Investigation of wind turbine wake superposition models using Reynolds‐averaged Navier‐Stokes simulations

It is well accepted that the wakes created by upstream turbines significantly impact on the power production and fatigue loading of downstream turbines and that this phenomenon affects wind farm performance. Improving the understanding of wake effects and overall efficiency is critical for the optimisation of layout and operation of increasingly large wind farms. In the present work, the NREL 5‐MW reference turbine was simulated using blade element embedded Reynolds‐averaged Navier‐Stokes computations in sheared onset flow at three spatial configurations of two turbines at and above rated flow speed to evaluate the effects of wakes on turbine performance and subsequent wake development. Wake recovery downstream of the rearward turbine was enhanced due to the increased turbulence intensity in the wake, although in cases where the downstream turbine was laterally offset from the upstream turbine this resulted in relatively slower recovery. Three widely used wake superposition models were evaluated and compared with the simulated flow‐field data. It was found that when the freestream hub‐height flow speed was at the rated flow speed, the best performing wake superposition model varied depending according to the turbine array layout. However, above rated flow speed where the wake recovery distance is reduced, it was found that linear superposition of single turbine velocity deficits was the best performing model for all three spatial layouts studied.     

Computational fluid dynamics analysis of the wake behind the MEXICO rotor in axial flow conditions

This paper presents a computational investigation of the wake of the MEXICO rotor. The compressible multi‐block solver of Liverpool University was employed, using a low‐Mach scheme to account for the low‐speed flow near the blade and in the wake. In this study, computations at wind speeds of 10, 15 and 24 m s ^{? 1} were performed, and the three components of the velocity were compared against experimental data around the rotor blade up to one and a half rotor diameters downstream. Overall, fair agreement was obtained with the computational fluid dynamics showing good vortex conservation near the blade. Vorticity values revealed discontinuities in the wake at approximately 70%R, where two different aerofoils with different zero‐lift angles are blended. The results suggest that all‐Mach schemes for compressible computational fluid dynamics methods can deliver good performance and accuracy over all wind speeds for flows around wind turbines, without the need to switch between incompressible and compressible flow methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Parametric dependencies of the yawed wind‐turbine wake development

Yaw misalignment is currently being treated as one of the most promising methods for optimizing the power of wind farms. Therefore, detailed knowledge of the impact of yaw on the wake development is necessary for a range of operating conditions. This study numerically investigates the wake development behind a single yawed wind turbine operating at different tip‐speed ratios and yaw angles using the actuator‐line method in the spectral‐element code Nek5000. It is shown that depending on the tip‐speed ratio, the blade loading varies along the azimuth, resulting in a wake that is asymmetric in both the horizontal and vertical directions. Large tip‐speed ratios as well as large yaw angles are shown to decrease the vertical asymmetry of the yaw‐induced counter‐rotating vortex pair. Both parameters have the effect that they increase the spanwise force induced by yaw relative to the wake rotation. However, while the strength of the counter‐rotating vortex pair in the far wake increases with yaw angle, it is shown to decrease with the tip‐speed ratio. The vertical shift in the wake center is found to be highly dependent on the yaw angle and the tip‐speed ratio. These detailed insights into the yawed wake are important when optimizing potential downstream turbines.     

Aerodynamic shape optimization of wind turbine blades using a Reynolds‐averaged Navier–Stokes model and an adjoint method

Computational fluid dynamics (CFD) is increasingly used to analyze wind turbines, and the next logical step is to develop CFD‐based optimization to enable further gains in performance and reduce model uncertainties. We present an aerodynamic shape optimization framework consisting of a Reynolds‐averaged Navier Stokes solver coupled to a numerical optimization algorithm, a geometry modeler, and a mesh perturbation algorithm. To efficiently handle the large number of design variables, we use a gradient‐based optimization technique together with an adjoint method for computing the gradients of the torque coefficient with respect to the design variables. To demonstrate the effectiveness of the proposed approach, we maximize the torque of the NREL VI wind turbine blade with respect to pitch, twist, and airfoil shape design variables while constraining the blade thickness. We present a series of optimization cases with increasing number of variables, both for a single wind speed and for multiple wind speeds. For the optimization at a single wind speed performed with respect to all the design variables (1 pitch, 11 twist, and 240 airfoil shape variables), the torque coefficient increased by 22.4% relative to the NREL VI design. For the multiple‐speed optimization, the torque increased by an average of 22.1%. Depending on the CFD mesh size and number of design variables, the optimization time ranges from 2 to 24h when using 256 cores, which means that wind turbine designers can use this process routinely. Copyright © 2016 John Wiley & Sons, Ltd.     

