Wind Turbine Wake Research Articles

A Comprehensive Review on Analytical Formulations of Wind Turbine Wake Models and Future Scope in the Development of Wind Farms of Assorted Configurations

Abstract Of late, the design and development of large and small wind farms are gaining importance to meet the growing energy demand. In this aspect, several wind turbine wake models have been proposed over the years, some of which are the legacy of Jensen, Larsen, Lissaman, Frandsen, and Ainslie wake models. Despite their robustness, the analytical formulations of these models are widely explored as research tools for estimating the performance of wind farms. However, because of several limitations and assumptions like top-hat shape, Gaussian profile, axisymmetric, negligible atmospheric boundary layer effect, and others, these models often overestimate the flow characteristics. In view of this, there is always a scope for developing better correlations to predict the performance of wind farms more accurately. This article gives a conspectus of various wind turbine wake models that have evolved over the years and then recommends some conceptual wind farm designs of assorted configurations.

A novel hybrid control strategy of wind turbine wakes in tandem configuration to improve power production

The wind turbines that operate in the wake region of the upstream turbines produce less power and may suffer serious structural issues due to highly unsteady flows, which can reduce the life expectancy of the turbines. In this study, a novel hybrid wake control strategy for the wind farm power generation enhancement is proposed, which is based on highly accurate large eddy simulations coupled with the actuator line method. The combined effects of yaw angle and tilt angle control methods on the performance improvement of downstream wind turbines in wind farm layouts have not yet been investigated. This work would be the first attempt to evaluate the hybrid wake-control strategy of tandem wind turbines. It is found that the vortex generation is stronger at lower tilt angles because more parts of the rotor are affected by the wakes of the upstream wind turbine. An optimisation analysis is also provided to find the optimum wake deflection angles of the upstream turbine to maximize the electrical power generation. The results show that an accumulative power production increment of 17.1% is achieved by controlling both yaw angle (θ=30o), and tilt angle (φ=24o). The power obtained in the present study is approximately 6.1% higher than previous wake control techniques. By using the hybrid control strategy, an annual energy production enhancement of 3.7% is achieved, which is higher than the previous wake-controlled wind farm layouts.

RANS modeling of a single wind turbine wake in the unstable surface layer

Abstract. Unstable atmospheric conditions are often observed during the daytime over land and for significant periods offshore and are hence relevant for wake studies. A simple k–ε RANS turbulence model for simulation of wind turbine wakes in the unstable surface layer is presented, which is based on Monin–Obukhov similarity theory (MOST). The turbulence model parametrizes buoyant production of turbulent kinetic energy (TKE) without the use of an active temperature equation, and flow balance is ensured throughout the domain by modifications of the turbulence transport equations. Large eddy simulations and experimental data from the literature are used for validation of the model.

Analytical all-induction state model for wind turbine wakes

Analytical wind turbine wake models are prone to failure when the turbine induction factor increases, as they do not account for the increasingly important effects of low wake pressure. This work proposes a novel analytical wake model which incorporates the effect of wake pressure in its predictions. Comparison with high-fidelity wind turbine simulations shows that the newly developed model is comparable to conventional ones at low induction factors, but continues to be accurate at higher induction factors where existing models break down.

Comparative study of decentralized instantaneous and wind-interval-based controls for in-line two scale wind turbines

The existing decentralized wind farm control incorporating the wind turbine wake interaction has almost all concentrated on the condition of fixed wind speed/direction without considering the variability of wind in nature. Meanwhile, most of the current wake models cannot meet the requirement for wind turbine control optimization research with the high demand of wake calculation speed and accuracy. In this paper, a novel decentralized control strategy, named the wind-interval-based (WIB) control which adopts the uniform operation among the same interval of variable wind speeds/directions, is proposed for the control optimization study of in-line two scaling wind turbines for demonstration. To prove the effectiveness of the new control mechanism, the ideal instantaneous control is introduced for the comparative study. At the same time, a wake model incorporating the two directly controllable parameters (i.e., the tip speed ratio λ and pitch angle γ) is established based on artificial neural network (ANN). The comparative results show that the total power output applying the instantaneous control and the new WIB control mechanisms are increased by 0.1%–4.1% and 0.45%–3.9% depending on the tested wind scenarios, respectively. By comparing the optimized power output with the two controls, it is found that the error between them is generally lower than 3%, while the proposed WIB control reduces the operational difficulty to a large extent facilitating its application to the real wind turbine operation in reality. In summary, this paper shows that the new proposed WIB control not only reduces the difficulties of the wind turbine control mechanism, but maintains the control effectiveness by achieving a comparable total power output with respect to the traditional instantaneous control, which is of great significance to the wind farm developer.

