Analysis of turbulent wake behind a wind turbine

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Abstract

The aim of this study is to improve the classical analytical model for estimation of the rate of wake expansion and the decay of wake velocity deficit in the far wake region behind a wind turbine. The relations for a fully turbulent axisymmetric far wake were derived by applying the mass and momentum conservations, the selfsimilarity of mean velocity profile and the eddy viscosity closure. The theoretical approach is validated using the numerical results obtained from large eddy simulations with an actuator line technique at 0.1% and 3% ambient turbulence level and ambient wind velocity of 10 m/s, and 0.1% ambient turbulence level and ambient wind velocity of 7 m/s. The obtained results showed that neglecting the nonlinear term of velocity in the momentum equation in the far wake region cannot be a fair assumption, unlike what is generally assumed in most of text books of fluid mechanics. Therefore the theoretical determination of the power law for the wake expansion and the decay of the wake velocity deficit may not be valid in the case of the wake generated behind a wind turbine with low ambient turbulence and high thrust coefficient. Although at higher ambient turbulence levels or lower ambient wind velocities (higher thrust coefficients), this trend may be improved due to the faster recovery of the wake and therefore closer values to the theoretical approach may be obtained. In addition, the assumption of self-similarity behavior of the mean velocity profile, when scaled with center line velocity deficit, could be correct in the far wake region of a wind turbine and low ambient turbulence levels.
Original languageEnglish
Title of host publicationProceedings of the 2013 International Conference on aerodynamics of Offshore Wind Energy Systems and wakes (ICOWES2013)
EditorsWenZhong Shen
Number of pages16
PublisherTechnical University of Denmark
Publication date2013
Publication statusPublished - 2013
EventInternational Conference on aerodynamics of Offshore Wind Energy Systems and wakes (ICOWES 2013) - Lyngby, Denmark
Duration: 17 Jun 201319 Jun 2013

Conference

ConferenceInternational Conference on aerodynamics of Offshore Wind Energy Systems and wakes (ICOWES 2013)
CountryDenmark
CityLyngby
Period17/06/201319/06/2013

Cite this

Kermani, N. A., Andersen, S. J., Sørensen, J. N., & Shen, W. Z. (2013). Analysis of turbulent wake behind a wind turbine. In W. Shen (Ed.), Proceedings of the 2013 International Conference on aerodynamics of Offshore Wind Energy Systems and wakes (ICOWES2013) Technical University of Denmark.
Kermani, Nasrin Arjomand ; Andersen, Søren Juhl ; Sørensen, Jens Nørkær ; Shen, Wen Zhong. / Analysis of turbulent wake behind a wind turbine. Proceedings of the 2013 International Conference on aerodynamics of Offshore Wind Energy Systems and wakes (ICOWES2013). editor / WenZhong Shen. Technical University of Denmark, 2013.
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abstract = "The aim of this study is to improve the classical analytical model for estimation of the rate of wake expansion and the decay of wake velocity deficit in the far wake region behind a wind turbine. The relations for a fully turbulent axisymmetric far wake were derived by applying the mass and momentum conservations, the selfsimilarity of mean velocity profile and the eddy viscosity closure. The theoretical approach is validated using the numerical results obtained from large eddy simulations with an actuator line technique at 0.1{\%} and 3{\%} ambient turbulence level and ambient wind velocity of 10 m/s, and 0.1{\%} ambient turbulence level and ambient wind velocity of 7 m/s. The obtained results showed that neglecting the nonlinear term of velocity in the momentum equation in the far wake region cannot be a fair assumption, unlike what is generally assumed in most of text books of fluid mechanics. Therefore the theoretical determination of the power law for the wake expansion and the decay of the wake velocity deficit may not be valid in the case of the wake generated behind a wind turbine with low ambient turbulence and high thrust coefficient. Although at higher ambient turbulence levels or lower ambient wind velocities (higher thrust coefficients), this trend may be improved due to the faster recovery of the wake and therefore closer values to the theoretical approach may be obtained. In addition, the assumption of self-similarity behavior of the mean velocity profile, when scaled with center line velocity deficit, could be correct in the far wake region of a wind turbine and low ambient turbulence levels.",
author = "Kermani, {Nasrin Arjomand} and Andersen, {S{\o}ren Juhl} and S{\o}rensen, {Jens N{\o}rk{\ae}r} and Shen, {Wen Zhong}",
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Kermani, NA, Andersen, SJ, Sørensen, JN & Shen, WZ 2013, Analysis of turbulent wake behind a wind turbine. in W Shen (ed.), Proceedings of the 2013 International Conference on aerodynamics of Offshore Wind Energy Systems and wakes (ICOWES2013). Technical University of Denmark, International Conference on aerodynamics of Offshore Wind Energy Systems and wakes (ICOWES 2013), Lyngby, Denmark, 17/06/2013.

