Remarks on the nonlinear dynamics of a typical aerofoil section in dynamic stall

We use standard tools of the theory of dynamical systems such as phase plots, bifurcation diagrams and basins of attraction to analyse and understand the dynamic behaviour of a typical aerofoil section under dynamic stall conditions. The structural model is linear and the aerodynamic loading is represented by the Leishman-Beddoes semi- empirical dynamic stall model. The loads given by this model are non- linear and non-smooth, therefore we have integrated the equation of motion using a Runge-Kutta-Fehlberg (RKF45) algorithm equipped with event detection. We perform simulations of the motion for a range of Mach numbers and show that the model is very sensitive to small variations. This is evidenced by the presence in the bifurcation diagram of co-existing attractors or, in other words, by the existence of more than one steady-state motion for a given Mach number. The mecha- nisms for the appearance and disappearance of the co-exisiing attractors are elucidated by analysing the evolution of their basins of attraction as the Mach number changes.