The k‐ε‐fP model applied to double wind turbine wakes using different actuator disk force methods

The newly developed k‐ε‐f_P eddy viscosity model is applied to double wind turbine wake configurations in a neutral atmospheric boundary layer, using a Reynolds‐Averaged Navier–Stokes solver. The wind turbines are represented by actuator disks. A proposed variable actuator disk force method is employed to estimate the power production of the interacting wind turbines, and the results are compared with two existing methods: a method based on tabulated airfoil data and a method based on the axial induction from 1D momentum theory. The proposed method calculates the correct power, while the other two methods overpredict it. The results of the k‐ε‐f_P eddy viscosity model are also compared with the original k‐ε eddy viscosity model and large‐eddy simulations. Compared to the large‐eddy simulations‐predicted velocity and power deficits, the k‐ε‐f_P is superior to the original k‐ε model. Copyright © 2014 John Wiley & Sons, Ltd.     

The k‐ϵ‐fP model applied to wind farms

The recently developed k‐?‐f_P eddy‐viscosity model is applied to one on‐shore and two off‐shore wind farms. The results are compared with power measurements and results of the standard k‐? eddy‐viscosity model. In addition, the wind direction uncertainty of the measurements is used to correct the model results with a Gaussian filter. The standard k‐? eddy‐viscosity model underpredicts the power deficit of the first downstream wind turbines, whereas the k‐?‐f_P eddy‐viscosity model shows a good agreement with the measurements. However, the difference in the power deficit predicted by the turbulence models becomes smaller for wind turbines that are located further downstream. Moreover, the difference between the capability of the turbulence models to estimate the wind farm efficiency reduces with increasing wind farm size and wind turbine spacing. Copyright © 2014 John Wiley & Sons, Ltd.     

The spectral signature of wind turbine wake meandering: A wind tunnel and field‐scale study

Field‐scale and wind tunnel experiments were conducted in the 2D to 6D turbine wake region to investigate the effect of geometric and Reynolds number scaling on wake meandering. Five field deployments took place: 4 in the wake of a single 2.5‐MW wind turbine and 1 at a wind farm with numerous 2‐MW turbines. The experiments occurred under near‐neutral thermal conditions. Ground‐based lidar was used to measure wake velocities, and a vertical array of met‐mounted sonic anemometers were used to characterize inflow conditions. Laboratory tests were conducted in an atmospheric boundary layer wind tunnel for comparison with the field results. Treatment of the low‐resolution lidar measurements is discussed, including an empirical correction to velocity spectra using colocated lidar and sonic anemometer. Spectral analysis on the laboratory‐ and utility‐scale measurements confirms a meandering frequency that scales with the Strouhal number St = fD/U based on the turbine rotor diameter D. The scaling indicates the importance of the rotor‐scaled annular shear layer to the dynamics of meandering at the field scale, which is consistent with findings of previous wind tunnel and computational studies. The field and tunnel spectra also reveal a deficit in large‐scale turbulent energy, signaling a sheltering effect of the turbine, which blocks or deflects the largest flow scales of the incoming flow. Two different mechanisms for wake meandering—large scales of the incoming flow and shear instabilities at relatively smaller scales—are discussed and inferred to be related to the turbulent kinetic energy excess and deficit observed in the wake velocity spectra.     

Simulating dynamic stall in a two‐dimensional vertical‐axis wind turbine: verification and validation with particle image velocimetry data

The implementation of wind energy conversion systems in the built environment has renewed the interest and the research on Vertical Axis Wind Turbines (VAWTs). The VAWT has an inherent unsteady aerodynamic behavior due to the variation of angle of attack and perceived velocity with azimuth angle. The phenomenon of dynamic stall is then an intrinsic effect of the operation at low tip speed ratios, impacting both loads and power. The complexity of the problem and the need for new design approaches for VAWTs for the built environment have driven the authors to focus this research on the CFD modeling of VAWTs on:

• Comparing the results between commonly used turbulence models: Unsteady Reynolds Averaged Navier‐Stokes – URANS (Spalart‐Allmaras and k‐?) and large eddy models (Large Eddy Simulation and Detached Eddy Simulation).
• Verifying the sensitivity of the model to its grid refinement (space and time).
• Evaluating the suitability of using Particle Image Velocimetry (PIV) experimental data for model validation.

