Effect of torsional stiffness and inertia on the dynamics of low aspect ratio flapping wings

Micro air vehicle-motivated aerodynamics in biological flight has been an important subject in the past decade. Inspired by the novel flapping wing mechanisms in insects, birds and bats, we have carried out a numerical study systematically investigating a three-dimensional flapping rigid wing with passively actuated lateral and rotational motion. Distinguishing it from the limited existing studies, this work performs a systematic examination on the effects of wing aspect ratio (AR = 1.0 to infinity), inertia (density ratio σ = 4–32), torsional stiffness (frequency ratio F = 1.5–10 and infinity) and pivot point (from chord-center to leading edge) on the dynamics response of a low AR rectangular wing under an initial zero speed flow field condition. The simulation results show that the symmetry breakdown of the flapping wing results in a forward/backward motion with a rotational pitching. When the wing reaches its stable periodic state, the induced pitching frequency is identical to its forced flapping frequency. However, depending on various kinematic and dynamic system parameters, (i.e. flapping frequency, density ratio and pitching axis), the lateral induced velocity shows a number of different oscillating frequencies. Furthermore, compared with a one degree of freedom (DoF) wing in the lateral direction only, the propulsion performance of such a two DoF wing relies very much on the magnitude of torsional stiffness adding on the pivot point, as well as its pitching axis. In all cases examined here, thrust force and moment generated by a long span wing is larger than that of a short wing, which is remarkably linked to the strong reverse von K´arm´an vortex street formed in the wake of a wing.