Articles | Volume 7, issue 2
https://doi.org/10.5194/wes-7-783-2022
© Author(s) 2022. 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-7-783-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
04 Apr 2022
Research article |
| 04 Apr 2022
| 04 Apr 2022
RANS modeling of a single wind turbine wake in the unstable surface layer
DTU Wind Energy, Technical University of Denmark, Risø Campus, Frederiksborgvej 399, 4000 Roskilde, Denmark
Maarten Paul van der Laan
DTU Wind Energy, Technical University of Denmark, Risø Campus, Frederiksborgvej 399, 4000 Roskilde, Denmark
Mark Kelly
DTU Wind Energy, Technical University of Denmark, Risø Campus, Frederiksborgvej 399, 4000 Roskilde, Denmark
Related authors
Mads Baungaard, Takafumi Nishino, and Maarten Paul van der Laan
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-50, https://doi.org/10.5194/wes-2025-50, 2025
Manuscript not accepted for further review
Short summary
Short summary
A systematic comparison between 2D and 3D Reynolds-averaged Navier-Stokes simulations of wind farm flows have been conducted. It is found that the 2D simulations are, at least, two orders of magnitude computationally cheaper than their corresponding 3D simulations, while the predicted farm power is within -30 % to 15 % for all cases considered. The large computational speed-ups and sensible results makes 2D simulations a promising option in the low- to mid-fidelity range.
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.
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.
Tuhfe Göçmen, Filippo Campagnolo, Thomas Duc, Irene Eguinoa, Søren Juhl Andersen, Vlaho Petrović, Lejla Imširović, Robert Braunbehrens, Jaime Liew, Mads Baungaard, Maarten Paul van der Laan, Guowei Qian, Maria Aparicio-Sanchez, Rubén González-Lope, Vinit V. Dighe, Marcus Becker, Maarten J. van den Broek, Jan-Willem van Wingerden, Adam Stock, Matthew Cole, Renzo Ruisi, Ervin Bossanyi, Niklas Requate, Simon Strnad, Jonas Schmidt, Lukas Vollmer, Ishaan Sood, and Johan Meyers
Wind Energ. Sci., 7, 1791–1825, https://doi.org/10.5194/wes-7-1791-2022, https://doi.org/10.5194/wes-7-1791-2022, 2022
Short summary
Short summary
The FarmConners benchmark is the first of its kind to bring a wide variety of data sets, control settings, and model complexities for the (initial) assessment of wind farm flow control benefits. Here we present the first part of the benchmark results for three blind tests with large-scale rotors and 11 participating models in total, via direct power comparisons at the turbines as well as the observed or estimated power gain at the wind farm level under wake steering control strategy.
Maarten Paul van der Laan, Mark Kelly, and Mads Baungaard
Wind Energ. Sci., 6, 777–790, https://doi.org/10.5194/wes-6-777-2021, https://doi.org/10.5194/wes-6-777-2021, 2021
Short summary
Short summary
Wind farms operate in the atmospheric boundary layer, and their performance is strongly dependent on the atmospheric conditions. We propose a simple model of the atmospheric boundary layer that can be used as an inflow model for wind farm simulations for isolating a number of atmospheric effects – namely, the change in wind direction with height and atmospheric boundary layer depth. In addition, the simple model is shown to be consistent with two similarity theories.
Julia Steiner, Emily Louise Hodgson, Maarten Paul van der Laan, Leonardo Alcayaga, Mads Pedersen, Søren Juhl Andersen, Gunner Larsen, and Pierre-Elouan Réthoré
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-200, https://doi.org/10.5194/wes-2025-200, 2025
Preprint under review for WES
Short summary
Short summary
Wake steering is a promising strategy for wind farm optimization, but its success hinges on accurate wake models. We assess models of varying fidelity for the IEA 22 MW turbine, comparing single- and two-turbine cases against LES. All reproduced qualitative trends for power and if applicable loads, but quantitative agreement varied and in general the error increased with increasing yaw angle.
