Articles | Volume 10, issue 11
https://doi.org/10.5194/wes-10-2515-2025
© Author(s) 2025. 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-10-2515-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
11 Nov 2025
Research article |
| 11 Nov 2025
| 11 Nov 2025
Computationally efficient aerodynamic modelling of swept wind turbine blades using coupled near-wake and vortex cylinder models
Department of Wind and Energy Systems, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark
Mac Gaunaa
Department of Wind and Energy Systems, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark
Georg Raimund Pirrung
Department of Wind and Energy Systems, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark
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Wind Energ. Sci., 10, 2299–2349, https://doi.org/10.5194/wes-10-2299-2025, https://doi.org/10.5194/wes-10-2299-2025, 2025
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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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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.
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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.
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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.
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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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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.
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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
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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, 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.
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
Short summary
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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.
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
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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.
Cited articles
Andersen, P. B., Gaunaa, M., Zahle, F., and Madsen, H. A.: A near wake model with far wake effects implemented in a multi body aero-servo-elastic code, in: Proceedings of European Wind Energy Conference and Exhibition 2010 (Ewec 2010), Warsaw, Poland, 20–23 April 2010, 1, 387–431, ISBN: 978-1-61782-310-7, 2010. a
Barlas, T., Ramos-García, N., Pirrung, G. R., and González Horcas, S.: Surrogate-based aeroelastic design optimization of tip extensions on a modern 10 MW wind turbine, Wind Energ. Sci., 6, 491–504, https://doi.org/10.5194/wes-6-491-2021, 2021. a
Barlas, T., Pirrung, G. R., Ramos-García, N., González Horcas, S., Li, A., and Madsen, H. A.: Atmospheric rotating rig testing of a swept blade tip and comparison with multi-fidelity aeroelastic simulations, Wind Energ. Sci., 7, 1957–1973, https://doi.org/10.5194/wes-7-1957-2022, 2022. a
Bortolotti, P., Tarres, H. C., Dykes, K. L., Merz, K., Sethuraman, L., Verelst, D., and Zahle, F.: IEA Wind TCP Task 37: Systems Engineering in Wind Energy – WP2.1 Reference Wind Turbines, National Renewable Energy Laboratory (NREL), Golden, Colorado, USA, NREL/TP-5000-73492, https://doi.org/10.2172/1529216, 2019. a, b, c, d, e
Branlard, E.: Wind Turbine Aerodynamics and Vorticity-Based Methods: Fundamentals and Recent Applications, 7, Research Topics in Wind Energy, Springer, ISBN 978-3-319-55163-0, https://doi.org/10.1007/978-3-319-55164-7, 2017. a
Branlard, E. and Gaunaa, M.: Superposition of vortex cylinders for steady and unsteady simulation of rotors of finite tip-speed ratio, Wind Energy, 19, 1307–1323, https://doi.org/10.1002/we.1899, 2015a. a, b, c, d
Branlard, E. and Gaunaa, M.: Cylindrical vortex wake model: right cylinder, Wind Energy, 18, 1973–1987, https://doi.org/10.1002/we.1800, 2015b. a, b
Dicholkar, A., Zahle, F., and Sørensen, N. N.: Convergence enhancement of SIMPLE-like steady-state RANS solvers applied to airfoil and cylinder flows, Journal of Wind Engineering and Industrial Aerodynamics, 220, 104863, https://doi.org/10.1016/j.jweia.2021.104863, 2022. a
