Wake Meandering Model Research Articles

Loads and fatigue characteristics assessment of wind farm based on dynamic wake meandering model

As the scale of wind farms continues to expand, the impact of the wake on the power generation and load of wind turbines is becoming increasingly prominent. This study delves into the wake characteristics, power generation, load, and fatigue behavior of an ideal layout wind farm using a dynamic wake meandering model, accounting for diverse spacing configurations, inflow conditions, and yaw angles. The findings reveal that increasing the axial spacing facilitates superior wake recovery, promoting a more evenly distributed load and reducing fatigue damage throughout the wind farm. Moreover, higher inflow wind speed or turbulence intensity exacerbates fatigue damage, especially at elevated wind, where the damage accumulates exponentially. Under yaw conditions, the wake deviates, reducing its adverse impact on downstream turbines and subsequently boosting the overall power generation of the wind farm. However, this deflection simultaneously introduces intricate and detrimental effects on the fatigue load. Notably, optimal yaw achieves a 7.9 % improvement in power generation, also resulting in the most significant fatigue damage at the blade root and tower base. This study provides theoretical and technical underpinnings for the layout optimization and control strategies of wind farms or wind farm clusters.

Improvements to the dynamic wake meandering model by incorporating the turbulent Schmidt number

Improvements to the dynamic wake meandering model by incorporating the turbulent Schmidt number

An improved statistical wake meandering model

A new statistical wake meandering (SWM) model is proposed that improves on existing models in the literature. Compared to the existing SWM models, the proposed model has a closed description that does not require simulations to create look-up tables while maintaining applicability to a wide range of flow conditions. The proposed SWM model is compared to the predictions of the Dynamic Wake Meandering (DWM) model and to wind speed measurements from a scanning Doppler lidar mounted on the nacelle of a utility-scale wind turbine for validation. The results show that the proposed model has a similar performance as the DWM model for the effect of wake meandering on the mean velocity deficit and the turbulence intensity, while being significantly faster to compute.

Optimizing Wind Farm Efficiency through Active Yaw Control: A Neural Network-Aided Game Theory Approach

This research investigates the potential of a game-theoretic-based Active Yaw Control (AYC) strategy to enhance power generation in wind farms. The proposed AYC strategy in this study replaces traditional look-up tables with a trained Artificial Neural Network (ANN) that determines the optimal yaw misalignment for turbines under time-varying atmospheric conditions. The study examines a hypothetical 3x2 rectangular arrangement of NREL 5-MW wind turbines. The FAST.Farm simulation tool, utilizing the dynamic wake meandering (DWM) model, is employed to assess both the power performance and structural load on the wind turbines. When tested with two different inflow directions and ambient turbulence (10%), the AYC strategy demonstrated a maximum increase in total power output of 2.6%, although it affected individual turbines differently. It also exhibits an increase in some structural loads, such as tower-top torque, while some components experience a slight reduction in load. The results underscore the effectiveness of the ANN-guided game-theoretic algorithm in improving wind farm power generation by mitigating the negative impact of wake interference, offering a scalable and efficient method for optimizing large-scale wind farm. However, it is essential to evaluate the overall impact of AYC on wind farm efficiency in terms of both Annual Energy Production (AEP) and structural loading under various atmospheric conditions.

Dynamic wake conditions tailored by an active grid in the wind tunnel

Well characterized test environments are required for novel wind turbine and wind farm control concepts. Aeroelastic simulations are mostly used to model turbine aerodynamic and structural response. For wind farm control, also the wake behaviour needs to be represented, including the impacts of dynamic wind direction changes, wake meandering and the interaction of wakes with the atmospheric boundary layer. This paper shows how wake-like inflow conditions can be emulated with an active grid in a wind tunnel, exciting a broad band of turbulent scales. The artificial wake conditions can be used as inflow for an exposed model turbine. A focus is put on the meandering dynamics, which are driven by large transversal turbulence patterns in the atmospheric boundary layer. Following the conjecture of the Dynamic Wake Meandering (DWM) model, such turbulent scales must have the size of multiple rotor diameters, to impact the entire wake deficit like a passive tracer. In conventional wind tunnel experiments, such spatial scale ratios are hard to reach, since wind tunnel sizes are bounded while the model turbines must be sufficiently large to have appropriate aerodynamic scaling and instrumentation. In this work, quasi-stochastic meandering trajectories are created, using scaled Ornstein-Uhlenbeck processes. Thus, the intrinsically stochastic process of wake meandering is made repeatable. The paper focuses at a thorough characterization of the inflow conditions with both lidar and hot-wire measurements, considering wake shape and spectral features. The results show an approximately axi-symmetric Gaussian deficit, which meanders as a coherent structure while having spectral features similar to a turbine wake.

