Articles | Volume 9, issue 6
https://doi.org/10.5194/wes-9-1363-2024
© 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-9-1363-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
20 Jun 2024
Research article |
| 20 Jun 2024
| 20 Jun 2024
Improvements to the dynamic wake meandering model by incorporating the turbulent Schmidt number
Wind Engineering and Renewable Energy Laboratory (WiRE), École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
Corey D. Markfort
IIHR–Hydroscience & Engineering, Department of Civil and Environmental Engineering, The University of Iowa, Iowa City, IA 52242, USA
Fernando Porté-Agel
Wind Engineering and Renewable Energy Laboratory (WiRE), École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
Related authors
Peter Brugger, Corey Markfort, and Fernando Porté-Agel
Wind Energ. Sci., 7, 185–199, https://doi.org/10.5194/wes-7-185-2022, https://doi.org/10.5194/wes-7-185-2022, 2022
Short summary
Short summary
Wind turbines create a wake of reduced wind speeds downstream of the rotor. The wake does not necessarily have a straight, pencil-like shape but can meander similar to a smoke plume. We investigated this wake meandering and observed that the downstream transport velocity is slower than the wind speed contrary to previous assumptions and that the evolution of the atmospheric turbulence over time impacts wake meandering on distances typical for the turbine spacing in wind farms.
Matthias Mauder, Andreas Ibrom, Luise Wanner, Frederik De Roo, Peter Brugger, Ralf Kiese, and Kim Pilegaard
Atmos. Meas. Tech., 14, 7835–7850, https://doi.org/10.5194/amt-14-7835-2021, https://doi.org/10.5194/amt-14-7835-2021, 2021
Short summary
Short summary
Turbulent flux measurements suffer from a general systematic underestimation. One reason for this bias is non-local transport by large-scale circulations. A recently developed model for this additional transport of sensible and latent energy is evaluated for three different test sites. Different options on how to apply this correction are presented, and the results are evaluated against independent measurements.
Peter Brugger, Mithu Debnath, Andrew Scholbrock, Paul Fleming, Patrick Moriarty, Eric Simley, David Jager, Jason Roadman, Mark Murphy, Haohua Zong, and Fernando Porté-Agel
Wind Energ. Sci., 5, 1253–1272, https://doi.org/10.5194/wes-5-1253-2020, https://doi.org/10.5194/wes-5-1253-2020, 2020
Short summary
Short summary
A wind turbine can actively influence its wake by turning the rotor out of the wind direction to deflect the wake away from a downstream wind turbine. This technique was tested in a field experiment at a wind farm, where the inflow and wake were monitored with remote-sensing instruments for the wind speed. The behaviour of the wake deflection agrees with the predictions of two analytical models, and a bias of the wind direction perceived by the yawed wind turbine led to suboptimal power gains.
Tirtha Banerjee, Peter Brugger, Frederik De Roo, Konstantin Kröniger, Dan Yakir, Eyal Rotenberg, and Matthias Mauder
Atmos. Chem. Phys., 18, 10025–10038, https://doi.org/10.5194/acp-18-10025-2018, https://doi.org/10.5194/acp-18-10025-2018, 2018
Short summary
Short summary
We studied the nature of turbulent transport over a well-defined surface heterogeneity (approximate scale 7 km) comprising a shrubland and a forest in the Yatir semiarid area in Israel. Using eddy covariance and Doppler lidar measurements, we studied the variations in the turbulent kinetic energy budget and turbulent fluxes, focusing especially on transport terms. We also confirmed the role of large-scale secondary circulations that transport energy between the shrubland and the forest.
Mou Lin and Fernando Porté-Agel
Wind Energ. Sci., 7, 2215–2230, https://doi.org/10.5194/wes-7-2215-2022, https://doi.org/10.5194/wes-7-2215-2022, 2022
Short summary
Short summary
Large-eddy simulation (LES) is a widely used method to study wind turbine flow. To save computational resources, the turbine-inducing forces in LES are often modelled by parametrisations. We validate three widely used turbine parametrisations in LES in different yaw and offset configurations with wind tunnel measurements, and we find that, in comparison with other parametrisations, the blade element actuator disk model strikes a good balance of accuracy and computational cost.
