Vortex filament methods can be used to model the velocity field induced by the three-dimensional, helicoidallike vortical wake structures produced behind wind turbines. To this end, the numerical accuracy of a straightline filament approximation to helicoidal vortices is considered. The problem is examined for different values of the helical pitch, the number of wake turns, and the wake skew angle. Results documenting both the accuracy and the relative errors of a discretized helical vortex and of a vortex ring are compared. It is found that with sufficiently small segments, straight-line segmentation gives at least a second-order accurate reconstruction of the induced velocity field. It is shown that the vortex ring can be viewed as a special case of a helical vortex as its pitch tends to zero. Based on the magnitude of the errors found for the two cases, a vortex ring is shown to be a more stringent case to model accurately compared to a helical vortex when using the filament approach. The accuracy of the induced velocity field when representing a skewed helix by straight-line segmentation is also performed, which is shown to be second-order accurate for various combinations of wake helical pitch and wake skew angle. A comparison with the unskewed helical vortex reveals that the errors in the induced velocity field are almost the same in two cases. NOMENCLATURE
[1]
J. Gordon Leishman,et al.
Principles of Helicopter Aerodynamics
,
2000
.
[2]
R. Lewis,et al.
Vortex Element Methods for Fluid Dynamic Analysis of Engineering Systems
,
1991
.
[3]
D. Wood,et al.
Assessment of the Accuracy of Representing a Helical Vortex by Straight Segments
,
2002
.
[4]
J. Gordon Leishman,et al.
Challenges in modelling the unsteady aerodynamics of wind turbines
,
2002
.
[5]
J. Gordon Leishman,et al.
Technical Note: Accuracy of Straight-Line Segmentation Applied to Curvilinear Vortex Filaments
,
2001
.
[6]
J. Boersma,et al.
On the motion of multiple helical vortices
,
2001,
Journal of Fluid Mechanics.
[7]
J. Gordon Leishman,et al.
Challenges in Modeling the Unsteady Aerodynamics of Wind Turbines
,
2002
.
[8]
J. Boersma,et al.
On the self-induced motion of a helical vortex
,
1999,
Journal of Fluid Mechanics.
[9]
A. J. Landgrebe,et al.
Helicopter rotor wake geometry and its influence in forward flight. Volume 2: Wake geometry charts
,
1983
.