Aeroelastic Analysis of the LMH64-5 Blade Concept · PREFACE Within the DOWEC research and development project for large size offshore wind turbines, an investigation was done into

JUNE 2003 ECN-C--03-020

Aeroelastic Analysis of theLMH64-5 Blade Concept

C. Lindenburg

PREFACE

Within the DOWEC research and development project for large size offshore wind turbines, aninvestigation was done into the aeroelastic stability of the 6MW concept study. The modellingof the 6MW turbine concept with LMH64-5 blade concept was done earlier but contained onlybending stiffnesses which was one of the reasons to re-define the blade properties on basis ofinformation from the FAROB file.

The DOWEC research project was supported by the EET programme of the Dutch Ministry ofEconomic Affairs.

The author wants to thank Henk-Jan Kooijman for his comments on draft versions of this document.

Abstract

Within the DOWEC project, investigations were performed into the development of large sizewind turbines for offshore applications. Many of the studies in this project were performed for a6MW concept of which the turbine was designed by NEG-Micon Holland and the LMH64-5 bladeby LM Glasfiber Holland. One of the tasks within this project was to investigate the aeroelasticstability problems for large size wind turbines which was performed for this 6MW concept. Theseanalyses were done with the program BLADMODE.

This document starts with a description of the modelling of the blade in basis of a set of 51files with the cross sectional layout. For the first bending modes the direction of blade motion’theta’ was calculated for the rotating and non-rotating state, which can be used as input for hinge-spring-damper analysis tools. The operational conditions as function of wind speed for which theaeroelastic stability was investigated, were calculated with the program PHATAS.

The aerodynamic damping was calculated for the original LMH64-5 blade concept, and also forsome parameter variations on structural and aerodynamic modelling aspects and on the so-called’Structural Pitch’. Finally a comparison was made of the aeroelastic damping calculated with theoriginal LMH64-5 geometry and a tapered variant.

It was concluded that for pitch-to-vane controlled wind turbines the flapwise blade vibrations havea positive aerodynamic damping. In general the aerodynamic damping for the edgewise modes ispositive for most of the operational conditions. For the 6MW concept the aerodynamic dampingof the edgewise blade motions can be improved with a small increase of the partial-load pitchangle, and with ’Structural Pitch’ modifications of the blade structure. It was also concludedthat increasing the torsional stiffness of the rotor shaft with a factor 1.7 avoids 6P resonanceproblems for the collective edgewise mode and reduces the negative contribution of the generatorcharacteristics to the damping of this mode.

Keywords

Aeroelastic stabilityBlade vibrationsOffshore windRotor bladesStructural pitchWind turbine

2 ECN-C--03-020

CONTENTS

TERMINOLOGY 4

1. INTRODUCTION 5

2. LMH64-5 BLADE PROPERTIES 72.1 Files with Sectional Description �� 72.2 Retrieving Sectional Properties �� 82.3 Aerodynamic Modelling �� 82.4 Modelling in PHATAS �� 92.5 Specific Items for BLADMODE �� 9

3. OVERALL MODEL PROPERTIES 113.1 Total Mass Properties �� 113.2 Frequencies �� 113.3 Blade-Effective Direction of Motion �� 123.4 Equivalent Model for Collective Edgewise Modes �� 123.5 Parametrisation of Blade Properties �� 12

4. OPERATIONAL ANALYSES 134.1 Quasi-Stationary Operational Conditions �� 134.2 Campbell Diagram �� 154.3 Stationary Flapping Moments �� 184.4 Linearised Stability Envelope �� 19

5. PARAMETER VARIATIONS 235.1 Stationary Deformed State and Torsion �� 235.2 Aerodynamic Pitch Angle �� 245.3 Non-linear and Instationary Aerodynamic Effects �� 265.4 Structural Pitch �� 275.5 Drive Train Interaction �� 30

6. INVESTIGATIONS FOR THE THE TAPERED VARIANT 316.1 Increased Shaft Torsional Stiffness �� 316.2 Description of the Tapered Variant �� 31

7. CONCLUSIONS 37

REFERENCES 39

APPENDIX A. DESCRIPTION OF THE PROGRAM BLADMODE 41

APPENDIX B. DESCRIPTION OF THE PROGRAM PHATAS 42

APPENDIX C. BLADMODE INPUT FILE 43

APPENDIX D. NACA64-618 AERODYNAMIC COEFFICIENTS 49

ECN-C--03-020 3

TERMINOLOGY

Expression Descriptiona.o.a. Aerodynamic angle of attack, defined as �� "!$# .Inflow angle Angle between the relative flow on the airfoil and the rotor plane.�%�&� Direction of the local blade chord for a zero blade setting angle.�� "!'# Blade setting angle, or ’pitch angle’.

