Load calculations play a key role in determining the design loads of different wind turbine components. To obtain the aerodynamic loads for these calculations, the industry relies heavily on the Blade Element Momentum (BEM) theory. BEM methods use several engineering correction models to capture the aerodynamic phenomena present in Design Load Cases (DLCs) with turbulent wind. Because of this, BEM methods can overestimate aerodynamic loads under challenging conditions when compared to higher-order aerodynamic methods – such as the Lifting-Line Free Vortex Wake (LLFVW) method – leading to unnecessarily high design loads and component costs. In this paper, we give a quantitative answer to the question of load overestimation of a particular BEM implementation by comparing the results of aeroelastic load calculations done with the BEM-based OpenFAST code and the QBlade code, which uses a particular implementation of the LLFVW method. We compare extreme and fatigue load predictions from both codes using sixty-six 10 min load simulations of the Danish Technical University (DTU) 10 MW Reference Wind Turbine according to the IEC 61400-1 power production DLC group.

Results from both codes show differences in fatigue and extreme load estimations for the considered sensors of the turbine. LLFVW simulations predict 9 % lower lifetime damage equivalent loads (DELs) for the out-of-plane blade root and the tower base fore–aft bending moments compared to BEM simulations. The results also show that lifetime DELs for the yaw-bearing tilt and yaw moments are 3 % and 4 % lower when calculated with the LLFVW code. An ultimate state analysis shows that extreme loads of the blade root out-of-plane bending moment predicted by the LLFVW simulations are 3 % lower than the moments predicted by BEM simulations. For the maximum tower base fore–aft bending moment, the LLFVW simulations predict an increase of 2 %. Further analysis reveals that there are two main contributors to these load differences. The first is the different way both codes treat the effect of the nonuniform wind field on the local blade aerodynamics. The second is the higher average aerodynamic torque in the LLFVW simulations. It influences the transition between operating modes of the controller and changes the aeroelastic behavior of the turbine, thus affecting the loads.

Load calculations are an essential process when designing large modern wind turbines. With the help of such simulations, turbine designers are able to derive the design loads for each of the turbine's components. International guidelines and standards prescribe a large number of aeroelastic simulations of the complete turbine for each load calculation loop

Current aeroelastic codes rely mostly on the Blade Element Momentum (BEM) aerodynamic model (

Over the past years, there have been several studies comparing BEM models with higher-order vortex models.

Several authors have also done aeroelastic comparative studies.

Other comparisons of vortex and BEM methods are done in

A hybrid implementation that uses a BEM method for the far wake and a Lifting-Line Vortex method for the near wake is presented in

Most of the studies comparing loads have so far focused on specific scenarios, simulating turbines under idealized inflow conditions or using a small number of turbulent load cases. If we wish to quantitatively answer how the results of load calculations differ when we use BEM-based and LLFVW-based methods, we need a large number of turbulent DLCs to level out statistical biases of individual realizations. Many of the mentioned studies also do not include the direct interaction with the turbine controller. Wind turbine load calculations are aero-servo-elastic in nature and the predicted loads are a result of the interaction of the aerodynamics with the turbine structure and controller. Not taking this interaction into account gives an incomplete picture of the effect that different aerodynamic models have on the design loads of the wind turbine.

In this paper, we compare the results of aero-servo-elastic load
calculations for the DTU 10 MW RWT. The turbine is simulated according to the IEC 61400-1 Ed.3 DLC groups 1.1 and 1.2 using two different aeroelastic codes: NREL's BEM-based OpenFAST v.2.2.0

For this study, we chose to use the DTU 10 MW RWT. It is representative of the new generation of wind turbines and has been used in several research studies. The complete description of the turbine can be found in

The following subsections briefly present the methods used for aerodynamic and structural modeling, the turbine controller, and the setup used for the load simulations.

