Articles | Volume 7, issue 1
https://doi.org/10.5194/wes-7-75-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-7-75-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
20 Jan 2022
Research article |
| 20 Jan 2022
| 20 Jan 2022
A computationally efficient engineering aerodynamic model for non-planar wind turbine rotors
Department of Wind Energy, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark
Mac Gaunaa
Department of Wind Energy, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark
Georg Raimund Pirrung
Department of Wind Energy, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark
Sergio González Horcas
Department of Wind Energy, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark
Related authors
Ang Li, Mac Gaunaa, and Georg Raimund Pirrung
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-109, https://doi.org/10.5194/wes-2025-109, 2025
Preprint under review for WES
Short summary
Short summary
Wind turbines with swept blades have the potential to improve power production and reduce loads, but their actual benefits are uncertain and they are difficult to analyze. We developed a simplified yet accurate aerodynamic model, coupling two engineering models, to predict their performance. Tests against high-fidelity simulations show that the method offers reliable results with low computational effort, making it ideal for load calculations and design optimization of swept blades.
Ang Li, Mac Gaunaa, Georg Raimund Pirrung, and Kenneth Lønbæk
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-30, https://doi.org/10.5194/wes-2025-30, 2025
Revised manuscript accepted for WES
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This study improves the analysis of curved wind turbine blades, such as those with sweep or prebend. Existing methods often blend different effects on blade performance, making design optimization challenging. We developed a framework that disentangles these effects, providing clearer insights. Our findings show that the aerodynamic influences of sweep and prebend can be modeled separately and combined, simplifying modeling processes and supporting more efficient blade design.
Thanasis Barlas, Georg Raimund Pirrung, Néstor Ramos-García, Sergio González Horcas, Ang Li, and Helge Aagaard Madsen
Wind Energ. Sci., 7, 1957–1973, https://doi.org/10.5194/wes-7-1957-2022, https://doi.org/10.5194/wes-7-1957-2022, 2022
Short summary
Short summary
An aeroelastically optimized curved wind turbine blade tip is designed, manufactured, and tested on a novel outdoor rotating rig facility at the Risø campus of the Technical University of Denmark. Detailed aerodynamic measurements for various atmospheric conditions and results are compared to a series of in-house aeroelastic tools with a range of fidelities in aerodynamic modeling. The comparison highlights details in the ability of the codes to predict the performance of such a curved tip.
Ang Li, Mac Gaunaa, Georg Raimund Pirrung, Alexander Meyer Forsting, and Sergio González Horcas
Wind Energ. Sci., 7, 1341–1365, https://doi.org/10.5194/wes-7-1341-2022, https://doi.org/10.5194/wes-7-1341-2022, 2022
Short summary
Short summary
A consistent method of using two-dimensional airfoil data when using generalized lifting-line methods for the aerodynamic load calculation of non-planar horizontal-axis wind turbines is described. The important conclusions from the unsteady two-dimensional airfoil aerodynamics are highlighted. The impact of using a simplified approach instead of using the full model on the prediction of the aerodynamic performance of non-planar rotors is shown numerically for different aerodynamic models.
Ang Li, Georg Raimund Pirrung, Mac Gaunaa, Helge Aagaard Madsen, and Sergio González Horcas
Wind Energ. Sci., 7, 129–160, https://doi.org/10.5194/wes-7-129-2022, https://doi.org/10.5194/wes-7-129-2022, 2022
Short summary
Short summary
An engineering aerodynamic model for the swept horizontal-axis wind turbine blades is proposed. It uses a combination of analytical results and engineering approximations. The performance of the model is comparable with heavier high-fidelity models but has similarly low computational cost as currently used low-fidelity models. The model could be used for an efficient and accurate load calculation of swept wind turbine blades and could eventually be integrated in a design optimization framework.
Filippo Trevisi, Gianni Cassoni, Mac Gaunaa, and Lorenzo Mario Fagiano
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-134, https://doi.org/10.5194/wes-2025-134, 2025
Preprint under review for WES
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This paper investigates the optimal aerodynamic design of the wing and of the onboard turbines of the aircraft of fly-gen Airborne Wind Energy Systems, named windplane here, with a novel comprehensive engineering aerodynamic model and with the vortex particle method implemented in DUST. Placing the turbines at the wing tips, rotating them inboard down with low tip speed ratio and using conventional efficient airfoils for the wing is found to be optimal for windplanes.
