The optimisation of the power output of wind turbines requires the consideration of various aspects including turbine design, wind farm layout and more. An improved understanding of the interaction of wind turbines with the atmospheric boundary layer is an essential prerequisite for such optimisations. With numerical simulations, a variety of different situations and turbine designs can be compared and evaluated. For such a detailed analysis, the output of an extensive number of turbine and flow parameters is of great importance. In this paper a coupling of the aeroelastic code FAST (fatigue, aerodynamics, structures, and turbulence) and the large-eddy simulation tool PALM (parallelised large-eddy simulation model) is presented. The advantage of the coupling of these models is that it enables the analysis of the turbine behaviour, among others turbine power, blade and tower loads, under different atmospheric conditions. The proposed coupling is tested with the generic National Renewable Energy Laboratory (NREL) 5 MW turbine and the operational eno114 3.5 MW turbine. Simulating the NREL 5 MW turbine allows for a first evaluation of our PALM–FAST coupling approach based on characteristics of the NREL turbine reported in the literature. The basic test of the coupling with the NREL 5 MW turbine shows that the power curve obtained is very close to the one when using FAST alone. Furthermore, a validation with free-field measurement data for the eno114 3.5 MW turbine for a site in northern Germany is performed. The results show a good agreement with the free-field measurement data. Additionally, our coupling offers an enormous reduction of the computing time in comparison to an actuator line model, in one of our cases by 89 %, and at the same time an extensive output of turbine data.

Wind energy poses a major contribution to today's renewable energy production

With the help of large-eddy simulations (LESs) the influence of different stabilities (i.e. neutral, stable or unstable stratification) on the power production of wind turbines and the calculation of loads on a turbine can be investigated under controllable conditions, which is also the scope of the present work. A wide range of differently stratified flows can be calculated with LES, from stable, as shown in e.g.

Most commonly used turbine models embedded in numerical flow models are either an actuator line model (ALM) or an actuator disk model with rotation (ADMR) or without rotation (ADM). In an ALM the blades are simulated separately as lines in the flow, whereas in ADM and ADMR the rotor is modelled in the flow as a disk. As shown in

To investigate turbine loads

Simplifications, to save computational resources, can lead to a lack of information about either the atmospheric flow or the turbine behaviour and, thus, possibly less accurate results

The objective of our work is to validate a further developed coupling method between the LES tool PALM

We developed one variation of an actuator sector method (ASM), where the blade movement is described as a segment of a circle. This allows for a larger time step in PALM than in FAST as the movement of the blade during that time step is captured in the area of the sector. A similar method is suggested in

In the present paper, we present an enhanced coupling framework. Furthermore, a systematic validation with measurement data for different atmospheric conditions with respect to a detailed set of variables is shown. A first comparison to other codes with a limited number of selected test cases, and without describing the coupling in detail, has been performed in the context of a joint study

In Sect.

With these comparisons, we show that the PALM–FAST coupling calculates realistic turbine output parameters to flows that are statistically stationary. The simulations also show that this is not only valid for the global turbine parameters like power output, but also for individual component parameters like blade and tower loads and that the differences in the turbine behaviour due to different atmospheric conditions can be seen in the simulations as well. Finally, Sect.

In the present work, the aeroelastic turbine code FAST

An earlier version of the coupling between FAST and PALM, described in

In an ALM the rotor blades are simulated as moving lines in the model domain and require a small computational time step in order to calculate the movement and in order not to miss information at the fast-moving blade tips. As the movement of the blades is reproduced, an ALM can give information on the turbine in general but also on separate blade data like blade loads. A more computational time-saving option is to simulate the turbine rotor as a disk, which is done in ADM simulations. Additionally to the obstruction the rotor causes for the flow, a rotation can be added to the simulation (ADMR), which increases the quality of the wake simulation. However, no information about individual blade parameters can be gained in such a simulation. To combine the advantages of both kinds of turbine models, i.e. the detailed output of the ALM and the low computational costs of the ADMR, a so-called actuator sector method (ASM) is used in this work.