*.buc files File-format that contains the geometry of a cross section, materialdefinition, and the layup, which was introduced for buckling analyses.

UD laminate Laminate with all fibres in the same direction, ’Uni Directional’.

Pre-bend Flatwise geometrical curvature of a blade without loading.LM Glasfiber uses a down-wind pre-bend which partly eliminatesthe elastic deformation under normal operating loading.In the programs BLADMODE and PHATAS the pre-bend is definedas the down-wind displacement of the blade tip.

Collective mode Mode of vibration of rotor blades of which the reaction loadson the rotor shaft add-up to each other, used for edgewise modes.For these edgewise modes the blade-tips vibrate simultaneouslyand in opposite direction as the drive-train.

Reaction-less mode Simultaneous mode of vibration of rotor blades that giveno reaction-loads on the rotor shaft, used for edgewise modes.The ’reaction-less’ edge modes do have an interaction with thetower sideways bending mode, if this tower bending frequency iseither 1P larger or 1P smaller than the reaction-less edge frequency.

Symmetric mode Simultaneous mode of vibration of rotor blades that havethe same phase, used for flapwise modes.

Asymmetric mode The opposite of ’Symmetric mode’.

Apparent mass Mass that is added to the blade mass to account forthe inertia loads of the air for blade vibration.For flatwise vibrations this mass is larger than for edgewise vibrations.

Aerodynamic stiffness Aerodynamic load variations on a rotating blade that are inthe opposite (’restoring’) direction of the amplitude of vibration.The flapping motion of blades with bending-torsion coupling is a clearexample of ’aerodynamic stiffness’, since a downwind flapping amplitudegoes together with a decreased angle-of-attack so a reduction inaerodynamic flapping forces.

Structural Pitch Modification of the blade structure that changes (’pitches’) the principalstiffness direction and thus also the directions of blade vibration.

4 ECN-C--03-020

1. INTRODUCTION

Within the Dutch research and development project DOWEC, investigations were done on futurelarge size wind turbines for offshore applications. The DOWEC project is partly addressed to thedevelopment of commercial types of wind turbines. For this last part of the DOWEC investigations,studies were performed on basis of a 3-bladed 6MW concept turbine that was designed by NEG-Micon Holland. The conceptual design of the rotor blades for the 6MW turbine was provided byLM Glasfiber Holland. These concept blades were named LMH64-5 and have a length of 62.7m.With a 1.8m hub-radius, a -2.5deg cone-angle, and a -2.05m pre-bend at the tip these blades givea 128.8m rotor diameter. Under loading, the blades are more-or-less straight so that the diametermay be slightly larger.

One of the tasks within the DOWEC project was to investigate the aeroelastic stability of the 6MWturbine. This task was performed by LM Glasfiber Holland, unit Wind Energy of ECN Petten,and the "Flight Mechanics and Propulsion" group of the faculty of Aerospace Engineering of theUniversity of Delft. The underlying report deals with the aeroelastic analyses done by ECN.

Chapter 2 of this document contains a description of the structural dynamic properties of theLMH64-5 blade concept.

To allow verification of the modelling of the LMH64-5 blade concept in the programs BLAD-MODE [9] and PHATAS [11, 12], the overall blade properties are summarised and compared inchapter 3.

The stability envelopes calculated with the different analysis tools for the normal operating statesof the 6MW NEG-Micon turbine, are reported in chapter 4. This chapter also includes someparameters of the stationary equilibrium state, which can be used for verification of other tools.

In chapter 5 the results of some sensitivity analyses are reported including some structural andaerodynamic aspects of the aeroelastic analysis, and the influence of ’Structural Pitch’.

A comparison was made with the aerodynamic damping of a tapered variant of the LMH64-5blade concept. For this comparison the shaft torsional stiffness was increased 1.7 times suchthat it avoids 6P resonance of the collective edgewise mode. These investigations are reported inchapter 6.

Finally, some conclusions are written in chapter 7.

Short descriptions of the programs BLADMODE and PHATAS are given in appendix A and Brespectively.

A listing of the input file for the program BLADMODE is given in appendix C and the aerodynamiccoefficients for the tip airfoil NACA64-618 are listed in appendix D.