Clemens Paul Zengler, Niels Troldborg, and Mac Gaunaa
Wind Energ. Sci., 10, 1485–1497, https://doi.org/10.5194/wes-10-1485-2025, https://doi.org/10.5194/wes-10-1485-2025, 2025
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Wind turbine power performance is mostly calculated based on the wind speed measured at the turbine position. The presented results imply that it is necessary to also assess how the undisturbed wind speed changes in the flow direction to accurately predict the power performance. In other words, the acceleration of the flow is relevant for the energy production. An outcome of this work is a simple model that can be used to include flow acceleration in power performance predictions.
Nanako Sasanuma, Akihiro Honda, Christian Bak, Niels Troldborg, Mac Gaunaa, Morten Nielsen, and Teruhisa Shimada
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-130, https://doi.org/10.5194/wes-2025-130, 2025
Preprint under review for WES
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We verify wake effects between two turbines in complex terrain using Supervisory Control and Data Acquisition data. By identifying “wake conditions” and “no-wake conditions” by the blade pitch angle of the upstream wind turbine, we evaluate wake effects on wind speed, turbulent intensity, and power output. Results show that flow downhill has a significant impact on wake effects compared to flow uphill. The method offers a practical alternative to field measurements in complex terrain.
Ang Li, Mac Gaunaa, and Georg Raimund Pirrung
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-109, https://doi.org/10.5194/wes-2025-109, 2025
Preprint under review for WES
Short summary
Short summary
Wind turbines with swept blades have the potential to improve power production and reduce loads, but their actual benefits are uncertain and they are difficult to analyze. We developed a simplified yet accurate aerodynamic model, coupling two engineering models, to predict their performance. Tests against high-fidelity simulations show that the method offers reliable results with low computational effort, making it ideal for load calculations and design optimization of swept blades.
Jelle Agatho Wilhelm Poland, Johannes Marinus van Spronsen, Mac Gaunaa, and Roland Schmehl
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-77, https://doi.org/10.5194/wes-2025-77, 2025
Revised manuscript under review for WES
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We tested a small model of an energy-generating kite in a wind tunnel to study its aerodynamic behavior. By comparing measurements to computer simulations, we validated the models and identified where they match the real performance and where they fall short. These insights will guide more accurate aerodynamic modeling and inform design choices for kites used in airborne wind energy systems.
Ang Li, Mac Gaunaa, Georg Raimund Pirrung, and Kenneth Lønbæk
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-30, https://doi.org/10.5194/wes-2025-30, 2025
Revised manuscript accepted for WES
Short summary
Short summary
This study improves the analysis of curved wind turbine blades, such as those with sweep or prebend. Existing methods often blend different effects on blade performance, making design optimization challenging. We developed a framework that disentangles these effects, providing clearer insights. Our findings show that the aerodynamic influences of sweep and prebend can be modeled separately and combined, simplifying modeling processes and supporting more efficient blade design.
Stefano Cioni, Francesco Papi, Leonardo Pagamonci, Alessandro Bianchini, Néstor Ramos-García, Georg Pirrung, Rémi Corniglion, Anaïs Lovera, Josean Galván, Ronan Boisard, Alessandro Fontanella, Paolo Schito, Alberto Zasso, Marco Belloli, Andrea Sanvito, Giacomo Persico, Lijun Zhang, Ye Li, Yarong Zhou, Simone Mancini, Koen Boorsma, Ricardo Amaral, Axelle Viré, Christian W. Schulz, Stefan Netzband, Rodrigo Soto-Valle, David Marten, Raquel Martín-San-Román, Pau Trubat, Climent Molins, Roger Bergua, Emmanuel Branlard, Jason Jonkman, and Amy Robertson
Wind Energ. Sci., 8, 1659–1691, https://doi.org/10.5194/wes-8-1659-2023, https://doi.org/10.5194/wes-8-1659-2023, 2023
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Simulations of different fidelities made by the participants of the OC6 project Phase III are compared to wind tunnel wake measurements on a floating wind turbine. Results in the near wake confirm that simulations and experiments tend to diverge from the expected linearized quasi-steady behavior when the reduced frequency exceeds 0.5. In the far wake, the impact of platform motion is overestimated by simulations and even seems to be oriented to the generation of a wake less prone to dissipation.
