Wind Turbine Wake Research Articles

Analysis of Wind Power Fluctuation in Wind Turbine Wakes Using Scale-Adaptive Large Eddy Simulation

In large wind farms, the interaction of atmospheric turbulence and wind turbine wakes leads to complex vortex dynamics and energy dissipation, resulting in reduced wind velocity and subsequent loss of wind power. This study investigates the influence of vortex stretching on wind power fluctuations within wind turbine wakes using scale-adaptive large eddy simulation. The proper orthogonal decomposition method was employed to extract the most energetic contributions to the wind power spectra. Vertical profiles of mean wind speed, Reynolds stresses, and dispersive stresses were analyzed to assess energy dissipation rates. Our simulation results showed excellent agreement when compared with wind tunnel data and more advanced numerical models, such as the actuator line model and the actuator line model with hub and tower effects. This highlights the important role of coherent and energetic flow components in the spectral behavior of wind farms. The findings indicate a persistent energy cascading length scale in the wake of wind turbines, emphasizing the vertical transport of energy to turbine blades. These results complement existing literature and provide new insights into the dynamics of wind turbine wakes and their impact on wind farm performance.

Wind turbine dynamic wake flow estimation (DWFE) from sparse data via reduced-order modeling-based machine learning approach

Wind turbine wake poses a significant challenge in wind farm operations, affecting power generation efficiency. This study introduces a Dynamic Wake Flow Estimation (DWFE) framework designed to predict wind turbine wake evolution from sparse measurement data. The framework integrates Gaussian Process Regression (GPR), Proper Orthogonal Decomposition (POD), and Long Short-Term Memory (LSTM) networks. Specifically, GPR plays a pivotal role in DWFE by enabling the transformation of flow fields discrete sensor signals into coherent, low-dimensional flow fields which is crucial for accurate flow field predictions, while POD aids in dimensionality reduction and LSTM forecasts temporal wake dynamics, improving both predictive accuracy and computational efficiency. Parametric analysis demonstrates that the robustness and adaptability of the framework improve prediction accuracy with increased sensor density and flexible POD modes. The DWFE framework demonstrates high accuracy in wake flow estimation even with limited data, effectively capturing dynamic wake behavior. Future work will extend this approach to various topographic and climatic conditions, optimizing computational efficiency, and improving interpretability. These advancements will expand the framework's applicability in wind energy and other engineering fields requiring precise flow prediction, emphasizing DWFE's potential in advancing wind farm design, operation and renewable energy optimization.

Impact of a two-dimensional steep hill on wind turbine noise propagation

Abstract. Wind turbine noise propagation in a hilly terrain is studied through numerical simulation in different scenarios. Linearized Euler equations are solved in a moving frame that follows the wavefront, and wind turbine noise is modeled with an extended moving source. We employ large-eddy simulations to simulate the flow around the hill and the wind turbine. The sound pressure levels (SPLs) obtained for a wind turbine in front of a 2D hill and a wind turbine on a hilltop are compared to a baseline flat case. First, the source height and wind speed strongly affect sound propagation downwind. We find that topography influences the wake shape, inducing changes in the sound propagation that drastically modify the SPL downwind. Placing the turbine on the hilltop increases the average sound pressure level and amplitude modulation downwind. For the wind turbine placed upstream of a hill, a strong shielding effect is observed. But, because of the refraction by the wind gradient, levels are comparable with the baseline flat case just after the hill. Thus, considering how terrain topography alters the flow and wind turbine wake is essential to accurately predict wind turbine noise propagation.

Discovering an interpretable mathematical expression for a full wind-turbine wake with artificial intelligence enhanced symbolic regression

The rapid expansion of wind power worldwide underscores the critical significance of engineering-focused analytical wake models in both the design and operation of wind farms. These theoretically derived analytical wake models have limited predictive capabilities, particularly in the near-wake region close to the turbine rotor, due to assumptions that do not hold. Knowledge discovery methods can bridge these gaps by extracting insights, adjusting for theoretical assumptions, and developing accurate models for physical processes. In this study, we introduce a genetic symbolic regression (SR) algorithm to discover an interpretable mathematical expression for the mean velocity deficit throughout the wake, a previously unavailable insight. By incorporating a double Gaussian distribution into the SR algorithm as domain knowledge and designing a hierarchical equation structure, the search space is reduced, thus efficiently finding a concise, physically informed, and robust wake model. The proposed mathematical expression (equation) can predict the wake velocity deficit at any location in the full-wake region with high precision and stability. The model's effectiveness and practicality are validated through experimental data and high-fidelity numerical simulations.