ECN-C--03-020 5

6 ECN-C--03-020

2. LMH64-5 BLADE PROPERTIES

2.1 Files with Sectional Description

For load-set calculations of the 6MW DOWEC turbine a description of the LMH64-5 blade conceptwas made earlier on basis of an EXCEL file received from LM Glasfiber Holland in November2001 [5]. The chord distribution over the midspan of the blade (between

�=20m and

�=55m)

nearly follows the linear relation: ��

�

� � � . Figure 1 and 2 show the bladecontour and blade twist distribution as modelled in the input for BLADMODE and PHATAS.

0 5 10 15 20 25 30 35 40 45 50 55 60 65Location from rotor centre [m]

−3

−2

−1

0

1

2

3

4

Cho

rdw

. coo

rdin

ate

[m]

Figure 1 Contour of the LMH64-5 blade concept


0

2

4

6

8

10

12

14

Tw

ist [

deg]

Figure 2 Twist distribution of the LMH64-5 blade concept

The description in the EXCEL file did not include the blade torsional stiffness, the transverseshear flexibility, nor the radii of gyration. Especially because the pre-bend of the LMH64-5blade concept causes interaction between edgewise bending and torsion, a correct modelling is ofimportance for aeroelastic stability analyses. To obtain the blade torsional stiffness, and torsion-related cross-sectional properties it was decided to use a set of so-called ’*.buc files’ as basis foraeroelastic investigations.

In June 2002 LM Glasfiber Holland sent the *.buc files to ECN for 51 spanwise locations.These files are confidential but the resulting sectional properties could be distributed among theparticipants. Some other *.buc files concern the hub (a radius smaller than 1.8m) and described avery stiff steel part. This part was not modelled in PHATAS and BLADMODE which means thatit has been treated as rigid. In the selection of the locations for which *.buc files were provided

ECN-C--03-020 7

special attention was paid to a detailed description of the locations where shear webs or otherstructural parts end. The following modifications were issued on the *.buc files:� The trailing edge was "closed" for a realistic torsional stiffness. This was done with the material

"GLUE" between 99% and 1% of the contour. The thickness of this "GLUE" was 4mm overthe root and middle section of the blade, and 3mm to 2mm towards the tip.

� It appeared that most shear webs were modelled with two panels: one for each of the 2 facings.These pairs of panels were re-defined as single webs, for which the material was assumedsymmetric with respect to the web centreline.

2.2 Retrieving Sectional Properties

With the tool CROSTAB [7] the sectional properties were calculated. Since the programCROSTAB does not solve the transverse shear deformation, the transverse shear flexibilitieswere calculated with the program MATEC [1]. The input files for MATEC were generated withthe program CROSTAB. Finally, the cross sectional properties were selected from the output filesof CROSTAB and MATEC and converted to [kg], [m], and [N].

The program MATEC also calculates the locations of the shear centre, which was not used for theaeroelastic stability analyses reported here, because the values of these data were not fully trusted.Instead it was chosen to use zero values for the shear centre location, although one could alsochose the shear centre on the blade mass centreline or on the elastic axis.

Unfortunately the program MATEC did not run correctly for some of the cross sections, so thatfor these locations the transverse shear flexibilities of neighbouring cross-sections were used.

2.3 Aerodynamic Modelling

The aerodynamic chord and twist of the LMH64-5 blade concept were still in accordance withthe contents of the EXCEL file of November 2001 [5]. Because the tip airfoil has a relative largecontribution to the aeroelastic stability, a comparison was made with the NACA64-618 airfoilcoefficients generated with ATG [2] for a Reynolds number

�� . The differences appeared tobe small. So finally the airfoil coefficients for the original design were used, which were for aReynolds number of � �� . Here it was realised that for aeroelastic stability it is important tohave realistic aerodynamic coefficients, also for drag (’drag-stall’), see section 5.2.

8 ECN-C--03-020

2.4 Modelling in PHATAS

In the beginning of 2002 a PHATAS input model for the 6MW turbine concept was composed,of which a description was published by Kooijman [6]. With this file as basis for the turbinedescription, the blade structural properties were replaced by the data from CROSTAB. The tablesin the input file of PHATAS are limited (by making a selection) to a maximum length of 25records. Tables with data selected for different locations were used for the mass distribution, thebending stiffnesses, and the torsional stiffnesses, so that a minimum discrepancy with the completedistributions arose. Special attention was paid to the distribution of the mass in the tip region andto the stiffness in the root region. The aerodynamic chord and twist were taken from the EXCELfile of November 2001 [5].

