A simple model of the wind turbine induction zone derived from numerical simulations

The induction zone in front of different wind turbine rotors is studied by means of steady‐state Navier‐Stokes simulations combined with an actuator disk approach. It is shown that, for distances beyond 1 rotor radius upstream of the rotors, the induced velocity is self‐similar and independent of the rotor geometry. On the basis of these findings, a simple analytical model of the induction zone of wind turbines is proposed.     

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.     

Comparison of wind turbine wake properties in non‐sheared inflow predicted by different computational fluid dynamics rotor models

The wake of the 5MW reference wind turbine designed by the National Renewable Energy Laboratory (NREL) is simulated using computational fluid dynamics with a fully resolved rotor geometry, an actuator line method and an actuator disc method, respectively. Simulations are carried out prescribing both uniform and turbulent inflows, and the wake properties predicted by the three models are compared. In uniform inflow, the wake properties predicted by the actuator disc and line methods are found to be in very close agreement but differ significantly from the wake of the fully resolved rotor, which is characterized by much higher turbulence levels. In the simulations with turbulent inflow, the wake characteristics predicted by the three methods are in close agreement, indicating that the differences observed in uniform inflow do not play an important role if the inflow is turbulent. Copyright © 2014 John Wiley & Sons, Ltd.     

An improved k‐ ϵ model applied to a wind turbine wake in atmospheric turbulence

An improved k‐ ? turbulence model is developed and applied to a single wind turbine wake in a neutral atmospheric boundary layer using a Reynolds averaged Navier–Stokes solver. The proposed model includes a flow‐dependent C_μ that is sensitive to high velocity gradients, e.g., at the edge of a wind turbine wake. The modified k‐ ? model is compared with the original k‐ ? eddy viscosity model, Large‐Eddy Simulations and field measurements using eight test cases. The comparison shows that the velocity wake deficits, predicted by the proposed model are much closer to the ones calculated by the Large‐Eddy Simulation and those observed in the measurements, than predicted by the original k‐ ? model. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical simulations of wake characteristics of a wind turbine in uniform inflow

The wake of a wind turbine operating in a uniform inflow at various tip speed ratios is simulated using a numerical method, which combines large eddy simulations with an actuator line technique. The computations are carried out in a numerical mesh with about 8.4·10⁶ grid points distributed to facilitate detailed studies of basic features of both the near and far wake, including distributions of interference factors, vortex structures and formation of instabilities. Copyright © 2009 John Wiley & Sons, Ltd.     

A simple atmospheric boundary layer model applied to large eddy simulations of wind turbine wakes

A simple model for including the influence of the atmospheric boundary layer in connection with large eddy simulations of wind turbine wakes is presented and validated by comparing computed results with measurements as well as with direct numerical simulations. The model is based on an immersed boundary type technique where volume forces are used to introduce wind shear and atmospheric turbulence. The application of the model for wake studies is demonstrated by combining it with the actuator line method, and predictions are compared with field measurements. Copyright © 2013 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.     

Modelling and measurements of power losses and turbulence intensity in wind turbine wakes at Middelgrunden offshore wind farm

Understanding of power losses and turbulence increase due to wind turbine wake interactions in large offshore wind farms is crucial to optimizing wind farm design. Power losses and turbulence increase due to wakes are quantified based on observations from Middelgrunden and state‐of‐the‐art models. Observed power losses due solely to wakes are approximately 10% on average. These are relatively high for a single line of wind turbines due in part to the close spacing of the wind farm. The wind farm model Wind Analysis and Application Program (WAsP) is shown to capture wake losses despite operating beyond its specifications for turbine spacing. The paper describes two methods of estimating turbulence intensity: one based on the mean and standard deviation (SD) of wind speed from the nacelle anemometer, the other from mean power output and its SD. Observations from the nacelle anemometer indicate turbulence intensity which is around 9% higher in absolute terms than those derived from the power measurements. For comparison, turbulence intensity is also derived from wind speed and SD from a meteorological mast at the same site prior to wind farm construction. Despite differences in the measurement height and period, overall agreement is better between the turbulence intensity derived from power measurements and the meteorological mast than with those derived from data from the nacelle anemometers. The turbulence in wind farm model indicates turbulence increase of the order 20% in absolute terms for flow directly along the row which is in good agreement with the observations. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluation of wind farm efficiency and wind turbine wakes at the Nysted offshore wind farm

