The engineering flow models used to estimate annual energy production (AEP) in offshore wind farm layout optimization typically assume inflow homogeneity over the model domain. This assumption lies in contrast with observations of horizontal wind speed gradients in coastal regions where many offshore wind farms are being constructed. Accounting for wind speed gradients in wind farm models may lead to reduced uncertainty in AEP estimates and reduced bias in optimized wind farm layouts. This thesis examines whether accounting for horizontal wind speed gradients with WRF simulated wind resource inputs to engineering wake models impacts AEP prediction for a wind farm cluster in the Irish Sea by comparing results with calculation methods which assume homogeneous inflow. Analysis of a wake free two turbine case under a gradient shows that the assumption of homogeneity leads to errors with the true power which a gradient based method is able to predict. Despite this, results suggest that the overall impact of modelling wind speed gradients on AEP predictions in the Irish Sea cluster is small. Homogeneous and gradient methods using the same wind resource data predicted differences in AEP of between 0.1% and 0.75%, with most cases below 0.75%. Filtering by wind direction reveals AEP differences larger than the assumed wake model uncertainty for two sectors with inflow from land. The AEP contribution from sectors with mean wind speed gradients is limited by low frequencies and mean wind speeds. Additionally, positive and negative power differences predicted by homogeneous and gradient methods were found to balance over the year.

Wind turbine wakes cause significant reductions in power production and increased fatigue damage for downwind turbines. Thus, they affect the wind levelized cost of energy. Computational Fluid Dynamics (CFD) can be used to quantify the wake characteristics, whereby Reynolds-averaged Navier-Stokes (RANS) has the most potential for industrial applications due to the relatively low computational costs. However, RANS models all turbulence scales, usually done by the linear κ-ε turbulence model, which has significant shortcomings in accurately representing the turbulence characteristics in wind turbine wake applications. This results in an underprediction of the wake deficit. Key reasons for these shortcomings are that the eddy viscosity assumption is not valid in the near wake and that the anisotropic Reynolds stresses are not properly modeled. Also, the direct effects of the turbine forcing is not incorporated in the transport equations. To address for these shortcomings, machine learning can be used to enhance the turbulence model with data-driven corrections. Recent developments showed for fundamental 2D flow cases that a novel algorithm referred to as SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) can be used to discover sparse algebraic turbulence model corrections. These corrections could lead to improved mean-flow fields when trained on high-fidelity data. Disadvantages of SpaRTA are however that it can only cope with a limited input feature set and that the models have difficulty generalizing towards multiple flow regions simultaneously (e.g. free-stream and wake region). To help resolve these disadvantages, mutual information, which is a measure from information theory that quantifies the general dependency between variables, is used to a priori measure the importance of a large number of features to the turbulence model corrections. As a result, the most important features can be used for correction model construction. In addition to this, to improve the model predictions in the turbine's wake, only the data samples located in the wake regions are used for training, discarding the free-stream data. Given that these data are discarded, it cannot be guaranteed that the correction models fit the trends in the free-stream. The correction models must therefore be neutralized by a newly constructed sparse algebraic logistic regression model, which distinguishes the wake from the free-stream region. The data used in this research consists of three time-averaged LES (Large Eddy Simulation) cases with multiple turbines on wind tunnel scale, under neutral conditions. This thesis shows that mutual information can detect most of the essential features, which leads to a good match between the model predictions and the corrections derived from high-fidelity data. Discarding the free-stream samples during model training leads to a further reduction in error in the wake region, both in mean-squared as maximum-squared error of the correction terms. By implementing the constructed algebraic models into CFD, significant improvements in mean-flow fields are obtained compared to the linear κ-ε turbulence model. Nevertheless, there remains room for improvement as well as further research. Although the mean-flow fields match the high-fidelity data in the near wake closely, a discrepancy remains in the far wake.

