Time domain simulation of airfoil flutter in the subsonic regime using fluid structure coupling through panel method

摘要

This report presents a brief theory of aeroelastic flutter of airfoils and the relevant algorithm for the development of a computer code in FORTRAN for dynamic coupling of the airfoil structure, in the time domain, to a two-dimensional subsonic aerodynamic flow, so that the aeroelastic motion can be simulated in the time domain and the flutter boundary be determined for a typical rigid airfoil (of heave and pitch degrees of freedom) in the subsonic flow. The relevant computer code with fluid structure coupling has been developed at the Structural Technologies Division (STTD) for the purpose. The present work starts with a brief introduction to the fundamental concepts of airfoil flutter. The relevant equations of motion of the airfoil in subsonic airflow have been derived from the first principles. First, the classical method, based on the eigenvalue approach is used to solve the equations of motion and to determine the flutter boundary of the airfoil in the subsonic flow regime. A symmetric NACA 0012 airfoil profile of unit chord and width is chosen for analysis, with suitable spring stiffness and inertia values so that flutter instability can occur in the subsonic regime. Results from the panel code for steady flow conditions over the NACA 0012 confirm the validity of the code. For the purpose of time domain flutter simulation the panel code with the Prandtl-Glauert compressibility correction factor is suitably coupled to the airfoil through a Newmark's implicit time integration scheme. Unsteady motion in the fluid-structure system is numerically simulated through the code with small initial conditions. Flutter boundary is indicated by the critical free stream flow speed (and dynamic pressure) beyond which oscillation amplitudes show divergence in time. Flutter frequencies and flutter velocities obtained by the various methods are then compared, and good agreement is observed. Present analysis with a simple airfoil coupled to a 2D subsonic flow (simulated by the panel method) indicate that it is possible, in principle, to simulate flutter even in the transonic and supersonic regimes, using more sophisticated aerodynamic codes (Navier Stokes).