Dicholkar, A., Lønbæk, K., Zahle, F., and Sørensen, N. N.: Stabilization of SIMPLE-like RANS solvers for computing accurate gradients using the complex-step derivative method, Journal of Physics: Conference Series, 2767, 052022, https://doi.org/10.1088/1742-6596/2767/5/052022, 2024. a
Dicholkar, A., Lønbæk, K., Madsen, M. H. A., Zahle, F., and Sørensen, N. N.: From bluff bodies to optimal airfoils: Numerically stabilized RANS solvers for reliable shape optimization, Aerospace Science and Technology, 161, 110153, https://doi.org/10.1016/j.ast.2025.110153, 2025. a
Eocycle Technologies Inc.: The EOX M-21, https://eocycle.com/wp-content/uploads/2021/05/15064-EocycleMerger-SpecSheet-M21-R4.pdf (last access: 17 June 2025), 2021a. a
Eocycle Technologies Inc.: The EOX M-26, https://eocycle.com/wp-content/uploads/2021/05/15064-EocycleMerger-SpecSheet-M26-R6.pdf (last access: 17 June 2025), 2021b. a
Fritz, E., Boorsma, K., and Ferreira, C.: Experimental analysis of a horizontal-axis wind turbine with swept blades using PIV data, Wind Energ. Sci., 9, 1617–1629, https://doi.org/10.5194/wes-9-1617-2024, 2024a. a
Fritz, E., Boorsma, K., and Ferreira, C.: Validation of a BEM correction model for swept blades using experimental data, Journal of Physics: Conference Series, 2767, 022035, https://doi.org/10.1088/1742-6596/2767/2/022035, 2024b. a, b
Fritz, E. K., Ferreira, C., and Boorsma, K.: An efficient blade sweep correction model for blade element momentum theory, Wind Energy, 25, 1977–1994, https://doi.org/10.1002/we.2778, 2022. a, b
Gaunaa, M., Sørensen, N. N., and Li, A.: A correction model for the effect of spanwise flow on the viscous force contribution in BEM and Lifting Line methods, Journal of Physics: Conference Series, 2767, 022068, https://doi.org/10.1088/1742-6596/2767/2/022068, 2024. a
Glauert, H.: Airplane Propellers, in: Division L in Aerodynamic Theory, vol. IV, edited by: Durand, W. F., 169–360, Springer, 1935. a
Hejlesen, M. M., Rasmussen, J. T., Chatelain, P., and Walther, J. H.: A high order solver for the unbounded Poisson equation, Journal of Computational Physics, 252, 458–467, https://doi.org/10.1016/j.jcp.2013.05.050, 2013. a
Hejlesen, M. M., Rasmussen, J. T., Chatelain, P., and Walther, J. H.: High order Poisson Solver for unbounded flows, Procedia IUTAM, 18, 56–65, https://doi.org/10.1016/j.piutam.2015.11.006, 2015. a
Hoerner, S. F. and Borst, H. V.: Fluid-dynamic lift: practical information on aerodynamic and hydrodynamic lift, LA Hoerner, ISBN 978-9998831636, 1985. a
Horcas, S. G., Ramos-García, N., Li, A., Pirrung, G., and Barlas, T.: Comparison of aerodynamic models for horizontal axis wind turbine blades accounting for curved tip shapes, Wind Energy, 26, 5–22, https://doi.org/10.1002/we.2780, 2023. a
Houchens, B. C., Sproul, E. G., Berg, J. C., Caserta, P. G., Hernandez, M. H., Houck, D. R., Lopez, H., Maniaci, D. C., Monroe, G., Paquette, J. A., Rodriguez, S., Tilles, J. N., deVelder, N. B., Williams, M., Westergaard, C. H., McIntosh, T., Payant, J. A., and Wetzel, K. K.: Techno-Economic Analysis of Additively-Manufactured Wind Turbine Blade Tips That Enable Technology Integration, Wind Energy, 27, 1467–1482, https://doi.org/10.1002/we.2950, 2024. a
Larsen, T. and Hansen, A.: How 2 HAWC2, the user's manual, no. 1597(ver. 3-1)(EN) in Denmark. Forskningscenter Risø. Risø-R, Risø National Laboratory, ISBN 978-87-550-3583-6, 2007. a
Larwood, S. M. and Zutek, M.: Swept wind turbine blade aeroelastic modeling for loads and dynamic behavior, in: WINDPOWER 2006 Conference in Pittsburgh, USA, 4–7 June 2006, https://scholarlycommons.pacific.edu/soecs-facpres/4/ (last access: 15 October 2025), 2006. a
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, Journal of Physics: Conference Series, 1618, 052038, https://doi.org/10.1088/1742-6596/1618/5/052038, 2020. a, b, c
Li, A., Gaunaa, M., Lønbæk, K., Zahle, F., and Pirrung, G. R.: Comparison of aerodynamic planform optimization of non-planar rotors using blade element momentum method and a vortex cylinder model, Journal of Physics: Conference Series, 2265, 032055, https://doi.org/10.1088/1742-6596/2265/3/032055, 2022a. a
Li, A., Gaunaa, M., Pirrung, G. R., Meyer Forsting, A., and Horcas, S. G.: How should the lift and drag forces be calculated from 2-D airfoil data for dihedral or coned wind turbine blades?, Wind Energ. Sci., 7, 1341–1365, https://doi.org/10.5194/wes-7-1341-2022, 2022c. a, b