Here, we quantify relationships between wind farm efficiency and wind speed, direction, turbulence and atmospheric stability using power output from the large offshore wind farm at Nysted in Denmark. Wake losses are, as expected, most strongly related to wind speed variations through the turbine thrust coefficient; with direction, atmospheric stability and turbulence as important second order effects. While the wind farm efficiency is highly dependent on the distribution of wind speeds and wind direction, it is shown that the impact of turbine spacing on wake losses and turbine efficiency can be quantified, albeit with relatively large uncertainty due to stochastic effects in the data. There is evidence of the ‘deep array effect’ in that wake losses in the centre of the wind farm are under‐estimated by the wind farm model WAsP, although overall efficiency of the wind farm is well predicted due to compensating edge effects. Copyright © 2010 John Wiley & Sons, Ltd.     

Impact of wall roughness and turbulence level on the performance of a horizontal axis wind turbine with the U‐RANS solver THETA

The presented work investigates the impact of different sheared velocity profiles in the atmospheric boundary layer on the characteristics of a wind turbine by modifying the wall roughness coefficients in the logarithmic velocity profile. Moreover, the rotor and wake characteristics in dependence of the turbulence boundary conditions are investigated. In variant I, the turbulence boundary conditions are defined in accordance to the logarithmic velocity profile with different wall roughness lengths. In variant II, the turbulent kinetic energy and turbulent viscosity remain independent of the velocity profile and represent the free‐stream turbulence level. With an increase of the shear in the velocity profile, the amplitudes in the 3/rev characteristics of rotor thrust and rotor torque, induction factors, and effective angles of attack are increased. In variant I, the overall levels of thrust coefficient are hardly affected by the velocity profiles resulting from different wall roughness length values. The power coefficient is reduced about 1%. Conversely, compared with variant II, a difference of 2% in the power coefficient has been detected. Moreover, the wake recovery process strongly depends on the turbulence boundary condition. Simulations are carried out on an industrial 900‐kW wind turbine with the incompressible U‐RANS solver THETA.     

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.     

Simulation and wake analysis of a single vertical axis wind turbine

Because of several design advantages and operational characteristics, particularly in offshore farms, vertical axis wind turbines (VAWTs) are being reconsidered as a complementary technology to horizontal axial turbines. However, considerable gaps remain in our understanding of VAWT performance since cross‐flow rotor configurations have been significantly less studied than axial turbines. This study examines the wakes of VAWTs and how their evolution is influenced by turbine design parameters. An actuator line model is implemented in an atmospheric boundary layer large eddy simulation code, with offline coupling to a high‐resolution blade‐scale unsteady Reynolds‐averaged Navier–Stokes model. The large eddy simulation captures the turbine‐to‐farm scale dynamics, while the unsteady Reynolds‐averaged Navier–Stokes captures the blade‐to‐turbine scale flow. The simulation results are found to be in good agreement with three existing experimental datasets. Subsequently, a parametric study of the flow over an isolated VAWT, carried out by varying solidities, height‐to‐diameter aspect ratios and tip speed ratios, is conducted. The analyses of the wake area and velocity and power deficits yield an improved understanding of the downstream evolution of VAWT wakes, which in turn enables a more informed selection of turbine designs for wind farms. Copyright © 2016 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.     

Analysis of axial‐induction‐based wind plant control using an engineering and a high‐order wind plant model

Wind turbines are typically operated to maximize their performance without considering the impact of wake effects on nearby turbines. Wind plant control concepts aim to increase overall wind plant performance by coordinating the operation of the turbines. This paper focuses on axial‐induction‐based wind plant control techniques, in which the generator torque or blade pitch degrees of freedom of the wind turbines are adjusted. The paper addresses discrepancies between a high‐order wind plant model and an engineering wind plant model. Changes in the engineering model are proposed to better capture the effects of axial‐induction‐based control shown in the high‐order model. Copyright © 2015 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.     

