Articles | Volume 9, issue 2
https://doi.org/10.5194/wes-9-453-2024
© Author(s) 2024. 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-9-453-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
27 Feb 2024
Research article |
| 27 Feb 2024
| 27 Feb 2024
Aerodynamic model comparison for an X-shaped vertical-axis wind turbine
Wind Energy Section, Flow Physics and Technology, Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, the Netherlands
Laurence Morgan
Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, G1 1XW, United Kingdom
Yan Wu
Wind Energy Section, Flow Physics and Technology, Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, the Netherlands
David Bretos
Wind Energy Department, Centro Nacional de Energías Renovables (CENER), Ciudad de la Innovación, no. 7, 31621 Sarriguren (Navarra), Spain
Aurelio Cascales
Wind Energy Department, Centro Nacional de Energías Renovables (CENER), Ciudad de la Innovación, no. 7, 31621 Sarriguren (Navarra), Spain
Oscar Pires
Wind Energy Department, Centro Nacional de Energías Renovables (CENER), Ciudad de la Innovación, no. 7, 31621 Sarriguren (Navarra), Spain
Carlos Ferreira
Wind Energy Section, Flow Physics and Technology, Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, the Netherlands
Related authors
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Laurence Boyd Morgan, Abbas Kazemi Amiri, William Leithead, and James Carroll
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2024-42, https://doi.org/10.5194/wes-2024-42, 2024
Preprint under review for WES
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This paper presents a systematic study into the effect of blade inclination angle, chord distribution, and blade length on vertical axis wind turbine performance. It is shown that for rotors of identical power production, both blade volume and rotor torque can be significantly reduced through the use of aerodynamically optimised inclined rotor blades. This demonstrates the potential of V-Rotors to reduce the cost of energy for offshore wind when compared to H-Rotors.
Erik Fritz, André Ribeiro, Koen Boorsma, and Carlos Ferreira
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2024-3, https://doi.org/10.5194/wes-2024-3, 2024
Revised manuscript accepted for WES
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This study presents results from a wind tunnel experiment on a model wind turbine. Using a non-intrusive measurement technique, the flow around the turbine blades was measured. In post-processing, the blade-level aerodynamics are derived from the measured flow fields. The detailed experimental database has great value in validating numerical tools of varying complexity, which aim at simulating wind turbine aerodynamics as accurately as possible.
Erik Fritz, Koen Boorsma, and Carlos Ferreira
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2024-11, https://doi.org/10.5194/wes-2024-11, 2024
Preprint under review for WES
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This study presents results from a wind tunnel experiment on a model wind turbine with swept blades, thus, blades curved in the rotor plane. Using a non-intrusive measurement technique, the flow around the turbine blades was measured from which blade-level aerodynamics are derived in post-processing. The detailed experimental database gives insight into swept blade aerodynamics and has great value in validating numerical tools, which aim at simulating swept wind turbine blades.
André F. P. Ribeiro, Damiano Casalino, and Carlos S. Ferreira
Wind Energ. Sci., 8, 661–675, https://doi.org/10.5194/wes-8-661-2023, https://doi.org/10.5194/wes-8-661-2023, 2023
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Floating offshore wind turbines move due to not having a rigid foundation. Hence, as the blades rotate they experience more complex aerodynamics than standard onshore wind turbines. In this paper, we show computational simulations of a wind turbine rotor moving in various ways and quantify the effects of the motion in the forces acting on the blades. We show that these forces behave in nonlinear ways in some cases.
David Bretos-Arguiñena and Beatriz Méndez-López
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2023-8, https://doi.org/10.5194/wes-2023-8, 2023
Revised manuscript not accepted
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Wind energy is crucial for dealing with the climatic change challenge. Society needs more efficient wind turbines reducing the costs and the operation and maintenance works. In addition, uncertainties should be also reduced. One of the biggest uncertainties in the wind energy field, is the wind turbine performance with regard to the blade status. Blades are living components and their surface changes with the wind turbine life evolution: they become dirty and or they suffer from erosion.
Felipe Vittori, José Azcona, Irene Eguinoa, Oscar Pires, Alberto Rodríguez, Álex Morató, Carlos Garrido, and Cian Desmond
Wind Energ. Sci., 7, 2149–2161, https://doi.org/10.5194/wes-7-2149-2022, https://doi.org/10.5194/wes-7-2149-2022, 2022
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This paper describes the results of a wave tank test campaign of a scaled SATH 10 MW INNWIND floating platform. The software-in-the-loop (SiL) hybrid method was used to include the wind turbine thrust and the in-plane rotor moments. Experimental results are compared with a numerical model developed in OpenFAST of the floating wind turbine. The results are discussed, identifying limitations of the numerical models and obtaining conclusions on how to improve them.
