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the Creative Commons Attribution 4.0 License.
| 27 May 2025
Impact of Yaw–Induced Unsteady Aerodynamics on BEM Prediction Accuracy: CFD Analysis Based on the NREL Phase VI Wind Turbine
Abstract. Accurately predicting the aerodynamic loads on wind turbine blades under yawed inflow remains a major challenge due to the complexity of three–dimensional unsteady flow phenomena. This study combines high-fidelity computational fluid dynamics (CFD) simulations and NREL Phase VI experimental data with a newly proposed normalized absolute error metric to evaluate the prediction accuracy of the modified blade element momentum (BEM) method under yawed and non-yawed inflow conditions, thereby quantitatively assessing the differences between different yaw angles, inflow velocities, and spanwise blade positions. In addition, the CFD results are employed to analyze the potential flow mechanisms responsible for the deterioration of BEM prediction accuracy. The results show that while the BEM method maintains high accuracy under non–yawed attached flow conditions, its performance deteriorates significantly under flow separation and yawed inflow. At a yaw angle of 30 and an inflow velocity of 15 m/s, the force coefficient (Cn) prediction error at the blade root increases to 48.6 %, exceeding the non–yawed case by more than 20 %. Flow field analyses reveal that yawed inflow intensifies vortex interactions on the leeward side and induces strong spanwise vortex bands driven by Coriolis forces, causing stall regions to propagate from blade tip to root. These phenomena lead to severe local aerodynamic load fluctuations that are not captured by conventional BEM formulations based on steady–state assumptions. This study quantitatively demonstrates the degradation of BEM prediction accuracy under yawed conditions and systematically reveals the direct impact of stall vortex evolution on aerodynamic load variations. These findings provide physical insights for the development of next–generation aerodynamic models incorporating three–dimensional unsteady flow corrections.
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RC1: 'Comment on wes-2025-81', Anonymous Referee #1, 30 Jun 2025
Review of
Impact of Yaw–Induced Unsteady Aerodynamics on BEM
Prediction Accuracy: CFD Analysis Based on the NREL Phase VI
Wind Turbine
By
JiaHong Hu, Hui Yang, and JiaXin Yuan
The paper describes a study of the NREL Phase-VI rotor in axial and yawed conditions, along with some supporting 2D dynamic stall cases for the S809, with the aim to provide understanding and data for improved yaw modelling. The paper addresses important issues and is related to activities in the IEA Annex 27 on rotor aerodynamics. Generally the paper is well structured, well written, and well aligned with previous analysis of rotor flows in yawed inflow.
Introduction and perspective with respect to other studies. The chosen references are mainly very recent, and much work was done on the Phase-VI rotor using both CFD and BEM between 1998-2016. The problem of need for dynamic stall modeling in wind turbines goes back to the late 1980’s.
The paper does not contain sufficient details on the applied methods, and the analysis is too qualitative to be directly useful for other researchers. As reflected by the conclusion the present findings are not new.
The experimental data used for validation on the NREL Phase-VI is very briefly discussed, and more specific references for the data set could be given. If assumption is correct, the reviewer applied the same data around 2014.
The paper lacks information about the details of the applied BEM, which models are included in the simulations, stall delay, dynamic stall model, source of airfoil data …
The CFD method is not described in any detail, is this compressible/incompressible, what type of discretization of the equations, time-stepping, convergence criteria and order of accuracy. Grid resolution is not discussed, neither chord, normal nor span-wise. Judging from the pictures of the separated structures, the resolution might be insufficient for detaille analysis of the vortex system. No information is given about time step size and for how long the simulations are carried out (number of revolutions for the rotor case, airfoil passages for the airfoil), and if the flow is deterministic as function of pitch angle. The authors have chosen to use RANS to predict the vortex dynamics in deep stall, but it might be insufficient for a correct analysis and e.g. IDDES or similar approaches should probably be preferred.
