Mechanism of Vortex Perturbation via Unsteady Pitching

Experiments indicate that vortices trailing finite wings can be perturbed by periodic wing pitching, leading to rapid dissipation and bursting. To illustrate the perturbation mechanism, Betz vortex rollup relations are combined with the Theodorsen theory for unsteady lift response. A sinusoidal pitch motion on a rigid elliptic planform wing is computed in this study as one example. Pitching modifies the instantaneous lift due to the planform variations, via the reduced frequency, and the rollup relations are applied to low-frequency experimental conditions. The combined Betz-Theodorsen theory shows that relatively large spanwise perturbations of the vortex centers can be achieved and may accelerate the exponential growth associated with the Crow instability. In fact, 84.2% of the displacement of the unsteady trailing vortices due to unsteady pitching is oriented in the direction of the Crow instability. Furthermore, the axial velocity in the vortex center, calculated based on the Batchelor method, varies on the order of the flight speed. This forms two types of stagnation points produced by approaching and retreating axial core velocities; in the former case, conservation of mass leads to observations of bursting. This observation can be explained adequately on the basis of quasi-steady considerations.