Articles | Volume 8, issue 6
https://doi.org/10.5194/wes-8-999-2023
© Author(s) 2023. 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-8-999-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
14 Jun 2023
Research article |
| 14 Jun 2023
| 14 Jun 2023
Vortex model of the aerodynamic wake of airborne wind energy systems
Filippo Trevisi
CORRESPONDING AUTHOR
Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156 Milan, Italy
Carlo E. D. Riboldi
Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156 Milan, Italy
Alessandro Croce
Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156 Milan, Italy
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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.
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The power equations of crosswind Ground-Gen and Fly-Gen airborne wind energy systems (AWESs) are refined to include the contribution from the aerodynamic wake. A novel power coefficient is defined by normalizing the aerodynamic power with the wind power passing through a disk with a radius equal to the AWES wingspan, allowing us to compare systems with different wingspans. Ground-Gen and Fly-Gen AWESs are compared in terms of their aerodynamic power potential.
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The optimal control problem for the flight trajectories of Fly-Gen AWESs is expressed with a novel methodology in the frequency domain through a harmonic balance formulation. The solution gives the optimal trajectory and the optimal control inputs. Optimal trajectories have a circular shape squashed along the vertical direction, and the optimal control inputs can be modeled with only one or two harmonics. Analytical approximations for optimal trajectory characteristics are also given.
Filippo Trevisi, Gianni Cassoni, Mac Gaunaa, and Lorenzo Mario Fagiano
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The power equations of crosswind Ground-Gen and Fly-Gen airborne wind energy systems (AWESs) are refined to include the contribution from the aerodynamic wake. A novel power coefficient is defined by normalizing the aerodynamic power with the wind power passing through a disk with a radius equal to the AWES wingspan, allowing us to compare systems with different wingspans. Ground-Gen and Fly-Gen AWESs are compared in terms of their aerodynamic power potential.
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
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Related subject area
Thematic area: Fluid mechanics | Topic: Wakes and wind farm aerodynamics
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Alessandro Fontanella, Alberto Fusetti, Stefano Cioni, Francesco Papi, Sara Muggiasca, Giacomo Persico, Vincenzo Dossena, Alessandro Bianchini, and Marco Belloli
Wind Energ. Sci., 10, 1369–1387, https://doi.org/10.5194/wes-10-1369-2025, https://doi.org/10.5194/wes-10-1369-2025, 2025
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Antonin Hubert, Boris Conan, and Sandrine Aubrun
Wind Energ. Sci., 10, 1351–1368, https://doi.org/10.5194/wes-10-1351-2025, https://doi.org/10.5194/wes-10-1351-2025, 2025
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Wessel van der Deijl, Martín Obligado, Stéphane Barre, and Christophe Sicot
Wind Energ. Sci., 10, 719–732, https://doi.org/10.5194/wes-10-719-2025, https://doi.org/10.5194/wes-10-719-2025, 2025
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YuanTso Li, Wei Yu, Andrea Sciacchitano, and Carlos Ferreira
Wind Energ. Sci., 10, 631–659, https://doi.org/10.5194/wes-10-631-2025, https://doi.org/10.5194/wes-10-631-2025, 2025
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Juan Felipe Céspedes Moreno, Juan Pablo Murcia León, and Søren Juhl Andersen
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Karim Ali, Pablo Ouro, and Tim Stallard
Wind Energ. Sci., 10, 511–533, https://doi.org/10.5194/wes-10-511-2025, https://doi.org/10.5194/wes-10-511-2025, 2025
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We introduce an innovative analytical method to better understand and optimise wind-farm performance by accurately calculating how turbine wakes affect each other. Unlike traditional numerical approaches, our method provides a precise way to measure the impact of upstream wakes on downstream turbines. This new approach, validated through numerical comparisons, enhances optimisation strategies, potentially leading to more efficient wind-farm operations and increased power generation.
Andrew Kirby, Takafumi Nishino, Luca Lanzilao, Thomas D. Dunstan, and Johan Meyers
Wind Energ. Sci., 10, 435–450, https://doi.org/10.5194/wes-10-435-2025, https://doi.org/10.5194/wes-10-435-2025, 2025
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Traditionally, the aerodynamic loss of wind farm efficiency is classified into wake loss and farm blockage loss. This study, using high-fidelity simulations, shows that neither of these two losses is well correlated with the overall farm efficiency. We propose new measures called turbine-scale efficiency and farm-scale efficiency to better describe turbine–wake effects and farm–atmosphere interactions. This study suggests the importance of better modelling farm-scale loss in future studies.