Figures are often very small, and the axes are not always well chosen e.g. Fig 12.,Fig 15, Fig 16, Fig 17
The error measure defined in Eqn. 4 and 5 would need more explanation. Why use Delta as a symbol. Normally Delta would be used as a difference. If I understand it correctly here it is just the value. The error measure is thus simply the difference between the experimental value and the computed value divided by a relatively arbitrary choice of constant of 3.6 not necessarily relevant for all cases.
Page 20: The present review is in doubt about the discussed vortex band, is it the shed vortex from the dynamic stall event that is referred to in this way.
From the picture we can see some radial flow, but we know from many other works that even the axial case will exhibit span-wise flow in the separated area. There is too little quantitative data to make the information useful for the reader.
Page 21: It is obvious from standard knowledge that variation in the loading of the blade is connected to vortex shedding, but the present discussion is not rigorously enough to add new aspects to this knowledge.
Typically, a BEM method would use a dynamic stall model to account for the dynamics of the angle of attack variation along with the yaw model.
How is the AOA determined in Fig 9. Again, on page 17, is the angle of attack or the geometrical angle of attack discussed.
From the BEM it should be possible to provide the actual AOAs, but I am not sure that this is what is done. The AOA in the CFD might easily differ as the loading is different.
Figure 19 indicates that the vortex structures are very coarsely resolved and only last until ~ a few chords away from the blade, which might easily be insufficient for the detailed vortex analysis. Additionally, the RANS eddy viscosity model, clearly dominates in the separated areas of the wing, which is not ideal for vortex analysis.
It is the present reviewer’s opinion that the present study might be valuable as an in-house study but do not have a broader interest, considering the many details not available in the study.Citation: https://doi.org/10.5194/wes-2025-81-RC1 -
RC2: 'Comment on wes-2025-81', Anonymous Referee #2, 03 Jul 2025
The paper describes results of BEM based as well as URANS CFD calculations on an oscillating airfoil and the NREL Phase VI rotor for different yaw angles. The results for the rotor are compared with existing measurement data. The authors aim to evaluate the prediction accuracy of BEM-based methods and intend to provide a basis for the development of improved BEM methods that better account for three-dimensional unsteady effects.
In general, I am missing new findings on the flow physics of rotor flows under yawed conditions, on the application limits of BEM methods or findings that could be used specifically to improve BEM or dynamic stall models. Further, the numerical setups are not sufficiently described for both, the BEM as for the CFD simulations. It can be doubted whether the chosen CFD turbulence model and resolution is adequate to resolve the structures of the separated flow. The authors essentially describe what can be seen on the result plots, without in-depth, well-founded flow-physical analyses. There is a lack of descriptions and literature citations on the current state of research on core aspects of the work, in particular on yaw influences, the flow physics of rotor blades with massive separations and on 3D effects (Himmelskamp effect), see specific remarks below. Compared to available publications on these topics, I cannot see any deeper analyses or new findings in the present manuscript that would make publication necessary.
Specific comments and remarks:
- Introduction: Not all citations in the text can be found in the list of references.
- 2, line 45ff: It is true that the common dynamic stall models make use of steady two-dimensional airfoil polars. However, these dynamic stall models are used to simulate unsteady aerodynamic effects, as described in the previous paragraph of the manuscript. I would therefore reformulate the sentence on lines 46/47. It is also possible to derive “3D polars” for BEM with the help of CFD single blade calculations, that inherently consider the 3D effects (Himmelskamp effect).
- 2, line 57: The authors write that yaw effects are poorly understood. However, there are quite a number of publications on this topic, none of which was mentioned. It is essential that the state of research is supplemented here and the own work is put in a context. Examples:
- Rahimi et al.: Investigation of the current yaw engineering models for simulation of wind turbines in BEM and comparison with CFD and experiment; 2016 J. Phys.: Conf. Ser. 753 022016; DOI 10.1088/1742-6596/753/2/022016
- MexNext final report: https://publications.tno.nl/publication/34643964/HkyADZwu/schepers-2021-final.pdf
- Chapter 2:
- Heading: What do “materials” mean here? Reference configurations?
