Analysis of 3D Stall Models for Wind Turbine Blades Using Data

from the MEXICO Experiment

Srinivas Guntura, Christian Bak

b, Niels N. Sørensen

c

a

Risø DTU, Roskilde, Denmark, srgu@risoe.dtu.dk b Risø DTU, Roskilde, Denmark, chba@risoe.dtu.dk

c Risø DTU, Roskilde, Denmark, nsqr@risoe.dtu.dk

1 INTRODUCTION

It is well known that the simple blade element momentum (BEM) models that use 2D airfoil

characteristics fail to accurately predict the loads on blades in rotating flow. It has been documented a

number of times that the observed thrust experienced by a wind turbine blade is higher than that

predicted by the BEM models due to a change in the separation characteristics in the inner part of the

blades in rotation. As a result, there is a difference in the lift and drag characteristics of airfoils between

2D and 3D (rotating) flows – this effect appears to have been documented first in 1945 by

Himmelskamp (as highlighted by Chaviaropoulos and Hansen (2000)), and later on its importance to

wind engineering was realized over time (for example, see Madsen and Rasmussen (1988)). Even

though modern wind turbines are pitch regulated and generally do not operate in stall, stall is

unavoidable in the inner part of the blades when rated power is obtained. With the increased

commercial focus on wind turbine aeroelastic codes and the need for even more accurate load

predictions over the last few years, there has been increased interest in the modeling of this

phenomenon. One of the first attempts to study and model this phenomenon was carried out under

European Commission project “Dynamic stall and three-dimensional effects” (see Björck (1995), Snel

et al. (1993)). Many modifications to the theory followed. However, the amount of experimental data

available to validate the existing 3D stall models has been limited due to the complexity of such

experiments. Of others, Bak et al. (2006) and Breton et al. (2008) have given a review of some existing

models along with a comparison study using a subset of the NREL/NASA Ames experimental data.

The MEXICO experiment (Snel et al. (2007)) generated a significant amount of data from a prototype

wind turbine in several operating conditions, and such data is useful for research in this area.

Additionally, CFD computations of the MEXICO rotor from Bechmann et al. (2011) that are not based

on the 2D data are also useful in such an analysis. In the current work, the empirical 3D stall models

are reviewed and applied to data from the MEXICO experiment, and a comparison study between the

models along with the predictions by the CFD is presented.

2 EXISTING METHODS TO MODEL 3D STALL

As shown in figure (1), separation occurs first close to the root due to the airfoil in that region being

thick, and then progresses radially outward as the angle of attack is increased. Most of the existing

models are based on the correction between 2D and 3D lift coefficients for a given airfoil being a

function of the ratio (c/r), where c is the chord at the spanwise position r, such that,

���� , … � � � � � (1)

where, � and � represents the coefficient of lift or drag (depending on the model) in 3D rotating flow and 2D flow respectively.

Figure 1. Streamlines in the separated region on the suction side of an airfoil subjected to rotation (source: Corten (2000)).

2.1 Snel et al. (1993) and Björck (1995)

The first model relating the difference between the 2D and 3D airfoil lift coefficients was perhaps

given by Snel et al. (1993) and Björck (1995) as,

� � 3 ���� . (2)

This model can be used for calculating only the 3D lift coefficients of the airfoil based on the 2D

values, unlike some of the other models given below that also correct the 3D drag coefficients.

2.2 Du and Selig (1998)

Du and Selig (1998) present an extension to equation (2). This model is based on the assumption that

the change in the net force on the rotating airfoil is a result of a change in its lift as well as drag

characteristics. The correction to the lift and drag coefficients is given as,

��� � � � � �.������.� �� ��������∆�!"������∆� � 1$, (3)

��% � � � � �.������.� �� ������ ��&∆�!"���� ��&∆� � 1$, (4)

where, a, b and d are empirical constants (here, a=b=d=1 are used), R is the radius of the turbine, and

∆� � '()*+& ��'(�&$. �5�

2.3 Chaviaropoulos and Hansen (2000)

Chaviaropoulos and Hansen (2000) describe a “simplified quasi 3-D model” to analyze the influence of

rotational effects on blade section characteristics. In this model, f is a function of the ratio (c/r) and the

blade twist angle -,

���,�% � . ����/ 012 -, �6� where, a, h, and n again are empirical constants (here, a=2.2, h=1, n=4 are used).