Peter Brugger, Corey Markfort, and Fernando Porté-Agel
Wind Energ. Sci., 7, 185–199, https://doi.org/10.5194/wes-7-185-2022, https://doi.org/10.5194/wes-7-185-2022, 2022
Short summary
Short summary
Wind turbines create a wake of reduced wind speeds downstream of the rotor. The wake does not necessarily have a straight, pencil-like shape but can meander similar to a smoke plume. We investigated this wake meandering and observed that the downstream transport velocity is slower than the wind speed contrary to previous assumptions and that the evolution of the atmospheric turbulence over time impacts wake meandering on distances typical for the turbine spacing in wind farms.
Matthias Mauder, Andreas Ibrom, Luise Wanner, Frederik De Roo, Peter Brugger, Ralf Kiese, and Kim Pilegaard
Atmos. Meas. Tech., 14, 7835–7850, https://doi.org/10.5194/amt-14-7835-2021, https://doi.org/10.5194/amt-14-7835-2021, 2021
Short summary
Short summary
Turbulent flux measurements suffer from a general systematic underestimation. One reason for this bias is non-local transport by large-scale circulations. A recently developed model for this additional transport of sensible and latent energy is evaluated for three different test sites. Different options on how to apply this correction are presented, and the results are evaluated against independent measurements.
Peter Brugger, Mithu Debnath, Andrew Scholbrock, Paul Fleming, Patrick Moriarty, Eric Simley, David Jager, Jason Roadman, Mark Murphy, Haohua Zong, and Fernando Porté-Agel
Wind Energ. Sci., 5, 1253–1272, https://doi.org/10.5194/wes-5-1253-2020, https://doi.org/10.5194/wes-5-1253-2020, 2020
Short summary
Short summary
A wind turbine can actively influence its wake by turning the rotor out of the wind direction to deflect the wake away from a downstream wind turbine. This technique was tested in a field experiment at a wind farm, where the inflow and wake were monitored with remote-sensing instruments for the wind speed. The behaviour of the wake deflection agrees with the predictions of two analytical models, and a bias of the wind direction perceived by the yawed wind turbine led to suboptimal power gains.
Shivendra Prakash and Corey D. Markfort
Wind Energ. Sci., 5, 745–758, https://doi.org/10.5194/wes-5-745-2020, https://doi.org/10.5194/wes-5-745-2020, 2020
Short summary
Short summary
Bat carcass surveys guided by likely fall zone distributions require accurate descriptions of carcass aerodynamics. This research introduces a new methodology resulting in the first direct measurements of bat carcass drag coefficients. The drag coefficient for three carcasses of three different species was found to be within a range of 0.70–1.23, with a terminal velocity between 6.63 and 17.57 m s−1. This information is useful for assessing the impact of wind farm projects on wildlife.
Jennifer Annoni, Paul Fleming, Andrew Scholbrock, Jason Roadman, Scott Dana, Christiane Adcock, Fernando Porte-Agel, Steffen Raach, Florian Haizmann, and David Schlipf
Wind Energ. Sci., 3, 819–831, https://doi.org/10.5194/wes-3-819-2018, https://doi.org/10.5194/wes-3-819-2018, 2018
Short summary
Short summary
This paper addresses the modeling aspect of wind farm control. To implement successful wind farm controls, a suitable model has to be used that captures the relevant physics. This paper addresses three different wake models that can be used for controls and compares these models with lidar field data from a utility-scale turbine.