A multi-fidelity approach for wind farm simulations and comparison with field data

The prediction of energy production and structural loads within wind farms is of high interest for wind industries to optimize the wind farm design and control under a variety of atmospheric conditions. However, it is still a key challenge to predict them accurately and efficiently due to the complex interactions between wind turbines and turbulent flows. Nowadays, high-fidelity simulations using Reynolds-Averaged Navier-Stokes (RANS) or Large-Eddy Simulation (LES) coupled with actuator disk or actuator line method are widely developed and used in wind farm analysis, but it still needs a huge computational resource, especially in the application of a commercial wind farm with large number of turbines. In this context, a mid-fidelity simulation tool based on the Dynamics Wake Meandering (DWM) model called FAST.Farm has been developed by National Renewable Energy Laboratory (NREL) in order to tackle this challenge. It allows to capture essential physics at the turbine scale as well as at the farm scale in a computational efficient manner. This study focuses on the calibration of DWM model which is the key to minimize inaccuracies between mid-fidelity and high-fidelity simulations regarding key performance indicators, e.g. thrust and power production. The calibration is made for DTU10MW wind turbine and shows a good improvement in accuracy compared to default parameters. The calibrated DWM model is finally employed to forecast the power generation for two turbines within a reference wind farm. A good improvement on the prediction is also obtained thanks to the calibrated parameters.

Influence of wake meandering path on floater motions

This study shows how different versions of the dynamic wake meandering (DWM) model will result in different dynamic behaviour of a floating wind turbine. In this study, different softwares as well as different input wind boxes are applied. The effect of these variations were studied using statistics from both the meandering behaviour of the wake and the response of a floating wind turbine. The yaw response is the most sensitive, and this study shows that the standard deviation of the yaw response is between 10% to 60%, depending on the DWM options used when generating the wake wind field.

Wake Modelling Based on the Stokes Stream Function and the Toroidal-Poloidal Decomposition

The Stokes stream function and its generalisation, the Toroidal-Poloidal decomposition, are well-suited for the derivation of axisymmetric engineering wake models, as they are solenoidal and fulfil conservation of mass of an incompressible fluid by construction. The presented model consists of a time-independent contribution based on Laguerre basis functions with a simple parametrisation that is well-suited for the diffusion-dominated far wake. A time-dependent part can be added based on a poloidal component that can model either helical or toroidal vortex structures, and its parametrisation can be closed towards the total thrust force on the rotor. Despite requiring an external solver, the presented model shows potential as a drop-in replacement for the Ainslie wake model that is widely used in the Wind Energy industry as part of the Dynamic Wake Meandering model.

Comparison of the dynamic wake meandering model against large eddy simulation for horizontal and vertical steering of wind turbine wakes

Accurately predicting the evolution of wake is crucial for power output and structural load estimation in wind farms. This study aims to validate the dynamic wake meandering (DWM) model, an efficient mid-fidelity wake model, against large eddy simulation (LES). The predictive capabilities of the DWM model for various wake properties, namely time-averaged wake deficit, mean wake center deflection, amplitude, and frequency spectrum of wake meandering, are comprehensively analyzed using the IEA 15MW reference wind turbine under different yaw and tilt misalignment angles. Two turbulent inflows with varying shear and turbulence intensity levels are considered. The comparison highlights the significance of the filter size (Cmeand) in DWM as a key parameter determining simultaneously the time-averaged wake deflection and meandering amplitude, with optimal values differing for horizontal and vertical wake displacements. When the appropriate Cmeand values are selected, the implementation of the DWM model in FAST.Farm demonstrates good agreement with LES data, particularly concerning time-averaged wake deficit, wake centerline deflection, and wake meandering amplitude at eight rotor diameters downstream. However, the DWM model tends to overestimate the energy in the lower frequency region with Strouhal’s number less than 0.1 and underestimate the wake oscillation induced by the shear-layer at higher frequencies, even though the wake motion standard deviation is accurately reproduced if the polar grid size is properly adjusted. Furthermore, the influence of the ground effect on downward wake deflection through tilt control is revealed. These findings clearly demonstrate the strengths and weaknesses of the current DWM model and can serve as a reference for the development of advanced wake models.