The current work investigates the impact of accurately modeling the separated shed wake resulting from dynamic stall, and the importance of validation of the flow field rather than validation with only load data. The structure and magnitude of the wake are validated with PIV results, and it demonstrated that the accuracy of the different models in simulating a correct wake structure has a large impact in loads.     

Active wake control: An approach to optimize the lifetime operation of wind farms

The wind turbines within a wind farm impact each other's power production and loads through their wakes. Wake control strategies, aiming to reduce wake effects, receive increasing interest by both the research community and the industry. A number of recent simulation studies with high fidelity wake models indicate that wake mitigation control is a very promising concept for increasing the power production of a wind farm and/or reducing the fatigue loading on wind turbines' components. The purpose of this paper is to study the benefits of wake mitigation control in terms of lifetime power production and fatigue loading on several existing full‐scale commercial wind farms with different scale, layouts, and turbine sizes. For modeling the wake interactions, Energy Research Centre of the Netherlands' FarmFlow software is used: a 3D parabolized Navier‐Stokes code, including a k‐? turbulence model. In addition, an optimization approach is proposed that maximizes the lifetime power production, thereby incorporating the fatigue loads into the optimization criterion in terms of a lifetime extension factor.     

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.     

Wind tunnel investigation on the effect of the turbine tower on wind turbines wake symmetry

In wind farms, the wake of the upstream turbines becomes the inflow for the downstream machines. Ideally, the turbine wake is a stable vortex system. In reality, because of factors like background turbulence, mean flow shear, and tower‐wake interaction, the wake velocity deficit is not symmetric and is displaced away from its mean position. The irregular velocity profile leads to a decreased efficiency and increased blade stress levels for the downstream turbines. The object of this work is the experimental investigation of the effect of the wind turbine tower on the symmetry and displacement of the wake velocity deficit induced by one and two in‐line model wind turbines (,D= 0.9 m). The results of the experiments, performed in the closed‐loop wind tunnel of the Norwegian University of Science and Technology in Trondheim (Norway), showed that the wake of the single turbine expanded more in the horizontal direction (side‐wall normal) than in the vertical (floor normal) direction and that the center of the wake vortex had a tendency to move toward the wind tunnel floor as it was advected downstream from the rotor. The wake of the turbine tandem showed a similar behavior, with a larger degree of non‐symmetry. The analysis of the cross‐stream velocity profiles revealed that the non‐symmetries were caused by a different cross‐stream momentum transport in the top‐tip and bottom‐tip region, induced by the turbine tower wake. In fact, when a second additional turbine tower, mirroring the original one, was installed above the turbine nacelle, the wake recovered its symmetric structure. Copyright © 2017 John Wiley & Sons, Ltd.     

Blade‐resolved simulations of a model wind turbine: effect of temporal convergence

Simulations of a model wind turbine at various tip‐speed‐ratios were carried out using Tenasi, a node‐centered, finite volume unstructured flow solver. The simulations included the tunnel walls, tower, nacelle, hub and the blades. The effect of temporal convergence on the predicted thrust and power coefficients is evaluated and guidelines for best practices are established. The results presented here are for tip‐speed‐ratios of 3, 6 and 10, with 6 being the design point. All simulations were carried out at a freestream velocity of 10 m s^?1 with an incoming boundary layer present and the wind turbine RPM was varied to achieve the desired tip‐speed‐ratio. The performance of three turbulence models is evaluated. The models include a one‐equation model (Spalart–Allmaras), a two‐equation model (Menter SST) and the DES version of the Menter SST. Turbine performance as well as wake data at various locations is compared to experiment. All the turbulence models performed well in terms of predicting power and thrust coefficients. The DES model was significantly better than the other two turbulence models for predicting the mean and fluctuating components of the velocity in the wake. Copyright © 2015 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.     

