A three-dimensional dynamic mode decomposition analysis of wind farm flow aerodynamics

Dai, Xuan; Xu, Da; Zhang, Mengqi; Stevens, Richard J. A. M.

doi:10.1016/j.renene.2022.03.160

Cited by 11 publications

(5 citation statements)

References 57 publications

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“…where αi is the amplitude of ith DMD mode. 1 X is written in the following form: (15) Equation (15) shows the development of the wakefield is controlled by the Vand matrix, and Vand contains r eigenvalues {μ1, μ2, …μr} of the similarity matrix A .…”

Section: Dynamic Mode Decompositionmentioning

confidence: 99%

“…The tradeoff is a higher loss of accuracy in the approximation of the original wakefield. And the loss function is defined as [15]: In Figure 3, the horizontal axis is the amount of dynamic modes chosen by the SPDMD method after optimization, and the vertical axis is the approximate accuracy loss of the original wakefield. The greater the number of dynamical modes retained, the higher the accuracy of the approximation to the original wakefield.…”

Section: Analysis Of the Modementioning

confidence: 99%

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Sparsity Promoting Dynamic Mode Decomposition for Data-Driven Modeling of Wind Turbine Wake

Zhang

Chang

Wei

et al. 2023

J. Phys.: Conf. Ser.

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High-fidelity numerical simulation is suitable for analyzing the complex unsteady flow field dynamics of wind turbines. For a better understanding of these flow characteristics, the dynamic mode decomposition method can be used to carry out a reduced-order model study on the wakefield of wind turbines based on large-eddy simulations (LES) numerical simulation. In this paper, we abstract material dynamic information from the wakefield of the wind turbine by applying the sparsity-promoting dynamic mode decomposition (SPDMD) method, and the decomposition results are contrasted with the standard dynamic mode decomposition (DMD) method. Indicated that both mode decomposition methods can abstract the dynamic characteristics of wake and reveal the development and variation law of wind turbine wake. However, the frequency and spatial structure of the selected modes are different. For the purpose of demonstrating the extraction impact of the DMD/SPDMD method on the wakefield of wind turbines, DMD/SPDMD reduced-order models are established respectively. The result indicated that the relatively limited number of SPDMD modes is adequate to validly rehabilitate the wakefield of the unabridged wind turbine while standard DMD methods prerequisite more decomposition modes. Therefore, compared with the standard DMD method, the SPDMD method has strong robustness in mode selection, eliminates the feature information that contributes weakly to the flow, and has a smaller performance loss in the reconstruction of the wakefield of the wind turbine. The consumption of computing resources is greatly reduced.

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Section: Dynamic Mode Decompositionmentioning

confidence: 99%

Section: Analysis Of the Modementioning

confidence: 99%

Sparsity Promoting Dynamic Mode Decomposition for Data-Driven Modeling of Wind Turbine Wake

Zhang

Chang

Wei

et al. 2023

J. Phys.: Conf. Ser.

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show abstract

“…Optimizing the layout of wind turbines [18] can reduce the impact of wake effects. Standard turbine layouts include series arrangement [19], horizontal offset [20], and vertical offset [21] arrangements. In studies focusing on series arrangements, Dou et al [19] experimented by adjusting the streamwise spacing between upstream and downstream turbines, concluding that increasing the spacing accelerates wake recovery.…”

Section: Introductionmentioning

confidence: 99%

“…Zhang et al [31] introduced vertical axis wind turbines into conventional arrayed wind farms and found that this vertically misaligned arrangement improved power output by 13.1% compared to traditional layouts. Dai et al [21] studied horizontally and vertically aligned or misaligned arrangements, and they concluded that layouts with misalignment in both horizontal and vertical directions are most favorable for increasing wind farm power output. Furthermore, the introduction of small wind turbines alters ground roughness, which has a significant impact on wake behavior.…”