Simplified Polynomial-asymptotic-distribution Actuator Disc (SPAD) method for wind turbine wake simulation based on k-[formula omitted]-[formula omitted] turbulence model

In large wind farms, wake effect has a negative impact on the annual production of wind turbines. As a result, wind turbine wake simulation is important for wind farm micro-sitting to minimize power loss and maximize energy production. Coupled with Reynolds Averaged Navier–Stokes turbulence model, Simplified Uniform-distribution Actuator Disc method is the most widely-used rotor model for wake simulation in engineering practice. The conventional simplified uniform-distribution actuator disc models suffer discrepancies of wake velocity prediction compared with the measurements in the near wake region. The novelty of the current research is to propose a Simplified Polynomial-asymptotic-distribution Actuator Disc method based on k−ϵ−fP turbulence model for cylindrical actuator disc cell region with finite thickness, which is simple for implementation and improves the accuracy of wake simulation compared with conventional method. The proposed method conforms to momentum conservation and is as simple as conventional method because of its polynomial formulation and no requirement for aerodynamics data in Generalized Actuator Disc model. From the verification and validation cases, it can be found that the proposed model has better agreement with both high-fidelity actuator line model and the field test measurements from Lillgrund wind farm compared with conventional model. The proposed actuator disc model has the potential to be applied to the micrositting of large offshore wind farms in the future.

Experimental evaluation of wind turbine wake turbulence impacts on a general aviation aircraft

Abstract. Continued development of wind farms near populated areas has led to rising concerns about the potential risk posed to general aviation aircraft when flying through wind turbine wakes. There is an absence of experimental flight test data available with which to assess this potential risk. This paper presents the results of an instrumented flight experiment in which a general aviation aircraft was flown through the wake of a utility-scale wind turbine at an operating wind farm. Wake passes were flown at different downwind distances from the turbine, and data were collected on the orientation disturbances, altitude and speed deviations, and acceleration loads experienced by the aircraft. Videos and pilot statements were also collected, providing qualitative information about the disturbances encountered in the wake. Results show that flight disturbances were small in all cases, with no difference observed between flight data inside and outside the wake at distances greater than six rotor diameters from the turbine. At distances closer than six rotor diameters, small load factor and orientation disturbances were noted but were commensurate with those experienced in light or moderate atmospheric turbulence. Overall, the loads and disturbances experienced were far smaller than those that would risk causing loss of control or structural damage.

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.

Potential of Wake Scaling Techniques for Vertical-Axis Wind Turbine Wake Prediction

Analytical wake models are widely used to predict wind turbine wakes. While these models are well-established for horizontal-axis wind turbines (HAWTs), the analytical wake models for vertical-axis wind turbines (VAWTs) remain under-explored in the wind energy community. In this study, the accuracy of two wake scaling techniques is evaluated to predict the change in the normalized maximum wake velocity deficit behind VAWTs by re-scaling the maximum wake velocity deficit behind an actuator disk with the same thrust coefficient. The wake scaling is defined in terms of equivalent diameter, considering the geometrical properties of the wake-generating object. Two different equivalent diameters are compared, namely the momentum diameter and hydraulic diameter. Different approaches are used to calculate the change in the normalized wake velocity deficit behind a disk with the same thrust coefficient as the VAWT. The streamwise distance is scaled with the equivalent diameter to predict the normalized maximum wake velocity deficit behind the desired VAWT. The performance of the proposed framework is assessed using large-eddy simulation data of VAWTs operating in a turbulent boundary layer with varying operating conditions and aspect ratios. For all of the cases, the momentum diameter scaling provides reasonable predictions of the VAWT normalized maximum wake velocity deficit.