Li, A., Gaunaa, M., Pirrung, G. R., and Lønbæk, K.: How does the blade element momentum method see swept or prebent blades?, Journal of Physics: Conference Series, 2767, 022033, https://doi.org/10.1088/1742-6596/2767/2/022033, 2024. a, b, c, d
Li, A., Gaunaa, M., and Pirrung, G. R.: Internet Appendix for: “Computationally efficient aerodynamic modeling of swept wind turbine blades using coupled near wake and vortex cylinder models”, Zenodo [data set], https://doi.org/10.5281/zenodo.15680486, 2025a. a
Liebst, B. S.: Wind turbine gust load alleviation utilizing curved blades, Journal of Propulsion and Power, 2, 371–377, https://doi.org/10.2514/3.22897, 1986. a
Madsen, H. 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, b, c
Madsen, M. H. Aa., Zahle, F., Horcas, S. G., Barlas, T. K., and Sørensen, N. N.: CFD-based curved tip shape design for wind turbine blades, Wind Energ. Sci., 7, 1471–1501, https://doi.org/10.5194/wes-7-1471-2022, 2022. a
Manolas, D. I., Serafeim, G. P., Chaviaropoulos, P. K., Riziotis, V. A., and Voutsinas, S. G.: Assessment of load reduction capabilities using passive and active control methods on a 10 MW-scale wind turbine, Journal of Physics: Conference Series, 1037, 032042, https://doi.org/10.1088/1742-6596/1037/3/032042, 2018. a
Menter, F. R.: Two-equation eddy-viscosity turbulence models for engineering applications, AIAA Journal, 32, 1598–1605, https://doi.org/10.2514/3.12149, 1994. a
Øye, S.: A simple vortex model, in: Proceedings of the Third IEA Symposium on the Aerodynamics of Wind Turbines, 4.1–4.15, ETSU, 16–17 November 1989, Harwell, UK, NTIS Issue number 199106, 1990. a
Pirrung, G. R., Hansen, M. H., and Madsen, H. A.: Improvement of a near wake model for trailing vorticity, Journal of Physics: Conference Series, 555, 012083, https://doi.org/10.1088/1742-6596/555/1/012083, 2014. 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, 2017a. a, b, c
Pirrung, G. R., Madsen, H. A., and Schreck, S.: Trailed vorticity modeling for aeroelastic wind turbine simulations in standstill, Wind Energ. Sci., 2, 521–532, https://doi.org/10.5194/wes-2-521-2017, 2017b. a, b, c
Ramos-García, N., Sørensen, J. N., and Shen, W. Z.: Three-dimensional viscous-inviscid coupling method for wind turbine computations, Wind Energy, 19, 67–93, https://doi.org/10.1002/we.1821, 2016. a
Ramos-García, N., Hejlesen, M. M., Sørensen, J. N., and Walther, J. H.: Hybrid vortex simulations of wind turbines using a three-dimensional viscous-inviscid panel method, Wind Energy, 20, 1871–1889, https://doi.org/10.1002/we.2126, 2017. a
Sørensen, J. N.: General Momentum Theory for Horizontal Axis Wind Turbines, vol. 4, Springer, ISBN 978-3-319-22114-4, https://doi.org/10.1007/978-3-319-22114-4, 2015. a
Sørensen, N. N.: HypGrid2D a 2-D Mesh Generator, No.1035(EN), Risø-R, Risø National Laboratory, Roskilde, Denmark, ISBN 8755023681, https://findit.dtu.dk/en/catalog/537f0cea7401dbcc12006a12 (last access: 15 October 2025), 1998. a
Technical University of Denmark (DTU): Sophia HPC Cluster, Research Computing at DTU [data set], https://doi.org/10.57940/fafc-6m81, 2019. a
Wilson, R. E. and Lissaman, P. B.: Applied aerodynamics of wind power machines, Tech. rep., Oregon State Univ., Corvallis, OR, USA, https://www.osti.gov/biblio/7359096 (last access: 13 April 2025), 1974. a
Zahle, F.: Parametric Geometry Library for Wind (PGLW), DTU Wind Energy [code], https://gitlab.windenergy.dtu.dk/frza/PGL (last access: 14 February 2025), 2019. a
Zahle, F., Li, A., Lønbæk, K., Sørensen, N. N., and Riva, R.: Multi-fidelity, steady-state aeroelastic modelling of a 22-megawatt wind turbine, Journal of Physics: Conference Series, 2767, 022065, https://doi.org/10.1088/1742-6596/2767/2/022065, 2024. a
Zuteck, M.: Adaptive blade concept assessment: curved platform induced twist investigation, Tech. rep., Sandia National Labs., Albuquerque, NM, USA, Sandia National Labs, https://doi.org/10.2172/803289, 2002. a
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 analyse. 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.
Wind turbines with swept blades have the potential to improve power production and reduce loads,...
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