Non-linear response and instabilities of a two-degree-of-freedom airfoil oscillating in dynamic stall.

摘要

The system under study is that of a two-dimensional, two-degree-of-freedom airfoil (NACA 0012) in a steady subsonic airstream with external forcing. This airfoil is flexibly mounted in both degrees-of-freedom, and thus, describes an aeroelastic system. Non-linearities arising from the aerodynamics are responsible for the phenomenon of dynamic stall when the airfoil oscillates past the static-stall angle of attack. These non-linearities also cause the system to produce non-linear classes of motion, the most important of which is chaotic motion. Aeroelastic instabilities are also present in the system. This thesis explores the instabilities present in this system as well as its non-linear behaviour.; A semi-empirical numerical model revolving around the concept of an indicial response is used to model the non-linear aerodynamics in both degrees-of-freedom. The structural components of the system are modeled using simple linear elements, such as translational and torsional springs. Structural damping is ignored. Simple force and moment balancing equations allow for the derivation of the pertinent aeroelastic equations, which are then solved using numerical techniques.; Self-excited oscillations, examples of aeroelastic instability, were found in the one-degree-of-freedom system for oscillations about the static-stall angle. Binary flutter, another form of aeroelastic instability, was found in the two-degree-of-freedom system. Every class of non-linear motion (equilibrium, periodic, quasi-periodic and chaotic) was discovered in the non-linear analysis, and several routes to chaos were discovered. These routes included the quasi-periodic route, period-doubling route and intermittency route. Some of the routes discovered compared well with classical examples.