the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Disentangling wake and projection effects in the aerodynamics of wind turbines with curved blades
Abstract. Advancements in wind turbine technology have led to larger, more flexible blades and an increasing interest in aerodynamic load calculations and design optimization of blades featuring significant sweep, prebend or coning. High-fidelity blade-resolved computational fluid dynamics (CFD) simulations provide precise rotor performance predictions but are computationally expensive. In contrast, the low-fidelity blade element momentum (BEM) method is computationally efficient but unable to model wake-induced effects of non-straight blades and coned rotors. To bridge this gap, mid-fidelity aerodynamic models, which balance accuracy and computational efficiency, are essential for design optimization tasks. Consistent aerodynamic benchmarks are crucial to effectively evaluate these models, particularly for modeling wake-induced effects across different blade geometries. Previous studies typically used the same chord and twist distributions across different curved blade geometries. However, this approach introduces inconsistencies, as it does not guarantee the same local aerodynamic conditions (e.g., angle of attack and local thrust coefficient) along the blade span due to projection effects of velocities and forces between the 2-D airfoil section and the 3-D flow. Consequently, wake-induced effects on loading and induction become entangled with unwanted projection effects, hindering the clear evaluation of how blade curvature alone influences the loads and induction. This study introduces a framework to disentangle wake-induced and projection effects in aerodynamic comparisons of curved blades. Within the BEM framework, we derive the necessary modifications to the chord and twist distributions of curved blades, ensuring the same spanwise circulation distribution as a baseline straight blade. These adjustments remove projection-driven discrepancies, enabling a consistent evaluation of wake-induced effects on loading and induction. Numerical validations using BEM and CFD confirm the effectiveness of these modifications. Additionally, projection effects in existing CFD results can be effectively isolated and removed. Using this framework, we discovered a novel insight from analysis of the CFD results: the wake-induced effects of moderate blade sweep and prebend can be modeled independently and then superimposed. This previously inaccessible insight significantly simplifies the modeling process and provides valuable guidance for developing mid-fidelity engineering aerodynamic models. Overall, this study advances the understanding of blade sweep and prebend effects on normal and tangential aerodynamic loads, supporting future blade design optimization.
Competing interests: DTU Wind and Energy Systems develops and distributes the Navier-Stokes solver EllipSys3D on commercial and academic terms.
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.- Preprint
(1811 KB) - Metadata XML
- BibTeX
- EndNote
Status: closed
-
RC1: 'Comment on wes-2025-30', Anonymous Referee #1, 04 May 2025
Overall, I am very pleased with this paper. However, please address the following comments:
1. From figures 8 to 18, the spanwise Ct and Cp show higher projection and wake effects on the outboard span of the blade. Please discuss why.
2. Nomenclature for parameters in Table 2 is missing in the appendix.
Citation: https://doi.org/10.5194/wes-2025-30-RC1 -
RC2: 'Comment on wes-2025-30', Anonymous Referee #2, 11 May 2025
An interesting article about curved blades and the issues that are accompanied by modelling these. The statement that the entanglement of the mentioned two effects hinders the evaluation of the effects of blade curvature on loads (abstract p1 line 12) can be argued to be subjective. For example, from the viewpoint of a manufacturer it could be desirable to evaluate the full effect (projection + wake) of curving a blade on its performance, keeping chord and twist distribution the same. This should be reflected upon more carefully. However from the viewpoint of modeling and design, the article provides new and valuable insights by separating projection and wake induced effects, and hence is worthy of publication.
It is recommended to follow up on the below suggestions for improvement:
-The article is rather lengthy for the message it brings, and it is advised to re-arrange the content in a more concise way, making it also more digestible.
-Many of the citations reach back to literature from own work and is on curved blades as well. To ensure there is no overlap between these, it would be good to clarify the relation between the articles.
-The introduction of projection and wake-induced effects (p2 line 53) could do with a visualization to clarify and define these effects more clearly to the reader.
-At several points the three-quarter chord point is explained to be used for angle of attack evaluation, following unsteady airfoil theory. Perhaps the authors can include a reference citation to the original work on airfoil theory as well?
-Section 3.1 p20 line 488. Is it true that the tip region does not affect the flow at the root? Or should tip and root be exchanged in this sentence?