A Nonlinear Wind Turbine Wake Expansion Model Considering Atmospheric Stability and Ground Effects

This study investigates the influence of atmospheric stability and ground effects on wind turbine wake recovery, challenging the conventional linear relationship between turbulence intensity and wake expansion coefficient. Through comprehensive field measurements and numerical simulations, we demonstrate that the linear wake expansion assumption is invalid at far-wake locations under high turbulence conditions, primarily due to ground effects. We propose a novel nonlinear wake expansion model that incorporates both atmospheric stability and ground effects by introducing a logarithmic relationship between the wake expansion coefficient and turbulence intensity. Validation results reveal the superior prediction accuracy of the proposed model compared to typical engineering wake models, with root mean square errors of wake wind speed predictions ranging from 0.04 to 0.063. The proposed model offers significant potential for optimizing wind farm layouts and enhancing overall wind energy production efficiency.

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.

Development and validation of a three-dimensional wind-turbine wake model based on high-order Gaussian function

Under natural conditions, the wake velocity distribution approximates top-hat shape in the near wake center, and a Gaussian shape in the far wake. To improve the prediction accuracy of the wake distribution, this paper proposes a three-dimensional high-order Gaussian linear entrainment wake model by modifying the wake velocity distribution with high-order Gaussian function. Field tests and wind tunnel tests are then conducted. The obtained results show that the proposed model can accurately describe the radial and vertical spatial distributions of the wake flow. Under different wind speeds, the maximum and minimum radial relative errors are respectively 7.29% and 1.4%, while the maximum and minimum vertical relative errors are respectively 7.64% and 3.87%. This demonstrates that the proposed model can accurately predict the velocity distribution in the whole wake region. The proposed model is simple, has low cost, and exhibits high accuracy. Thus, it can be used in wind farm layout optimization and wake control.

Wake interference of tandem wind turbines considering pitch strategy based on the AL-LDS-Ωnew coupling method

This paper establishes a high-fidelity and efficient Computational Fluid Dynamics (CFD) numerical method (AL-LDS-Ωnew) for wind turbine wake by combining the actuator line (AL), the localized dynamic Smagorinsky (LDS) sub-grid scale (SGS), and the new generation Ωnew vortex identification method under the framework of large eddy simulation. The model advantages are encouraging: 1) In terms of turbine modeling, the AL model is adopted to replace the traditional three-dimensional solid model, which avoids solving the boundary layer on the blade surface and improves computational efficiency; 2) In terms of wake simulation, the LDS SGS model is used to model turbulence, reducing vortex dissipation and further improving the refinement of turbine wake; 3) In terms of vortex identification, the new generation Ωnew vortex identification method avoids the difficult threshold selection in previous vortex identification and captures more refined vortex structures. The accuracy of the model is validated against published data of a NREL 5 MW wind turbine, and then extended to simulate the wake interference of tandem twin-rotor turbines by changing the pitch angle of the upstream wind turbine (WT1). The influence mechanisms between array wake interference and energy conversion efficiency under the pitch strategy are explored, demonstrating the AL-LDS-Ωnew coupling method is computationally accurate and efficient for simulating the complex wake interference. From analyses, the pitch strategy can effectively suppress the wake effect of the upstream turbine (WT1) and increase the power output of the downstream turbine (WT2), thus improving the overall output power of the array farm. Compared with the non-pitch condition (0 pitch angle), a pitch angle of (2°) maximizes the global energy conversion efficiency of the twin-rotor array: power augmentation by 0.29%, and thrust reduction by 5%. This optimal state reduces the fatigue load of the turbine and is more conducive to long-term operation. The findings, whilst preliminary, encourage the use of turbine pitch strategies in the wind farm planning and operation.