Atmospheric stability‐dependent infinite wind‐farm models and the wake‐decay coefficient

We extend the infinite wind‐farm boundary‐layer (IWFBL) model of Frandsen to take into account atmospheric static stability effects. This extended model is compared with the IWFBL model of Emeis and to the Park wake model used in Wind Atlas Analysis and Application Program (WAsP), which is computed for an infinite wind farm. The models show similar behavior for the wind‐speed reduction when accounting for a number of surface roughness lengths, turbine to turbine separations and wind speeds under neutral conditions. For a wide range of atmospheric stability and surface roughness length values, the extended IWFBL model of Frandsen shows a much higher wind‐speed reduction dependency on atmospheric stability than on roughness length (roughness has been generally thought to have a major effect on the wind‐speed reduction). We further adjust the wake‐decay coefficient of the Park wake model for an infinite wind farm to match the wind‐speed reduction estimated by the extended IWFBL model of Frandsen for different roughness lengths, turbine to turbine separations and atmospheric stability conditions. It is found that the WAsP‐recommended values for the wake‐decay coefficient of the Park wake model are (i) larger than the adjusted values for a wide range of neutral to stable atmospheric stability conditions, a number of roughness lengths and turbine separations lower than ～ 10 rotor diameters and (ii) too large compared with those obtained by a semiempirical formulation (relating the ratio of the friction to the hub‐height free velocity) for all types of roughness and atmospheric stability conditions. © 2013 The Authors. Wind Energy published by 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.     

Wind turbine performance in shear flow and in the wake of another turbine through high fidelity numerical simulations with moving mesh technique

We present numerical simulations of two horizontal axis wind turbines, one operating under the wake of the other, under an incoming sheared velocity profile. We use a moving mesh technique to represent the rotation of the turbine blades and solve the unsteady Reynolds averaged Navier–Stokes equations with a shear stress transport k ? ω turbulence model. Temporal evolution of the lift and drag coefficients of the front turbine show a phase shift in the periodic cycle due to the non‐uniform incoming free stream velocity. Comparisons of the lift and drag coefficients for the back turbine with the unperturbed behaviour of the front demonstrate the complex non‐linear interactions of the blades with the wake, with a significant decrease in overall performance and two peaks at specific points in the cycle associated with local angle of attack modification in the wake. The vorticity field in the near wake shows tilting of the vortex lines in the wake due to the shear and a faster diffusion of the tip vortical signature compared with the uniform free stream velocity case. Observations of the wake–wake interaction show good agreement with recent studies that use different methodologies. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental study of a small wind turbine for low‐ and medium‐wind regimes

The results of an experimental assessment of a small prototype battery charging wind turbine designed for low‐ and medium‐wind regimes are presented. The turbine is based on a newly designed axial flow permanent magnet synchronous generator and a three‐bladed rotor with variable twist and taper blades. Overspeed control is performed by a furling mechanism. The turbine has the unique feature of being capable of operating at either 12, 24 or 48 V system voltage, requiring no load control in any case. In the 48 V configuration, the system is capable of providing 2 kWh day^?1 for an average wind speed as low as 3.5 m s^?1 and an air density of 85% of the standard pressure and temperature value. The experimental assessment has been conducted under field conditions with the turbine mounted on a 20 m guy‐wired tubular tower. The experimental power curves are shown to be in good agreement with a detailed aerodynamical and electromechanical model of the turbine for non‐furling conditions and for wind speeds above the theoretical cut‐in speed. In the case of the rapidly spinning load configurations, a finite power production at wind speeds below the theoretical cut‐in speed can be observed, which can be explained in terms of inertia effects. During the measurement campaigns with high loads, we were able to observe bifurcations of the power curve, which can be explained in terms of instabilities arising in situations of transition from attached to separated flow. A full experimental C_p(λ)‐curve has been constructed by operating the turbine under different load conditions and the findings are in good agreement with a variable Reynolds‐number blade‐element momentum model. The three proposed system configurations have been found to operate with a high aerodynamic efficiency with typical values of the power coefficient in the 0.40–0.45 range. Copyright © 2009 John Wiley & Sons, Ltd.     

