Numerical simulation of interaction between turbulent flow and a vibrating airfoil

Abstract

The subject of this paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil. A solid elastically supported airfoil with two degrees of freedom, which can rotate around the elastic axis and oscillate in the vertical direction, is considered. The numerical simulation consists of the stabilized finite element treatment of the Reynolds averaged Navier–Stokes (RANS) approach, the use of turbulence models and the solution of the system of ordinary differential equations describing the airfoil motion. The time dependent computational domain and a moving grid are taken into account with the aid of the Arbitrary Lagrangian–Eulerian (ALE) formulation of the Navier–Stokes equations. High Reynolds numbers up to 106 require to use a suitable stabilization of the finite element discretization and the application of a turbulence model. We apply the algebraic turbulence model, which was designed by Baldwin and Lomax and modified by Rostand. The developed technique was tested by the simulation of flow past a flat rigid plate and the computation of pressure distribution around a rotating airfoil with prescribed motion. Finally, the method was applied to the simulation of flow induced airfoil vibrations.