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Turbulent wakes are often characterized by dominant coherent structures over disparate scales. Dynamics of their behaviour can be attributed to interscale energy dynamics and triadic interactions. We develop a methodology to quantify the dynamics of kinetic energy of specific scales. Coherent motions are characterized by the triple decomposition and used to define mean, coherent and random velocity. Specific scales of coherent structures are identified through dynamic mode decomposition, whereby the total coherent velocity is separated into a set of velocities classified by frequency. The coherent kinetic energy of a specific scale is defined by a frequency triad of scale-specific velocities. Equations for the balance of scale-specific coherent kinetic energy are derived to interpret interscale dynamics. The methodology is demonstrated on three wake flows: (i)$${Re}=175$$flow over a cylinder; (ii) a direct numerical simulation of$${Re}=3900$$flow over a cylinder; and (iii) a large-eddy simulation of a utility-scale wind turbine. The cylinder wake cases show that energy transfer starts with vortex shedding and redistributes energy through resonance of higher harmonics. The scale-specific coherent kinetic energy balance quantifies the distribution of transport and transfer among coherent, mean and random scales. The coherent kinetic energy in the rotor scales and the hub vortex scale in the wind turbine interact to produce new scales. The analysis reveals that vortices at the blade root interact with the hub vortex formed behind the nacelle, which has implications for the proliferation of scales in the downwind near wake.
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Assessment of scale interactions associated with wake meandering using bispectral analysis methodologies
Large atmospheric boundary layer fluctuations and smaller turbine-scale vorticity dynamics are separately hypothesized to initiate the wind turbine wake meandering phenomenon, a coherent, dynamic, turbine-scale oscillation of the far wake. Triadic interactions, the mechanism of energy transfers between scales, manifest as triples of wavenumbers or frequencies and can be characterized through bispectral analyses. The bispectrum, which correlates the two frequencies to their sum, is calculated by two recently developed multi-dimensional modal decomposition methods: scale-specific energy transfer method and bispectral mode decomposition. Large-eddy simulation of a utility-scale wind turbine in an atmospheric boundary layer with a broad range of large length-scales is used to acquire instantaneous velocity snapshots. The bispectrum from both methods identifies prominent upwind and wake meandering interactions that create a broad range of energy scales including the wake meandering scale. The coherent kinetic energy associated with the interactions shows strong correlation between upwind scales and wake meandering.
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- Award ID(s):
- 2136371
- PAR ID:
- 10487172
- Publisher / Repository:
- Theoretical and Applied Mechanics Letters
- Date Published:
- Journal Name:
- Theoretical and Applied Mechanics Letters
- ISSN:
- 2095-0349
- Page Range / eLocation ID:
- 100497
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.taml.2024.100497
