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https://doi.org/10.5194/wes-2025-214
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-2025-214
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
29 Oct 2025
| 29 Oct 2025
Status: this preprint is currently under review for the journal WES.
Turbulence Distortion Matters in Predicting Inflow Turbulence Noise of Future Wind Turbines
Abstract. This study examines the role of turbulence distortion in predicting inflow turbulence (IT) noise generation from large wind turbines via Amiet's theory. Two subsequent distortion mechanisms are investigated: (i) the streamtube expansion in the rotor induction zone and (ii) the interaction with the surface of thick blade profiles. Large-eddy simulations reveal that the turbulence spectra, which reflect distortion effects, remain largely unaffected by rotor induction within the frequency range relevant for noise generation. As for the other mechanism, the distortion of the turbulence approaching a blade leading edge is modeled with a simplified closed-form solution of Goldstein’s Rapid Distortion Theory. This vorticity-deflection-based model is extended here beyond the high-frequency approximation and integrated into an analytical Amiet-based IT noise tool. Applications to representative test cases show that while distortion effects are minimal for current turbine sizes, they become relevant for future configurations featuring larger rotor sizes and thicker airfoils. The developed model reveals that IT noise levels do not necessarily scale with rotor size, but are shaped by spectral changes induced by the blade geometry, operational parameters, and inflow conditions. This model offers a physically consistent, computationally efficient framework for aeroacoustic assessment of next-generation wind turbine design.
How to cite. Yalçın, Ö., Piccolo, A., Zamponi, R., Ragni, D., and Merino-Martinez, R.: Turbulence Distortion Matters in Predicting Inflow Turbulence Noise of Future Wind Turbines, Wind Energ. Sci. Discuss. [preprint], https://doi.org/10.5194/wes-2025-214, in review, 2025.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.
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Status: final response (author comments only)
Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor
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- RC1: 'Comment on wes-2025-214', Anonymous Referee #1, 14 Nov 2025
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RC2: 'Comment on wes-2025-214', Anonymous Referee #2, 30 Nov 2025
The paper is well written and covers a highly relevant topic. The study is very interesting and demonstrates the importance of accurately modelling TI noise in the design of quieter wind turbines for the future. Below, the authors can find a few points that should be addressed.
Specific comments:
- In line 290, the authors mention the turbulent length scale and turbulence intensity obtained from simulations. As these parameters are crucial for the TI noise predictions, more details should be provided regarding how they were obtained, such as the type of simulation performed, how the turbulent length scale was calculated / determined, the location (altitude) at which the parameters were obtained, and whether this altitude is representative of the wind turbine test case (is it at the centre of the wind turbine rotor?).
- In line 291, the authors state that these turbulence quantities were obtained for Case 2 and assumed to remain unchanged for the other cases. How realistic is this? The turbulence intensity and length scale typically vary with the inflow velocity, which differs by about 25% for the other cases compared with Case 2. Could the authors please elaborate on the justification for this assumption and discuss its potential implications?
- In Section 3.1, it is not clear whether an artificial turbulence generator was used to initially create the turbulence in the flow. Could you please include more details on this matter? Additionally, what were the values of the turbulence intensity and the turbulence length scale? How does the size of the turbulence length scale compare with the rotor? This information is relevant to the reader and should be added to the paper.
- In Section 3.1, please include the cut-off frequency used for the simulations, as well as any dependence of this frequency on the locations where the energy spectrum was analysed in Section 3.2. The cut-off frequency should also be reported in Section 3.2 and Section 5.
- Figure 4: How was the turbulence length scale determined, which was used as input to the von Kármán spectrum?
- In line 357, the authors mention that the focus will be on mid- to high-frequency ranges. However, the definitions of low, mid, and high frequencies are not clear. Please specify earlier in the manuscript the frequency ranges that the authors consider to represent low, mid, and high frequencies.
- In Section 3.2, the authors conclude that the turbulence distortion due to streamtube expansion is negligible for frequencies relevant to noise generation. Out of curiosity, have the authors analysed lower frequencies as well? If so, did they observe any distortion of the turbulence at these larger length scales? Additionally, was it possible to simulate very low frequencies (i.e., very large length scales) accurately within the domain used?
- In line 500, the authors justify the modelling of an airfoil by a representative circle of a certain diameter, which is a common approach in aeroacoustics. This matter has also been investigated experimentally before (see dos Santos et al., 2024, https://arc.aiaa.org/doi/10.2514/1.J063122), where the authors suggested a different approach for determining the representative cylinder diameter than the one used in the current manuscript. What is the difference between the method applied in this study and the approach proposed in that work? How comparable are the cylinder diameters obtained using both methods? What are the implications of using a different cylinder diameter for the results and conclusions of the present paper? As this parameter (l_dist) is highly relevant to the results presented in the manuscript under review, please discuss the assumptions made and their consequences, in light of the findings from both studies in the literature (dos Santos et al., 2024; Piccolo et al., 2024), including answers to the questions above.
- In Section 5, the authors refer to trends that are “more than linear.” Please clarify what is meant by this.
