the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Edgewise instabilities of a wind turbine blade section in attached flow conditions
Abstract. With the persistent trend towards larger, lighter turbine blades and the resulting increase in blade flexibility, the risk of edgewise instabilities is elevated. This emphasizes the need for a better understanding of the accuracy of simulation models and the mechanisms affecting the damping of edgewise modes. This study investigates edgewise instabilities in wind turbines under attached flow conditions using a two-dimensional, three-degree-of-freedom typical section model. The primary goal of this work is to validate the stability analysis predictions from common low-fidelity aerodynamic models by comparing them with a high-fidelity computational fluid dynamics (CFD) reference result. In addition, the study aims to deepen the understanding of the fundamental mechanisms behind edgewise instabilities. The comparison of the stability analysis results obtained with aerodynamic models of different fidelity demonstrates excellent agreement in both the trends and quantitative damping predictions for the edgewise mode. An additional sensitivity study highlights the importance of the steady load vector on the damping prediction. The flutter mechanism analysis shows that the edgewise instabilities are caused by a coupling of flapwise motion with the structurally coupled edgewise-torsional motion. Edgewise instabilities can occur when there is sufficient structural edge-twist coupling, both in edge-twist coupling to stall or edge-twist coupling to feather. The findings in the paper increase the confidence in common low-fidelity aerodynamic models and contribute to a better understanding of edgewise instabilities.
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RC1: 'Comment on wes-2026-9', Anonymous Referee #1, 01 Apr 2026
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Dear authors,first of all I would like to say that I think this is a great and extremely detailed manuscript.However, in my opinion it would be easier to digest if it was split in 2 parts:* Edgewise instabilities of a blade section part 1: Validation of attached flow unsteady airfoil aerodynamics modeling* Sections 2 and 3 of the article* Edgewise instabilities of a blade section part 2: Analysis of the instability mechanism* Sections 4 and 5 of the articleThis is of course just a suggestion.I am not sure how the process for such a splitting would be at WES: reducing the length of the current article and resubmitting the second part?The article is very clearly written, and the plots are very clear as well.Apart from the above suggestion of splitting the article, I have some detailed comments for minor revisions below.Best regards,GeorgDetailed comments:* page 2, line 36 'an edgewise flutter-like instability was observed during overspeed operation in experimental tests': I would probably write 'dedicated experimental tests' to highlight that the tests were targeted towards the instability* page 2, line 53-54 'They furthermore showed that the aerodynamic lift and moment caused by harmonic edgewise motion did not significantly change the flutter speed.': This description is not fully clear to me, can you extend it a bit?* page 3, line 74 'but additionally showing that this sensitivity depends strongly on the operating point.' Is that due to geometric edge-twist coupling due to the flapwise deflection?* page 3, line 81: 'If the torsional motion leads flapwise motion, the flapwise force induced by torsional motion will perform positive work': maybe for clarity this could be extended to 'the flapwise force induced by torsional motion will be in phase with the flapwise velocity and thus perform positive work'* page 3: line 85 'in edgewise flutter, the torsional motion is introduced by the structural edge-twist coupling': I would think there is also - at least for a full blade - an aerodynamic coupling where edgewise motion causes the steady state flapwise force to move, which causes a torsional moment.* page 4, line 96: 'potential theory' => potential flow theory* page 4, line 111: 'This presented work serves a couple goals.' => The present work serves a couple of goals.* page 5, Figure 1: I think the collocation point and aerodynamic center should be defined somewhere (name and location)* page 6, line 159: 'For realistic, full turbine systems, the edge-twist coupling is mainly driven by the out-of-plane deflection of the blade, either by prebend or by flapwise deformation under load.': I think this could also be mentioned in the introduction, to clarify where the edge-twist coupling could come from.* page 7, line 182: 'As the model is not perfectly linear': Maybe write 'airfoil properties are not perfectly linear' instead.* page 8, Section 2.2.1: What timestep was used?* page 10, line 259 'effects due to the airfoil camber through both the tuned CLα and the effective angle of attack': how is the lift slope tuned?* page 13, section 2.3: I propose to slightly change the title to '2.3 Summary and corrections of the methodology by Stäblein et al. (2017a)* page 15, line 35: I believe the components should be Fyy, Fy \theta, Mθ y, M \theta \theta* page 16, Figure 4: In modern wind turbines, I believe the reduced frequency range for outboard parts of the blade would be roughly in the range of 0.05 to 0.1 for a first edgewise and maybe 0.1 to 0.2 for a second edgewise mode. Maybe it would make sense to mention this in the description of the figure, and to provide a plot ranging only from 0 to 0.2 in the appendix, where this very relevant area is visible in more detail?* page 16, Figure 4, Fx \theta: Might the increasing difference in the imaginary part for high reduced frequencies be due to neglecting the pitch rate squared term in the tangential force? (Equation ⑬ in https://doi.org/10.5194/wes-7-1341-2022)* page 16, line 397 'An even better agreement was found for a comparison with a thin, uncambered NACA 0006 profile.': Could an equivalent of Figure 4 for the NACA 0006 be included in an appendix? Also, Bergami et al have investigated changes of the circulatory response due to changing airfoil thickness in https://doi.org/10.1002/we.1516* page 19, line 477: 'In the six selected cases': Maybe you could write six selected coupling combinations? I would argue that it is 12 cases, 6 coupling combinations and 2 steady angles of attack.* page 25, table 3: 'Theodorsen - without steady load': maybe you could briefly describe how this is achieved in the model equations?* page 26, 27, Figures 11 and 12: using different types of lines (solid, dashed, dash-dotted,...) might be helpful in figures 11 and 12 to identify cases where several lines are on top of each other* page 28, line 561: 'edgewise induced forces': I understand what it means, but somehow the term is not totally clear to me. Maybe calling it edgewise-motion-induced forces or forces due to edgewise motion would be more clear?* page 29, Equations (42) to (43): could this reduction from 3 to 2 DOF be shown in more detail? for example, how is B chosen for the different cases that will be investigated in the following?* page 31, line 635 'moving from −360◦ (out-of-phase with torsion) to −180◦ (trailing torsion)': I guess -360 would be in-phase and -180 would be out-of-phase?* page 32, line 660 'altogether, these diagrams illustrate a straightforward mechanism': I just wanted to say that I think this is a great paragraph!* page 33, Figure 14 h): is the flapwise force amplitude due to torsion exactly on top of each other for the 2DOF and 3DOF model? If this is the case, please mention it* pages 33 and 35, Figures 14 and 15: maybe the total aerodynamic work line thickness could be reduced to make sure that they don't hide other lines* page 36, line 713: 'The simplified 3DOF model is still a good approximation of the full CFD reference result.': I am not sure I can agree with this. The 'critical speed' in the CFD result is at about 90 m/s, while the 3DOF simplified model predicts maybe 50 m/s (difficult to see)* page 36, line 717 'Edge-twist coupling to feather (gamma_x= -0.3)': I believe this should be: 'Edge-twist coupling to stall (gamma_x= 0.3)'* page 48, line 907, reference for Li et al. (2025): Sometimes in the text, I believe you refer to this, when you intend to refer to Li et al. (2022). Please double check.ReplyCitation: https://doi.org/
10.5194/wes-2026-9-RC1
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