Olivier Ndindayino, Augustin Puel, and Johan Meyers
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-6, https://doi.org/10.5194/wes-2025-6, 2025
Revised manuscript accepted for WES
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Our aim is to understand the relationship between flow blockage and improved wind farm efficiency using large-eddy simulations, as well as developing an analytical model that shows promise for improving turbine power predictions under blockage. We found that blockage enhances turbine power and thrust by inducing a favourable pressure drop across the turbine row, while simultaneously inducing an unfavourable pressure increase downstream which has minimal direct impact on far wake development.
Kenneth Brown, Gopal Yalla, Lawrence Cheung, Joeri Frederik, Dan Houck, Nate deVelder, Eric Simley, and Paul Fleming
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2024-191, https://doi.org/10.5194/wes-2024-191, 2025
Revised manuscript accepted for WES
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This paper presents a one half of a companion-paper series that studies strategies to reduce negative aerodynamic interference (i.e., wake effects) between nearby wind turbines in a wind farm. The approach leverages high-fidelity flow simulations of an open-source design for an offshore wind turbine. Complimenting the companion paper’s analysis of the power and loading effects of the wake-control strategies, this article uncovers the underlying fluid-dynamic causes for these effects.
James Cutler, Christopher Bay, and Andrew Ning
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2024-172, https://doi.org/10.5194/wes-2024-172, 2025
Revised manuscript accepted for WES
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This study compares two methods for modeling wakes from tilted wind turbines. An optimized analytical model improves accuracy but is limited by assumptions about wake shape. In contrast, a deep learning approach captures complex wake patterns without these constraints, matching high-fidelity simulations with minimal computational effort. The comparison highlights the potential of deep learning to transform wake modeling, offering greater accuracy and efficiency for wind energy optimization.
Flavio Avila Correia Martins, Alexander van Zuijlen, and Carlos Simão Ferreira
Wind Energ. Sci., 10, 41–58, https://doi.org/10.5194/wes-10-41-2025, https://doi.org/10.5194/wes-10-41-2025, 2025
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This study examines regenerative wind farming with multirotor systems fitted with atmospheric boundary layer control (ABL-control) wings near the rotor's wake. These wings create vortices that boost vertical momentum transfer and speed up wake recovery. Results show that ABL-control wings can restore 95 % of wind power within six rotor diameters downstream, achieving a recovery rate nearly 10 times faster than that without ABL control.
Diederik van Binsbergen, Pieter-Jan Daems, Timothy Verstraeten, Amir R. Nejad, and Jan Helsen
Wind Energ. Sci., 9, 1507–1526, https://doi.org/10.5194/wes-9-1507-2024, https://doi.org/10.5194/wes-9-1507-2024, 2024
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Wind farm yield assessment often relies on analytical wake models. Calibrating these models can be challenging due to the stochastic nature of wind. We developed a calibration framework that performs a multi-phase optimization on the tuning parameters using time series SCADA data. This yields a parameter distribution that more accurately reflects reality than a single value. Results revealed notable variation in resultant parameter values, influenced by nearby wind farms and coastal effects.
Anantha Padmanabhan Kidambi Sekar, Paul Hulsman, Marijn Floris van Dooren, and Martin Kühn
Wind Energ. Sci., 9, 1483–1505, https://doi.org/10.5194/wes-9-1483-2024, https://doi.org/10.5194/wes-9-1483-2024, 2024
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We present induction zone measurements conducted with two synchronised lidars at a two-turbine wind farm. The induction zone flow was characterised for free, fully waked and partially waked flows. Due to the short turbine spacing, the lidars captured the interaction of the atmospheric boundary layer, induction zone and wake, evidenced by induction asymmetry and induction zone–wake interactions. The measurements will aid the process of further improving existing inflow and wake models.
Kelsey Shaler, Eliot Quon, Hristo Ivanov, and Jason Jonkman
Wind Energ. Sci., 9, 1451–1463, https://doi.org/10.5194/wes-9-1451-2024, https://doi.org/10.5194/wes-9-1451-2024, 2024
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This paper presents a three-way verification and validation between an engineering-fidelity model, a high-fidelity model, and measured data for the wind farm structural response and wake dynamics during an evolving stable boundary layer of a small wind farm, generally with good agreement.