Christian Grinderslev, Felix Houtin-Mongrolle, Niels Nørmark Sørensen, Georg Raimund Pirrung, Pim Jacobs, Aqeel Ahmed, and Bastien Duboc
Wind Energ. Sci., 8, 1625–1638, https://doi.org/10.5194/wes-8-1625-2023, https://doi.org/10.5194/wes-8-1625-2023, 2023
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In standstill conditions wind turbines are at risk of vortex-induced vibrations (VIVs). VIVs can become large and lead to significant fatigue of the wind turbine structure over time. Thus it is important to have tools that can accurately compute this complex phenomenon. This paper studies the sensitivities to the chosen models of computational fluid dynamics (CFD) simulations when modelling VIVs and finds that much care is needed when setting up simulations, especially for specific flow angles.
Paul Veers, Carlo L. Bottasso, Lance Manuel, Jonathan Naughton, Lucy Pao, Joshua Paquette, Amy Robertson, Michael Robinson, Shreyas Ananthan, Thanasis Barlas, Alessandro Bianchini, Henrik Bredmose, Sergio González Horcas, Jonathan Keller, Helge Aagaard Madsen, James Manwell, Patrick Moriarty, Stephen Nolet, and Jennifer Rinker
Wind Energ. Sci., 8, 1071–1131, https://doi.org/10.5194/wes-8-1071-2023, https://doi.org/10.5194/wes-8-1071-2023, 2023
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Critical unknowns in the design, manufacturing, and operation of future wind turbine and wind plant systems are articulated, and key research activities are recommended.
Roger Bergua, Amy Robertson, Jason Jonkman, Emmanuel Branlard, Alessandro Fontanella, Marco Belloli, Paolo Schito, Alberto Zasso, Giacomo Persico, Andrea Sanvito, Ervin Amet, Cédric Brun, Guillén Campaña-Alonso, Raquel Martín-San-Román, Ruolin Cai, Jifeng Cai, Quan Qian, Wen Maoshi, Alec Beardsell, Georg Pirrung, Néstor Ramos-García, Wei Shi, Jie Fu, Rémi Corniglion, Anaïs Lovera, Josean Galván, Tor Anders Nygaard, Carlos Renan dos Santos, Philippe Gilbert, Pierre-Antoine Joulin, Frédéric Blondel, Eelco Frickel, Peng Chen, Zhiqiang Hu, Ronan Boisard, Kutay Yilmazlar, Alessandro Croce, Violette Harnois, Lijun Zhang, Ye Li, Ander Aristondo, Iñigo Mendikoa Alonso, Simone Mancini, Koen Boorsma, Feike Savenije, David Marten, Rodrigo Soto-Valle, Christian W. Schulz, Stefan Netzband, Alessandro Bianchini, Francesco Papi, Stefano Cioni, Pau Trubat, Daniel Alarcon, Climent Molins, Marion Cormier, Konstantin Brüker, Thorsten Lutz, Qing Xiao, Zhongsheng Deng, Florence Haudin, and Akhilesh Goveas
Wind Energ. Sci., 8, 465–485, https://doi.org/10.5194/wes-8-465-2023, https://doi.org/10.5194/wes-8-465-2023, 2023
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This work examines if the motion experienced by an offshore floating wind turbine can significantly affect the rotor performance. It was observed that the system motion results in variations in the load, but these variations are not critical, and the current simulation tools capture the physics properly. Interestingly, variations in the rotor speed or the blade pitch angle can have a larger impact than the system motion itself.
Mac Gaunaa, Niels Troldborg, and Emmanuel Branlard
Wind Energ. Sci., 8, 503–513, https://doi.org/10.5194/wes-8-503-2023, https://doi.org/10.5194/wes-8-503-2023, 2023
Short summary
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We present an analytical vortex model. Despite its simplicity, the model is fully consistent with 1D momentum theory. It shows that the flow through a non-uniformly loaded rotor operating in non-uniform inflow behaves locally as predicted by 1D momentum theory. As a consequence, the local power coefficient (based on local inflow) of an ideal rotor is unaltered by the presence of shear. Finally, the model shows that there is no cross-shear deflection of the wake of a rotor in sheared inflow.