Harmonic balance Navier‐Stokes aerodynamic analysis of horizontal axis wind turbines in yawed wind

Multimegawatt horizontal axis wind turbines often operate in yawed wind transients, in which the resulting periodic loads acting on blades, drive‐train, tower, and foundation adversely impact on fatigue life. Accurately predicting yawed wind turbine aerodynamics and resulting structural loads can be challenging and would require the use of computationally expensive high‐fidelity unsteady Navier‐Stokes computational fluid dynamics. The high computational cost of this approach can be significantly reduced by using a frequency‐domain framework. The paper summarizes the main features of the COSA harmonic balance Navier‐Stokes solver for the analysis of open rotor periodic flows, presents initial validation results on the basis of the analysis of the NREL Phase VI experiment, and it also provides a sample application to the analysis of a multimegawatt turbine in yawed wind. The reported analyses indicate that the harmonic balance solver determines the considered periodic flows from 30 to 50 times faster than the conventional time‐domain approach with negligible accuracy penalty to the latter.     

CFD simulations of the MEXICO rotor

The wake behind a wind turbine model is investigated using Computational Fluid Dynamics (CFD), and results are compared with measurements. The turbine investigated is the three‐bladed test rotor (D = 4.5 m) used in the Model Experiments in Controlled Conditions (MEXICO) wind tunnel experiment. During the MEXICO experiment, particle image velocimetry measurements of the induction upstream and downstream of the rotor were performed for different operating conditions, giving a unique dataset to verify theoretical models and CFD models. The present paper first describes the efforts in reproducing the experimental results using the Reynold‐Averaged Navier‐Stokes method. Second, three‐dimensional airfoil characteristics are extracted that allow simulations with simpler wake models. Copyright © 2011 John Wiley & Sons, Ltd.     

HAWT near‐wake aerodynamics,Part I: axial flow conditions

An improved physical understanding of the rotor aerodynamics of a horizontal axis wind turbine (HAWT) is required to reduce the uncertainties associated with today's design codes. Wind tunnel experiments contribute to increased knowledge and enable validation and construction of models. The present study focuses on the near‐wake of a model HAWT in both axial and yawed flow conditions. At three downstream planes parallel to the rotor plane, single‐sensor hot‐film traverses are made. The phase‐locked unsteady three‐dimensional flow velocity vector is determined by a novel data reduction method. A series of two papers discusses the near‐wake aerodynamics of a model HAWT. The main goals are to obtain a detailed understanding of the near‐wake development and to arrive at a base for model construction and validation. The first paper presents the experimental setup, data reduction and the results for the baseline case (axial flow conditions). In the second paper, the results for the yawed flow cases are presented and the effect of yaw misalignment on the near‐wake development is discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical study of the wake induced by a porous disk under deflected inflow

This study examines the wake of a porous disk that generates a velocity deficit equivalent to that of a wind turbine. Three-dimensional unsteady numerical simulations based on the finite volume method are performed. The URANS-SST (k–ω) model is applied for the turbulence closure. Two investigations are carried out in this study: (i) the influence of the disk porosity on the wake, for porosities values (p) ranging from 0 to 0.55 in the case of a perpendicular flow; and (ii) the influence of the yaw angle on the wake deviation, for yaw angles ranging from 5° to 30°. Good agreements with the available experimental data are obtained for the mean x-velocity component. The results confirm that wake length increases as porosity decreases. For nonporous disks, most part of the fluid is deflected toward the mast and above the disk. The y-velocity contours highlight two contra-rotating vortices in the vicinity of the disk. In both cases (nonporous and porous disks), a high turbulent kinetic energy is obtained near the disk area, with a higher maximum value for the nonporous disk.     

Measurements behind model wind turbines: further evidence of wake meandering

The frequency of wind turbine wake meandering was studied using wind turbine models with one, two and three blades. The one‐bladed turbine did not give rise to any meandering motion, whereas meandering was observed for both the two‐ and three‐bladed turbines at high enough rotational speeds. It was shown that both the thrust of the turbine and the tip‐speed ratio influence the meandering. Copyright © 2007 John Wiley & Sons, Ltd.     

CFD study on the impact of yawed inflow on loads,power and near wake of a generic wind turbine

This article deals with the influence of yawed inflow conditions on the performance of a single generic 2.4MW wind turbine. It presents the results of studies performed at the Institute of Aerodynamics and Gas Dynamics by means of computational fluid dynamics , using a fully meshed wind turbine with all boundary layers being resolved. The block‐structured flow solver FLOWer is used; a dual‐time stepping method for temporal discretization and a second‐order Jameson–Schmidt–Turkel method for the calculation of the convective fluxes are applied. All simulations are carried out using a detached eddy simulation approach. In detail, two different wind speeds and a yaw angle range between ?50° and +50° are evaluated in the paper. Based on these data, it is shown that the reduction of power output follows a cosine to the power of X function of the yaw angle. Furthermore, the growing azimuthal non‐uniformity of the load distributions with increasing yaw angle magnitude is analysed by spanwise load distributions. As a central influence on the load distributions, the advancing and retreating blade effect is identified. Moreover, the deflection of the wake as a result of the inflow is investigated, and the deflection angles are compared with a modelling approach. A connection line between wake deflection and load asymmetry is drawn. The results are of particular importance for wind park situations with downstream turbines facing the distorted inflow created from upstream ones. Copyright © 2016 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.     