Peter Brugger, Corey D. Markfort, and Fernando Porté-Agel
Wind Energ. Sci., 9, 1363–1379, https://doi.org/10.5194/wes-9-1363-2024, https://doi.org/10.5194/wes-9-1363-2024, 2024
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The dynamic wake meandering model (DWMM) assumes that wind turbine wakes are transported like a passive tracer by the large-scale turbulence of the atmospheric boundary layer. We show that both the downstream transport and the lateral transport of the wake have differences from the passive tracer assumption. We then propose to include the turbulent Schmidt number into the DWMM to account for the less efficient transport of momentum and show that it improves the quality of the model predictions.
Mohammad Mehdi Mohammadi, Hugo Olivares-Espinosa, Gonzalo Pablo Navarro Diaz, and Stefan Ivanell
Wind Energ. Sci., 9, 1305–1321, https://doi.org/10.5194/wes-9-1305-2024, https://doi.org/10.5194/wes-9-1305-2024, 2024
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This paper has put forward a set of recommendations regarding the actuator sector model implementation details to improve the capability of the model to reproduce similar results compared to those obtained by an actuator line model, which is one of the most common ways used for numerical simulations of wind farms, while providing significant computational savings. This includes among others the velocity sampling method and a correction of the sampled velocities to calculate the blade forces.
Franz V. Mühle, Florian M. Heckmeier, Filippo Campagnolo, and Christian Breitsamter
Wind Energ. Sci., 9, 1251–1271, https://doi.org/10.5194/wes-9-1251-2024, https://doi.org/10.5194/wes-9-1251-2024, 2024
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Wind turbines influence each other, and these wake effects limit the power production of downstream turbines. Controlling turbines collectively and not individually can limit such effects. We experimentally investigate a control strategy increasing mixing in the wake. We want to see the potential of this so-called Helix control for power optimization and understand the flow physics. Our study shows that the control technique leads to clearly faster wake recovery and thus higher power production.
Pascal Weihing, Marion Cormier, Thorsten Lutz, and Ewald Krämer
Wind Energ. Sci., 9, 933–962, https://doi.org/10.5194/wes-9-933-2024, https://doi.org/10.5194/wes-9-933-2024, 2024
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This study evaluates different approaches to simulate the near-wake flow of a wind turbine. The test case is in off-design conditions of the wind turbine, where the flow is separated from the blades and therefore very difficult to predict. The evaluation of simulation techniques is key to understand their limitations and to deepen the understanding of the near-wake physics. This knowledge can help to derive new wind farm design methods for yield-optimized farm layouts.
Nikolaos Bempedelis, Filippo Gori, Andrew Wynn, Sylvain Laizet, and Luca Magri
Wind Energ. Sci., 9, 869–882, https://doi.org/10.5194/wes-9-869-2024, https://doi.org/10.5194/wes-9-869-2024, 2024
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This paper proposes a computational method to maximise the power production of wind farms through two strategies: layout optimisation and yaw angle optimisation. The proposed method relies on high-fidelity computational modelling of wind farm flows and is shown to be able to effectively maximise wind farm power production. Performance improvements relative to conventional optimisation strategies based on low-fidelity models can be attained, particularly in scenarios of increased flow complexity.
Benyamin Schliffke, Boris Conan, and Sandrine Aubrun
Wind Energ. Sci., 9, 519–532, https://doi.org/10.5194/wes-9-519-2024, https://doi.org/10.5194/wes-9-519-2024, 2024
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This paper studies the consequences of floater motions for the wake properties of a floating wind turbine. Since wake interactions are responsible for power production loss in wind farms, it is important that we know whether the tools that are used to predict this production loss need to be upgraded to take into account these aspects. Our wind tunnel study shows that the signature of harmonic floating motions can be observed in the far wake of a wind turbine, when motions have strong amplitudes.
Erwan Jézéquel, Frédéric Blondel, and Valéry Masson
Wind Energ. Sci., 9, 97–117, https://doi.org/10.5194/wes-9-97-2024, https://doi.org/10.5194/wes-9-97-2024, 2024
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Wind turbine wakes affect the production and lifecycle of downstream turbines. They can be predicted with the dynamic wake meandering (DWM) method. In this paper, the authors break down the velocity and turbulence in the wake of a wind turbine into several terms. They show that it is implicitly assumed in the DWM that some of these terms are neglected. With high-fidelity simulations, it is shown that this can lead to some errors, in particular for the maximum turbulence added by the wake.
