Turbulence characterization in the far wake of a wind turbine

The power output and aerodynamic loading of a wind farm depend strongly on the turbulence in the far wake of the individual turbines. Predicting such turbulence is vital to wind-farm optimization but is challenging for existing turbine wake models. To accurately model the far-wake turbulence, it is necessary to understand how turbulence itself is generated in the wake region as well as in the atmospheric flow. Here this challenge is addressed in three successive stages.

In the first stage, a large-eddy simulation (LES) solver is coupled with an actuator-disk model to simulate wind-turbine wakes under various atmospheric inflow and tip-speed conditions. Setting nearly isotropic grid elements and using a Lagrangian-averaged scale-dependent subgrid-scale model are shown to be crucial for capturing all components of the velocity fluctuations as predicted by the attached eddy  hypothesis-based scaling laws, providing a reliable turbulent inflow condition. It is also found that different components of the velocity fluctuations contribute differently to the wake meandering, the turbulent kinetic energy (TKE) generation and the thrust fluctuations. These results highlight the importance of accounting for the velocity fluctuation components individually.

In the second stage, resolvent analysis is performed on the simulated mean wake flow to predict the far-wake energetic structures, which are generated by the convective instability mechanism, and the results are validated against spectral proper orthogonal decomposition. The resolvent gain between the forcing and the response is found to peak at a Strouhal number of 0.2 and at an absolute azimuthal wavenumber of 1. The forcing modes are concentrated upstream of the turbine itself, while the response modes are concentrated in the downstream region. It isfound that forresolvent analysisto correctly predict the energetic structures in the far-wake region, the resolvent operator needs to be augmented with the eddy viscosity. This eddy iscosity is shown to be conveniently calculated based on the mean flow predicted by existing turbine wake models, demonstrating the potential of combining resolvent analysis with existing wake models for computing the far-wake turbulence.

In the third stage, a comprehensive wake model is developed from the above findings. The scale dependence of the wake-center deflection observed in the LES is used to predict the wake meandering caused by the passive wake meandering mechanism. The dominant role of convective instabilities in generating turbulence is accounted for to predict the far-wake TKE eneration.

 Compared with its original version, the proposed model can better predict the mean wake evolution, the wake meandering spectra and the TKE spectra.
Crucially, the proposed model can efficiently capture both the static and
dynamic wake evolution, making it suitable for real-time computations of windfarm performance. Finally,suggestions are made for further  development of the wake model.

In this thesis, the turbulence characteristics in the far wake of wind turbines have been predicted with resolvent analysis and dynamic modeling, based on the far-wake dynamics elucidated by LES. This framework can improve the design and operation of wind farms, even under realistic atmospheric conditions, accelerating our transition towards a ero-carbon world

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