Lift generation by a two-dimensional symmetric flapping wing: immersed boundary-lattice Boltzmann simulations

Abstract

Two-dimensional (2D) symmetric flapping flight is investigated by an immersed boundary-lattice Boltzmann method (IB-LBM). In this method, we can treat the moving boundary problem efficiently on the Cartesian grid. We consider a model consisting of 2D symmetric flapping wings without mass connected by a hinge with mass. Firstly, we investigate the effect of the Reynolds number in the range of 40-200 on flows around symmetric flapping wings under no gravity field and find that for high Reynolds numbers (Re 55), asymmetric vortices with respect to the horizontal line appear and the time-averaged lift force is induced on the wings, whereas for low Reynolds numbers (Re 50), only symmetric vortices appear around the wings and no lift force is induced. Secondly, the effect of the initial position of the wings is investigated, and the range of the initial phases where the upward flight is possible is found. The effects of the mass and flapping amplitude are also studied. Finally, we carry out free flight simulations under gravity field for various Reynolds numbers in the range 60 Re 300 and Froude numbers in the range 3 Fr 60 and identify the region where upward flight is possible.

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

“…The vortex ring is observed also in the free flight simulation of a butterfly by Huang & Sun (2012). As for lift generation, it has been reported in Iima & Yanagita (2001) and Ota et al (2012) that for a two-dimensional symmetric flapping wing the symmetry breaking of flows generates a mean lift force. The two-dimensional symmetric flapping wing corresponds to the present wing-body model with c → ∞ and α m = 0…”

“…On the other hand, several studies on butterfly's flights (e.g. Ota et al 2012;Yokoyama et al 2013) have used the definition of the Reynolds number based on the wing length in the same way as equation (3.3).…”

“…It can be expected that both mean lift and thrust forces are induced as reactions to the induced flows. Ota et al (2012) and Kimura et al (2014) reported that the symmetry breaking occurs with respect to the longitudinal plane in the two-dimensional symmetric flapping wings. However, in all results for Re ⩽ 500 of this study, the flow field is symmetrical with respect to the longitudinal plane.…”

“…The authors also proposed a new IB-LBM (Suzuki & Inamuro 2011), which is more accurate for satisfying the no-slip boundary condition at a moving boundary than other IB-LBMs. The IB-LBM (Suzuki & Inamuro 2011) has already been applied to researches on flows and lift generation by the 2D symmetric flapping wing (Ota et al 2012;Kimura et al 2014) and by a dragonfly-like flapping wing-body model (Minami et al 2015).…”

Ground-induced lift enhancement in a tandem of symmetric flapping wings: Lattice Boltzmann-immersed boundary simulations

“…Results in terms of time history of the position of the centers of mass are discussed, together with considerations about the velocity field. This paper presents new insights with respect to previous efforts carried out by different authors [13,20,[51][52][53][54]. Specifically, the behavior of a tandem of butterfly-like wings is investigated, whereas the literature focuses mainly on isolated bodies.…”