Hopf bifurcation analysis of typical sections with structural nonlinearities in transonic flow

The paper is concerned with direct aeroelastic bifurcation analyses of an airfoil system in which both aerodynamic and structural nonlinearities are considered. Here, structural dynamics is treated in terms of polynomial nonlinearities associated with the pitching stiffness. Two CFD tools are employed in the present work and they are based on the Euler formulation. For Hopf bifurcation analysis, a structured grid CFD code is used and flutter boundaries are found with the inverse power method. Previous work has demonstrated the applicability of such approach for both airfoil and wing configurations with a linear structural model. The novelty of the present effort is the use of this procedure for the investigation of the aeroelastic behavior with structural nonlinearities. Time-marching aeroelastic analysis is also performed and compared with direct calculation of Hopf bifurcation points in order to verify the approach. In the time-marching case, a CFD code solves the flowfield using an unstructured computational domain discretization. The results shown in the present paper are particularly concentrated in the investigation of flutter boundaries and typical limit cycle oscillation nonlinear effects for high-subsonic and transonic flows over a NACA 0012 airfoil-based typical section. The investigation reveals interesting nonlinear dynamics when both aerodynamic and structural nonlinearities interact.