the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Influence of inflow turbulence intensity on static and dynamic stall of NACA 0021 at Re= 5.5 × 106 using DDES method
Abstract. Airfoil aerodynamics at high Reynolds numbers (on the order of 106) are of significant interest due to the increasing dimensions of wind turbine rotors. Recent studies indicate that the stall mechanisms at high Reynolds numbers differ from those at lower values, raising questions regarding the validity of conventional low-order prediction tools for simulating aerodynamic performance under these conditions. In this study, static and dynamic stall simulations employing Unsteady Reynolds-Averaged Navier–Stokes (URANS) and Delayed Detached Eddy Simulation (DDES) methods are validated against experimental data for a NACA 0021 airfoil at Re=5.5 x 106. Firstly, two spanwise extensions of a Q3D model are simulated using URANS. Results demonstrate that an aspect ratio (AR) of 0.25 is insufficient for accurately capturing large-scale stall cells, resulting in overpredicted lift values. Subsequent simulations with AR=2.5 confirm that the assumption of fully turbulent boundary layers is valid at such high Reynolds numbers. The DDES method—a hybrid approach combining RANS and LES—shows promise in predicting both the abrupt onset of stall and turbulent flow separation with minimal additional computational cost. Further simulations using DDES with varying inflow turbulence intensities reveal a stall-delay effect as freestream turbulence increases. While the sensitivity of freestream turbulence on dynamic stall during airfoil pitching is negligible, it significantly influences post-stall behaviour. Spectral analysis indicates that the post-stall regime is dominated by the shedding of dynamic stall vortices at a Strouhal number of 0.5.
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RC1: 'Comment on wes-2026-155', Anonymous Referee #1, 28 Sep 2026
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CC1: 'Reply on RC1, 2, and 3', Lars Wein, 07 Oct 2026
We would like to thank you for your insightful comments and we are sorry for our late response. We agree with most of your comments and agree, that the additional information you requested will help to improve the manuscript. Some studies you request are part of our regular internal QA process. We just did not report in the manuscript. For example, the sensitivity of spectral analysis to the resampling rate, interpolation, and more was of course already checked and was found to be negligible. We will add these information to the revised paper. You are absolutely correct, that our discussion about turbulence kinetic energy (k) in URANS and DDES is not yet precise. The required distinction between resolved and modelled k slipped our attention.
Using and evaluating the potential of a rather coarse mesh resolution for DDES is motivated by our plan to investigate turbine profiles under even higher Reynolds-Number next (for example AVATER test case with Re>15 10^6). At this high Reynolds-Number it will not be feasible to use a fine grid for DDES. The improved prediction of the sudden breakdown in lift for ramp up motion in this paper supports this idea.
A mesh dependency study was shown in the appendix and for static stall condition. It shows a small influence of the spanwise mesh-resolution on the lift. Therefore, we did not increase the number of cells in spanwise direction, increasing the size of the computational in spanwise direction. Again, this was motivated by a compromise between accuracy and numerical effort with the intention to apply the same numerical for even higher Reynolds numbers and as much load cases as possible. Of course, we explain this motivation and choice of numerical model better within the manuscript.
We will address all of your suggestions and will incorporated them into the revised manuscript. We are already working on the revisions and recommended analysis.
Disclaimer: this community comment is written by an individual and does not necessarily reflect the opinion of their employer.Citation: https://doi.org/10.5194/wes-2026-155-CC1 -
AC2: 'Reply on RC1', Hye Rim Kim, 05 Nov 2026
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2026-155/wes-2026-155-AC2-supplement.pdf
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CC1: 'Reply on RC1, 2, and 3', Lars Wein, 07 Oct 2026
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RC2: 'Comment on wes-2026-155', Anonymous Referee #2, 05 Oct 2026
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AC3: 'Reply on RC2', Hye Rim Kim, 05 Nov 2026
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2026-155/wes-2026-155-AC3-supplement.pdf
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AC3: 'Reply on RC2', Hye Rim Kim, 05 Nov 2026
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RC3: 'Comment on wes-2026-155', Anonymous Referee #3, 06 Oct 2026
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AC4: 'Reply on RC3', Hye Rim Kim, 05 Nov 2026
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2026-155/wes-2026-155-AC4-supplement.pdf
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AC4: 'Reply on RC3', Hye Rim Kim, 05 Nov 2026
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AC1: 'General response to all referees', Hye Rim Kim, 05 Nov 2026
Dear Referees,
We would like to thank you for your insightful comments. The majority of your suggestions are either incorporated in the revised manuscript or supplemented in the individual rebuttal. In cases where certain comments have not been incorporated into the revised manuscript, a clear explanation is provided in the individual responses.
To all referees, we would like to emphasize that the main objective of this paper is not to produce the most accurate numerical results, rather to investigate the influence of the modelled turbulence intensity on stall behavior with DDES method, using the numerical setup equivalent to RANS simulations. So far, RANS methods or other numerical methods relying on 2D geometry had not been able to produce the abrupt static stall onset under high Reynolds numbers, which had been reported from the experimental studies. The focus of this paper is to demonstrate that DDES method has potential to predict this phenomenon with only negligible increase in the computational cost. I believe that the results we produced can certainly contribute to the community, where the relevance on high Reynolds number is increasingly important, and to find an optimal method compromising accuracy and cost.
Many numerical sensitivity studies had been previously conducted, such as spanwise extension, mesh refinement in the spanwise direction, CFL number, etc. Those are not fully reported in the manuscript as those were limited to only certain boundary conditions. We are confident that further numerical simulations will have no major impact on the conclusions already made.
As we are fully aware of the limitations of the current work, and I believe, those are thoroughly acknowledged in the manuscript. In accordance with your comments, the objectives and conclusions have been revised in more restricted manner with appropriate limitation.
Sincerely,
Hye Rim Kim on behalf of the authors
Citation: https://doi.org/10.5194/wes-2026-155-AC1
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