OpenFAST and QBlade are set up so that their only difference is the implemented aerodynamic model. OpenFAST uses AeroDyn – an implementation of the BEM method – and QBlade uses an implementation of the LLFVW method. The following subsections describe the details of these two particular implementations of the BEM and LLFVW methods.

The BEM method calculates the aerodynamic loads by combining the Blade Element theory and the Momentum theory of an actuator disc to obtain the induced velocities on every discretized element of the blades

Modeling differences of the two aerodynamic codes. I stands for intrinsic, and EM stands for engineering model.

The LLFVW method is based on inviscid potential flow theory and a vortex representation of the flow field

Equations (

In order to avoid a singularity when evaluating Eq. (

Representation of the LLFVW method and concepts on a wind turbine blade.

While capturing the flow physics of a wind turbine rotor much more accurately, LLFVW methods still use some correction models to account for all the aerodynamic phenomena present in turbulent load calculations, briefly explained here.

Table

The LLFVW method explicitly includes most of the phenomena present in DLC simulations with turbulent wind conditions. Usual DLC configurations include sheared and oblique inflow as well as temporal and spatial variations in the incoming wind speed. Unlike the BEM method that solves for the axial and tangential induction factors at each blade element, the LLFVW method solves for the complete flow around the rotor.

Turbine configurations can have coned blades. Including cone angles, as well as the blade prebend and blade deflections in the case of aeroelastic calculations, violates the assumption made in many BEM methods that the momentum balance takes place in independently acting annuli in the rotor plane.
Recently, a BEM method that can model the effect of coned blades and radial induction has been proposed in

The structural model used for this study in both OpenFAST and QBlade is ElastoDyn

Both OpenFAST and QBlade have additional models that allow for a more accurate representation of the wind turbine structural dynamics. The module BeamDyn in OpenFAST is able to model the blade as a geometrically exact beam

This indicates that the differences in aerodynamic loads from BEM-based and LLFVW-based codes will certainly be more marked when studied in conjunction with a more accurate structural model that allows for the torsional degree of freedom. Nonetheless, we decided to use ElastoDyn as the structural model for our study. It is shared by both aeroelastic codes, so by using it, we keep the modeling differences only in the aerodynamic module and ensure that the latter is the only source of the load differences.

To enable aero-servo-elastic studies, we implemented a wind turbine controller that is compatible with both codes. The controller is based on the DTU Wind Energy Controller

The controller parameters were obtained via BEM calculations, so it is expected that the controller will behave differently if used in LLFVW calculations. In a normal design situation, each controller is tuned to the aeroelastic turbine model in order to optimize for the control objectives (i.e., maximize energy capture and minimize turbine loads). Since the aeroelastic models are inherently different due to the aerodynamic models, the tuning of the controller would result in different parameters depending on the aerodynamic model. We deliberately did not retune the controller parameters for the LLFVW simulations. Since the controller parameters were optimized for BEM simulations, we expect that the energy capture or the load level (or even both) will not be optimal in the LLFVW simulations. By doing this though, we ensure that the load differences arise only from the different aerodynamic models themselves and their interaction with identical turbine controllers. With the structural models also being identical, we can clearly attribute the load differences to the aerodynamic models.

In order to use the presented methods in load calculations, several practical considerations had to be taken into account. Given that Eq. (

The second method is the wake cutoff. After a given amount of rotor revolutions, the wake is cut off. The influence of these far-wake vortex
elements on the velocity in the rotor plane is negligible. Removing these elements helps speeding up the calculations. Figure

Wake-coarsening methods for the LLFVW simulations: the wake is split into three regions with decreasing amounts of wake elements. After a given number of revolutions, the wake is cut off.

Simulation parameters for aerodynamic and aeroelastic simulations.

To do a baseline comparison of our aerodynamic models, we ran a series of idealized aerodynamic simulations. The parameters for these simulations are summarized in Table

Figure

Performance coefficients for aerodynamic simulations with idealized conditions:

Figure

The turbulent load calculations described in Sect.

