Validation of the standalone implementation of the dynamic wake meandering model for power production

This paper presents validation for using the standalone implementation of the dynamic wake meandering (DWM) model to conduct numerical simulations of power production of rows of wind turbines. The standalone DWM model is an alternative formulation of the conventional DWM model that does not require information exchange with an aeroelastic code. As a consequence, the standalone DWM model has significantly shorter computational times and lower demands on the user environment. The drawback of the standalone DWM model is that it does not have the capability to predict turbine loads. Instead, it should be seen as an alternative for simulating the power production of a wind farm. The main advantage of the standalone DWM model is the ability to capture the key physics for wake dynamics such as the turbine specific induction, the build‐up of wake turbulence and wake deficit in the wind farm, and the effect of ambient turbulence intensity and atmospheric stability. The predicted power production of the standalone DWM model is compared with that of full scale measurements from Horns Rev, Lillgrund, Nysted and Weingermeer wind farms. Overall, the difference between the models predictions and the reference data is on the order of 5%. Copyright © 2014 John Wiley & Sons, Ltd.     

On the application of the Jensen wake model using a turbulence‐dependent wake decay coefficient: the Sexbierum case

We present a methodology to process wind turbine wake simulations, which are closely related to the nature of wake observations and the processing of these to generate the so‐called wake cases. The method involves averaging a large number of wake simulations over a range of wind directions and partly accounts for the uncertainty in the wind direction assuming that the same follows a Gaussian distribution. Simulations of the single and double wake measurements at the Sexbierum onshore wind farm are performed using a fast engineering wind farm wake model based on the Jensen wake model, a linearized computational fluid dynamics wake model by Fuga and a nonlinear computational fluid dynamics wake model that solves the Reynolds‐averaged Navier–Stokes equations with a modified k‐ε turbulence model. The best agreement between models and measurements is found using the Jensen‐based wake model with the suggested post‐processing. We show that the wake decay coefficient of the Jensen wake model must be decreased from the commonly used onshore value of 0.075 to 0.038, when applied to the Sexbierum cases, as wake decay is related to the height, roughness and atmospheric stability and, thus, to turbulence intensity. Based on surface layer relations and assumptions between turbulence intensity and atmospheric stability, we find that at Sexbierum, the atmosphere was probably close to stable, although the stability was not observed. We support these assumptions using detailed meteorological observations from the Høvsøre site in Denmark, which is topographically similar to the Sexbierum region. © 2015 The Authors. Wind Energy published by John Wiley & Sons Ltd.     

Actuator volumes and hr‐adaptive methods for three‐dimensional simulation of wind turbine wakes and performance

This paper presents a three‐dimensional numerical model for horizontal axis wind turbines, capable of simulating both the dynamic response of the turbine to changing flow conditions, and the full wake generated by the turbine. The turbine model is coupled to computational fluid dynamics software using Large Eddy Simulation to solve for unsteady flow conditions, with the Smagorinsky method handling sub‐grid turbulence. Wind tunnel simulations are compared with experimental data, and then a simulation of a real turbine in complex terrain is compared with LIDAR data from the same site, in both cases agreeing favourably. Copyright © 2011 John Wiley & Sons, Ltd.     

An experimental and numerical study of the atmospheric stability impact on wind turbine wakes

In this paper, the impact of atmospheric stability on a wind turbine wake is studied experimentally and numerically. The experimental approach is based on full‐scale (nacelle based) pulsed lidar measurements of the wake flow field of a stall‐regulated 500 kW turbine at the DTU Wind Energy, Risø campus test site. Wake measurements are averaged within a mean wind speed bin of 1 m s^?1 and classified according to atmospheric stability using three different metrics: the Obukhov length, the Bulk–Richardson number and the Froude number. Three test cases are subsequently defined covering various atmospheric conditions. Simulations are carried out using large eddy simulation and actuator disk rotor modeling. The turbulence properties of the incoming wind are adapted to the thermal stratification using a newly developed spectral tensor model that includes buoyancy effects. Discrepancies are discussed, as basis for future model development and improvement. Finally, the impact of atmospheric stability on large‐scale and small‐scale wake flow characteristics is presently investigated. Copyright © 2015 John Wiley & Sons, Ltd.     

