Comparison of Blade Resolved and Actuator Disk Simulations of a Ducted Wind Turbine

Tchapdieu, Junior E.; Helenbrook, Brian T.; Visser, Kenneth D.

doi:10.5194/wes-2025-207

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https://doi.org/10.5194/wes-2025-207

Preprints

20 Oct 2025

| 20 Oct 2025

Status: this preprint is currently under review for the journal WES.

Comparison of Blade Resolved and Actuator Disk Simulations of a Ducted Wind Turbine

Junior E. Tchapdieu, Brian T. Helenbrook, and Kenneth D. Visser

Abstract. 3-D blade-resolved and 2-D actuator-disk simulations of a ducted wind turbine (DWT) were performed to investigate the fidelity of actuator disc predictions and the impact of 3-D effects on performance. Both simulations used Reynolds-averaged Navier-Stokes (RANS) equations with a k-ϵ turbulence model. The DWT had a five-bladed rotor with a GOE417a airfoil, and the duct utilized an E423 airfoil. The Reynolds number based on the diameter of the rotor was 1.24 × 10^6. The design tip speed ratio was 2.9. The performance of the DWT from the blade-resolved simulation was 26 % lower than the actuator disk simulation, with a significantly larger separation region inside the duct. These observations suggest that, while 2-D actuator disk simulations have a lower computational cost, predictions of the coefficient of power and flow separation may not be accurate. A possible reason is that the actuator disc model did not include swirl, which near the hub was observed to reach nearly 80 % of the free stream velocity. Another possible reason is blade intermittency effects. The separation region on the duct increased as the blade passed and then reduced, but it was always larger than that in the actuator disk simulations.

Received: 10 Oct 2025 – Discussion started: 20 Oct 2025

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Junior E. Tchapdieu, Brian T. Helenbrook, and Kenneth D. Visser

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RC1:
'Comment on wes-2025-207', Anonymous Referee #1, 01 Dec 2025 reply
This study performs steady Reynolds Averaged Navier Stokes (RANS) simulations of ducted wind turbines using a full geometric representation of the turbine (3-D blade resolved) and an actuator disk representation of the turbine. The k-\epsilon RANS turbulence model is used within the commercial Ansys CFD tool. There are some differences in the coefficient of power between the two turbine representations, which are interpreted by looking at the flow separation and mean flow fields from the two simulations.
Investigation of ducted wind turbines is interesting, but in my view, this article offers somewhat limited new physics or engineering concepts/results. Most importantly, there is no experimental validation of the RANS simulation model, which is also not state-of-the-art. The blade resolved and actuator disk simulations are compared, but it is actually not clear which one is more accurate without validation. Minor differences in flow separation are described, but flow separation predictions in RANS can be unreliable, and the k-\epsilon model specifically has limitations in predicting flow separation. The blockage of 4.2% is relatively large for a CFD calculation and this also must be investigated. Finally, aspects of the actuator disk model are not clear. Numerical issues with an actuator disk model implementation can cause major uncertainties and coefficient of power overprediction which may be a major driver of the results.
Point comments:
Line 50: The authors perform RANS simulations of rotating airfoils at low/transitional Reynolds numbers where previous experimental studies have shown Reynolds number dependency for different airfoils [e.g., 1]. The aspect of Reynolds number dependence should be more clearly discussed and justified. Simulations are performed for a 3 meter turbine. Is that the expected size for the real application of interest or is this a ‘lab scale’ device? This requires more justification and discussion.

Line 50: Relatedly - what validation has been performed to demonstrate that 1) RANS and the selected turbulence model and 2) the resulting airfoil polars are reliable at these Reynolds numbers? This validation should be shown and discussed explicitly.

Line 65: The simulations are performed using 4.2% blockage. At this blockage ratio, there will be blockage effects on the results. An Appendix should be added where the effects of blockage are quantified, rather than relying on a reference to literature.