Figure

Comparison of aerodynamic and aeroelastic calculations on turbine performance:

The rotor speeds and pitch angles for the aerodynamic and aeroelastic
calculations are shown in Fig.

The higher rotor speeds obtained in QBlade simulations at those wind speeds can be explained from the higher power coefficients seen in Fig.

An important result from Fig.

The turbulent wind load cases were calculated following the DLC groups 1.1/1.2 from the IEC61400-1 standard

Comparison of statistical values for turbulent calculations:

For the analysis of the turbulent wind load calculations, we considered a selection of load sensors that is representative of the dynamics and load level of the entire turbine. For the blade analysis, we included the blade root in-plane and out-of-plane bending moments and the blade tip in-plane and out-of-plane deflections. These sensors give a good overview of the overall blade dynamics. The in-plane quantities are mainly driven by gravity loads. Our focus is more on the out-of-plane quantities that are mostly driven by the aerodynamic loads. Differences in the aerodynamic models will have the highest impact on these latter quantities. We also included the yaw-bearing roll, tilt, and yaw moments and the tower top fore–aft and side–side deflections. These sensors characterize the tower top loads and dynamics. All of these sensors, with the exception of the tower top side–side deflection, are directly affected by the aerodynamic loads. Finally we included the tower base fore–aft, side–side and torsional bending moment as indicators of the tower loads. Here, our focus is on the tower base fore–aft bending moment, as it is the sensor most affected by the aerodynamic loads. To analyze if the different aerodynamic models also affect the controller behavior, we included the collective pitch angle and the rotor speed in our analysis.

Table

Considered sensors and analysis type for turbulent load calculations. CS stands for coordinate system, F stands for fatigue and U stands for ultimate.

Figure

As a general observation, we can see that statistical values for the shown sensors are similar in both codes. There are some differences though.

Let us consider the rotor thrust in Fig.

The comparison of electrical power from the turbulent wind simulations (Fig.

The rotor speed signal (Fig.

Finally, Fig.

While the median values of the sensors shown in Fig.

As for the other three sensors, we see that (particularly for the wind speeds between 8 and 14 m s

It is clear that the aerodynamic models have an influence on the overall turbine behavior and loads. However, the mechanisms of how these models affect the loads are not straightforward. In the subsequent sections a quantitative analysis and discussion of these effects is presented.

In this section, we discuss the influence of the aerodynamic models on the variability of controller signals and fatigue loads of different turbine sensors. The analysis is based on the results of the turbulent load calculations described in the previous section. In this and the following sections, the subscripts

To quantify the variability of the control signals, we used the standard deviation

Figure

Normalized averaged standard deviations vs. wind speed:

If we consider the rotor speed (Fig.

Why do we have these differences in the wind speed bins 4 and 12 m s

As for

For the pitch angle signal we can see that the normalized

The fatigue loads are quantified using the damage equivalent loads (DELs) metric. DELs are derived from the time series of the load sensor using a rain flow counting algorithm. In this algorithm, the time-varying signal is broken down into individual cycles by matching local minima and maxima in the time series

Figure

Normalized lifetime DELs for the considered turbine load sensors. Sensor notation is given in Table

When considering the yaw bearing, Fig.

Normalized averaged 1 Hz DEL as a function of the wind speed bin:

When calculating the lifetime fatigue loads, we take into account the loading of all the wind speed bins. In different wind speed bins, the turbine can see
qualitatively different loading scenarios leading to significant differences in fatigue loading when simulated with different aerodynamic models. To further understand which phenomena are contributing to the differences in fatigue loads, we also analyzed the contribution of the individual wind speed bins to the fatigue loading of the sensors. As we can see in Fig.