Numerical Investigations of Wake Expansion in the Offshore Wind Farm Using a Large Eddy Simulation

Due to abundant wind resources and land saving, offshore wind farms have been vigorously developed worldwide. The wake of wind turbines is an important topic of offshore wind farms, in which the wake expansion is a key issue for the wake model and the layout optimization of a wind farm. The large eddy simulation (LES) is utilized to investigate various offshore wind farms under different operating conditions. The numerical results indicate that it is more accurate to calculate the wake growth rate using the streamwise turbulence intensity or the total turbulence intensity in the environment. By fitting the results of the LES, two formulae are proposed to calculate the wake growth rate of the upstream wind turbine. The wake expansion of the downstream wind turbine is analyzed, and the method of calculating the wake growth rate is introduced. The simulation indicates that the wake expansion of the further downstream wind turbines is significantly reduced. The smaller lateral distance of wind turbines in the offshore wind farm has the less wake expansion of the wind turbines. The wake expansion under different inflow wind speeds is also analyzed, while the wake expansion of wind turbines under more complex conditions needs to be further studied.

Numerical Investigation on the Effects of Forest Heterogeneity on Wind-Turbine Wake

This work aims at investigating the effects of forest heterogeneity on a wind-turbine wake under a neutrally stratified condition. Three types of forests, homogeneous (idealized), a real forest having natural heterogeneity, and an idealized forest having a strong heterogeneity, are considered in this study. For each type, three forest densities with Leaf Area Index (LAI) values of 0.42,1.7, and 4.25 are investigated. The data of the homogeneous forest are estimated from a dense forest site located in Ryningsnäs, Sweden, while the real forest data are obtained using an aerial LiDAR scan over a site located in Pihtipudas, about 140 km north of Jyväskylä, Finland. The idealized forest is made up of small forest patches to represent a strong heterogeneous forest. The turbine definition used to model the wake is the NREL 5 MW reference wind turbine, which is modeled in the numerical simulations by the Actuator Line Model (ALM) approach. The numerical simulations are implemented with OpenFOAM based on the Unsteady Reynolds Averaged Navier–Stokes (U-RANS) approach. The results highlight the effects of forest heterogeneity levels with different densities on the wake formation and recovery of a stand-alone wind-turbine wake. It is observed that the homogeneous forests have higher turbulent kinetic energy (TKE) compared to the real forests for an LAI value less than approximately 2, while forests with an LAI value above 2 show a higher TKE in the real forest than in the homogeneous and the strong heterogeneous (patched) forest. Technically, the deficits in the wake region are more pronounced in the strong heterogeneous forests than in other forest cases.

A new three-dimensional analytical model for wind turbine wake turbulence intensity predictions

In wind farm design, accurately predicting the wake turbulence level is crucial for turbine power and load evaluation. However, a knowledge gap still exists on the characteristics of wake turbulence, meanwhile there has been little work on the development of related engineering models. In view of this, firstly, one-dimensional analytical models that can estimate the wake width and maximum wake turbulence level at any streamwise positions are proposed and validated. Based on these, a highly simple three-dimensional cosine shape (3D-COTI) model is proposed for estimating the wake turbulence intensity in an effective way. Moreover, by taking into account the wind shear and ground effects, this proposed model is capable of describing the anisotropic property of the 3-D wake field. Afterwards, model evaluations are performed through several test cases consisting various types of turbines operating under a wide range of inflow conditions. Overall, the proposed model shows a good agreement with the measurements about the spatial distribution of turbulence enhancement within the wake flow. Because of its good accuracy, simplicity and universality, the present model has potential for large-scale wind farm applications.

