the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 28 Apr 2026
Multi-Objective Evolutionary Optimization of Wind Turbine Airfoils Incorporating Leading-Edge Roughness Insensitivity
Abstract. Wind turbine airfoil design has historically targeted three objectives: high lift coefficient (CL), high lift-to-drag ratio (CL/CD), and insensitivity to leading-edge roughness (LER). The airfoils developed in the 1980s and 1990s for these objectives remain in widespread use today, yet the trade-offs among these competing goals have never been systematically mapped using modern global optimization methods. This paper develops a multi-objective evolutionary strategy (ES) to compute Pareto-optimal airfoil sets that reveal these trade-offs explicitly. The ES is initialized from a symmetric NACA airfoil rather than an existing wind turbine design, uses a Chebyshev-based CST parameterization, and is rigorously tuned via parameter studies. At the outer bounds of the Pareto front, the optimized airfoils improve upon the DU 93-210 reference by 87 % in CL, 26 % in CL/CD, and reduce ∆C̄L,LER to near zero. These gains are driven largely by increased camber; when a practical camber constraint of 5 % is applied, improvements of 33 % in CL and 16 % in CL/CD are still realized with near-complete LER insensitivity. A key finding is that, counter to conventional design wisdom, aft-loading correlates with reduced LER insensitivity for the optimized airfoils: roughness forces boundary-layer transition near the leading edge, producing a thicker turbulent boundary layer that separates earlier in the aft recovery region, negating the expected benefit of aft-loaded lift distributions. The framework, including the tuned ES and optimized airfoil database, is made available for public use.
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Status: open (until 06 Jun 2026)
- RC1: 'Comment on wes-2026-72', Anonymous Referee #1, 18 May 2026 reply
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RC2: 'Comment on wes-2026-72', Anonymous Referee #2, 21 May 2026
reply
General comments
This paper concerns an investigation of how wind turbine airfoils can be designed for high insensitivity to leading-edge roughness. Many optimized airfoil designs are carried out and analysed and studied in Parato fronts plotting three relevant parameters: cl, cl/cd and cl,Clean-cl,LER. The work is interesting because a systematic study has been made to investigate the parameters.
However, the approach is influenced by assumptions that I find questionable and also influenced by missing references. I will touch upon some of them below:
* It is claimed that increasing cl is good for wind turbine airfoils. That is in general not the case because we aim for a thrust coefficient in wind turbine rotor design of around CT=8/9 to obtain maximum performance. More CT than this is not good. Since CT is approximately proportional to cl*c*W^2 and if we assume that the rotor speed is constant, then the local CT is proportional to cl*c. Some blade manufacturers do not like too slender blades because we get structural issues and therefore there is a limit to how high cl should be – see e.g. [Bak C, Gaudern N, Zahle F, Vronsky T. Airfoil design: Finding the balance between design lift and structural stiffness. Journal of Physics: Conference Series (Online). 2014;524:012017]. Therefore, high cl is mainly a quality because we can make the blade slender so that stand still loads do not become a problem, but we do not produce more power because of high cl as you write. However, high cl/cd is directly proportional to high power.
* You optimize for cl and cl/cd at an absolute AoA=6deg. If you try to maximize cl at a fixed AoA, then the airfoil will be very cambered because cambering is an efficient way of increasing cl for a given AoA. However, you should rather optimize for a given cl or an AoA relative to AoA@cl=0. Then the airfoil will only camber according to the cl,max (that I would prefer should be used as a constraint).
* You refer to early airfoil design for wind turbines and that they relied on inverse methods. Some airfoils were based on inverse design, but not all - see below about missing references.
* You claim that airfoils developed in this era also established a widely adopted design heuristic: aft-loaded airfoils are more insensitive to LER because lift generation is shifted away from the roughness affected leading edge (Timmer and Bak, 2023). I am not sure this is stated in their text even though some airfoil designers worked along these lines.
* You have only referenced rather old work. Please also refer airfoil design after 2003 because there has been several attempts in the direction of leading edge roughness insensitivity, acoustics, stiffness etc. Please be aware of these references:
- [Fuglsang P, Bak C, Gaunaa M, Antoniou I. Design and verification of the Risø-B1 airfoil family for wind turbines. Journal of Solar Energy Engineering. 2004 Nov;126(4).]