Effect of atmospheric stability on the dynamic wake meandering model applied to two 12 MW floating wind turbines

AbstractCurrent global analysis tools for floating wind turbines (FWTs) do not account for the combined effects of atmospheric stability and wakes from neighboring turbines. This work uses the mid‐fidelity dynamic wake meandering model, together with turbulent wind fields generated based on stable, neutral, and unstable atmospheric conditions, to study the low‐frequency content of the global responses of two semisubmersible FWTs separated by eight rotor diameters. Incoming wind fields based on the Kaimal spectrum and exponential coherence model, the Mann spectral tensor model, and a time‐series input‐based turbulence model are used. The respective input parameters for these models are fitted to high‐fidelity large eddy simulation data.In unstable, below‐rated conditions, meandering leads to an increase in the yaw standard deviation of the downwind turbine of almost three times larger than the upwind turbine. Deficit and the upwards wake deflection affect the mean pitch and yaw, especially for the below‐rated wind speed scenario. The mean pitch of the downwind turbine is reduced up to half the mean pitch value of the upwind turbine, whereas the mean yaw changes direction due to the enhanced effect of shear. The effect of meandering on the structural loading is highest on the standard deviation of the tower‐top yaw moment of the downstream turbine, which increases more than 2.2 times compared to the upwind turbine value. Based on these findings, atmospheric stability affects wake deficit and meandering which in turn have a profound effect on the low‐frequency global motions and structural response of floating wind turbines.

Extending the dynamic wake meandering model in HAWC2Farm: a comparison with field measurements at the Lillgrund wind farm

Abstract. With the increasing growth of wind farm installations, the impact of wake effects caused by wind turbines on power output, structural loads, and revenue has become more relevant than ever. Consequently, there is a need for precise simulation tools to facilitate efficient and cost-effective design and operation of wind farms. To address this need, we present HAWC2Farm, a dynamic and versatile aeroelastic wind farm simulation methodology that combines state-of-the-art engineering models to accurately capture the complex physical phenomena in wind farms. HAWC2Farm employs the aeroelastic wind turbine simulator, HAWC2, to model each individual turbine within the wind farm. It utilises a shared, large-scale turbulence box to represent atmospheric flow field effects at the farm level. The methodology incorporates a modified version of the dynamic wake meandering model to accurately capture wake interactions. This approach not only ensures computational efficiency but also provides valuable insights for wind farm design and operation. To assess its performance, HAWC2Farm is compared using time series extracted from field measurements at the Lillgrund wind farm, encompassing various scenarios involving wake steering via yaw control and a turbine shutdown. The results indicate that HAWC2Farm effectively addresses the challenges associated with modelling the complex dynamics within wind farms, thereby enabling more precise, informed, and cost-effective design and operation strategies.

Comparison of three DWM-based wake models at above-rated wind speeds

In this study we investigate three mid-fidelity wind turbine wake models based on the dynamic wake meandering (DWM) model principle, and compare their performance with a reference dataset, produced with large-eddy simulations using the actuator line model. The models are compared with respect to flow field, power, and loads on a row of four 5MW reference turbines experiencing above-rated wind conditions. In general, the DWM models show fairly good agreement with large-eddy simulation for the time-averaged flow fields, blade forces and power, with increasing differences along the turbine row. Also when comparing fatigue loads of blade root moments, the differences between the models increase further into the row, with deviations up to 25 % of the reference case. However, while the development in blade root moment fatigue along the turbine row is predominantly driven by the energy content at the frequency corresponding to the turbine’s rotational period (1P) for the DWM models, the large-eddy simulation results suggest that the key drivers for the blade root and tower loads are the increase in meandering and energy at higher frequencies (> 1P) deeper into the turbine row. For the tower loads, the DWM models highly underestimate the fatigue for the waked turbines. From these results, we suggest priorities for future model developments so that robust model implementations can be used in wind farm design and operation.