Mads Baungaard, Takafumi Nishino, and Maarten Paul van der Laan
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-50, https://doi.org/10.5194/wes-2025-50, 2025
Manuscript not accepted for further review
Short summary
Short summary
A systematic comparison between 2D and 3D Reynolds-averaged Navier-Stokes simulations of wind farm flows have been conducted. It is found that the 2D simulations are, at least, two orders of magnitude computationally cheaper than their corresponding 3D simulations, while the predicted farm power is within -30 % to 15 % for all cases considered. The large computational speed-ups and sensible results makes 2D simulations a promising option in the low- to mid-fidelity range.
Mark Kelly
Wind Energ. Sci., 10, 535–558, https://doi.org/10.5194/wes-10-535-2025, https://doi.org/10.5194/wes-10-535-2025, 2025
Short summary
Short summary
Industrial standards for wind turbine design are based on 10 min statistics of wind speed at turbine hub height, treating fluctuations as turbulence. But recent work shows that the effect of strong transients is described by flow acceleration. We devise a method to measure the acceleration that turbines encounter; the extremes offshore defy 10 min averages due to various phenomena beyond turbulence. These findings are translated into a recipe supporting statistical design.
Maarten Paul van der Laan, Mark Kelly, Mads Baungaard, Antariksh Dicholkar, and Emily Louise Hodgson
Wind Energ. Sci., 9, 1985–2000, https://doi.org/10.5194/wes-9-1985-2024, https://doi.org/10.5194/wes-9-1985-2024, 2024
Short summary
Short summary
Wind turbines are increasing in size and operate more frequently above the atmospheric surface layer, which requires improved inflow models for numerical simulations of turbine interaction. In this work, a novel steady-state model of the atmospheric boundary layer (ABL) is introduced. Numerical wind turbine flow simulations subjected to shallow and tall ABLs are conducted, and the proposed model shows improved performance compared to other state-of-the-art steady-state models.
Mark Kelly and Maarten Paul van der Laan
Wind Energ. Sci., 8, 975–998, https://doi.org/10.5194/wes-8-975-2023, https://doi.org/10.5194/wes-8-975-2023, 2023
Short summary
Short summary
The turning of the wind with height, which is known as veer, can affect wind turbine performance. Thus far meteorology has only given idealized descriptions of veer, which has not yet been related in a way readily usable for wind energy. Here we derive equations for veer in terms of meteorological quantities and provide practically usable forms in terms of measurable shear (change in wind speed with height). Flow simulations and measurements at turbine heights support these developments.
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.
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.
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.
Tuhfe Göçmen, Filippo Campagnolo, Thomas Duc, Irene Eguinoa, Søren Juhl Andersen, Vlaho Petrović, Lejla Imširović, Robert Braunbehrens, Jaime Liew, Mads Baungaard, Maarten Paul van der Laan, Guowei Qian, Maria Aparicio-Sanchez, Rubén González-Lope, Vinit V. Dighe, Marcus Becker, Maarten J. van den Broek, Jan-Willem van Wingerden, Adam Stock, Matthew Cole, Renzo Ruisi, Ervin Bossanyi, Niklas Requate, Simon Strnad, Jonas Schmidt, Lukas Vollmer, Ishaan Sood, and Johan Meyers
Wind Energ. Sci., 7, 1791–1825, https://doi.org/10.5194/wes-7-1791-2022, https://doi.org/10.5194/wes-7-1791-2022, 2022
Short summary
Short summary
The FarmConners benchmark is the first of its kind to bring a wide variety of data sets, control settings, and model complexities for the (initial) assessment of wind farm flow control benefits. Here we present the first part of the benchmark results for three blind tests with large-scale rotors and 11 participating models in total, via direct power comparisons at the turbines as well as the observed or estimated power gain at the wind farm level under wake steering control strategy.
Jana Fischereit, Kurt Schaldemose Hansen, Xiaoli Guo Larsén, Maarten Paul van der Laan, Pierre-Elouan Réthoré, and Juan Pablo Murcia Leon
Wind Energ. Sci., 7, 1069–1091, https://doi.org/10.5194/wes-7-1069-2022, https://doi.org/10.5194/wes-7-1069-2022, 2022
Short summary
Short summary
Wind turbines extract kinetic energy from the flow to create electricity. This induces a wake of reduced wind speed downstream of a turbine and consequently downstream of a wind farm. Different types of numerical models have been developed to calculate this effect. In this study, we compared models of different complexity, together with measurements over two wind farms. We found that higher-fidelity models perform better and the considered rapid models cannot fully capture the wake effect.