Koen Boorsma, Gerard Schepers, Helge Aagard Madsen, Georg Pirrung, Niels Sørensen, Galih Bangga, Manfred Imiela, Christian Grinderslev, Alexander Meyer Forsting, Wen Zhong Shen, Alessandro Croce, Stefano Cacciola, Alois Peter Schaffarczyk, Brandon Lobo, Frederic Blondel, Philippe Gilbert, Ronan Boisard, Leo Höning, Luca Greco, Claudio Testa, Emmanuel Branlard, Jason Jonkman, and Ganesh Vijayakumar
Wind Energ. Sci., 8, 211–230, https://doi.org/10.5194/wes-8-211-2023, https://doi.org/10.5194/wes-8-211-2023, 2023
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Within the framework of the fourth phase of the International Energy Agency's (IEA) Wind Task 29, a large comparison exercise between measurements and aeroelastic simulations has been carried out. Results were obtained from more than 19 simulation tools of various fidelity, originating from 12 institutes and compared to state-of-the-art field measurements. The result is a unique insight into the current status and accuracy of rotor aerodynamic modeling.
Christian Grinderslev, Niels Nørmark Sørensen, Georg Raimund Pirrung, and Sergio González Horcas
Wind Energ. Sci., 7, 2201–2213, https://doi.org/10.5194/wes-7-2201-2022, https://doi.org/10.5194/wes-7-2201-2022, 2022
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As wind turbines increase in size, the risk of flow-induced instabilities increases. This study investigates the phenomenon of vortex-induced vibrations (VIVs) on a large 10 MW wind turbine blade using two high-fidelity methods. It is found that VIVs can occur with multiple equilibrium states for the same flow case, showing an dependence on the initial conditions. This means that a blade which is stable in a flow can become unstable if, e.g., a turbine operation provokes an initial vibration.
Thanasis Barlas, Georg Raimund Pirrung, Néstor Ramos-García, Sergio González Horcas, Ang Li, and Helge Aagaard Madsen
Wind Energ. Sci., 7, 1957–1973, https://doi.org/10.5194/wes-7-1957-2022, https://doi.org/10.5194/wes-7-1957-2022, 2022
Short summary
Short summary
An aeroelastically optimized curved wind turbine blade tip is designed, manufactured, and tested on a novel outdoor rotating rig facility at the Risø campus of the Technical University of Denmark. Detailed aerodynamic measurements for various atmospheric conditions and results are compared to a series of in-house aeroelastic tools with a range of fidelities in aerodynamic modeling. The comparison highlights details in the ability of the codes to predict the performance of such a curved tip.
Mads H. Aa. Madsen, Frederik Zahle, Sergio González Horcas, Thanasis K. Barlas, and Niels N. Sørensen
Wind Energ. Sci., 7, 1471–1501, https://doi.org/10.5194/wes-7-1471-2022, https://doi.org/10.5194/wes-7-1471-2022, 2022
Short summary
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This work presents a shape optimization framework based on computational fluid dynamics. The design framework is used to optimize wind turbine blade tips for maximum power increase while avoiding that extra loading is incurred. The final results are shown to align well with related literature. The resulting tip shape could be mounted on already installed wind turbines as a sleeve-like solution or be conceived as part of a modular blade with tips designed for site-specific conditions.
Ang Li, Mac Gaunaa, Georg Raimund Pirrung, Alexander Meyer Forsting, and Sergio González Horcas
Wind Energ. Sci., 7, 1341–1365, https://doi.org/10.5194/wes-7-1341-2022, https://doi.org/10.5194/wes-7-1341-2022, 2022
Short summary
Short summary
A consistent method of using two-dimensional airfoil data when using generalized lifting-line methods for the aerodynamic load calculation of non-planar horizontal-axis wind turbines is described. The important conclusions from the unsteady two-dimensional airfoil aerodynamics are highlighted. The impact of using a simplified approach instead of using the full model on the prediction of the aerodynamic performance of non-planar rotors is shown numerically for different aerodynamic models.