- [Fuglsang P, Bak C. Development of the Risø wind turbine airfoils. Wind Energy. 2004;7:145-162.]
- [Lutz T, Wuerz W, Herrig A, Braun K, Wagner S (2004) Numerical optimization of silent airfoil
sections. Institut für Aerodynamik und Gasdynamik (IAG), Universität Stuttgart, Pfaffenwaldring
21, D-70550 Stuttgart]- [Bak C, Andersen PB, Madsen Aagaard H, Gaunaa M, Fuglsang P, Bove S. Design and verification of airfoils resistant to surface contamination and turbulence intensity. In Collection of Technical Papers - AIAA Applied Aerodynamics Conference. Reston, VA (US): American Institute of Aeronautics and Astronautics. p. AIAA 2008-7050]
...but maybe also something not that old:
- [Cheng J, Zhu WJ, Fischer A, Garcia NR,Madsen J, Chen J, ShenWZ (2014) Design and validation
of the high performance and low noise CQU-DTU-LN1 airfoils. Wind Energy 17(12):1817–
1833]- [Grasso F (2014) ECN airfoils for large offshore wind turbines: design and wind tunnel testing,
EWEA 2014, Barcelona]- [Mendez B, Munduate X, SanMiguel U (2014) Airfoil family design for large offshore wind turbine
blades. The science of making torque from wind (TORQUE 2014), IOP Publishing Journal of
Physics: Conference Series 524, 012022. https://doi.org/10.1088/1742-6596/524/1/012022]- [Zahle F, Bak C, Soerensen NN, Vronsky T, Gaudern N (2014) Design of the LRP airfoil series
using 2D CFD. The science of making torque from wind 2014 (TORQUE 2014). J Phys Conf
Ser 524:012020. https://doi.org/10.1088/1742-6596/524/1/012020]- [Boorsma K, Munoz A, Mendez B, Gomez S, Irisarri A, Munduate X, Sieros MG, Chaviaropoulos
P, Voutsinas S, Prospathopoulos J, Manolesos M, Shen WZ, Zhu WJ, Madsen HA (2015) New
airfoils for high rotational speed wind turbines, innwind.eu, Deliverable 2.12]- [Caboni M, Minisci E, Riccardi A (2018) Aerodynamic design optimization of wind turbine airfoils
under aleatory and epistemic uncertainty. The Science ofMaking Torque fromWind (TORQUE
2018), IOP Conf. Series: J Phys Conf Ser 1037:042011. https://doi.org/10.1088/1742-6596/
1037/4/042011]- [Hansen TH (2018) Airfoil optimization for wind turbine application. Wind Energy 21:502–514.
https://doi.org/10.1002/we.2174]- [Cody J. Karcher, David C. Maniaci, Chris Kelley, Alan Hsieh, Nathaniel deVelder and Anurag Gupta. "Design of a Preliminary Family of Airfoils for High Reynolds Number Wind Turbine Applications," AIAA 2025-0840. AIAA SCITECH 2025 Forum. January 2025]
You are also missing a more general reference “Airfoil Design”:
- [Bak C. Airfoil Design. In Stoevesandt B, Schepers G, Fuglsang P, Yuping S, editors, Handbook of Wind Energy Aerodynamics. 2022. p. 95-122]
Here the approach in airfoil design is not inverse design and a method to how to handle LER in the design process is described.
* You claim that “The airfoils developed during this period, notably the DU, FFA, NREL S, and NACA 6-digit families, remain in widespread use in modern blade designs”. It is not my experience that these airfoils are used for modern wind turbine blades – or have been used the last decade or two. Do you have any references on this?
Despite of the above comments, I still find the study interesting because it illustrates the dependency between the different parameters important in airfoil design. However, the paper should have less focus on cl as a “goodness” parameter and the paper also needs a focus on cl/cd with high turbulence/in LER conditions (n=1 or better with forced transition close to LE). However, it is fine to show how cl/cd is affected by different design cl’s. Also, it is fine to show cl/cd in clean condition, but it would be even more interesting to see cl/cd in LER condition and how this is affected by cl. Also, it is very important to reduce the gap between cl,max,clean and cl,max,LER because at a real turbine the maximum load that hits a turbine can very likely be affected by operation at cl,max and if this can change too much then the loading becomes unreliable and either you have too little cl to produce power or you have too much cl that gives rise to too much thrust.