A numerical study of tilt‐based wake steering using a hybrid free‐wake method

This study investigates the potential of using tilt‐based wake steering to alleviate wake shielding problems experienced by downwind turbines. Numerical simulations of turbine wakes have been conducted using a hybrid free‐wake analysis combining vortex lattice method (VLM) and an innovative free‐wake model called constant circulation contour method (CCCM). Simulation results indicate tilting a horizontal axis wind turbine's shaft upward causes its wake to ascend, carrying energy‐depleted air upward and pumping more energetic replacement air into downstream turbines, thereby having the potential to recover downstream turbine power generation. Wake cross section vorticity and velocity distributions reveal that the wake upward transport is caused by the formation of near‐wake streamwise vorticity components, and furthermore, the wake velocity deficit is weakened because of the skewed wake structure. Beyond the single turbine wake simulation, an inline two‐turbine case is performed as an assessment of the wake steering influence on the two‐turbine system and as an exploratory work of simulating turbine‐wake interactions using the hybrid free‐wake model. Individual and total turbine powers are calculated. A comparison between different tilting angles suggests turbine power enhancement may be achieved by tilting the upstream turbine and steering its wakes away from the downstream turbine.     

Performance and wake comparison of horizontal and vertical axis wind turbines under varying surface roughness conditions

A numerical study of both a horizontal axis wind turbine (HAWT) and a vertical axis wind turbine (VAWT) with similar size and power rating is presented. These large scale turbines have been tested when operating stand‐alone at their optimal tip speed ratio (TSR) within a neutrally stratified atmospheric boundary layer (ABL). The impact of three different surface roughness lengths on the turbine performance is studied for the both turbines. The turbines performance, the response to the variation in the surface roughness of terrain, and the most relevant phenomena involved on the resulting wake were investigated. The main goal was to evaluate the differences and similarities of these two different types of turbine when they operate under the same atmospheric flow conditions. An actuator line model (ALM) was used together with the large eddy simulation (LES) approach for predicting wake effects, and it was implemented using the open‐source computational fluid dynamics (CFD) library OpenFOAM to solve the governing equations and to compute the resulting flow fields. This model was first validated using wind tunnel measurements of power coefficients and wake of interacting HAWTs, and then employed to study the wake structure of both full scale turbines. A preliminary study test comparing the forces on a VAWT blades against measurements was also investigated. These obtained results showed a better performance and shorter wake (faster recovery) for an HAWT compared with a VAWT for the same atmospheric conditions.     

A pragmatic approach to wind farm simulations using the dynamic wake meandering model

This paper presents a computationally efficient method for using the dynamic wake meandering model to conduct simulations of wind farm power production. The method is based on creating a database, which contains the time and rotor‐averaged wake effect at any point downstream of a wake‐emitting turbine operating in arbitrary ambient conditions and at an arbitrary degree of wake influence. This database is later used as a look‐up table at runtime to estimate the operating conditions at all turbines in the wind farm, thus eliminating the need to run the dynamic wake meandering model at runtime. By using the proposed method, the time required to conduct wind farm simulations is reduced by three orders of magnitude compared with running the standalone dynamic wake meandering model at runtime. As a result, the wind farm production dynamics for a farm of 100 turbines at 10,000 different sets of ambient conditions run on a normal laptop in 1 h. The method is validated against full scale measurements from the Smøla and OWEZ wind farms, and fair agreement is achieved. Copyright © 2014 John Wiley & Sons, Ltd.     

