The actuator line method for modeling wind turbine blades in wind farm flow simulations often offers a good compromise between accuracy and computational cost. A variety of methods have been proposed to correct the force prediction by the actuator line near the tip and root due to smearing the force in the flow domain. This article compares the two most commonly used methods (the filtered lifting line and the vortex-based smearing correction) in terms of accuracy, applicability and computational performance. Both corrections perform well for a single turbine, significantly reducing the force and power overprediction. The effect on power is larger than on thrust. Applying the corrections leads to more accurate results even at lower resolutions. The application of the corrections in an ALM simulation of a wind farm with 30 turbines reduces power by up to 10% compared to a case without correction. Different turbines in the farm are affected differently. The improvements in accuracy due to the corrections far outweigh the additional computational cost.

The current change of the Earth's climate necessitates actions to strongly reduce the human carbon footprint. For the energy sector, this implies moving to renewable energy sources like wind. The wind resource is spatially heterogeneous, where wind speeds and power densities are particularly favourable offshore. The favourable offshore wind resource, together with the limited availability of onshore land area for wind energy, motivates the move to offshore wind energy generation. Economic, spatial and environmental considerations suggest clustering wind turbines offshore into wind farms.
Wind turbines clustered in a wind farm operate on average at a lower efficiency than they would achieve in isolation. One major source of this efficiency loss is wake interaction. As wind turbines extract kinetic energy from the wind, they leave behind a region of low wind speed, the so-called wake. When wakes generated by upstream turbines impinge on downstream turbines in the farm, they reduce their power output and thus the overall farm efficiency. In the design phase, the wind farm layout is optimised to minimise wake losses; however, even in an optimal layout wake losses are significant. From the desire to further mitigate the remaining wake losses, the field of wind farm flow control (WFFC) arose, which aims to reduce wake losses by farm-wide coordinated control of the wind turbines.
Wind farm flow control strategies differ based on their working mechanism, e.g. control strategies aim to either reduce the initial wake deficit of upstream turbines by reducing the turbine thrust or redirecting wakes past downstream turbines by intentionally misaligning upstream turbines with the incoming wind direction. A newer category of strategies for WFFC is active wake control (AWC). Compared to the former quasi-steady strategies, AWC strategies are inherently dynamic as their working mechanism relies on unsteady actuation, which aims to trigger underlying instability modes of the wake flow. One of the most recently developed AWC strategies is helix active wake control. It makes use of the individual pitch control capabilities (IPC) of modern wind turbines in order to intentionally force the first instability mode of the wake.
This thesis is concerned with high-fidelity modelling of helix active wake control using large-eddy simulation (LES) of the atmospheric flow, where the effect of IPC is captured by representing the turbine in the LES by means of the actuator line model (ALM). Judging the potential of helix active wake control requires (i) quantifying the arising power-load trade-off, (ii) comparing it to established WFFC strategies like wake steering, and (iii) ultimately testing it in realistic transient atmospheric boundary layers. To this end, the overall objective of this thesis is to
"Assess the performance of helix active wake control in quasi-steady atmospheric boundary layers and develop actuator line model capabilities for its study in coarse grid real weather large-eddy simulations."

In a first step, the sensitivity of helix active wake control to the amplitude of the pitch actuation is quantified for a full wake overlap scenario. It is found that the activation of the control leads to a trade-off between power gain and additional turbine loading in terms of the incurred damage equivalent loads (DEL). While the power gain monotonically increases for pitch amplitudes between one and six degrees, the same trend is observed for the DELs of the actuated turbine. Hence, the value of activating the control and selecting its pitch amplitude setpoint will need to be determined based on a higher-level metric like the current electricity price. 
In a second step, the sensitivity of the power gain achieved with helix active wake control to varying degrees of wake overlap and turbine spacing is compared to wake steering. It is found that wake steering outperforms the helix except for dense spacing combined with full wake overlap. However, when considering a varying wind direction around full wake overlap without an immediate control response, the results suggest that the power gain achieved by the helix control setpoint is more robust.
The previous finding suggests that time-varying wind directions are important for selecting the best control strategy. Hence, in a third step, an actuator line model is implemented into an atmospheric LES code, which allows for driving microscale LES with mesoscale forcing derived from numerical weather prediction models in order to include additional time scales in the problem. The correctness of the ALM implementation is verified with reference to results from four other research LES codes. Additionally, the emphasis is on ensuring accurate thrust and power predictions on coarser LES grids. To this end, the filtered lifting line correction is included in the ALM implementation.
Current corrections for coarse grid ALM-LES, e.g. the filtered lifting line correction, do not consider the complete unsteady problem. Thus, as a last step, we take the IPC actuation underlying helix active wake control as an opportunity to formally investigate unsteadiness in the ALM for scenarios corresponding to unsteady attached flow below stall. By deriving a semi-analytical solution for the two-dimensional "ALM'' its connection to Theodorsen theory is established. Further, this solution allows for determining the optimal kernel width for the unsteady ALM, which is approximately 40% of the chord length and determining bounds of its validity. Importantly, we find that even when using the optimal kernel width, the magnitude of the unsteady force cannot be accurately captured anymore by the ALM if the reduced frequency exceeds k>0.2.
In summary, this thesis contributed to the understanding of under which circumstances the application of helix active wake control for the mitigation of wake effects might be a viable option. Given that the benefits and drawbacks of the helix are at least partially complementary with wake steering control, both control strategies could be seen as pieces of a more comprehensive toolbox of wind farm flow control strategies. The activation of a respective control strategy would then happen only during periods corresponding to its identified favourable conditions. Hence, the model development conducted in the second part of this thesis aims towards building a simulation environment - spanning from mesoscale effects down to airfoil aerodynamics - within which such a selection process of WFFC strategies can be studied in realistic weather conditions.

