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 ...

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.

In this paper, the impact of atmospheric stability on a wind turbine wake is studied experimentally and numerically. The experimental approach is based on full-scale (nacelle based) pulsed lidar measurements of the wake flow field of a stall-regulated 500 kW turbine at the DTU Wind Energy, Risø campus test site. Wake measurements are averaged within a mean wind speed bin of 1 m s 1 and classified according to atmospheric stability using three different metrics: the Obukhov length, the Bulk-Richardson number and the Froude number. Three test cases are subsequently defined covering various atmospheric conditions. Simulations are carried out using large eddy simulation and actuator disk rotor modeling. The turbulence properties of the incoming wind are adapted to the thermal stratification using a newly developed spectral tensor model that includes buoyancy effects. Discrepancies are discussed, as basis for future model development and improvement. Finally, the impact of atmospheric stability on large-scale and small-scale wake flow characteristics is presently investigated.

The present study investigates a new approach for capturing the effects of atmospheric stability on wind turbine wake evolution and wake meandering by using the dynamic wake meandering model. The most notable impact of atmospheric stability on the wind is the changes in length and velocity scales of the atmospheric turbulence. The length and velocity scales in the turbulence are largely responsible for the way in which wind turbine wakes meander as they convect downstream. The hypothesis of the present work is that appropriate turbulence scales can be extracted from the oncoming atmospheric turbulence spectra and applied to the dynamic wake meandering model to capture the correct wake meandering behaviour. The ambient turbulence in all stability classes is generated using the Mann turbulence model, where the effects of non-neutral atmospheric stability are approximated by the selection of input parameters.In order to isolate the effect of atmospheric stability, simulations of neutral and unstable atmospheric boundary layers using large-eddy simulation are performed at the same streamwise turbulence intensity level. The turbulence intensity is kept constant by calibrating the surface roughness in the computational domain. The changes in the turbulent length scales due to the various atmospheric stability states impact the wake meandering characteristics and thus the power generation by the individual turbines.The proposed method is compared with results from both large-eddy simulation coupled with an actuator line model and field measurements, where generally good agreement is found with respect to the velocity, turbulence intensity and power predictions.

A wind farm layout optimization framework based on a multi-fidelity optimization approach is applied to the offshore test case of Middelgrunden, Denmark as well as to the onshore test case of Stag Holt -Coldham wind farm, UK. While aesthetic considerations have heavily influenced the famous curved design of the Middelgrunden wind farm, this work focuses on demonstrating a method that optimizes the profit of wind farms over their lifetime based on a balance of the energy production income, the electrical grid costs, the foundations cost, and the cost of wake turbulence induced fatigue degradation of different wind turbine components. A multi-fidelity concept is adapted, which uses cost function models of increasing complexity (and decreasing speed) to accelerate the convergence to an optimum solution. In the EU-FP6 TOP-FARM project, three levels of complexity are considered. The first level uses a simple stationary wind farm wake model to estimate the Annual Energy Production (AEP), a foundations cost model depending on the water depth and an electrical grid cost function dictated by cable length. The second level calculates the AEP and adds a wake-induced fatigue degradation cost function on the basis of the interpolation in a database of simulations performed for various wind speeds and wake setups with the aero-elastic code HAWC2 and the dynamic wake meandering model. The third level, not considered in this present paper, includes directly the HAWC2 and the dynamic wake meandering model in the optimization loop in order to estimate both the fatigue costs and the AEP. The novelty of this work is the implementation of the multi-fidelity approach in the context of wind farm optimization, the inclusion of the fatigue degradation costs in the optimization framework, and its application on the optimal performance as seen through an economical perspective.

The dynamic wake meandering (DWM) model is an engineering wake model designed to physically model the wake deficit evolution and the unsteady meandering that occurs in wind turbine wakes. The present study aims at improving two features of the model: The effect of the atmospheric boundary layer shear on the wake deficit evolution by including a strain‐rate contribution in the wake turbulence calculation.The method to account for the increased turbulence at a wake‐affected turbine by basing the wake‐added turbulence directly on the Reynolds stresses of the oncoming wake. This also allows the model to simulate the build‐up of turbulence over a row of turbines in a physically consistent manner. The performance of the modified model is validated against actuator line (AL) model results and field data from the Lillgrund offshore wind farm. Qualitatively, the modified DWM model is in fair agreement with the reference data. A quantitative comparison between the mean flow field of the DWM model with and without the suggested improvements, to that of the AL model, shows that the root‐mean‐square difference in terms of wind speed and turbulence intensity is reduced on the order of 30% and 40%, respectively, by including the proposed corrections for a row of eight turbines. Furthermore, it is found that the root‐mean‐square difference between the AL model and the modified DWM model in terms of wind speed and turbulence intensity does not increase over a row of turbines compared with the root‐mean‐square difference of a single turbine. Copyright © 2013 John Wiley & Sons, Ltd.

The work presented in this paper focuses on improving the description of wake evolution due to turbulent mixing in the dynamic wake meandering (DWM) model. From wake investigations performed with high-fidelity actuator line simulations carried out in ELLIPSYS3D, it is seen that the current DWM description, where the eddy viscosity is assumed to be constant in each cross-section of the wake, is insufficient. Instead, a two-dimensional eddy viscosity formulation is proposed to model the shear layer generated turbulence in the wake, based on the classical mixing length model. The performance of the modified DWM model is verified by comparing the mean wake velocity distribution with a set of ELLIPSYS3D actuator line calculations. The standard error (defined as the standard deviation of the difference between the mean velocity field of the DWM and the actuator line model), in the wake region extending from 3 to 12 diameters behind the rotor, is reduced by 27% by using the new eddy viscosity formulation.