Figure

A different behavior can be seen for the

The behavior of the fatigue damage on the yaw-bearing sensors is also
qualitatively different from the tower base fore–aft and the blade root
out-of-plane bending moments. Figure

Power spectral density plots for

To better understand the differences in the fatigue loads and the variability
of the controller signals, we can categorize the wind speed bins into three
qualitatively different wind speed regions: Regions A–C.

Region A includes wind speed bins between 4 and 10 m s

Region B encompasses wind speed bins between 10 and 16 m s

Region C covers wind speed bins between 18 and 24 m s

Because we are analyzing turbulent load calculations with varying wind speed, the limits between the regions cannot be exactly defined. We will consider one wind speed bin for each region as a representative set of simulations for that region. For each chosen wind speed bin, the qualitative turbine behavior will be the same as in the corresponding region described above. For Region A the chosen wind speed bin is 8 m s

It should be stressed here that the analysis done in this section is valid only for the two particular aerodynamic codes considered in this study. The LLFVW implementation of QBlade does not take into account the interaction between the vorticity of the wind shear and the vorticity due to the wake. This affects the shape of the turbine wake and influences the loading on the turbine

Figure

Figure

When we consider the PSDs of the turbulent load calculations (Fig.

The second peak is at the 1P frequency. If we compare the amplitudes between the aerodynamic codes at that frequency we can see that, for both the 8 and 0

These loading differences are also seen between different implementations of BEM codes.

The behavior of the PSD plots changes when we compare simulations in Region B (Fig.

We finally consider Region C in Fig.

Like

Power spectral density plots for

For turbulent wind speed calculations in Region A (Fig.

If we now concentrate on Region B simulations, we can see in Fig.

For simulations in Region C the PSD(

We note a large difference in peaks of PSD(

In absolute terms,

For turbulent simulations in Region A, the main difference in PSD(

When we consider Region C, we can see in Fig.

The last sensor analyzed in this section is

For Region A, there are two peaks where PSD

This phenomenon is also responsible for the fatigue load differences in Regions B and C. As we can see in Fig.

In the previous section, we discussed the contribution of the periodic oscillations on the turbine loading. This section considers the extreme events that the turbine sensors experienced in the turbulent wind load calculations. The ultimate state analysis was done for all the sensors listed
in Table

Normalized extreme values of deflections and controller signals:

The extreme values presented in this subsection are obtained by taking the maximum and minimum occurring values in the time series of all the simulations. In addition, the extreme values of the blade-related
sensors – i.e.,

Analogously to the fatigue analysis, we will use the notation
Max

Figure

When looking at the blade deflections, it is remarkable to see that the extrema of

The tower top deflections show larger differences in extreme values from the
different calculations than the blade tip deflections. If we consider the extrema of the fore–aft deflection, we see that the normalized values of Max

Finally, Fig.

Performing load calculations with different aerodynamic models also has an
impact on practically all the considered extreme loads of the turbine, as Fig.

Normalized extreme values of turbine load sensors:

Let us start with the blade root loads. We can see in Fig.

In the case of the yaw bearing, the most notable difference in extreme loads occurs for the tilting moment. The normalized Max

For the tower base loads we see large differences in the extrema of the fore–aft bending moment. The normalized values of Max

As with the fatigue loads, the reason for these differences in the extreme loads must ultimately come from the different aerodynamic models.

In order to limit the extension of this analysis, we will only consider a selection of the sensors. These are

For the extreme values of the tower sensors, we see in Figs.

A selection of the load case time series is shown in Fig.

Time series of the extreme tower event:

Let us focus on Max

If we now consider on Max

The difference in the controller behavior affecting the maxima of the tower sensors can be traced back to the higher aerodynamic torque of the LLFVW simulations (Fig.

A similar analysis to that in the previous subsection was also carried out for

For the BEM simulations, Max

From Fig.