The actuator line model (ALM) is an approach commonly used to represent lifting and dragging devices like wings and blades in large-eddy simulations (LES). The crux of the ALM is the projection of the actuator point forces onto the LES grid by means of a Gaussian regularisation kernel. The minimum width of the kernel is constrained by the grid size; however, for most practical applications like LES of wind turbines, this value is an order of magnitude larger than the optimal value that maximises accuracy. This discrepancy motivated the development of corrections for the actuator line, which, however, neglect the effect of unsteady spanwise shed vorticity. In this work we develop a model for the impact of spanwise shed vorticity on the unsteady loading of an aerofoil modelled as a Gaussian body force distribution, where the model is applicable within the regime of unsteady attached flow. The model solution is derived both in the time and frequency domain and features an explicit dependence on the Gaussian kernel width. We verify the model with ALM-LES for both pitch steps and periodic pitching. The model solution is compared withTheodorsen theory and validated with both computational fluid dynamics using body fitted grids and experiment. It is concluded that the optimal kernel width for unsteady aerodynamics is approximately 40 % of the chord. The ALM is able to predict the magnitude of the unsteady loading up to a reduced frequency of k ≈ 0.2.

Within a wind farm, each wind turbine extracts kinetic energy from the flow to convert it into electric energy. Unavoidably, this reduces the downstream availability of kinetic energy, diminishing the power generation of turbines operating in the waked region. These wake-induced power losses cumulate throughout the wind farm, posing a risk to its economic feasibility. One method that mitigates these power losses is helix active wake control. By leveraging individual blade pitch control, it induces an uneven thrust distribution over the rotor plane, which rotates either in clockwise (CW) or counterclockwise (CCW) direction around the rotor center. The wake deforms into a helical shape that recovers faster than the wake of a conventionally controlled turbine and thereby increases the total generated power. Notably, the CCW helix consistently outperforms the CW helix across all available studies. This work investigates the physical principles underlying these wake recovery enhancements using large eddy simulations (LES) of a wind turbine exposed to laminar, uniform flow. We observe a spatially coherent helical vortex structure in the wake boundary, which actively transports mean kinetic energy into the wake and, therefore, poses a fundamental contributor to the wake recovery enhancement. The opposing rotational directions of CW and CCW helixes result in distinct interactions of the helical vortex with the hub vortex, leading to different wake recovery mechanisms. In the investigated laminar inflow, the CCW helix has transported 44.8% more mean kinetic energy into the wake than the CW helix up to a streamwise position of 5D, explaining their differing efficacies observed in previous studies.

In recent years, the relevance of the interaction between neighboring wind farms has grown steadily. As one farm extracts energy from the wind, a downstream one can systematically experience lower wind speeds which threatens the economic viability of the farm. Significant progress has been made in understanding these farm-farm wake interactions, but we still lack methodologies to mitigate their undesired effects. In this study, we introduce Active Cluster Wake Mixing (ACWM). This novel method aims to accelerate the recovery of the cluster wake using dynamic control actions: By exciting the thrust of the individual turbines depending on their relative location, we generate non-uniform patterns of energy extraction. Phase offsets between the individual excitation signals propagate these regions through the wind farm. This results in large-scale velocity gradients inside the farm, which also affect the flow in the cluster wake region. An in-depth exploration and optimization of ACWM requires significant computational effort. Therefore, we compare three different wind farm modeling approaches in Large Eddy Simulations (LES) that differ in their computational costs regarding their suitability for further exploration of ACWM. For this purpose, we use an unoptimized ACWM scheme with two different excitation frequencies. For the first time ever we successfully show that ACWM manipulates the flow inside the wind farm with favorable effects on the wake velocity. We also demonstrate that the modeling of cluster wakes is challenging and has a significant effect on the potential gain.

