Wake Meandering Research Articles

Similarities in the meandering of yawed rotor wakes

This study investigated the meandering of yawed wind turbine rotor wakes, focusing on the similarities across different yaw angle scenarios. Spectrum analysis of velocity fluctuations reveals that the meandering of the yawed rotor wake is symmetrical about the wake center, despite its skewness. The non-zero lateral force of the yawed rotor enhances meandering in the lateral direction compared to the vertical direction. However, the lateral profiles of meandering strength exhibit similarities across different yaw angle scenarios, indicating a consistent wake meandering mode. The wake meandering frequency increases with the yaw angle. A relationship involving wake meandering frequency, drag coefficient, and yaw angle is formulated for wind turbine rotor wakes under different yaw angles. This relationship is also applicable to thin plate wakes within a certain range of inclination angles/yaw angles. The present study reveals the similarity in wake meandering characteristics across different yaw angle scenarios, which is instrumental in improving our understanding of wake meandering and in developing analytical wake models for wind turbines.

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.

Investigating the interactions between wakes and floating wind turbines using FAST.Farm

Abstract. As floating offshore wind progresses to commercial maturity, wake and array effects across a farm of floating offshore wind turbines (FOWTs) will become increasingly important. While wakes of land-based and bottom-fixed offshore wind turbines have been extensively studied, only recently has this topic become relevant for floating turbines. This work presents an investigation of the mutual interaction between the motions of floating wind turbines and wakes using FAST.Farm. While FAST.Farm has been extensively validated across a wide range of conditions, it has never been validated for FOWT applications. Hence, in the first part of this work, we validate FAST.Farm by comparing simulations of a single FOWT against high-fidelity results from large-eddy simulations available in the literature. The validation is based on wake meandering, mean wake deflection, and velocity deficit at different downstream locations. This validation showed that the original axisymmetric (polar) wake model of FAST.Farm overpredicts the vertical wake deflection induced by shaft tilt and floater pitch, while the new curled wake model is capable of properly capturing the vertical wake deflection. In the second part, we use FAST.Farm to analyze a small three-unit array of FOWTs with a spacing of 7 diameters across a wide range of environmental conditions. The same National Renewable Energy Laboratory 5 MW reference wind turbine atop the OC4-DeepCwind semisubmersible is adopted for the three FOWTs and for the validation against high-fidelity simulations. To assess the effect of the floating substructure, we compare the power production, tower-base moments, and blade-root moments obtained for the floating turbines with the results obtained in a fixed-bottom configuration. The main differences introduced by the floating substructure are the motions induced by the waves, the change in the natural frequencies of the tower caused by differences in the boundary condition at its base, and the larger vertical deflection of the wake deficit due to the mean pitch of the platform. The impact of these differences, as well as other minor effects, are analyzed in detail.

Effect of Atmospheric Stability on Meandering and Wake Characteristics in Wind Turbine Fluid Dynamics

This study investigates the impact of atmospheric stability on wind turbine flow dynamics, focusing on wake deflection and meandering. Using the high-fidelity large-eddy simulation coupled with the Actuator Line model, we explore three stability conditions for the Vestas V80 turbine, both with and without yaw. The results indicate that wake meandering occurs predominantly along the deflected wake axis. Despite varying wake deficits and meandering behaviors, neutral and stable conditions exhibit similar wake deflection trajectories during yawed turbine operations. Spectral analysis of meandering reveals comparable cutoff and peak frequencies between neutral and stable cases, with a consistent Strouhal number (St=0.16). The unstable condition shows significant deviations, albeit with associated uncertainties. Overall, increased stability decreases both oscillation amplitude and frequency, highlighting the complex interplay between atmospheric stability and wind turbine wake dynamics.

