Large eddy simulations of the flow past wind turbines: actuator line and disk modeling

Large eddy simulations of the flow through wind turbines have been carried out using actuator disk and actuator line models for the turbine rotor aerodynamics. In this study, we compare the performance of these two models in producing wind turbine wakes. We also examine parameters that strongly affect the performance of these models, namely, grid resolution and the way in which the actuator force is projected onto the flow field. The proper choice of these two parameters has not been adequately addressed in previous works. We see that as the grid is coarsened, the predicted power decreases. As the width of the body force projection function is increased, the predicted power increases. The actuator disk and actuator line models produce similar wake profiles and predict power within 1% of one another when subject to the same uniform inflow. The actuator line model is able to generate flow structures near the blades such as root and tip vortices which the actuator disk model does not, but in the far wake, the predicted mean wakes are very similar. In order to perform validation against experimental data, the actuator line model output was compared with data from the wind tunnel experiment conducted at the Norwegian University of Science and Technology, Trondheim. Agreement between measured and predicted power, wake profiles, and turbulent kinetic energy has been observed for most tip speed ratios; larger discrepancies in power and thrust coefficient, though, have been found for tip speed ratios of 9 and 12. Copyright © 2014 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.     

Benefits of collocating vertical‐axis and horizontal‐axis wind turbines in large wind farms

In this study, we address the benefits of a vertically staggered (VS) wind farm, in which vertical‐axis and horizontal‐axis wind turbines are collocated in a large wind farm. The case study consists of 20 small vertical‐axis turbines added around each large horizontal‐axis turbine. Large‐eddy simulation is used to compare power extraction and flow properties of the VS wind farm versus a traditional wind farm with only large turbines. The VS wind farm produces up to 32% more power than the traditional one, and the power extracted by the large turbines alone is increased by 10%, caused by faster wake recovery from enhanced turbulence due to the presence of the small turbines. A theoretical analysis based on a top‐down model is performed and compared with the large‐eddy simulation. The analysis suggests a nonlinear increase of total power extraction with increase of the loading of smaller turbines, with weak sensitivity to various parameters, such as size, and type aspect ratio, and thrust coefficient of the vertical‐axis turbines. We conclude that vertical staggering can be an effective way to increase energy production in existing wind farms. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Large‐eddy simulations with extremum‐seeking control for individual wind turbine power optimization

Large‐eddy simulations of the flow past an array of three aligned turbines have been performed. The study is focused on below rated (Region 2) wind speeds. The turbines are controlled through the generator torque gain, as usually done in Region 2. Two operating strategies are considered: (i) preset individual optimum torque gain based on a model for the power coefficient (baseline case) and (ii) real‐time optimization of torque gain for maximizing each individual turbine power capture during operation. The real‐time optimization is carried out through a model‐free approach, namely, extremum‐seeking control. It is shown that ESC is capable of increasing the power production of the array by 6.5% relative to the baseline case. The extremum‐seeking control reduces the torque gain of the downstream turbines, thus increasing the angular speed of the blades. This results in improved aerodynamics near the tip of the blade that is the portion contributing mostly to the torque and power. In addition, an increase in angular speed leads to a larger entrainment in the wake, which also contributes to provide additional available power downstream. It is also shown that the tip speed ratio may not be a reliable performance indicator when the turbines are in waked conditions. This may be a concern when using optimal parameter settings, determined from isolated turbine models, in applications with waked turbines. Copyright © 2017 John Wiley & Sons, Ltd.     

Evaluation of layout and atmospheric stability effects in wind farms using large‐eddy simulation

Large‐eddy simulation (LES) has been used previously to study the effect of either configuration or atmospheric stability on the power generated by large wind farms. This is the first study to consider both stability and wind farm configuration simultaneously and methodically with LES. Two prevailing wind directions, two layouts (turbines aligned versus staggered with respect to the wind) and three stabilities (neutral and moderately unstable and stable) were evaluated. Compared with neutral conditions, unstable conditions led to reduced wake losses in one configuration, to enhanced wake losses in two and to unchanged wake losses in one configuration. Conversely, stable conditions led to increased wake losses in one, decreased wake losses in two and unchanged wake losses in one configuration. Three competing effects, namely, rates of wake recovery due to vertical mixing, horizontal spread of wakes and localized regions of acceleration caused by multiple upstream wakes, were identified as being responsible for the observed trends in wake losses. The detailed flow features responsible for these non‐linear interactions could only be resolved by the LES. Existing analytical models ignore stability and non‐linear configuration effects, which therefore need to be incorporated. Copyright © 2017 John Wiley & Sons, Ltd.     