Alessandro Bianchini, Galih Bangga, Ian Baring-Gould, Alessandro Croce, José Ignacio Cruz, Rick Damiani, Gareth Erfort, Carlos Simao Ferreira, David Infield, Christian Navid Nayeri, George Pechlivanoglou, Mark Runacres, Gerard Schepers, Brent Summerville, David Wood, and Alice Orrell
Wind Energ. Sci., 7, 2003–2037, https://doi.org/10.5194/wes-7-2003-2022, https://doi.org/10.5194/wes-7-2003-2022, 2022
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The paper is part of the Grand Challenges Papers for Wind Energy. It provides a status of small wind turbine technology in terms of technical maturity, diffusion, and cost. Then, five grand challenges that are thought to be key to fostering the development of the technology are proposed. To tackle these challenges, a series of unknowns and gaps are first identified and discussed. Improvement areas are highlighted, within which 10 key enabling actions are finally proposed to the wind community.
Daan van der Hoek, Joeri Frederik, Ming Huang, Fulvio Scarano, Carlos Simao Ferreira, and Jan-Willem van Wingerden
Wind Energ. Sci., 7, 1305–1320, https://doi.org/10.5194/wes-7-1305-2022, https://doi.org/10.5194/wes-7-1305-2022, 2022
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The paper presents a wind tunnel experiment where dynamic induction control was implemented on a small-scale turbine. By periodically changing the pitch angle of the blades, the low-velocity turbine wake is perturbed, and hence it recovers at a faster rate. Small particles were released in the flow and subsequently recorded with a set of high-speed cameras. This allowed us to reconstruct the flow behind the turbine and investigate the effect of dynamic induction control on the wake.
Carlos Ferreira, Wei Yu, Arianna Sala, and Axelle Viré
Wind Energ. Sci., 7, 469–485, https://doi.org/10.5194/wes-7-469-2022, https://doi.org/10.5194/wes-7-469-2022, 2022
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Floating offshore wind turbines may experience large surge motions that, when faster than the local wind speed, cause rotor–wake interaction.
We derive a model which is able to predict the wind speed at the wind turbine, even for large and fast motions and load variations in the wind turbine.
The proposed dynamic inflow model includes an adaptation for highly loaded flow, and it is accurate and simple enough to be easily implemented in most blade element momentum design models.
G. A. M. van Kuik, J. Peinke, R. Nijssen, D. Lekou, J. Mann, J. N. Sørensen, C. Ferreira, J. W. van Wingerden, D. Schlipf, P. Gebraad, H. Polinder, A. Abrahamsen, G. J. W. van Bussel, J. D. Sørensen, P. Tavner, C. L. Bottasso, M. Muskulus, D. Matha, H. J. Lindeboom, S. Degraer, O. Kramer, S. Lehnhoff, M. Sonnenschein, P. E. Sørensen, R. W. Künneke, P. E. Morthorst, and K. Skytte
Wind Energ. Sci., 1, 1–39, https://doi.org/10.5194/wes-1-1-2016, https://doi.org/10.5194/wes-1-1-2016, 2016
Related subject area
Thematic area: Fluid mechanics | Topic: Wind turbine aerodynamics
Quantifying the impact of modeling fidelity on different substructure concepts – Part 2: Code-to-code comparison in realistic environmental conditions
Wind turbine rotors in surge motion: new insights into unsteady aerodynamics of floating offshore wind turbines (FOWTs) from experiments and simulations
An insight into the capability of the actuator line method to resolve tip vortices
Aerodynamic characterisation of a thrust-scaled IEA 15 MW wind turbine model: Experimental insights using PIV data
Development and application of a mesh generator intended for unsteady vortex-lattice method simulations of wind turbines and wind farms
An experimental study on the aerodynamic loads of a floating offshore wind turbine under imposed motions
Developing a digital twin framework for wind tunnel testing: validation of turbulent inflow and airfoil load applications
Influence of rotor blade flexibility on the near-wake behavior of the NREL 5 MW wind turbine
Field-data-based validation of an aero-servo-elastic solver for high-fidelity large-eddy simulations of industrial wind turbines
An analytical linear two-dimensional actuator disc model and comparisons with computational fluid dynamics (CFD) simulations
On the characteristics of the wake of a wind turbine undergoing large motions caused by a floating structure: an insight based on experiments and multi-fidelity simulations from the OC6 project Phase III
Forced-motion simulations of vortex-induced vibrations of wind turbine blades – a study of sensitivities
Towards smart blades for vertical axis wind turbines: different airfoil shapes and tip speed ratios
Numerical study of the unsteady blade root aerodynamics of a 2 MW wind turbine equipped with vortex generators
Going Beyond BEM with BEM: an Insight into Dynamic Inflow Effects on Floating Wind Turbines
Generalized analytical body force model for actuator disc computations of wind turbines
Nonlinear inviscid aerodynamics of a wind turbine rotor in surge, sway, and yaw motions using a free-wake panel method
OC6 project Phase III: validation of the aerodynamic loading on a wind turbine rotor undergoing large motion caused by a floating support structure
A simple vortex model applied to an idealized rotor in sheared inflow
Comparison of free vortex wake and blade element momentum results against large-eddy simulation results for highly flexible turbines under challenging inflow conditions
Numerical simulations of ice accretion on wind turbine blades: are performance losses due to ice shape or surface roughness?