- The first paragraph summarises properties of the NREL turbine and mentions that simulations were carried out for this purpose. Chapter 2.1 then initially refers to the S809 airfoil and the input data for the unsteady 2D calculations are given in Table 1. This is somewhat confusing. At the beginning of Chapter 2, the first sentence should mention that both, unsteady 2D calculations on an airfoil section and 3D rotor calculations are conducted.
- In my view, Fig. 3 can be omitted. Ditto Fig. 5.
- 6: Further information on the CFD setup would be desirable here, e.g. number of cells along the blade section, number of cell layers within the boundary layer, number of cells in radial direction, total number of cells, information on whether the calculation was carried out fully turbulent, tripped or for natural transition. It is also important to specify the time step size used (including information on the number of time steps per period for 2D calculations or the number of time steps per revolution for rotor calculations), the total number of time steps or revolutions as well as the numerical method for time integration.
- Chapter 3.1: There are numerous experimental and numerical studies on the dynamic stall phenomenon available, including DES and LES simulations and flow-physical interpretations. It is important to supplement the state of research in this area. Compared to the present state of research I cannot find any new findings in the manuscript (description p. 8/9 and Fig. 8).
- 7: How do the authors explain the fact that the BEM method provides significantly better results for the downstroke (with massive flow separation) compared to the experiment than the CFD calculation?
- 9, Fig. 18 and associated text on p. 16/17: How were the effective angles of attack determined in the CFD calculations (“Analysis of the streamline patterns” is very vague.)? There are established methods for AoA extraction from CFD flow fields, e.g. reduced axial velocity method, method by Shen, line-average approach.
- 10, line 165: I suggest to add information about the corresponding tip speed ratio for the different wind speeds considered.
- 10, line 169ff: How is “stall intensity” defined? The blade stall characteristics cannot be generalised but depends on the TSR.
- Chapter 3.2: How do the results compare with other, published results for the NREL rotor? The present results should be put in a context to published results and analyses. There are also numerous publications on the 3D effects on the rotor, which describe the mechanisms well. Exemplary publications should also be cited here. Compared to the current state of research, I cannot see any new findings in the present manuscript.
- 11, line 172ff: Why should the centrifugal effects be more pronounced in the hub area? The text essentially describes what can be seen on the result plots, but does not contain a well-founded and in-depth flow physics analyses.
- 11, line 189ff: At what wind speed should the flow be fully attached? In the wall streamlines and also in the off surface streamlines around the airfoil sections, separations can be observed also for the lowest wind speed of 7 m/s.
- 13: What are the rings highlighted by the red dotted line?
- 13: The text does not contain any in-depth analyses or new findings.
- 17, line 256: It was not described how the effective angles of attack were determined in the URANS rotor calculations. The determination is not trivial. A larger stall angle could also result partly due to inaccuracies in the determination of the effective angles of attack.
- 19, 20: For me, these illustrations and the accompanying text provide no added value. On p. 20, line 289, the authors write that these illustrations provide “a deeper insight into the mechanisms”. I don't get that from the text.
- Chapter 3.5: In my view, this summary of chapter 3 is superfluous.
- 22, line 358: Which “corrected BEM method” is meant here, which correction was introduced?
- 22., 359ff: The authors write: “Future work can build on the vortex dynamics revealed in this study to develop new BEM models incorporating unsteady rotational effects and spanwise vortex corrections.” To what extent can new BEM models build on the present studies? What new ideas or modelling approaches has the study provided?
Minor remarks & typos:
- Missing space at end of sentence: 1, line 7; P. 2, line 40; p.12, line 210; p. 13, line 230
- Missing space between words: P. 8, line 125, p. 8, line 137, caption fig. 7
- Missing full stop at the end of a sentence: p. 8, line 138
- 1, line 8: “30” à “30°”
- 1, line 19: Why is an accurate load calculation essential to ensure power output?
