Linearised CFD Models for Wakes

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Abstract

This report describes the development of a fast and reasonably accurate model for the prediction of energy production in oshore wind farms taking wake eects into account. The model has been implemented as a windows application called Fuga which can run in batch mode or as a graphical user interface. Fuga is brie y described. The model is based on alinearization technique which is described in some detail, and linearized, governing equations are derived and written in a standard form based on a mixed{spectral formulation. A new solution method is used to solve the equations which involves intensive use of look{up tables for storage of intermediate results. Due to the linearity of the model, multiple wakes from many turbines can be constructed from the wake of a single, solitary turbine. These are in turn constructed from Fourier components by a fast Fourier integral transform of results derived from generic look{up tables. Three dierent models, based on three dierent closures, are examined:
 - the 'simple closure' using an unperturbed eddy viscosity uz
 - the mixing length closure
 - the E-ε closure
Model results are evaluated against oshore wind farm production data from Horns Rev I and the Nysted wind farm, and a comparison with direct wake measurements in an onshore turbine (Nibe B) is also made. A very satisfactory agreement with data is found for the simple closure. The exception is the near wake, just behind the rotor, where all three linearized models fail. The mixing length closure underestimates wake eects in all cases. The E-ε closure overestimates wake losses in the oshore farms while it predicts a too shallow and too wide the wake in the onshore case. The simple closure performs distinctly better than the other two. Wind speed data from the the Horns rev met masts are used to further validate Fuga results with the 'simple' closure. Finally, Rdsand 1 and 2 are used as an example to illustrate the interaction between wind farms.
Original languageEnglish
Place of PublicationRoskilde
PublisherDanmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi
Number of pages39
ISBN (Print)978-87-550-3892-9
Publication statusPublished - 2011
SeriesDenmark. Forskningscenter Risoe. Risoe-R
Number1772(EN)
ISSN0106-2840

Keywords

  • Risø-R-1772
  • Risø-R-1772(EN)

Cite this

Ott, S., Berg, J., & Nielsen, M. (2011). Linearised CFD Models for Wakes. Roskilde: Danmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi. Denmark. Forskningscenter Risoe. Risoe-R, No. 1772(EN)
Ott, Søren ; Berg, Jacob ; Nielsen, Morten. / Linearised CFD Models for Wakes. Roskilde : Danmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi, 2011. 39 p. (Denmark. Forskningscenter Risoe. Risoe-R; No. 1772(EN)).
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Ott, S, Berg, J & Nielsen, M 2011, Linearised CFD Models for Wakes. Denmark. Forskningscenter Risoe. Risoe-R, no. 1772(EN), Danmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi, Roskilde.

Linearised CFD Models for Wakes. / Ott, Søren; Berg, Jacob; Nielsen, Morten.

Roskilde : Danmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi, 2011. 39 p. (Denmark. Forskningscenter Risoe. Risoe-R; No. 1772(EN)).

Research output: Book/ReportReport

TY - RPRT

T1 - Linearised CFD Models for Wakes

AU - Ott, Søren

AU - Berg, Jacob

AU - Nielsen, Morten

PY - 2011

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N2 - This report describes the development of a fast and reasonably accurate model for the prediction of energy production in oshore wind farms taking wake eects into account. The model has been implemented as a windows application called Fuga which can run in batch mode or as a graphical user interface. Fuga is brie y described. The model is based on alinearization technique which is described in some detail, and linearized, governing equations are derived and written in a standard form based on a mixed{spectral formulation. A new solution method is used to solve the equations which involves intensive use of look{up tables for storage of intermediate results. Due to the linearity of the model, multiple wakes from many turbines can be constructed from the wake of a single, solitary turbine. These are in turn constructed from Fourier components by a fast Fourier integral transform of results derived from generic look{up tables. Three dierent models, based on three dierent closures, are examined: - the 'simple closure' using an unperturbed eddy viscosity uz - the mixing length closure  - the E-ε closure Model results are evaluated against oshore wind farm production data from Horns Rev I and the Nysted wind farm, and a comparison with direct wake measurements in an onshore turbine (Nibe B) is also made. A very satisfactory agreement with data is found for the simple closure. The exception is the near wake, just behind the rotor, where all three linearized models fail. The mixing length closure underestimates wake eects in all cases. The E-ε closure overestimates wake losses in the oshore farms while it predicts a too shallow and too wide the wake in the onshore case. The simple closure performs distinctly better than the other two. Wind speed data from the the Horns rev met masts are used to further validate Fuga results with the 'simple' closure. Finally, Rdsand 1 and 2 are used as an example to illustrate the interaction between wind farms.

AB - This report describes the development of a fast and reasonably accurate model for the prediction of energy production in oshore wind farms taking wake eects into account. The model has been implemented as a windows application called Fuga which can run in batch mode or as a graphical user interface. Fuga is brie y described. The model is based on alinearization technique which is described in some detail, and linearized, governing equations are derived and written in a standard form based on a mixed{spectral formulation. A new solution method is used to solve the equations which involves intensive use of look{up tables for storage of intermediate results. Due to the linearity of the model, multiple wakes from many turbines can be constructed from the wake of a single, solitary turbine. These are in turn constructed from Fourier components by a fast Fourier integral transform of results derived from generic look{up tables. Three dierent models, based on three dierent closures, are examined: - the 'simple closure' using an unperturbed eddy viscosity uz - the mixing length closure  - the E-ε closure Model results are evaluated against oshore wind farm production data from Horns Rev I and the Nysted wind farm, and a comparison with direct wake measurements in an onshore turbine (Nibe B) is also made. A very satisfactory agreement with data is found for the simple closure. The exception is the near wake, just behind the rotor, where all three linearized models fail. The mixing length closure underestimates wake eects in all cases. The E-ε closure overestimates wake losses in the oshore farms while it predicts a too shallow and too wide the wake in the onshore case. The simple closure performs distinctly better than the other two. Wind speed data from the the Horns rev met masts are used to further validate Fuga results with the 'simple' closure. Finally, Rdsand 1 and 2 are used as an example to illustrate the interaction between wind farms.

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KW - Risø-R-1772(EN)

M3 - Report

SN - 978-87-550-3892-9

T3 - Denmark. Forskningscenter Risoe. Risoe-R

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PB - Danmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi

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Ott S, Berg J, Nielsen M. Linearised CFD Models for Wakes. Roskilde: Danmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi, 2011. 39 p. (Denmark. Forskningscenter Risoe. Risoe-R; No. 1772(EN)).