A study on the dynamic characteristics of alternative arrangements of floating wind farms with varying hub heights

Wind farms with multiple hub heights have the potential to effectively mitigate velocity deficits resulting from wake effects and reduce the levelized cost of energy (LCOE). While existing research has predominantly focused on studying wake effects on floating wind farms with identical hub heights, there is a notable absence of research on floating wind farms with multiple hub heights. Therefore, a comprehensive understanding of the impact of vertical arrangements on floating wind farms is essential. In light of this gap, this study examines the characteristics of two distinct arrangements of a semi-submersible floating wind farm with multiple hub heights. The configuration includes two 15 MW semi-submersible floating offshore wind turbines (FOWT) and two 5 MW semi-submersible FOWTs. A novel wind farm modeling tool utilizing dynamic wake meandering (DWM) is employed to investigate the power production performance, wake characteristics, global dynamic responses, and fatigue damage of crucial components of each individual FWT, associated with the two different arrangements. The paper presents a discussion of the advantages and disadvantages of the two arrangements, accompanied by a summary of the key findings. The insights gained from this research can serve as a foundational basis for improving the design and analysis processes of floating wind farms with various arrangements.

Wind farm structural response and wake dynamics for an evolving stable boundary layer: computational and experimental comparisons

Abstract. The wind turbine design process requires performing thousands of simulations for a wide range of inflow and control conditions, which necessitates computationally efficient yet time-accurate models, especially when considering wind farm settings. To this end, FAST.Farm is a dynamic-wake-meandering-based mid-fidelity engineering tool developed by the National Renewable Energy Laboratory targeted at accurately and efficiently predicting wind turbine power production and structural loading in wind farm settings, including wake interactions between turbines. This work is an extension of a study that addressed constructing a diurnal cycle evolution based on experimental data (Quon, 2024). Here, this inflow is used to validate the turbine structural and wake-meandering response between experimental data, FAST.Farm simulation results, and high-fidelity large-eddy simulation results from the coupled Simulator fOr Wind Farm Applications (SOWFA)–OpenFAST tool. The validation occurs within the nocturnal stable boundary layer when corresponding meteorological and turbine data are available. To this end, we compared the load results from FAST.Farm and SOWFA–OpenFAST to multi-turbine measurements from a subset of a full-scale wind farm. Computational predictions of blade-root and tower-base bending loads are compared to 10 min statistics of strain gauge measurements during 3.5 h of the evolving stable boundary layer, generally with good agreement. This time period coincided with an active wake-steering campaign of an upstream turbine, resulting in time-varying yaw positions of all turbines. Wake meandering was also compared between the computational solutions, generally with excellent agreement. Simulations were based on a high-fidelity precursor constructed from inflow measurements and using state-of-the-art mesoscale-to-microscale coupling.

Large eddy simulation and linear stability analysis of active sway control for wind turbine array wake

The convective instability of wind turbine wakes allows specific upstream forcing to amplify downstream, leading to increased wake meandering and replenishment, thereby providing a theoretical basis for active wake control. In this study, the active sway control—a strategy previously proven to enhance wake recovery at the single wind turbine level—is analyzed at the turbine array level. The similarity and differences between individual turbine wakes and the wake array are analyzed using large eddy simulations and linear stability analysis, considering both uniform and turbulent inflow conditions. For cases with uniform inflow, large eddy simulations reveal significant meandering motion in the wake array induced by active sway control at a motion amplitude of 1% rotor diameter, consistent with previous studies of standalone wind turbine wakes. Nevertheless, the sensitive frequency for the wake array extends down to St = 0.125 below the limit of St > 0.2 for a single wake, and the optimal control frequency for the standalone turbine wake becomes suboptimal for the array. Linear stability analysis reveals the underlying mechanism of this frequency shift as changes in the shear-layer instability due to the overlap of upstream and downstream wakes and is capable to provide fast estimation of optimal control frequencies. When inflow turbulence intensity increases, the gain of active sway control is reduced, underscoring the importance of low-turbulence environment for successfully implementing the active sway control. The reduction in wake response is captured by the linear stability analysis if the base flow accounts for the faster wake expansion caused by inflow turbulence.