- 1, line 20: “are influenced” à “is influenced”
- 1, line 23: What is meant here by “aerodynamic environment”?
- 2, line 52: The authors write that CFD methods are not widely used for wind farm design. Irrespective of the fact that one could discuss this statement, the manuscript discusses yaw effects on a single turbine. Wind farms do not play a role in the paper.
- 1, line 53: What is meant with “refine airfoil characteristics”?
- 4, Tab. 1: “Reynolds” à “Reynolds number”
- In most pictures, the legends and labelling of the axes are too small.
- 9: Areas (a) and (b) should be marked more visibly.
- 20, line 291: What does “the degree of attachment becomes stronger” mean?
Citation: https://doi.org/10.5194/wes-2025-81-RC2
Status: closed
-
RC1: 'Comment on wes-2025-81', Anonymous Referee #1, 30 Jun 2025
Review of
Impact of Yaw–Induced Unsteady Aerodynamics on BEM
Prediction Accuracy: CFD Analysis Based on the NREL Phase VI
Wind Turbine
By
JiaHong Hu, Hui Yang, and JiaXin Yuan
The paper describes a study of the NREL Phase-VI rotor in axial and yawed conditions, along with some supporting 2D dynamic stall cases for the S809, with the aim to provide understanding and data for improved yaw modelling. The paper addresses important issues and is related to activities in the IEA Annex 27 on rotor aerodynamics. Generally the paper is well structured, well written, and well aligned with previous analysis of rotor flows in yawed inflow.
Introduction and perspective with respect to other studies. The chosen references are mainly very recent, and much work was done on the Phase-VI rotor using both CFD and BEM between 1998-2016. The problem of need for dynamic stall modeling in wind turbines goes back to the late 1980’s.
The paper does not contain sufficient details on the applied methods, and the analysis is too qualitative to be directly useful for other researchers. As reflected by the conclusion the present findings are not new.
The experimental data used for validation on the NREL Phase-VI is very briefly discussed, and more specific references for the data set could be given. If assumption is correct, the reviewer applied the same data around 2014.
The paper lacks information about the details of the applied BEM, which models are included in the simulations, stall delay, dynamic stall model, source of airfoil data …
The CFD method is not described in any detail, is this compressible/incompressible, what type of discretization of the equations, time-stepping, convergence criteria and order of accuracy. Grid resolution is not discussed, neither chord, normal nor span-wise. Judging from the pictures of the separated structures, the resolution might be insufficient for detaille analysis of the vortex system. No information is given about time step size and for how long the simulations are carried out (number of revolutions for the rotor case, airfoil passages for the airfoil), and if the flow is deterministic as function of pitch angle. The authors have chosen to use RANS to predict the vortex dynamics in deep stall, but it might be insufficient for a correct analysis and e.g. IDDES or similar approaches should probably be preferred.
Figures are often very small, and the axes are not always well chosen e.g. Fig 12.,Fig 15, Fig 16, Fig 17
The error measure defined in Eqn. 4 and 5 would need more explanation. Why use Delta as a symbol. Normally Delta would be used as a difference. If I understand it correctly here it is just the value. The error measure is thus simply the difference between the experimental value and the computed value divided by a relatively arbitrary choice of constant of 3.6 not necessarily relevant for all cases.
Page 20: The present review is in doubt about the discussed vortex band, is it the shed vortex from the dynamic stall event that is referred to in this way.
From the picture we can see some radial flow, but we know from many other works that even the axial case will exhibit span-wise flow in the separated area. There is too little quantitative data to make the information useful for the reader.
Page 21: It is obvious from standard knowledge that variation in the loading of the blade is connected to vortex shedding, but the present discussion is not rigorously enough to add new aspects to this knowledge.