On atmospheric stability in the dynamic wake meandering model

The present study investigates a new approach for capturing the effects of atmospheric stability on wind turbine wake evolution and wake meandering by using the dynamic wake meandering model. The most notable impact of atmospheric stability on the wind is the changes in length and velocity scales of the atmospheric turbulence. The length and velocity scales in the turbulence are largely responsible for the way in which wind turbine wakes meander as they convect downstream. The hypothesis of the present work is that appropriate turbulence scales can be extracted from the oncoming atmospheric turbulence spectra and applied to the dynamic wake meandering model to capture the correct wake meandering behaviour. The ambient turbulence in all stability classes is generated using the Mann turbulence model, where the effects of non‐neutral atmospheric stability are approximated by the selection of input parameters. In order to isolate the effect of atmospheric stability, simulations of neutral and unstable atmospheric boundary layers using large‐eddy simulation are performed at the same streamwise turbulence intensity level. The turbulence intensity is kept constant by calibrating the surface roughness in the computational domain. The changes in the turbulent length scales due to the various atmospheric stability states impact the wake meandering characteristics and thus the power generation by the individual turbines. The proposed method is compared with results from both large‐eddy simulation coupled with an actuator line model and field measurements, where generally good agreement is found with respect to the velocity, turbulence intensity and power predictions. Copyright © 2013 John Wiley & Sons, Ltd.     

Empirical modeling of single‐wake advection and expansion using full‐scale pulsed lidar‐based measurements

In the present paper, single‐wake dynamics have been studied both experimentally and numerically. The use of pulsed lidar measurements allows for validation of basic dynamic wake meandering modeling assumptions. Wake center tracking is used to estimate the wake advection velocity experimentally and to obtain an estimate of the wake expansion in a fixed frame of reference. A comparison shows good agreement between the measured average expansion and the Computational Fluid Dynamics (CFD) large eddy simulation–actuator line computations. Frandsen's expansion model seems to predict the wake expansion fairly well in the far wake but lacks accuracy in the outer region of the near wake. An empirical relationship, relating maximum wake induction and wake advection velocity, is derived and linked to the characteristics of a spherical vortex structure. Furthermore, a new empirical model for single‐wake expansion is proposed based on an initial wake expansion in the pressure‐driven flow regime and a spatial gradient computed from the large‐scale lateral velocities, and thus inspired by the basic assumption behind the dynamic wake meandering model. Copyright © 2014 John Wiley & Sons, Ltd.     

Reynolds number dependence of turbulence statistics in the wake of wind turbines

A wind tunnel experiment has been performed to quantify the Reynolds number dependence of turbulence statistics in the wake of a model wind turbine. A wind turbine was placed in a boundary layer flow developed over a smooth surface under thermally neutral conditions. Experiments considered Reynolds numbers on the basis of the turbine rotor diameter and the velocity at hub height, ranging from Re = 1.66 × 10⁴ to 1.73 × 10⁵. Results suggest that main flow statistics (mean velocity, turbulence intensity, kinematic shear stress and velocity skewness) become independent of Reynolds number starting from Re ≈ 9.3 × 10⁴. In general, stronger Reynolds number dependence was observed in the near wake region where the flow is strongly affected by the aerodynamics of the wind turbine blades. In contrast, in the far wake region, where the boundary layer flow starts to modulate the dynamics of the wake, main statistics showed weak Reynolds dependence. These results will allow us to extrapolate wind tunnel and computational fluid dynamic simulations, which often are conducted at lower Reynolds numbers, to full‐scale conditions. In particular, these findings motivates us to improve existing parameterizations for wind turbine wakes (e.g. velocity deficit, wake expansion, turbulence intensity) under neutral conditions and the predictive capabilities of atmospheric large eddy simulation models. Copyright © 2011 John Wiley & Sons, Ltd.     

