Aerodynamic stability of a wind turbine section including dynamic stall and dynamic inflow

The dynamics of a rigid airfoil section under aerodynamic forces is a classic aero-elastic problem, where: 1) the effects of unsteady aerodynamics and induced velocities are often neglected; and, 2) the dynamics of the section is simplified by neglecting effects related to offsets of the center of mass, elastic center, shear center and principal axes.

In this work, we include a dynamic stall model and a dynamic inflow model in state-space form. The dynamic inflow model accounts for slow variation of induced velocities in wind energy applications. The airfoil section is modeled as a rigid body, but the location of the center of mass, shear center, elastic axis, and aerodynamic center are parameters of the model, and the direction of the principal axes of inertia and elasticity are not assumed to coincide with the chord axis. 

We present the equations of the aero-elastic state space model and linearize them. We analyse the problem in time and frequency domain and study the parameters affecting the stability of the airfoil section. In particular, we study the influence of the locations of the different structural points and the point where the angle of attack is defined. The stiffnening and damping contributions from the aerodynamics are assessed.