Large eddy simulations of the effect of vertical staggering in large wind farms

In order to study the effect of vertical staggering in large wind farms, large eddy simulations (LES) of large wind farms with a regular turbine layout aligned with the given wind direction were conducted. In the simulations, we varied the hub heights of consecutive downstream rows to create vertically staggered wind farms. We analysed the effect of streamwise and spanwise turbine spacing, the wind farm layout, the turbine rotor diameter, and hub height difference between consecutive downstream turbine rows on the average power output. We find that vertical staggering significantly increases the power production in the entrance region of large wind farms and is more effective when the streamwise turbine spacing and turbine diameter are smaller. Surprisingly, vertical staggering does not significantly improve the power production in the fully developed regime of the wind farm. The reason is that the downward vertical kinetic energy flux, which brings high velocity fluid from above the wind farm towards the hub height plane, does not increase due to vertical staggering. Thus, the shorter wind turbines are effectively sheltered from the atmospheric flow above the wind farm that supplies the energy, which limits the benefit of vertical staggering. In some cases, a vertically staggered wind farm even produced less power than the corresponding non vertically staggered reference wind farm. In such cases, the production of shorter turbines is significantly negatively impacted while the production of the taller turbine is only increased marginally.     

Large eddy simulation study of the humidity variation in the shadow of a large wind farm

Numerous studies have shown that wind turbine wakes within a large wind farm bring about changes to both the dynamics and thermodynamics of the atmospheric boundary layers (ABL). Previously, we investigated the relative humidity budget within a wind farm via field measurements in the near‐wake region and large eddy simulations (LES). The effect of the compounding wakes within a large wind farm on the relative humidity was also investigated by LES. In this study, we investigate how the areas of relative humidity variation, that was observed in the near‐wake, develop downstream in the shadow region of a large wind farm. To this end, LES of a wind farm consisting of 8x6 wind turbines with periodic boundary condition in the lateral direction (inferring an infinitely wide farm) interacting with a stable ABL is carried out. Two wind farm layouts, aligned and staggered, are considered in the analysis and the results from both configurations are compared to each other. It is observed that a decrease of relative humidity underneath the hub height and an increase above the hub height build up within the wind farm, and are maintained in the downstream of the farm for long distances. The staggered farm layout is more effective in keeping a more elongated region of low relative humidity underneath the hub, when compared to the aligned layout.     

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.     

State‐space representation of the wind flow model in wind farms

A dynamic model for the wind flow in wind farms is developed in this paper. The model is based on the spatial discretization of the linearized Navier–Stokes equation combined with the vortex cylinder theory. The spatial discretization of the model is performed using the finite difference method, which provides the state‐space form of the dynamic wind farm model. The model provides an approximation of the behavior of the flow in the wind farm and obtains the wind speed in the vicinity of each wind turbine. Afterwards, the model is validated using measurement data of Energy research Center of the Netherlands’ Wind turbine Test site in Wieringermeer in the Netherlands and by employing the outcomes of two other wind flow models. The end goal of this work is to present the wind farm flow model by ordinary differential equations, to be applied in wind farm control algorithms along with load and power optimizations. Copyright © 2013 John Wiley & Sons, Ltd.     

Filtered actuator disks: Theory and application to wind turbine models in large eddy simulation

The actuator disk model (ADM) continues to be a popular wind turbine representation in large eddy simulations (LES) of large wind farms. Computational restrictions typically limit the number of grid points across the rotor of each actuator disk and require spatial filtering to smoothly distribute the applied force distribution on discrete grid points. At typical grid resolutions, simulations cannot capture all of the vorticity shed behind the disk and subsequently overpredict power by upwards of 10%. To correct these modeling errors, we propose a vortex cylinder model to quantify the shed vorticity when a filtered force distribution is applied at the actuator disk. This model is then used to derive a correction factor for numerical simulations that collapses the power curve for simulations at various filter widths and grid resolutions onto the curve obtained using axial momentum theory. The proposed correction, which is analytically derived from first principles, facilitates accurate power measurements in LES without resorting to highly refined numerical grids or empirical correction factors.     