Simulation of wind turbine wake interaction using the vorticity transport model

The aerodynamic interactions that can occur within a wind farm can result in the constituent turbines generating a lower power output than would be possible if each of the turbines were operated in isolation. Tightening of the constraints on the siting of wind farms is likely to increase the scale of the problem in the future. The aerodynamic performance of turbine rotors and the mechanisms that couple the fluid dynamics of multiple rotors can be most readily understood by simplifying the problem and considering the interaction between only two rotors. The aerodynamic interaction between two rotors in both co‐axial and offset configurations has been simulated using the Vorticity Transport Model. The aerodynamic interaction is a function of the tip speed ratio, and both the streamwise and crosswind separation between the rotors. The simulations show that the momentum deficit at a turbine operating within the wake developed by the rotor of a second turbine is governed by the development of instabilities within the wake of the upwind rotor, and the ensuing structure of the wake as it impinges on the downwind rotor. If the wind farm configuration or wind conditions are such that a turbine rotor is subject to partial impingement by the wake produced by an upstream turbine, then significant unsteadiness in the aerodynamic loading on the rotor blades of the downwind turbine can result, and this unsteadiness can have considerable implications for the fatigue life of the blade structure and rotor hub. Copyright © 2009 John Wiley & Sons, Ltd.     

A stochastic wind turbine wake model based on new metrics for wake characterization

Understanding the detailed dynamics of wind turbine wakes is critical to predicting the performance and maximizing the efficiency of wind farms. This knowledge requires atmospheric data at a high spatial and temporal resolution, which are not easily obtained from direct measurements. Therefore, research is often based on numerical models, which vary in fidelity and computational cost. The simplest models produce axisymmetric wakes and are only valid beyond the near wake. Higher‐fidelity results can be obtained by solving the filtered Navier–Stokes equations at a resolution that is sufficient to resolve the relevant turbulence scales. This work addresses the gap between these two extremes by proposing a stochastic model that produces an unsteady asymmetric wake. The model is developed based on a large‐eddy simulation (LES) of an offshore wind farm. Because there are several ways of characterizing wakes, the first part of this work explores different approaches to defining global wake characteristics. From these, a model is developed that captures essential features of a LES‐generated wake at a small fraction of the cost. The synthetic wake successfully reproduces the mean characteristics of the original LES wake, including its area and stretching patterns, and statistics of the mean azimuthal radius. The mean and standard deviation of the wake width and height are also reproduced. This preliminary study focuses on reproducing the wake shape, while future work will incorporate velocity deficit and meandering, as well as different stability scenarios. Copyright © 2016 John Wiley & Sons, Ltd.     

Verification and validation of an actuator disc model

Wind turbine wake can be studied in computational fluid dynamics with the use of permeable body forces (e.g. actuator disc, line and surface). This paper presents a general flexible method to redistribute wind turbine blade forces as permeable body forces in a computational domain. The method can take any kind of shape discretization, determine the intersectional elements with the computational grid and use the size of these elements to redistribute proportionally the forces. This method can potentially reduce the need for mesh refinement in the region surrounding the rotor and, therefore, also reduce the computational cost of large wind farm wake simulations. The special case of the actuator disc is successfully validated with an analytical solution for heavily loaded turbines and with a full‐rotor computation in computational fluid dynamics. Copyright © 2013 John Wiley & Sons, Ltd.     

Validation of the dynamic wake meander model for loads and power production in the Egmond aan Zee wind farm

This paper investigates wake effects on load and power production by using the dynamic wake meander (DWM) model implemented in the aeroelastic code HAWC2. The instationary wind farm flow characteristics are modeled by treating the wind turbine wakes as passive tracers transported downstream using a meandering process driven by the low frequent cross‐wind turbulence components. The model complex is validated by comparing simulated and measured loads for the Dutch Egmond aan Zee wind farm consisting of 36 Vestas V90 turbine located outside the coast of the Netherlands. Loads and production are compared for two distinct wind directions—a free wind situation from the dominating southwest and a full wake situation from northwest, where the observed turbine is operating in wake from five turbines in a row with 7D spacing. The measurements have a very high quality, allowing for detailed comparison of both fatigue and min–mean–max loads for blade root flap, tower yaw and tower bottom bending moments, respectively. Since the observed turbine is located deep inside a row of turbines, a new method on how to handle multiple wakes interaction is proposed. The agreement between measurements and simulations is excellent regarding power production in both free and wake sector, and a very good agreement is seen for the load comparisons too. This enables the conclusion that wake meandering, caused by large scale ambient turbulence, is indeed an important contribution to wake loading in wind farms. Copyright © 2012 John Wiley & Sons, Ltd.     