Simulating low-frequency wind fluctuations

Abstract. Large-scale flow structures are vital in influencing the dynamic response of floating wind turbines and wake meandering behind large offshore wind turbines. It is imperative that we develop an inflow wind turbulence model capable of replicating the large-scale and low-frequency wind fluctuations occurring in the marine atmosphere since the current turbulence models do not account well for this phenomenon. Here, we present a method to simulate low-frequency wind fluctuations. This method employs the two-dimensional (2D) spectral tensor for low-frequency, anisotropic wind fluctuations presented by Syed and Mann (2024) to generate stochastic wind fields. The simulation method generates large-scale 2D spatial wind fields for the longitudinal u and lateral v wind components, which can be converted into a frequency domain using Taylor's frozen turbulence hypothesis. The low-frequency wind turbulence is assumed to be independent of the high-frequency turbulence; thus, a broad spectral representation can be obtained just by superposing the two turbulent wind fields. The method is tested by comparing the simulated and theoretical spectra and co-coherences of the combined low- and high-frequency fluctuations. Furthermore, the low-frequency wind fluctuations can also be subjected to anisotropy. The resulting wind fields from this method can be used to analyze the impact of low-frequency wind fluctuations on wind turbine loads and dynamic response and to study the wake meandering behind large offshore wind farms.

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.

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.

Development and Verification of an Improved Wake-Added Turbulence Model in FAST.Farm

We introduce a generalized wake-added turbulence (WAT) model in the multiphysics, multiturbine simulation tool FAST.Farm. The WAT model introduces additional small-scale turbulence that represents the breakdown of vortical structures and shear layers in the wake. The article describes the development, implementation, calibration, and verification of the model. The novelties of the model include support for wake asymmetry, buildup of WAT across the wind farm, and secondary effects of wake-induced turbulence (e.g., wake meandering) driven by smaller-scale turbulence structures that arise from wake breakdown. Large-eddy simulations were run to support the calibration of the WAT parameters and verification of the model. Previous studies hypothesized that the lack of WAT modeling was the source of underprediction of fatigue loads, in particular for cases at low turbulence intensities and/or stable atmospheric boundary layers. This study confirms that the newly implemented WAT model enhances the loads predictions in these cases.

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.

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.

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.

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.

LES-based validation of a dynamic wind farm flow model under unsteady inflow and yaw misalignment

This work presents the validation of an extended version of the control-oriented, dynamic wind farm flow solver SPLINTER. The two-dimensional model is applied to use cases of wake steering by yaw misalignment and inflow wind direction variations and the results are compared to large-eddy simulations (LES). While SPLINTER is able to reproduce the antagonal behaviour of decreasing upstream and increasing downstream turbine power under wake deflection, a systematic deviation of the downstream power is detected and quantified, which is connected to underrepresented three-dimensional wake effects. In case of changing inflow wind direction, SPLINTER is capable of computing movement and shape of the bending wakes. The model smooths small-scale turbulent structures and disturbances and does not reproduce wake meandering, but manages to describe the evolution of the mean flow, which is tested by averaging over an ensemble of LES and comparing the resulting flow fields and turbine power time series. Under dynamic inflow conditions, SPLINTER is able to predict at which time intervals and at which rates downstream turbines will be influenced by wakes, which can improve the accuracy of short-term power and load forecasting and enables its application to online model predictive wind farm control.

Numerical analysis of aero-hydrodynamic wake flows of a floating offshore wind turbine subjected to atmospheric turbulence inflows

