the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 12 Jan 2026
A Computational Fluid Dynamics surrogate model for wind turbine interaction including atmospheric stability
Abstract. Wind turbine wake and blockage effects can reduce the energy yield in wind farms and fast models are required to mitigate these effects by wind farm layout optimization. However, most fast models do not account for important physics that impact wake and blockage effects, as for example atmospheric stability. In this work, we propose a surrogate model of a Reynolds-averaged Navier-Stokes (RANS) wind farm model including atmospheric surface layer stability that is about five orders of magnitude faster than the original model. The surrogate model is based on a single wake database of stream-wise velocity deficit and wake-added turbulence intensity, generated by a RANS model. The surrogate model is evaluated against the RANS model for different inflow conditions and wind farms. The errors of the surrogate model are reduced by a factor two to four when taking into account wake-added turbulence intensity and the use of a rotor-averaging model in combination with a momentum-based wake superposition method. However, the computational effort of the surrogate model is still an order of magnitude larger compared to traditional engineering wake models and more research is required to reduce it.
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Status: open (until 09 Mar 2026)
- RC1: 'Comment on wes-2025-287', Anonymous Referee #1, 02 Feb 2026 reply
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RC2: 'Comment on wes-2025-287', Anonymous Referee #2, 27 Feb 2026
reply
This manuscript proposes a RANS Look-Up Table (RANS-LUT) surrogate model derived from a single-turbine RANS Actuator Disk (AD) wake database. Expanding upon previous research, the authors incorporate dimensions for atmospheric stability—utilizing Monin-Obukhov Similarity Theory (MOST)—and wake-added turbulence intensity (TI). Furthermore, they implement an iterative superposition framework within PyWake to facilitate wind farm simulations. Methodologically, the study defines a comprehensive test matrix (comprising 1×8 and 8×8 arrays, 4D/8D turbine spacings, 11/14 m/s wind speeds, and stable/neutral/unstable atmospheric conditions) and integrates rotor-averaging techniques alongside a weighted-sum limiter during the superposition phase. In the results section, the authors present a comparative analysis of flow field discrepancies, power output errors, wind farm efficiency errors, and computational overhead. Ultimately, they highlight the critical role of wake-added TI in mitigating errors and note that while the proposed surrogate model accelerates computations significantly compared to full RANS simulations, it remains more computationally demanding than traditional engineering wake models.
I appreciate the ambition of this work and the extensive simulations conducted. The topic is highly relevant, and the manuscript shows clear potential. However, the presentation requires significant improvement. In particular, the methodological coupling lacks the clarity necessary to ensure reproducibility. Therefore, I recommend rejection in its current form, but I encourage the authors to revise and resubmit.Specific Comments:
1) Lines 10-15: For wind turbines, fatigue loads typically arise from wake-induced unsteady turbulence. The current statement claiming that blockage effects inherently lead to increased loads is inaccurate, or at least requires heavy qualification regarding specific operating conditions.
2) Lines 15-20: The phrase "as the thrust force distribution and wake rotation" should be revised to "including the thrust force distribution and wake rotation."
3) General Note on Language: There are numerous grammatical errors throughout the manuscript. A thorough proofreading is necessary to meet publication standards.
4) Introduction Structure: A paragraph should be added immediately following the first paragraph of the introduction. This new paragraph needs to explicitly discuss how atmospheric stability and blockage effects influence wake modeling.
5) Lines 20-25: Assuming the proposed model does not use linearized RANS, the authors should clarify this distinction upfront. I recommend starting this paragraph by outlining the different methodological approaches, explicitly distinguishing between linearized RANS and direct RANS solvers, to better position your chosen method.
6) Lines 20-40: The review of past methodologies in this section is currently too scattered. It must be reorganized to provide a clear, logical storyline that properly contextualizes the evolution of these methods and leads smoothly into the current work.