Mark Kelly, Søren Juhl Andersen, and Ásta Hannesdóttir
Wind Energ. Sci., 6, 1227–1245, https://doi.org/10.5194/wes-6-1227-2021, https://doi.org/10.5194/wes-6-1227-2021, 2021
Short summary
Short summary
Via 11 years of measurements, we made a representative ensemble of wind ramps in terms of acceleration, mean speed, and shear. Constrained turbulence and large-eddy simulations were coupled to an aeroelastic model for each ensemble member. Ramp acceleration was found to dominate the maxima of thrust-associated loads, with a ramp-induced increase of 45 %–50 % plus ~ 3 % per 0.1 m/s2 of bulk ramp acceleration magnitude. The LES indicates that the ramps (and such loads) persist through the farm.
Maarten Paul van der Laan, Mark Kelly, and Mads Baungaard
Wind Energ. Sci., 6, 777–790, https://doi.org/10.5194/wes-6-777-2021, https://doi.org/10.5194/wes-6-777-2021, 2021
Short summary
Short summary
Wind farms operate in the atmospheric boundary layer, and their performance is strongly dependent on the atmospheric conditions. We propose a simple model of the atmospheric boundary layer that can be used as an inflow model for wind farm simulations for isolating a number of atmospheric effects – namely, the change in wind direction with height and atmospheric boundary layer depth. In addition, the simple model is shown to be consistent with two similarity theories.
Cited articles
Abkar, M. and Porté-Agel, F.: The effect of atmospheric stability on
wind-turbine wakes: A large-eddy simulation study, J. Phys.: Conf. Ser., 524, 1–9, https://doi.org/10.1088/1742-6596/524/1/012138, 2014. a
Abkar, M. and Porté-Agel, F.: Influence of atmospheric stability on
wind-turbine wakes: A large-eddy simulation study, Phys. Fluids, 27, 035104,
https://doi.org/10.1063/1.4913695, 2015. a, b, c, d
Alinot, C. and Masson, C.: Aerodynamic simulations of wind turbines operating
in atmospheric boundary layer with various thermal stratifications, ASME 2002 Wind Energy Symposium, WIND2002, 206–215, https://doi.org/10.1115/wind2002-42, 2002. a, b
Apsley, D. D. and Castro, I. P.: A limited-length-scale k–ϵ model
for the neutral and stably-stratified atmospheric boundary layer, Bound.-Lay. Meteorol., 83, 75–98, https://doi.org/10.1023/A:1000252210512, 1997. a
Apsley, D. D. and Leschziner, M. A.: A new low-Reynolds-number nonlinear
two-equation turbulence model for complex flows, Int. J. Heat Fluid Flow, 19, 209–222, https://doi.org/10.1016/S0142-727X(97)10007-8, 1998. a
Chougule, A., Mann, J., Kelly, M., and Larsen, G. C.: Simplification and
Validation of a Spectral-Tensor Model for Turbulence Including Atmospheric
Stability, Bound.-Lay. Meteorol., 167, 371–397, https://doi.org/10.1007/s10546-018-0332-z, 2018. a
Crespo, A., Manuel, F., Moreno, D., Fraga, E., and Hernandez, J.: Numerical
analysis of wind turbine wakes, in: Proceedings of the Delphi Workshop on
Wind Energy Applications, 15–25, https://www.academia.edu/15318618/Numerical_Analysis_of_Wind_Turbine_Wakes (last access: 30 March 2022), 1985. a
Doubrawa, P., Quon, E. W., Martinez‐Tossas, L. A., Shaler, K., Debnath, M.,
Hamilton, N., Herges, T. G., Maniaci, D., Kelley, C. L., Hsieh, A. S.,
Blaylock, M. L., Laan, P., Andersen, S. J., Krueger, S., Cathelain, M., Schlez, W., Jonkman, J., Branlard, E., Steinfeld, G., Schmidt, S., Blondel,
F., Lukassen, L. J., and Moriarty, P.: Multimodel validation of single wakes
in neutral and stratified atmospheric conditions, Wind Energy, 23, we.2543,
https://doi.org/10.1002/we.2543, 2020. a, b, c, d, e, f
Dyer, A. J.: A review of flux-profile relationships, Bound.-Lay. Meteorol., 7, 363–372, 1974. a
El-Askary, W. A., Sakr, I. M., AbdelSalam, A. M., and Abuhegazy, M. R.:
Modeling of wind turbine wakes under thermally-stratified atmospheric
boundary layer, J. Wind Eng. Indust. Aerodynam., 160, 1–15, https://doi.org/10.1016/j.jweia.2016.11.001, 2017. a, b
Foken, T.: 50 years of the Monin-Obukhov similarity theory, Bound.-Lay.