The maxima of

In this paper we analyzed the effect of two different aerodynamic models on the performance and especially on the loads of the DTU 10 MW RWT. The first aerodynamic model – used in the aeroelastic simulation software OpenFAST – is an implementation of the BEM method, the standard method used in the industry. The second aerodynamic model – used in TU Berlin's aeroelastic software QBlade – is an implementation of the LLFVW method.

We did a baseline comparison of both codes by calculating the performance of the turbine under constant uniform wind speeds, a configuration where many of the engineering correction models do not contribute to the aerodynamic loads. The performance coefficients of the turbine simulated with both codes were similar for all relevant wind speeds where the turbine is in power production. The largest differences were seen at wind speeds below the rated wind speed, where the axial induction factor plays an important role. Including measures to speed up the LLFVW simulations as well as elasticity did not have a significant impact on the performance of the wind turbine.

We also simulated the wind turbine under turbulent wind conditions following the requirements of the IEC 61400-1 Ed.3 DLC groups 1.1 and 1.2. The average performance of the turbine in the turbulent wind simulations is comparable to the performance in the idealized simulations with constant uniform wind speed. Yet there is considerable variation in the thrust and power of the turbine due to the unsteady aerodynamic phenomena present in the turbulent wind load calculations. Those variations are more marked in the BEM simulations than in the LLFVW simulations, with the former showing a higher activity in the controller signals – i.e., the rotor speed and the pitch angle. This leads to considerable differences in the fatigue and extreme loads of the turbine.

In order to quantify the differences in the fatigue loads, we carried out a fatigue analysis that includes the lifetime DELs and the per-wind-bin-averaged 1 Hz DELs of selected load sensors of the turbine. For the lifetime DELs, the LLFVW simulations show a 9 % decrease in DEL

For the yaw-bearing moment, we found that the LLFVW simulations predicted a
decrease of 4 % and 3 % in DEL

We also did an ultimate state analysis on the results of the turbulent wind load calculations. For the out-of-plane loads and deflections of the blade, we found that the BEM simulations predicted higher extrema than the LLFVW simulations. The maxima of

The results of this paper show that there are significant differences in the fatigue and extreme loads if we use a higher-order aerodynamic model in the load calculations. The fact that lower fatigue loads were obtained for the considered sensors when using the LLFVW method indicates that there is a real potential to reduce the design loads of modern multi-megawatt wind turbines by adopting higher-order aerodynamic models in load calculations. Yet more work needs to be done before this can be stated as a general conclusion. In order to improve our quantification of the load differences, future work will include simulations with a higher-order representation of the structural dynamics. By including the torsional degree of freedom, we will be able to model the flap–twist coupling that greatly influences the loads on the turbine. In order to better quantify the differences in extreme loads, more DLC groups from the current guidelines and standards should be included. Performing an ultimate state analysis of the IEC 64100-1 DLC 1.1 and 1.2 groups gave us some insight into the influence of the aerodynamic codes on the extreme loads. Including DLC groups that are known to induce design driving extreme loads on the turbine will help us to better understand and quantify the effect of higher-order aerodynamic models on the extreme loads.

This appendix contains the wake-coarsening parameters we used in our LLFVW simulations. They are summarized in Table

Wake-coarsening parameters for aerodynamic and aeroelastic LLFVW simulations.

Both OpenFAST and QBlade are open-source code that is available online. The latest version of OpenFAST is available at

SPB prepared the manuscript with the help of all co-authors. DM is the main developer of QBlade and developed the aerodynamic code. JS developed the structural code. SPB and FP performed the calculations and the analysis of the results. AB and COP provided assistance with the paper review.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Wind Energy Science Conference 2019”. It is a result of the Wind Energy Science Conference 2019, Cork, Ireland, 17–20 June 2019.

Sebastian Perez-Becker wishes to thank WINDnovation Engineering Solutions GmbH for supporting his research.

This open-access publication was funded by Technische Universität Berlin.

This paper was edited by Katherine Dykes and reviewed by Emmanuel Branlard and Georg Raimund Pirrung.