Combination of Betz's vortex roll-up theory with Theodorsen's theory for unsteady lift response
Source: BAM, Division Non-destructive Testing Methods for Civil Engineering
A lift-producing finite wing always generates a wing tip vortex. This strong and hazardous longitudinal vortex then affects other objects further downstream in its wake, such as aircrafts or wind energy turbines. This phenomenon limits the capacity of airports and reduces the efficiency of wind farms. Experiments indicate that periodic wing-pitching significantly accelerates vortex decay. Several authors suggest that periodic wing pitching excites the Crow-instability. However, no theory exists to describe this interaction so far.
In this paper, Betz's vortex roll-up theory is combined with Theodorsen's theory for unsteady lift response. As shown, the unsteady lift response leads to a variation of the centroid position in spanwise direction. Furthermore, 84.2 % of the generated displacement of the tip vortex is oriented in the direction of the Crow-instability. This new theoretical approach may yield the optimal pitch frequency and amplitude for fast trailing vortex decay. In the future, this should help to increase the efficiency of wind energy turbines within wind farms.
Mechanism of Vortex Perturbation via Unsteady Pitching
Christoph Strangfeld, C. N. Nayeri, C. O. Paschereit, D. Greenblatt
Journal of Aircraft, Vol. 55, No. 5 (2018), pp. 1831-1838
BAM Department Non-destructive testing, Division Non-destructive Testing Methods for Civil Engineering