Ang Li, Georg Raimund Pirrung, Mac Gaunaa, Helge Aagaard Madsen, and Sergio González Horcas
Wind Energ. Sci., 7, 129–160, https://doi.org/10.5194/wes-7-129-2022, https://doi.org/10.5194/wes-7-129-2022, 2022
Short summary
Short summary
An engineering aerodynamic model for the swept horizontal-axis wind turbine blades is proposed. It uses a combination of analytical results and engineering approximations. The performance of the model is comparable with heavier high-fidelity models but has similarly low computational cost as currently used low-fidelity models. The model could be used for an efficient and accurate load calculation of swept wind turbine blades and could eventually be integrated in a design optimization framework.
Thanasis Barlas, Georg Raimund Pirrung, Néstor Ramos-García, Sergio González Horcas, Robert Flemming Mikkelsen, Anders Smærup Olsen, and Mac Gaunaa
Wind Energ. Sci., 6, 1311–1324, https://doi.org/10.5194/wes-6-1311-2021, https://doi.org/10.5194/wes-6-1311-2021, 2021
Short summary
Short summary
Curved blade tips can potentially have a significant impact on wind turbine performance and loads. A swept tip shape optimized for wind turbine applications is tested in a wind tunnel. A range of numerical aerodynamic simulation tools with various levels of fidelity are compared. We show that all numerical tools except for the simplest blade element momentum based are in good agreement with the measurements, suggesting the required level of model fidelity necessary for the design of such tips.
Christian Grinderslev, Niels Nørmark Sørensen, Sergio González Horcas, Niels Troldborg, and Frederik Zahle
Wind Energ. Sci., 6, 627–643, https://doi.org/10.5194/wes-6-627-2021, https://doi.org/10.5194/wes-6-627-2021, 2021
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This study investigates aero-elasticity of wind turbines present in the turbulent and chaotic wind flow of the lower atmosphere, using fluid–structure interaction simulations. This method combines structural response computations with high-fidelity modeling of the turbulent wind flow, using a novel turbulence model which combines the capabilities of large-eddy simulations for atmospheric flows with improved delayed detached eddy simulations for the separated flow near the rotor.
Thanasis Barlas, Néstor Ramos-García, Georg Raimund Pirrung, and Sergio González Horcas
Wind Energ. Sci., 6, 491–504, https://doi.org/10.5194/wes-6-491-2021, https://doi.org/10.5194/wes-6-491-2021, 2021
Short summary
Short summary
A method to design advanced tip extensions for modern wind turbine blades is presented in this work. The resulting design concept has high potential in terms of actual implementation in a real rotor upscaling with a potential business case in reducing the cost of energy produced by future large wind turbine rotors.
Cited articles
Bergami, L. and Gaunaa, M.: ATEFlap Aerodynamic Model, a dynamic stall model including the effects of trailing edge flap deflection, Danmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi, 52 pp., ISBN 8755039340, 9788755039346, 2012. a
Bortolotti, P., Tarrés, H. C., Dykes, K., Merz, K., Sethuraman, L.,
Verelst, D., and Zahle, F.: Systems Engineering in Wind Energy – WP2.1
Reference Wind Turbines, Tech. rep., NREL – National Renewable Energy Laboratory [data set], available at:
https://www.osti.gov/biblio/1529216-iea-wind-tcp-task-systems-engineering-wind-energy
-wp2-reference-wind-turbines (last access: 2 April 2021), 2019. a, b, c, d
Branlard, E.: Wind Turbine Aerodynamics and Vorticity-Based Methods, Springer, https://doi.org/10.1007/978-3-319-55164-7, 2017. a
Branlard, E. and Gaunaa, M.: Development of new tip-loss corrections based on
vortex theory and vortex methods, J. Phys.: Conf. Ser., 555, 012012, https://doi.org/10.1088/1742-6596/555/1/012012, 2014. a, b
