the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 03 Apr 2025
Validation of the near-wake of a scaled X-Rotor vertical-axis wind turbine predicted by a free-wake vortex model
Abstract. Vertical-axis wind turbines (VAWTs) are gaining research attention in offshore energy due to their ability to operate in omnidirectional wind, simpler design characteristics, and potential for faster wake recovery. As part of this interest, a novel X-shaped VAWT (X-Rotor) has been proposed to minimise the levelised cost of energy. While existing studies on the X-Rotor rely on numerical tools to analyse rotor performance, experimental validation remains limited, making it essential to assess the accuracy of these models in predicting the flowfield around the rotor. This study compares a free-wake vortex model (CACTUS) against stereoscopic particle image velocimetry (PIV) results for a scaled X-Rotor. Both qualitative and quantitative comparisons are performed, examining flowfield features with and without blade pitch offsets. Additionally, the study provides insights into the three-dimensional aerodynamics introduced into the wake by the turbine’s coned blades. Results indicate that CACTUS effectively replicates the flowfield within the rotor volume and the very near wake when no pitch offsets are applied. However, with pitch offsets, significant deviations from experimental data are observed, suggesting the need for careful model tuning for full-scale X-Rotor analysis. Furthermore, the introduction of coned blades enhances three-dimensional effects, generating notable upwash and downwash in the wake. These findings highlight the importance of using 3D aerodynamic tools over 2D approaches in future X-Rotor analyses to accurately capture vertical flow components.
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Status: open (until 01 May 2025)
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RC1: 'Comment on wes-2025-54', Anonymous Referee #1, 15 Apr 2025
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This manuscript investigates the aerodynamic wake downstream of an X-type vertical axis wind turbine (VAWT) using the CACTUS free-wake vortex solver and compares the numerical predictions with experimental data obtained from stereoscopic particle image velocimetry (PIV) measurements on a scaled model. The topic is relevant and timely, and the combination of numerical and experimental approaches adds value to the study. Below are my specific comments.
The comparison between the free-wake vortex model (CACTUS) and stereoscopic PIV measurements for a scaled X-Rotor significantly enhances the value of the study, providing both numerical and experimental perspectives that strengthen the overall credibility of the findings.
Comment (line 2 of the abstract): The phrase "to minimise the levelised cost of energy" is somewhat broad. If possible, please clarify in one sentence how the proposed X-Rotor specifically contributes to lowering the LCOE (e.g., through reduced manufacturing costs, improved efficiency, easier maintenance, etc.).
Comment (line 36, Introduction): It would be helpful to clarify whether the study by Morgan et al. (2025) also employed a BEM-based approach, and whether it included a quantitative comparison of power coefficients between the classical and X-type rotor configurations. This information would support the claim of performance benefits associated with the X-type design.
Comment (Section 2.1): The manuscript mentions that the scaled model was derived from a large turbine design. Please clarify whether the scaling was purely geometric, or if similarity parameters (e.g., Reynolds number, tip-speed ratio) were also considered in the design process. Additionally, it would be useful to specify whether the blades were clean or if any flow tripping devices were used to promote separation. Finally, please provide details on the blade mounting configuration — specifically, was the mounting point located at the quarter-chord (c/4) position from the leading edge?
Comment (line 153): The authors state that the simulations were run for 10 revolutions to ensure convergence. Please clarify whether 10 revolutions represent the total simulated time. Is this duration sufficient to obtain both converged blade loads and a fully developed wake structure?
Comment (starting around line 167): I am not sure whether the figure numbering is consistent starting from line 167. The paragraph beginning at line 162 discusses Figs. 5 and 6, but, if I’m reading correctly, there appears to be no reference to Fig. 7, and the text jumps directly to Fig. 9. Moreover, Fig. 9 already refers to the case with pitched blades, suggesting that an intermediate figure (possibly Fig. 7 or 8) might be missing or misnumbered.
Comment (around line 175): The authors rightly note that the numerical approach fails in certain regions. I believe two factors may contribute to this discrepancy: the accuracy of the airfoil characteristics at such low Reynolds numbers, and potential limitations of the dynamic model used. A brief discussion of these aspects would strengthen the interpretation of the results.
Citation: https://doi.org/10.5194/wes-2025-54-RC1 -
RC2: 'Comment on wes-2025-54', Anonymous Referee #2, 19 Apr 2025
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The authors benchmarked the CACTUS tool, based on the Lifting Line Free Vortex Wake (LLFVW) method, against experimental measurements on a scaled version of the X-Rotor prototype. In particular, the accuracy of the numerical tool to predict the rotor wake in different operative regimes was assessed. The Reviewer believes the topic and activity are very interesting, innovative, and worthy of investigation. The manuscript is well written and structured, with a clear presentation of both the methodology and results. However, the employed methodology presents several significant limitations, which, although acknowledged by the authors, undermine the reliability of the findings. More in detail:
- There is significant uncertainty in the polar data and overall aerodynamic modeling, particularly in both pre- and post-stall regimes. Assuming similar airfoil behavior at Re = 80k and 150k is a strong simplification, especially considering the chosen airfoil and the experimental turbulence intensity. Using XFOIL with Ncrit = 8 is also questionable, as the experimental TI suggests a lower Ncrit ≈ 4. This likely introduces notable errors in force predictions and may account for discrepancies with the experiments such as the reduced wake expansion. Additionally, the treatment of post-stall behavior is unclear—was any extrapolation method used?
- Flow curvature, which becomes significant for blade sections with chord-to-radius ratios c/R > 0.1, is ignored in the simulations. This is a critical omission, given that most of the blade operates beyond this limit and flow curvature has a strong effect on the lift characteristics at low angles of attack;
- The chosen core radius for the LLFVW simulations appears excessively large. While the authors justify this choice on the grounds of numerical stability, this compromises the fidelity of tip vortex resolution—a crucial aspect of wake recovery. It is difficult to draw reliable conclusions about the wake behavior when tip vortex dynamics are under-resolved.
Some specific considerations:
1. The introduction is a bit vague, especially concerning the technological background of the work. What is the idea behind the X-Rotor and what role is it supposed to play in the future offshore wind industry compared to traditional HAWTs or VAWTs? Why is it advantageous to further develop numerical tools to simulate complex shape VAWTs?2. Section 2.1: in this case, the strategy used to scale the X-Rotor to wind tunnel size plays a crucial role in the soundness of the study. Please provide additional details on this;
3. Flow curvature effects do not come from time-varying inflow, as stated by the authors, rather from the variation of the angle of attack along the blade chord, even in quasi-steady conditions, i.e., in absence of significant dynamic effects;
4. Figures 6 and 9 are difficult to read due to the figure dimensions and adopted colorscale. It is recommended to switch to higher contrast colorscale or make a selection and show fewer 2D views on a bigger scale.
Citation: https://doi.org/10.5194/wes-2025-54-RC2
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