Nonlinear Airfoil Limit Cycle Analysis Using Continuation Method and Filtered Impulse Function

Abstract

In this study, an adaptive step size control algorithm incorporated in the continuation method (CM) is developed and combined with the filtered impulse function method based on aerostructural solvers and applied to two aeroelastic analysis tasks concerned with modes tracking and parameter variation. The nonlinear limit cycle oscillation (LCO) of a NACA0012 airfoil with control surface free-play behavior is considered to illustrate how this adaptive step can achieve a balance between the stability, accuracy, and efficiency in the modes crossing region in modes tracking, the flutter point region in modes tracking, and the detrimental LCO region in parameter variation. It is shown that the computation time for modes tracking using this approach can be reduced by more than 65% while achieving almost the same estimate of the flutter speed as when using a fixed step size. The study also addresses a few unique and important phenomena in parameter variation such as modes jumping in the LCO curve that occur frequently using this adaptive step size algorithm. Furthermore, a combination of the modes tracking results to provide an estimate for the restart point for the CM solver to overcome the occurrence of possible extraneous solutions or divergence is proposed. The results of flutter analysis for linear structural system and nonlinear LCO analysis are validated against the results from experiments and the classical Theodorsen theory. The effect of viscous damping on the occurrence of detrimental LCO phenomena is also discussed and compared with the corresponding nondamping cases.