2.4 Lindenburg (2004)

This model presents another modification equation (2). It is referred to as the “centrifugal pumping

model” taking the dynamics due to the centrifugal and Coriolis forces into account that act on the

separated region of air that rotates along with the blade:

��� � 3.1 � '(*�45� ���� . (7)

2.5 Bak et al. (2006)

The model by Bak et al. (2006) is different from the other models in that it uses the chord-wise pressure

distribution which has to be integrated to obtain the forces (or the polars). This model borrows ideas

from both the theory as well as experimental observations. Here, a correction for the net force on the

airfoil is computed and the lift and drag forces would be the components of that force. The correction is

applied to the pressure as, 678 � .9:;<�<.=<0> ? 1@.:A, (8)

where, the amplification is derived theoretically as the ratio between the forces BCD�4EF�GHIJK5" CD�L�GL5GMB BCDN�4MB , as

.9:;<�<.=<0> � )1 O �(�� P ���� P ���"Q�2&�R"S��, (9)

and the shape was determined based on the experimental observations from the NREL/NASA Ames

wind tunnel test, given by

1@.:A � TU �1 � V�� P W R�RHXYRHXZ�RHXY[ \,

max(shape) = �U � (10)

where, ] is the effective angle of attack, ]^_� is the 2D angle of attack at which the flow over the

airfoil is fully separated, and ]^_� is the angle of attack for which the flow over the airfoil is just about

to separate. From the 2D lift curve in figure (3), ]^_� � 25� and ]^_� � 5� have been used in the

current work. Based on the Cp, the 3D normal and tangential force coefficients can be calculated as,

672 � a 678b�V��c�_Q��d�d2e f%efc�_�f�%d2e f%ef ,

67Q � a 678b�g��h�_Q��d�d2e f%efh�_�f�%d2e f%ef , (11)

and thereby,

72,� � 72, � O 672 , 7Q,� � 7Q, � O 67Q . (12)

The lift and drag coefficients can be derived using Cn,3D, Ct,3D and the effective angle of attack ].

3 THE MEXICO EXPERIMENT

The MEXICO (Model Experiments in Controlled Conditions) experiment was a project that was par-tially funded by the European commission and was conducted in 2006 in the large scale facility of the DNW (German-Dutch) wind tunnel in the Netherlands (see Snel et al. (2007)). This experiment gener-ated, among other signals, surface pressure data on the blades of a wind turbine rotor of 4.5 m diameter that can be used to extract the forces on the blades. Each blade in this rotor consists of a series of airfoil sections and transition regions (see table (1)). The experiments consisted of several pitch angles, three tip speed ratios, and chord-wise surface pressure profiles at five span-wise locations. The combination of these parameters gives rise to various effective angles of attack at different positions on the blade. Availability of such airfoil pressure of data, along with the CFD computations from Bechmann et al. (2011), has generated scope for analysis and comparison of the 3D stall models. The original MEXICO database consisted of many different cases, like yaw, different pitch angles, dynamic tests, etc. In this work, the only cases that were considered were with steady inflow, zero yaw, fixed pitching angle (-2.3

0), rotor speed ω = 425 rpm, and wind speeds 5m/s<u<30m/s.

r/R 0.1-0.133 0.133-0.2 0.2-0.456 0.456-0.544 0.544-0.656 0.656-0.744 0.744-1.0

Profile

name

Cylinder Transition DU91-W2-250 Transition RISØ A1-21 Transition NACA64-418

Table 1. Geometric properties of the MEXICO blade.

4 CURRENT WORK

Although attempts to validate the above models were made in the respective papers, a collective

comparison of the models would be more useful in highlighting their relative advantages. One such

effort was carried out by Breton et al. (2008) where some of the mentioned 3D correction models were

compared with the NREL Phase VI experimental data. Below, a collective comparison of the loads

predicted by the above mentioned models compared to the experimental data from the MEXICO

experiment and those from the CFD computations is presented.

(a) (b) Figure 2. Estimates of the torque and the axial thrust (force normal to the rotor plane) on the rotor at different wind speeds,

by BEM theory with and without the different 3D stall models, CFD, and the MEXICO experimental data.

4.1 Importance of analysis on existing Stall-Delay models

Figure (2) shows the power estimated by a BEM model, with and without the aforementioned correc-tion models. The predicted power is similar at lower wind speeds, but at higher wind speeds the spread

in the predicted power output is almost 50%. Therefore, the importance of 3D stall is critical in predict-ing loads, especially in extreme conditions or over large time scales like health monitoring over the life of the turbine.

(a) (b)

(c) (d) Figure 3. The Cl and Cd values of the airfoils on the MEXICO rotor, as predicted by the different 3D stall models at two

spanwise positions, r/R = 0.25 and 0.35, are shown here. Also shown are the Cl and Cd values obtained using the inverse

BEM on the MEXICO as well as CFD data.

4.2 The classical BEM model

A simple BEM model was used to generate the estimated shown in figure (2). The code was imple-mented as outlined in Hansen (2000) with 50 annular elements between r/R = 0.1 and r/R =1.0. The 2D polars for the three airfoil geometries shown in table (1) were obtained from the MEXNEXT database, and the values in the transition regions were obtained through linear interpolation (shown in figure (3)). Prandtl’s tip loss factor and Glauert’s correction for high induction were used. The 3D stall models were coupled dynamically to the BEM code, so that models do not act as simple pre- or post-processors to BEM.