PALM, when run in a normal set-up without FAST, uses either the Courant–Friedrichs–Levy (CFL) criteria or the diffusion criteria to determine the largest possible time step, which in general is larger than a time step needed for a proper ALM simulation. Therefore, using the same time step in both FAST and PALM affects the computational time required for the LES. In the present work, we decouple the time step and allow the pure LES time step criteria (CFL and diffusion criteria), which were mentioned above, to determine the time step in PALM and with this reduce the total computational time significantly.

In more detail, we use an ASM model for the projection of forces in PALM, whereas in FAST we still use the ALM model. Through this set-up, the computing time can be reduced tremendously, since the more time-consuming operations take place in PALM and not in FAST. However, for simplicity, our whole coupling routine described in this work is simply abbreviated as ASM hereafter.

Our ASM works as follows (see Fig.

Schematic of the operation mode of the PALM–FAST ASM coupling.

FAST therefore receives wind speeds of this frozen wind field and calculates the responding forces for the blades. During the larger PALM time step, the rotor blades cover a segment of the rotor area, a sector. The width of the sector

This smearing of the forces is realised by a polynomial resulting in a Gaussian shape that distributes the forces over the area surrounding the rotor blade in all three direction of space (

In general, the forces acting on the blades are calculated based on the wind speed that is present at the blade position, i.e. the positions in the rotor plane. However, this wind speed does not represent the actual wind speed entirely as it depends on the grid resolution and has to be interpolated to the desired positions. Close to the last known blade positions this interpolation leads to higher wind speeds than in reality, which leads to an overestimation of the power output. Additionally, the projection width of the forces, i.e. the width defined by the regularisation function, influences the wind speed close to the blade immensely. To circumvent these issues, we take the wind speeds for the ASM in positions upstream of the turbine.

Far enough upstream of the rotor, the flow can be assumed to be almost undisturbed by the rotor. The wind speeds at the rotor area are then estimated using the induction model SWIRL of FAST. SWIRL uses the so-called Taylor frozen turbulence hypothesis (Taylor, 1938) and calculates the induced velocity in axial and tangential direction. In

The validation of the coupling is divided into two parts. The first part is the evaluation of results using the generic NREL 5 MW turbine. The second part is the comparison to measurement data for a more extended analysis, for which a non-generic turbine is simulated.

The NREL 5 MW turbine

As this is a generic turbine, no comparison with measured data is possible. But the availability of the turbine data allows an evaluation of our enhanced coupling method, also in terms of turbulent flows. Additionally, the availability of the turbine data offers the opportunity to compare different methods and their computational resources. Therefore, two cases were considered, firstly a laminar and secondly a turbulent flow.

A comparison of four different methods is made, as summarised in Table

Overview of the turbine models that were used in the comparisons. The new enhanced coupling method is ASM, the respective time steps in PALM and FAST are denoted as

To evaluate the different methods, at first, a laminar case with a constant wind speed with height, i.e. zero vertical gradient of the streamwise velocity, is considered. The LES simulations use a resolution of 5 m and 384

In Fig.

A comparison of quantities along the 62 blade nodes shows a difference between the methods using wind speeds at the rotor blade positions (ALM and ASM without SWIRL) and the two methods using a different inflow, namely ASM and FAST (figures can be seen in Appendix

As a second case a turbulent flow is calculated. However, no comparison to FAST alone is done here since there is no literature value available to compare the results with. For the turbulent case, a neutral flow is simulated with neither heating nor cooling of the surface. A resolution of 4 m is used with 1200

Figure

As for the laminar case, the ASM leads to a lower power output than the other models, whereas the differences are comparable to the laminar case in Fig.

Furthermore, these simulations are used to compare the computational times of the ALM and ASM. In the laminar case the ASM is 9 times faster than the ALM while using the same amount of cores; i.e. the computational time is reduced by up to 89 %. The turbulent case is calculated with a difference in the allocated cores: the ALM uses 4 times more cores than the ASM; however, the ASM is still about 3.5 times faster than the ALM. Consequently, the ASM provides the same set of output parameters as the ALM but is significantly faster.

Through these simple simulations it can be seen that the sector methods offer savings in the computing time in comparison to the ALM. However, the ASM without SWIRL does not provide the expected results. Therefore, it is considered useful to compare the ASM with measurement data in the following.