Therefore, I suggest that you expand your work a bit more to include tracking of cl,max,clean-cl,max,LER and cl/cd,LER for each airfoil. This is because I am in doubt if the entire design space of interest is included in your study. However, even though a “real” airfoil design would require simultaneous optimization of several AoA in both clean and LER conditions and inclusion of some constraints to keep the geometry in place, an optimization at 1 AoA as you do can probably be ok just to limit the cost of the optimization. Also, the choice of an absolute AoA=6deg could also work because you “accidently” often get the required cl-reserve of cl,max-cl,design between 0.3 and 0.5 (as can be seen in Figure 8). But it is not always so. So, you could keep your setup as is, but you need to elaborate a bit more on the weaknesses of this approach and that you for a final airfoil design ought to include many AoA’s in both clean and LER conditions.
To conclude:
* I think you need a major revision of the paper where you add more work to the study - and I think you should:
- Include tracking of cl,max,clean-cl,max,LER and cl/cd,LER – and also try to optimize for cl/cd,LER
- You could also track cl,max-cl,design (the cl reserve)
- Explain that optimization at AoA=6deg
> automatically will result in extra camber – but this method will still be able to end up with many different realizations of airfoil designs
> is a simplification and that you ought to design at more AoA’s, but that AoA=6deg represent the design lift in many cases
- Explain that high cl/cd (in clean and LER) is good for power – but cl is only good to obtain a thrust coefficient of around 8/9 (therefore: less focus on cl as a “goodness” parameter). But it is important to be able to maintain CT around 8/9 not to lose power.
- Explain that we need small values of cl,clean-cl,LER to ensure reliable power and that we need small cl,max,clean-cl,max,LER to ensure reliable max loads
- Include missing references
- Please be clear that not all airfoil designers in the past went for aft loaded airfoils
I am recommending this paper for publication with major revisions and I am willing to review it again. Overall, I think the work is interesting and relevant, but a bit more work is needed.
Specific comments
* Some figures are referred to backwards. Please always refer to figures that are shown after the first reference – refer forward.
* Section 3.1: You do not refer to the Risø airfoils. Please do so, because they were designed with another approach than many others and they have also been used extensively. But they are used on license, so you cannot find the geometry.
* Figure 8: I am not completely sure I understand this figure. Could you spend a bit more text explaining what we see? Maybe use an example(?)
* Figure 10: I don’t understand what is plotted. What is the AoA? Also, you have made a lot of designs, and it is hard to follow what is “Max cl” and “Min d(cl,ler)”. Please make this more clear.
* Figure 11: Good idea to filter the camber. It shows that you know that many designs are extreme, and that actually just a fraction of the designed airfoils can be used in real life.
Citation: https://doi.org/10.5194/wes-2026-72-RC2
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- 1
Abstract
- Improvements in CL are not cited or proven as a performance metric, this tradeoff is very complex
- Cites "conventional design wisdom", no evidence
- "Reduced insensitiviy", meaning aft loading makes things more sensitive? This is uncelar
Introduction
- Cited paper (Timmer and Bak 2023) does not appear to suggest high CL as being the desired metric, and instead talks about CL*c
- This element of the design philosophy is perhaps the weakest element of the foundation of the paper, and should be strentghened since it is being stated as one of 3 key objectives
- Choosing CL is often a complex blade design decision, simply maximizing is rarely the correct answer
- Claim that aft loading decreases leading edge roughness senstivity could not be found in the cited paper (Timmer and Bak 2023)
- It is possible that I missed it, but this claim appears to be unspported
- Aft loading often requires a stronger inverse pressure gradient on the upper surface, which could theoretically make it more senstive to roughness depending on the detailed airfoil design. This claim appears critical to the work, but is not clearly supported
Methods
- 250 generations is not many, would need to see convergence studies (line 93)
- Selection of 1 for the rough Ncrit is somewhat arbitrary, though cites Hansen 2018 (Table 1)
- Locking in an angle of attack of 7 degrees is again somewhat arbitrary, but will apparently be discussed later (line 118)
- The relationship between Chebyshev and CST is unclear, though will perhaps be discussed later
- Toothpick constraints are being used at 70 and 80% of chord, will look for this in final shapes
- Paper mis-cites Karcher et. al. which makes no such claim about maximum camber. Upper surface curvature was limited in that study (line 162)
- Population size of 80 is quite low, generally accepted practice is 20*N_design_variables (Table 2)
- Methodology for determining proper 'hyperparameters' (Table 2) has some significant weaknesses and does not follow conventional approaches
