Articles | Volume 7, issue 4
https://doi.org/10.5194/wes-7-1341-2022
© 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-7-1341-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
05 Jul 2022
Research article |
| 05 Jul 2022
| 05 Jul 2022
How should the lift and drag forces be calculated from 2-D airfoil data for dihedral or coned wind turbine blades?
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
Alexander Meyer Forsting
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
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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
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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
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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, 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
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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.
Ang Li, Mac Gaunaa, Georg Raimund Pirrung, and Sergio González Horcas
Wind Energ. Sci., 7, 75–104, https://doi.org/10.5194/wes-7-75-2022, https://doi.org/10.5194/wes-7-75-2022, 2022
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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.
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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
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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
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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
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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.
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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
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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.
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Wind Energ. Sci., 8, 819–848, https://doi.org/10.5194/wes-8-819-2023, https://doi.org/10.5194/wes-8-819-2023, 2023
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Offshore wind farms are more commonly installed in wind farm clusters, where wind farm interaction can lead to energy losses. In this work, an efficient numerical method is presented that can be used to estimate these energy losses. The novel method is verified with higher-fidelity numerical models and validated with measurements of an existing wind farm cluster.
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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
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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.
Niels Troldborg, Søren J. Andersen, Emily L. Hodgson, and Alexander Meyer Forsting
Wind Energ. Sci., 7, 1527–1532, https://doi.org/10.5194/wes-7-1527-2022, https://doi.org/10.5194/wes-7-1527-2022, 2022
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This article shows that the power performance of a wind turbine may be very different in flat and complex terrain. This is an important finding because it shows that the power output of a given wind turbine is governed by not only the available wind at the position of the turbine but also how the ambient flow develops in the region behind the turbine.
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
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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.
Alessandro Sebastiani, Alfredo Peña, Niels Troldborg, and Alexander Meyer Forsting
Wind Energ. Sci., 7, 875–886, https://doi.org/10.5194/wes-7-875-2022, https://doi.org/10.5194/wes-7-875-2022, 2022
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The power performance of a wind turbine is often tested with the turbine standing in a row of several wind turbines, as it is assumed that the performance is not affected by the neighbouring turbines. We test this assumption with both simulations and measurements, and we show that the power performance can be either enhanced or lowered by the neighbouring wind turbines. Consequently, we also show how power performance testing might be biased when performed on a row of several wind turbines.
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.
Ang Li, Mac Gaunaa, Georg Raimund Pirrung, and Sergio González Horcas
Wind Energ. Sci., 7, 75–104, https://doi.org/10.5194/wes-7-75-2022, https://doi.org/10.5194/wes-7-75-2022, 2022
Short summary
Short summary
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.
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
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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
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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.
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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.
A consistent method of using two-dimensional airfoil data when using generalized lifting-line...
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