7) Lines 30-35: The statement that "the effect of the thrust coefficient is nonlinear even for low thrust coefficients (e.g., C_T = 0.1) because the wake recovery increases with C_T" lacks a clear physical justification. The authors must elaborate on the underlying aerodynamics to explain exactly why this relationship results in the observed nonlinearity.
8) Lines 40-45: The sentence beginning with "In this work..." introduces the core contributions of this study. It should start a new paragraph to clearly delineate the end of the literature review from the present methodology.
9) Lines 40-45: The articulation of the study's contributions is confusing. The text mentions an "extension" of previous work alongside an "alternative superposition method." The authors need to clarify the hierarchy of these updates: is the improved superposition method a core component of the main "extension," or does it represent a secondary, distinct improvement to the model?
10) Table 1: The use of the term "dimensions" in this table is currently confusing. It is unclear how these dimensions link to the proposed model, for example, whether they represent dependent variables of what, without searching through the main text. Furthermore, the relationship between the "velocity deficit," "wake-added TI," and the LUTs is ambiguous. The authors must clarify whether these are the specific output parameters retrieved from the lookup database or if they serve another function. As tables in scientific manuscripts should be entirely self-contained, I recommend redesigning the table for clearer categorization or providing comprehensive explanations in the footnotes.
11) Lines 50-55: "The RANS-LUT surrogate model is based on a database of single wake simulations" should be changed to "The proposed RANS-LUT surrogate model for all atmospheric stability conditions, including stable conditions, is based on a database of single wake simulations" to make it more specific.
12) Lines 50-55: "RANS-AD simulations are employed" should be changed to "RANS-AD simulations are employed to generate the aforementioned database and to validate the RANS-LUT model."
13) Lines 50-55: "The RANS-LUT model of Criado Risco et al. (2023) and proposed extensions are discussed in Sect. 2.3." should be changed to "The original RANS-LUT model of Criado Risco et al. (2023) for the neutral case and its proposed extensions are discussed in Sect. 2.3." This clarifies the relationship between the original model and the current one.
14) Lines 55-60: The phrase "a wind turbine row and a square wind farm" lacks scientific precision. Please use more formal terminology (e.g., "an array of wind turbines" or "a regular grid wind farm").
15) Lines 55-60: Regarding the "270 and 315 degree" inflow angles: what are these angles relative to, and why was zero not used? Please make this crystal clear in the text.
16) Lines 60-65: Regarding the "below- and above-rated wind speeds": why was it necessary to select these two extremes? Please specify your reasoning.
17) Lines 60-65: You have three reference turbulence intensities (TIs) and three reference stability parameters. Should these be paired? For example, under stable conditions, the typical TI should be very low; therefore, 5% might be a better choice than 10%.
18) Lines 65-70: How is the "NREL-5MW reference turbine" linked to the general turbine model? If you are only using a general turbine model, you could simply state that you use a general model that could also represent the NREL-5MW reference turbine.
19) Lines 75-80: Please provide a more detailed introduction to the Actuator Disk (AD) model and explain how it is used to simulate wind turbine effects in your framework.
20) Lines 80-85: This section is confusing. If there is no detailed information provided about the AD, why is a polar grid needed? Furthermore, under what framework are the thrust and tangential forces calculated?
21) Lines 80-85: Regarding the statement, "The force distributions are scaled with the local shear, while maintaining the input integral forces": why is this necessary? What does this mean, how does it fit into your framework, and which specific components are affected?
22) Lines 85-90: Please explain why an "inner refined domain" is needed.
23) Lines 90-95: You state that "A finer grid spacing may be necessary for stable inflow cases depending on the user’s quantity of interest." If this is the case, a grid resolution sensitivity test should be provided to justify the chosen spacing.
24) Lines 95-100: Regarding the statement, "We employ a two-equation $k$-$\epsilon$ turbulence model that is in balance with MOST": Please clarify how it is in balance with Monin-Obukhov Similarity Theory (MOST) and explain why this balance is necessary for your methodology.
25) Equations 2-4: Is this a realizable two-layer RANS model based on your formulation in Equation 2? If so, please specify the formulation of $f_p$ and explain how $\epsilon$ is formulated as it approaches the ground.
