Articles | Volume 3, issue 1
Wind Energ. Sci., 3, 345–352, 2018
Wind Energ. Sci., 3, 345–352, 2018
Research article
07 Jun 2018
Research article | 07 Jun 2018

The second curvature correction for the straight segment approximation of periodic vortex wakes

David H. Wood

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Cited articles

Bhagwat, M. J. and Leishman, J. G.: Self-Induced Velocity of a Vortex Ring Using Straight-Line Segmentation, AIAA Journal, 59, 1–7, 2014. a, b
Govindarajan, B. M. and Leishman, J. G.: Curvature Corrections to Improve the Accuracy of Free-Vortex Methods, J. Aircraft, 53, 378–386, 2016. a, b, c
Katz, J. and Plotkin, A.: Low-Speed Aerodynamics, 2nd edition, C.U.P., Cambridge, 2001. a
Kim, C. J., Park, S. H., Sung, S. K., and Jung, S. N.: Dynamic modeling and analysis of vortex filament motion using a novel curve-fitting method, Chinese J. Aeronaut., 29, 53–65, 2016. a, b
Kuibin, P. A. and Okulov, V. L.: Self-induced motion and asymptotic expansion of the velocity field in the vicinity of a helical vortex filament, Phys. Fluids, 10, 607–614, 1998. a
Short summary
The vortices in the wakes of wind turbines are often approximated by short, straight vortex segments, which cannot reproduce the curvature singularity in the induced velocity. They can also have a second error due to the periodicity: the vortices return to close proximity of the point at which the velocity is calculated. The second error is assessed by representing the far wake of a turbine as a row of vortex rings. The error is quantified and a simple correction is developed.