Aeroelastic analysis of a non-linear airfoil based on unsteady vortex lattice model

Recent years have witnessed a successful model of unsteady vortex lattice to predict the limit cycle oscillations of an airfoil section. The aerodynamic model is usually in the form of discrete time, and hence, is not convenient for the analysis of non-linear aeroelastic systems. In this paper, the aerodynamic model of unsteady vortex lattice is formulated in continuous time domain and expressed in a dimensionless form. The order of aerodynamic model is greatly reduced in terms of a few aerodynamic eigenmodes to describe the unsteady vortex. Meanwhile, a static correction is included in the modal reduction to take the effects of truncated higher aerodynamic modes into account. The accuracy of the reduced-order model of aerodynamics is compared with Theodorsen's model. Using the modified aerodynamic model, the aeroelastic analysis of a two-dimensional airfoil section with combined non-linearity of freeplay and cubic stiffening in pitch is made. The numerical results indicate that the modified aerodynamic model is capable of predicting the flow about airfoil accurately and detecting the complex non-linear aeroelastic behaviors.