Technical modeling challenges for large idling wind turbines

This paper presents comprehensive investigations into idling instability occurring on the IEA 15 MW reference turbine. The systematic studies are carried out by means of Blade Element Momentum (BEM) and free wake vortex (Vortexline) methods. Two state-of-the-art dynamic stall models are tested in the present investigations, namely the Beddoes-Leishman and the IAG dynamic stall models, implemented into a development version of the wind turbine design code Bladed. The studies highlight the importance of unsteady aerodynamic modeling to predict idling instabilities and emphasize the characteristics of each modeling strategy. It is demonstrated that the IAG dynamic stall model predicts a more physically reasonable idling instabilities. Furthermore, Vortexline enables the calculations of the induced velocities even under idling conditions in contrast to BEM. The combination of the Vortexline method and the IAG model is considered to provide the most reasonable turbine response. The studies will be helpful for load engineers to select appropriate modeling strategies and shed some light into future engineering modeling improvements of wind turbines.


Introduction
The loads acting on wind turbine play an important role for determining the performance, stability, lifetime and safety of wind turbines under operation.This aspect is especially important during the design and certification processes for any modern wind turbines.In practice, the operation of a wind turbine is limited by the safety standard especially when the wind speed is too large.Under such conditions, the turbine is shut down and the blade is oriented at a certain pitch angle to minimize the resulting loads, usually at a pitch angle of 90 • .Two approaches may be adopted when the turbine is operating in stand-still, one is a parked condition where the rotor is hold at a certain position by applying brake or an idling condition where the rotor is still allowed to rotate (albeit at a much smaller rotational speed) with the total rotor and generator inertia as well as friction being the main drivers for rotation limiter.
The idling case where the turbine is exposed to the extreme wind speed at large yaw misalignment is known to drive high ultimate loads and often faces strong instabilities in the field and from simulation results.For large wind turbines, this becomes one of the major challenges because the blade is longer, more flexible and more slender than conventional turbines, thus the movement and vibration of the blade can be significant for the resulting loads.The angle of attack (α) experienced by the blades varies significantly in idling mode under the combined effects of inflow turbulence, flow inclination and yaw misalignment.The variation of the angle of attack can be substantial even in small yaw misalignment within the range of ±15 • [1].The angle of attack interval between [+60 • ,+130 • ] is especially prone to strong vibrations [2].It was pointed out that aerodynamic instabilities existed in specific wind deviation angles, causing divergence in edgewise motions of the blade [3].This phenomenon is complex and not well understood but holds an important factor for designing reliable turbines.This is true especially because the blade position can change from one time instance to another.
To fully understand the characteristics of wind turbine loads, a comprehensive inclusion of aeroelastic effects in CFD will be necessary [4].The accuracy of engineering models commonly used in industry are challenged by these complex situations.Blade element momentum theory (BEM) is originally not designed for this condition because the induction based on momentum theory will no longer applicable, and only the dynamic stall (DS) model plays a role for governing the unsteady loads.In contrast, free-wake models like Vortexline calculate the induction directly from the dynamics of the wake filaments.The present studies are intended to provide detailed evaluations into the influence of dynamic stall modeling and wake induction on the load characteristics of a 15 MW wind turbine.Two dynamic stall models implemented in the latest development of Bladed [5] will be tested in the studies, namely the incompressible version of the Beddoes-Leishman (BL) model [6] and the first order version of the IAG model [7].These tests are carried out by means of BEM and Vortexline calculations which differentiate the inclusion of the wake induction effects.
The present paper is organized as following.Section 2 provides a description of the numerical modeling and the test case of interest.The results are presented and discussed in Section 3, focusing on the loads acting on the blade and the aerodynamic characteristics associated with the test cases.Finally, the paper will be concluded with suggestions for follow up studies in Section 4.