4.3 Determination of the effective angle of attack

One of the critical tasks of extracting polars from the MEXICO data is the calculation of the effective (induced) angle of attack. In this work, this has been done by implementing an inverse of the BEM al-gorithm, which is described below (for details on classical BEM, see Hansen (2000)):

(a) (b)

(c) (d)

(e) (f)

Figure 4. The normal (thrust) and the tangential (driving) force distributions along the blade span at different wind

speeds from a 2D BEM model with and without 3D stall modeling, CFD data, and data from the MEXICO experiment.

1. Initialize the induction factors a and a’ typically a=a’=0.

2. Compute the inflow angle f ==.>�� i �����*L��"�j��wk. (13)

3. Obtain sectional Cn and Ct values – in this case these are determined experimentally.

4. Calculate new values of a and a’ as,

.2fl � T�8no 1<> p�qr7s72 O 1\��, .t2fl � i�u�� vd2 w �rv w�*LxyxF � 1k��. (14)

5. Check for difference between a, a’ and anew, a’new – if the difference is more than a tolerance, go

to step 2. Else, continue.

6. Calculate f from eq. (10), and thereby the new 3D polars as, 7�,� � 72 01 p O 7Q 1<> p, 7%,� � 72 1<> p � 7Q 01 p. (15)

Hence, this method utilizes the experimentally obtained values of Cn (normal force coefficient) and Ct

(tangential force coefficient) to calculate the induction, and outputs the corresponding effective angle

of attack, whereby the 3D lift and drag characteristics are determined. This inverse BEM code has been

implemented for the sectional positions for which the MEXICO surface pressure data was available –

r/R = {0.25, 0.35, 0.60, 0.82, 0.92}. Here, Glauert’s correction for high induction was implemented,

but no tip loss factor was used.

5 RESULTS

The results from the simulations are shown in figures (2), (3) and (4). The range of the angle of attack (α) in figure (3) is divided into three regions for convenience: the linear region, α<5

0; the intermediate

region, 50<α<25

0; and the fully separated region, α<25

0. Of the models discussed, the one by Chaviaro-

poulos and Hansen (2000) appears to consistently over predict the lift as well as the overall power out-put, and the rest of the models seem to consistently under predict the lift in the linear region and the in-termediate regions. The model by Snel et al. (1993) and Björck (1995) appears to be closest to the 3D data. However, the behavior in the fully separated region between figures (3a.) and (3b.) is quite differ-ent relative to the experimental data. In case of r/R = 0.25 (figure (3a.)) almost all models over predict the lift in the fully separated region, and this behavior is clearly different in the r/R = 0.35 case (figure (3b.)). An ideal 3D stall model should be able to capture these effects, but the fact that none of the models consistently do highlights the complexity of the problem and the need for further research in this area. The graphs in figure (4) show the forces (normal and tangential) plotted against the span r/R. The force distribution along the blade changes due to presence of different airfoil profiles (see table (1)). It is in-teresting to note the behavior of the tangential (driving) force in case of u=24 m/s in figure (4f.). A sharp jump in the tangential force at r/R º 0.3 is seen to occur, and that is possibly because the effec-tive angle of attack at that position becomes around α=25

0, which is where the flow over the airfoil be-

comes fully separated. It is noted that such a change in forces implies a change in the bound circulation, which would result in vortex shedding and thereby some complex 3D effects in that region. This effect (which may be specific only to this experiment) may be a reason for the inconsistency in the behavior of the models in the fully separated region seen in figures (3(a.)) and (3(b.)).

As for the drag, the CFD data was the closest match to the experimental data. The rest of the models showed significant deviation from the experimental data, far more than the difference between the ex-perimental (3D) and the BEM prediction without stall models (2D). Similar results were also seen in Bak et al. (2006). This suggests that 3D correction for drag may be unnecessary for all practical pur-poses. Of all methods applied, the CFD results seem to be most accurate in predicting the loads over all – par-ticularly in the linear and the intermediate regions. Therefore, CFD could be used as an inexpensive way of validating engineering models, as opposed to carrying out large scale experiments. 6 CONCLUSION

A comparison between the loads predicted by the CFD computations, the 3D correction models, and

the MEXICO experimental data has been given. This was done for the lift, drag, normal and tangential

forces on the blades. The CFD computations have given better results, but of course it is computation-

ally much more expensive than the simple 3D stall models. On the other hand, it seems that the CFD

simulations can be used as a supplement for the validation/calibration of the 3D stall models, limiting

the number of required large scale experiments. Moreover, the complexity of the problem of construct-

ing a generalized 3D stall model that can be applied to any airfoil on any wind turbine, especially in the

fully separated region, is highlighted.

7 ACKNOWLEDGEMENTS

This work is a part of the project SYSWIND, under the Marie Curie framework (FP7) funded by the European commission. The coordinators of the MEXNEXT project are acknowledged for granting access to the data from the MEXICO experiment.

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