A variety of wind farm control strategies exist in order to reduce unfavorable wake effects in large wind farms. While strategies like wake steering already reached a high maturity level, it is interesting to compare them to more recently proposed strategies. Such a comparison can form the basis for the development of a symbiotic wind farm control toolbox, from which a control strategy is chosen and activated depending on the operating conditions. The present study compares wake steering with helix control across a wide range of turbine spacings and wind directions using large-eddy simulation (LES). The size of the search space is made computationally tractable for LES by adopting a setup based on one physical upstream turbine and a distribution of virtual downstream turbines which do not exert any thrust force. It is found that helix control is beneficial for full wake overlap and turbine spacing of less than six rotor diameters whereas wake steering proves to be optimal further downstream and for partial wake overlap. Furthermore, the results show that the helix control setpoint in the proximity of full wake overlap scenarios is less susceptible to wind direction variations. This finding indicates that the combination of wake steering and helix control has potential for the design of a wind farm controller which is more robust in full wake overlap scenarios and can reduce the need for large yaw offset adjustments.

The development of new wind farm control strategies can benefit from combined analysis of flow dynamics in the farm and the behavior of individual turbines within one simulation environment. In this work, we present such an environment by developing a new coupling between the large-eddy simulation (LES) code GRASP and the multiphysics wind turbine simulation tool OpenFAST via an actuator line model (ALM). In addition, the implementation of the recently proposed filtered actuator line model (FALM) within the coupling is described. The new ALM implementation is cross-verified with results from four other commonly used research LES codes. The results for the blade loads and the near wake obtained with the new coupling are consistent with the other codes. Deviations are observed in the far wake. The results further indicate that the FALM is able to reduce the lift and power overprediction from which the traditional ALM suffers on coarse LES grids. This new simulation environment paves the way for future wind farm simulations under realistic weather conditions by leveraging GRASP's ability to impose data from large-scale meteorological models as boundary conditions.

In most current offshore wind farms, the turbines are controlled greedily, neglecting any coupling by wake effects with other turbines. By neglecting these effects of aerodynamic interactions, the power production performance is substantially reduced. Besides the well-known wake steering and dynamic induction control wake control strategies, a novel wind farm flow control strategy called the Helix approach has been recently proposed to mitigate the impacts of wake effects and optimize wind farm performance. The Helix approach adopts the individual pitch control (IPC) technique to dynamically deform the wake into the helical shape, which induces wake instability and thereby stimulates wake recovery. The first results employing a single-harmonic signal have demonstrated promising enhancement in wake recovery effects. However, more complex signals to potentially improve the effectiveness of the Helix approach have never been studied. This paper explores the potential of using higher-harmonic signals in the Helix approach to further enhance wake mixing. The aeroelastic simulator, OpenFAST, with its recently developed free vortex wake codes is adopted to simulate the dynamic wake evolution. A Fourier stability analysis is used to quantitatively identify the wake breakdown position. Results show that in the baseline case where no Helix signals are implemented, the wake breaks down at 3.25 rotor diameter (D) from the rotor. When using the designed multi-sine Helix signals, the wake breaks down at 1.75 D from the rotor, which is a significant improvement over the breakdown distance at 2.50 D using the conventional single-sine Helix. The earlier wake breakdown indicates faster wake recovery and is to be validated by future higher-fidelity simulation studies.

The performance of wind farms can substantially increase when their individual turbines deviate from their own greedy control strategy and instead also take into account downstream turbines operating in the wake. The helix approach is a recently introduced dynamic wind farm control strategy that tackles this issue by leveraging individual pitch control to accelerate wake recovery. Its effective implementation requires detailed knowledge about the scaling between control input and the resulting power gain and turbine loading across the farm. In the present work this scaling is explored by means of large-eddy simulation of a two-turbine farm in the conventionally neutral atmospheric boundary layer. A parameter sweep for the amplitude of the helix is performed showing monotonous increase of the farm's power output with increasing pitch amplitude within the considered range of zero to six degrees. The scaling of the power gain suggests that a threshold amplitude should be exceeded for effective speed-up of the wake recovery, whereas the damage equivalent loads computed for the turbines indicate an upper limit for the amplitude despite increasing power gains.