Nonlinear Approximate Aeroelastic Analysis of Flapping Wings in Hover and Forward Flight.

Abstract

The development of a nonlinear approximate aeroelastic model suitable for representing the behavior of flexible anisotropic flapping wings in hover and forward flight is described. The structural dynamic component of the flapping wing aeroelastic problem is modeled using MSC MARC, a commercially available nonlinear finite element package, and the aerodynamic loads are computed from an approximate aerodynamic model that incorporates leading edge vortices and a wake model. The aerodynamic formulation, originally developed for rigid wings in hover, is modified to account for wing flexibility, viscosity, and free stream due to forward flight.

The results contain validation studies conducted in MARC, aerodynamic studies using rigid airfoils and wings in hover and forward flight, and aeroelastic studies on isotropic and anisotropic Zimmerman wings in hover and forward flight. The structural dynamic studies demonstrate the capabilities of the MARC code to model anisotropic bio-inspired flapping wings. For the rigid cases considered, the approximate aerodynamic model shows reasonable agreement with CFD-based results and predicts accurate trends. Results indicate that the forces generated by rigid wings are insensitive to Reynolds number (626<Re<17551) and scale with the square of the flapping frequency. Comparisons of transient and time-averaged forces for isotropic and anisotropic wings in hover indicate that the approximate aeroelastic model shows reasonable agreement with CFD-based computations and experimental measurements for the cases considered. Important trends in forces are also predicted accurately. The aerodynamic loads acting on the anisotropic wings are found to be comparable to inertia loads. This finding is contrary to what was found in previous studies and suggests that the relative importance of aerodynamic and inertia loads in flapping wings is configuration dependent. Finally, trends obtained for anisotropic wings indicate that wing flexibility has beneficial effects in both hover and forward flight. The choice of the ‘best’ flexible configuration depends on the wing kinematics as well as the flapping frequency.