STUDY ON WAKE MODEL OF WIND TURBINE BASED ON SPARSITY PROMOTING DYNAMIC MODE DECOMPOSITION

Zhang Hu; Xu Chang; Wei Shangshang; Huo Zhihong; Han Xingxing; Xue Feifei

doi:10.19912/j.0254-0096.tynxb.2023-0406

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Acta Energiae Solaris Sinica ›› 2024, Vol. 45 ›› Issue (7) : 681-690. DOI: 10.19912/j.0254-0096.tynxb.2023-0406

STUDY ON WAKE MODEL OF WIND TURBINE BASED ON SPARSITY PROMOTING DYNAMIC MODE DECOMPOSITION

Zhang Hu, Xu Chang, Wei Shangshang, Huo Zhihong, Han Xingxing, Xue Feifei

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Abstract

This study investigates the reduced-order model of wind turbine wakes based on the sparsity promoting dynamic mode decomposition （SPDMD） method using large eddy simulation （LES） results. A comparison is made between the decomposition outcomes obtained from SPDMD and the standard DMD method. The findings demonstrate that the dynamic mode decomposition approach can extract the dynamic characteristics of wake flow, thereby revealing the underlying evolution patterns of wind turbine wakes. The standard DMD method tends to prioritize modes with small scales and high frequencies, whereas the SPDMD method selects large-scale flow features with low frequencies. In comparison to the standard DMD method, the SPDMD approach constructs a reduced-order model of wind turbine unsteady wake fields in a lower-dimensional subspace. By utilizing a smaller number of modes, the SPDMD method improves computational efficiency in the reconstruction and prediction of wind turbine wake fields.

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wind turbines / wakes / dynamic mode decomposition / reduced-order model

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Zhang Hu, Xu Chang, Wei Shangshang, Huo Zhihong, Han Xingxing, Xue Feifei. STUDY ON WAKE MODEL OF WIND TURBINE BASED ON SPARSITY PROMOTING DYNAMIC MODE DECOMPOSITION[J]. Acta Energiae Solaris Sinica. 2024, 45(7): 681-690 https://doi.org/10.19912/j.0254-0096.tynxb.2023-0406

