Characterization of aeroelastic response and aerodynamic stiffness effect of an airfoil in the presence of dynamic stall

Abstract

The response characteristics and aerodynamic stiffness characteristics of the self-excited aeroelastic system under the influence of dynamic stall are investigated adopting CFD (computational fluid dynamics) method. It is found that as velocity increases, the response type changes from asymmetric LCOs (limit cycle oscillations) to symmetric LCOs due to the effect of dynamic stall. Special stable fixed-point responses and low-amplitude LCOs are also found between the asymmetric and symmetric high-amplitude LCO state. The stability of the fixed point is analyzed by combining traditional linearization method and energy map. By observing the flow field variations, it is found that the occurrence of these special responses is related to the separation of the boundary layer of lower surface near the trailing edge, and its mechanism is completely different from the high-amplitude limit-cycle oscillation dominated by dynamic stall. Systems with small equilibrium angular position enter the symmetric limit-cycle state more quickly after the Hopf bifurcation and dynamic stall occur on both upper and lower surfaces of the airfoil, as the velocity increases. While in the case of systems with large equilibrium angular position, the minimum angle of attack of aeroelastic responses decreases slowly before reaching the negative angle that allows dynamic stall to occur on the lower surface, the system remains in the asymmetric limit-cycle state over a wide range of velocities. Thus, aerodynamic stiffness of system with large equilibrium angular position changes non-monotonically due to the varying aerodynamic moment characteristics at the minimum angle of attack of asymmetric LCOs. Furthermore, by increasing the initial angular velocity, we found that the system responses all become symmetric LCOs and therefore the aerodynamic stiffness increases monotonically with the flow velocity. As to the effect of structural stiffness, it is found that the variation of the LCO amplitude with the structural stiffness coefficients will show different trends at different free-stream velocities. Energy maps show that different parametric distributions of the energy transfer at different free-stream velocities contribute to this phenomenon. Aerodynamic stiffness maps based on equivalent linearization method are also established to explain the aerodynamic stiffness variation. Moreover, when entering the symmetric LCO state, the structural stiffness no longer has a significant effect on the aerodynamic stiffness of the system, as the LCO amplitude and the aerodynamic moment characteristics do not vary much, which results in constant dimensionless aerodynamic stiffness coefficient for this stage.