High-fidelity aeroelastic computations of a flapping wing with spanwise flexibility

Abstract

A high-order (up to 6th order) Navier-Stokes solver is coupled with a structural solver that decomposes the equations of three-dimensional elasticity into cross-sectional, smalldeformation and spanwise, large-deformation analyses for slender wings. The resulting high-fidelity aeroelastic solver is applied to the investigation of rigid, moderately flexible and highly flexible rectangular wings undergoing a pure plunging motion. Comparisons of the computed results with available experimental measurements demonstrate good agreement. A description of the complex interaction between the unsteady aerodynamics and the flexible wing structural dynamics is given. Connections between the results of this analysis and enhanced loads for the moderately flexible wing are made. Results presented suggest that an optimum amount of flexibility exists for the case of a plunging wing and is associated with wing motions where the wing tip deflection and wing root motion are in phase over much of the plunge cycle.

Effects of spanwise flexibility on the performance of flapping flyers in forward flight

“…These incompressible and inviscid models are particularly accurate for forward flight, where any vortical structures convect away downstream due to the presence of a dominant freestream. For example, the lift predicted by Theodorsen's linearized unsteady aerodynamics model agrees well with the high-fidelity numerical results for a three-dimensional rectangular wing [19].…”

“…The thrust generation and efficiency characteristics of these spanwise flexible wings in forward flight were studied experimentally by Heathcote et al [15]. The accuracy of the presented analytical model will be assessed by comparing the wing deformation, lift and propulsive force with the numerical results [10,16,19] that agreed well with the experimental results [15] for the variables shown in table 1.…”

“…rigid and flexible wings, with the density ratio r* ¼ 7.8 are considered. For the rigid wing, the structure is assumed to be infinitely stiff [19]. Young's modulus is E ¼ 210 GPa for the flexible wing.…”

“…Aono et al [16] Reynolds-averaged Navier -Stokes and quasi-three-dimensional finite-element structural dynamics u tip /h a , a e , C T Kang et al [10] Reynolds-averaged Navier -Stokes and geometrically nonlinear structural dynamic solver u a /h a , f tip , kC P l, kC T l, h Gordnier et al [19] implicit large-eddy simulation and geometrically nonlinear structural dynamic solver u tip /h a , a e , C L , C T Heathcote et al [15] water tunnel experiment…”

Flow pattern similarities in the near wake of three bird species suggest a common role for unsteady aerodynamic effects in lift generation

“…While the aeroelasticity of birds' wings was addressed thoroughly, as well as the motion of wings in fluids [31], the coupling between the phenomena with regards to bird aerodynamics is still lacking. Gordnier et al [32] solved the flow behind a flexible flapping wing using a large eddy simulation modelling approach. Yet, the wings were modelled as experiencing pure plunging motion, which does not replicate the wing motion found in nature.…”