Analysis of transonic limit cycle oscillation using aerodynamic describing functions and superposition principle

Limit cycle oscillation (LCO) for an airfoil in transonic air flow considering aerodynamic nonlinearity is studied. Transonic nonlinear aerodynamic forces are calculated by solving Euler equations with respect to harmonic airfoil plunging/pitching motion, and then the aerodynamic describing functions and the superposition principle are used to build an equivalent linearized aerodynamic model in frequency domain, hence the LCO characteristics can be computed by frequency domain method. The procedures for building the aerodynamic describing functions and for obtaining the LCO solution are described in details. Three examples are adopted to verify the accuracy of the present method. The Isogai Wing Model is used as the first example to verify the accuracy of flutter solution of the present method. Secondly, a NACA64A010 airfoil model is adopted to study its LCO characteristics considering only aerodynamic nonlinearity. And in the third example, the NACA0012 airfoil model with both aerodynamic and structural nonlinearities is investigated for its LCO properties. The results obtained by the present method are in good agreement with those obtained by the literatures with harmonic balance method and time marching method.