Wake impacts on downstream wind turbine performance and yaw alignment

Aerodynamic wake interaction between commercial scale wind turbines can be a significant source of power losses and increased fatigue loads across a wind farm. Significant research has been dedicated to the study of wind turbine wakes and wake model development. This paper profiles influential wake regions for an onshore wind farm using 6 months of recorded SCADA (supervisory control and data acquisition) data. An average wind velocity deficit of over 30% was observed corresponding to power coefficient losses of 0.2 in the wake region. Wind speed fluctuations are also quantified for an array of turbines, inferring an increase in turbulence within the wake region. A study of yaw data within the array showed turbine nacelle misalignment under a range of downstream wake angles, indicating a characteristic of wind turbine behaviour not generally considered in wake studies. The turbines yaw independently in order to capture the increased wind speeds present due to the lateral influx of turbulent wind, contrary to many experimental and simulation methods found in the literature. Improvements are suggested for wind farm control strategies that may improve farm‐wide power output. Additionally, possible causes for wind farm wake model overestimation of wake losses are proposed.Copyright © 2012 John Wiley & Sons, Ltd.     

Application and validation of incrementally complex models for wind turbine aerodynamics,isolated wind turbine in uniform inflow conditions

A comparison of several incrementally complex methods for predicting wind turbine performance, aeroelastic behavior, and wakes is provided. Depending on a wind farm's design, wake interference can cause large power losses and increased turbulence levels within the farm. The goal is to employ modeling methods to reach an improved understanding of wake effects and to use this information to better optimize the layout of new wind farms. A critical decision faced by modelers is the fidelity of the model that is selected to perform simulations. The choice of model fidelity can affect the accuracy, but will also greatly impact the computational time and resource requirements for simulations. To help address this critical question, three modeling methods of varying fidelity have been developed side by side and are compared in this article. The models from low to high complexity are as follows: a blade element‐based method with a free‐vortex wake, an actuator disc‐based method, and a full rotor‐based method. Fluid/structure interfaces are developed for the aerodynamic modeling approaches that allow modeling of discrete blades and are then coupled with a multibody structural dynamics solver in order to perform an aeroelastic analysis. Similar methods have individually been tested by researchers, but we suggest that by developing a suite of models, they can be cross‐compared to grasp the subtleties of each method. The modeling methods are applied to the National Renewable Energy Laboratory Phase VI rotor to predict the turbine aerodynamic and structural loads and then also the wind velocities in the wake. The full rotor method provides the most accurate predictions at the turbine and the use of adaptive mesh refinement to capture the wake to 20 radii downstream is proven particularly successful. Though the full rotor method is unmatched by the lower fidelity methods in stalled conditions and detailed prediction of the downstream wake, there are other less complex conditions where these methods perform as accurately as the full rotor method. Copyright © 2014 John Wiley & Sons, Ltd.     

Simulating the aerodynamic performance and wake dynamics of a vertical‐axis wind turbine

The accurate prediction of the aerodynamics and performance of vertical‐axis wind turbines is essential if their design is to be improved but poses a significant challenge to numerical simulation tools. The cyclic motion of the blades induces large variations in the angle of attack of the blades that can manifest as dynamic stall. In addition, predicting the interaction between the blades and the wake developed by the rotor requires a high‐fidelity representation of the vortical structures within the flow field in which the turbine operates. The aerodynamic performance and wake dynamics of a Darrieus‐type vertical‐axis wind turbine consisting of two straight blades is simulated using Brown's Vorticity Transport Model. The predicted variation with azimuth of the normal and tangential force on the turbine blades compares well with experimental measurements. The interaction between the blades and the vortices that are shed and trailed in previous revolutions of the turbine is shown to have a significant effect on the distribution of aerodynamic loading on the blades. Furthermore, it is suggested that the disagreement between experimental and numerical data that has been presented in previous studies arises because the blade–vortex interactions on the rotor were not modelled with sufficient fidelity. Copyright © 2010 John Wiley & Sons, Ltd.     