Typically, a BEM method would use a dynamic stall model to account for the dynamics of the angle of attack variation along with the yaw model.
How is the AOA determined in Fig 9. Again, on page 17, is the angle of attack or the geometrical angle of attack discussed.
From the BEM it should be possible to provide the actual AOAs, but I am not sure that this is what is done. The AOA in the CFD might easily differ as the loading is different.
Figure 19 indicates that the vortex structures are very coarsely resolved and only last until ~ a few chords away from the blade, which might easily be insufficient for the detailed vortex analysis. Additionally, the RANS eddy viscosity model, clearly dominates in the separated areas of the wing, which is not ideal for vortex analysis.
It is the present reviewer’s opinion that the present study might be valuable as an in-house study but do not have a broader interest, considering the many details not available in the study.Citation: https://doi.org/10.5194/wes-2025-81-RC1 -
RC2: 'Comment on wes-2025-81', Anonymous Referee #2, 03 Jul 2025
The paper describes results of BEM based as well as URANS CFD calculations on an oscillating airfoil and the NREL Phase VI rotor for different yaw angles. The results for the rotor are compared with existing measurement data. The authors aim to evaluate the prediction accuracy of BEM-based methods and intend to provide a basis for the development of improved BEM methods that better account for three-dimensional unsteady effects.
In general, I am missing new findings on the flow physics of rotor flows under yawed conditions, on the application limits of BEM methods or findings that could be used specifically to improve BEM or dynamic stall models. Further, the numerical setups are not sufficiently described for both, the BEM as for the CFD simulations. It can be doubted whether the chosen CFD turbulence model and resolution is adequate to resolve the structures of the separated flow. The authors essentially describe what can be seen on the result plots, without in-depth, well-founded flow-physical analyses. There is a lack of descriptions and literature citations on the current state of research on core aspects of the work, in particular on yaw influences, the flow physics of rotor blades with massive separations and on 3D effects (Himmelskamp effect), see specific remarks below. Compared to available publications on these topics, I cannot see any deeper analyses or new findings in the present manuscript that would make publication necessary.
Specific comments and remarks:
- Introduction: Not all citations in the text can be found in the list of references.
- 2, line 45ff: It is true that the common dynamic stall models make use of steady two-dimensional airfoil polars. However, these dynamic stall models are used to simulate unsteady aerodynamic effects, as described in the previous paragraph of the manuscript. I would therefore reformulate the sentence on lines 46/47. It is also possible to derive “3D polars” for BEM with the help of CFD single blade calculations, that inherently consider the 3D effects (Himmelskamp effect).
- 2, line 57: The authors write that yaw effects are poorly understood. However, there are quite a number of publications on this topic, none of which was mentioned. It is essential that the state of research is supplemented here and the own work is put in a context. Examples:
- Rahimi et al.: Investigation of the current yaw engineering models for simulation of wind turbines in BEM and comparison with CFD and experiment; 2016 J. Phys.: Conf. Ser. 753 022016; DOI 10.1088/1742-6596/753/2/022016
- MexNext final report: https://publications.tno.nl/publication/34643964/HkyADZwu/schepers-2021-final.pdf
- Chapter 2:
- Heading: What do “materials” mean here? Reference configurations?
- The first paragraph summarises properties of the NREL turbine and mentions that simulations were carried out for this purpose. Chapter 2.1 then initially refers to the S809 airfoil and the input data for the unsteady 2D calculations are given in Table 1. This is somewhat confusing. At the beginning of Chapter 2, the first sentence should mention that both, unsteady 2D calculations on an airfoil section and 3D rotor calculations are conducted.
- In my view, Fig. 3 can be omitted. Ditto Fig. 5.
- 6: Further information on the CFD setup would be desirable here, e.g. number of cells along the blade section, number of cell layers within the boundary layer, number of cells in radial direction, total number of cells, information on whether the calculation was carried out fully turbulent, tripped or for natural transition. It is also important to specify the time step size used (including information on the number of time steps per period for 2D calculations or the number of time steps per revolution for rotor calculations), the total number of time steps or revolutions as well as the numerical method for time integration.