Comparison of different simulation methods for the generator power of the 5 MW NREL turbine in a laminar flow with 8 m s

Comparison of different simulation methods for the generator power of the 5 MW NREL turbine in a turbulent flow at about 7.4 m s

As the generic NREL 5 MW does not allow for a comparison to measurement data, a free-field turbine is used for further analyses. Measurement data of an eno114 3.5 MW turbine, manufactured by eno energy

First, we consider laminar cases with uniform wind speed over height for the eno114 3.5 MW in order to establish a power curve. The reference power curve is obtained from stand-alone FAST runs, with a laminar inflow. The FAST turbine model is provided by eno energy, but the source code of the turbine controller was not available to us; only an executable file was provided. The calculated reference power curve coincides well with the published power curve of eno energy

Comparison of different simulation methods for the generator power of the eno114 3.5 MW turbine in a laminar case with a wind speed of 8 m s

The onshore measurement site, from which data were available, is situated in northern Germany close to the village of Brusow. At the measurement site two eno114 3.5 MW turbines are present. For one turbine (turbine 1 in Fig.

Apart from the two eno energy turbines the measurement site was also equipped with a met mast. Figure

From the 20 Hz data provided by the eddy-covariance stations, turbulence statistics with a resolution of 30 min are obtained by applying the eddy-covariance software TK3

Schematic of the measurement site in Brusow. The remaining wind directions in the measurement data, after filtering, are indicated in red;

Data of all sensors is available from 10 May until 30 June in 2017. To the east of the site of the turbines and met mast a forest is located, which influences the measurements greatly. Therefore, the measurement data are filtered for the westerly wind directions, where mostly grainfields are situated.

We estimate the roughness length of the surrounding area using the wind speed

Roughness length distribution for varying wind directions for the measurement period. Two methods of averaging the roughness length values gained by Eq. (

From the data of the eddy-covariance stations the stability parameter

Figure

It can be seen that the measurement data deviate only slightly from the simulation data. Also, no clear trend between the different stratifications can be observed. Differences for the stratifications can be seen in the turbulence intensity and the shear (see Figs.

Power data determined from the measurement data for May/June 2017, normalised by the corresponding power of the eno114 3.5 MW power curve determined by FAST in laminar conditions, for different stabilities (determined from eddy-covariance data).

Standard deviation for 10 min intervals of the measured turbine power output, calculated according to

Classification of atmospheric stability according to Obukhov length

In the following, the simulation set-ups for PALM and FAST that are used for the comparison to the measurement data are described.

In order to compare simulation results to the measurement data, simulations are computed that result in flow conditions similar to those observed under neutral boundary layer (NBL) and stable boundary layer (SBL) flow at Brusow. As can be seen in Figs.

Precursor simulations without a turbine are performed in order to reach a stationary state and evaluate the produced inflow conditions prior to the main simulations containing a wind turbine. The resolution for both neutral and stable conditions is set to 4 m in the

Set-up of the precursor simulations: size of the model domain in the streamwise

Resulting flow parameters after reaching a stationary state in the precursor simulations, averaged over 3600 s: the magnitude of the wind speed at hub height averaged over the model domain

For the respective main runs including the turbine a larger model domain and non-cyclic boundary conditions were used to avoid influences of the wake onto the turbine. The model domain of the neutral case is larger than the one of the stable case, as in neutral conditions the turbulent structures tend to be larger than in stable conditions: the neutral model domain is set to 7680 m

To reduce local effects caused by possible persistent structures in the flow, the main run is simulated three times with three different turbine positions in the

Turbine positions along the

Figures

Turbulence intensity

Shear of the measurement data (green) in comparison to the resulting shear of the precursor runs sorted in neutral and stable (red – neutral; blue – stable).

