Claudia Muscari

Wind plays a fundamental role in the energy transition and, by 2050, is expected to be the main energy source in the European Union. Trends in the field include increasing the dimension of the rotors and clustering into wind farms. The area of fluid downstream of a wind turbine is called a wake and is mainly characterized by a wind velocity deficit and increased turbulence intensity. Therefore, clustering wind turbines calls for an effort to better understand wake dynamics and account for wake interaction in order to maximize the power production and the turbines’ lifetime.

Wind Farm control is the branch of wind energy that pursues these objectives by coordinating the turbines’ actions. Shifting from greedy control (operating each turbine at its individual optimum) to more sophisticated strategies significantly increases the energy yield and reduces structural loads.

This thesis focuses on dynamic induction control for power maximization. Dynamic induction control consists of periodically varying the induction factor, generally by means of blade pitch actuation, in order to enhance the mixing in the wake and accelerate the velocity recovery. The two techniques currently dominating the field are the pulse and the helix. They rely on sinusoidal excitations of the blades’ collective and individual pitch, respectively. Despite a large number of numerical and experimental tests and, as of late, linear stability analyses, incomplete knowledge of the physics of manipulated wakes prevents the community from embedding dynamic induction control into analytical control-oriented models. This thesis addresses this gap. The thesis objective was formalized as:
"Development of numerical methods reliably modeling wind turbine wake dynamics as a tool for optimized solutions of wind farm control."

The research work was conducted over two main phases: preparation of the numerical framework and characterization of dynamically manipulated wind turbine wakes. The first sub-question related to the development part was: When does the accuracy obtainable by coupling high fidelity computational fluid dynamics and computational structural dynamics models justify the increased computational cost?

This question is motivated by the trend of increasing rotor dimensions: the bigger the blades become, the higher their flexibility and its effect on the aero-servo-elastic performance of the rotor. To answer the question, we tested the coupling between the state-of-the-art high-fidelity framework for wind turbines and farms aerodynamics SOWFA and the linear structural model from the FAST suite, ElastoDyn. The object of the simulations was a wind tunnel scaled model (1:75) of the DTU 10MW turbine. The reference data was obtained during the UNAFLOW project (2018). Experiments were carried out in the PoliMi Wind Tunnel boundary layer section with different operational parameters. The study did not result in general guidelines but gave a good indication of whether or not we needed to account for flexibility effects in the next research steps. In particular, we concluded that if tip deflections remain under 4.2% of the blade length, flexibility has no noticeable effect on the wake description. This notion guided the first methodological choice not to consider blade flexibility in the following. A further step in the definition of the framework was to focus on the turbine model and ascertain its capability to deliver reliable results. The actuator line model has been the go-to approach for wind turbines and (small) wind farm simulations in academic contexts for more than a decade.

The second research question in this thesis was: What are the limitations of actuator line models for wind turbines, and how can we address them?

The motivation for asking and answering this question is that using different actuator line models and, sometimes, even different users using the same model can lead to very different results. No consensus has been reached over important issues, such as evaluating the free-stream velocity and choosing the width of the smearing function used to project volume forces into the computational domain. The thesis discusses how these issues are connected and proposes an alternative approach to velocity sampling. From comparison with the pre-existing methods, the conclusion is that the results obtainable with our approach are more independent of the smearing function width and better match a reference power curve. However, the thrust curve, which, for its connection to the wake, is very important for wind farm applications, is not as closely matched. A more high-level conclusion is that, even if the actuator line guarantees the best trade-off between accuracy and computational efficiency for the simulation of wind turbine wakes, its formulation should be revised at its core. The insight coming from the development phase converged into the subsequent characterization study. However confident we can be in our high-fidelity computational framework, it is clear that it cannot be directly used for the optimization of wind farm control strategies as this should, ideally, happen in real-time.

This motivates the final question which is: Can we leverage the amount of data obtainable from the high fidelity simulations to characterize manipulated wake behavior and embed this knowledge into control-oriented models?

High-fidelity actuator line simulations were ran in both idealized and realistic atmospheric conditions and with both standard turbine-level control and dynamic induction control. Wake velocity and pressure data was collected over a significant time range to produce a proper data base. The data was organised into snapshot matrices and fed to a dynamic mode decomposition (DMD) algorithm. DMD splits the data into purely spatial modes, scalar amplitudes, and purely temporal signals. This makes it suitable for the identification of dominant frequencies. Its applications to fluid dynamics in general and wind energy, in particular, include diagnostic and future state prediction.

With this approach, a reduced order model is obtained, which, for the analysed cases, is able to reconstruct the full flow field with a maximum 9% relative root mean square error, with only two modes. This is sufficient to answer positively to the formulated research question, but the analysis of the derived wake dynamic modes leads to the following additional conclusions.

As in previous studies, the helix proves to be a more effective power maximization technology than the pulse (given the same signal parameters), particularly in its counter clock-wise variant. The dominant modes are characterized by a frequency equal to the pitch excitation one and its harmonics. Temporal amplitude and spatial decay of the helix modes are a function of turbulence intensity. Using the helix always leads to farm power gains for neutral stability of the atmospheric boundary layer and turbulence intensity levels that are representative of offshore operation. The optimal frequency is in a distinct Strouhal number range (0.25 to 0.4) but ultimately depends on both the inflow and the considered downstream distance. The thesis, finally, discusses a few hypothesis on how the helix triggers wake destabilization.

To sum up, this thesis contributes to the state of the art of wind farm control by providing a reliable (stable and accurate) numerical framework for high-fidelity simulations and advancing the understanding of dynamic induction control techniques such as the helix and the pulse.