Progress in the validation of rotor aerodynamic codes using field data
A comparison of dynamic inflow models for the blade element momentum method
Multiple limit cycle amplitudes in high-fidelity predictions of standstill wind turbine blade vibrations
Model tests of a 10 MW semi-submersible floating wind turbine under waves and wind using hybrid method to integrate the rotor thrust and moments
Atmospheric rotating rig testing of a swept blade tip and comparison with multi-fidelity aeroelastic simulations
A WaveNet-based fully stochastic dynamic stall model
Experimental analysis of the dynamic inflow effect due to coherent gusts
High-Reynolds-number wind turbine blade equipped with root spoilers – Part 2: Impact on energy production and turbine lifetime
Wind tunnel investigation of the aerodynamic response of two 15 MW floating wind turbines
Vertical wake deflection for floating wind turbines by differential ballast control
High-fidelity aeroelastic analyses of wind turbines in complex terrain: fluid–structure interaction and aerodynamic modeling
Development of a wireless, non-intrusive, MEMS-based pressure and acoustic measurement system for large-scale operating wind turbine blades
How should the lift and drag forces be calculated from 2-D airfoil data for dihedral or coned wind turbine blades?
Francesco Papi, Giancarlo Troise, Robert Behrens de Luna, Joseph Saverin, Sebastian Perez-Becker, David Marten, Marie-Laure Ducasse, and Alessandro Bianchini
Wind Energ. Sci., 9, 981–1004, https://doi.org/10.5194/wes-9-981-2024, https://doi.org/10.5194/wes-9-981-2024, 2024
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Wind turbines need to be simulated for thousands of hours to estimate design loads. Mid-fidelity numerical models are typically used for this task to strike a balance between computational cost and accuracy. The considerable displacements of floating wind turbines may be a challenge for some of these models. This paper enhances comprehension of how modeling theories affect floating wind turbine loads by comparing three codes across three turbines, simulated in a real environment.
Christian W. Schulz, Stefan Netzband, Umut Özinan, Po Wen Cheng, and Moustafa Abdel-Maksoud
Wind Energ. Sci., 9, 665–695, https://doi.org/10.5194/wes-9-665-2024, https://doi.org/10.5194/wes-9-665-2024, 2024
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Understanding the underlying physical phenomena of the aerodynamics of floating offshore wind turbines (FOWTs) is crucial for successful simulations. No consensus has been reached in the research community on which unsteady aerodynamic phenomena are relevant and how much they can influence the loads acting on a FOWT. This work contributes to the understanding and characterisation of such unsteady phenomena using a novel experimental approach and comprehensive numerical investigations.
Pier Francesco Melani, Omar Sherif Mohamed, Stefano Cioni, Francesco Balduzzi, and Alessandro Bianchini
Wind Energ. Sci., 9, 601–622, https://doi.org/10.5194/wes-9-601-2024, https://doi.org/10.5194/wes-9-601-2024, 2024
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The actuator line method (ALM) is a powerful tool for wind turbine simulation but struggles to resolve tip effects. The reason is still unclear. To investigate this, we use advanced angle of attack sampling and vortex tracking techniques to analyze the flow around a NACA0018 finite wing, simulated with ALM and blade-resolved computational fluid dynamics. Results show that the ALM can account for tip effects if the correct angle of attack sampling and force projection strategies are adopted.
Erik Fritz, André Ribeiro, Koen Boorsma, and Carlos Ferreira
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2024-3, https://doi.org/10.5194/wes-2024-3, 2024
Revised manuscript accepted for WES
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This study presents results from a wind tunnel experiment on a model wind turbine. Using a non-intrusive measurement technique, the flow around the turbine blades was measured. In post-processing, the blade-level aerodynamics are derived from the measured flow fields. The detailed experimental database has great value in validating numerical tools of varying complexity, which aim at simulating wind turbine aerodynamics as accurately as possible.
Bruno A. Roccia, Luis R. Ceballos, Marcos L. Verstraete, and Cristian G. Gebhardt
Wind Energ. Sci., 9, 385–416, https://doi.org/10.5194/wes-9-385-2024, https://doi.org/10.5194/wes-9-385-2024, 2024
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In the literature there is a lack of meshing tools when it comes to building aerodynamic grids of wind turbines/farms to be used along with potential flow solvers. In this work, we present a detailed description of the geometric modeling and computational implementation of an interactive mesh generator, named UVLMeshGen, for onshore/offshore wind farms. The work is completed by providing a series of aerodynamic results related to wind turbines/farms to show the capacity of the mesh generator.
Federico Taruffi, Felipe Novais, and Axelle Viré
Wind Energ. Sci., 9, 343–358, https://doi.org/10.5194/wes-9-343-2024, https://doi.org/10.5194/wes-9-343-2024, 2024
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Floating wind turbines are subject to complex aerodynamics that are not yet fully understood. Lab-scale experiments are crucial for capturing these phenomena and validate numerical tools. This paper presents a new wind tunnel experimental setup able to study the response of a wind turbine rotor when subjected to prescribed motions in 6 degrees of freedom. The observed unsteady effects underscore the importance of pursuing research on the impact of floater motions on wind turbine performance.
