Hopf-bifurcation analysis of airfoil flutter at transonic speeds

Hopf-bifurcation analysis is used to determine flutter onset for a pitch-an d-plunge airfoil at transonic Mach number conditions. The pitch-and-plunge model is a coupling of the Euler equations and a two-degree-of-freedom stru ctural model composed of linear and torsional springs. The Euler equations are discretized using the upwind total variation diminishing scheme of Hart en and Yee. Equilibrium solutions of the aeroelastic model are computed usi ng Newton's method, and dynamic solutions are explicitly integrated in time with first-order accuracy. The Hopf-bifurcation point, which models the pu tter condition, is computed directly using a modified form of the Griewank and Reddien algorithm. A path of Hopf points is computed as a function of M ach number to produce a Mach putter boundary. The flutter boundary is valid ated by time integration, Flutter boundaries are also obtained through vari ation of static pretwist and pitch and plunge damping. The direct, Hopf-poi nt method is found to be precise and efficient for grids typical of invisci d, transonic airfoil calculations.