  We present a numerical study to characterize nonlinear unsteady aeroelastic
interactions of two-dimensional flexible wings at high angles of attack. The
coupled fluid-flexible wing system is solved by a body-fitted variational
aeroelastic solver based on the fully-coupled Navier-Stokes and nonlinear
structural equations. Using the coupled fluid-structure analysis, this study is
aimed to provide physical insight and correlations for the aeroelastic behavior
of flexible wings in the parameter space of the angle of attack and the
aeroelastic number. The phase diagrams of the aerodynamic performance are
established to obtain the envelope curves of the optimal performance and
determine the transition line of the drag variation. The effects of the angle
of attack and the aeroelastic number on the aeroelastic behaviors are
systematically examined. The time-averaged membrane deformation is positively
correlated with a non-dimensional number, the so-called Weber number. A new
scaling relation is proposed based on the dynamic equilibrium between the
aerodynamic force fluctuation and the combined inertia-elastic fluctuation. The
unsteady aerodynamic force can be adjusted by manipulating the membrane
vibration, the mass ratio, the Strouhal number and the aeroelastic number. The
numerical investigations provide design guidelines and have the potential to
enhance the maneuverability and flight agility of micro air vehicles with
flexible wing structures.