Rishabh Mishra, Emmanuel Guilmineau, Ingrid Neunaber, and Caroline Braud
Wind Energ. Sci., 9, 235–252, https://doi.org/10.5194/wes-9-235-2024, https://doi.org/10.5194/wes-9-235-2024, 2024
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To investigate the impact of turbulence on aerodynamic forces, we first model turbulent kinetic energy decay theoretically using the Taylor length scale and employ this model to create a digital wind tunnel replica for simulating grid-generated turbulence. Experimental validation shows good alignment among theory, simulations, and experiments, paving the way for aerodynamic simulations. Finally, we successfully use the digital replica to obtain force coefficients for a 2D rotor blade section.
Leo Höning, Laura J. Lukassen, Bernhard Stoevesandt, and Iván Herráez
Wind Energ. Sci., 9, 203–218, https://doi.org/10.5194/wes-9-203-2024, https://doi.org/10.5194/wes-9-203-2024, 2024
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This study analyzes the impact of wind turbine rotor blade flexibility on the aerodynamic loading of the blades and the consequential wind characteristics in the near wake of the turbine. It is shown that gravitation leads to rotational periodic fluctuations of blade loading, which directly impacts the trajectory of the blade tip vortex at different rotor blade positions while also resulting in a non-uniform wind velocity deficit in the wake of the wind turbine.
Etienne Muller, Simone Gremmo, Félix Houtin-Mongrolle, Bastien Duboc, and Pierre Bénard
Wind Energ. Sci., 9, 25–48, https://doi.org/10.5194/wes-9-25-2024, https://doi.org/10.5194/wes-9-25-2024, 2024
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This article presents an advanced tool designed for the high-fidelity and high-performance simulation of operating wind turbines, allowing for instance the computation of a blade deformation, as well as of the surrounding airflow. As this tool relies on coupling two existing codes, the coupling strategy is first described in depth. The article then compares the code results to field data for validation.
Helge Aagaard Madsen
Wind Energ. Sci., 8, 1853–1872, https://doi.org/10.5194/wes-8-1853-2023, https://doi.org/10.5194/wes-8-1853-2023, 2023
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We present a linear analytical solution for a two-dimensional (2-D) actuator disc (AD) for a plane disc, a yawed disc and a coned disc. Comparisons of the 2-D model with three-dimensional computational fluid dynamics (CFD) AD simulations for a circular yawed disc and with an axis-symmetric CFD simulation of a coned disc show good correlation for the normal velocity component of the disc. This indicates that the 2-D AD model could form the basis for a consistent, simple new rotor induction model.
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.
Mohammad Rasoul Tirandaz, Abdolrahim Rezaeiha, and Daniel Micallef
Wind Energ. Sci., 8, 1403–1424, https://doi.org/10.5194/wes-8-1403-2023, https://doi.org/10.5194/wes-8-1403-2023, 2023
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Vertical axis wind turbines experience a variation of torque and power throughout their rotation. Traditional non-morphing blades are intrinsically not able to respond to this variation, resulting in a turbine which has suboptimal performance. In principle, it is possible to have a morphing blade that adapts to the blade's rotation and changes its geometry in such a way as to optimise the performance of the turbine. This paper addresses the question of how such blade should morph as it rotates.
Ferdinand Seel, Thorsten Lutz, and Ewald Krämer
Wind Energ. Sci., 8, 1369–1385, https://doi.org/10.5194/wes-8-1369-2023, https://doi.org/10.5194/wes-8-1369-2023, 2023
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Vortex generators are evaluated on a 2 MW wind turbine rotor blade by computational fluid dynamic methods. Those devices delay flow separation on the airfoils and thus increase their efficiency. On the wind turbine blade, rotational phenomena (e.g. rotational augmentation) appear and interact with the vortices from the vortex generators. The understanding of those interactions is crucial in order to optimise the placement of the vortex generators and evaluate their real efficiency on the blade.
Francesco Papi, Jason Jonkman, Amy Robertson, and Alessandro Bianchini
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2023-109, https://doi.org/10.5194/wes-2023-109, 2023
Revised manuscript accepted for WES
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Blade Element Momentum theory (BEM) is the backbone of many industry-standard aerodynamic models. However, the analysis of Floating Offshore Wind Turbines (FOWTs) introduces new challenges, which could put BEM models to the test. This study systematically compares four aerodynamic models, ranging from BEM to Computational Fluid Dynamics, in an attempt to shed light on the unsteady aerodynamic phenomena that are at stake in FOWTs and whether BEM is able to model them appropriately.
Jens N. Sørensen
Wind Energ. Sci., 8, 1017–1027, https://doi.org/10.5194/wes-8-1017-2023, https://doi.org/10.5194/wes-8-1017-2023, 2023
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The paper presents a simple analytical model that, with surprisingly good accuracy, represents the loading for virtually any horizontal axis wind turbine, independent of size and operating regime. The aim of the model is to have a simple tool that may represent the loading of any wind turbine without having access to the details regarding the specific geometry and airfoil data, information that is normally kept confidential by the manufacturer of the turbine.
