The aerodynamics of the curled wake: a simplified model in view of flow control

Martínez-Tossas, Luis A.; Annoni, Jennifer; Fleming, Paul A.; Churchfield, Matthew J.

doi:https://doi.org/10.5194/wes-4-127-2019

Articles | Volume 4, issue 1

https://doi.org/10.5194/wes-4-127-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/wes-4-127-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 4, issue 1

Research article

|

05 Mar 2019

Research article |

| 05 Mar 2019

The aerodynamics of the curled wake: a simplified model in view of flow control

Luis A. Martínez-Tossas, Jennifer Annoni, Paul A. Fleming, and Matthew J. Churchfield

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Final revised paper (published on 05 Mar 2019)
Preprint (discussion started on 07 Aug 2018)

Interactive discussion

Status: closed

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

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- Supplement

RC1: 'Review', Anonymous Referee #1, 24 Aug 2018
- AC1: 'Response Reviewer 1', Luis Martinez, 05 Nov 2018
RC2: 'Review of Manuscript # wes-2018-57', Anonymous Referee #2, 05 Oct 2018
- AC2: 'Response Reviewer 2', Luis Martinez, 06 Nov 2018

Peer-review completion

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

AR by Luis Martinez on behalf of the Authors (06 Nov 2018) Author's response Manuscript

ED: Referee Nomination & Report Request started (13 Nov 2018) by Jens Nørkær Sørensen

RR by Anonymous Referee #2 (03 Dec 2018)

RR by Anonymous Referee #3 (22 Dec 2018)

Suggestions for revision or reasons for rejection

Review of "The aerodynamics of the curled wake: A simplified model in view of flow control"

I have joined the review process from this round, so my comments will be based on the latest version of the manuscript as well as previous reviewers’ comments. In this manuscript, a model based on linearized form of Navier-Stokes equations is developed that can capture and predict the curled wakes of yawed turbines. The paper is overall clear, well written, and it contains results that are indeed interesting and useful for the wind energy community, especially for those interested in yaw angle control. I especially appreciate the part where model advantages as well as its limitations are clearly presented. However, I have some major concerns over the way results are presented in this manuscript. I therefore believe the paper will merit publication in the wind energy science (WES), provided the authors can address my comments:

• It is useful that the model results are compared with those of the Gaussian model. However, the paper still suffers from the lack of quantitative comparison with the more conceptually similar model proposed by Shapiro et al. (2018). In my opinion, it is quite important to explicitly clarify the difference of the present work with the mentioned study in terms of model derivation, and then also add predictions of Shapiro et al. model to Figs. 8 and 9. I believe this comparison can be informative and useful for readers.

• Eq. 4: u’*du’/dx is neglected although it is later considered in Eq. 16.

• Figure 6: I understand that incoming turbulence is not directly used in the proposed model, but I think it is of interest to report the vertical profile of turbulence intensity, or at least please report the value of the streamwise turbulence intensity at hub height.

• Page 14, line 10: “It is interesting to note that both models under-predict the displacement in the far wake compared to the LES”. I found the previous sentence in contrast to what is reported in the Figure 8 for the Gaussian model predictions at x=8D.

• Figure 10: For the downwind turbine, which initial conditions are used for V and W? If, as mentioned in the introduction, each turbine is treated individually, and turbine wakes are added later using the sum of squares, I cannot understand how the curl of the first turbine can affect the wake of the second turbine.

• Figure 8: I found the near-wake deflection predicted by the Gaussian model much bigger than what I expect. For instance, the wake center deflection at x/D=3 seems to be less than 0.2D in model predictions reported by Bastankhah and Porte-Agel (2016) (See Fig. 21 in the original paper), whereas it is more than 0.5D in figure 8 of the current paper. Please report input parameters such as the wake growth rate, etc. and insure that the model is implemented properly.

Minor comments:

• Introduction: I think “controls community” should be replaced by “control’s community”.
• Eq. 1: I suppose u, v and w are time-averaged velocity components as the effective viscosity is used. Please mention if that is the case.
• Page 3, Line 3: Please explain here what U, V, W and u,v,w mean physically so that it is easier for readers to understand the assumptions made in the following.
• Eq 9: If I understood well, z_i should be the location of i-th vortice with respect to the rotor coordinate system as opposed to z_i defined in Eq. 7 as the one with respect to each vortex position. Please clarify this.
• Figs. 4 and 5: Please change the color for LES results as they can be hardly seen in a printed version. Add “axial” before “velocity” in the figure captions.
• Page 11, line 1: Add “line” after “vertical”.
• Page 11, line 3: Replace “capture” with “captured”.

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ED: Reconsider after major revisions (23 Dec 2018) by Jens Nørkær Sørensen

AR by Luis Martinez on behalf of the Authors (04 Jan 2019) Author's response Manuscript

ED: Referee Nomination & Report Request started (15 Jan 2019) by Jens Nørkær Sørensen

RR by Anonymous Referee #2 (28 Jan 2019)

RR by Anonymous Referee #3 (29 Jan 2019)

ED: Publish as is (29 Jan 2019) by Jens Nørkær Sørensen

ED: Publish as is (06 Feb 2019) by Joachim Peinke (Chief editor)

AR by Luis Martinez on behalf of the Authors (12 Feb 2019)

Short summary

A new control-oriented model is developed to compute the wake of a wind turbine under yaw. The model uses a simplified version of the Navier–Stokes equation with assumptions. Good agreement is found between the model-proposed and large eddy simulations of a wind turbine in yaw.