The turbine model of the eno114 3.5 MW turbine for FAST was provided by eno energy, including structural information and a pitch, a speed and a yaw control in the format of a Bladed .dll file, which was not accessible to us. However, the yaw of the turbine is neglected, as the flow in PALM was directed in such a way that the turbine is aligned with the wind. In FAST the modules ElastoDyn, AeroDyn and ServoDyn were used, and the degrees of freedom for the blade and tower were set to true except the rotor-teeter and yaw flag. All the platform degrees of freedom were neglected, i.e. set to false. The time step throughout all modules was set to

In the following plots the output data of the turbine in the simulations are compared to the measurement data. The main runs of the simulations are run for a simulation time of 650 s, and the results are averaged over 600 s, discarding the first 50 s as a spin-up of the turbine simulation; this time frame is derived from the laminar case (see Fig.

In Fig.

The measurement data of Brusow, with the wind speed at hub height as reference, does not show any clear tendency for the dependency of the wind turbine power on atmospheric stability (see Figs.

Figure

To check whether this distribution is comparable to the measurement data, a plot of the standard deviation of the power with respect to the TI is made (Fig.

Normalised standard deviation of the power with respect to the wind speed determined from measurement data in comparison to the simulation results (

Standard deviation of the power with respect to the TI determined from measurement data (green – all wind speeds; blue and red asterisks – stable and neutral measurements at wind speeds of 8–9 m s

Blade root bending moment

The flap-wise and edgewise blade root bending moments are evaluated, but also data for the tower top and base loads are available and examined. Figure

We filtered the data with respect to westerly winds, stability and rotor speed. The analysis of the rotor speed showed a difference in the controller behaviour of the real system compared to the modelled one. This can be seen in Figs.

For the stable case some of the time intervals have to be discarded due to a varying quality of the load sensors, leaving one interval for the stable case where data are continuous for the blade and tower moments. For the neutral case the longest remaining interval covers a span 165 s long. The conditions of the chosen intervals are shown in Table

Summary of the parameters of the measurement interval data used for the spectra of the blade and turbine loads: wind speed at hub height

In the following the stable case will be discussed in detail. The neutral case also shows a good agreement between simulation and measurement data but covers only a short time interval of only 165 s; the corresponding spectra can be found in Appendix

Figure

The spectra of the blade root bending moments are normalised by the same maximum value from both moments. The spectra of the tower top and tower base bending moments are normalised with their respective maximum values as well. The frequency is normalised by the rotor speed

Spectrum of the blade root bending moment

Spectrum of the tower top bending moment in

In the spectra of the stable case it can be observed that the torsion loads show comparable results (see Fig.

Spectrum of the tower moments:

Comparison of the

It can also be seen that the 1P peak is of different height in the tower load spectra. The peak of the simulation data reaches higher than the one of the measurement data. This is probably due to an overestimated blade imbalance in the simulation which has been used to respect weight and pitch differences between the blades (cf.

Notable is also that there seems to be a discrepancy between the simulation and measurement data in the tower top side-to-side bending moment in stable and neutral conditions. This might be caused by the difference in the tower model to the real behaviour of the turbine tower. It can be seen that the first tower eigenfrequency is slightly lower on the real turbine and therefore more prone to the rotational excitation. In the measurement data the first tower eigenfrequency is closer to the 1P peak, and therefore the vibrations are less damped.
Differences can also be observed in the 6P peak, especially in Fig.

To investigate the loads further, rain flow counts and the value of the equivalent load range

A comparison between the measurement data and the simulation results is not useful in this case as the available intervals vary in their inflow parameters and therefore the rotor speed. However, a comparison between the results of the simulation of the neutral and stable boundary layer flow shows the influence of the stability on the load outputs of the LES coupling. Table

Power output normalised by the maximum measured power, plotted with respect to the rotor speed, and normalised with the maximum measured rotor speed with an added offset for the measurement data in comparison to the simulation data.

The values can be linked to the power spectra shown in Fig.

This should be considered as a qualitative result. For a final quantitative analysis simulations with considerably larger run times or a number of simulations with different seeding would be required. Also, in the papers

Comparison of the equivalent load range

As can be found in Fig.

Relation between the rotor speed

In this paper we presented a new computing framework which combines the advantages of an atmospheric flow simulation using the LES tool PALM and the detailed calculation of the turbine response by FAST. To quantify the output of the results a comparison to the generic NREL 5 MW turbine and a more extensive comparison to measurement data of a real turbine are shown.