Tirtha Banerjee, Peter Brugger, Frederik De Roo, Konstantin Kröniger, Dan Yakir, Eyal Rotenberg, and Matthias Mauder
Atmos. Chem. Phys., 18, 10025–10038, https://doi.org/10.5194/acp-18-10025-2018, https://doi.org/10.5194/acp-18-10025-2018, 2018
Short summary
Short summary
We studied the nature of turbulent transport over a well-defined surface heterogeneity (approximate scale 7 km) comprising a shrubland and a forest in the Yatir semiarid area in Israel. Using eddy covariance and Doppler lidar measurements, we studied the variations in the turbulent kinetic energy budget and turbulent fluxes, focusing especially on transport terms. We also confirmed the role of large-scale secondary circulations that transport energy between the shrubland and the forest.
G. V. Iungo and F. Porté-Agel
Adv. Sci. Res., 10, 71–75, https://doi.org/10.5194/asr-10-71-2013, https://doi.org/10.5194/asr-10-71-2013, 2013
Related subject area
Thematic area: Fluid mechanics | Topic: Wakes and wind farm aerodynamics
Hyperparameter tuning framework for calibrating analytical wake models using SCADA data of an offshore wind farm
Synchronised WindScanner field measurements of the induction zone between two closely spaced wind turbines
Wind farm structural response and wake dynamics for an evolving stable boundary layer: computational and experimental comparisons
An actuator sector model for wind power applications: a parametric study
Wind tunnel investigations of an individual pitch control strategy for wind farm power optimization
The near-wake development of a wind turbine operating in stalled conditions – Part 1: Assessment of numerical models
Data-driven optimisation of wind farm layout and wake steering with large-eddy simulations
Floating wind turbine motion signature in the far-wake spectral content – a wind tunnel experiment
Breakdown of the velocity and turbulence in the wake of a wind turbine – Part 1: Large-eddy-simulation study
Breakdown of the velocity and turbulence in the wake of a wind turbine – Part 2: Analytical modelling
Free-vortex models for wind turbine wakes under yaw misalignment – a validation study on far-wake effects
A method to correct for the effect of blockage and wakes on power performance measurements
Vortex model of the aerodynamic wake of airborne wind energy systems
A new RANS-based wind farm parameterization and inflow model for wind farm cluster modeling
Investigating energy production and wake losses of multi-gigawatt offshore wind farms with atmospheric large-eddy simulation
The wind farm as a sensor: learning and explaining orographic and plant-induced flow heterogeneities from operational data
Multi-point in situ measurements of turbulent flow in a wind turbine wake and inflow with a fleet of uncrewed aerial systems
Addressing deep array effects and impacts to wake steering with the cumulative-curl wake model
Actuator line model using simplified force calculation methods
Brief communication: A clarification of wake recovery mechanisms
Predictive and stochastic reduced-order modeling of wind turbine wake dynamics
Wind turbine wake simulation with explicit algebraic Reynolds stress modeling
Including realistic upper atmospheres in a wind-farm gravity-wave model
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
Filippo Trevisi, Carlo E. D. Riboldi, and Alessandro Croce
Wind Energ. Sci., 8, 999–1016, https://doi.org/10.5194/wes-8-999-2023, https://doi.org/10.5194/wes-8-999-2023, 2023
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
Cited articles
Abdulrahman, M. A.: Wind Farm Layout Optimization Considering Commercial Turbine Selection and Hub Height Variation, PhD thesis, University of Calgary, Calgary, Canada, https://doi.org/10.11575/PRISM/28711, 2017.