Research Methodology
The studies presented in this paper were carried out using a latest development of the Bladed software, an engineering tool used in numerous wind turbine industries and in research communities.The Bladed software has been developed from early 90s at the Garrad Hassan consulting office, and now is one of the major software for wind turbine design and analysis at DNV.The code has been improved over the time accommodating several latest development in the field.Several publications documented verification studies of the Bladed code performance [8][9][10][11].
The aerodynamic modeling in Bladed is based on BEM theory where the axial and tangential Glauert momentum equations are expressed in dimensional form.The dynamic sub-models such as the skew wake correction are represented in a full state space forms which allow a direct integration of the aerodynamic and structural states.The tip loss effect was modeled by employing the Prandtl tip loss correction [12].Furthermore, Bladed solutions were also coupled with the high induction correction according to Glauert [13].In addition to the BEM model, a fully coupled free wake lifting line (Vortexline) model in Bladed was also used in the present investigations.This model is currently available for internal purpose only and not commercially released into the market.The code is run in parallel and adopts vectorized implementation to accelerate the running time.The Vortexline model in Bladed has been recently improved for better convergence treatment and capabilities in calculating the loads at the blade sections.The influence of the shed vortex inductions were purposely investigated in the present work.Three main unsteady modeling strategies were adopted in the present work: (1) without dynamic stall model, (2) using the incompressible version of the Beddoes-Leishman (BL) model [6] and (3) using the first order version of the IAG model [7,14].The IAG model has shown a promising performance when it was compared against experimental data of pitching airfoils at deep stall conditions in Ref. [7] and the state-space version of the model has been implemented in Bladed and verified in Ref. [14].For the present studies, the time step size for the fixed step integration was set to 0.01 s.
The IEA 15 MW reference wind turbine version 1.1 [15] was used in the present investigations.The turbine has a rotor diameter of about 242 m constructed by three slender blades with each spanning along 117 m in length.In the studies, the turbine was exposed to a complex condition associated with the design load case (DLC) 6.3 [16] assuming an idling situation.The turbulent wind data has a mean wind speed of 40 m/s and turbulence intensities in longitudinal, lateral and vertical directions of 11%, 8.8% and 5.5%, respectively.The wind field was generated using a Kaimal wind field generator with the length scales defined as 340.2 m (longitudinal), 113.4 m (lateral) and 27.72 m (vertical) with a coherence decay parameter of 340.2 m and a coherence decay constant of 12.A superposition of the turbulent wind data with a constant wind shear with a shear exponent of 0.11 was applied during the simulation run time.The main wind direction was aligned such that mean yaw misalignment angles (ψ) of [-20 • , 0 • , +20 • ] were set.

Effects of shed vortex induction in Vortexline calculations
Since Vortexline method calculates the induction effects in all conditions without relying on the momentum theory, the method is deemed more accurate for edge cases like idling instabilities.Figure 1 demonstrates how the blade root torsional moment and rotational deflection at the blade tip are influenced by such modeling.Note that attached flow state calculations in the BL and IAG dynamic stall models are deactivated when they are paired with Vortexline calculations  It becomes apparent that the shed vortex effects are dominant only when no dynamic stall model is applied in the calculations, which helps Vortexline to deal with idling instability to some degree.However, once any of the BL or IAG model is adopted, the difference between the Vortexline calculations including and excluding the shed vortex effects are less apparent, though the loads and tip rotational deflection are still reduced slightly when the effect is included.In Figure 1, it can be observed that the IAG model yields the smallest load fluctuations and tip rotational deflection which are likely closer to what the turbine experiences in reality under the design load case being considered.Further detail on the evaluations between the dynamic stall models will be given in subsequent sections.
Figure 2 presents the dynamics of the axial and tangential induced velocities predicted using BEM and Vortexline calculations.Timeseries results and the power spectral density of the signals are presented.The induction calculations are turned off and thus the values remain zero for both variables.In contrast, Vortexline calculations yield strong induction dynamics especially in tangential component.A similar observation was made in [10] even for power production case.The inclusion of the shed vortex effect further increase the dynamics to a certain degree.These induced velocity fluctuations increase the aerodynamic damping because the energy of the flow is partially extracted.The power spectral density in Figure 2 shows that the inclusion of the shed vortex effects further increases the energy content.Now it becomes apparent that including the shed vortex effect is beneficial for predicting wind turbine loads in idling condition.In the subsequent discussions, this effect is always turned on for the Vortexline calculations except stated otherwise.

