Comparison between flapping wings with hindwing and hindwing-less at low Reynolds number

Abstract

In recent decades, biological creatures with flapping wings have been studied. Particularly, insects are the most investigated, and many researchers have been interested in low Reynolds numbers, various wing shapes and kinematics for the insect flapping wings. Among them, insects have various wing shapes due to degeneration or role change. Representative cases are drosophila and cicada. The drosophila wing has a simple shape and has been used as a simulation or experimental model in many studies. In contrast, the cicada wing has a hindwing that is relatively small compared to the forewing. Because of its hindwing, it seems that the cicada has two trailing edges. This distinction can induce differences in vortex structures around the wings. In the present work, the immersed boundary – lattice Boltzmann method (IB-LBM) simulations is conducted to investigate effects of hindwings. The studied wings are drosophila, cicada and two test wings. The test wings consist of ellipse shapes, inspired by the drosophila and cicada wings. Reynolds number based on the flapping motion is fixed at 150, which is focused on a flapping wing micro aerial vehicle. We consider a simple stroke and an angle of attack of flapping motion for the wing kinematics. From the numerical results, this study shows two major differences in terms of the vortex structures. Firstly, on the wing with hindwing, two trailing edge vortices(TEVs) are formed due to the wing shape. On the other hand, the wings without hindwing develop a leading edge vortex(LEV) and a TEV due to their simple shape. For this reason, the two edge vortices generate a strong spanwise flow. However, in the case of hindwings, the two trailing edge vortices generate a flow in another direction due to the two TEVs. The TEVs and leading edge vortex(LEV) make the spanwise velocity lower. The low spanwise flow results in a reduced spanwise vorticity flux. However, when the angle of attack is lower than 90 degrees, the flapping wing with hindwing has a merit in enhancing lift at the beginning of the stroke due to the TEV on the hindwing. Secondly, in the case of the hindwing, a smaller-scaled vortex structure emanates from the unbalanced edge vortices, i.e. the TEVs and LEV. The smaller vortex contributes to an enhancement of the spanwise flow, but its magnitude is very small. As a result, it is demonstrated that the flapping wings with hindwing and hindwing-less has not only geometrical, but also vortex dynamical distinction from each other. Therefore, this study indicates that whether the hindwing or hindwing-less is a factor to consider in flapping micro air vehicle designs.