Aerodynamic performance and flow field characteristics of wind turbines under shear incoming flow conditions

Abstract With the large size of the units, wind farms are evaluated in order to improve the accuracy of the incoming flow measurement and to improve the unit control strategy. In this paper, the turbulent wind field generated by autoregressive linear filtering using a large eddy simulation turbulence model is used to study the wind speed-induced zone under shear incoming flow conditions. At the same time, the wake and aerodynamic performances of the wind turbine under different incoming flow conditions are investigated, and conclusions are obtained. 1) The larger the shear index is, the larger the amplitude is at the first frequency component of the power and the thrust, and the larger the fatigue load is for the wind turbine. 2) For the wind turbine wake flow in the case of smaller wind turbine size, the wake velocity profiles at different shear indices cross and overlap in the transition and far wake regions. At position 0.5 D, the turbulence profiles with different shear indices basically overlap; the larger the shear index is, the more intense the wake flow exchange is and the greater the turbulence intensity in the wake region will be. 3) For the wind speed-induced region, at position −0.1 D, the incoming flow velocity distribution is subject to the combined effect of induction and shear, and the induction effect of the wind turbine wheel is a little larger. The larger the shear index, the greater the turbulence intensity.

Numerical simulation of wind turbine wake characteristics by flux reconstruction method

In the paper, a CFD method that employs the flux reconstruction (FR) method and the actuator line method (ALM) is proposed, to develop a novel numerical framework to improve the efficiency and accuracy of turbulent wake predictions of horizontal axis wind turbines (HAWT). The PyFR solver, which is an open-source program that uses the FR method is applied. The ALM is for the first time implemented in the FR solver to simulate HAWTs. To increase the fidelity of the wake prediction, the nacelle and tower of the HAWT are also modeled, and the proposed numerical simulation method is named as AL-PyFR(N&T) model. The NTNU “Blind Test 1” wind turbine is used to validate the proposed model. First, the mesh and time step dependence of the AL-PyFR(N&T) model are verified. Second, the accuracy of the proposed model is verified by comparing the velocity deficits and turbulent kinetic energy results at different downstream locations with the measured values and the results from other CFD studies. By comparison of the results with and without the effect of the nacelle and tower, it is found that tower wake plays a significant role in wake asymmetry. Crucially, the AL-PyFR(N&T) model demonstrates a capacity for accurate wake predictions with fewer mesh requirements compared to conventional CFD models. This efficiency marks a significant advancement for high-fidelity numerical simulations of offshore wind farms.

Synchronised WindScanner field measurements of the induction zone between two closely spaced wind turbines

Abstract. Field measurements of the flow interaction between the near wake of an upstream wind turbine and the induction zone of a downstream turbine are scarce. Measuring and characterising these flow features in wind farms under various operational states can be used to evaluate numerical flow models and design of control systems. In this paper, we present induction zone measurements of a utility-scale 3.5 MW turbine with a rotor diameter of 126 m in a two-turbine wind farm operating under waked and unwaked conditions. The measurements were acquired by two synchronised continuous-wave WindScanner lidars that could resolve longitudinal and lateral velocities by dual-Doppler reconstruction. An error analysis was performed to quantify the uncertainty in measuring complex flow situations with two WindScanners. This is done by performing a large-eddy simulation while using the same measurement layout, modelling the WindScanner sensing characteristics and simulating similar inflow conditions observed in the field. The flow evolution in the induction zone of the downstream turbine was characterised by performing horizontal-plane dual-Doppler scans at hub height. The measurements were conducted for undisturbed, fully waked and partially waked flows. Evaluation of the engineering models of the undisturbed induction zone showed good agreement along the rotor axis. In the full-wake case, the measurements indicated a deceleration of the upstream turbine wake due to the downstream turbine induction zone as a result of the very short turbine spacing. During a wake steering experiment, the interaction between the laterally deflected wake of the upstream turbine and the induction zone of the downstream turbine could be measured for the first time in the field. Additionally, the analyses highlight the affiliated challenges while conducting field measurements with synchronised lidars.