-Section 3.2 p20 line 503. Are the 2D airfoil data from CFD consistent with the 3D-CFD method described in section 3.1 (e.g. both turbulent but also in general terms of performance prediction)? That would be a prerequisite for a sound comparison between BEM and CFD.
-Section 4.3.2 Modified curved blades. Please include a visualization of the planform modification comparison to the original curved blade.
-Section 4.6 Swept blade case. I find some of the results description difficult to follow as different points are being made in an alternating way (how well does the projection removal work and how relevant are projection effects in comparison to wake effects). It would be great if the structure can be re-arranged to improve readability in that sense (e.g. instead of sections about different operational conditions, separate sections by the points that are to be made).
It is stated that CFD simulations of the original swept blades are unsuitable to determine the wake induced effect at low loading conditions. But are we interested in this effect at low loading conditions as it is rather small? And after all, what kind of % difference in terms of rotor integral Cp and Ct are we talking about? It would be good to clarify the relevance.
Do we need to see all wind speeds (p31 Fig 10) or can we do with the 20m/s case to illustrate the point of projection effects being dominant (which was to be expected at low induction) and the confirmation of the modified blade performance? It is nice to see that the BEM based adjustments applied to the original blade CFD agree with the modified blade CFD.
-Section 4.7 Prebend. It seems a bit much to arrive at more than 4 pages to draw a similar conclusion as for the swept blades section 4.6. The summaries in 4.6.3 / 4.7.3 / 4.8.3 seem very similar
-The motivation behind having curved blades sometimes originates from unsteady load alleviation. The subject of the present work is on steady performance. Could the authors comment/hypothesize on the effect of the removal of the projection effects on dynamic loading? Also, the current analysis features rigid blades. What would be the order of magnitude of the proposed twist modifications in comparison to the expected torsion angle deformations?Citation: https://doi.org/10.5194/wes-2025-30-RC2 -
RC3: 'Comment on wes-2025-30', Anonymous Referee #3, 04 Jun 2025
The results presented in this study account for projection effects on predictions of aerodynamic loading for a wind turbine with curved blades, allowing for wake-induced loading effects to be isolated. Verifying that effects from sweep and prebend can be determined independently and superimposed will have significant benefits for this area of study. The process of finding these results is well documented and clearly explains the motivation and relevance to similar studies.
Please explain whether "dihedral" is dependent only on prebend or relies on coning/blade deflection as well. Is this related to the toe/cant angles of the blade?
It would be helpful to include a reference justifying the decision to not consider the effect of wake rotation effect on thrust coefficient (Section 2.5).
The derivation of Eqs. 50 and 51 was not described clearly.
Discussion of results in Sections 4.6-4.8 is somewhat repetitive - it would be helpful to summarize this information in a more concise way.
Appendix A is not comprehensive, and is missing several relevant variables and subscripts used throughout the work, such as those used in Section 2.6 and Section 4.3.1.
The label of "CFD - Delta BEM, Original" is unclear.
In Section 4, the notation used to describe the curved blades and modified curved blades is overly complex.
Citation: https://doi.org/10.5194/wes-2025-30-RC3 - AC1: 'Comment on wes-2025-30', Ang Li, 06 Jun 2025
Status: closed
-
RC1: 'Comment on wes-2025-30', Anonymous Referee #1, 04 May 2025
Overall, I am very pleased with this paper. However, please address the following comments:
1. From figures 8 to 18, the spanwise Ct and Cp show higher projection and wake effects on the outboard span of the blade. Please discuss why.
2. Nomenclature for parameters in Table 2 is missing in the appendix.
Citation: https://doi.org/10.5194/wes-2025-30-RC1 -
RC2: 'Comment on wes-2025-30', Anonymous Referee #2, 11 May 2025
An interesting article about curved blades and the issues that are accompanied by modelling these. The statement that the entanglement of the mentioned two effects hinders the evaluation of the effects of blade curvature on loads (abstract p1 line 12) can be argued to be subjective. For example, from the viewpoint of a manufacturer it could be desirable to evaluate the full effect (projection + wake) of curving a blade on its performance, keeping chord and twist distribution the same. This should be reflected upon more carefully. However from the viewpoint of modeling and design, the article provides new and valuable insights by separating projection and wake induced effects, and hence is worthy of publication.
It is recommended to follow up on the below suggestions for improvement:
-The article is rather lengthy for the message it brings, and it is advised to re-arrange the content in a more concise way, making it also more digestible.
