Estimation of the flutter derivatives of an NACA airfoil by means of Navier-Stokes simulation

The paper presents a numerical determination of the aeroelastic characteristics of a two-dimensional airfoil. A numerical method is described for the resolution of the incompressible Navier-Stokes equations, based on a streamfunction/vorticity formulation in relative frame. The solution method employs influence matrix techniques to determine the exact boundary conditions and a conformal mapping of the physical space. Validation of the method is presented based on several test cases, and the code is then applied to the flutter derivatives of an airfoil. Two methodologies are tested for the calculation of the aerodynamics coefficients associated to the motion-related force functions proposed by Scanlan and Tomko. These are based on forced-motion and spring-mounted airfoil experiments. Results are compared with theoretical values based on the Theodorsen function. Good agreement with the inviscid theory is generally observed, except for the coefficients related to the angular velocity. The effects of the Reynolds number and the thickness of the airfoil are also investigated. The results indicate that, while the spring-mounted approach provides correct estimates of the flutter coefficients, the forced-motion approach is better suited for their computation.