The effect of wake dynamics on rotor eigenvalues in forward flight

An eigenvalue study can provide stability information for a system, and it is also an important part of aeroelastic analysis. In this work, a 2-D approximation to a set of 3-D generalized dynamic wake equations is studied first to obtain an overview of the characteristics of unsteady aerodynamics in forward flight. The generalized dynamic wake model employed is based on incompressible potential flow theory with an induced flow distribution expanded in a set of harmonic and radial shape functions, including undetermined time dependent coefficients as aerodynamic states.;The second part of this work utilizes a 3-D wake eigen-analysis. Results with varying numbers of harmonies are computed, and the mode shapes of each eigenvalue are studied to understand the physical meaning of wake dynamics.;The third part of this work is to investigate the damping of a blade-wake coupled system. The frequency response of this coupled model is also studied and compared with results from the 2-D approximation. A set of rigid-blade flapping equations is used to simplify the results. For this eigen-analysis, the blade-wake coupled system is represented by a set of periodic-coefficient differential equations in forward flight. Thus, Floquet Theory is applied to this stability problem. The eigenvalues of this matrix determine system characteristics. The flapping modes can be identified by the corresponding eigenvectors of each eigenvalue, and the stability of the whole aeroelastic system can be analyzed.;This work gives us insight into the interaction of blade flapping and wake dynamics. The effect of wake dynamics on rotor eigenvalues in forward flight can be seen by comparison with the no inflow case. One can see from the results of this work that the inflow has a profound effect on blade dynamics even at high advance ratios.