Meteorol., 119, 431–447, https://doi.org/10.1007/s10546-006-9048-6, 2006. a
Ghaisas, N. S., Archer, C. L., Xie, S., Wu, S., and Maguire, E.: Evaluation of layout and atmospheric stability effects in wind farms using large-eddy
simulation, Wind Energy, 20, 1227–1240, https://doi.org/10.1002/we.2091, 2017. a
Gryning, S. E., Batchvarova, E., Brümmer, B., Jørgensen, H., and
Larsen, S.: On the extension of the wind profile over homogeneous terrain
beyond the surface boundary layer, Bound.-Lay. Meteorol., 124, 251–268, https://doi.org/10.1007/s10546-007-9166-9, 2007. a
Han, X. X., Liu, D. Y., Xu, C., Shen, W. Z., Li, L. M., and Xue, F. F.: A
BEM-based actuator disk model for wind turbine wakes considering atmospheric
stability, Preprint, 1–24, https://doi.org/10.20944/preprints201907.0029.v1, 2019. a
Hancock, P. E. and Zhang, S.: A Wind-Tunnel Simulation of the Wake of a Large
Wind Turbine in a Weakly Unstable Boundary Layer, Bound.-Lay. Meteorol., 156, 395–413, https://doi.org/10.1007/s10546-015-0037-5, 2015. a
Hansen, K. S., Barthelmie, R. J., Jensen, L. E., and Sommer, A.: The impact of turbulence intensity and atmospheric stability on power deficits due to wind turbine wakes at Horns Rev wind farm, Wind Energy, 15, 183–196,
https://doi.org/10.1002/we.512, 2012. a, b
Hansen, M. O. L.: Aerodynamics of Wind Turbines, 3rd Edn., Routledge, https://doi.org/10.4324/9781315769981, 2015. a
Jonkman, J., Butterfield, S., Musial, W., and Scott, G.: Definition of a 5-MW
Reference Wind Turbine for Offshore System Development, NREL technical
report, NREL, https://doi.org/10.2172/947422, 2009. a, b, c
Kaimal, J. and Finnigan, J. J.: Atmospheric Boundary Layer Flows, Oxford
University Press, https://doi.org/10.1093/oso/9780195062397.001.0001, 1994. a
Kasmi, A. E. and Masson, C.: An extended k2 model for turbulent flow through
horizontal-axis wind turbines, J. Wind Eng. Indust. Aerodynam., 96, 103–122, https://doi.org/10.1016/j.jweia.2007.03.007, 2008. a
Kelly, M. and Gryning, S. E.: Long-Term Mean Wind Profiles Based on Similarity Theory, Bound.-Lay. Meteorol., 136, 377–390, https://doi.org/10.1007/s10546-010-9509-9, 2010. a, b
Li, N., Liu, Y., Li, L., Chang, S., Han, S., Zhao, H., and Meng, H.: Numerical simulation of wind turbine wake based on extended k–ϵ turbulence model coupling with actuator disc considering nacelle and tower, IET Renewable Power Generation, https://doi.org/10.1049/iet-rpg.2020.0416, 2020. a
Machefaux, E., Larsen, G. C., Koblitz, T., Troldborg, N., Kelly, M. C.,
Chougule, A., Hansen, K. S., and Rodrigo, J. S.: An experimental and numerical study of the atmospheric stability impact on wind turbine wakes,
Wind Energy, 19, 1785–1805, https://doi.org/10.1002/we.1950, 2016. a, b, c, d, e, f, g
Magnusson, M. and Smedman, A. S.: Influence of Atmospheric Stability on Wind
Turbine Wakes, Wind Eng., 18, 139–152, 1994. a
Maronga, B. and Reuder, J.: On the formulation and universality of