Estimating the angle of attack from blade pressure measurements on the NREL Phase VI rotor using a free wake vortex model: axial conditions

Blade element momentum (BEM) methods are still the most common methods used for predicting the aerodynamic loads during the aeroelastic design of wind turbine blades. However, their accuracy is limited by the availability of reliable aerofoil data. Owing to the 3D nature of the flow over wind turbine blades, the aerofoil characteristics will vary considerably from the 2D aerofoil characteristics, especially at the inboard sections of the blades. Detailed surface pressure measurements on the blade surfaces may be used to derive more realistic aerofoil data. However, in doing so, knowledge of the angle of attack distributions is required. This study presents a method in which a free wake vortex model is used to derive such distributions for the NREL Phase VI wind turbine under different operating conditions. The derived free wake geometry solutions are plotted together with the corresponding wake circulation distribution. These plots provide better insight into how circulation formed at the blades is eventually diffused into the wake. The free wake model is described and its numerical behaviour is examined. Copyright © 2006 John Wiley &Sons, Ltd.     

Measurements on a wind turbine wake: 3D effects and bluff body vortex shedding

The velocity field in the wake of a two‐bladed wind turbine model (diameter 180 mm) has been studied under different conditions using a two‐component hot wire. All three velocity components were measured both for the turbine rotor normal to the oncoming flow as well as with the turbine inclined to the freestream direction (the yaw angle was varied from 0° to 20°). The measurements showed, as expected, a wake rotation in the opposite direction to that of the turbine. A yawed turbine is found to clearly deflect the wake flow to the side, showing the potential of controlling the wake by yawing the turbine. An unexpected feature of the flow was that spectra from the time signals showed the appearance of a low‐frequency fluctuation both in the wake and in the flow outside the wake. This fluctuation was found both with and without freestream turbulence and also with a yawed turbine. The frequency expressed as a Strouhal number was shown to be independent of the freestream velocity or turbulence level, but the low frequency was only observed when the tip speed ratio (or equivalently the drag coefficient) was high. The shedding frequency changed also with the yaw angle. This is in agreement with the idea that the turbine sheds structures as a bluff body. The phenomenon, noticeable in all the velocity components, was further investigated using two‐point cross‐correlations of the velocity signals. Copyright © 2005 John Wiley & Sons, Ltd.     

Application of a LES technique to characterize the wake deflection of a wind turbine in yaw

When a wind turbine works in yaw, the wake intensity and the power production of the turbine become slightly smaller and a deflection of the wake is induced. Therefore, a good understanding of this effect would allow an active control of the yaw angle of upstream turbines to steer the wake away from downstream machines, reducing its effect on them. In wind farms where interaction between turbines is significant, it is of interest to maximize the power output from the wind farm as a whole and to reduce fatigue loads on downstream turbines due to the increase of turbulence intensity in wakes. A large eddy simulation model with particular wind boundary conditions has been used recently to simulate and characterize the turbulence generated by the presence of a wind turbine and its evolution downstream the machine. The simplified turbine is placed within an environment in which relevant flow properties like wind speed profile, turbulence intensity and the anisotropy of turbulence are found to be similar to the ones of the neutral atmosphere. In this work, the model is used to characterize the wake deflection for a range of yaw angles and thrust coefficients of the turbine. The results are compared with experimental data obtained by other authors with a particle image velocimetry technique from wind tunnel experiments. Also, a comparison with simple analytical correlations is carried out. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparison of the near‐wake between actuator‐line simulations and a simplified vortex model of a horizontal‐axis wind turbine

The flow around an isolated horizontal‐axis wind turbine is estimated by means of a new vortex code based on the Biot–Savart law with constant circulation along the blades. The results have been compared with numerical simulations where the wind turbine blades are replaced with actuator lines. Two different wind turbines have been simulated: one with constant circulation along the blades, to replicate the vortex method approximations, and the other with a realistic circulation distribution, to compare the outcomes of the vortex model with real operative wind‐turbine conditions (Tjæreborg wind turbine). The vortex model matched the numerical simulation of the turbine with constant blade circulation in terms of the near‐wake structure and local forces along the blade. The results from the Tjæreborg turbine case showed some discrepancies between the two approaches, but overall, the agreement is qualitatively good, validating the analytical method for more general conditions. The present results show that a simple vortex code is able to provide an estimation of the flow around the wind turbine similar to the actuator‐line approach but with a negligible computational effort. Copyright © 2015 John Wiley & Sons, Ltd.     