The influence of atmospheric turbulence inflow on coupled dynamic behaviors and wakes of floating offshore wind turbine (FOWT) is pronounced, especially as blade size increases. In this study, we explore the effects of atmospheric inflow on aero-hydrodynamics and wake characteristics of a spar-type FOWT. A well-validated in-house computational fluid dynamic (CFD) solver, FOWT-UALM-SJTU, is utilized to conduct the numerical simulations. To generate the realistic atmospheric inflow condition, the large eddy simulation (LES) with long-duration is employed. Two other cases involving uniform inflow and shear inflow are conducted to provide some comparable results. Compared to uniform inflow and shear inflow, the power and thrust of FOWT under atmospheric inflow display greater instability, with their power spectrums exhibiting higher intensity in high frequency region. The variation of yaw moment in atmospheric scenario is significantly drastic, leading to a remarkable response in platform yaw motion. Notably, the dominant frequency in this scenario is the blade passage frequency, as opposed to the incident wave frequency observed in the uniform and shear scenarios. The atmospheric inflow promotes the manifestation of wake breakdown and wake meandering, resulting in the faster wake recovery of FOWT. Besides, the meandering in the far wake is more significant compared to uniform and shear scenarios. The absence of vortex rings in atmospheric scenario is observed, along with the presence of more complex and smaller vortices in far wake. Our findings highlight the remarkable impacts of atmospheric inflow on dynamic responses and wake evolution of FOWT, and it is recommended that the atmospheric inflow be taken into account when assessing wake interactions between multiple FOWTs.

A physics-guided machine learning framework for real-time dynamic wake prediction of wind turbines

Efficient and accurate prediction of the wind turbine dynamic wake is crucial for active wake control and load assessment in wind farms. This paper proposes a real-time dynamic wake prediction model for wind turbines based on a physics-guided neural network. The model can predict the instantaneous dynamic wake field under various operating conditions using only the inflow wind speed as input. The model utilizes Taylor's frozen-flow hypothesis and a steady-state wake model to convert instantaneous inflow wind speed and turbine parameters into neural network input features. A deep convolutional neural network then maps these features to desired wake field snapshots, enabling dynamic wake predictions for wind turbines. To train the model, we generated approximately 255 000 instantaneous flow field snapshots of single-turbine wakes using the large eddy simulation, covering different thrust coefficients and yaw angles. The model was trained using the supervised learning method and verified on the test set. The results indicate that the model can effectively predict the dynamic wake characteristics, including the dynamic wake meandering and the wake deflection of the yawed turbines. The model can also assess both the instantaneous wake velocity and the instantaneous wake center of a wind turbine. At a thrust coefficient of 0.75, the root mean square error for the predicted instantaneous wake velocity is around 6.53%, while the Pearson correlation coefficient for the predicted instantaneous wake center can reach 0.624. Furthermore, once the model is trained, its prediction accuracy does not decrease with the increase in the time span.

Fluid-Dynamic Mechanisms Underlying Wind Turbine Wake Control with Strouhal-Timed Actuation

A reduction in wake effects in large wind farms through wake-aware control has considerable potential to improve farm efficiency. This work examines the success of several emerging, empirically derived control methods that modify wind turbine wakes (i.e., the pulse method, helix method, and related methods) based on Strouhal numbers on the O(0.3). Drawing on previous work in the literature for jet and bluff-body flows, the analyses leverage the normal-mode representation of wake instabilities to characterize the large-scale wake meandering observed in actuated wakes. Idealized large-eddy simulations (LES) using an actuator-line representation of the turbine blades indicate that the n=0 and ±1 modes, which correspond to the pulse and helix forcing strategies, respectively, have faster initial growth rates than higher-order modes, suggesting these lower-order modes are more appropriate for wake control. Exciting these lower-order modes with periodic pitching of the blades produces increased modal growth, higher entrainment into the wake, and faster wake recovery. Modal energy gain and the entrainment rate both increase with streamwise distance from the rotor until the intermediate wake. This suggests that the wake meandering dynamics, which share close ties with the relatively well-characterized meandering dynamics in jet and bluff-body flows, are an essential component of the success of wind turbine wake control methods. A spatial linear stability analysis is also performed on the wake flows and yields insights on the modal evolution. In the context of the normal-mode representation of wake instabilities, these findings represent the first literature examining the characteristics of the wake meandering stemming from intentional Strouhal-timed wake actuation, and they help guide the ongoing work to understand the fluid-dynamic origins of the success of the pulse, helix, and related methods.