Ainslie, J.: Calculating the flowfield in the wake of wind turbines, J. Wind Eng. Ind. Aerod., 27, 213–224, https://doi.org/10.1016/0167-6105(88)90037-2, 1988. a, b
Antonia, R., Zhou, Y., and Matsumura, M.: Spectral characteristics of momentum and heat transfer in the turbulent wake of a circular cylinder, Exp. Therm. Fluid Sci., 6, 371–375, https://doi.org/10.1016/0894-1777(93)90015-B, 1993. a
Bastankhah, M. and Porté-Agel, F.: Experimental and theoretical study of wind turbine wakes in yawed conditions, J. Fluid Mech., 806, 506–541, https://doi.org/10.1017/jfm.2016.595, 2016. a, b, c
Bastankhah, M. and Porté-Agel, F.: A New Miniature Wind Turbine for Wind Tunnel Experiments. Part II: Wake Structure and Flow Dynamics, Energies, 10, 923, https://doi.org/10.3390/en10070923, 2017. a
Brugger, P., Debnath, M., Scholbrock, A., Fleming, P., Moriarty, P., Simley, E., Jager, D., Roadman, J., Murphy, M., Zong, H., and Porté-Agel, F.: Lidar measurements of yawed-wind-turbine wakes: characterization and validation of analytical models, Wind Energ. Sci., 5, 1253–1272, https://doi.org/10.5194/wes-5-1253-2020, 2020. a
Brugger, P., Markfort, C., and Porté-Agel, F.: Improvements to the dynamic wake meandering model by incorporating the turbulent Schmidt number, Zenodo [data set], https://doi.org/10.5281/zenodo.11505778, 2024.
Carbajo Fuertes, F., Markfort, C. D., and Porté-Agel, F.: Wind Turbine Wake Characterization with Nacelle-Mounted Wind Lidars for Analytical Wake Model Validation, Remote Sens.-Basel, 10, 668, https://doi.org/10.3390/rs10050668, 2018. a
Cheng, W.-C. and Porté-Agel, F.: A simple physically-based model for wind-turbine wake growth in a turbulent boundary layer, Bound.-Lay. Meteorol., 169, 1–10, https://doi.org/10.1007/s10546-018-0366-2, 2018. a, b, c, d
Conti, D., Dimitrov, N., Peña, A., and Herges, T.: Probabilistic estimation of the Dynamic Wake Meandering model parameters using SpinnerLidar-derived wake characteristics, Wind Energ. Sci., 6, 1117–1142, https://doi.org/10.5194/wes-6-1117-2021, 2021. a, b
Crank, J. and Nicolson, P.: A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Math. Proc. Cambridge, 43, 50–67, https://doi.org/10.1017/S0305004100023197, 1947. a
España, G., Aubrun, S., Loyer, S., and Devinant, P.: Wind tunnel study of the wake meandering downstream of a modelled wind turbine as an effect of large scale turbulent eddies, J. Wind Eng. Ind. Aerod., 101, 24–33, https://doi.org/10.1016/j.jweia.2011.10.011, 2012. a
Keck, R.-E.: Validation of the standalone implementation of the dynamic wake meandering model for power production, Wind Energy, 18, 1579–1591, https://doi.org/10.1002/we.1777, 2015. a
Keck, R.-E., Veldkamp, D., Wedel-Heinen, J. J., and Forsberg, J.: A consistent turbulence formulation for the dynamic wake meandering model in the atmospheric boundary layer, PhD thesis, DTU Wind Energy, https://orbit.dtu.dk/en/publications/a-consistent-turbulence-formulation-for-the-dynamic-wake-meanderi (last access: 16 March 2022), 2013. a
Keck, R.-E., Mikkelsen, R., Troldborg, N., de Maré, M., and Hansen, K. S.: Synthetic atmospheric turbulence and wind shear in large eddy simulations of wind turbine wakes, Wind Energy, 17, 1247–1267, https://doi.org/10.1002/we.1631, 2014b. a, b
Larsen, G. C., Aagaard Madsen, H., and Bingöl, F.: Dynamic wake meandering modeling, Technical report, Risø National Laboratory, Roskilde, Denmark, https://orbit.dtu.dk/en/publications/dynamic-wake-meandering-modeling (last access: 27 January 2022), 2007. a
