Far-wake meandering induced by atmospheric eddies in flow past a wind turbine

Xiaojian Mao*, J. N. Sorensen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

170 Downloads (Pure)

Abstract

A novel algorithm is developed to calculate the nonlinear optimal boundary perturbations in three-dimensional incompressible flow. An optimal step length in the optimization loop is calculated without any additional calls to the Navier-Stokes equations. The algorithm is applied to compute the optimal inflow eddies for the flow around a wind turbine to clarify the mechanisms behind wake meandering, a phenomenon usually observed in wind farms. The turbine is modelled as an actuator disc using an immersed boundary method with the loading prescribed as a body force. At Reynolds number (based on free-stream velocity and turbine radius) Re = 1000, the most energetic inflow perturbation has a frequency omega = 0.8-2, and is in the form of an azimuthal wave with wavenumber m = 1 and the same radius as the actuator disc. The inflow perturbation is amplified by the strong shear downstream of the edge of the disc and then tilts the rolling-up vortex rings to induce wake meandering. This mechanism is verified by studying randomly perturbed flow at Re
Original languageEnglish
JournalJournal of Fluid Mechanics
Volume846
Pages (from-to)190-209
Number of pages20
ISSN0022-1120
DOIs
Publication statusPublished - 2018

Bibliographical note

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Keywords

  • Nonlinear instability
  • Vortex shedding
  • Wakes

Cite this

@article{d860ee117d5644b0819224dc977cb3d4,
title = "Far-wake meandering induced by atmospheric eddies in flow past a wind turbine",
abstract = "A novel algorithm is developed to calculate the nonlinear optimal boundary perturbations in three-dimensional incompressible flow. An optimal step length in the optimization loop is calculated without any additional calls to the Navier-Stokes equations. The algorithm is applied to compute the optimal inflow eddies for the flow around a wind turbine to clarify the mechanisms behind wake meandering, a phenomenon usually observed in wind farms. The turbine is modelled as an actuator disc using an immersed boundary method with the loading prescribed as a body force. At Reynolds number (based on free-stream velocity and turbine radius) Re = 1000, the most energetic inflow perturbation has a frequency omega = 0.8-2, and is in the form of an azimuthal wave with wavenumber m = 1 and the same radius as the actuator disc. The inflow perturbation is amplified by the strong shear downstream of the edge of the disc and then tilts the rolling-up vortex rings to induce wake meandering. This mechanism is verified by studying randomly perturbed flow at Re",
keywords = "Nonlinear instability, Vortex shedding, Wakes",
author = "Xiaojian Mao and Sorensen, {J. N.}",
note = "This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.",
year = "2018",
doi = "10.1017/jfm.2018.275",
language = "English",
volume = "846",
pages = "190--209",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

Far-wake meandering induced by atmospheric eddies in flow past a wind turbine. / Mao, Xiaojian; Sorensen, J. N.

In: Journal of Fluid Mechanics, Vol. 846, 2018, p. 190-209.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Far-wake meandering induced by atmospheric eddies in flow past a wind turbine

AU - Mao, Xiaojian

AU - Sorensen, J. N.

N1 - This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

PY - 2018

Y1 - 2018

N2 - A novel algorithm is developed to calculate the nonlinear optimal boundary perturbations in three-dimensional incompressible flow. An optimal step length in the optimization loop is calculated without any additional calls to the Navier-Stokes equations. The algorithm is applied to compute the optimal inflow eddies for the flow around a wind turbine to clarify the mechanisms behind wake meandering, a phenomenon usually observed in wind farms. The turbine is modelled as an actuator disc using an immersed boundary method with the loading prescribed as a body force. At Reynolds number (based on free-stream velocity and turbine radius) Re = 1000, the most energetic inflow perturbation has a frequency omega = 0.8-2, and is in the form of an azimuthal wave with wavenumber m = 1 and the same radius as the actuator disc. The inflow perturbation is amplified by the strong shear downstream of the edge of the disc and then tilts the rolling-up vortex rings to induce wake meandering. This mechanism is verified by studying randomly perturbed flow at Re

AB - A novel algorithm is developed to calculate the nonlinear optimal boundary perturbations in three-dimensional incompressible flow. An optimal step length in the optimization loop is calculated without any additional calls to the Navier-Stokes equations. The algorithm is applied to compute the optimal inflow eddies for the flow around a wind turbine to clarify the mechanisms behind wake meandering, a phenomenon usually observed in wind farms. The turbine is modelled as an actuator disc using an immersed boundary method with the loading prescribed as a body force. At Reynolds number (based on free-stream velocity and turbine radius) Re = 1000, the most energetic inflow perturbation has a frequency omega = 0.8-2, and is in the form of an azimuthal wave with wavenumber m = 1 and the same radius as the actuator disc. The inflow perturbation is amplified by the strong shear downstream of the edge of the disc and then tilts the rolling-up vortex rings to induce wake meandering. This mechanism is verified by studying randomly perturbed flow at Re

KW - Nonlinear instability

KW - Vortex shedding

KW - Wakes

U2 - 10.1017/jfm.2018.275

DO - 10.1017/jfm.2018.275

M3 - Journal article

VL - 846

SP - 190

EP - 209

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -