Numerical analysis of flow-induced nonlinear vibrations of an airfoil with three degrees of freedom

The subject of the paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil with large amplitudes. A solid airfoil with three degrees of freedom performs rotation around an elastic axis, oscillations in the vertical direction and rotation of a flap. The numerical simulation consists of the finite element solution of the Navier–Stokes equations coupled with a system of nonlinear ordinary differential equations describing the airfoil motion. The time-dependent computational domain and a moving grid are treated by the arbitrary Lagrangian–Eulerian (ALE) formulation of the Navier–Stokes equations. High Reynolds numbers require the application of a suitable stabilization of the finite element discretization. With the aid of numerical experiments we analyze the convergence of the method, if the computational mesh is refined and the time step is successively decreased. Also the effect of the loose (weak) and strong coupling of the flow and structure problems is tested. The applicability of the method is demonstrated by the comparison with NASTRAN computations and the solution of the coupled fluid–structure problem with increasing far-field velocity up to and behind the flutter instability. The developed method can be used in theoretical prediction of dynamic behaviour of aeroelastic systems especially when the system stability has been lost.