the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
On optimizing the sensor spacing for pressure measurements on wind turbine airfoils
Abstract. This research article presents a robust approach to optimizing the layout of pressure sensors around an airfoil. A genetic algorithm and a sequential quadratic programming algorithm are employed to derive a sensor layout best suited to represent the expected pressure distribution and, thus, the lift force.
The fact that both optimization routines converge to almost identical sensor layouts suggests that an optimum exists and is reached. By comparing against a cosine-spaced sensor layout, it is demonstrated that the underlying pressure distribution can be captured more accurately with the presented layout optimization approach. Conversely, a 39–55 % reduction in the number of sensors compared to cosine spacing is achievable without loss in lift prediction accuracy. Given these benefits, an optimized sensor layout improves the data quality, reduces unnecessary equipment and saves cost in experimental setups.
While the optimization routine is demonstrated based on the generic example of the IEA 15 MW reference wind turbine, it is suitable for a wide range of applications requiring pressure measurements around airfoils.
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RC1: 'Comment on wes-2024-4', Anonymous Referee #1, 13 May 2024
This study introduces an optimization-based approach to determining the optimal number and
positioning of pressure sensors required for accurately deducing pressure distribution. The findings
indicate that this optimization procedure offers a more cost-effective and space-efficient sensor
layout compared to the traditional cosine spacing method.
I would like to extend my congratulations to the authors for conducting this study. The method-
ology presented here has a potential to greatly benefit the wind energy and aerodynamics commu-
nities by enabling the cost-effective placement of pressure sensors. However, for the future work
it would be interesting to write full CFD analysis version of the paper. Xfoil is a great tool but it
has it’s limitations. The paper is well-written and easy to read.
I believe this paper fits well within the scope of Wind Energy Science and has significant potential
for publication.
However, I would like the authors to consider the following comments and make the necessary
adjustments to the manuscript.Comment 1: Refer to line 55: Please explain the rationale behind the specific choice of these two opti-
mization schemes among others available should be explained. What are the competitive
advantages of using these two optimization schemes?
Comment 2: Refer to line 74: Explain what the authors mean by blended and non-blended profiles. Does
blending refer to combining two or more standard airfoils to achieve a more aerodynami-
cally optimized airfoil? This question arises because the authors have specifically chosen
non-blended profiles, even though the optimization procedure they present seems applica-
ble to blended profiles as well. This specific choice suggests that there may be particular
characteristics unique to non-blended profiles.
Comment 3: Refer lines 97 and 98: Please reference any papers that demonstrate tangential induction has
minimal impact within the chosen range of r/R for this study. Including this evidence would
enhance the article, as this assumption is crucial in determining the angle of attack.
Comment 4: Suggestion for the equation 10: The Euclidean dot product between a scalar and a vector
is equivalent to multiplying the scalar throughout the vector. Therefore, cp · n(s) can be
simplified to cpn(s). Thus, the dot product is redundant in this context.
Comment 5: Refer to the equation 14: I suggest that the absolute value of (Cl,int(α)−Cl,exp(α)) should be
included in the equation. Without the absolute values, positive and negative error values may
cancel each other out when summing across the range of angles of attack, which could obscure
the true magnitude of the error. If the omission of the modulus sign is merely a typographical
error, that is acceptable; however, if the equation has been applied as it appears in the paper,
I am concerned it may not accurately reflect the error values and trends depicted in Figures
7(b) and 10(b). Please calculate Eprob(cl) using the absolute value |(Cl,int(α) − Cl,exp(α))|
and include this comparison in your response to this review.
Comment 6: Suggestion for the equation 15: It would be more appropriate if the authors also placed
’min' on the right-hand side of the equation, given that they are minimizing this function.
Alternatively, if the authors prefer to include ’min’ on only one side, they should enclose the
entire equation in brackets after ’min'.Citation: https://doi.org/10.5194/wes-2024-4-RC1 -
AC1: 'Comment on wes-2024-4', Erik Fritz, 13 Jun 2024
Dear reviewers,
The authors would like to thank you for the time and effort that you have dedicated to providing valuable feedback on our manuscript. We have been able to incorporate changes to reflect your suggestions. Please find a point-by-point response to your comments and a version of our manuscript highlighting all made changes in the attached file.Kind regards,
Erik Fritz, Christopher Kelley, Kenneth Brown
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AC1: 'Comment on wes-2024-4', Erik Fritz, 13 Jun 2024
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RC2: 'Comment on wes-2024-4', Anonymous Referee #2, 24 May 2024
General:
Very good paper, with a relevant topic.
The paper has clear descriptions of the methods and clear presentations of the results. The conclusions wraps up the study in a good way and make relevant suggestions for further studies.
As the estimated pressure Cd is very sensitive on the used (discrete) pressure distribution, a note on the predicted Cd from the optimised distribution would be very informative and enhance the understanding of the usefulness of the optimised distribution. It is mentioned as future work, but just a small paragraph/figure to show how bad/good it is would be very beneficial.
Only a few smaller corrections are suggested
Detailed comments:
Eq. 2: Check these expressions, I think there is a typo; the factor on the exp-function should be pi*Uinf/Uavg^2?
Line between Eq (3) and (4), give the value for CT2 as you do for Ct1
Figure 3: Do you include the controller in the simulations?
Table 1: High Re, is this an issue for XFoil?
Section 2.4.2: I am missing a reference to a general description of the GA algorithm
Eq (15): Perhaps emphasise that the objective function is an integral and not a summation of the pressure difference at the discrete points, where the objective function would be zero. I was a little confused during the first read through, as my mind was focused on a discrete distribution. It is a good comment about the potential of improving the Cl prediction by using other interpolation functions.
Citation: https://doi.org/10.5194/wes-2024-4-RC2 -
AC1: 'Comment on wes-2024-4', Erik Fritz, 13 Jun 2024
Dear reviewers,
The authors would like to thank you for the time and effort that you have dedicated to providing valuable feedback on our manuscript. We have been able to incorporate changes to reflect your suggestions. Please find a point-by-point response to your comments and a version of our manuscript highlighting all made changes in the attached file.Kind regards,
Erik Fritz, Christopher Kelley, Kenneth Brown
-
AC1: 'Comment on wes-2024-4', Erik Fritz, 13 Jun 2024
-
AC1: 'Comment on wes-2024-4', Erik Fritz, 13 Jun 2024
Dear reviewers,
The authors would like to thank you for the time and effort that you have dedicated to providing valuable feedback on our manuscript. We have been able to incorporate changes to reflect your suggestions. Please find a point-by-point response to your comments and a version of our manuscript highlighting all made changes in the attached file.Kind regards,
Erik Fritz, Christopher Kelley, Kenneth Brown
Data sets
Supporting data belonging to the publication On optimizing the sensor spacing for pressure measurements on wind turbine airfoils Erik Fritz, Christopher Kelley, and Kenneth Brown https://doi.org/10.4121/99662eaf-ac79-4952-ad80-6d7de3708427
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