26) Lines 105-110: "The MOST profiles are in balance with the turbulence model using an additional source term $S_k$ and a height-dependent $C_{\epsilon,3}$." Please provide more detail on exactly how this balance is achieved.
27) Lines 110-115: "We use a constant turbulent buoyancy source term, $B = u_*^3/(\kappa L)$, that is better suited for wind turbine wakes subjected to unstable conditions." Please explain the physical reasoning behind why this formulation is better suited for unstable conditions.
28) Lines 110-115: "Using a constant buoyancy source term for stable conditions can lead to numerical instabilities." Please elaborate on the root cause of these numerical instabilities.
29) Equation 5: The reasoning behind this modification is confusing. Please provide a clearer physical or mathematical justification for why this modification is needed.
30) Lines 115-120: How is the parameter $f_p$ linked to the typical formulation of the two-layer realizable $k$-$\epsilon$ model? Please clarify this relationship.
31) Lines 125-130: "Even though a turbulence model is employed that is analytically in balance with the turbulence model..." This appears to be a typo or redundant phrasing. Please review and revise.
32) Lines 130-135: "The friction velocity from Eq. (6) is rescaled to get the desired wind speed at the reference height. These scaling factors are 0.9901, 0.9959 and 0.9962, for the Stable, Neutral and Unstable cases, respectively." Please explain the physical or numerical justification for why this scaling is necessary, and detail exactly how it is applied.
33) Lines 135-140: Are "free stream velocity" and "inflow wind speed" referring to the exact same quantity in this context? If they are synonymous, please use consistent terminology throughout the manuscript to avoid reader confusion.
34) Line 140: You state that "the inflow wind speed is not a relevant parameter." However, the transition between below-rated and above-rated wind speeds causes significant changes in turbine operation (such as thrust coefficient variations) and subsequent wake behavior. Please clarify this statement or revise it to reflect these operational differences.
35) Lines 140-150: The explanation of how to reduce eight dependent variables to two is well-written and clear. The rest of the manuscript should strive to follow this level of clarity.
36) Lines 155-160: The statement, "This is overcome by replacing the stable single wake cases for $I_{\text{ref}} \ge 0.1$ in the database with the neutral single wake cases," is unclear. Please elaborate on the justification and the mechanics behind this replacement.
37) Lines 160-165: Why are there 153 cases? Based on your selected combination of parameters, there should be $7 \times 3 \times 9 = 189$ cases. A follow-up question: for stable conditions, some of these parameter combinations seem unrealistic (as mentioned previously). For instance, a lower Turbulence Intensity (TI) should be selected for stable conditions. Please clarify this discrepancy in case numbers and parameter selection.
38) Lines 165-170: How is "background shear" defined in this context? Please provide the exact mathematical definition or formulation.
39) Line 175: Please define the acronym "AEP" (Annual Energy Production) upon its first use in the text.
40) Lines 175-180: "An iterative approach is employed to obtain the effective wind speed and TI." Please explain why an iterative method is necessary here rather than a direct calculation.
41) Lines 175-180: The text mentions "engineering wake and blockage models." However, I do not see any description in the methodology of how blockage effects are simulated. Please ensure the methodology explicitly covers blockage if it is being referenced here.
42) Lines 175-180: "...by interpolating and scaling a wake and blockage shape from the LUTs using the local wind speed ($C_T$) and TI at each turbine position." This phrasing is confusing. Please clarify exactly what is being interpolated and how the local wind speed and thrust coefficient ($C_T$) are utilized in this scaling process.
43) Lines 180-185: Assuming that the effect of inflow TI on a single turbine is identical to the effect of wake-added TI on a turbine inside a farm is a very strong assumption. Please explicitly justify this assumption and validate it, either through references to existing literature or by comparison with an open database.
44) Lines 180-185: "Finally, the inflow shear following MOST is added as a post step to the superposed wind farm flow." Why is this added as a post-processing step rather than being integrated natively? Please explain the physical or numerical rationale.
