The phenomenon of wake meandering is long known empirically, but has so far not been treated in a satisfactory manner on the wind turbine load modelling side. We present a consistent, physically based theory for wake meandering, which we consider of crucial importance for the overall description of wind turbine loadings in wind farms. In its present version, the model is confined to single wake situations-including a simple heuristic description of wake interaction with a reflecting surface. Contrary to previous attempts to model wind turbine wake loading, the present approach opens for a unifying description in the sense that turbine power and load aspects can be treated simultaneously. This capability is a direct and attractive consequence of the model being based on the underlying physical process, and it potentially opens for optimization of wind farm topology, wind farm operation, as well as control strategies for the individual turbine.The application of the proposed dynamic wake meandering methodology with existing aeroelastic codes is straightforward and does not involve any code modifications. The strategy is simply to embed the combined effect of atmospheric turbulence, added wake turbulence and the intermittent 'turbulence contribution', caused by wake meandering, in files replacing the traditional turbulence file input to aeroelastic computations. Copyright wake profi le is typically assumed Gaussian, 4 and the centreline defi cit decays monotonically with a rate strongly dependent on the ambient turbulence, but also on the turbulence generated by the velocity defi cit profi le itself and the turbulence generated by the mechanical mixing process in the rotor plane. The development of the far wake was modelled with an eddy viscosity model by Ainslie 4 taking into account the ambient turbulence as well as the defi cit-shear-generated turbulence.The problems and uncertainties, by comparing model results with full-scale measurements, were noticed by Taylor et al., 5 based on an investigation where model results were compared with wake measurements on the Nibe 630 kW turbines. He describes that the variations in on-site wind direction shift the wake across the downstream rotor disc, and this will increase the average power output from the downstream turbine measured over some time-a mechanism not taken into account in the modelling. Ainslie 6 discusses the subject in more detail and mentions that wake meandering effects can have considerable infl uence on measured wake defi cits, in particular under non-stable atmospheric conditions. It seems that Ainslie 6 is the fi rst to model the effect from wake meandering on wake defi cits by correlating the wake meandering to the variability in the wind direction. In this way, he computes the averaging of wake defi cits for two full-scale experiments, and the infl uence from the meandering is signifi cant in reducing the depth of the defi cits. 6 Further comparisons of model and experimental results, including the correction for meandering for a number of different ...

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As the major part of new wind turbines are installed in clusters or wind farms, there is a strong need for reliable and accurate tools for predicting the increased loadings due to wake operation and the associated reduced power production. The dynamic wake meandering (DWM) model has been developed on this background, and the basic physical mechanisms in the wake—i.e., the velocity deficit, the meandering of the deficit, and the added turbulence—are modeled as simply as possible in order to make fast computations. In the present paper, the DWM model is presented in a version suitable for full integration in an aeroelastic model. Calibration and validation of the different parts of the model is carried out by comparisons with actuator disk and actuator line (ACL) computations as well as with inflow measurements on a full-scale 2 MW turbine. It is shown that the load generating part of the increased turbulence in the wake is due almost exclusively to meandering of the velocity deficit, which causes “apparent” turbulence when measuring the flow in a fixed point in the wake. Added turbulence, originating mainly from breakdown of tip vortices and from the shear of the velocity deficit, has only a minor contribution to the total turbulence and with a small length scale in the range of 10–25% of the ambient turbulence length scale. Comparisons of the calibrated DWM model with ACL results for different downstream positions and ambient turbulence levels show good correlation for both wake deficits and turbulence levels. Finally, added turbulence characteristics are compared with correlation results from literature.

This paper investigates wake effects on load and power production by using the dynamic wake meander (DWM) model implemented in the aeroelastic code HAWC2. The instationary wind farm flow characteristics are modeled by treating the wind turbine wakes as passive tracers transported downstream using a meandering process driven by the low frequent cross-wind turbulence components. The model complex is validated by comparing simulated and measured loads for the Dutch Egmond aan Zee wind farm consisting of 36 Vestas V90 turbine located outside the coast of the Netherlands. Loads and production are compared for two distinct wind directions-a free wind situation from the dominating southwest and a full wake situation from northwest, where the observed turbine is operating in wake from five turbines in a row with 7D spacing. The measurements have a very high quality, allowing for detailed comparison of both fatigue and min-mean-max loads for blade root flap, tower yaw and tower bottom bending moments, respectively. Since the observed turbine is located deep inside a row of turbines, a new method on how to handle multiple wakes interaction is proposed. The agreement between measurements and simulations is excellent regarding power production in both free and wake sector, and a very good agreement is seen for the load comparisons too. This enables the conclusion that wake meandering, caused by large scale ambient turbulence, is indeed an important contribution to wake loading in wind farms.

Abstract. We show that the upscaling of wind turbines from rotor diameters of 15–20 m to presently large rotors of 150–200 m has changed the requirements for the aerodynamic blade element momentum (BEM) models in the aeroelastic codes. This is because the typical scales in the inflow turbulence are now comparable with the rotor diameter of the large turbines. Therefore, the spectrum of the incoming turbulence relative to the rotating blade has increased energy content on 1P, 2P, …, nP, and the annular mean induction approach in a classical BEM implementation might no longer be a good approximation for large rotors. We present a complete BEM implementation on a polar grid that models the induction response to the considerable 1P, 2P, …, nP inflow variations, including models for yawed inflow, dynamic inflow and radial induction. At each time step, in an aeroelastic simulation, the induction derived from a local BEM approach is updated at all the stationary grid points covering the swept area so the model can be characterized as an engineering actuator disk (AD) solution. The induction at each grid point varies slowly in time due to the dynamic inflow filter but the rotating blade now samples the induction field; as a result, the induction seen from the blade is highly unsteady and has a spectrum with distinct 1P, 2P, …, nP peaks. The load impact mechanism from this unsteady induction is analyzed and it is found that the load impact strongly depends on the turbine design and operating conditions. For operation at low to medium thrust coefficients (conventional turbines at above rated wind speed or low induction turbines in the whole operating range), it is found that the grid BEM gives typically 8 %–10 % lower 1 Hz blade root flapwise fatigue loads than the classical annular mean BEM approach. At high thrust coefficients that can occur at low wind speeds, the grid BEM can give slightly increased fatigue loads. In the paper, the implementation of the grid-based BEM is described in detail, and finally several validation cases are presented. Comparisons with blade loads from full rotor CFD, wind tunnel experiments and a field experiment show that the model can predict the aerodynamic forces in half-wake, yawed flow, dynamic inflow and turbulent inflow conditions.