André F. P. Ribeiro, Damiano Casalino, and Carlos S. Ferreira
Wind Energ. Sci., 8, 661–675, https://doi.org/10.5194/wes-8-661-2023, https://doi.org/10.5194/wes-8-661-2023, 2023
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Floating offshore wind turbines move due to not having a rigid foundation. Hence, as the blades rotate they experience more complex aerodynamics than standard onshore wind turbines. In this paper, we show computational simulations of a wind turbine rotor moving in various ways and quantify the effects of the motion in the forces acting on the blades. We show that these forces behave in nonlinear ways in some cases.
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
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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.
Kelsey Shaler, Benjamin Anderson, Luis A. Martínez-Tossas, Emmanuel Branlard, and Nick Johnson
Wind Energ. Sci., 8, 383–399, https://doi.org/10.5194/wes-8-383-2023, https://doi.org/10.5194/wes-8-383-2023, 2023
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Free-vortex wake (OLAF) and low-fidelity blade-element momentum (BEM) structural results are compared to high-fidelity simulation results for a flexible downwind turbine for varying inflow conditions. Overall, OLAF results were more consistent than BEM results when compared to SOWFA results under challenging inflow conditions. Differences between OLAF and BEM results were dominated by yaw misalignment angle, with varying shear exponent and turbulence intensity causing more subtle differences.
Francesco Caccia and Alberto Guardone
Wind Energ. Sci., 8, 341–362, https://doi.org/10.5194/wes-8-341-2023, https://doi.org/10.5194/wes-8-341-2023, 2023
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Ice roughness deteriorates wind turbine aerodynamics. We have shown numerically that this also occurs when complex ice shapes are present on the leading edge, as long as the blade's wet region extends beyond the ice shape itself and roughness elements are high enough. Such features are typical of icing events on wind turbines but are not captured by current icing simulation tools. Future research should focus on correctly computing both the wet region of the blade and the roughness height.
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.
Simone Mancini, Koen Boorsma, Gerard Schepers, and Feike Savenije
Wind Energ. Sci., 8, 193–210, https://doi.org/10.5194/wes-8-193-2023, https://doi.org/10.5194/wes-8-193-2023, 2023
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Modern wind turbines are subject to complex wind conditions that are far from the hypothesis of steady uniform inflow at the core of blade element momentum methods (the current industry standard for wind turbine design). Various corrections have been proposed to model this complexity. The present work focuses on modelling the unsteady evolution of wind turbine wakes (dynamic inflow), comparing the different corrections available and highlighting their effects on design load predictions.
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.
Felipe Vittori, José Azcona, Irene Eguinoa, Oscar Pires, Alberto Rodríguez, Álex Morató, Carlos Garrido, and Cian Desmond
Wind Energ. Sci., 7, 2149–2161, https://doi.org/10.5194/wes-7-2149-2022, https://doi.org/10.5194/wes-7-2149-2022, 2022
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This paper describes the results of a wave tank test campaign of a scaled SATH 10 MW INNWIND floating platform. The software-in-the-loop (SiL) hybrid method was used to include the wind turbine thrust and the in-plane rotor moments. Experimental results are compared with a numerical model developed in OpenFAST of the floating wind turbine. The results are discussed, identifying limitations of the numerical models and obtaining conclusions on how to improve them.
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.
Jan-Philipp Küppers and Tamara Reinicke
Wind Energ. Sci., 7, 1889–1903, https://doi.org/10.5194/wes-7-1889-2022, https://doi.org/10.5194/wes-7-1889-2022, 2022
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Airfoils play a major role in the technical harnessing of energy from currents such as wind and water. When the angle of attack of a wing changes dynamically, the forces on the wing often change more than would have been assumed from static measurements alone. Since these dynamic forces have a strong influence, e.g., on the performance of airplanes and wind turbines, a neural-network-based model was created that can predict these loads and their stochastic fluctuations.
Frederik Berger, Lars Neuhaus, David Onnen, Michael Hölling, Gerard Schepers, and Martin Kühn
Wind Energ. Sci., 7, 1827–1846, https://doi.org/10.5194/wes-7-1827-2022, https://doi.org/10.5194/wes-7-1827-2022, 2022
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We proof the dynamic inflow effect due to gusts in wind tunnel experiments with MoWiTO 1.8 in the large wind tunnel of ForWind – University of Oldenburg, where we created coherent gusts with an active grid. The effect is isolated in loads and rotor flow by comparison of a quasi-steady and a dynamic case. The observed effect is not caught by common dynamic inflow engineering models. An improvement to the Øye dynamic inflow model is proposed, matching experiment and corresponding FVWM simulations.
Thomas Potentier, Emmanuel Guilmineau, Arthur Finez, Colin Le Bourdat, and Caroline Braud
Wind Energ. Sci., 7, 1771–1790, https://doi.org/10.5194/wes-7-1771-2022, https://doi.org/10.5194/wes-7-1771-2022, 2022
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A wind turbine blade equipped with root spoilers is analysed using time domain aeroelastic simulations to assess the impact of passive devices on the turbine AEP and lifetime. A novel way to account for aerofoil-generated unsteadiness in the fatigue calculation is proposed and detailed. The outcome shows that spoilers, on average, can increase the AEP of the turbine. However, the structural impacts on the turbine can be severe if not accounted for initially in the turbine design.
