The Second Curvature Correction for the Straight Segment Approximation of Periodic Vortex Wakes

Abstract

Abstract. The periodic, helical vortex wakes of wind turbines, propellers, and helicopters are often approximated using straight vortex segments which cannot reproduce the binormal velocity associated with the local curvature. This leads to the need for the first curvature correction which is well known and understood. It is less well known that under some circumstances, the binormal velocity determined from straight segments needs a second correction when the periodicity returns the vortex to the proximity of the point at which the velocity is required. This paper analyzes the second correction by modeling the helical

Helical vortices and wind turbine aerodynamics

“…The 1=p term arises from the periodic return of the vortex to the proximity of the point at which the velocity is required, primarily by the¯rst return on either side of the point. Just as straight segments cannot reproduce the logarithmic curvature term, they also miss the 1=p \proximity" term, 28 where a simple correction is developed. A procedure for using a vortex ring as a model for the e®ects of vortex curvature on any vortex was introduced by Moore and Sa®man, 29 and applied by Ricca 30 to helical vortices.…”

“…These results, taken from Ref. 28, are the¯rst to use HVT to calculate F u and F w . It is highly likely that numerical issues have not been entirely resolved.…”