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.     

Large‐eddy simulations of wind‐farm wake characteristics associated with a low‐level jet

In this study, we performed a suite of flow simulations for a 12‐wind‐turbine array with varying inflow conditions and lateral spacings, and compared the impacts of the flow on velocity deficit and wake recovery. We imposed both laminar inflow and turbulent inflows, which contain turbulence for the Ekman layer and a low‐level jet (LLJ) in the stable boundary layer. To solve the flow through the wind turbines and their wakes, we used a large‐eddy simulation technique with an actuator‐line method. We compared the time series for the velocity deficit at the first and rear columns to observe the temporal change in velocity deficit for the entire wind farm. The velocity deficit at the first column for LLJ inflow was similar to that for laminar inflow. However, the magnitude of velocity deficit at the rear columns for the case with LLJ inflow was 11.9% greater because of strong wake recovery, which was enhanced by the vertical flux of kinetic energy associated with the LLJ. To observe the spatial transition and characteristics of wake recovery, we performed statistical analyses of the velocity at different locations for both the laminar and LLJ inflows. These studies indicated that strong wake recovery was present, and a kurtosis analysis showed that the probability density function for the streamwise velocity followed a Gaussian distribution. In a quadrant analysis of the Reynolds stress, we found that the ejection and sweep motions for the LLJ inflow case were greater than those for the laminar inflow case.     

Evaluation of log‐of‐power extremum seeking control for wind turbines using large eddy simulations

The extremum seeking control (ESC) algorithm has been proposed to determine operating parameters that maximize power production below rated wind speeds (region II). This is usually done by measuring the turbine's power signal to determine optimal values for parameters of the control law or actuator settings. This paper shows that the standard ESC with power feedback is quite sensitive to variations in mean wind speed, with long convergence time at low wind speeds and aggressive transient response, possibly unstable, at high wind speeds. The paper also evaluates the performance, as measured by the dynamic and steady state response, of the ESC with feedback of the logarithm of the power signal (LP‐ESC). Large eddy simulations (LES) demonstrate that the LP‐ESC, calibrated at a given wind speed, exhibits consistent robust performance at all wind speeds in a typical region II. The LP‐ESC is able to achieve the optimal set‐point within a prescribed settling time, despite variations in the mean wind speed, turbulence, and shear. The LES have been conducted using realistic wind input profiles with shear and turbulence. The ESC and LP‐ESC are implemented in the LES without assuming the availability of analytical gradients.     

Improving farm efficiency of interacting vertical‐axis wind turbines through wake deflection using pitched struts

This work presents a numerical study of the obtained performance and the resulting flow field between two interacting large scale vertical‐axis wind turbines (VAWTs), under the influence of a deflected wake through the struts pitching of the upwind turbine. The configuration consists of two VAWTs aligned in the direction of the incoming flow in which a wide range of fixed struts pitching angles in the upwind turbine have been investigated. The main goal is to evaluate the influence of the wake deflection on the turbines performance while they are operating at their optimal tip speed ratio (TSR), and to reproduce the most relevant phenomena involved in the flow pattern of the interacting wake. Arrangements with cross‐stream offsets have also been tested for quantifying the contribution of this modification into the overall performance. For this purpose, an actuator line model (ALM) has been implemented using the open‐source CFD library OpenFOAM in order to solve the governing equations and to calculate the resulting flow. The Large eddy simulation (LES) approach is considered to reproduce the turbulence flow effects. A preliminary study to identify the optimal TSR of the interacting downwind turbine has been investigated.     