The far wake of porous disks and a model wind turbine: Similarities and differences assessed by hot-wire anemometry

The wakes of two different porous disks have been evaluated experimentally. Such disks are commonly used as physical actuator disk analogs for wind turbines. One disk is made of a uniform wire mesh, while the other has a nonuniform design with radial spars connected by rings. The disks have the same solidity and produce approximately the same drag. The wakes have also been compared to the wake of a model wind turbine and a solid disk. In contrast to earlier studies, the far wake, up to 30 diameters downstream, is included in the comparison. In the near wake, the velocity deficit and turbulence intensity profiles of the disk wakes differ significantly. High levels of turbulence intensity in the wake of the nonuniform disk increase the transverse transport in the wake, which leads to faster spreading and lower velocity deficits in the far wake, compared to the uniform disk and the wind turbine. High velocity gradients in the wake of the uniform disk give rise to turbulence production farther downstream, maintaining higher turbulence levels in the far wake. In addition, coherent vortex shedding is only identified in the wake of the nonuniform disk. None of the disks were able to replicate the asymmetric features of the wind turbine wake. Nonetheless, the results highlight important flow physics that should be considered in the design process of a porous disk used as a wind turbine surrogate.

Piloted Simulation of the Rotorcraft Wind Turbine Wake Interaction during Hover and Transit Flights

Helicopters are used for offshore wind farms for maintenance and support flights. The number of helicopter operations is increasing with the expansion of offshore wind energy, which stresses the point that the current German regulations have not yet been validated through scientific analysis. A collaborative research project between DLR, the Technical University of Munich, the University of Stuttgart and the University of Tübingen has been conducted to examine the sizes of the flight corridors on offshore wind farms and the lateral safety clearance for helicopter hoist operations at offshore wind turbines. This paper details the results of piloted helicopter simulations in a realistic offshore wind farm scenario. The far-wake of rotating wind turbines and the near-wake of non-rotating wind turbines have been simulated with high-fidelity computational fluid dynamics under realistic turbulent inflow conditions. The resulting flow fields have been processed by superposition during piloted simulations in the research flight simulator AVES to examine the flight corridors in transit flights and the lateral safety clearance in hovering flights. The results suggest a sufficient size for the flight corridor and sufficient lateral safety clearance at the offshore wind turbines in the considered scenarios.

Meso- to microscale modeling of atmospheric stability effects on wind turbine wake behavior in complex terrain

Abstract. Terrain-induced flow phenomena modulate wind turbine performance and wake behavior in ways that are not adequately accounted for in typical wind turbine wake and wind plant design models. In this work, we simulate flow over two parallel ridges with a wind turbine on one of the ridges, focusing on conditions observed during the Perdigão field campaign in 2017. Two case studies are selected to be representative of typical flow conditions at the site, including the effects of atmospheric stability: a stable case where a mountain wave occurs (as in ∼ 50 % of the nights observed) and a convective case where a recirculation zone forms in the lee of the ridge with the turbine (as occurred over 50 % of the time with upstream winds normal to the ridgeline). We use the Weather Research and Forecasting Model (WRF), dynamically downscaled from the mesoscale (6.75 km resolution) to microscale large-eddy simulation (LES) at 10 m resolution, where a generalized actuator disk (GAD) wind turbine parameterization is used to simulate turbine wakes. We compare the WRF–LES–GAD model results to data from meteorological towers, lidars, and a tethered lifting system, showing good qualitative and quantitative agreement for both case studies. Significantly, the wind turbine wake shows different amounts of vertical deflection from the terrain and persistence downstream in the two stability regimes. In the stable case, the wake follows the terrain along with the mountain wave and deflects downwards by nearly 100 m below hub height at four rotor diameters downstream. In the convective case, the wake deflects above the recirculation zone over 40 m above hub height at the same downstream distance. Overall, the WRF–LES–GAD model is able to capture the observed behavior of the wind turbine wakes, demonstrating the model's ability to represent wakes over complex terrain for two distinct and representative atmospheric stability classes, and, potentially, to improve wind turbine siting and operation in hilly landscapes.

