Discrete vortex modeling of perching and hovering maneuvers

Perching and hovering are two bio-inspired flight maneuvers that have relevance in engineering, especially for small-scale uncrewed air vehicles. In a perching maneuver, the vehicle decelerates to zero velocity while pitching or plunging, and in hovering the pitch and plunge motion kinematics are used to generate fluid dynamic forces even when the vehicle velocity is zero. Even for an airfoil, the fluid dynamics of such maneuvers pose challenges for low-order modeling because of the time-varying freestream velocity, high amplitudes and rates of the motion kinematics, intermittent formation and shedding of the leading-edge vortex (LEV), and the strong effects of the shed vorticity on the loads. In an earlier work by the authors, a leading-edge suction parameter (LESP) was developed to predict intermittent LEV formation for round-leading-edge airfoils undergoing arbitrary variation in pitch and plunge at a constant freestream velocity. In this research, the LESP criterion is extended to situations where the freestream velocity is varying or zero. A discrete vortex method based on this criterion is developed and the results are compared against those from a computational fluid dynamics (CFD) method. Abstractions of perching and hovering maneuvers are used to validate the predictions in highly unsteady vortex-dominated flows, where the time-varying freestream/translational velocity is small in magnitude compared to other contributions to the velocity experienced by the airfoil. Time instants of LEV formation, flow features, and force coefficient histories for the various motion kinematics from the method and CFD are obtained and compared. The LESP criterion is seen to be successful in predicting the start of LEV formation, and the discrete vortex method is effective in modeling the flow development and forces on the airfoil.