The comparison of the NREL 5 MW turbine was intended to compare different model approaches with respect to power output and computing time. These showed very good agreement in terms of power output. Additionally, in the considered cases a saving of computational time of up to 89 % could be observed in relation to the equally detailed ALM coupling.

In a second step, the enhanced coupling was compared to measurement data. The results resemble the measured data of the eno114 3.5 MW turbine well. For example the power output is reproduced very well, which is mostly due to the method of taking the wind speed in front of the turbine instead of directly at the rotor area to avoid an overestimation of the power. Also, the standard variation of the power shows a good resemblance to the measurement data. The parameter reflects the influence of the turbulence in the flow and therefore the stability, which is also present in the simulated results. Keeping in mind that the simulations were still idealised, i.e. only one homogeneous roughness length and no topography, there is good agreement between the simulated and the measured data.

The blade and tower loads are representative of the measurements in general. Deviations in the aeroelastic simulation model, especially the tower eigenfrequency, the selected rotor imbalance, the used controller and wind speeds led to slightly different resulting loads compared to the measurements. However, the load spectra still show a very good agreement. Variations due to the atmospheric stability are clearly found. This indicates that the PALM–FAST coupling is suitable to investigate the effects of different atmospheric flows on turbine behaviour.

In the current work, the constraints of the frozen wind field, e.g. the assumption of Taylor’s frozen turbulence hypothesis, do not limit the outcome, as in the current simulations the statistics of the flow are not subject to varying wind conditions. However, there are also situations where the hypothesis will reach its limits, e.g. with temporally variable wind fields or changing wind direction. The case of a turbine in a wake also needs further investigation, as the recovery of the wake in the frozen wind field has not been considered so far. Therefore, for future work, a further comparison to measurement data of different situations, such as unstable stratification or in a turbine wake, is worth considering to further substantiate the results. However, due to the reduced computing time, the coupling is basically well suited for carrying out load analyses of a single turbine in a wind farm. As up to now ADM or ADMR has mostly been used in wind farms, since the use of ALM is too computationally intensive due to the required large model domains.

In addition, thanks to the time-saving detailed simulations, there is a multitude of possible applications. Apart from calculating load analyses for wind farms, another possible application is to investigate the relationship between environment and turbine performance in footprint analyses. Furthermore, phenomena in atmospheric flows and their impact on turbine loads can be investigated, such as low-level jets.

The following plots show the dynamic pressure, the angle of attack, and the lift and drag coefficients for the NREL 5 MW turbine in the laminar case.

Dynamic pressure

Lift

The following plots show the blade and tower load spectra for the neutral case.

Spectrum of the blade root bending moment

Spectrum of the tower top bending moment in

Spectrum of the tower moments:

Here, the comparison of the wind profiles for the stable case is shown.

Wind profiles, calculated by the shear and wind speed, of the measurement interval and the simulation data used in the comparison of the loads for the stable case. The black lines indicate the rotor area, and the dashed line indicates the hub height.

The simulation and supervisory control and data acquisition (SCADA) data of the eno114 3.5 MW turbine are confidential and therefore not available to the public.

SK developed the actuator sector method for the PALM–FAST coupling, performed the simulations and data analyses, and wrote the paper. GS contributed to acquiring the funding for the work presented in the paper and provided intensive consultation on the development of the method and the scientific analyses. MK provided intensive reviews on the load analyses. LJL provided intensive consultation on the scientific analyses and had a supervising function.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The computations of the presented work were performed on the high-performance computing system EDDY of the University of Oldenburg funded by the Federal Ministry of Economic Affairs and Energy. We acknowledge the wind turbine manufacturer eno energy for providing SCADA data and the FAST turbine model, as well as for their support of the work.

The presented work is the result of the research projects WIMS-Cluster and ventus efficiens. The WIMS-Cluster project (FKZ 0324005) was funded by the German Federal Ministry for Economic Affairs and Energy on the basis of a decision by the German Bundestag. The ventus efficiens project (ZN3024) was funded by the Lower Saxony Ministry of Science and Culture.

This paper was edited by Jens Nørkær Sørensen and reviewed by two anonymous referees.