Branlard, E. and Gaunaa, M.: Cylindrical vortex wake model: skewed cylinder,
application to yawed or tilted rotors, Wind Energy, 19, 345–358,
https://doi.org/10.1002/we.1838, 2016. a, b
Branlard, E. and Meyer Forsting, A.: Using a cylindrical vortex model to assess the induction zone infront of aligned and yawed rotors, in: Proceedings of EWEA Offshore 2015 Conference, European Wind Energy
Association (EWEA), EWEA Offshore 2015 Conference, 10–12 March 2015, Copenhagen, Denmark, 2015. a
Branlard, E. and Meyer Forsting, A.: Assessing the blockage effect of wind
turbines and wind farms using an analytical vortex model, Wind Energy, 23,
2068–2086, https://doi.org/10.1002/we.2546, 2020. a
Burton, T., Jenkins, N., Sharpe, D., Bossanyi, E., and Graham, M.: Wind energy handbook, Wiley, ISBN 978-1-119-45116-7, 2021. a
Crawford, C.: Re-examining the precepts of the blade element momentum theory
for coning rotors, Wind Energy, 9, 457–478, https://doi.org/10.1002/we.197, 2006. a, b, c
Gaunaa, M.: Unsteady Aerodynamic Forces on NACA 0015 Airfoil in Harmonic
Translatory Motion, PhD thesis, available at: https://orbit.dtu.dk/en/publications/unsteady-aerodynamic-forces-on-naca-0015-airfoil-in-harmonic-tran
(last access: 18 January 2022), 2002. a
Glauert, H.: Airplane Propellers, in: Division L in Aerodynamic Theory, vol. IV, edited by: Durand, W. F., Springer, 169–360, https://doi.org/10.1007/978-3-642-91487-4_3, 1935. a, b
Larsen, J., Nielsen, S., and Krenk, S.: Dynamic stall model for wind turbine
airfoils, J. Fluid. Struct., 23, 959–982, https://doi.org/10.1016/j.jfluidstructs.2007.02.005, 2007. a
Leishman, J. G.: Principles of helicopter aerodynamics, Cambridge University
Press, ISBN 0521858607, 2005. a
Leishman, J. G. and Nguyen, K. Q.: State-space representation of unsteady
airfoil behavior, AIAA J., 28, 836–844, https://doi.org/10.2514/3.25127, 1990. a
Li, A., Pirrung, G., Madsen, H. A., Gaunaa, M., and Zahle, F.: Fast trailed and bound vorticity modeling of swept wind turbine blades, J. Phys.: Conf. Ser., 1037, 062012, https://doi.org/10.1088/1742-6596/1037/6/062012, 2018. a, b, c
Li, A., Gaunaa, M., Pirrung, G. R., Ramos-García, N., and Horcas, S. G.:
The influence of the bound vortex on the aerodynamics of curved wind turbine
blades, J. Phys.: Conf. Ser., 1618, 052038, https://doi.org/10.1088/1742-6596/1618/5/052038, 2020. a, b, c, d
Li, A., Pirrung, G. R., Gaunaa, M., Madsen, H. A., and Horcas, S. G.: A computationally efficient engineering aerodynamic model for swept wind turbine blades, Wind Energ. Sci. Discuss. [preprint], https://doi.org/10.5194/wes-2021-96, in review, 2021. a, b
Madsen, H. and Rasmussen, F.: The influence on energy conversion and induction from large blade deflections, in: Wind energy for the next millennium, Proceedings, edited by: Petersen, E. L., Hjuler Jensen, P., Rave, K., Helm, P., and Ehmann, H., James and James Science Publishers, 1999 European Wind Energy Conference and Exhibition, 1–5 March 1999, Nice, France, 138–141, ISBN 1-902916-00-X, 1999. a
Madsen, H. Å.: A CFD analysis of the actuator disc flow compared with momentum theory results, in: IEA Joint action. Aerodynamics of wind turbines, edited by: Pedersen, M. B., Technical University of Denmark, Department of Fluid Mechanics, in: 10th IEA Meeting on Aerodynamics, IEA, 16–17 December 1996, Edinburgh, UK, 109–124, 1997. a
Madsen, H. Å. and Rasmussen, F.: A near wake model for trailing vorticity
compared with the blade element momentum theory, Wind Energy, 7, 325–341,
https://doi.org/10.1002/we.131, 2004. a
Madsen, H. Å., Mikkelsen, R., Øye, S., Bak, C., and Johansen, J.: A Detailed investigation of the Blade Element Momentum (BEM) model based on analytical and numerical results and proposal for modifications of the BEM model, J. Phys.: Conf. Ser., 75, 012016, https://doi.org/10.1088/1742-6596/75/1/012016, 2007. a
