Investigation of Three-Dimensional Low Reynolds Number Tandem Flapping Wings

Abstract

In this paper we extend our previous two-dimensional tandem wing study to three-dimensions. In our previous study we found that tandem wing performance highly depended on the phase lag angle and spacing between the forewing and hingwing. High resultant force is produced when the two wings flap in phase while high power efficiency is reached when the wings flap in counter phase. In this paper the effect of the phase lag angle between the fore and hind wings on the wing-wing interactions, force production, and power efficiency was studied for three different phase lag angles, 0°, 90° and 180°. Both wings experienced pitch-plunge motion at a Strouhal number of 0.3 and a Reynolds number of 200. The simulations were based on the incompressible Navier-Stokes equations, discretized on overlapping grids. The wing motion was represented by a series of transformation matrices. Our three dimensional study confirmed conclusions drawn in our two dimensional study, i.e., the wing/wing interaction significantly affects tandem wing performance, in phase flapping leads to high resultant force and counter phase flapping results in high power efficiency. We also found that the LEV on the 3D wing was noticeably weaker than in the corresponding 2D case, as were the vortex interactions between the fore and hind wings. While the 3D results exhibited interactions between wing and tip vortices, the effect was insignificant as the tip vortices shed from forewing only encounter the near tip region of the hind wing. Nomenclature ψ = phase angle u = flow velocity p = pressure