the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Jul 2025
CFD analysis of dynamic wind turbine airfoil characteristics in transonic flow using URANS
Abstract. Modern large wind turbine rotors can encounter airflow at inflow Mach numbers around 0.3 and a Reynolds number of the order of ten million at the blade tip. Our previous study (Vitulano et al., 2025) showed that for these operational conditions, the incompressibility assumption is violated and supersonic flow can occur locally. This follow-up study reports on a numerical investigation of the dynamic behavior of the FFA-W3-211 wind turbine tip airfoil in transonic flow using Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations. The simulations are performed for a highly unsteady aerodynamic regime by imposing a dynamic sinusoidal pitching motion across the transonic threshold determined in our previous study. This way, the airfoil is forced to enter and leave the supersonic flow regime. The simulations are conducted by varying the reduced frequency and the inflow Mach number, while keeping the Reynolds number constant at nine million. The choice of non-negligible inflow Mach numbers combined with high Reynolds numbers represents a realistic combination for full-scale wind turbines, but it is still challenging to be achieved experimentally with the test facilities available nowadays. The dynamic pitching motion is found to lead to the formation of a hysteresis loop with an extent depending on both reduced frequency and inflow Mach number. In particular, it is observed that an increase in one of these two parameters induces an expansion of the hysteresis loop with the consequences of (1) an increase in the magnitude and variability of loads experienced by the airfoil, (2) a delay in the beginning and ending of the transonic flow regime, and (3) the onset of shock waves, that take place at inflow Mach numbers lower than those estimated under static conditions. Moreover, since the formation of a hysteresis loop implies a range of conditions in which transonic flow can occur, this needs to be better understood and considered when defining any safety margin in the definition of the transonic threshold for turbine design and operation purposes. In general, the study suggests the need to take into account dynamic compressibility effects when predicting aerodynamic loads and performance for next-generation wind turbine rotors.
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RC1: 'Comment on wes-2025-125', Anonymous Referee #1, 04 Aug 2025
The authors presented ”CFD analysis of dynamic wind turbine airfoil characteristics in transonic flow using URANS”. This study investigates the effects of aerodynamic performance for unsteady dynamic wind turbines airfoil on compressible and transonic flow condition. URANS method is used to simulate flowfield of wind turbines airfoil. The findings are presented in manuscript, and the conclusions are supported by the results. The study falls within the scope of wind energy science. It is recommended that the manuscript be accepted after the following comments are addressed.
- I think that the authors need to improve the writing of manuscript, mainly the structure manuscript and named of title .
- In introduction, the reviewed referenced paper is not enough on compressible study of wind turbine. I suggest that the literature review of this relational study should be added, such as :
“Study of air compressibility effects on the aerodynamic performance of the IEA-15 MW offshore wind turbine” in Energy Conversion and Management journal. And “Quantification of air compressibility on large wind turbine blades using Computational Fluid Dynamics” in Renewable Energy journal.
3. For simulation method, the validation case should be considered.
4. In simulation case, did you make the independent of mesh? I think the authors should do independent of mesh.
5. In case setting, the authors simulate the range angle within negative angle of attack, if considering within positive angle of attack when the airfoil pitch condition.
6. For figure 7, it is better that three sub-figures become a figure.
7. In figure 12 and 13, can you explain that the small white areas is found, especially figure 12 (b) and figure (13) close pressure face of airfoil? What happen and what reason?
Citation: https://doi.org/10.5194/wes-2025-125-RC1 -
RC2: 'Comment on wes-2025-125 Reviewer2', Anonymous Referee #2, 18 Aug 2025
The paper addresses a physical phenomenon that concerns modern and future multi-MW wind turbines, that is to say, the possible appearance of supersonic flow over some parts of the blade tip sections, in some specific operating points. URANS simulations are carried out on a pitching FFA-W3-211 airfoil section (representative of the cross section of the tip of an IEA-15MW or IEA 22MW RWT wind turbine blade).
