Dynamic modeling and analysis of vortex filament motion using a novel curve-fitting method

Kim, Chang-Joo; Park, Soo Hyung; Sung, Sang Kyung; Jung, Sung-Nam

doi:10.1016/j.cja.2015.12.019

Cited by 8 publications

(8 citation statements)

References 19 publications

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“…It is noted that the correction developed here is simple in the sense that the vortex curvature is known a priori. As pointed out by Govindarajan and Leishman (2016), however, and shown by the analysis of Kim et al (2016), the modelling of three-dimensional wakes of varying geometry can be considerably more complex. One of these complexities is that the control point may not align with the junction of segments on (in this case) adjacent rings.…”

Section: Straight Segment Approximation Of Vortex Rings and Its Accuracymentioning

confidence: 99%

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

Wood

2018

Wind Energ. Sci.

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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 modelling the helical far wake of a wind turbine as an infinite row of equispaced vortex rings of constant radius and circulation. The ring spacing is proportional to the helix pitch. The second correction is required at small vortex pitch, which is typical of the operating conditions of large modern turbines. Then the velocity induced by the periodic wake can greatly exceed the local curvature contribution. The second correction is quadratic in the inverse of the number of segments per ring and linear in the inverse spacing. An approximate expression is developed for the second correction and shown to reduce the errors by an order of magnitude.

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Section: Straight Segment Approximation Of Vortex Rings and Its Accuracymentioning

confidence: 99%

“…Bhagwat and Leishman, 2014, Govindarajan and Leishman, 2016, and Kim et al, 2016. This leads to the need for the first curvature correction.…”

Section: Introductionmentioning

confidence: 99%

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

Wood

2018

Wind Energ. Sci.

View full text Add to dashboard Cite

show abstract

“…A well-known difficulty of the straight segment approximation is that it does not reproduce the binormal velocity due to the curvature of the vortex line (e.g. Bhagwat and Leishman, 2014, Govindarajan and Leishman, 2016, and Kim et al, 2016. This leads to the need for the first curvature correction.…”

Section: Introductionmentioning

confidence: 99%

response to reviewer comments

Wood¹

2018

Preprint

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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 modelling the helical far wake of a wind turbine as an infinite row of equispaced vortex rings of constant radius and circulation. The ring spacing is proportional to the helix pitch. The second correction is required at small vortex pitch, which is typical of the operating conditions of large modern turbines. Then the velocity induced by the periodic wake can greatly exceed the local curvature contribution. The second correction is quadratic in the inverse of the number of segments per ring and linear in the inverse spacing. An approximate expression is developed for the second correction and shown to reduce the errors by an order of magnitude.

show abstract

“…A well known difficulty of the straight segment approximation is that it does not reproduce the binormal velocity due to the curvature of the vortex line, eg Bhagwat & Leishman (2014), Govindarajan & Leishman (2016), and Kim et al (2016). This 20 leads to the need for the first curvature correction.…”

Section: Introductionmentioning

confidence: 99%

“…Govindarajan & Leishman (2016), however, and shown by the analysis of Kim et al (2016), the modeling of three-dimensional wakes of varying geometry can be considerably more complex.…”

mentioning

confidence: 99%

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

Wood¹

2018

Preprint

View full text Add to dashboard Cite

show abstract

Dynamic modeling and analysis of vortex filament motion using a novel curve-fitting method

Cited by 8 publications

References 19 publications

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

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

response to reviewer comments

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

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