Vortex gust interactions with a freely-flying rigid airfoil
This study numerically investigates the interaction between an isolated vortex gust and a freely-flying airfoil, introducing a theoretical framework for interpreting the coupled lift and heave response. This complex and coupled dynamics is important for modern light-weight aircraft where gusts may easily perturb the wing, generating transient changes in trajectory and attitude. Here, the freely-flying airfoil is modeled with a single degree-of-freedom in heave, and is impacted by an isolated vortex gust generated upstream. Computational results demonstrate that the freely-flying airfoil reaches a maximum heave displacement after vortex impingement and subsequently rebounds with a comparable magnitude. The lift coefficient is then modeled by augmenting the lift from a corresponding stationary airfoil interaction with motion induced contributions associated with the induced angle of attack and added-mass. A comparison of the modeled lift with the simulation data confirms that the dynamics of the airfoil before impingement is dominated by these two terms, however the rebound after impingement is only partially explained by the model since it is also influenced by the gust-induced vortex shedding. Comparisons across various parameters show that the pre-impingement motion depends primarily on vortex rotation direction, whereas the post-impingement and induced shedding patterns vary with respect to angle of attack and vortex transverse position. With the lift coefficient of the corresponding stationary airfoil interaction as an input, the model can successfully predict the heave trajectory, thus providing a mechanism to assess the dynamic motion of an airfoil from experimental/computational data of gusts interacting with fixed airfoils.