Wing-wake interaction destabilizes hover equilibrium of a flapping insect-scale wing

Abstract

Wing-wake interaction is a characteristic nonlinear flow feature that can enhance unsteady lift in flapping flight. However, the effects of wing-wake interaction on the flight dynamics of hover are inadequately understood. We use a well-validated 2D Navier-Stokes equation solver and a quasi-steady model to investigate the role of wing-wake interaction on the hover stability of a fruit fly scale flapping flyer. The Navier-Stokes equations capture wing-wake interaction, whereas the quasi-steady models do not. Both aerodynamic models are tightly coupled to a flight dynamic model, which includes the effects of wing mass. The flapping amplitude, stroke plane angle, and flapping offset angle are adjusted in free flight for various wing rotations to achieve hover equilibrium. We present stability results for 152 simulations which consider different kinematics involving the pitch amplitude and pitch axis as well as the duration and timing of pitch rotation. The stability of all studied motions was qualitatively similar, with an unstable oscillatory mode present in each case. Wing-wake interaction has a destabilizing effect on the longitudinal stability, which cannot be predicted by a quasi-steady model. Wing-wake interaction increases the tendency of the flapping flyer to pitch up in the presence of a horizontal velocity perturbation, which further destabilizes the unstable oscillatory mode of hovering flight dynamics.

Effects of flapping-motion profiles on insect-wing aerodynamics

“…These coefficients differ strongly from those for other motion waveforms, as observed in the present study. A computational study of pitch waveforms of a 2-D wing by Bluman & Kang (2017) has shown results contradictory to those of Berman & Wang (2007). Bluman & Kang (2017) have investigated the stability of the flapping system and showed that slow pitching, i.e.…”

Chordwise wing flexibility may passively stabilize hovering insects

“…Extensive validation on the flexible wing's computation framework has been previously reported [28,31,32]. Also, careful validation studies have been conducted on the open-loop stability derivatives and power required in hover for fruit fly scale rigid [33] and flexible wings [9].…”

“…The net rearward translational drag force, acting above the body CG, induces nose-up pitch [8]. Also, the stronger rotational lift during stroke reversal from the advancing to retreating strokes causes a larger nose-up pitch moment than in the opposite half-stroke [5,33]. Finally, the wing-wake interaction, where the wing gains momentum from the near-field vortex structures immediately following stroke reversal, creates a fore-to-aft lift imbalance and induces a nose-up tendency under a gust [33].…”

Quasi-Steady versus Navier–Stokes Solutions of Flapping Wing Aerodynamics

“…A quasi-steady model from Sane and Dickinson [8,18,30], • A 3D Navier-Stokes equations solution of the rigid wing motion.…”

“…They show that the QS model to be low fidelity but suitable for initial results. Although there has been significant work by researchers to improve Sane and Dickinson's QS model [27,28], as well as additional QS implementations [19,29,30], the present work seeks to use Sane and Dickinson's original formulation. This allows the focus to remain on a systematic study that compares the QS model to the NSe solutions under a wide range of three-dimensional rotational flapping wing kinematics.…”