Analysis of turbulent wake behind a wind turbine. / Kermani, Nasrin Arjomand; Andersen, Søren Juhl; Sørensen, Jens Nørkær; Shen, Wen Zhong.

Proceedings of the 2013 International Conference on aerodynamics of Offshore Wind Energy Systems and wakes (ICOWES2013). ed. / WenZhong Shen. Technical University of Denmark, 2013.

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

TY - GEN

T1 - Analysis of turbulent wake behind a wind turbine

AU - Kermani, Nasrin Arjomand

AU - Andersen, Søren Juhl

AU - Sørensen, Jens Nørkær

AU - Shen, Wen Zhong

PY - 2013

Y1 - 2013

N2 - The aim of this study is to improve the classical analytical model for estimation of the rate of wake expansion and the decay of wake velocity deficit in the far wake region behind a wind turbine. The relations for a fully turbulent axisymmetric far wake were derived by applying the mass and momentum conservations, the selfsimilarity of mean velocity profile and the eddy viscosity closure. The theoretical approach is validated using the numerical results obtained from large eddy simulations with an actuator line technique at 0.1% and 3% ambient turbulence level and ambient wind velocity of 10 m/s, and 0.1% ambient turbulence level and ambient wind velocity of 7 m/s. The obtained results showed that neglecting the nonlinear term of velocity in the momentum equation in the far wake region cannot be a fair assumption, unlike what is generally assumed in most of text books of fluid mechanics. Therefore the theoretical determination of the power law for the wake expansion and the decay of the wake velocity deficit may not be valid in the case of the wake generated behind a wind turbine with low ambient turbulence and high thrust coefficient. Although at higher ambient turbulence levels or lower ambient wind velocities (higher thrust coefficients), this trend may be improved due to the faster recovery of the wake and therefore closer values to the theoretical approach may be obtained. In addition, the assumption of self-similarity behavior of the mean velocity profile, when scaled with center line velocity deficit, could be correct in the far wake region of a wind turbine and low ambient turbulence levels.

AB - The aim of this study is to improve the classical analytical model for estimation of the rate of wake expansion and the decay of wake velocity deficit in the far wake region behind a wind turbine. The relations for a fully turbulent axisymmetric far wake were derived by applying the mass and momentum conservations, the selfsimilarity of mean velocity profile and the eddy viscosity closure. The theoretical approach is validated using the numerical results obtained from large eddy simulations with an actuator line technique at 0.1% and 3% ambient turbulence level and ambient wind velocity of 10 m/s, and 0.1% ambient turbulence level and ambient wind velocity of 7 m/s. The obtained results showed that neglecting the nonlinear term of velocity in the momentum equation in the far wake region cannot be a fair assumption, unlike what is generally assumed in most of text books of fluid mechanics. Therefore the theoretical determination of the power law for the wake expansion and the decay of the wake velocity deficit may not be valid in the case of the wake generated behind a wind turbine with low ambient turbulence and high thrust coefficient. Although at higher ambient turbulence levels or lower ambient wind velocities (higher thrust coefficients), this trend may be improved due to the faster recovery of the wake and therefore closer values to the theoretical approach may be obtained. In addition, the assumption of self-similarity behavior of the mean velocity profile, when scaled with center line velocity deficit, could be correct in the far wake region of a wind turbine and low ambient turbulence levels.

M3 - Article in proceedings

BT - Proceedings of the 2013 International Conference on aerodynamics of Offshore Wind Energy Systems and wakes (ICOWES2013)

A2 - Shen, WenZhong

PB - Technical University of Denmark

ER -

Kermani NA, Andersen SJ, Sørensen JN, Shen WZ. Analysis of turbulent wake behind a wind turbine. In Shen W, editor, Proceedings of the 2013 International Conference on aerodynamics of Offshore Wind Energy Systems and wakes (ICOWES2013). Technical University of Denmark. 2013