Numerical evaluation of multivariate power curves for wind turbines in wakes using nacelle lidars

The IEC standards describe how to measure the power performance of an isolated wake-free wind turbine. However, most wind turbines operate under waked conditions for a substantial amount of time, calling for the need of a new methodology for power performance evaluation. We define multivariate power curves in the form of multivariate polynomial regressions, whose input variables are several wind speed and turbulence measurements retrieved with nacelle lidars. We use a dataset of synthetic power performance tests including both waked and wake-free conditions. The dataset is generated through aeroelastic simulations combined with both virtual nacelle lidars and the dynamic wake meandering model. A feature-selection algorithm is used to select the input variables among the available measurements, showing that the optimal model includes four input variables: three correspondent to wind speed and one to turbulence measures. Additionally, we give insights on the optimal nacelle-lidar scanning geometry needed to implement the multivariate power curve. Results show that the multivariate power curves predict the power output with accuracy of the same order under both waked and wake-free operation. For the in-wake cases, the accuracy is much higher than that of the IEC standard power curve, with an error reduction of up to 88%.

Comparison of time averaged wake flow fields between LiDAR measurements and DWM

The Dynamic Wake Meandering model (DWM) promises an accurate way of assessing wake effect through time-resolved simulation of wake flow fields. This study aims to validate the DWM model by comparing 10-minute time averaged wake flow fields to measurements from a LiDAR campaign carried out on the Lillgrund offshore wind farm. An implementation of the DWM model following the parametrization proposed in the IEC61400 standard is used. Two superposition assumptions are tested. Results show a good visual match and relative convergence of a quantitative error metric for downstream distances of 3 to 3.5 turbine diameters. Results in the immediate near wake show a clear mismatch, as expected considering model assumptions. Linear superposition of all wakes performs best, provided that local conditions at the wake emitting turbines are estimated. The present study uses a limited dataset of only one week of LiDAR data, making the results susceptible to measurement uncertainties.

Dynamic wake tracking based on wind turbine rotor loads and Kalman filtering

In a wind farm setting, the location of the wake to which a downwind turbine is exposed is of high interest. It can be used for closed-loop active wake control, ultimately leading to fatigue load reduction and higher power generation. This work proposes a method for dynamic tracking of the meandering wake centre. The rotor takes the role of a sensor, with its blades sampling through the incoming wind field. The measurement of the flapwise blade root bending moment and its decomposition into the non-rotating yaw and tilt moments is used. The latter are linked to the lateral and vertical wake location via a parametric model, tuned with training data from aeroelastic simulations. The implementation of an Extended Kalman Filter (EKF) adds robustness to the tracking and allows to include physical knowledge of the wake meandering to the estimation. For this, the governing equations of the dynamic wake meandering model (DWM) are used to describe the meandering motion as a random walk process. The performance, possibilities and limitations of the tracking method in various inflow conditions are shown and discussed. Generally the wake tracking works satisfying, with estimation errors below 10% of the rotor diameter under moderate turbulence intensity. The Extended Kalman Filter formulation provides the confidence in the tracked wake position. The work shows how this can be effectively used for wake impingement detection.

Probabilistic estimation of the Dynamic Wake Meandering model parameters using SpinnerLidar-derived wake characteristics

Abstract. We study the calibration of the Dynamic Wake Meandering (DWM) model using high-spatial- and high-temporal-resolution SpinnerLidar measurements of the wake field collected at the Scaled Wind Farm Technology (SWiFT) facility located in Lubbock, Texas, USA. We derive two-dimensional wake flow characteristics including wake deficit, wake turbulence, and wake meandering from the lidar observations under different atmospheric stability conditions, inflow wind speeds, and downstream distances up to five rotor diameters. We then apply Bayesian inference to obtain a probabilistic calibration of the DWM model, where the resulting joint distribution of parameters allows for both model implementation and uncertainty assessment. We validate the resulting fully resolved wake field predictions against the lidar measurements and discuss the most critical sources of uncertainty. The results indicate that the DWM model can accurately predict the mean wind velocity and turbulence fields in the far-wake region beyond four rotor diameters as long as properly calibrated parameters are used, and wake meandering time series are accurately replicated. We show that the current DWM model parameters in the IEC standard lead to conservative wake deficit predictions for ambient turbulence intensities above 12 % at the SWiFT site. Finally, we provide practical recommendations for reliable calibration procedures.