A coupled near and far wake model for wind turbine aerodynamics

In this paper, an aerodynamic model consisting of a lifting line‐based trailed vorticity model and a blade element momentum (BEM) model is described. The focus is on the trailed vorticity model, which is based on the near wake model (NWM) by Beddoes and has been extended to include the effects of downwind convection and to enable a faster and more accurate computation of the induction, especially close to the blade root and tip. The NWM is introduced to model the detailed steady and unsteady induction from the first part of the trailed vorticity behind the individual rotor blades. The model adds a radial coupling between the blade sections and provides a computation of tip loss effects that depends on the actual blade geometry and the respective operating point. Moreover, the coupling of the NWM with a BEM theory‐based far wake model is presented. To avoid accounting for the near wake induction twice, the induction from the BEM model is reduced by a coupling factor, which is continuously updated during the computation to ensure a good behavior of the model in varying operating conditions. The coupled near and far wake model is compared with a simple prescribed wake lifting line model, a BEM model and full rotor computational fluid dynamics (CFD) to evaluate the steady‐state results in different cases. The model is shown to deliver good results across the whole operation range of the NREL 5‐MW reference wind turbine. Copyright © 2016 John Wiley & Sons, Ltd.     

A generalized framework for reduced‐order modeling of a wind turbine wake

A reduced‐order model for a wind turbine wake is sought from large eddy simulation data. Fluctuating velocity fields are combined in the correlation tensor to form the kernel of the proper orthogonal decomposition (POD). Proper orthogonal decomposition modes resulting from the decomposition represent the spatially coherent turbulence structures in the wind turbine wake; eigenvalues delineate the relative amount of turbulent kinetic energy associated with each mode. Back‐projecting the POD modes onto the velocity snapshots produces dynamic coefficients that express the amplitude of each mode in time. A reduced‐order model of the wind turbine wake (wakeROM) is defined through a series of polynomial parameters that quantify mode interaction and the evolution of each POD mode coefficients. The resulting system of ordinary differential equations models the wind turbine wake composed only of the large‐scale turbulent dynamics identified by the POD. Tikhonov regularization is used to recalibrate the dynamical system by adding additional constraints to the minimization seeking polynomial parameters, reducing error in the modeled mode coefficients. The wakeROM is periodically reinitialized with new initial conditions found by relating the incoming turbulent velocity to the POD mode coefficients through a series of open‐loop transfer functions. The wakeROM reproduces mode coefficients to within 25.2%, quantified through the normalized root‐mean‐square error.  A high‐level view of the modeling approach is provided as a platform to discuss promising research directions, alternate processes that could benefit stability and efficiency, and desired extensions of the wakeROM.     

An experimental investigation on the effect of individual turbine control on wind farm dynamics

Individual wind turbines in a wind farm typically operate to maximize their performance with no consideration of the impact of wake effects on downstream turbines. There is potential to increase power and reduce structural loads within a wind farm by properly coordinating the turbines. To effectively design and analyze coordinated wind turbine controllers requires control‐oriented turbine wake models of sufficient accuracy. This paper focuses on constructing such a model from experiments. The experiments were conducted to better understand the wake interaction and impact on voltage production in a three‐turbine array. The upstream turbine operating condition was modulated in time, and the dynamic impact on the downstream turbine was recorded through the voltage output time signal. The flow dynamics observed in the experiments were used to improve a static wake model often used in the literature for wind farm control. These experiments were performed in the atmospheric boundary layer wind tunnel at the Saint Anthony Falls Laboratory at the University of Minnesota using particle image velocimetry for flow field analysis and turbine voltage modulation to capture the physical evolution in addition to the dynamics of turbine wake interactions. Copyright © 2015 John Wiley & Sons, Ltd.