Open Access

ARTICLE

Calculation of a Deformable Membrane Airfoil in Hovering Flight

D.M.S. Albuquerque¹, J.M.C. Pereira¹, J.C.F. Pereira^1,2

1 Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais, 1, 1049-001, Lisbon, Portugal.
2 email: jcfpereira@ist.utl.pt

Computer Modeling in Engineering & Sciences 2011, 72(4), 337-366. https://doi.org/10.3970/cmes.2011.072.337

Abstract

A numerical study of fluid-structure interaction is presented for the analysis of viscous flow over a resonant membrane airfoil in hovering flight. A flexible membrane moving with a prescribed stroke period was naturally excited to enter into 1st, 2nd and 3rd mode of vibration according to the selected membrane tension. The Navier-Stokes equations were discretized on a moving body unstructured grid using the finite volume method. The instantaneous membrane position was predicted by the 1D unsteady membrane equation with input from the acting fluid flow forces. Following initial validation against reported rigid airfoils predictions, the model is applied to the dragonfly hovering case for a flapping membrane, pinned at both ends, at a Reynolds number based on the chord length of 157 and 1570. For a prescribed membrane tension corresponding to the first resonance mode, the membrane adopts a stable equilibrium shape that reduces both drag and lift forces relatively to the rigid airfoil values. For higher vibration resonant modes a weak interaction was predicted between the coherent membrane inflated shape and the resulting unsteady wake. For these cases the leading and trailing edges vortices dominate over the membrane shape fluid interaction. Most of the airfoil flexion occurs not from the aero-elastic interactions between the airfoil and the fluid but from the inertial bending of the airfoil on account of its density and tension.

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