Aeroelastic interactions and trajectory selection of vortex gusts impinging upon Joukowski airfoils

The dynamically-coupled interactions of vortex gusts encountering a symmetric Joukowski airfoil on linear elastic supports is formulated analytically and evaluated numerically using a time-dependent conformal mapping. The Brown and Michael framework models the unsteady shedding of vorticity from the airfoil into the wake, and the aeroelastic motion of the airfoil is analyzed using quasi-steady, apparent mass, and fully-unsteady aerodynamic models. Special attention is paid to the influences of the strength of the incident vortex and the airfoil natural frequency on the initial upstream placement of a vortex gust that achieves direct impingement. These results are weakly sensitive to the initial vortex position in the limits of either large or small structural natural frequency, and the initial vertical vortex position to achieve impingement changes monotonically with the vortex strength. A comparison of the numerical model with available experimental vortex gust measurements over stationary airfoils highlights the appropriate use of the point-vortex model for inviscid vortex–airfoil interaction problems without significant vortex strength decay, which occurs for predominantly viscous interactions of close vortex–airfoil encounters.