Bifurcations of limit-cycle oscillations of a two degree-of-freedom airfoil caused by aerodynamic non-linearities

Abstract

Flutter is usually predicted using linearised theory. In reality, flutter is always non-linear and might already occur below the linearly predicted flutter boundary. Whether this is the case for limit-cycle oscillations (LCOs) caused by aerodynamic non-linearities is not known, since these LCOs can only be predicted using expensive wind-tunnel tests or coupled Computational Fluid Dynamics (CFD)-Computational Structural Mechanics (CSM) simulations. However, it is important to know whether a sufficiently large disturbance can already cause LCOs below the flutter boundary predicted from linearised theory. Furthermore, since structural properties and the flow conditions will vary, it is necessary to study the resulting variations of the Hopf bifurcation behaviour of the LCO solutions near the flutter point. In this work viscous and inviscid transonic flows are considered. The LCO bifurcation behaviour was found to vary significantly when the uncoupled structural natural frequency ratio and the location of the elastic axis are changed. When the non-linearity is relatively weak, a change in the Hopf bifurcation type might result. A Mach number variation in inviscid flow showed that the effective flutter boundary might significantly deviate from that predicted using linearised theory. For both the structural parameter variations and the Mach number variation, LCOs were observed below the linearly predicted flutter boundary. At the nominal structural parameters, the amplitude-dependent behaviour of the phase of the lift was found to be responsible for the type of bifurcation of the LCO solution that occurs. Inspection of the local force distributions at various pitch amplitudes showed that the motion of the shock wave on the lower surface is responsible for the behaviour of the phase of the lift and hence for the bifurcation behaviour of the LCOs observed in this work.