Line 69: Why is the k-\epsilon turbulence model chosen? This should be justified through literature references and also validation (see general comment), especially in capturing flow separation. The k-\epsilon model has very well known deficiencies in capturing flow separation effects.

Line 72: Why were 5% turbulence intensity and 1 meter integral length scale set? This requires much more discussion and is likely to influence the results substantially, given the focus on flow separation.

Section 2.3: The naming of this section should be more precise - the authors perform a grid convergence test and ‘validation’ (comparison to experimental measurements) is absent

Section 2.3: Related to the point above, RANS calculations are well known to result in grid convergence to a final answer that is not equal to experimental measurements given inaccuracies with RANS turbulence models

Section 3: Much more technical detail is required to explain the actuator disk setup. Actuator disk models are strongly sensitive to the numerical method used, especially the method used to smear the force in the three-dimensional domain, which has benefited from recent theory for LES modelling [2]. These numerical issues are especially prevalent at high thrust coefficients (C_T=1 in the present calculations). To what extent has the selected actuator disk method been verified? This should be shown explicitly in an appendix and additional simulations with and without the duct. Does the actuator disk implementation reproduce momentum theory relationships?

Figure 7: This figure is consistent with a well known issue that actuator disk models can overpredict thrust and power because of an incorrect representation of the induction (see Ref. [2]). Such an effect is likely to be even worse in ducted flow. The discussion attributes the overprediction to ‘wake rotation and tip vortices.’ The induction should be checked in detail first, as this is the most likely reason, and is straightforward to correct.

Figure 7: It is unclear what the red C_T curve is from. Is this from the “3-D” RANS?

Line 175: “Another possible cause of the difference between the 2-D and 3-D simulations is that in the actuator disk simulation, the disk acts as a uniform resistance.”

This could be investigated by implementing a nonuniform loading on the actuator disk

Figure 12 is challenging to see, consider increasing the resolution and making the visualization more clear. Coordinate directions are missing.

References
[1] Kiefer, Janik, Claudia E. Brunner, Martin OL Hansen, and Marcus Hultmark. "Dynamic stall at high Reynolds numbers induced by ramp-type pitching motions." Journal of Fluid Mechanics 938 (2022): A10.
[2] Shapiro, Carl R., Dennice F. Gayme, and Charles Meneveau. "Filtered actuator disks: Theory and application to wind turbine models in large eddy simulation." Wind Energy 22, no. 10 (2019): 1414-1420.

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Citation: https://doi.org/10.5194/wes-2025-207-RC1
RC2:
'Comment on wes-2025-207', Anonymous Referee #2, 06 Dec 2025 reply
This manuscript compares a 3‑D blade‑resolved RANS simulation with an axisymmetric 2D actuator‑disk simulation of the same ducted wind turbine (DWT).
The authors report that the 3D power coefficient prediction is almost 26% lower than the corresponding 2D actuator‑disk result at the design point, and they attribute the differences primarily to wake rotation (not accounted for in their actuator‑disk model) and to blade intermittency effects that modulate separation inside the duct. They also identify a larger flow-separation region near the duct trailing edge in 3D than in 2D.
The topic (fidelity of actuator‑disk vs. blade‑resolved simulations for DWT design and performance prediction) is clearly of interest to the Wind Energy Science readership and fits the journal’s scope on wind‑turbine aerodynamics, modeling, and numerical methods.
Overall, the manuscript is clear and well organized, with a logical flow from setup to performance comparison and flow features. Figures are generally informative.

MAIN COMMENTS
The main criticisms of the manuscript concern the over‑generalized conclusions about actuator‑disk accuracy (especially in the most relevant sections, i.e., the abstract and conclusions) and the lack of strong originality and innovative contribution, which stems from an over‑simplified implementation of the actuator‑disk model.
The proposed actuator‑disk formulation is overly simplified, which compromises a fair comparison with 3D simulations. The model applies a uniform pressure drop across the disk, completely disregards wake rotation, finite‑blade effects (including tip and hub corrections), and profile losses. Given this highly simplified setup, it is unsurprising that the power coefficient is largely overpredicted; a similar overprediction would occur in the open‑rotor case, too. This weakness of the manuscript is strongly exacerbated by the presence of references in the bibliography where, for the ducted case, more advanced actuator‑disk models have been successfully compared with 3D blade‑resolved data and experimental measurements.

