3-D shear-layer model for the simulation of multiple wind turbine wakes: description and first assessment

Trabucchi, Davide; Vollmer, Lukas; Kühn, Martin

doi:https://doi.org/10.5194/wes-2-569-2017

Articles | Volume 2, issue 2

https://doi.org/10.5194/wes-2-569-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue:

The Science of Making Torque from Wind (TORQUE) 2016

https://doi.org/10.5194/wes-2-569-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 2, issue 2

Research article

|

22 Nov 2017

Research article |

| 22 Nov 2017

3-D shear-layer model for the simulation of multiple wind turbine wakes: description and first assessment

Davide Trabucchi, Lukas Vollmer, and Martin Kühn

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Final revised paper (published on 22 Nov 2017)
Preprint (discussion started on 06 Feb 2017)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC1: 'Review of the paper “3D Shear layer simulation model for the mutual interaction of wind turbine wakes: Description and first assessment”', Anonymous Referee #1, 06 Mar 2017
- AC1: 'Response to referee #1', Davide Trabucchi, 14 Mar 2017
RC2: 'Review of the paper 3D shear layer model for the mutual interaction of wind turbine wakes', Nicolai Gayle Nygaard, 12 Mar 2017
- AC2: 'Response to referee #2', Davide Trabucchi, 17 Mar 2017

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (07 Apr 2017) by Jens Nørkær Sørensen

AR by Davide Trabucchi on behalf of the Authors (27 Jun 2017) Author's response Manuscript

ED: Referee Nomination & Report Request started (03 Jul 2017) by Jens Nørkær Sørensen

RR by Nicolai Gayle Nygaard (03 Aug 2017)

Suggestions for revision or reasons for rejection

Review of 3D shear layer model for the simulation of multiple wind turbine wakes – revised edition
By Trabucchi, Vollmer and Kühn

The authors have incorporated the suggestions by both reviewers and expanded and improved the paper. I recommend publication without further review, but in the proofs the authors should consider the points below.

• Eq. (1) – The form of u_i(z) is never specified. The description of the LES setup in section 3.1 specifies a neutral boundary layer, but in the description of the shear layer models this is not made clear. Since the z-dependence in Eq. (1) is explicit, I assume that the calculations were performed with a shear profile for the background flow.
• As a matter of language, I am not sure that it is optimal to call u_D a deficit. Outside the wake it approaches 1, whereas the deficits typically defined in the literature approach zero outside the wake region. To me u_D is more aptly described as a normalized velocity. This may be a matter of taste, but consider it.
• The inclusion of the z-dependent term u_i(z) in the definition of u_D confuses me, when it comes to equations (2), (3) and (6). In the terms containing the partial derivative with respect to z of u_D there will be the normal derivative of the u-part of u_D. But there will be an additional contribution from the derivative of u_i with respect to z. Where do those additional terms come from in the RANS and eddy viscosity equations? Unless there is a typo in the equations and u_D should have been u in the z-derivative terms, maybe a brief remark would help reader. In the local strain rate u’_z above Eq. (17) you use u and not u_D.
• A reference to the numerical stability of the problem stated in Eq. (7) is needed.
• Eq. (14) should the k in the first term be \kappa?
• Is there a square root missing in Eq. (18)? Dimensionally (not considering the normalization with u_H) the left-hand side is a velocity, while the right-hand side is a velocity squared.
• What is (A/S) at the bottom of page 9?
• The parameter N_j In Eqs. (19) and (20) is not defined.
• In table 1 the first line under Test case 3 has value 0.17 and 0.38, but the text on page 13 states that the two models differ by 11 percentage points. Which is right?
• P. 13, line 21: I believe the reference to figure 9 should have been to figure 11.
• P. 14, line 12: add ‘a’ in before possible.
• P.14, line 23: change add to adds.
• In connection with the regression plot figures (6, 8 , 10 and 12) the authors should comment on the curved shape of u_model vs. u_LES. Especially for figure 6 and 12 there are regions with overestimation and regions with underestimation of the wind speed by both models. My interpretation of this is that the wind speeds plotted are takes at different locations in the wake. If true, this should be made clear. One could get the impression that the different wind speeds corresponded to the inflow wind speed, and the figures summarized multiple flow calculations. That would then lead to the misconception that the models are unsuitable at low wind speeds. To remove the possibility of confusion (and further elaborate on the regression results, for example in the discussion on page 14) I suggest including comments making it clear that the low wind speeds come from the near wake region and the higher wind speeds from the far wake region, where the wind speed has recovered towards the free stream value. Figures 1 and 4 indicate that the modelled wind speed in the near wake are too small. Coupled with the subsequent overestimation at intermediate wind speeds this conservative initial condition further suggests that the wake expansion in the model is initially too fast. This links directly to the discussion on 14, but could be made clearer in the paper.

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RR by Anonymous Referee #3 (31 Aug 2017)

Suggestions for revision or reasons for rejection

Review of paper submitted to WES
Title: " 3D Shear layer model for the simulation of multiple wind turbine wakes: Description and first assessment "
Code wes-2017-1
Date of review: 31-August-2017

The authors present a numerical simulation of the rotor wakes behind the different combination of wind turbines. The paper aim is clearly described and motivated. Undoubtedly, the topic covered in this paper has a strong practical interest.
Nevertheless, their wake modeling includes many assumptions: 1) RANS equations was used; 2) the steady case of the shear layer approximation was considered; 3) the viscous term is not considered; 4) the shear stress terms of the Eqs. was modelled by means of an eddy viscosity; 5) the wind velocity components were defined by a conservative vector field with a scalar potential function; 6) a disc actuator model was applied for the initial condition etc.
Each assumption looks as a reasonable step, but the prediction of the total errors in their combination is impossible. The authors tested it by a comparison with other numerical models in which other assumption were used. From my point of view, the correct comparison should be made with experimental data. The suitable natural experiments for the wake development are absent now, the laboratory tests can be utilized for this purpose e.g.
1) Bartl J, Pierella F, Sætran L. Wake measurements behind an array of two model wind turbines. Energy Procedia 2012; 24:305-312.
2) Okulov VL, Mikkelsen RF, Naumov IV, Litvinov IV, Gesheva E, Sørensen JN. Comparison of the far wake behind dual rotor and dual disk configurations. Journal of Physics: Conference Series 2016; 753: 032060.
etc.
Thus, I can recommend this paper for publication, but the comparison with the experiments is desirable.

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ED: Publish subject to minor revisions (review by editor) (03 Sep 2017) by Jens Nørkær Sørensen

AR by Davide Trabucchi on behalf of the Authors (22 Sep 2017) Author's response Manuscript

ED: Publish as is (01 Oct 2017) by Jens Nørkær Sørensen

ED: Publish as is (02 Oct 2017) by Jakob Mann (Chief editor)

AR by Davide Trabucchi on behalf of the Authors (12 Oct 2017)

Short summary

The wakes of wind turbines cause losses in the energy production of a wind farm. The accuracy of models applied to predict wake losses is a key factor for new wind projects. This paper presents an engineering wake model that can simulate merging wakes on the basis of physical principles. We used high-fidelity simulations of merging wakes to assess this model and found a better agreement with the reference than commonly used models implementing the superposition of individual wakes.