A wind‐tunnel study of the wake development behind wind turbines over sinusoidal hills

In the present work, the wake development behind small‐scale wind turbines is studied when introducing local topography variations consisting of a series of sinusoidal hills. Additionally, wind‐tunnel tests with homogeneous and sheared turbulent inflows were performed to understand how shear and ambient turbulence influence the results. The scale of the wind‐turbine models was about 1000 times smaller than full‐size turbines, suggesting that the present results should only be qualitatively extrapolated to real‐field scenarios. Wind‐tunnel measurements were made by means of stereoscopic particle image velocimetry to characterize the flow velocity in planes perpendicular to the flow direction. Over flat terrain, the wind‐turbine wake was seen to slowly approach the ground while it propagated downstream. When introducing hilly terrain, the downward wake deflection was enhanced in response to flow variations induced by the hills, and the turbulent kinetic energy content in the wake increased because of the speed‐up seen over the hills. The combined wake observed behind 2 streamwise aligned turbines was more diffused and when introducing hills, it was more prone to deflect towards the ground compared to the wake behind an isolated turbine. Since wake interactions are common at sites with multiple turbines, this suggested that it is important to consider the local hill‐induced velocity variations when onshore wind farms are analysed. Differences in the flow fields were seen when introducing either homogeneous or sheared turbulent inflow conditions, emphasizing the importance of accounting for the prevailing turbulence conditions at a given wind‐farm site to accurately capture the downstream wake development.     

Tip‐vortex breakdown of wind turbines subject to shear

Sheared velocity profiles pervade all wind‐turbine applications, thus making it important to understand their effect on the wake. In this study, a single wind turbine is modeled using the actuator‐line method in the incompressible Navier–Stokes equations. The tip vortices are perturbed harmonically, and the growth rate of the response is evaluated under uniform inflow and a linear velocity profile. Whereas previous investigations of this kind were conducted in the rotating frame of reference, this study evaluates the excitation response in the fixed frame of reference, thus necessitating a frequency transformation. It is shown that increasing the shear decreases the spatial growth rate in the upper half of the wake while increasing it in the lower half. When scaled with the local tip vortex parameters, the growth rate along the entire azimuth collapses to a single value for the investigated wavenumbers. We conclude that even though the tip‐vortex breakdown is asymmetric in sheared flow, the scaled growth rates follow the behavior of axisymmetric helical vortices. An excitation amplitude reduction by an order of magnitude extends the linear growth region of the wake by one radius for uniform inflow. In the sheared setup, the linear growth region is extended further in the top half than in the bottom half because of the progressive distortion of the helical tip vortices. An existing model to determine the stable wake length was shown to be in close agreement with the observed numerical results when adjusted for shear.     

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.     

Modeling space‐time correlations of velocity fluctuations in wind farms

An analytical model for the streamwise velocity space‐time correlations in turbulent flows is derived and applied to the special case of velocity fluctuations in large wind farms. The model is based on the Kraichnan‐Tennekes random sweeping hypothesis, capturing the decorrelation in time while including a mean wind velocity in the streamwise direction. In the resulting model, the streamwise velocity space‐time correlation is expressed as a convolution of the pure space correlation with an analytical temporal decorrelation kernel. Hence, the spatiotemporal structure of velocity fluctuations in wind farms can be derived from the spatial correlations only. We then explore the applicability of the model to predict spatiotemporal correlations in turbulent flows in wind farms. Comparisons of the model with data from a large eddy simulation of flow in a large, spatially periodic wind farm are performed, where needed model parameters such as spatial and temporal integral scales and spatial correlations are determined from the large eddy simulation. Good agreement is obtained between the model and large eddy simulation data showing that spatial data may be used to model the full spatiotemporal structure of fluctuations in wind farms.     

Effects of spatial and temporal resolution of the turbulent inflow on wind turbine performance estimation

The effects of spatial and temporal resolution of wind inflows generated using large eddy simulations (LES) on the scales of turbulence present in the wind inflow, and the resulting changes in wind turbine performance were investigated for neutral atmospheric boundary layer conditions. Wind inflows with four different spatial resolutions and five different temporal resolutions were used to produce different turbine responses. An aero‐elastic code assessed the dynamic response of two wind turbines to the different inflows. Auto‐spectral density functions (ASDF) of turbine responses, such as blade deflection and bending moment, that are representative of the turbine response were used to assess the effect of the inflow. The results indicated that, as additional turbulence scales were resolved, the wind turbines showed a similar increased response that was evident in both the ASDF and variance of the different wind turbine performance parameters. As a result, the amount to which turbulence is resolved in the inflow, particularly using tools such as LES, will be important to consider when using these inflows for wind turbine design and performance prediction. Copyright © 2015 John Wiley & Sons, Ltd.