A study on the prediction of aerofoil trailing‐edge noise for wind‐turbine applications

This paper presents a comparative study between the so‐called BPM and TNO models for the prediction of aerofoil trailing‐edge noise with particular emphasis on wind‐turbine applications (the BPM model is named after Brooks, Pope and Marcolini who first proposed the model, and the TNO model is named after the TNO institute of Applied Physics where it was first proposed). In this work, two enhanced versions of the BPM model are proposed, and their performances are compared against two recent anisotropic TNO models that require more detailed boundary‐layer information than the BPM‐based models. The two current enhanced models are denoted as BPMM‐PVII and BPMM‐BLkω, where the former uses a panel method with viscous‐inviscid interaction implemented (PVII) for boundary‐layer calculations, the latter estimates the boundary‐layer (BL) properties using a two‐dimensional k‐ω turbulence model (kω), and BPMM stands for BPM‐Modified. By comparing the predicted sound spectra with existing measurement data for seven different aerofoils tested in the current study, it is shown that the BPMM‐PVII model exhibits superior results to those by the other models for most cases despite the simplicity without considering anisotropy. The BPMM‐PVII model is then combined with Prandtl's nonlinear lifting‐line theory to calculate and investigate three‐dimensional rotor noise characteristics of an NREL UAE Phase‐VI wind turbine (NREL UAE stand for the National Renewable Energy Laboratory Unsteady Aerodynamic Experiment). It is demonstrated that the current approach may provide an efficient solution for the prediction of rotor aerodynamics and noise facilitating industrial design and development for low‐noise wind turbines. Copyright © 2016 John Wiley & Sons, Ltd.     

Performance and wake of a Savonius vertical‐axis wind turbine under different incoming conditions

In this study, the performance, drag, and horizontal midplane wake characteristics of a vertical‐axis Savonius wind turbine are investigated experimentally. The turbine is drag driven and has a helical configuration, with the top rotated 180° relative to the bottom. Both performance and wake measurements were conducted in four different inflow conditions, using Reynolds numbers of Re_D≈1.6×10⁵ and Re_D≈2.7×10⁵ and turbulence intensities of 0.6% and 5.7%. The efficiency of the turbine was found to be highly dependent on the Reynolds number of the incoming flow. In the high Reynolds number flow case, the efficiency was shown to be considerably higher, compared with the lower Reynolds number case. Increasing the incoming turbulence intensity was found to mitigate the Reynolds number effects. The drag of the turbine was shown to be independent of the turbine's rotational speed over the range tested, and it was slightly lower when the inflow turbulence was increased. The wake was captured for the described inflow conditions in both optimal and suboptimal operating conditions by varying the rotational speed of the turbine. The wake was found to be asymmetrical and deflected to the side where the blade moves opposite to the wind. The largest region of high turbulent kinetic energy was on the side where the blade is moving in the same direction as the wind. Based on the findings from the wake measurements, some recommendations on where to place supplementary turbines are made.     

Effect of tower and nacelle on the flow past a wind turbine

Large eddy simulations (LES) of the flow past a wind turbine with and without tower and nacelle have been performed at 2 tip speed ratios (TSR, ), λ=3 and 6, where the latter corresponds to design conditions. The turbine model is placed in a virtual wind tunnel to reproduce the “Blind test 1” experiment performed at the Norwegian University of Science and Technology (NTNU) closed‐loop wind tunnel. The wind turbine was modeled using the actuator line model for the rotor blades and the immersed boundary method for the tower and nacelle. The aim of the paper is to highlight the impact of tower and nacelle on the turbine wake. Therefore, a second set of simulations with the rotating blades only (neglecting the tower and nacelle) has been performed as reference. Present results are compared with the experimental measurements made at NTNU and numerical simulations available in the literature. The tower and nacelle not only produce a velocity deficit in the wake but they also affect the turbulent kinetic energy and the fluxes. The wake of the tower interacts with that generated by the turbine blades promoting the breakdown of the tip vortex and increasing the mean kinetic energy flux into the wake. When tower and nacelle are modeled in the numerical simulations, results improve significantly both in the near wake and in the far wake.     