A study on rotational augmentation using CFD analysis of flow in the inboard region of the MEXICO rotor blades

This work presents an analysis of data from existing as well as new full‐rotor computational fluid dynamics computations on the MEXICO rotor, with focus on the flow around the inboard parts of the blades. The boundary layer separation characteristics on the airfoil sections in the inboard parts of the rotor are analysed using the pressure and the skin friction data at a range of angles of attack. These data are used to gain insight on the relative behaviour of separated boundary layers in 3D flow compared with 2D flow. It has been found that separation on airfoils in rotating flows is different from that in 2D flows in two respects: (i) there is a chord‐wise postponement (or delay) of the separation point, and (ii) the angle of attack at which separation is initiated is higher in 3D compared with 2D. Comments are made on the mechanism of stall delay, and the main differences between the skin friction and pressure distribution behaviours in 2D and 3D rotating flows are highlighted. Copyright © 2014 John Wiley & Sons, Ltd.     

Actuator line/Navier–Stokes computations for the MEXICO rotor: comparison with detailed measurements

In the European collaborative MEXICO (Model Experiments in Controlled Conditions) project, a series of experiments was carried out on a 4.5 m diameter wind turbine rotor to validate numerical diagnostics tools. Here, some of the measured data are compared with computations of the combined actuator line/Navier–Stokes (AL/NS) model developed at the Technical University of Denmark. The AL/NS model was combined with a large eddy simulation technique and used to compute the flow past the MEXICO rotor in free air and in the DNW German‐Dutch wind tunnel for three commonly defined test cases at wind speeds of 10, 15 and 24 m s ^?1. Two sets of airfoil data were used. Comparisons of blade loadings showed that the AL/NS technique with the modified airfoil data is in better agreement with the measurements than with the original 2D airfoil data. Comparisons of detailed near‐wake velocities showed good agreement with the measurements. Computations including the influence of the geometry of the wind tunnel showed that tunnel effects are not significant and the effect of the geometry of the wind tunnel only results in a speedup of 3% at a thrust coefficient of C_T = 1.Copyright © 2011 John Wiley & Sons, Ltd.     

Estimating the angle of attack from blade pressure measurements on the National Renewable Energy Laboratory phase VI rotor using a free wake vortex model: yawed conditions

Wind turbine design codes for calculating blade loads are usually based on a blade element momentum (BEM) approach. Since wind turbine rotors often operate in off‐design conditions, such as yawed flow, several engineering methods have been developed to take into account such conditions. An essential feature of a BEM code is the coupling of local blade element loads with an external (induced) velocity field determined with momentum theory through the angle of attack. Local blade loads follow directly from blade pressure measurements as performed in the National Renewable Energy Laboratory (NREL) phase IV campaign, but corresponding angles of attack cannot (on principle) be measured. By developing a free wake vortex method using measured local blade loads, time‐dependent angle of attack and induced velocity distributions are reconstructed. In a previous paper, a method was described for deriving such distributions in conjunction with blade pressure measurements for the NREL phase VI wind turbine in axial (non‐yawed) conditions. In this paper, the same method is applied to investigate yawed conditions on the same turbine. The study considered different operating conditions in yaw in both attached and separated flows over the blades. The derived free wake geometry solutions are used to determine induced velocity distributions at the rotor blade. These are then used to determine the local (azimuth time dependent) angle of attack, as well as the corresponding lift and drag for each blade section. The derived results are helpful to develop better engineering models for wind turbine design codes. Copyright © 2008 John Wiley & Sons, Ltd.     

Simulation comparison of wake mitigation control strategies for a two‐turbine case

Wind turbines arranged in a wind plant impact each other through their wakes. Wind plant control is an active research field that attempts to improve wind plant performance by coordinating control of individual turbines to take into account these turbine–wake interactions. In this paper, high‐fidelity simulations of a two‐turbine fully waked scenario are used to investigate several wake mitigation strategies, including modification of yaw and tilt angles of an upstream turbine to induce wake skew, as well as repositioning of the downstream turbine. The simulation results are compared through change relative to a baseline operation in terms of overall power capture and loading on the upstream and downstream turbine. Results demonstrated improved power production for all methods. Analysis of control options, including individual pitch control, shows potential to minimize the increase of, or even reduce, turbine loads.Copyright © 2014 John Wiley & Sons, Ltd.