Monin–Obukhov similarity functions for mean gradients and standard deviations in the unstable surface layer: Results from surface-layer-resolving large-eddy simulations, J. Atmos. Sci., 74, 989–1010, https://doi.org/10.1175/JAS-D-16-0186.1, 2017. a
Monin, A. S. and Obukhov, A. M.: Basic laws of turbulent mixing in the surface layer of the atmosphere, Tr. Akad. Nauk SSSR Geophiz. Inst., 24, 163–187, 1954. a
Okulov, V. L. and Sørensen, J. N.: Maximum efficiency of wind turbine
rotors using Joukowsky and Betz approaches, J. Fluid Mech., 649, 497–508, https://doi.org/10.1017/S0022112010000509, 2010. a
Panofsky, H. and Dutton, J.: Atmospheric Turbulence, John Wiley & Sons, Ltd,
ISBN 0471057142, 1984. a
Pope, S. B.: Turbulent Flows, Cambridge University Press, https://doi.org/10.1017/CBO9780511840531, 2000. a
Porté-Agel, F., Wu, Y. T., Lu, H., and Conzemius, R. J.: Large-eddy
simulation of atmospheric boundary layer flow through wind turbines and wind
farms, J. Wind Eng. Indust. Aerodynam., 99, 154–168, https://doi.org/10.1016/j.jweia.2011.01.011, 2011. a, b
Porté-Agel, F., Bastankhah, M., and Shamsoddin, S.: Wind-Turbine and
Wind-Farm Flows: A Review, vol. 174, Springer Netherlands,
https://doi.org/10.1007/s10546-019-00473-0, 2020. a
Rados, K. G., Prospathopoulos, J. M., Stefanatos, N. C., Politis, E. S.,
Chaviaropoulos, P. K., and Zervos, A.: CFD modeling issues of wind turbine
wakes under stable atmospheric conditions, in: European Wind Energy Conference and Exhibition 2009, EWEC 2009, 6, Marseille, 4085–4092, ISBN 9781615677467, https://www.researchgate.net/publication/237819589_CFD_modeling_issues_of_wind_turbine_wake_under_stable_atmospheric_conditions, (last access: 30 March 2022), 2009. a, b
Réthoré, P.-E.: Wind Turbine Wake in Atmospheric Turbulence,
PhD thesis, Aalborg University, Aalborg, https://orbit.dtu.dk/en/publications/wind-turbine-wake-in-atmospheric-turbulence (last access: 30 March 2022), 2009. a
Réthoré, P.-E., van der Laan, P., Troldborg, N., Zahle, F., and
Sørensen, N. N.: Verification and validation of an actuator disc model, Wind Energy, 17, 919–937, https://doi.org/10.1002/we.1607, 2014. a
Sathe, A., Mann, J., Barlas, T., Bierbooms, W., and van Bussel, G.: Influence
of atmospheric stability on wind turbine loads, Wind Energy, 16, 1013–1032,
https://doi.org/10.1002/we.1528, 2013. a
Sørensen, J. N. and Andersen, S. J.: Validation of analytical body force
model for actuator disc computations, J. Phys.: Conf. Ser., 1618, 1–8, https://doi.org/10.1088/1742-6596/1618/5/052051, 2020. a
Sørensen, J. N. and Kock, C. W.: A model for unsteady rotor aerodynamics,
J. Wind Eng. Indust. Aerodynam., 58, 259–275, https://doi.org/10.1016/0167-6105(95)00027-5, 1995. a
Sørensen, J. N., Nilsson, K., Ivanell, S., Asmuth, H., and Mikkelsen, R. F.: Analytical body forces in numerical actuator disc model of wind turbines,
Renew. Energy, 147, 2259–2271, https://doi.org/10.1016/j.renene.2019.09.134, 2020. a, b
Sørensen, N. N., Bechmann, A., Johansen, J., Myllerup, L., Botha, P.,