Alessandro Fontanella, Alan Facchinetti, Simone Di Carlo, and Marco Belloli
Wind Energ. Sci., 7, 1711–1729, https://doi.org/10.5194/wes-7-1711-2022, https://doi.org/10.5194/wes-7-1711-2022, 2022
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The aerodynamics of floating wind turbines is complicated by large motions permitted by the foundation. The interaction between turbine, wind, and wake is not yet fully understood. The wind tunnel experiments of this paper shed light on the aerodynamic force and wake response of the floating IEA 15 MW turbine subjected to platform motion as would occur during normal operation. This will help future research on turbine and wind farm control.
Emmanouil M. Nanos, Carlo L. Bottasso, Simone Tamaro, Dimitris I. Manolas, and Vasilis A. Riziotis
Wind Energ. Sci., 7, 1641–1660, https://doi.org/10.5194/wes-7-1641-2022, https://doi.org/10.5194/wes-7-1641-2022, 2022
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A novel way of wind farm control is presented where the wake is deflected vertically to reduce interactions with downstream turbines. This is achieved by moving ballast in a floating offshore platform in order to pitch the support structure and thereby tilt the wind turbine rotor disk. The study considers the effects of this new form of wake control on the aerodynamics of the steering and wake-affected turbines, on the structure, and on the ballast motion system.
Giorgia Guma, Philipp Bucher, Patrick Letzgus, Thorsten Lutz, and Roland Wüchner
Wind Energ. Sci., 7, 1421–1439, https://doi.org/10.5194/wes-7-1421-2022, https://doi.org/10.5194/wes-7-1421-2022, 2022
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Wind turbine aeroelasticity is becoming more and more important because turbine sizes are increasingly leading to more slender blades. On the other hand, complex terrains are of interest because they are far away from urban areas. These regions are characterized by low velocities and high turbulence and are mostly influenced by the presence of forest, and that is why it is necessary to develop high-fidelity tools to correctly simulate the wind turbine's response.
Sarah Barber, Julien Deparday, Yuriy Marykovskiy, Eleni Chatzi, Imad Abdallah, Gregory Duthé, Michele Magno, Tommaso Polonelli, Raphael Fischer, and Hanna Müller
Wind Energ. Sci., 7, 1383–1398, https://doi.org/10.5194/wes-7-1383-2022, https://doi.org/10.5194/wes-7-1383-2022, 2022
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Aerodynamic and acoustic field measurements on operating large-scale wind turbines are key for the further reduction in the costs of wind energy. In this work, a novel cost-effective MEMS (micro-electromechanical systems)-based aerodynamic and acoustic wireless measurement system that is thin, non-intrusive, easy to install, low power and self-sustaining is designed and tested.
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.
Cited articles
Balduzzi, F., Bianchini, A., Maleci, R., Ferrara, G., and Ferrari, L.: Blade design criteria to compensate the flow curvature effects in h-darrieus wind turbines, J. Turbomach., 137, 1–10, https://doi.org/10.1115/1.4028245, 2014. a
Belabes, B. and Paraschivoiu, M.: CFD modeling of vertical-axis wind turbine wake interaction, T. Can. Soc. Mech. Eng., 47, 449–458, https://doi.org/10.1139/TCSME-2022-0149, 2023. a
Cheng, Z., Madsen, H. A., Gao, Z., and Moan, T.: Aerodynamic Modeling of Floating Vertical Axis Wind Turbines Using the Actuator Cylinder Flow Method, Enrgy. Proced., 94, 531–543, https://doi.org/10.1016/J.EGYPRO.2016.09.232, 2016. a
Dassault Systemes: SIMULIA PowerFLOW User's Guide, https://www.3ds.com/products/simulia/powerflow (last access: 25 February 2024), 2021. a
Delft High Performance Computing Centre (DHPC): DelftBlue Supercomputer (Phase 1), https://www.tudelft.nl/dhpc/ark:/44463/DelftBluePhase1 (last access: 25 February 2024), 2022.