Comparison between different calculation models
In this section, the loads obtained from different calculations will be compared and discussed.Figure 3 shows the characteristics of the loads at the blade root and rotational deflection at the blade tip.These variables are usually sensitive to instability behavior at high angle of attack.The test case being shown is for the yaw misalignment angle of +20 • .It can be seen in Figure 3 that the magnitude and trend of the blade root loads change considerably depending on the unsteady modeling strategy being adopted.The loads instability reduces when a dynamic stall model is applied in BEM simulations.This is due to the inclusion of the aerodynamic damping which helps the turbine dynamics to reduce the nonlinear oscillations.The instability is shown to be smaller for the IAG model when compared to the BL model.Instability in idling is often observed in aero-elastic codes and it is widely assumed in the industry that the codes are underestimating the true aerodynamic damping.Therefore, the usage of the newly implemented IAG model is seen to be helpful for the instability problem in idling condition.Furthermore, the results are likely also to be more accurate because the IAG model was designed purposely for deep-stall aerodynamics, see Bangga et al. [7] for comparison with measurement data of pitching airfoils.A direct observation can be made for the blade tip rotational deflection compared to the case without dynamic stall model and the case with the BL model.These two cases predict instabilities of the tip rotational deflection within the range of [-10 • ,+10 • ] or even larger, and this is seemingly too large to be physically correct.
The same conclusion can be observed also for the Vortexline calculations -to some extent even to higher degree.The combination of the Vortexline approach with the IAG model yields the more stable oscillations of the blade root torsional moment and tip rotational deflection.The effect is also observed for the oscillation of the rotational speed and blade-1 azimuth angle in Figure 4. Using a different modeling strategy causes a time shift which allows the same blade section to experience different wind conditions.This is one of the main complexity of idling simulations where the position of the blade and the applied wind data will be different depending on the modeling strategy.

Detailed aerodynamic characteristics
To further evaluate the blade regions that are mostly affected by the modeling strategy, the aerodynamic characteristics at three blade stations are presented in Figure 5 and Figure 6.One can see that a time shift of the angle of attack and blade sectional normal force (relative to local chord orientation) is observed of the IAG model when combined with BEM, and for both dynamic stall models when combined with Vortexline.Again, this can be explained by observing the blade position in Figure 4.This is a direct influence of the blade seeing a different wind timeseries in space.More interesting to see is the behavior of the angle of attack and loads instabilities.Actually the root and middle parts of the blade are not massively affected by the instability (see also the range of the minimum to maximum angle of attack), while the outer part of the blade does.This is due to a lower value of the structural stiffness at the blade outer part, especially for a long-slender blade.
Figure 7 and Figure 8 present the resulting dynamic polar data computed using different calculation strategies.Both lift (C L ) and pitching moment (C M ) coefficients around the quarter chord position at two radial locations are displayed.The polar data are the driver as well as the result of the unsteady aerodynamics and structural dynamics effects.This is due to the fact that the coupled simulations take the aerodynamic forces as the input to compute the blade motions and deflections, which in turn influence back the range of the angle of attack according to the well known collar triangle of the aeroelastic coupling mechanism [17].
Figure 7 shows that the case without adopting any dynamic stall model causes the range of the angle of attack to be extremely large at the outer blade station.This case reaches the whole range within [-180 • ,+180 • ], which looks likely incorrect.This occurs because the velocities of the blade motion near the tip are high, leading to high variation in the angle of attack.The reason behind that is that the hysteresis loop from the dynamic stall effects actually provides a damping mechanism, adding an additional stability on the blade on top of the structural damping.This is clearly shown when a dynamic stall model is being adopted in the simulations.Note that dynamic stall effects change the behavior of the lift, drag and pitching moment from their stationary conditions.This includes the increase of the stall angle of attack, steeper pitching moment curve and increased drag during the upstroke motion (increased angle of attack).The behavior is opposite during the downstroke motion (decreased angle of attack) and these characteristics create hysteresis effects, see e.g., [18,19].
Although the ranges of the angle of attack for BL model and IAG model are similar in the blade middle part, the IAG model is shown to reduce the minimum operating angle of attack for the blade outer part, see Figure 7.This is the main reason the pitching moment in the negative stall area for the IAG model is a bit damped compared to the BL model.There is no enough aerodynamic damping generated by the BL model to withstand the instability, and this causes the model to predict a larger range of the angle of attack than the IAG model.
A similar story can be told for the Vortexline model in Figure 8 for the outer blade part, but now the results are improved for all dynamic stall models (range of the angle of attack   decreases).The reason stems from the fact that Vortexline still calculates the effect of induced velocity for a turbine in stand-still.Note that the blade induction in Vortexline is calculated based on the strength of the vortices in the wake, which makes it suitable for both rotating, slowly rotating (idling) and non rotating turbine.In contrast, the momentum theory analogy in BEM assumes that the rotor rotates and extracts the energy from the wind, causing the reduction in the axial velocity (and increased tangential velocity due to wake rotation).This assumption does not hold any longer for wind turbines in stand-still.

