Unsteady aerodynamic forces of a flapping wing

Abstract

It has been shown that conventional aerodynamic theory, which was based on steady flow conditions, cannot explain the generation of large lift by the wings of small insects (for reviews, see Ellington, 1984a;Spedding, 1992). In the past few years, much progress has been made in revealing the unsteady high-lift mechanisms of flapping insect wings. Dickinson and Götz (1993) measured the aerodynamic forces of an airfoil started rapidly at high angles of attack in the Reynolds number (Re) range of the fruit fly wing (Re=75-225; for a flapping wing, Re is based on the mean chord length and the mean translation velocity at radius of the second moment of wing area). They showed that lift was enhanced by the presence of a dynamic stall vortex, or leading edge vortex (LEV). After the initial start, lift coefficient (CL) of approximately 2 was maintained within 2-3 chord lengths of travel. Afterwards, CL started to decrease due to the shedding of the LEV. But the decrease was not rapid, possibly because the shedding of the LEV was slow at such low Re; and The unsteady aerodynamic forces of a model fruit fly wing in flapping motion were investigated by numerically solving the Navier-Stokes equations. The flapping motion consisted of translation and rotation [the translation velocity (ut) varied according to the simple harmonic function (SHF), and the rotation was confined to a short period around stroke reversal]. First, it was shown that for a wing of given geometry with ut varying as the SHF, the aerodynamic force coefficients depended only on five non-dimensional parameters, i.e. Reynolds number (Re), stroke amplitude (Φ), mid-stroke angle of attack (αm), non-dimensional duration of wing rotation (∆τr) and rotation timing [the mean translation velocity at radius of the second moment of wing area (U), the mean chord length (c) and c/U were used as reference velocity, length and time, respectively]. Next, the force coefficients were investigated for a case in which typical values of these parameters were used (Re=200; Φ=150°; αm=40°; ∆τr was 20% of wingbeat period; rotation was symmetrical). Finally, the effects of varying these parameters on the force coefficients were investigated.In the Re range considered (20-1800), when Re was above ~100, the lift (CL) and drag (CD) coefficients were large and varied only slightly with Re (in agreement with results previously published for revolving wings); the large force coefficients were mainly due to the delayed stall mechanism. However, when Re was below ~100, CL decreased and CD increased greatly. At such low Re, similar to the case of higher Re, the leading edge vortex existed and attached to the wing in the translatory phase of a half-stroke; but it was very weak and its vorticity rather diffused, resulting in the small CL and large CD. Comparison of the calculated results with available hovering flight data in eight species (Re ranging from 13 to 1500) showed that when Re was above ~100, lift equal to insect weight could be produced but when Re was lower than ~100, additiona...

Lift and thrust generation by a butterfly-like flapping wing–body model: immersed boundary–lattice Boltzmann simulations

“…These results are consistent with earlier findings (e.g. Wu & Sun 2004;Lentink & Dickinson 2009;Zheng et al 2013). …”

“…The planform of the fruit fly's wing used here (see figure 25) is copied from that in Wu & Sun (2004), which is the same as that of the robotic fruit fly wing used by Dickinson et al (1999 figures 3A, B, and C of Dickinson et al (1999). In these experiments, the stroke amplitude is Φ = 160…”

Stable vertical takeoff of an insect-mimicking flapping-wing system without guide implementing inherent pitching stability

“…Some very informative studies on the principles of insect flight include works of Weis-Fogh [14] , Ellington [15,16] , Dickinson et al. [17,18] , Sun and Tang [19] , Sane [20] , Wang et al [21] , Wu and Sun [22] , Ansari et al [23] , and Shyy et al [24] . These studies contributed to theoretically and/or experimentally explaining how an insect can produce extraordinary aerodynamic force in an unsteady environment.…”

On the quasi-steady aerodynamics of normal hovering flight part I: the induced power factor

“…For comparison, figure 6 also shows mean flapping cycle lift coefficient as a function of Reynolds number from CFD results of Wu & Sun [32]. Although the quantities shown in figure 6 are different, the span efficiency will directly influence the lift coefficient values attained during a flapping cycle, hence allowing a meaningful comparison of the shape of variation with Reynolds number.…”