De Tavernier, D., Ferreira, C., Paulsen, U., and Madsen, H.: The 3D effects of a vertical-axis wind turbine: rotor and wake induction, J. Phys. Conf. Ser., 1618, 052040, https://doi.org/10.1088/1742-6596/1618/5/052040, 2020a. a
De Tavernier, D., Sakib, M., Griffith, T., Pirrung, G., Paulsen, U., Madsen, H., Keijer, W., and Ferreira, C.: Comparison of 3D aerodynamic models for vertical-axis wind turbines: H-rotor and Φ-rotor, J. Phys. Conf. Ser., 1618, 052041, https://doi.org/10.1088/1742-6596/1618/5/052041, 2020b. a
Drela, M.: XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils, in: Low Reynolds Number Aerodynamics, edited by: Mueller, T. J., Lecture Notes in Engineering, Springer, Berlin, Heidelberg, https://doi.org/10.1007/978-3-642-84010-4_1, pp. 1–12, 1989. a
Ferreira, C. S., Madsen, H. A., Barone, M., Roscher, B., Deglaire, P., and Arduin, I.: Comparison of aerodynamic models for Vertical Axis Wind Turbines, J. Phys. Conf. Ser., 524, 012125, https://doi.org/10.1088/1742-6596/524/1/012125, 2014. a, b, c
Flannigan, C., Carroll, J., and Leithead, W.: Operations expenditure modelling of the X-Rotor offshore wind turbine concept, in: J. Phys. Conf. Ser., 2265, 032054, https://doi.org/10.1088/1742-6596/2265/3/032054, 2022. a, b
Franchina, N., Kouaissah, O., Persico, G., and Savini, M.: Three-dimensional CFD simulation and experimental assessment of the performance of a h-shape vertical-axis wind turbine at design and off-design conditions, International Journal of Turbomachinery, Propulsion and Power, 4, 30, https://doi.org/10.3390/IJTPP4030030, 2019. a
Freris, L. L.: Wind Energy Conversion Systems, Prentice Hall, New York, ISBN 0139605274, ISBN 9780139605277, 1990. a
Giri Ajay, A., Morgan, L., Wu, Y., Bretos, D., Cascales, A., Pires, O., and Ferreira, C.: Aerodynamic model comparison for an X-shaped vertical-axis wind turbine, Zenodo [data set], https://doi.org/10.5281/zenodo.8208638, 2023. a
Huang, M., Sciacchitano, A., and Ferreira, C.: On the wake deflection of vertical axis wind turbines by pitched blades, Wind Energy, pp. 365–387, https://doi.org/10.1002/we.2803, 2023. a, b
Katz, J. and Plotkin, A.: Low-Speed Aerodynamics, Springer, https://doi.org/10.1007/978-1-4020-8664-9_3, 2009. a
Keijer, W. J. T.: 3D aerodynamic effects and circulation control of vertical axis wind turbines, MSc thesis, http://resolver.tudelft.nl/uuid:765b00ba-7a80-4588-8476-774d7badc6cb (last access: 25 February 2024), 2020. a
Kolios, A., Chahardehi, A., and Brennan, F.: Experimental determination of the overturning moment and net lateral force generated by a novel vertical axis wind turbine: Experiment design under load uncertainty, Exp. Techniques, 37, 7–14, https://doi.org/10.1111/j.1747-1567.2011.00727.x, 2013. a
Kozak, P. A., Vallverdú, D., and Rempfer, D.: Modeling vertical-axis wind turbine performance: Blade element method vs. finite volume approach, in: 12th International Energy Conversion Engineering Conference, IECEC 2014, 28–30 July 2014, Cleveland, OH, USA, https://doi.org/10.2514/6.2014-3861, 2014. a
Le Fouest, S. and Mulleners, K.: The dynamic stall dilemma for vertical-axis wind turbines, Renew. Energ., 198, 505–520, https://doi.org/10.1016/J.RENENE.2022.07.071, 2022. a
Leishman, J. G.: Principles of helicopter aerodynamics, 2nd Edn., SE – xxxvii, illustrations; 27 cm, Cambridge University Press, Cambridge, 826 pp., ISBN 978-1-107-01335-3, 2006. a
Leithead, W., Camciuc, A., Amiri, A. K., and Carroll, J.: The X-Rotor Offshore Wind Turbine Concept, J. Phys. Conf. Ser., 1356, https://doi.org/10.1088/1742-6596/1356/1/012031, 2019. a, b, c
Madsen, H. A.: The actuator cylinder: a flow model for vertical axis wind turbine., PhD thesis, ResearchGate, https://doi.org/10.13140/RG.2.1.2512.3040, 1982. a
Madsen, H. A., Paulsen, U. S., and Vitae, L.: Analysis of VAWT aerodynamics and design using the Actuator Cylinder flow model, J. Phys. Conf. Ser., 555, 012065, https://doi.org/10.1088/1742-6596/555/1/012065, 2014. a, b
Marten, D.: QBlade: a modern tool for the aeroelastic simulation of wind turbines, PhD thesis, Technische Universität Berlin, Berlin, https://doi.org/10.14279/depositonce-10646, 2020. a
Marten, D., Wendler, J., Pechlivanoglou, G., Nayeri, C. N., and Paschereit, C. O.: QBLADE: an open source tool for design and simulation of horizontal and vertical axis wind turbines, International Journal of Emerging Technology and Advanced Engineering, 3, 264–269, 2013. a
Massie, L., Ouro, P., Stoesser, T., and Luo, Q.: An Actuator Surface Model to Simulate Vertical Axis Turbines, Energies, 12, 4741, https://doi.org/10.3390/EN12244741, 2019. a
Masson, C., Leclerc, C., and Paraschivoiu, I.: Appropriate dynamic-stall models for performance predictions of VAWTs with NLF blades, International Journal of Rotating Machinery, 4, 129–139, https://doi.org/10.1155/S1023621X98000116, 1998. a
