Articles | Volume 10, issue 7
https://doi.org/10.5194/wes-10-1485-2025
© 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-10-1485-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Modeling the influence of streamwise flow field acceleration on the aerodynamic performance of an actuator disk
Department of Wind and Energy Systems, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark
Niels Troldborg
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
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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.
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
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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.
Stefan Ivanell, Warit Chanprasert, Luca Lanzilao, James Bleeg, Johan Meyers, Antoine Mathieu, Søren Juhl Andersen, Rem-Sophia Mouradi, Eric Dupont, Hugo Olivares-Espinosa, and Niels Troldborg
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-88, https://doi.org/10.5194/wes-2025-88, 2025
Preprint under review for WES
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This study explores how the height of the atmosphere's boundary layer impacts wind farm performance, focusing on how this factor influences energy output. By simulating different boundary layer heights and conditions, the research reveals that deeper layers promote better energy recovery. The findings highlight the importance of considering atmospheric conditions when simulating wind farms to maximize energy efficiency, offering valuable insights for the wind energy industry.
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.
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.
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.
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
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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.
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
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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.
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.
Cited articles
Betz, A.: Das Maximum der theoretisch möglichen Ausnützung des Windes durch Windmotoren, Zeitschrift für das gesamte Turbinenwesen, 26, 307–309, 1920. a
Cai, T., Cheng, S., Segalini, A., and Chamorro, L. P.: Local topography-induced pressure gradient effects on the wake and power output of a model wind turbine, Theor. Appl. Mech. Lett., 11, 100297, https://doi.org/10.1016/j.taml.2021.100297, 2021. a, b
Chamorro, L. P. and Arndt, R.: Non-uniform velocity distribution effect on the Betz–Joukowsky limit, Wind Energy, 16, 279–282, https://doi.org/10.1002/we.549, 2013. a
Crespo, A., Hernández, J., and Frandsen, S.: Survey of Modelling Methods for Wind Turbine Wakes and Wind Farms, Wind Energy, 2, 1–24, https://doi.org/10.1002/(SICI)1099-1824(199901/03)2:1<1::AID-WE16>3.0.CO;2-7, 1999. a, b, c
Dar, A. S. and Porté-Agel, F.: An Analytical Model for Wind Turbine Wakes under Pressure Gradient, Energies, 2022, 5345, https://doi.org/10.3390/en15155345, 2022. a, b, c
Dar, A. S., Gertler, A. S., and Porté-Agel, F.: An experimental and analytical study of wind turbine wakes under pressure gradient, Phys. Fluids, 35, 045140, https://doi.org/10.1063/5.0145043, 2023. a, b, c
Draper, S., Nishino, T., Adcock, T. A. A., and Taylor, P. H.: Performance of an ideal turbine in an inviscid shear flow, J. Fluid Mech., 796, 86–112, https://doi.org/10.1017/jfm.2016.247, 2016. a
DTU Sophia: Sophia HPC cluster, Technical University of Denmark, https://doi.org/10.57940/FAFC-6M81, 2019. a
Gaunaa, M., Troldborg, N., and Branlard, E.: A simple vortex model applied to an idealized rotor in sheared inflow, Wind Energ. Sci., 8, 503–513, https://doi.org/10.5194/wes-8-503-2023, 2023. a
Glauert, H.: A general theory of the autogyro, Tech. Rep. 1111, Scientific Research Air Ministry, 1926. a
Heck, K., Johlas, H., and Howland, M.: Modelling the induction, thrust and power of a yaw-misaligned actuator disk, J. Fluid Mech., 959, A9, https://doi.org/10.1017/jfm.2023.129, 2023. a
Hodgson, E. L., Andersen, S. J., Troldborg, N., Forsting, A. M., Mikkelsen, R. F., and Sørensen, J. N.: A Quantitative Comparison of Aeroelastic Computations using Flex5 and Actuator Methods in LES, J. Phys. Conf. Ser., 1934, 012014, https://doi.org/10.1088/1742-6596/1934/1/012014, 2021. a
Hunt, J. C. R., Leibovich, S., and Richards, K. J.: Turbulent shear flows over low hills, Q. J. Roy. Meteor. Soc., 114, 1435–1470, https://doi.org/10.1002/qj.49711448405, 1988. a