Vinther, S., and Nielsen, B. S.: Identification of severe wind conditions
using a Reynolds Averaged Navier-Stokes solver, J. Phys.: Conf. Ser., 75, 012053, https://doi.org/10.1088/1742-6596/75/1/012053, 2007. a
Stull, R. B.: An introduction to boundary layer meteorology, An introduction
to boundary layer meteorology, Kluwer Academic Publishers,
https://doi.org/10.1007/978-94-009-3027-8, 1988. a
Troldborg, N., Sørensen, N. N., Réthoré, P.-E., and van der Laan, M. P.: A consistent method for finite volume discretization of body forces on collocated grids applied to flow through an actuator disk, Comput. Fluids, 119, 197–203, https://doi.org/10.1016/J.COMPFLUID.2015.06.028, 2015. a, b
van der Laan, M. P.: PyWakeEllipSys documentation,
https://topfarm.pages.windenergy.dtu.dk/cuttingedge/pywake/pywake_ellipsys/,
last access: 30 March 2022. a
van der Laan, M. P., Sørensen, N. N., Réthoré, P.-E., Mann, J.,
Kelly, M. C., and Troldborg, N.: The k-ϵ-fp model applied to
double wind turbine wakes using different actuator disk force methods, Wind
Energy, 18, 2223–2240, https://doi.org/10.1002/we.1816, 2015a. a, b
van der Laan, M. P., Sørensen, N. N., Réthoré, P. E., Mann, J.,
Kelly, M. C., Troldborg, N., Schepers, J. G., and Machefaux, E.: An improved
k-ϵ model applied to a wind turbine wake in atmospheric turbulence, Wind Energy, 18, 889–907, https://doi.org/10.1002/we.1736, 2015b. a, b, c
van der Laan, P., Sørensen, N. N., Réthoré, P.-E., Mann, J.,
Kelly, M. C., Troldborg, N., Hansen, K. S., and Murcia, J. P.: The
k-ϵ-fp model applied to wind farms, Wind Energy, 18, 2065–2084,
https://doi.org/10.1002/we.1804, 2015c.
a
van der Laan, M. P., Andersen, S. J., Kelly, M., and Baungaard, M. C.: Fluid
scaling laws of idealized wind farm simulations, J. Phys.: Conf. Ser., 1618, 1–10, https://doi.org/10.1088/1742-6596/1618/6/062018, 2020. a, b, c
Wyngaard, J. C.: Turbulence in the atmosphere, Cambridge University Press,
https://doi.org/10.1017/CBO9780511840524, 2010. a, b
Xie, S. and Archer, C. L.: A Numerical Study of Wind-Turbine Wakes for Three
Atmospheric Stability Conditions, Bound.-Lay. Meteorol., 165, 87–112,
https://doi.org/10.1007/s10546-017-0259-9, 2017. a
Zhang, W., Markfort, C. D., and Porté-Agel, F.: Wind-Turbine Wakes in a
Convective Boundary Layer: A Wind-Tunnel Study, Bound.-Lay. Meteorol., 146, 161–179, https://doi.org/10.1007/s10546-012-9751-4, 2013. a
Short summary
Wind turbine wakes are dependent on the atmospheric conditions, and it is therefore important to be able to simulate in various different atmospheric conditions. This paper concerns the specific case of an unstable atmospheric surface layer, which is the lower part of the typical daytime atmospheric boundary layer. A simple flow model is suggested and tested for a range of single-wake scenarios, and it shows promising results for velocity deficit predictions.
Wind turbine wakes are dependent on the atmospheric conditions, and it is therefore important to...
Altmetrics
Final-revised paper
Preprint