Melani, P. F., Balduzzi, F., Ferrara, G., and Bianchini, A.: An annotated database of low Reynolds aerodynamic coefficients for the NACA0021 airfoil, AIP Conf. Proc., 2191, 20111, https://doi.org/10.1063/1.5138844, 2019. a
Menter, F. R.: Zonal two equation κ-ω turbulence models for aerodynamic flows, in: AIAA 23rd Fluid Dynamics, Plasmadynamics, and Lasers Conference, 6–9 July 1993, Orlando, FL, USA, https://doi.org/10.2514/6.1993-2906, 1993. a
Migliore, P. G., Wolfe, W. P., and Fanucci, J. B.: Flow Curvature Effects on Darrieus Turbine Blade Aerodynamics., J. Energy, 4, 49–55, https://doi.org/10.2514/3.62459, 1980. a
Morgan, L. and Leithead, W.: Aerodynamic modelling of a novel vertical axis wind turbine concept, in: J. Phys. Conf. Ser., 2257, 012001, https://doi.org/10.1088/1742-6596/2257/1/012001, 2022. a, b, c
Murray, J. and Barone, M.: The Development of CACTUS, a Wind and Marine Turbine Performance Simulation Code, in: AIAA 49th Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition 4–7 January 2011, Orlando, Florida, 1–21, https://doi.org/10.2514/6.2011-147, 2011. a
Paraschivoiu, I.: Double-multiple streamtube model for Darrieus in turbines, in: 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 4–7 January 2011, Orlando, Florida, USA, Document number 19820015811, https://ntrs.nasa.gov/citations/19820015811 (last access: 25 February 2024), 1981. a
Paraschivoiu, I.: Aerodynamic Loads and Performance of the Darrieus Rotor, J. Energy, 6, 406–412, https://doi.org/10.2514/3.62621, 1982. a
Posa, A. and Balaras, E.: Large Eddy Simulation of an isolated vertical axis wind turbine, J. Wind Eng. Ind. Aerod., 172, 139–151, https://doi.org/10.1016/J.JWEIA.2017.11.004, 2018. a
Prandtl, L., Betz, A., Klassiker der Strömungsmechanik, G., and Abhandlungen, V.: Vier Abhandlungen zur Hydrodynamik und Aerodynamik, Universit atsverlag Göttingen, Göttingen, https://doi.org/10.17875/gup2010-106, 1927. a, b
Rainbird, J. M., Bianchini, A., Balduzzi, F., Peiró, J., Graham, J. M. R., Ferrara, G., and Ferrari, L.: On the influence of virtual camber effect on airfoil polars for use in simulations of Darrieus wind turbines, Energ. Convers. Manage., 106, 373–384, https://doi.org/10.1016/j.enconman.2015.09.053, 2015. a
Rezaeiha, A., Kalkman, I., and Blocken, B.: CFD simulation of a vertical axis wind turbine operating at a moderate tip speed ratio: Guidelines for minimum domain size and azimuthal increment, Renew. Energ., 107, 373–385, https://doi.org/10.1016/J.RENENE.2017.02.006, 2017a. a, b
Rezaeiha, A., Kalkman, I., Montazeri, H., and Blocken, B.: Effect of the shaft on the aerodynamic performance of urban vertical axis wind turbines, Energ. Convers. Manage., 149, 616–630, https://doi.org/10.1016/J.ENCONMAN.2017.07.055, 2017b. a
Shamsoddin, S. and Porté-Agel, F.: Large eddy simulation of vertical axis wind turbine wakes, Energies, 7, 890–912, https://doi.org/10.3390/EN7020890, 2014. a
Shan, X., Yuan, X. F., and Chen, H.: Kinetic theory representation of hydrodynamics: A way beyond the Navier–Stokes equation, J. Fluid Mech., 550, 413–441, https://doi.org/10.1017/S0022112005008153, 2006. a
Shires, A.: Design optimisation of an offshore vertical axis wind turbine, Proceedings of Institution of Civil Engineers: Energy, 166, 7–18, https://doi.org/10.1680/ener.12.00007, 2013. a
Su, J., Chen, Y., Han, Z., Zhou, D., Bao, Y., and Zhao, Y.: Investigation of V-shaped blade for the performance improvement of vertical axis wind turbines, Appl. Energ., 260, 114326, https://doi.org/10.1016/J.APENERGY.2019.114326, 2020. a
Viterna, L. and Janetzke, D.: Theoretical and experimental power from large horizontal-axis wind turbines, NASA Technical Memorandum, OSTI.GOV, https://doi.org/10.2172/6763041, 1982. a
Weller, H. G., Tabor, G., Jasak, H., and Fureby, C.: A tensorial approach to computational continuum mechanics using object-oriented techniques, Comput. Phys., 12, 620–631, https://doi.org/10.1063/1.168744, 1998. a
XROTOR: X-ROTOR: X-shaped Radical Offshore wind Turbine for Overall cost of energy Reduction, https://cordis.europa.eu/project/id/101007135 (last access: 16 April 2023), 2020. a
Short summary
This paper compares six different numerical models to predict the performance of an X-shaped vertical-axis wind turbine, offering insights into how it works in 3D when its blades are fixed at specific angles. The results showed the 3D models here reliably predict the performance while still taking this turbine's complex aerodynamics into account compared to 2D models. Further, these blade angles caused more complexity in predicting the turbine's behaviour, which is highlighted in this paper.
This paper compares six different numerical models to predict the performance of an X-shaped...
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