Large‐eddy simulations of the Lillgrund wind farm

The power production of the Lillgrund wind farm is determined numerically using large‐eddy simulations and compared with measurements. In order to simulate realistic atmospheric conditions, pre‐generated turbulence and wind shear are imposed in the computational domain. The atmospheric conditions are determined from data extracted from a met mast, which was erected prior to the establishment of the farm. In order to allocate most of the computational power to the simulations of the wake flow, the turbines are modeled using an actuator disc method where the discs are imposed in the computational domain as body forces which for every time step are calculated from tabulated airfoil data. A study of the influence of imposed upstream ambient turbulence is performed and shows that higher levels of turbulence results in slightly increased total power production and that it is of great importance to include ambient turbulence in the simulations. By introducing ambient atmospheric turbulence, the simulations compare very well with measurements at the studied inflow angles. A final study aiming at increasing the farm production by curtailing the power output of the front row turbines and thus letting more kinetic energy pass downstream is performed. The results, however, show that manipulating only the front row turbines has no positive effect on the farm production, and therefore, more complex curtailment strategies are needed to be tested. Copyright © 2014 John Wiley & Sons, Ltd.     

Survey of modelling methods for wind turbine wakes and wind farms

This article provides an overview and analysis of different wake‐modelling methods which may be used as prediction and design tools for both wind turbines and wind farms. We also survey the available data concerning the measurement of wind magnitudes in both single wakes and wind farms, and of loading effects on wind turbines under single‐ and multiple‐wake conditions. The relative merits of existing wake and wind farm models and their ability to reproduce experimental results are discussed. Conclusions are provided concerning the usefulness of the different modelling approaches examined, and difficult issues which have not yet been satisfactorily treated and which require further research are discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

An actuator sector method for efficient transient wind turbine simulation

This paper investigates a new method for transient simulation of flow through a wind turbine using an actuator technique. The aim, in the context of wind turbine wake simulation, is to develop an alternative to the widely used actuator disc model with an increased resolution and range of applications, for the same or less computational expense. In this new model, the actuator sector method, forces applied to the fluid are distributed azimuthally to maintain a continuous flow solution for increased time‐step intervals compared with the actuator line method. Actuator sector results are presented in comparison with actuator disc and actuator line models initially for a non‐dimensionalized turbine in laminar onset flow. Subsequent results are presented for a turbine operating in a turbulent atmospheric boundary layer. Results show significant increases in flow fidelity compared with actuator disc model results; this includes the resolution of diametric variation in rotor loading caused by horizontal or vertical wind shear and the helical vortex system shed from the turbine blade tips. Significant reductions in computational processing time were achieved with wake velocities and turbulence statistics comparable with actuator line model results. The actuator sector method offers an improved alternative to applications employing conventional actuator disc models, with little or no additional computational cost. This technique in conjunction with a Cartesian mesh‐based parallel flow solver leads to efficient simulation of turbines in atmospheric boundary layer flows. Copyright © 2014 John Wiley & Sons, Ltd.     

Mesoscale modeling of offshore wind turbine wakes at the wind farm resolving scale: a composite‐based analysis with the Weather Research and Forecasting model over Horns Rev

The use of mesoscale modeling to reproduce the power deficits associated with wind turbine wakes in an offshore environment is analyzed. The study is based on multiyear (3 years) observational and modeling results at the Horns Rev wind farm. The simulations are performed with the Weather Research and Forecasting mesoscale model configured at a high horizontal resolution of 333 m over Horns Rev. The wind turbines are represented as an elevated momentum sink and a source of turbulent kinetic energy. Composites with different atmospheric conditions are extracted from both the observed and simulated datasets in order to inspect the ability of the model to reproduce the power deficit in a wide range of atmospheric conditions. Results indicate that mesoscale models such as Weather Research and Forecasting are able to qualitatively reproduce the power deficit at the wind farm scale. Some specific differences are identified. Mesoscale modeling is therefore a suitable framework to analyze potential downstream effects associated with offshore wind farms. Copyright © 2014 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.