Jackson, P. S. and Hunt, J. C. R.: Turbulent wind flow over a low hill, Q. J. Roy. Meteor. Soc., 101, 929–955, https://doi.org/10.1002/qj.49710143015, 1975. a
Jamieson, P. M.: Beating Betz: Energy Extraction Limits in a Constrained Flow Field, J. Sol. Energ., 131, 031008, https://doi.org/10.1115/1.3139143, 2009. a
Joukowsky, N. E.: Windmill of the NEJ type, Transactions of the Central Institute for Aero-hydrodynamics of Moscow, 1920. a
Leonard, B.: A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comput. Method. Appl. M., 19, 59–98, https://doi.org/10.1016/0045-7825(79)90034-3, 1979. 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
Michelsen, J.: Basis3D – a Platform for Development of Multiblock PDE Solvers, Tech. rep., Technical University of Denmark, 1992. a
Mikkelsen, R.: Actuator disc methods applied to wind turbines, Ph.D. thesis, Technical University of Denmark, Lyngby, Denmark, 2004. a
Mikkelsen, R. F. and Sørensen, J. N.: Modelling of Wind Tunnel Blockage, in: 15th IEA Symposium on the Aerodynamics of Wind Turbines, FOI Swedish Defence Research Agency, Paris, 2002. a
Mishra, A., Arya, N., and Bhattacharya, A.: Wake steering of wind turbine in the presence of a two-dimensional hill, Phys. Fluids, 36, 045125, https://doi.org/10.1063/5.0185842, 2024. a
Okulov, V. L. and Van Kuik, G. A.: The Betz–Joukowsky limit: on the contribution to rotor aerodynamics by the British, German and Russian scientific schools, Wind Energy, 15, 335–344, https://doi.org/10.1002/we.464, 2012. a
Réthoré, P.-E., Van Der Laan, P., Troldborg, N., Zahle, F., and Sørensen, N. N.: Verification and validation of an actuator disc model, Wind Energy, 17, 919–937, https://doi.org/10.1002/we.1607, 2014. a
Revaz, T. and Porté-Agel, F.: Effect of hills on wind turbine flow and power efficiency: A large-eddy simulation study, Phys. Fluids, 36, 095180, https://doi.org/10.1063/5.0226544, 2024. a, b
Rhie, C. M. and Chow, W. L.: Numerical study of the turbulent flow past an airfoil with trailing edge separation, AIAA Journal, 21, 1525–1532, https://doi.org/10.2514/3.8284, 1983. a
Roache, P. J.: Perspective: A Method for Uniform Reporting of Grid Refinement Studies, J. Fluids Eng., 116, 405–413, https://doi.org/10.1115/1.2910291, 1994. a
Roache, P. J.: Quantification of Uncertainty in Computational Fluid Dynamics, Annu. Rev. Fluid Mech., 29, 123–160, https://doi.org/10.1146/annurev.fluid.29.1.123, 1997. a
Shamsoddin, S. and Porté-Agel, F.: A model for the effect of pressure gradient on turbulent axisymmetric wakes, J. Fluid Mech., 837, R3, https://doi.org/10.1017/jfm.2017.864, 2018. a
Sørensen, J. N.: General momentum theory for horizontal axis wind turbines, no. volume 4 in Research topics in wind energy, Springer, Cham Heidelberg New York, 1st edn., ISBN 978-3-319-22113-7, 2016. a
Sørensen, N. N.: General purpose flow solver applied to flow over hills, Ph.D. thesis, Risø National Laboratory, 1995. a
Sørensen, N. N.: EllipSys2D/3D User Manual, Tech. rep., DTU Wind Energy, Roskilde, Denmark, 2018. a
Tamaro, S., Campagnolo, F., and Bottasso, C. L.: On the power and control of a misaligned rotor – beyond the cosine law, Wind Energ. Sci., 9, 1547–1575, https://doi.org/10.5194/wes-9-1547-2024, 2024. a
Troldborg, N., Sørensen, N., Réthoré, P.-E., and Van Der Laan, M.: A consistent method for finite volume discretization of body forces on collocated grids applied to flow through an actuator disk, Comput. Fluids, 119, 197–203, https://doi.org/10.1016/j.compfluid.2015.06.028, 2015. a
Troldborg, N., Andersen, S. J., Hodgson, E. L., and Meyer Forsting, A.: Brief communication: How does complex terrain change the power curve of a wind turbine?, Wind Energ. Sci., 7, 1527–1532, https://doi.org/10.5194/wes-7-1527-2022, 2022. a, b, c
Wagner, R., Courtney, M., Gottschall, J., and Lindelöw-Marsden, P.: Accounting for the speed shear in wind turbine power performance measurement, Wind Energy, 14, 993–1004, https://doi.org/10.1002/we.509, 2011. a
Zengler, C. P.: Supplementary data for manuscript “Modeling the influence of streamwise flow field acceleration on the aerody- namic performance of an actuator disk”, Technical University of Denmark [data set], https://doi.org/10.11583/DTU.27222912.v3, 2024. a
Short summary
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.
Wind turbine power performance is mostly calculated based on the wind speed measured at the...
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