Effects of yaw misalignment angles
This section provides an overview about the effects of dynamic stall modeling on the rotor loads in idling conditions at different yaw angles.The results are presented and compared to each other in Figure 9, which describes the power spectral density of the resultant load acting at the hub.It can be seen that the loads are affected by the yaw misalignment angle.The smallest variations between different unsteady aerodynamic modeling strategies can be seen when there is no yaw misalignment (ψ = 0 • ).In this case, dynamic stall effect plays a minor role on the loads characteristics.On the other hand, the importance of the dynamic stall modeling becomes more prominent as the yaw angle is increased or decreased.Both positive and negative yaw angle consistently show the smallest load amplitudes when the IAG model is adopted.This story is true both for BEM and Vortexline calculations.This observation sheds some light in idling instability modeling because the load fluctuations are often overestimated by engineering calculations, which enforce load engineers to "artificially" increase the structural damping in edgewise direction.The real problem with this solution is that there is no silver bullet on how much the structural damping shall be increased.Using the newly implemented IAG model potentially allows load engineers to evaluate idling instability (e.g., for DLC 6.2 or 6.3) without having to tune the structural damping unnecessarily.

Conclusions and Remarks
Comprehensive evaluations of the technical challenges in idling instability modeling for large wind turbines were carried out in this paper.The studies investigated the performance of two state-of-the-art dynamic stall models incorporated into blade element momentum (BEM) and Vortexline computations.The paper discussed several considerations and the following conclusions can be derived: • Idling instability predictions depend on the unsteady aerodynamic modeling especially the inclusion of the dynamic stall model.• Calculations without dynamic stall model yield massive instabilities which are unlikely to be physically correct.• The IAG dynamic stall model predicts more reasonable instability level which can be helpful for the loads analysis.• Vortexline calculations incorporate induction dynamics even for idling conditions which allows the induced velocity especially in tangential direction to vary.• The dynamics of the induced velocities partially extracts the energy of the flow and increases the aerodynamic damping.This effect is more pronounced when the shed vortex effect is included.
Since the present studies are limited to code comparison, the validity of the dynamic stall modeling generally requires further investigations especially by considering an extremely large angle of attack when it is much larger than 30 • .The studies shall also be expanded to verification of thick airfoil sections of greater than 30%.Future investigations may be aimed at incorporating the higher harmonic effects from the vortex shedding.This may be done by implementing the second order term of the IAG dynamic stall model.Furthermore, studies in parked conditions and their correlation with idling instabilities will be of interest for engineering evaluations.The studies may also be expanded by considering different ranges of the angle of attack and for different turbines.Last but not least, BEM may be corrected to allow induction calculations even under idling/parked conditions.Vortexline results might be employed for verifying the dynamics of the induced velocities.

Figure 1 :
Figure 1: Blade-1 torsional moment at the root and z−rotational deflection at the tip obtained using Vortexline calculations at ψ = +20 • .Calculations incorporating and excluding shed induction effects are presented.Note that the y-axis scales are different depending on the case.

Figure 2 :
Figure 2: Axial (u i ) and tangential (v i ) induced velocities obtained from BEM and Vortexline calculations at the blade outer region at ψ = +20 • .The calculations incorporate the IAG dynamic stall model.

Figure 3 :
Figure 3: Blade-1 torsional moment at the root and z−rotational deflection at the tip obtained using various modeling strategies at ψ = +20 • .Vortexline calculations were done by including the shed vortex induction effects.DS: dynamic stall, BL: Beddoes-Leishman.

Figure 4 :
Figure 4: Rotor rotational speed and azimuth angle of blade-1 obtained using various modeling strategies at ψ = +20 • .Vortexline calculations were done by including the shed vortex induction effects.DS: dynamic stall, BL: Beddoes-Leishman.

Figure 6 :
Figure 6: Sectional magnitude of the angle of attack (left) and blade normal force (right) obtained from Vortexline computations at ψ = +20 • .Vortexline calculations were done by including the shed vortex induction effects.DS: dynamic stall, BL: Beddoes-Leishman.