Investigation of three-dimensional wake width for offshore wind turbines under complex environmental conditions by large eddy simulation

Abstract The wake of wind turbines is a main concern for offshore wind farms, in which the wake width is a key index and needs to be accurately predicted. However, the existing wake width models have shortcomings in predicting the wake of wind turbines in different offshore environments. In view of this, large eddy simulation (LES) is adopted to simulate offshore wind turbines under various environmental conditions. The analyses show that there are evident differences in wake widths between horizontal and vertical directions. The variations of turbulence intensity and wind speed in the environment have significant effects on the wake width. By fitting the simulation results, a three-dimensional (3-D) wake width model is proposed to predict the wake widths in horizontal and vertical directions, which considers the effects of lateral and vertical turbulence intensities on the wake width in different directions, and uses the thrust coefficient to reflect the effect of wind speed. The proposed 3-D model is then compared with existing models through test cases, indicating that it is more accurate in predicting wake widths in horizontal and vertical directions under different environmental conditions, meanwhile shows good applicability in complex offshore environments.

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.

Tailoring anisotropic synthetic inflow turbulence generator for wind turbine wake simulations

In computational fluid dynamics, defining precise boundary conditions, especially at inlets, is of great importance. Inlet flows typically exhibit natural turbulence, which is managed in various ways in scale-resolving simulations. Methods to establish turbulent inlet conditions are commonly created using natural transition, uncorrelated oscillations, periodic boundary conditions from auxiliary simulations, or synthetic turbulent fields. In this study, we explore a technique aimed at generating a divergence-free synthetic inflow turbulence with arbitrary anisotropy. The methodology is based on the conventional portrayal of turbulence as consisting of several coherent structures. While our approach adeptly emulates predefined statistical characteristics across different scales, its primary focus is on generating input parameters that impact the airflow within the wake of individual wind turbines and the atmospheric boundary layer within a wind farm. The results are compared with high-resolution velocity experimental measurements, large eddy simulations, and the digital filter-based inlet boundary condition already available in OpenFOAM. The findings demonstrate that the applied inflow generator outperforms the default OpenFOAM filter, particularly in the context of a single wind turbine.

Research on three-dimensional wake model of horizontal axis wind turbine based on Weibull function

In wind turbine wake models, Gaussian models depend on multidimensional integration to ascertain the distribution of wake velocity deficits. These integrations, which often involve complex boundary conditions, significantly enhance the complexity of mathematical computations. Due to the difficulty of obtaining analytical solutions, numerical integration methods such as Monte Carlo or other numerical integration techniques are commonly employed. This study presents a three-dimensional wake model (3DJW) for horizontal axis wind turbines, utilizing the Weibull function to simplify wake deficit characterization instead of traditional Gaussian distribution methods. The 3DJW model considers wind shear effects and mass conservation laws to enhance predictions of vertical wake velocities. By integrating incoming wind conditions and turbine parameters, the model efficiently computes downstream wake velocities, improving computational efficiency. To enhance predictions in the ultra-far wake region, an improved three-dimensional Weibull wake model is proposed using the exponential fitting method. Validation through wind tunnel experiments and wind farm data demonstrates the model's accuracy in predicting wake deficits at the hub height, with relative errors in horizontal and vertical profiles mostly within 5% and 3%, respectively. The proposed model enables accurate and rapid calculation of wake velocities at any spatial location downstream, facilitating enhanced energy utilization and reduced costs.

Influence of wind direction on flow over a cliff and its interaction with a wind turbine wake

This work investigates the effect of wind direction on the flow over a cliff and its interaction with the wake of a wind turbine sited on the cliff. The cliff is modeled as a forward-facing step, and five wind directions are tested (θ=0∘, 15∘, 30∘, 45∘, and −45∘), where 0∘ represents a wind direction perpendicular to the cliff edge. The flow becomes increasingly three-dimensional with the increase in the wind direction magnitude and a cross-stream flow separation develops from the cliff leading edge. The turbulence kinetic energy decreases for wind directions higher than 15∘, which is due to the absence of the streamwise flow separation for higher wind directions. The cross-stream flow development in the base flow affects the shape of the turbine wake. A two-dimensional Gaussian fit is performed on the wake velocity deficit, which shows a slight departure from self-similarity in the lateral direction. The wake recovery slows down for wind directions higher than 15∘, which is consistent with the decrease in the wake growth rate for θ>15∘. The wake shows higher deflection and tilt angle for higher wind directions. Analysis of the streamwise momentum in the wake reveals that the advection terms play a role in slowing the wake recovery for higher wind directions. Published by the American Physical Society 2024