The recurred idea of developing multi-rotor wind turbines has led to the need of more accurate surrogate wake models which allow for a fast annual energy production (AEP) calculation and further understanding of the aerodynamic power losses of multi-rotor wind turbines. The present thesis develops a surrogate wake model of a multi-rotor-two turbine validated against computational fluid dynamics (CFD) simulations of type RANS-AD. The outcome is a superposition model of an analytical representation of the wake which base function coefficients are stored in look-up tables as a function of the wind inflow conditions affecting the turbine. The derived surrogate model is able to predict the overall wind farm efficiency with more than 90% accuracy while compared to RANS-AD models. Towards the end of the thesis, a comparison between a single-rotor wind farm of 18 V29 turbines and a multi-rotor wind farm composed by nine 2R-V29 turbines (hypothetical turbine) is evaluated through RANS-AD simulations within the same wind-farm area. The energy ouput showed to be highly dependent on the wind-farm geometry, and the wind direction average suggest that 5% more energy yield is obtained from the multi-rotor-farm for velocities below rated speed.

With the growing global utilisation of wind energy, lowering of its levelised cost of energy is pursued. This effort is hindered by wind turbine wakes and their detrimental effects on wind farm profitability. Most currently researched wake mitigation methods are based on wind farm system-level interventions, and there is a research gap on individual wind turbine design wake alleviation measures. This thesis investigates the wake-diffusion rotor concept, a wind turbine design with an outboard shifted thrust distribution along the blade, and its effects on wake mitigation and power generation in wind farms. Three wind turbine rotors with equivalent thrust coefficient are modelled as actuator disks in a RANS CFD software PyWakeEllipSys, corresponding to an inboard shifted thrust distribution, a conventional thrust distribution, and an outboard shifted thrust distribution representing the wake-diffusion rotor concept. Investigated scenarios include a single wind turbine and rows of three and ten wind turbines aligned to the inflow. Compared to the baseline case, outboard thrust distribution produces lower wake velocity deficits, increased momentum transfer and increased turbulence generation. The wake-diffusion rotor concept increases the wind farm power generation by 3.8 % and 2.5 % in the three and ten wind turbine row scenarios respectively, with the largest relative gain in wind turbine power of 13.9 % for the second wind turbine in the row. Consecutive wind turbines in the row experience diminishing gains. The inboard shifted thrust distribution had opposite effects for all of these aspects. The benefits in wake mitigation and power generation in wind farms from using the wake-diffusion rotor concept are concluded to come from higher turbulence mixing caused by the outboard shifted thrust distribution. Recommendations on its use for maximum effectiveness are given. Future research could focus on the design implementation of this concept, investigate combinations with other wake mitigation methods and perform parametric wind farm AEP studies.

This thesis sets out to improve the physical grounding and predictive accuracy of cumulative wake effect modelling within wind farms with yawed turbines. It derives an analytical solution for the lateral velocity field within a wind farm and compares its predictions to those of computational fluid dynamics. A parametric study is performed using a Reynolds-averaged Navier-Stokes (RANS) solver with the k-ε-fP turbulence model, Joukowsky rotor-based actuator disc, and neutral log-law inflow within the PyWakeEllipSys framework to determine the effects of yaw angle, thrust coefficient, and turbulence intensity on the lateral wake. The results of this parametric study are used to solve an approximate form of conservation of mass and momentum in the lateral direction for a turbine within a wind farm. The solution is an explicit equation predicting the lateral velocity distribution and lateral wake deflection within a wind farm of arbitrary layout and with arbitrarily yawed turbines. It also provides a first mathematical proof of secondary wake steering. The solution is implemented in Python and used to predict the velocity distributions in several wind farm cases, including for a single turbine, a two-turbine arrangement, and two wind farm cases with aligned and staggered layouts. These predictions are then compared against those of the RANS setup. The model significantly overestimates wake deflections unless corrected to neglect the near wake, but the corrected version shows promise, particularly in predicting wind farm power of the staggered layout, where the prediction is 19% closer to the RANS result than the prediction that considers lateral velocities equal to zero.