The abstract states that, although 2‑D actuator‑disk simulations are computationally efficient, “predictions of the coefficient of power and flow separation may not be accurate,” citing the present 26% discrepancy and larger separation region as evidence. This conclusion is too strong as a general statement about actuator‑disk models. The lack of accuracy is mainly due to the strong simplifying assumptions adopted in the specific actuator‑disk implementation presented in the manuscript. The authors should, at minimum, soften the abstract and conclusions and attribute the limitations to the specific actuator‑disk formulation used here, rather than to actuator‑disk methods in general. For example, consider revising to: “…the specific actuator‑disk implementation used in this paper is not accurate in predicting the power coefficient and flow.” In addition, the abstract and conclusions should clearly describe all the over‑simplified assumptions adopted in the model to make readers fully aware of them.

From the introduction: “there is a lack of research on how the performance of DWTs designed using actuator disk simulations translates to blade‑resolved simulations, and … the accuracy of predicting the flow separation zone … remains unexplored.”

This statement is overly broad. A simple review of the literature clearly shows that some studies have applied actuator‑disk models to ducted configurations and compared their results with more advanced methods (such as 3‑D blade‑resolved simulations) and experimental data, addressing power coefficient, wake development, and duct flow field. This significantly undermines both the originality and the motivation of the present manuscript, especially considering that the proposed model is highly oversimplified compared to those available in the literature.

The manuscript states that DWTs may “exceed the performance ceiling set by the Betz limit” and later defines performance with respect to rotor‑swept area and duct exit area. To assess the potential of DWTs, please clarify whether “exceeding Betz” refers to the rotor area or to the duct cross‑sectional area. This distinction should be made explicit, and the discussion should compare the results reported in the literature with those shown in Figure 7, where the power coefficient falls below the Betz limit when normalized by the duct exit area.

If I understand correctly, the final mesh used for the simulations is not the one shown in Figure 6, which appears rather coarse, particularly in the wake region. The manuscript should include an image of the final mesh actually used for the simulations, ensuring that it is sufficiently refined, particularly in the wake region near the duct exit. A mesh that is not adequately dense in this area could compromise the prediction of flow separation, which is a key aspect of the analysis.

In the introduction the authors state that prior work suggests tip vortices can energize the boundary layer on the duct and delay separation, implying 3D may delay stall relative to 2D. However, in your results, separation appears in the 3D case while almost absent in 2D. Please discuss this contradiction.

MINOR COMMENTS
The 3‑D and 2‑D domains both have 4.2% blockage. Given the sensitivity of ducted devices to far‑field BCs, please quantitatively discuss if this size is suitable.

“To simulate the rotor rotation, the domain was rotated … with a tip‑speed ratio of 2.9”. The tip‑speed ratio is a property of the turbine, not of the computational domain. Please adjust the wording.

Please explicitly state in the captions whether Figures 8–12 (velocity, streamlines, skin friction, swirl) are shown at the design TSR or at another operating point.

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Citation: https://doi.org/10.5194/wes-2025-207-RC2

Junior E. Tchapdieu, Brian T. Helenbrook, and Kenneth D. Visser

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Short summary

To improve the design of ducted wind turbines, 2D simulations are usually used. This research compared 2D and 3D simulations of airflow around a ducted turbine. The 3D results showed that airflow separates from the duct earlier and that energy output is about 26 % lower than in 2D results. These findings show that 2D models, while simpler and faster to compute, can significantly overestimate real-world performance. Understanding these differences can guide more accurate turbine designs.


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