Abstract
The analysis of the self-induced velocity of a single helical vortex (Boersma &
Wood 1999) is extended to include equally spaced multiple vortices. This arrangement
approximates the tip vortices in the far wake of multi-bladed wind turbines, propellers,
or rotors in ascending, descending, or hovering flight. The problem is reduced to
finding, from the Biot–Savart law, the additional velocity of a helix due to an identical
helix displaced azimuthally. The resulting Biot–Savart integral is further reduced to a
Mellin–Barnes integral representation which allows the asymptotic expansions to be
determined for small and for large pitch. The Biot–Savart integral is also evaluated
numerically for a total of two, three and four vortices over a range of pitch values.
The previous finding that the self-induced velocity at small pitch is dominated by
a term inversely proportional to the pitch carries over to multiple vortices. It is
shown that a far wake dominated by helical tip vortices is consistent with the one-dimensional
representation that leads to the Betz limit on the power output of wind
turbines. The small-pitch approximation then allows the determination of the blade&s
bound vorticity for optimum power extraction. The present analysis is shown to give
reasonable estimates for the vortex circulation in experiments using a single hovering
rotor and a four-bladed propeller.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
31 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献