the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A Data-Driven Reduced Order Model for Rotor Optimization
Nicholas Peters
Christopher Silva
John Ekaterinaris
Abstract. For rotor design applications, such as wind turbine rotor or Urban Air Mobility (UAM) rotorcraft and flying car design, there is a significant challenge in quickly and accurately modeling rotors operating in complex turbulent flow fields. One potential path for deriving high-fidelity but low-cost rotor performance predictions is available through the application of data-driven surrogate modeling. In this study, an initial investigation is undertaken to apply a proper orthogonal decomposition (POD) based reduced order model (ROM) for predicting rotor distributed loads. The POD ROM was derived based on computational fluid dynamics (CFD) results and utilized to produce distributed pressure predictions on rotor blades subjected to topology change due to variations in twist and taper ratio. Rotor twist, θ, was varied between 0°, 10°, 20°, and 30° while taper ratio, λ, was varied as 1.0, 0.9, 0.8, and 0.7. For a demonstration of the approach, all rotors consisted of a single blade. The POD ROM was validated for three operation cases; a high pitch or a high thrust rotor in hover, a low pitch or a low thrust rotor in hover, and a rotor in forward flight at a low speed resembling wind turbine operation with wind shear. Results showed highly accurate distributed load predictions could be achieved and the resulting surrogate model can predict loads at a minimal computational cost. The computational cost for the hovering blade surface pressure prediction was reduced from 12 hours on 440 cores required for CFD to a fraction of a second on a single core required for POD. For rotor in forward flight cost was reduced from 20 hours on 440 cores to less than a second on a single core. The POD ROM was used to undergo a design optimization of the rotor such that figure of merit was maximized for hovering rotor cases and the lift to drag effective ratio was maximized in forward flight.
Nicholas Peters et al.
Status: final response (author comments only)
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RC1: 'Comment on wes-2022-95', Anonymous Referee #1, 19 Dec 2022
The paper presents an interesting framework for ROM-based analysis and optimization of rotors. While this work clearly represents the product of a great deal of thinking and work, I do not think it is sufficient for publication without major revisions. It seems that this paper is proposing a workflow where a ROM is trained using CFD, then the ROM is optimized to obtain a final design. This workflow assumes the ROM is remarkably accurate, and does not verify that the optimal designs found using the ROM correspond to the optimum of the CFD model, or even if the CFD model predicts favorable performance of the ROM. I think the paper should be revised either to stress the limitations of this framework, include CFD validation of the ROM-based optimum design, or to suggest a multifidelity formulation in future work.
Major Comments:
- The paper does not validate the optimal designs found via the ROM model. I suggest validating the designs using the CFD model, or providing a caveat explaining that these designs would need to be validated with CFD before being used in production.
- I strongly recommend discuss the pros and cons of how this framework could be extended via a multifidelity formulation (for example, on P3L60).
Minor Comments:
- Throughout the paper, phrases like "highly accurate" are used in a way I perceived to be subjective. The errors between the ROM and CFD seem significant, and it seems subjective to call the ROM highly accurate, or even accurate. I would instead focus on quantitative differences between the models, and refer to errors you are happy with as "reasonably accurate".
- It would be useful to compare ROM and CFD predictions using relative error, instead of the absolute error presented in Figures 12, 13, 14, and 15.
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RC2: 'Reply on RC1', Anonymous Referee #1, 28 Dec 2022
Please include more detail in exactly how ϕ_i(x) is constructed, since each set of blade parameters would be associated with a different set of basis functions, ϕ_i i(x,λ,θ).Citation: https://doi.org/
10.5194/wes-2022-95-RC2
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RC2: 'Reply on RC1', Anonymous Referee #1, 28 Dec 2022
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RC3: 'Comment on wes-2022-95', Anonymous Referee #2, 19 Feb 2023
Summary: 'A Data-Driven Reduced Order Model for Rotor Optimization' applies Proper Orthogonal Decomposition to develop a reduced-order model for rotor loads. The authors simulate single blade rotor operation via CFD. Pressure loads are computed for a parametric study across rotor twist angles, taper ratios, and rotor operating points designed to recreate hover and forward flight dynamics. The authors identify the minimum node requirement to capture a significant portion of the energy content for each type of operation. From here, they recreate CFD pressure loads and replicate rotor design optimizations using the reduced-order model.
Key Points: The authors demonstrate the utility of reduced-order modeling by successfully estimating rotor pressure loads across blade geometries and flight modes. Evaluating the capabilities of their approach in forward flight is a welcome addition as these findings are more representative of typical flow conditions and are broadly applicable to rotor operation. The authors provide an in-depth discussion on each aspect of the work although the article would be improved by including additional references. Overall, the article is well-written and articulates several important results.
Recommendation: Although the manuscript should be published, the following comments should be first taken into consideration.
Comments:
Line 42: Please include additional studies on estimating wind turbine loads with LES beyond the single reference. While wind energy is not the focus of the manuscript, many recent works employ tools such as OpenFAST within a LES framework to compute rotor loads in highly turbulent flows which is of relevance.
Line 51: This section would benefit from including reduced order modeling studies specific to turbulent rotor wakes. A list to include is herein provided:
https://www.sciencedirect.com/science/article/pii/S0376042123000039
https://aip.scitation.org/doi/abs/10.1063/1.5006527
https://www.sciencedirect.com/science/article/abs/pii/S0960148121013240
https://www.sciencedirect.com/science/article/abs/pii/S0960148122012885
https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.4.024610
https://aip.scitation.org/doi/abs/10.1063/5.0036281
https://aip.scitation.org/doi/abs/10.1063/5.0004393
https://www.mdpi.com/2504-186X/6/4/44
https://wes.copernicus.org/articles/3/43/2018/
https://link.springer.com/article/10.1007/s00521-021-06799-6
https://aip.scitation.org/doi/abs/10.1063/5.0091980
https://aip.scitation.org/doi/abs/10.1063/1.4968032
https://doi.org/10.1017/jfm.2017.492
https://onlinelibrary.wiley.com/doi/abs/10.1002/we.2167
It would be beneficial to include a visual of the CFD results for hover operation similar to the contours presented in Section 4.2.
Figure 5, Line 305 - 325: Comment further on the relationship between the pressure snapshot and POD energy content here. The POD contains at least 99.5% energy with only two modes and achieves reconstruction errors below 1% with only eight modes which is surprising. This could stem from over-simplifying the pressure solution by only including spatial information but it is difficult to be certain without additional context.
Line 404: How did the authors decide on 4.5 degrees for saving pressure distributions as opposed to saving at specified times? Does this approach introduce spatial artifacts?
Investigating the impact of sampling density is well received as this is a driving consideration which is often overlooked.
In general, there is no verification of the framework and shortcomings should be clearly highlighted. This is likely the most important point to address.
Citation: https://doi.org/10.5194/wes-2022-95-RC3
Nicholas Peters et al.
Nicholas Peters et al.
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