-Many of the citations reach back to literature from own work and is on curved blades as well. To ensure there is no overlap between these, it would be good to clarify the relation between the articles.
-The introduction of projection and wake-induced effects (p2 line 53) could do with a visualization to clarify and define these effects more clearly to the reader.
-At several points the three-quarter chord point is explained to be used for angle of attack evaluation, following unsteady airfoil theory. Perhaps the authors can include a reference citation to the original work on airfoil theory as well?
-Section 3.1 p20 line 488. Is it true that the tip region does not affect the flow at the root? Or should tip and root be exchanged in this sentence?
-Section 3.2 p20 line 503. Are the 2D airfoil data from CFD consistent with the 3D-CFD method described in section 3.1 (e.g. both turbulent but also in general terms of performance prediction)? That would be a prerequisite for a sound comparison between BEM and CFD.
-Section 4.3.2 Modified curved blades. Please include a visualization of the planform modification comparison to the original curved blade.
-Section 4.6 Swept blade case. I find some of the results description difficult to follow as different points are being made in an alternating way (how well does the projection removal work and how relevant are projection effects in comparison to wake effects). It would be great if the structure can be re-arranged to improve readability in that sense (e.g. instead of sections about different operational conditions, separate sections by the points that are to be made).
It is stated that CFD simulations of the original swept blades are unsuitable to determine the wake induced effect at low loading conditions. But are we interested in this effect at low loading conditions as it is rather small? And after all, what kind of % difference in terms of rotor integral Cp and Ct are we talking about? It would be good to clarify the relevance.
Do we need to see all wind speeds (p31 Fig 10) or can we do with the 20m/s case to illustrate the point of projection effects being dominant (which was to be expected at low induction) and the confirmation of the modified blade performance? It is nice to see that the BEM based adjustments applied to the original blade CFD agree with the modified blade CFD.
-Section 4.7 Prebend. It seems a bit much to arrive at more than 4 pages to draw a similar conclusion as for the swept blades section 4.6. The summaries in 4.6.3 / 4.7.3 / 4.8.3 seem very similar
-The motivation behind having curved blades sometimes originates from unsteady load alleviation. The subject of the present work is on steady performance. Could the authors comment/hypothesize on the effect of the removal of the projection effects on dynamic loading? Also, the current analysis features rigid blades. What would be the order of magnitude of the proposed twist modifications in comparison to the expected torsion angle deformations?Citation: https://doi.org/10.5194/wes-2025-30-RC2 -
RC3: 'Comment on wes-2025-30', Anonymous Referee #3, 04 Jun 2025
The results presented in this study account for projection effects on predictions of aerodynamic loading for a wind turbine with curved blades, allowing for wake-induced loading effects to be isolated. Verifying that effects from sweep and prebend can be determined independently and superimposed will have significant benefits for this area of study. The process of finding these results is well documented and clearly explains the motivation and relevance to similar studies.
Please explain whether "dihedral" is dependent only on prebend or relies on coning/blade deflection as well. Is this related to the toe/cant angles of the blade?
It would be helpful to include a reference justifying the decision to not consider the effect of wake rotation effect on thrust coefficient (Section 2.5).
The derivation of Eqs. 50 and 51 was not described clearly.
Discussion of results in Sections 4.6-4.8 is somewhat repetitive - it would be helpful to summarize this information in a more concise way.
Appendix A is not comprehensive, and is missing several relevant variables and subscripts used throughout the work, such as those used in Section 2.6 and Section 4.3.1.
The label of "CFD - Delta BEM, Original" is unclear.
In Section 4, the notation used to describe the curved blades and modified curved blades is overly complex.
Citation: https://doi.org/10.5194/wes-2025-30-RC3 - AC1: 'Comment on wes-2025-30', Ang Li, 06 Jun 2025
Viewed
HTML | XML | Total | BibTeX | EndNote | |
---|---|---|---|---|---|
273 | 62 | 22 | 357 | 25 | 42 |
- HTML: 273
- PDF: 62
- XML: 22
- Total: 357
- BibTeX: 25
- EndNote: 42
Viewed (geographical distribution)
Country | # | Views | % |
---|
Total: | 0 |
HTML: | 0 |
PDF: | 0 |
XML: | 0 |
- 1