For the former load set calculations of the 6MW turbine with PHATAS by STENTEC, an input filehas been made in which each blade was modelled with 14 elements. In the STABTOOL-3 project[3] it was found that for aeroelastic stability research one would preferably use at least 15 elements.For a model of the LMH64-5 blade concept with 17 elements the so-called "airfoil matching" was96%, while the frequencies (from the eigenvalue module) were close to those calculated for 24blade elements. So finally 17 blade elements were used. The first 2 elements (near the blade root)had a drag coefficient only, as for a cylinder.

Other modifications with respect to the "load-set" input file are:� Blade torsional deformation (0.48% damping);� Rotor shaft torsion, with a torsional stiffness of 3.29E+8Nm/rad (NEG-Micon specifications);� A pre-bend of -2.05m, (this was -2.072m for other DOWEC work, see [6]).

2.5 Specific Items for BLADMODE

In BLADMODE the complete distributions of mass, bending stiffness, and torsional stiffness wereused, while the geometrical properties were taken from the EXCEL file of November 2001 [5].

For calculations with BLADMODE release "APR-2002" [9] the pre-bend of the LMH64-5 bladeconcept was modelled from

�=17.9m to

�=35.7m, while the pre-bend at the tip was -2.05m.

In the BLADMODE input the turbine properties were taken from the description by NEG-MiconHolland. The tower fore-aft bending was modelled with a fore-aft translation of the nacelle witha stiffness of 742.39kN/m and a lumped mass (at the top) for tower motion of 267 468kg. Thislast value includes the nacelle mass but not the 30 000kg hub mass. With the more accurate towermodel in PHATAS, the first fore-aft frequency was calculated as 0.2258Hz. In order to matchthis fore-aft tower bending frequency, the lumped tower-top mass in the BLADMODE input wasincreased to 283 000kg.

The drive train was modelled with an inertia of 5025 500kg*m�

with respect to the slow speedshaft. At the rotor-side of the shaft a hub inertia of 50 700kg*m

�

was added.

ECN-C--03-020 9

10 ECN-C--03-020

3. OVERALL MODEL PROPERTIES

This chapter reports on some overall blade properties and comparisons between the calculationswith BLADMODE and PHATAS. Also some parameter representations are given that can be usedfor specific applications such as controller design or the dedicated model of the TU-Delft, [4].

3.1 Total Mass Properties

For a straight geometry (without pre-bend), the following overall mass properties were calculated:

BLADMODE PHATASRotor radius [m] 64.439 64.439Aerodynamic area [m

�

] 182.740Aspect ratio 16.165 16.387Total mass [kg] 17334.160 17357.936Apparent mass [kg] 737.0217Static moment X [kgm] 741.3336Static moment Y [kgm] 2602.7812Static moment Z [kgm] 355051.312 355304.000Idem w.r.t. centre [kgm] 386252.812 386548.285Inertia [kgm

�

] 11493796.000 1.2835E+07 (PHATAS: w.r.t. rotor centre)Rotor inertia [kgm

�

] 38461908.000 3.8484E+07Pitch inertia [kgm

�

] 28268.20703 19156.0

The total mass properties are close to each other, except for the smaller value of the pitch inertiain the PHATAS model. This difference is explained by the fact that in the PHATAS model theout-of-chord locations of the mass distribution are not included.

3.2 Frequencies

With BLADMODE [9] and with PHATAS [11] the eigen-frequencies were calculated for a rota-tional speed of 11.844rpm, without apparent mass, and without pre-bend or elastic deformation.The frequencies from PHATAS are the eigenvalue solutions and do not include the couplingbetween e.g. edgewise bending and torsion. Except for the tower bending frequency and thecollective edgewise frequency, the eigenmodes from BLADMODE listed below were calculatedwithout interactions from the drive train or the tower, the so-called ’reaction-less’ modes.

BLADMODE PHATASTower 0.2257Hz 0.22582HzFlat-1 0.6801Hz 0.6928HzFlat-2 1.8632Hz 1.837HzEdge-1 1.0657Hz 1.0704HzEdge-2 3.7414Hz 3.887HzColl. edge 1 1.2480Hz 0.451Hz (PHATAS: excluding the influence of the generator)Coll. edge 2 2.6014Hz 2.714Hz (PHATAS: excluding the influence of the generator)Torsion 7.1500Hz 7.156Hz

Most frequencies from PHATAS match well with those from BLADMODE except for the collectiveedgewise frequencies. This is caused by the fact that the PHATAS solution for the edgewise modesdoesn’t include the drive train dynamics in much detail. The blade torsional frequency shows areasonable agreement.