- In Section 5, the reviewer notes the absence of a discussion on the relevance of turbulence distortion for the future wind turbines taking into account the frequency range at which trailing-edge noise is dominant. The authors mention that the effects of the turbulence distortion are even more relevant for high frequencies, which are usually dominated by trailing-edge noise. Therefore, a clear definition of what constitutes low and high frequencies should be provided. Additionally, a discussion considering trailing-edge noise should be added, indicating the frequency range in which turbulence distortion is expected to have an impact. This should also be included in the conclusions, specifying the relevant frequency range (with numerical values) and the expected level differences in dB when turbulence distortion is taken into account.
Technical corrections:
- Please recheck the nomenclature table, as some variables appear to be duplicated (e.g., U – mean velocity), and some are unclear. For example, do the variables v (unsteady velocity) and u (fluctuating flow speed) represent the same quantity?
- In line 196, the reviewer suggests adding the steps immediately after the colon. Currently, the colon implies that a list will follow, but the authors are referring to the subsubsections instead.
- Please include in the caption of Figure 10 a description of what the continuous line represents.
Citation: https://doi.org/10.5194/wes-2025-214-RC2
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Latest update: 06 Dec 2025
Department of Flow Physics and Technology, Delft University of Technology, Kluyverweg 1, 2629HS Delft, the Netherlands
Andrea Piccolo
Department of Flow Physics and Technology, Delft University of Technology, Kluyverweg 1, 2629HS Delft, the Netherlands
Riccardo Zamponi
Department of Flow Physics and Technology, Delft University of Technology, Kluyverweg 1, 2629HS Delft, the Netherlands
Environmental and Applied Fluid Dynamics Department, von Karman Institute for Fluid Dynamics, Waterloosesteenweg 72, B-1640 Sint-Genesius-Rode, Belgium
Daniele Ragni
Department of Flow Physics and Technology, Delft University of Technology, Kluyverweg 1, 2629HS Delft, the Netherlands
Roberto Merino-Martinez
Department of Control and Operations, Delft University of Technology, Kluyverweg 1, 2629HS Delft, the Netherlands
Short summary
This study, a part of the Blade Extensions for Silent Turbines project, explores how turbulent air flows affect the noise generated by large onshore wind turbines. Using advanced simulations and an analytical model, we show that as turbine blades grow larger and thicker, turbulence behaves differently near the blade, changing how noise scales. These insights help design quieter, more efficient next-generation wind turbines.
This study, a part of the Blade Extensions for Silent Turbines project, explores how turbulent...
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This article is providing a correction to the well-known Amiet model for inflow turbulence (IT) noise. This correction accounts for the deformation of the turbulent flowfield due to the thickness of the airfoil. It generalizes the Rapid Distortion Theory by including also large structures. It is also investigated if the atmospheric flow axial flow expansion does have an effect on the turbulent characteristics.
The article is clearly and well written. The mathematical derivations are well described.
Nevertheless, the reviewer notices a few inconsistencies and details that should be corrected, but do not compromise the pertinence of the article and validity of the results and conclusions.
One is related to the terminology used to describe the change in slope for the turbulence spectra. It is formulated in p.5 and p.16 that the slope (e.g. of -5/3) is "reduced", when the reviewer would rather in both case that the slope is increased. The reviewer assumes here that the authors mean that the coefficient of the logarithmic slope is increased. It is possibly a matter of taste about how to formulate this information.
The length scale of 312 m appears quite large to the reviewer. At which altitude is it evaluated?
There exist an inconsistency in Fig.3. Fig.3(f) is a zoom-in of Fig.3(c), however in 3(c) the model results overestimate the measurements in the frequency range 40-100 Hz, while it is the opposite in 3(f).
p.14, l.325: It is not clear to the reviewer why it can be concluded that the turbulence is isotropic.
p.16, l.360: A Blade-Passage-Frequency of 0.45Hz is consistent with 9 RPM. However, in Fig. 7, the first spectral peak is located at 0.9Hz... which is inconsistent.
Furthermore, in Fig.7 the slope "decrease" above, say, 0.1 Hz, which corresponds to the mesh cut-off frequency in Fig.4, is not clearly explained. In the reviewer's opinion, the low resolution upstream of the refined mesh zone contains large scale turbulence. During the time period for the turbulent flow to reach the measurement point, e.g. at -0.25D, smaller structures don't have the time to develop through the energy cascade of turbulence, which could explain the lower energy level (above 0.1Hz) than expected.
The reviewer is not familiar with the RDT equations and their derivation. However, the argument that the second order Lagrangian derivative disappear from Eq. 19 to give Eq. 29 is not clear for the reviewer.
The phrasing in p.23, l. 498-500 is not clear. The distortion length is first defined as the/a (?) circle radius. Then, it is defined by the "length between the LE radius and half of the max. thickness" which doesn't make sense as it does not describe a length per se... or does the reviewer misunderstand?
p.23, l.507: The spectra are plotted for a position in the vicinity of the LE, but it is not specifically defined.
All in all, this is an interesting paper that should be published without major revision. The small inconsistencies and details mentioned above should be addressed though.