Madsen, H. Å., Bak, C., Døssing, M., Mikkelsen, R. F., and Øye, S.:
Validation and modification of the Blade Element Momentum theory based on
comparisons with actuator disc simulations, Wind Energy, 13, 373–389,
https://doi.org/10.1002/we.359, 2010. a
Madsen, H. Å., Zahle, F., Meng, F., Barlas, T., Rasmussen, F., and Rudolf, R. T.: Initial performance and load analysis of the LowWind turbine in comparison with a conventional turbine, J. Phys.: Conf. Ser., 1618, 032011, https://doi.org/10.1088/1742-6596/1618/3/032011, 2020b. a
Mann, J.: The spatial structure of neutral atmospheric surface-layer turbulence, J. Fluid Mech., 273, 141–168, 1994. a
Menter, F. R.: Two-equation eddy-viscosity turbulence models for engineering
applications, AIAA J., 32, 1598–1605, 1994. a
Michelsen, J. A.: Basis3D – a Platform for Development of Multiblock PDE
Solvers, Tech. Rep. AFM 92-05, Technical University of Denmark, 1992. a
Michelsen, J. A.: Block structured Multigrid solution of 2D and 3D elliptic
PDE's, Tech. Rep. AFM 94-06, Technical University of Denmark, 1994. a
Mikkelsen, R.: Actuator Disc Methods Applied to Wind Turbines, PhD thesis,
Technical University of Denmark, available at: https://orbit.dtu.dk/en/publications/actuator-disc-methods-applied-to-wind-turbines
(last access: 18 January 2022), 2004. a
Okulov, V., Sørensen, J., and Wood, D.: The rotor theories by Professor
Joukowsky: Vortex theories, Prog. Aerosp. Sci., 73, 19–46,
https://doi.org/10.1016/j.paerosci.2014.10.002, 2015. a
Øye, S.: A Simple Vortex Model, in: Proceedings of the third IEA Symposium
on the Aerodynamics of Wind Turbines, ETSU, Harwell, UK, 4.1–4.15, 1990. a
Pirrung, G., Riziotis, V., Madsen, H., Hansen, M., and Kim, T.: Comparison of a coupled near- and far-wake model with a free-wake vortex code, Wind Energ. Sci., 2, 15–33, https://doi.org/10.5194/wes-2-15-2017, 2017. a
Pirrung, G. R. and Gaunaa, M.: Dynamic stall model modifications to improve the modeling of vertical axis wind turbines, DTU Wind Energy E-0171, DTU, Roskilde, Denmark, 2018. a
Schepers, J. G. and Snel, H.: Joint investigation of dynamic inflow effects and implementation of an engineering method., Tech. rep. ECN-C-94-107, ECN,
available at: https://publications.ecn.nl/E/1995/ECN-C--94-107 (last access: 18 January 2022), 1995. a
Sørensen, J. N.: General Momentum Theory for Horizontal Axis Wind Turbines, in: vol. 4, Springer, ISBN 978-3-319-22114-4, 2015. a
Sørensen, N. N.: General Purpose Flow Solver Applied to Flow over Hills,
Risø-R-827-(EN), Risø National Laboratory, Roskilde, Denmark, 1995. a
Sørensen, N. N.: HypGrid2D a 2-D Mesh Generator, Risø-R-1035-(EN),
Risø National Laboratory, Roskilde, Denmark, 1998. a
Yu, W., Tavernier, D., Ferreira, C., van Kuik, G. A. M., and Schepers, G.: New dynamic-inflow engineering models based on linear and nonlinear actuator disc vortex models, Wind Energy, 22, 1433–1450, https://doi.org/10.1002/we.2380, 2019. a, b
Zahle, F.: Parametric Geometry Library (PGL), Tech. rep., DTU Wind Energy,
available at: https://gitlab.windenergy.dtu.dk/frza/PGL (last access: 23 November 2020), 2019. a
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An engineering aerodynamic model for non-planar horizontal-axis wind turbines is proposed. The performance of the model is comparable with high-fidelity models but has similarly low computational cost as currently used low-fidelity models, which do not have the capability to model non-planar rotors. The developed model could be used for an efficient and accurate load calculation of non-planar wind turbines and eventually be integrated in a design optimization framework.
An engineering aerodynamic model for non-planar horizontal-axis wind turbines is proposed. The...
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