Fast prediction of transonic aeroelastic stability and limit cycles

The exploitation of computational fluid dynamics for aeroelastic simulations is mainly based on time-domain simulations. There is an intense research effort to overcome the computational cost of this approach. Significant aeroelastic effects driven by nonlinear aerodynamics include the transonic flutter dip and limit-cycle oscillations. The paper describes the use of Hopf bifurcation and center manifold theory to compute flutter speeds and limit-cycle responses of wings in transonic flow when the aerodynamics are modeled by the Euler equations. The cost of the calculations is comparable to steady-state calculations based on computational fluid dynamics. The paper describes two methods for finding stability boundaries and then an approach to reducing the full-order system to two degrees of freedom in the critical mode. Details of the three methods are given, including the calculation of first, second, and third Jacobians nd the solution of sparse linear systems. Results for the AGARD wing, a supercritical transport type of wing, and the limit-cycle response of the Goland wing are given.