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

Firstly, an atmospheric boundary layer is studied for its ability to represent the lower region of the atmosphere in which wind farms operate. A large-eddy simulation (LES) solver is used to examine the effects of (i) the subgrid-scale model, (ii) the wall model, (iii) t...[ Read more ]

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

Firstly, an atmospheric boundary layer is studied for its ability to represent the lower region of the atmosphere in which wind farms operate. A large-eddy simulation (LES) solver is used to examine the effects of (i) the subgrid-scale model, (ii) the wall model, (iii) the von-Kármán constant and (iv) the grid-cell aspect ratio. It is found that although all of these factors influence the accuracy of the solution, it is the grid-cell aspect ratio that has the greatest effect on the variances of the spanwise and vertical velocity components. In particular, applying nearly isotropic grid cells causes all three components of the velocity variance to match the turbulence scaling laws prescribed by the attached eddy hypothesis. Based on these findings, the LES solver is improved such that it captures all components of the attached eddy hypothesis-based scaling laws, providing a reliable turbulent inflow condition for wind-turbine simulations.

Secondly, the improved LES solver is coupled with an actuator disk model to simulate wind-turbine wakes under various atmospheric boundary layer inflow and tip-speed ratio conditions. It is found that different components of the velocity fluctuations contribute differently towards the far-wake evolution: (i) at low frequencies, e.g. St < 0.3 (St = ƒD/U is the Strouhal number, where ƒ is the frequency, D is the turbine diameter and U is the mean incident velocity), the spanwise (v′) and vertical (w′) velocity fluctuations are responsible for deflecting the wake via the passive wake meandering mechanism, (ii) at 0.1 < St < 1.0 all three components of the velocity fluctuations contribute to turbulent kinetic energy (TKE) generation via convective instabilities but v′ and w′ cause greater TKE generation than streamwise fluctuations u′ of the same magnitude, and (iii) at low frequencies, e.g. St < 0.3, u′ generates thrust fluctuations via fluctuations in the angle-of-attack, which also introduces near-wake corrections in the mean-wake deficit profiles. Simulation- and resolvent-based componentwise input-output analyses are used to explain why v′ and w′ play dominant roles in generating TKE: the convective instabilities in turbine wakes are more receptive to transverse forcing than to streamwise forcing. These results highlight the importance of accounting for the velocity fluctuation components individually when modeling the wake evolution. Another key conclusion is that the wake deflection from the passive wake meandering mechanism and the TKE generation from the convective instability mechanism can be modeled separately, because they mostly occur in different frequency ranges and thus interact mainly via the mean flow.

Thirdly, resolvent analysis is performed on the simulated mean wake flow to exploit the convective instability mechanism for predicting the far-wake turbulence. In the formulation of the resolvent operator, the mean wake flow is assumed to be axisymmetric, with the effects of small-scale flow structures modeled via an eddy-viscosity term. Singular value decomposition of the resolvent operator is then used to identify a set of forcing and response modes ranked by their energy gain. The resolvent gain is found to peak at a Strouhal number of around 0.2 and at an absolute azimuthal wavenumber of 1. The forcing modes are concentrated upstream of the response modes. These findings reveal the role of convective instabilities in generating far-wake turbulence. The eddy-viscosity models enable the response modes to agree reasonably well with modes educed using spectral orthogonal decomposition on the instantaneous wake flow. To summarize, eddy-viscosity- based resolvent analysis can not only capture the role of convective instabilities, but can also predict the energetic structures in the far wake region.

Finally, a comprehensive wake model is developed from the above findings. The scale dependence of the wake-center deflection observed in the LES is incorporated for predicting wake meandering caused by the passive wake meandering mechanism. The dominant role of convective instabilities in generating turbulence is accounted for to predict the TKE generation in the far wake. Compared with its original version, the present wake model significantly improves the predictions of the mean wake evolution, the wake meandering spectra and the TKE spectra. Moreover, the present wake model is efficient in capturing both the static and dynamic wake evolution, making it suitable for real-time calculations of wind farm performance.

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