- Chapter 3.1: There are numerous experimental and numerical studies on the dynamic stall phenomenon available, including DES and LES simulations and flow-physical interpretations. It is important to supplement the state of research in this area. Compared to the present state of research I cannot find any new findings in the manuscript (description p. 8/9 and Fig. 8).
- 7: How do the authors explain the fact that the BEM method provides significantly better results for the downstroke (with massive flow separation) compared to the experiment than the CFD calculation?
- 9, Fig. 18 and associated text on p. 16/17: How were the effective angles of attack determined in the CFD calculations (“Analysis of the streamline patterns” is very vague.)? There are established methods for AoA extraction from CFD flow fields, e.g. reduced axial velocity method, method by Shen, line-average approach.
- 10, line 165: I suggest to add information about the corresponding tip speed ratio for the different wind speeds considered.
- 10, line 169ff: How is “stall intensity” defined? The blade stall characteristics cannot be generalised but depends on the TSR.
- Chapter 3.2: How do the results compare with other, published results for the NREL rotor? The present results should be put in a context to published results and analyses. There are also numerous publications on the 3D effects on the rotor, which describe the mechanisms well. Exemplary publications should also be cited here. Compared to the current state of research, I cannot see any new findings in the present manuscript.
- 11, line 172ff: Why should the centrifugal effects be more pronounced in the hub area? The text essentially describes what can be seen on the result plots, but does not contain a well-founded and in-depth flow physics analyses.
- 11, line 189ff: At what wind speed should the flow be fully attached? In the wall streamlines and also in the off surface streamlines around the airfoil sections, separations can be observed also for the lowest wind speed of 7 m/s.
- 13: What are the rings highlighted by the red dotted line?
- 13: The text does not contain any in-depth analyses or new findings.
- 17, line 256: It was not described how the effective angles of attack were determined in the URANS rotor calculations. The determination is not trivial. A larger stall angle could also result partly due to inaccuracies in the determination of the effective angles of attack.
- 19, 20: For me, these illustrations and the accompanying text provide no added value. On p. 20, line 289, the authors write that these illustrations provide “a deeper insight into the mechanisms”. I don't get that from the text.
- Chapter 3.5: In my view, this summary of chapter 3 is superfluous.
- 22, line 358: Which “corrected BEM method” is meant here, which correction was introduced?
- 22., 359ff: The authors write: “Future work can build on the vortex dynamics revealed in this study to develop new BEM models incorporating unsteady rotational effects and spanwise vortex corrections.” To what extent can new BEM models build on the present studies? What new ideas or modelling approaches has the study provided?
Minor remarks & typos:
- Missing space at end of sentence: 1, line 7; P. 2, line 40; p.12, line 210; p. 13, line 230
- Missing space between words: P. 8, line 125, p. 8, line 137, caption fig. 7
- Missing full stop at the end of a sentence: p. 8, line 138
- 1, line 8: “30” à “30°”
- 1, line 19: Why is an accurate load calculation essential to ensure power output?
- 1, line 20: “are influenced” à “is influenced”
- 1, line 23: What is meant here by “aerodynamic environment”?
- 2, line 52: The authors write that CFD methods are not widely used for wind farm design. Irrespective of the fact that one could discuss this statement, the manuscript discusses yaw effects on a single turbine. Wind farms do not play a role in the paper.
- 1, line 53: What is meant with “refine airfoil characteristics”?
- 4, Tab. 1: “Reynolds” à “Reynolds number”
- In most pictures, the legends and labelling of the axes are too small.
- 9: Areas (a) and (b) should be marked more visibly.
- 20, line 291: What does “the degree of attachment becomes stronger” mean?
Citation: https://doi.org/10.5194/wes-2025-81-RC2
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