Nonlinear aeroelastics of a three-degree-of-freedom airfoil with control surface hysteresis stiffness in a dynamic stall flow

The increasingly stringent performance requirements of modern flight vehicles expose the possibilities of their coupled nonlinearities. Nevertheless, the aeroelastic response of a flight vehicle is generally predicted with isolated aerodynamic or structural nonlinearity. In this study, a Three-Degree-of-Freedom (3-DOF) aeroelastic model is proposed, which combines control surface hysteresis stiffness and dynamic stall aerodynamics. A control surface hysteretic model is applied to represent the nonlinear structural dynamics. The Office National d'Etudes et de Recherches Aérospatiales (ONERA) dynamic stall model is extended to a 3-DOF airfoil, considering the dynamic behavior of the control surface. The nonlinear aeroelastic model of a 3-DOF airfoil is described using a monolithic state-space equation. Henon's event-driven scheme is used to investigate the post-flutter behavior of a 3-DOF airfoil with control surface hysteresis stiffness in a dynamic stall flow. The results indicate that the proposed model improves the numerical precision of nonlinear aerodynamic load by almost double that of the ONERA model that does not consider the dynamic behavior of the control surface. The flutter onset speed of the coupled nonlinear airfoil is overestimated by 10% using decoupled nonlinear analysis. Furthermore, the airfoil is dominated by the structural hysteresis nonlinearity and aerodynamic energy from the plunge motion at low airspeeds. As the airspeed increases, the airfoil is governed by the aerodynamic stall nonlinearity and aerodynamic energy from the pitch motion. The switch of the dominant nonlinearity induces topological changes in the aerodynamic curves, along with a threefold increase in the aerodynamic power. Excited by the increased energy, the airfoil undergoes a period-doubling bifurcation and transition to a higher-amplitude limit cycle. The theoretical results of this study are beneficial for the load design of modern flight vehicles under coupled nonlinear conditions.