Larsen, T. J., Madsen, H. A., Larsen, G. C., and Hansen, K. S.: Validation of the dynamic wake meander model for loads and power production in the Egmond aan Zee wind farm, Wind Energy, 16, 605–624, https://doi.org/10.1002/we.1563, 2013. a
Machefaux, E., Larsen, G. C., Troldborg, N., Gaunaa, M., and Rettenmeier, A.: Empirical modeling of single-wake advection and expansion using full-scale pulsed lidar-based measurements, Wind Energy, 18, 2085–2103, https://doi.org/10.1002/we.1805, 2015. a, b, c, d
Madsen, H. A., Larsen, G. C., Larsen, T. J., Troldborg, N., and Mikkelsen, R.: Calibration and Validation of the Dynamic Wake Meandering Model for Implementation in an Aeroelastic Code, J. Sol. Energ.-T. ASME, 132, 041014, https://doi.org/10.1115/1.4002555, 041014, 2010. a
Mann, J.: The spatial structure of neutral atmospheric surface-layer turbulence, J. Fluid Mech., 273, 141–168, https://doi.org/10.1017/S0022112094001886, 1994. a
Medici, D. and Alfredsson, P. H.: Measurements on a wind turbine wake: 3D effects and bluff body vortex shedding, Wind Energy, 9, 219–236, https://doi.org/10.1002/we.156, 2006. a
Mehta, D., van Zuijlen, A., Koren, B., Holierhoek, J., and Bijl, H.: Large Eddy Simulation of wind farm aerodynamics: A review, J. Wind Eng. Ind. Aerod., 133, 1–17, https://doi.org/10.1016/j.jweia.2014.07.002, 2014. a
Moeng, C.-H. and Sullivan, P. P.: A Comparison of Shear- and Buoyancy-Driven Planetary Boundary Layer Flows, J. Atmos. Sci., 51, 999–1022, https://doi.org/10.1175/1520-0469(1994)051<0999:ACOSAB>2.0.CO;2, 1994. a
Pearson, G., Davies, F., and Collier, C.: An analysis of the performance of the UFAM pulsed Doppler lidar for observing the boundary layer, J. Atmos. Ocean Tech., 26, 240–250, https://doi.org/10.1175/2008JTECHA1128.1, 2009. a, b
Qian, G.-W. and Ishihara, T.: A New Analytical Wake Model for Yawed Wind Turbines, Energies, 11, 665, https://doi.org/10.3390/en11030665, 2018. a
Reinwardt, I., Gerke, N., Dalhoff, P., Steudel, D., and Moser, W.: Validation of wind turbine wake models with focus on the dynamic wake meandering model, J Phys. Conf. Ser., 1037, 072028, https://doi.org/10.1088/1742-6596/1037/7/072028, 2018. a, b
Reynolds, A.: The variation of turbulent Prandtl and Schmidt numbers in wakes and jets, Int. J. Heat Mass Tran., 19, 757–764, https://doi.org/10.1016/0017-9310(76)90128-9, 1976. a, b, c
Taylor, G., Milborrow, D., McIntosh, D., and Swift-Hook, D.: Wake measurements on the Nibe windmills, in: Proceedings of Seventh BWEA Wind Energy Conference, Oxford, 67–73, ISBN 978-0852985762, 1985. a
Taylor, G. I.: Diffusion by continuous movements, P. Lond. Math. Soc., 2, 196–212, 1922. a
Taylor, G. I.: The spectrum of turbulence, P. Roy. Soc. Lond. A. Mat., 164, 476–490, 1938. a
Thøgersen, E., Tranberg, B., Herp, J., and Greiner, M.: Statistical meandering wake model and its application to yaw-angle optimisation of wind farms, J Phys. Conf. Ser., 854, 012017, https://doi.org/10.1088/1742-6596/854/1/012017, 2017. a
Trujillo, J.-J., Bingöl, F., Larsen, G. C., Mann, J., and Kühn, M.: Light detection and ranging measurements of wake dynamics. Part II: two-dimensional scanning, Wind Energy, 14, 61–75, 2011. a
Short summary
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.
The dynamic wake meandering model (DWMM) assumes that wind turbine wakes are transported like a...
Altmetrics
Final-revised paper
Preprint