45) Lines 190-195: You note that this method "leads to a well performing model in terms of the flow field but strongly underpredicts wind turbine power production." Consider clarifying in the text that this occurs because the flow field depends linearly on velocity ($u$), whereas power production depends on the cube of the velocity ($u^3$). Taking the average of the flow field will naturally underpredict the power due to Jensen's inequality.
46) Lines 195-200: The explanation regarding calculating "superposition weights iteratively based on the ratio of the single wake convection velocity and the summed convection velocity" is hard to follow. Please rephrase this for clarity or provide a supporting equation to guide the reader.
47) Lines 200-205: "The weighted superposition method is implemented with efficient analytical integrals assuming a Gaussian velocity deficit." This assumption is questionable, as a Gaussian profile may not be applicable under stable atmospheric conditions. Please justify this choice and discuss its potential limitations.
48) Methodology Section: It is highly recommended that you include a detailed flowchart of your methodology. The current text-only description makes it very difficult to follow the complex sequence of steps, iterations, and inputs.
49) Figures 3 and 5: It appears that the stable conditions yield the best results. This is counterintuitive compared to typical modeling expectations. Please discuss this finding in the text and explain why the model performs best under these conditions.
50) Figure 6: There is a significant difference upstream between the RANS-AD and RANS-LUT results under stable conditions. What is the cause of this discrepancy? Please address and explain this in the text.
Citation: https://doi.org/10.5194/wes-2025-287-RC2
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Overall evaluation
This article presents a new wake and blockage model for wind farm flow simulation, based on the Look Up Table (LUT) constructed from single wake simulations using RANS CFD model with an actuator disk. The proposed methodology aims to fill a current gap in RANS-based models by modeling the effects of atmospheric stability and providing estimates for the wake-added turbulence. Both effects are known to have a strong influence on the build-up of wakes in wind farms and limit the accuracy of many existing models. From that perspective the work presented in this paper is relevant quite novel.
The benefits of the proposed approach are clearly demonstrated by the results of the two tests-cases presented in the article . The authors are also transparent about the remaining limitations of their approach - particularly with regard to computation time - while proposing clear tracks for potential improvement to be explored by future research.
Comparing the results of the RANS LUT using the RANS-AD shows that the model's performances are comparable to that of the full CFD model, while offering significant gains in computational time. Such a validation strategy makes sense, since the accuracy of the LUT depends on that of the underlying CFD model, as the conclusions rightly point out.
The paper is also well structured. The section on methodology provides detailed information that allows the relevance of the approach to be assessed and ensures the reproducibility of the results - at least in theory. The results are presented in a clear way and provide sufficient evidence to support the authors' claims. The paragraph discussing the performances of the various superposition models repeats some elements already covered in the methodology section, making it a bit long and harder to read than the remainder of the paper. It could probably be shortened, but this is a minor issue.
Overall, the quality of the scientific content is high and results demonstrate an appropriate technical depth. I would only point out that a lot of emphasis is put on the ability of the RANS-LUT to reconstruct the wake flow while the authors comment very little about the models performance regarding blockage and speed ups regions. Focusing on the wake makes sense, given the preeminence of the phenomena on the wind farm losses. However, the ability to accurately reproduce the entire flow field around the wind turbine is one of the main advantages of the RANS-LUT approach over engineering models. For instance, when discussing the results of the 8x8 wind farm, it would have been a great addition to address the behavior of the first row of turbines - especially for non-row aligned wind direction where some turbines are expected to benefit from local flow acceleration of the flow caused by their neighbors. Demonstrating the ability of the RANS-LUT to accurately reproduce these complex patterns - which many engineering models fail to capture - would have strengthened the overall argument.
Overall, this paper is very strong, relevant for the community and that introduce a novel approach to fill some of the current modeling gaps. Therefore, my recommendation would be to accept it for publication provided that the authors address the few minor comment listed below.
Technical questions
Minor comments