Two-Dimensional Flapping Wing Aerodynamics: Unsteady Mechanisms and Influence of Flexibility

M. VALDEZ; B. BALACHANDRAN

Columbus, Ohio

Congreso; USNCCM X - 10th U.S. National Congress on Computational Mechanics (USNCCM1-X); 2009

United States Association for Computational Mechanics

An unsteady, nonlinear vortex model is developed and used to understand the relationships between kinematics, vortex structures, and aerodynamic performance of two-dimensional flapping wings that move with prescribed motions. Numerical investigations into vortex-shedding patterns associated with the different aerodynamic mechanisms are carried out. A simple model of a flexible wing section is implemented in order to explore the effects of flexibility on the aerodynamic performance (Vanella et al., 2009).It is well known that unsteady aerodynamic mechanisms employed by small birds and insects, namely, wake capture, delayed stall, and wing rotation, play a key role in the generation of lift and thrust at low Re. Other mechanisms, which are based on wing-to wing interaction (clap and fling) and wing flexibility, are thought to contribute to the enhancement of aerodynamic performance of these flying creatures. Although the flight regime of insects and small birds spans low to moderate Re, it is argued here that it is still reasonable to consider the viscous effects to be restricted to the boundary layers on the wing surfaces and vorticity to be confined to the boundary layers and wakes. This hypothesis allows the treatment of the compact vorticity containing regions of the flow as vortex sheets. A modification of the classic unsteady vortex-lattice method (UVLM), which enables leading edge separation is implemented to numerically solve for the motion of the vortex sheets, as well as for the aerodynamic loads generated on the solid surfaces (Valdez et al., 2008). A bound vortex sheet is used to represent the wing section and its circulation is determined through enforcement of the Kutta condition, velocity continuity at the wing-fluid interface, and Kelvin's circulation theorem. Free vortex sheets, which separate from the edges of the moving wing, are used to explore vortex shedding and wakes patterns. These sheets account for the viscous effects due to the separation of the boundary layer on the body. A fourth-order Hamming´s predictor-corrector scheme is implemented to iteratively solve for the coupled fluid-structure phenomenon in the case of flexible wing section. Results obtained from Direct Numerical Simulations of the Navier-Stokes equations at the Reynolds number Re = 1000 are presented for comparison and analyzed.