Random binary (coalescence) flutter of a two-dimensional linear airfoil

Abstract

The binary flutter mechanism of a two-dimensional linear airfoil (typical section) in turbulent flow is investigated numerically. The airfoil is modelled as a flexibly mounted rigid flat plate, with degrees of freedom in pitch and heave. The unsteady aerodynamics is represented using both Wagner's function, accounting for arbitrary motion and longitudinal turbulence, and küssner's function, accounting for vertical turbulence. The flutter stability/instability boundary is examined according to the concept of sample stability, as given by the largest Lyapunov exponent. Results show that, for all airfoil and turbulence parameters considered, the longitudinal component of turbulence lowers the flutter speed. This decrease in flutter speed is determined essentially by the small and very small frequencies of the turbulence excitation, specifically due to principal and secondary combination difference type parametric resonances. Furthermore, there is strong evidence that the random excitation, specifically the longitudinal component, modifies the modal characteristics of the system, and in turn the coalescence of the two aeroelastic modal frequencies. In this sense, the nature of the shift of the flutter point is typical of the deterministic classical binary flutter problem.