- This needs additional explaination by the authors as to how these parameters were obtained and the consequences of the assumptions
- Figure 1 shows significant variation in the objectives and indicates that convergence has not been reached
- This data should either be reframed or explained in more depth (see line 196). Present discussion is insufficient
- It appears that a large population size is forgone in favor of running multiple GA shots. (Table 3)
- The reason for this is not explained, and methodology for doing so needs additional justification
Results
- The S809 is a stall regulated airfoil. The S830 is likely the more appropriate choice for comparison (Figure 4)
- The toothpick constraints apprar to be active across all airfoils and are therefore critical (Figure 5)
- These selections should be justified in the methodology section
- There are clear data drops in Figure 5 on the CL vs. alpha plot. These are easy to fix and should be addressed
- Lower left plot of Figure 5 is ugly and unhelpful. Plotting all historical population data is probably unecessary
- Personal preference: Upper left of figure 5 is not on equal axis, which distorts airfoil shapes
- Again highlighting that increases in CL have not been sufficiently justified (Line 253)
- Lines 260-264: This statement is understandable, but has significant impact on the results. The consequences of this really need to be explored by the authors if generalizations are to be claimed
- Toothpick constraints are again very obvious in Figure 6
- The only metric for sensitivity being used is Delta CL. It is unclear that this is more important than say Delta CL/CD (line 275)
- Figure 7 is poor. Would recommend a single plot of just the pareto front, CL (x) vs CL/CD (y) with multiple curves at different Delta CL values. A monochromatic color map would be appropriate for these curves showing increasing Delta CL with darker or lighter shades
- Figure 8 again has clear data drops that should be filled
- Figure 10 would benefit from showing the geometries of the airfoils being considered
- Figure 11: See recommendation on Figure 7 above
- Figure 12: Data drops
- Figure 13: Legend covers the airfoil geometries. Data drops are also present.
- I feel section 3.4 (beginning line 340) is not adding value to the work. I would advise consideration of removing it from the paper, though this is not critical to my recommendation
- Section 3.5 does discuss consideration of a single off-design alpha, but this is not sufficient given the magnitude of the assumption. One single study with one degree of difference does not demonstrate insensivitiy to the design choice.
- Figure 15 has similar issues to those described above
- Re mentioned for the first time in Line 409. This corresponds to small on-shore turbines.
Summary thoughts
- The work here identifies the need for airfoil design in wind turbines
- Analysis is stong and for the most part well presented
- The motivation of the three primary objectives is underdeveloped. It is unclear how the selected objectives translate to higher performing turbines
- In general, assumptions are not critically evaluated and discussed
- Some unsupported claims are made, and some critically do not appear to be supported by the cited references
- Methodology is mostly clear, but lacks explaination in some critical areas
- Specifically, the selection of hyperparameters requires more justification and explaination
- The toothpick constraints are clearly playing a significant role in the final geometry shapes, and require more justification and study
- This appears to be the First Author's first publication. It is a strong effort and shows great promise. Though I feel some additional edits are required, the work is of high quality and deserves to be published.
Recommendations:
- Strengthen the argument for maximizing CL or consider opening this as a design variable
- Generally, the argument for these three identified objectives needs to be strengthened. Why were others not considered?
- Reduce/eliminate the emphasis on the claim that aft camber decreases sensitivity to LER and allow results to speak for themselves
- This appears to be central to the authors' narrative, but would require signifiant expansion and discussion if it were to be kept as a highlight of the work
- More explaination of how the geometry is being represented is required. I am still unsure of CST or Chebyshev is being used.
- Expand the explaination for how the hyperparameters were selected. Figure A1 is difficult to understand and provides little insight
- Explain the consequences of the fixed alpha selection (this may require additional runs to explore)
- Reynods number is not mentioned until line 490, this is a significant factor that at least needs to be adressed by the paper. How would the results vary with changes in Re?
- There are some issues with the plots (legends covering data, clarity) that should be addressed
I am recommending this paper for publication with major revisions and would be happy to review it again. Overall I feel this work is interesting, relevant, and of sufficient quality for publication in this journal, though some edits are still needed.