Section: Introductionmentioning

confidence: 99%

Experimental Study of Wake Evolution under Vertical Staggered Arrangement of Wind Turbines of Different Sizes

Zhang,

Feng,

Zhao

et al. 2024

JMSE

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During the expansion of a wind farm, the strategic placement of wind turbines can significantly improve wind energy utilization. This study investigates the evolution of wake turbulence in a wind farm after introducing smaller wind turbines within the gaps between larger ones, focusing on aspects such as wind speed, turbulence intensity, and turbulence integral length scale. The flow field conditions are described using parameters like turbulence critical length and power spectral density, as determined through wind tunnel experiments. In these experiments, a single large wind turbine model and nine smaller wind turbine models were used to create a small wind farm unit, and pressure distribution behind the wind turbines was measured under various operating conditions. The results indicate that downstream wind speed deficits intensify as the number of small wind turbines in operation increases. The impact of these smaller turbines varies with height, with a relatively minor effect on the upper blade tip and increasingly adverse effects as you move from the upper blade tip to the lower blade tip. Through an analysis of power spectral density, the contribution of vortex motion to wake turbulence kinetic energy is further quantified. In the far wake region, the number of small wind turbines has a relatively small impact on wind speed fluctuations.

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“…The axial force in centrifugal pumps demonstrates pronounced non-stationary characteristics throughout its spatiotemporal evolution, involving coherent structures of different scales and diverse morphologies [16][17][18]. To gain deeper insight into the evolutionary mechanism of axial forces in centrifugal pumps, it is imperative to utilize low-dimensional system decomposition techniques for extracting coherent structures at various scales to facilitate analysis.…”

Section: Introductionmentioning

confidence: 99%

Based on Wavelet and Windowed Multi-Resolution Dynamic Mode Decomposition, Transient Axial Force Analysis of a Centrifugal Pump under Variable Operating Conditions

Jiang,

Dong,

et al. 2023

Energies

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This study analyzes the transient axial force of a centrifugal pump under variable operating conditions using wavelet analysis and a novel technique called windowed multi-resolution dynamic mode decomposition (wmrDMD). Numerically simulating the sampled time series allows the reconstruction of the impeller’s axial force information, providing validation for this innovative data-driven analysis technique. The comparison between the reconstructed results and the original axial force data demonstrates a remarkable agreement, as all data points exhibit error values below 2.49%. The wmrDMD technique systematically decomposes the impeller’s axial force field into dynamically significant modes across various time scales. Removing the mean flow field in this study resolves the transient motion of the impeller’s axial force, facilitating the identification of positions with high-frequency axial force oscillations and fluctuations in intensity amplitude. The high-frequency axial force of the impeller exhibits stable periodic variations within the operating range of 1.0nr-1.0Qr, whereas the changes are insignificant within the range of 0.4nr-0.4Qr. However, within the operating range of 1.0nr-0.4Qr, both the position and intensity amplitude of the axial force exhibit significant variations without a stable trend. Furthermore, cross-wavelet and wavelet coherence analyses reveal that within the operating range of 0.4nr-0.4Qr, the axial forces on the front and rear cover plates show the strongest correlation at the periodic scale. Within the operating range of 1.0nr-1.0Qr, the next highest correlation is observed, whereas the correlation is lowest within the 1.0nr-0.4Qr operating range.

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A three-dimensional dynamic mode decomposition analysis of wind farm flow aerodynamics

Cited by 11 publications

References 57 publications

Sparsity Promoting Dynamic Mode Decomposition for Data-Driven Modeling of Wind Turbine Wake

Sparsity Promoting Dynamic Mode Decomposition for Data-Driven Modeling of Wind Turbine Wake

Experimental Study of Wake Evolution under Vertical Staggered Arrangement of Wind Turbines of Different Sizes

Based on Wavelet and Windowed Multi-Resolution Dynamic Mode Decomposition, Transient Axial Force Analysis of a Centrifugal Pump under Variable Operating Conditions

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