Erwan Jézéquel, Frédéric Blondel, and Valéry Masson
Wind Energ. Sci., 9, 119–139, https://doi.org/10.5194/wes-9-119-2024, https://doi.org/10.5194/wes-9-119-2024, 2024
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Analytical models allow us to quickly compute the decreased power output and lifetime induced by wakes in a wind farm. This is achieved by evaluating the modified velocity and turbulence in the wake. In this work, we present a new model based on the velocity and turbulence breakdowns presented in Part 1. This new model is physically based, allows us to compute the whole turbulence profile (rather than the maximum value) and is built to take atmospheric stability into account.
Maarten J. van den Broek, Delphine De Tavernier, Paul Hulsman, Daan van der Hoek, Benjamin Sanderse, and Jan-Willem van Wingerden
Wind Energ. Sci., 8, 1909–1925, https://doi.org/10.5194/wes-8-1909-2023, https://doi.org/10.5194/wes-8-1909-2023, 2023
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As wind turbines produce power, they leave behind wakes of slow-moving air. We analyse three different models to predict the effects of these wakes on downstream wind turbines. The models are validated with experimental data from wind tunnel studies for steady and time-varying conditions. We demonstrate that the models are suitable for optimally controlling wind turbines to improve power production in large wind farms.
Alessandro Sebastiani, James Bleeg, and Alfredo Peña
Wind Energ. Sci., 8, 1795–1808, https://doi.org/10.5194/wes-8-1795-2023, https://doi.org/10.5194/wes-8-1795-2023, 2023
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The power curve of a wind turbine indicates the turbine power output in relation to the wind speed. Therefore, power curves are critically important to estimate the production of future wind farms as well as to assess whether operating wind farms are functioning correctly. Since power curves are often measured in wind farms, they might be affected by the interactions between the turbines. We show that these effects are not negligible and present a method to correct for them.
Maarten Paul van der Laan, Oscar García-Santiago, Mark Kelly, Alexander Meyer Forsting, Camille Dubreuil-Boisclair, Knut Sponheim Seim, Marc Imberger, Alfredo Peña, Niels Nørmark Sørensen, and Pierre-Elouan Réthoré
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.
Peter Baas, Remco Verzijlbergh, Pim van Dorp, and Harm Jonker
Wind Energ. Sci., 8, 787–805, https://doi.org/10.5194/wes-8-787-2023, https://doi.org/10.5194/wes-8-787-2023, 2023
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This work studies the energy production and wake losses of large offshore wind farms with a large-eddy simulation model. Therefore, 1 year of actual weather has been simulated for a suite of hypothetical 4 GW wind farm scenarios. The results suggest that production numbers increase significantly when the rated power of the individual turbines is larger while keeping the total installed capacity the same. Also, a clear impact of atmospheric stability on the energy production is found.
Robert Braunbehrens, Andreas Vad, and Carlo L. Bottasso
Wind Energ. Sci., 8, 691–723, https://doi.org/10.5194/wes-8-691-2023, https://doi.org/10.5194/wes-8-691-2023, 2023
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The paper presents a new method in which wind turbines in a wind farm act as local sensors, in this way detecting the flow that develops within the power plant. Through this technique, we are able to identify effects on the flow generated by the plant itself and by the orography of the terrain. The new method not only delivers a flow model of much improved quality but can also help in understanding phenomena that drive the farm performance.
Tamino Wetz and Norman Wildmann
Wind Energ. Sci., 8, 515–534, https://doi.org/10.5194/wes-8-515-2023, https://doi.org/10.5194/wes-8-515-2023, 2023
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In the present study, for the first time, the SWUF-3D fleet of multirotors is deployed for field measurements on an operating 2 MW wind turbine (WT) in complex terrain. The fleet of multirotors has the potential to fill the meteorological gap of observations in the near wake of WTs with high-temporal and high-spatial-resolution wind vector measurements plus temperature, humidity and pressure. The flow up- and downstream of the WT is measured simultaneously at multiple spatial positions.