Parabolic RANS solver for low‐computational‐cost simulations of wind turbine wakes

A numerical framework for simulations of wake interactions associated with a wind turbine column is presented. A Reynolds‐averaged Navier‐Stokes (RANS) solver is developed for axisymmetric wake flows using parabolic and boundary‐layer approximations to reduce computational cost while capturing the essential wake physics. Turbulence effects on downstream evolution of the time‐averaged wake velocity field are taken into account through Boussinesq hypothesis and a mixing length model, which is only a function of the streamwise location. The calibration of the turbulence closure model is performed through wake turbulence statistics obtained from large‐eddy simulations of wind turbine wakes. This strategy ensures capturing the proper wake mixing level for a given incoming turbulence and turbine operating condition and, thus, accurately estimating the wake velocity field. The power capture from turbines is mimicked as a forcing in the RANS equations through the actuator disk model with rotation. The RANS simulations of the wake velocity field associated with an isolated 5‐MW NREL wind turbine operating with different tip speed ratios and turbulence intensity of the incoming wind agree well with the analogous velocity data obtained through high‐fidelity large‐eddy simulations. Furthermore, different cases of columns of wind turbines operating with different tip speed ratios and downstream spacing are also simulated with great accuracy. Therefore, the proposed RANS solver is a powerful tool for simulations of wind turbine wakes tailored for optimization problems, where a good trade‐off between accuracy and low‐computational cost is desirable.     

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.     

Self‐similarity and turbulence characteristics of wind turbine wakes via large‐eddy simulation

Mean and turbulent properties of the wake generated by a single wind turbine are studied in this paper with a new large eddy simulation (LES) code, the wind turbine and turbulence simulator (WiTTS hereafter). WiTTS uses a scale‐dependent Lagrangian dynamical model of the sub‐grid shear stress and actuator lines to simulate the effects of the rotating blades. WiTTS is first tested by simulating neutral boundary layers without and with a wind turbine and then used to study the common assumptions of self‐similarity and axisymmetry of the wake under neutral conditions for a variety of wind speeds and turbine properties. We find that the wind velocity deficit generally remains self similarity to a Gaussian distribution in the horizontal. In the vertical, the Gaussian self‐similarity is still valid in the upper part of the wake, but it breaks down in the region of the wake close to the ground. The horizontal expansion of the wake is always faster and greater than the vertical expansion under neutral stability due to wind shear and impact with the ground. Two modifications to existing equations for the mean velocity deficit and the maximum added turbulence intensity are proposed and successfully tested. The anisotropic wake expansion is taken into account in the modified model of the mean velocity deficit. Turbulent kinetic energy (TKE) budgets show that production and advection exceed dissipation and turbulent transport. The nacelle causes significant increase of every term in the TKE budget in the near wake. In conclusion, WiTTS performs satisfactorily in the rotor region of wind turbine wakes under neutral stability. Copyright © 2014 John Wiley & Sons, Ltd.     

The helix approach: Using dynamic individual pitch control to enhance wake mixing in wind farms

Wind farm control using dynamic concepts is a research topic that is receiving an increasing amount of interest. The main concept of this approach is that dynamic variations of the wind turbine control settings lead to higher wake turbulence, and subsequently faster wake recovery due to increased mixing. As a result, downstream turbines experience higher wind speeds, thus increasing their energy capture. In dynamic induction control (DIC), the magnitude of the thrust force of an upstream turbine is varied. Although very effective, this approach also leads to increased power and thrust variations, negatively impacting energy quality and fatigue loading. In this paper, a novel approach for the dynamic control of wind turbines in a wind farm is proposed: using individual pitch control, the fixed‐frame tilt and yaw moments on the turbine are varied, thus dynamically manipulating the wake. This strategy is named the helix approach because the resulting wake has a helical shape. Large eddy simulations of a two‐turbine wind farm show that this approach leads to enhanced wake mixing with minimal power and thrust variations.