References

[1] SANDERSE B, PIJL S P, KOREN B.Review of computational fluid dynamics for wind turbine wake aerodynamics[J]. Wind energy, 2011, 14(7): 799-819.
[2] STEVENS R J A M, MENEVEAU C. Flow structure and turbulence in wind farms[J]. Annual review of fluid mechanics, 2017, 49: 311-339.
[3] BARTHELMIE R J, HANSEN K, FRANDSEN S T, et al.Modelling and measuring flow and wind turbine wakes in large wind farms offshore[J]. Wind energy, 2009, 12(5): 431-444.
[4] 李雄威, 徐家豪, 朱润泽, 等. 基于偏航尾流模型的风电场功率协同优化研究[J]. 太阳能学报, 2022, 43(10): 144-151.
LI X W, XU J H, ZHU R Z, et al.Study on power collaborative optimization of wind farm based on yaw wake model[J]. Acta energiae solaris sinica, 2022, 43(10): 144-151.
[5] IVANELL S, LEWEKE T, SARMAST S, et al.Comparison between experiments and Large-Eddy Simulations of tip spiral structure and geometry[J]. Journal of physics: conference series, 2015, 625: 012018.
[6] 许昌, 黄海琴, 施晨, 等. 基于LBM-LES方法的典型复杂地形作用下风力机尾流数值模拟[J]. 中国电机工程学报, 2020, 40(13): 4236-4244.
XU C, HUANG H Q, SHI C, et al.Numerical simulation of wind turbine wakes in typical complex terrains based on LBM-LES method[J]. Proceedings of the CSEE, 2020, 40(13): 4236-4244.
[7] GHOREYSHI M, JIRÁSEK A, CUMMINGS R M. Reduced order unsteady aerodynamic modeling for stability and control analysis using computational fluid dynamics[J]. Progress in aerospace sciences, 2014, 71: 167-217.
[8] BRUNTON S L, NOACK B R.Closed-loop turbulence control: progress and challenges[J]. Applied mechanics reviews, 2015, 67(5): 050801.
[9] XIAO D, YANG P, FANG F, et al.Non-intrusive reduced order modelling of fluid-structure interactions[J]. Computer methods in applied mechanics and engineering, 2016, 303: 35-54.
[10] SCHMID P J.Dynamic mode decomposition of numerical and experimental data[J]. Journal of fluid mechanics, 2010, 656: 5-28.
[11] NOACK B R.From snapshots to modal expansions-bridging low residuals and pure frequencies[J]. Journal of fluid mechanics, 2016, 802: 1-4.
[12] TABIB M, SIDDIQUI M S, FONN E, et al.Near wake region of an industrial scale wind turbine: comparing LES-ALM with LES-SMI simulations using data mining (POD)[J]. Journal of physics: conference series, 2017, 854: 012044.
[13] ANDERSEN S J, SØRENSEN J N, MIKKELSEN R F. Turbulence and entrainment length scales in large wind farms[J]. Philosophical transactions series a, mathematical, physical, and engineering sciences, 2017, 375(2091): 20160107.
[14] FORTES-PLAZA A, CAMPAGNOLO F, WANG J, et al.A POD reduced-order model for wake steering control[J]. Journal of physics: conference series, 2018, 1037: 032014.
[15] 寇家庆, 张伟伟. 动力学模态分解及其在流体力学中的应用[J]. 空气动力学学报, 2018, 36(2): 163-179.
KOU J Q, ZHANG W W.Dynamic mode decomposition and its applications in fluid dynamics[J]. Acta aerodynamica sinica, 2018, 36(2): 163-179.
[16] SARMAST S, DADFAR R, MIKKELSEN R F, et al.Mutual inductance instability of the tip vortices behind a wind turbine[J]. Journal of fluid mechanics, 2014, 755: 705-731.
[17] DEBNATH M, SANTONI C, LEONARDI S, et al.Towards reduced order modelling for predicting the dynamics of coherent vorticity structures within wind turbine wakes[J]. Philosophical transactions series a, mathematical, physical, and engineering sciences, 2017, 375(2091): 20160108.
[18] PREMARATNE P, HU H. Analysis of turbine wake characteristics by using dynamic mode decomposition method[C]//Proceedings of the 35th AIAA Applied Aerodynamics Conference. Denver, Colorado, 2017: AIAA2017-4214.
[19] SUN C, TIAN T, ZHU X C, et al.Investigation of the near wake of a horizontal-axis wind turbine model by dynamic mode decomposition[J]. Energy, 2021, 227: 120418.
[20] CASSAMO N, VAN WINGERDEN J W. On the potential of reduced order models for wind farm control: a koopman dynamic mode decomposition approach[J]. Energies, 2020, 13(24): 6513.
[21] JOVANOVIĆ M R, SCHMID P J, NICHOLS J W.Sparsity-promoting dynamic mode decomposition[J]. Physics of fluids, 2014, 26(2): 024301.
[22] GAO M, CAO X Q, LIU B N, et al.Comparison of the atmospheric 200 hPa jet's analyses between proper orthogonal decomposition and advanced dynamic mode decomposition method[J]. Advances in meteorology, 2020, 2020(4): 1-15.
[23] BOYD S, PARIKH N, CHU E, et al.Distributed optimization and statistical learning via the alternating direction method of multipliers[J]. Foundations and trends® in machine learning, 2011, 3(1): 1-122.
[24] VAN DER LAAN M P, SØRENSEN N N, RÉTHORÉ P E, et al. An improved k-ε model applied to a wind turbine wake in atmospheric turbulence[J]. Wind energy, 2015, 18(5): 889-907.
[25] DAI X, XU D, ZHANG M Q, et al.A three-dimensional dynamic mode decomposition analysis of wind farm flow aerodynamics[J]. Renewable energy, 2022, 191: 608-624.