Christopher J. Bay, Paul Fleming, Bart Doekemeijer, Jennifer King, Matt Churchfield, and Rafael Mudafort
Wind Energ. Sci., 8, 401–419, https://doi.org/10.5194/wes-8-401-2023, https://doi.org/10.5194/wes-8-401-2023, 2023
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This paper introduces the cumulative-curl wake model that allows for the fast and accurate prediction of wind farm energy production wake interactions. The cumulative-curl model expands several existing wake models to make the simulation of farms more accurate and is implemented in a computationally efficient manner such that it can be used for wind farm layout design and controller development. The model is validated against high-fidelity simulations and data from physical wind farms.
Gonzalo Pablo Navarro Diaz, Alejandro Daniel Otero, Henrik Asmuth, Jens Nørkær Sørensen, and Stefan Ivanell
Wind Energ. Sci., 8, 363–382, https://doi.org/10.5194/wes-8-363-2023, https://doi.org/10.5194/wes-8-363-2023, 2023
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In this paper, the capacity to simulate transient wind turbine wake interaction problems using limited wind turbine data has been extended. The key novelty is the creation of two new variants of the actuator line technique in which the rotor blade forces are computed locally using generic load data. The analysis covers a partial wake interaction case between two wind turbines for a uniform laminar inflow and for a turbulent neutral atmospheric boundary layer inflow.
Maarten Paul van der Laan, Mads Baungaard, and Mark Kelly
Wind Energ. Sci., 8, 247–254, https://doi.org/10.5194/wes-8-247-2023, https://doi.org/10.5194/wes-8-247-2023, 2023
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Understanding wind turbine wake recovery is important to mitigate energy losses in wind farms. Wake recovery is often assumed or explained to be dependent on the first-order derivative of velocity. In this work we show that wind turbine wakes recover mainly due to the second-order derivative of the velocity, which transport momentum from the freestream towards the wake center. The wake recovery mechanisms and results of a high-fidelity numerical simulation are illustrated using a simple model.
Søren Juhl Andersen and Juan Pablo Murcia Leon
Wind Energ. Sci., 7, 2117–2133, https://doi.org/10.5194/wes-7-2117-2022, https://doi.org/10.5194/wes-7-2117-2022, 2022
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Simulating the turbulent flow inside large wind farms is inherently complex and computationally expensive. A new and fast model is developed based on data from high-fidelity simulations. The model captures the flow dynamics with correct statistics for a wide range of flow conditions. The model framework provides physical insights and presents a generalization of high-fidelity simulation results beyond the case-specific scenarios, which has significant potential for future turbulence modeling.
Mads Baungaard, Stefan Wallin, Maarten Paul van der Laan, and Mark Kelly
Wind Energ. Sci., 7, 1975–2002, https://doi.org/10.5194/wes-7-1975-2022, https://doi.org/10.5194/wes-7-1975-2022, 2022
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Wind turbine wakes in the neutral atmospheric surface layer are simulated with Reynolds-averaged Navier–Stokes (RANS) using an explicit algebraic Reynolds stress model. Contrary to standard two-equation turbulence models, it can predict turbulence anisotropy and complex physical phenomena like secondary motions. For the cases considered, it improves Reynolds stress, turbulence intensity, and velocity deficit predictions, although a more top-hat-shaped profile is observed for the latter.
Koen Devesse, Luca Lanzilao, Sebastiaan Jamaer, Nicole van Lipzig, and Johan Meyers
Wind Energ. Sci., 7, 1367–1382, https://doi.org/10.5194/wes-7-1367-2022, https://doi.org/10.5194/wes-7-1367-2022, 2022
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Recent research suggests that offshore wind farms might form such a large obstacle to the wind that it already decelerates before reaching the first turbines. Part of this phenomenon could be explained by gravity waves. Research on these gravity waves triggered by mountains and hills has found that variations in the atmospheric state with altitude can have a large effect on how they behave. This paper is the first to take the impact of those vertical variations into account for wind farms.
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Short summary
Modeling the aerodynamic wake of airborne wind energy systems (AWESs) is crucial to properly estimating power production and to designing such systems. The velocities induced at the AWES from its own wake are studied with a model for the near wake and one for the far wake, using vortex methods. The model is validated with the lifting-line free-vortex wake method implemented in QBlade.
Modeling the aerodynamic wake of airborne wind energy systems (AWESs) is crucial to properly...
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