Wind turbine wake calculation model with exponential reciprocal attenuation

This paper studies the general wind turbine wake mathematical model—Jensen model based on some famous wind tunnel experimental data. Based on the study of the initial Jensen wake model equation, the improved semi empirical Jensen model equation was studied in this paper considering the factors of wind turbine wake attenuation in the distance. According to the form of exponential reciprocal attenuation, the model was modified again. Corresponding Jensen exponential reciprocal attenuation wake model was obtained. The simulations and contrast experiments were carried out in the advanced calculation tool. Corresponding comparison experiments of various wake equations were carried out. The theoretical and experimental results show that Jensen exponent reciprocal attenuation wake model can accurately calculate the variation of general wind turbine wake. Its development and application have important theoretical significance and practical value for wind energy utilization.

Development of a curled wake of a yawed wind turbine under turbulent and sheared inflow

Abstract. Redirecting the wake from an upstream wind turbine by yawing its rotor can reduce the negative impact of the wake on a downstream turbine. The present research investigated wind turbine wake behaviour for three yaw angles [-30,0,30∘] at different inflow turbulence levels and shear profiles under controlled conditions. Experiments were conducted using a model wind turbine with 0.6 m diameter (D) in a large wind tunnel. A short-range lidar WindScanner was used to map the wake with high spatial and temporal resolution in vertical, cross-stream planes at different downstream locations and in a horizontal plane at hub height. The lidar WindScanner enabled fast measurements at multiple locations in comparison to the standard hot-wire measurements. The flow structures and the energy dissipation rate of the wake were measured from 1 up to 10 D, and for one inflow case up to 16 D, downstream of the turbine rotor. A strong dependency of the wake characteristics on both the yaw angle and the inflow conditions was observed. In addition, the curled wake that develops under yaw misalignment due to the counter-rotating vortex pair was more pronounced with a boundary layer (sheared) inflow condition than for uniform inflow with different turbulence levels. Furthermore, the lidar velocity data and calculated quantities such as the energy dissipation rate compared favourably with hot-wire data from previous experiments with a similar inflow condition and wind turbine model in the same facility, lending credibility to the measurement technique and methodology used here. The results of this measurement campaign provided a deeper understanding of the development of the wake for different yaw angles and inflow conditions which can help improve wake models.

Application of the Townsend–George theory for free shear flows to single and double wind turbine wakes – a wind tunnel study

Abstract. The evolution of the mean velocity and the turbulence downstream of wind turbine wakes within the atmospheric boundary layer has been studied over the past decades, but an analytical description is still missing. One possibility to improve the comprehension of this is to look into the modeling of turbulent bluff body wakes. There, by means of the streamwise scaling of the centerline mean velocity deficit, the nature of the turbulence inside a wake can be classified. In this paper, we introduce the analytical model of classical wake theory as introduced by Albert Alan Townsend and William Kenneth George. To test the theories, data were obtained from wind tunnel experiments using hot-wire anemometry in the wakes of a single model wind turbine and a model wind turbine operating in the wake of an upstream model wind turbine. First, we test whether the requirements under which the Townsend–George theory is valid are fulfilled in the wake of a wind turbine. Based on this verification we apply the Townsend–George theory. Further, this framework allows for distinguishing between two types of turbulence, namely equilibrium and non-equilibrium turbulence. We find that the turbulence at the centerline is equilibrium turbulence and that non-equilibrium turbulence may be present at outer parts of the wake. Finally, we apply the Townsend–George theory to characterize the wind turbine wake, and we compare the results to the Jensen and the Bastankhah–Porté-Agel models. We find that the recent developments from the classical bluff body wake formalism can be used to further improve the wind turbine wake models. Particularly, the classical bluff body wake models perform better than the wind turbine wake models due to the presence of a virtual origin in the scalings, and we demonstrate the possibility of improving the wind turbine wake models by implementing this parameter. We also see how the dissipation changes across the wake, which is important to model wakes within wind farms correctly.

