewing and the intensity of the vortices shed into the wake, and a hindwing whose flexibility must be tuned to maximize wake capture effects.