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A simple analytical vortex model is presented and used to study an idealized wind turbine rotor in uniform and sheared inflow, respectively. Our model predicts that 1D momentum theory should be applied locally when modelling a non-uniformly loaded rotor in a sheared inflow. Hence the maximum local power coefficient (expressed with respect to the local, upstream velocity) of an ideal rotor is not affected by the presence of shear. We study the interaction between the wake vorticity generated by the rotor and the wind shear vorticity and find that their mutual interaction results in no net generation of axial vorticity: the wake effects and the shear effects exactly cancel each other out. This means that there are no resulting cross-shear-induced velocities and therefore also no cross-shear deflection of the wake in this model.

The power performance of a wind turbine in complex terrain is studied by means of large eddy simulations (LESs). The simulations show that the turbine performance is significantly different compared to what should be expected from the available wind. The reason for this deviation is that the undisturbed flow field behind the turbine is non-homogeneous and therefore results in a very different wake development and induction than seen for a turbine in flat homogeneous terrain.

Blockage effects due to the interaction of five wind turbines in a row are investigated through both Reynolds-averaged Navier–Stokes simulations and site measurements. Since power performance tests are often carried out at sites consisting of several turbines in a row, the objective of this study is to evaluate whether the power performance of the five turbines differs from that of an isolated turbine. A number of simulations are performed, in which we vary the turbine inter-spacing (1.8, 2 and 3 rotor diameters) and the inflow angle between the incoming wind and the orthogonal line to the row (from 0 to 45∘). Different values of the free-stream velocity are considered to cover a broad wind speed range of the power curve. Numerical results show consistent power deviations for all five turbines when compared to the isolated case. The amplitude of these deviations depends on the location of the turbine within the row, the inflow angle, the inter-spacing and the power curve region of operation. We show that the power variations do not cancel out when averaging over a large inflow sector (from −45 to +45∘) and find an increase in the power output of up to +1 % when compared to the isolated case under idealised conditions (neutral atmospheric conditions, no vertical wind shear or ground effects). We simulate power performance “measurements” with both a virtual mast and nacelle-mounted lidar and find a combination of power output increase and upstream velocity reduction, which causes an increase of +4 % in the power coefficient under idealised conditions. We also use measurements from a real site consisting of a row of five wind turbines to validate the numerical results. From the analysis of the measurements, we also show that the power performance is impacted by the neighbouring turbines. Compared to when the inflow is perpendicular to the row, the power output varies by +1.8 % and −1.8 % when the turbine is the most downwind and upwind of the line, respectively.

In order to design future large wind turbines, knowledge is needed about the impact of aero-elasticity on the rotor loads and performance and about the physics of the atmospheric flow surrounding the turbines. The objective of the present work is to study both effects by means of high-fidelity rotor-resolved numerical simulations. In particular, unsteady computational fluid dynamics (CFD) simulations of a 2.3 MW wind turbine are conducted, this rotor being the largest design with relevant experimental data available to the authors. Turbulence is modeled with two different approaches. On one hand, a model using the well-established technique of improved delayed detached eddy simulation (IDDES) is employed. An additional set of simulations relies on a novel hybrid turbulence model, developed within the framework of the present work. It consists of a blend of a large-eddy simulation (LES) model by Deardorff for atmospheric flow and an IDDES model for the separated flow near the rotor geometry. In the same way, the assessment of the influence of the blade flexibility is performed by comparing two different sets of computations. The first group accounts for a structural multi-body dynamics (MBD) model of the blades. The MBD solver was coupled to the CFD solver during run time with a staggered fluid–structure interaction (FSI) scheme. The second set of simulations uses the original rotor geometry, without accounting for any structural deflection. The results of the present work show no significant difference between the IDDES and the hybrid turbulence model. In a similar manner, and due to the fact that the considered rotor was relatively stiff, the loading variation introduced by the blade flexibility was found to be negligible when compared to the influence of inflow turbulence. The simulation method validated here is considered highly relevant for future turbine designs, where the impact of blade elasticity will be significant and the detailed structure of the atmospheric inflow will be important.

We perform large eddy simulation of flow in a complex terrain under neutral atmospheric stratification. We study the self-similar behavior of a turbine wake as a function of varying terrain complexity and perform comparisons with a flat terrain. By plotting normalized velocity deficit profiles in different complex terrain cases, we verify that self-similarity is preserved as we move downstream from the turbine. We find that this preservation is valid for a shorter distance downstream compared to what is observed in a flat terrain. A larger spread of the profiles toward the tails due to varying levels of shear is also observed.

For load calculations on wind turbines it is usually assumed that the turbulence approaching the rotor does not change its statistics as it goes through the induction zone. We investigate this assumption using a nacelle-mounted forward-looking pulsed lidar that measures low-frequency wind fluctuations simultaneously at distances between 0.5 and 3 rotor diameters upstream. The measurements show that below rated wind speed the low-frequency wind variance is reduced by up to 10 % at 0.5 rotor diameters upstream and above rated enhanced by up to 20 %. A quasi-steady model that takes into account the change in thrust coefficient with wind speed explains these variations partly. Large eddy simulations of turbulence approaching an actuator disk model of a rotor support the finding that the slope of the thrust curve influences the low-frequency fluctuations.