Wind turbine wake computation with the ST-VMS method and isogeometric discretization: Directional preference in spatial refinement

Wind turbine wake computation with the ST-VMS method and isogeometric discretization: Directional preference in spatial refinement

Onset of wake meandering for a floating offshore wind turbine under side-to-side motion

Wind turbine wakes, being convectively unstable, may behave as an amplifier of upstream perturbations and make downstream turbines experience strong inflow fluctuations. In this work, we investigate the effects of the side-to-side motion of a floating offshore wind turbine (FOWT) on wake dynamics using large-eddy simulation and linear stability analysis (LSA). When the inflow turbulence intensity is low, simulation results reveal that the turbine motion with certain Strouhal numbers$St = fD/U_\infty \in (0.2,0.6)$(where$f$is the motion frequency,$D$is the rotor diameter, and$U_\infty$is the incoming wind speed), which overlap with the Strouhal numbers of wake meandering induced by the shear layer instability, can lead to wake meandering with amplitudes being one order of magnitude larger than the FOWT motion for the most unstable frequency. For high inflow turbulence intensity, on the other hand, the onset of wake meandering is dominated by the inflow turbulence. The probability density function of the spanwise instantaneous wake centres is observed being non-Gaussian and closely related to that of the side-to-side motion. This complements the existing wake meandering mechanisms, that the side-to-side motion of an FOWT can be a novel origin for the onset of wake meandering. It is also found that LSA can predict the least stable frequencies and the amplification factor with acceptable accuracy for motion amplitude$0.01D$. Effects of nonlinearity are observed when motion amplitude increases to$0.04D$, for which the most unstable turbine oscillations shift slightly to lower frequencies and the amplification factor decreases.

Data-driven wind turbine wake modeling via probabilistic machine learning

Wind farm design primarily depends on the variability of the wind turbine wake flows to the atmospheric wind conditions and the interaction between wakes. Physics-based models that capture the wake flow field with high-fidelity are computationally very expensive to perform layout optimization of wind farms, and, thus, data-driven reduced-order models can represent an efficient alternative for simulating wind farms. In this work, we use real-world light detection and ranging (LiDAR) measurements of wind-turbine wakes to construct predictive surrogate models using machine learning. Specifically, we first demonstrate the use of deep autoencoders to find a low-dimensional latent space that gives a computationally tractable approximation of the wake LiDAR measurements. Then, we learn the mapping between the parameter space and the (latent space) wake flow fields using a deep neural network. Additionally, we also demonstrate the use of a probabilistic machine learning technique, namely, Gaussian process modeling, to learn the parameter-space-latent-space mapping in addition to the epistemic and aleatoric uncertainty in the data. Finally, to cope with training large datasets, we demonstrate the use of variational Gaussian process models that provide a tractable alternative to the conventional Gaussian process models for large datasets. Furthermore, we introduce the use of active learning to adaptively build and improve a conventional Gaussian process model predictive capability. Overall, we find that our approach provides accurate approximations of the wind-turbine wake flow field that can be queried at an orders-of-magnitude cheaper cost than those generated with high-fidelity physics-based simulations.