Low-frequency dynamic wake meandering: comparison of FAST.Farm and DIWA software tools

Most of the global dynamic response models used today for the design of wind turbines are based on the aero-hydro-servo-elastic analysis of one single turbine. However, research on bottom- fixed offshore wind turbines has shown that interactions among turbines in a farm influence both the power production and the structural loading. Furthermore, floating wind turbines (FWTs) are sensitive to low-frequency variations, and therefore to wake meandering perturbations. In the current work, we use the Dynamic Wake Meandering (DWM) model as implemented in DIWA and FAST.Farm, to study the low-frequency content of the meandering at a target turbine placed 8 diameters downstream. At frequencies in the range of the natural frequencies of rigid body motions of semisubmersible floaters, the two models yield different results. These differences are seen for every wind speed and wind turbine model, even though they decrease as the wind speed increases. The observed differences may affect low-frequency motions and consequently mooring system design.

Simplified wake modelling for wind farm load prediction

This paper presents a simple numerical wind farm model, where pragmatic choices are made in the modelling of underlying physical processes, with the aim of making useful power production and wind turbine load estimates. The numerical model decomposes the wind farm, inspired by the approach of the dynamic wake meandering model (DWM), into simple sub-models for a single wake deficit (1D Gaussian), wake meandering (statistical), and wake added turbulence (eddy viscosity based). Particular attention is given to selecting a momentum conserving wake summation method, because of its critical role in coupling the influence of individual wakes. Results are presented to illustrate the influence that wake summation methods have on equilibrium velocity and power production in a row of turbines, for different inter-turbine spacing and inflow velocities. Comparisons against published data from the Lillgrund wind farm illustrate that the suggested modelling approach reproduces important trends observed in the field data.

Wind turbine load validation in wakes using wind field reconstruction techniques and nacelle lidar wind retrievals

Abstract. This study proposes two methodologies for improving the accuracy of wind turbine load assessment under wake conditions by combining nacelle-mounted lidar measurements with wake wind field reconstruction techniques. The first approach consists of incorporating wind measurements of the wake flow field, obtained from nacelle lidars, into random, homogeneous Gaussian turbulence fields generated using the Mann spectral tensor model. The second approach imposes wake deficit time series, which are derived by fitting a bivariate Gaussian shape function to lidar observations of the wake field, on the Mann turbulence fields. The two approaches are numerically evaluated using a virtual lidar simulator, which scans the wake flow fields generated with the dynamic wake meandering (DWM) model, i.e., the target fields. The lidar-reconstructed wake fields are then input into aeroelastic simulations of the DTU 10 MW wind turbine for carrying out the load validation analysis. The power and load time series, predicted with lidar-reconstructed fields, exhibit a high correlation with the corresponding target simulations, thus reducing the statistical uncertainty (realization-to-realization) inherent to engineering wake models such as the DWM model. We quantify a reduction in power and loads' statistical uncertainty by a factor of between 1.2 and 5, depending on the wind turbine component, when using lidar-reconstructed fields compared to the DWM model results. Finally, we show that the number of lidar-scanned points in the inflow and the size of the lidar probe volume are critical aspects for the accuracy of the reconstructed wake fields, power, and load predictions.

Validation of the dynamic wake meandering model with respect to loads and power production

Abstract. The outlined analysis validates the dynamic wake meandering (DWM) model based on loads and power production measured at an onshore wind farm with small turbine distances. Special focus is given to the performance of a version of the DWM model that was previously recalibrated at the site. The recalibration is based on measurements from a turbine nacelle-mounted lidar system. The different versions of the DWM model are compared to the commonly used Frandsen wake-added turbulence model. The results of the recalibrated wake model agree very well with the measurements, whereas the Frandsen model overestimates the loads drastically for short turbine distances. Furthermore, lidar measurements of the wind speed deficit as well as the wake meandering are incorporated in the DWM model definition in order to decrease the uncertainties.