The paper presents the results of six 2D URANS simulations, three with a variable reduced frequency at M = 0.35 and three with a variable inflow Mach number and k = 0.6.Generally speaking, the paper is well written and of good quality and results of lift and drag coefficients for such applications are relevant. Additional information would however be necessary to give the reader a better confidence in the results presented. Details will be provided in the next sections.
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Section addressing individual scientific questions/issues ("specific comments")-> The airfoil section is shown in Fig. 2 but it would be good to present it at the very beginning of the paper, together with the definition of what is a negative or positive angle of attack (AoA) in this case. I.e., an additional figure would be welcome.
-> You should give a little more explanation on the range of angles of attack experienced by the tip of the blade and what does the range that you have selected (-15° to -5°) correspond to. Is it due to the atmospheric boundary layer, to gusts, combination of phenomena? Also, make clear why reduced frequency of 0.4 to 0.6 are relevant to wind turbine applications (by providing simple examples).
-> providing the static stall AoA of the airfoil at the studied Re would be nice.
-> section 2.2: be more specific about "second order" scheme (ideally add a table with the main parameters of the fvScheme file, are limiters used?) and give more details about their ability to capture shocks or not by comparison to the literature.
-> Even if you have done it in a previous paper, you should give a minimum set of information about the mesh generation and verification study in this paper (you can still refer to the other one for the details). We need to know the y+ distribution on the airfoil, and to get confidence in the mesh refinement based on a new figure. You should also mention the tool used to generate the mesh.
-> you do mention that experimental data do not exist for such Mach and Reynolds number but some validation with an "as similar as possible" case would help gain confidence in your results. If it is in your earlier
-> in section 3.1.1 (varying k), you often mention that k has a "strong" effect on the results or that the results have a "significant dependence" on k. This is not what I see in the figures. And actually, it would be interesting to see the mesh sensitivity study to evaluate the relevance of the "small" differences observed. Figures show that there is an effect, but not that strong as far as I see. Maybe you could be more balanced in your writing.
-> At some point you mention that it is possible to observe a supersonic flow without the presence of shock wave but then you mention M = 1 as a criteria for the presence of shock wave. Can you give a little more details on this point?
-> section 3.2: can you explain how you keep Re constant? variable c or variable viscosity?
-> you mention flow separation in some cases but we have no figure backing this. It would be good to show the wall shear stress (x-component) to give more details about the flow recirculation on the airfoil.
-> line 248-249: seems quite logical
-> number of periods of oscillation simulated to ensure convergence?
-> what is the difference between the "local" and the "effective" angle of attack? You use these two words all along the article without explaining the difference (if any). If there is no difference, it would be more clear if you keep only one way to refer to it.
-> it would be nice if the conclusion can contain a short paragraph that would link the results obtained with the expected outcome on the performance of a wind turbine: what is the effect of properly taking into account the compressibility effect? Cd seems to decrease when M increases (Fig. 9) and Cl does not seem too affected... the effect is not so clear and would benefit from your analysis.
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Compact listing of purely technical corrections at the very end ("technical corrections": typing errors, etc.)
-> Fig. 1: x-axis of Fig. (a) => double check the expression of PHI and the variation of it from 0 to 360 (°?).
-> Fig. 2: it is difficult to get a good quality figure of a mesh and I have troubles properly seeing the mesh details on my printed version. Tools like fluidFoam (https://fluidfoam.readthedocs.io/en/latest/) allow to export OpenFOAM meshes in vectorized format. You may consider trying something like that. Also, keep an aspect ratio of 1:1 for the computational domain (left part of Fig. 2) and explain why keeping only 2 cells in the outer (stator) region.
-> Fig. 6: a closer view would help seeing better the differences between the shocks + (b) is not well defined in the caption (downstroke?).
-> Fig. 7: make clear what the orange line correspond to (fixed airfoil configuration, I guess)
-> Fig. 10: problem in the labels in the caption for the lower row (d,e,f).
-> Fig. 11: issue in the labels written in the caption (twice the same value M = 0.35, while second one should be M = 0.45, I guess)Citation: https://doi.org/10.5194/wes-2025-125-RC2
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