Decoupling wind–wave–wake interactions in a fixed-bottom offshore wind turbine

The interest and benefits of offshore wind energy have also brought along legitimate challenges. In the golden age of renewables, offshore wind-energy holds the most potential for growth, but the burgeoning benefits of offshore energy are also entangled in dynamics not fully understood, such as the dynamic coupling of the atmospheric boundary layer, the wind-turbine generated wake, and the surface waves. This study establishes the first experimental turbulent-interaction between the traditionally distinct fields of airflow-dynamics above the air–sea interface and the characterization of wind-turbine wakes. The study details a non-trivial experimental setup combining a wave tank, wind tunnel, and scaled fixed-bottom wind turbine. Particle image velocimetry (PIV) was performed on three successive image planes to visualize wind–wake, wind–wave, and wave–wake interaction far downstream of the turbine. The wave phase-dependent dynamics of the turbine wake on the passing ocean-wave profile and location are outlined. The velocity and stress profiles showed a horizontal wake-pumping motion along with vertical wake-lifting of the offshore turbulent wake. The data were decomposed into incremental wave-phases revealing localized and predictable velocity maxima, stress maxima, and wake modulation that is normally obscured by a time-averaged mean. The results quantified wake pumping and meandering, as well as the Reynolds stress and wave-induced phase-averaged fluctuations. There is a phase-dependent oscillation in both the horizontal (streamwise) direction, as well as a vertical displacement of the wake. The shear stress and advection terms show this imbalance along the vertical direction of the turbine. The results illustrate a more complete picture of offshore wind-energy dynamics, which have implications for insidious mechanical issues, design optimization and/or control strategies.

A novel actuator line-immersed boundary (AL-IB) hybrid approach for wake characteristics prediction of a horizontal-axis wind turbine

The core idea of the actuator line (AL) model is to simplify the horizontal-axis wind turbine (HAWT) into a line with force distributed along the radial direction. The body force on the AL is employed to simulate the effect of the HAWT on the flow field, and the Navier-Stokes (N-S) equation is solved to obtain the aerodynamic and wake characteristics of the HAWT. Recently, the AL model has been comprehensively implemented in the investigation of wind turbine wakes. However, the existing standard AL model ignores or inaccurately describes the nacelle effects, which have been proven to considerably affect the accuracy of the near wake simulation. This paper develops an actuator line-immersed boundary (AL-IB) hybrid approach for the HAWT with high-accuracy and low-computational cost to address the physics problem underlying here. The wind turbine adopts the AL model instead of the body-fitted mesh method, and the nacelle is realized by the immersed boundary (IB) method. The large eddy simulation (LES) with a new localized dynamic Smagorinsky (LDS) sub-grid scale (SGS) model is adopted to model the turbulence to improve simulation accuracy of the near wake, thereby forming a set of high-fidelity numerical simulation framework of the HAWT wake. Firstly, the simulation accuracy of the AL-IB hybrid approach is validated by comparing the mean wake velocity profiles and turbulent kinetic energy (TKE) profiles of the HAWT with the experimental measurement results of the NTNU “Blind test 1”. Furthermore, the research is extended to the wake difference of the HAWT under two different numerical methods (AL and AL-IB). The results show that the solver developed based on AL-IB hybrid approach has higher accuracy than the standard AL model, which provides a feasible way for the refined numerical simulation of the large-scale wind farm.

Experimental study on application of nacelle-mounted LiDAR for analyzing wind turbine wake effects by distance

The blade rotation of wind turbines causes the wake effect, which affects energy production of downstream wind turbines, and its magnitude and intensity vary with distance. To optimize the wind turbine layout for maximum efficiency, it is necessary to quantitatively evaluate the wake effect by distance. Using a nacelle LiDAR, it is possible to concurrently measure wind conditions at multiple positions. This study presents the results of analyzing the wake effects by distance, behind a 3 MW wind turbine, using a nacelle LiDAR. Wake wind data measured at 10 points by a nacelle LiDAR, mounted on the nacelle of a 1.5 MW downstream wind turbine, were analyzed against freestream wind data obtained from a 70-m-high met mast installed near the turbine. Variations in wind conditions in the wake region were analyzed as a function of distance and wind direction, and the influence of these factors on the power production of the downstream wind turbine was estimated using SCADA. The variations in wind speeds and turbulence intensities at multiple distances between 0.9D and 4.8D were quantitatively evaluated. Additionally, it was confirmed that the wake effects reduced the power performance by 23% at 5.7D under a wind speed of 8.5 m/s.