ECN-C--03-020 11

3.3 Blade-Effective Direction of Motion

For each of the eigenmodes the program BLADMODE calculates a blade-effective direction ofmotion for the aerodynamic loading. This is done by integration of the flapwise and the lagwisecomponents of the eigenmodes multiplied by: � the chord, � the radius, and � the amplitude of theeigenmode. The vectorial representation for the flatwise and edgewise components is expressed inthe so-called angle � , ’theta’. This angle � can be used in models with fixed directions of edgewiseand flatwise motion, such as the dedicated model for "flap-lag-stall" instability [4] developed atthe "Flight Mechanics and Propulsion" group of the faculty of Aerospace Engineering of the TU-Delft. The angle � is measured similar as the geometric pitch and/or twist angle of the blade. Theangles � of the LMH64-5 blade modes in the following table were calculated with BLADMODE,omitting the apparent mass, aerodynamic stiffness, and pre-bend. For the collective edgewisemodes the shaft torsional flexibility and the variable speed characteristics were included while thetower was assumed rigid.

Frequency�Hz � Direction � � deg �

Mode: Speed � 0rpm 11.844rpm 0rpm 11.844rpmAsymmetric flat 1 0.6476 0.6985 98.30 99.02Symmetric flat 1 0.6513 0.7028 92.81 92.85Reaction-less edge 1 1.0570 1.0996 9.95 10.96Collective edge 1 1.2459 1.2480 8.83 9.12Collective edge-2 2.5820 2.6046 5.00 5.16

Barring the 90deg difference between flatwise and edgewise direction the angles � of these modesare similar. An exception is the direction of the symmetric flat motion which is more in thedownwind direction because of the interaction with tower bending.

For a hinge-spring model in which the terms for centrifugal loads are present, the reaction-lessmodes for the non-rotating state should be used giving an angle � of 9deg to 9.5deg. This angle� can be modified by shifting the UD-layers (Uni Directional) within the cross section, called’Structural Pitch’. The influence of this Structural Pitch is reported in section 5.4.

3.4 Equivalent Model for Collective Edgewise Modes

For some applications, such as the design of controller algorithms, the collective edgewise modeshave to be described with a 1-d.o.f. model of which the deformation is generalised in a shafttorsional stiffness. This model has 3 parameters: Rotor inertia, Drive train inertia, and Torsionalstiffness of the shaft located in between. Using conservation of1. total rotational inertia (43509.5E+3kg*m

�

),2. collective edgewise frequency (1.254Hz),3. and ratio between kinetic energy and generator speed variations

finally gives an effective drive-train inertia of 389.03kg*m�

, a 43509.1E+3kg*m�

rotor inertia,and a 24 141Nm/rad shaft torsional stiffness. It seems strange that the effective drive-train inertiais much smaller than the 5025 474kgm

�

generator inertia aft of the ’flexible’ shaft.

3.5 Parametrisation of Blade Properties

For some other applications, the blade mass properties can be described with a few parameters.Using conservation of the blade mass static moment w.r.t. the root, and of the rotor rotationalinertia, a linearised mass distribution �� as function of the span � is found with

��

12 ECN-C--03-020

4. OPERATIONAL ANALYSES

4.1 Quasi-Stationary Operational Conditions

The DOWEC 6MW concept has a variable speed generator. The characteristics of this generatorare determined by power electronics that give a constant generator power above the nominal speedof 11.844rpm, up to a maximum speed of 14rpm. This implies that the torque-speed relation has anegative slope above nominal speed, see figure 3. For variable speed turbines the rotor speed above

7 8 9 10 11 12 13 14Rotor speed [rpm]

0

1000

2000

3000

4000

5000

6000

Sha

ft to

rque

[kN

m]

Figure 3 Generator torque-speed relation

nominal speed is kept between the nominal speed and 13.5rpm by a controller algorithm. Since notall stability analysis tools do have an option to model the controller algorithm, the envelope of theoperational parameters was obtained from the power curve calculated with the program PHATAS.This power curve was calculated for an air density of 1.225kg/m

�

, for a constant wind speed, avertical shear exponent of 0.082, a pitch error (related to blade 1) of +0.18deg and -0.18deg forblade 2 and 3 respectively, and solving the blade bending and torsional deformation.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Wind speed [m/s]

0123456789

1011121314

Rotor speed [rpm]Pitch angle [deg]Aerodynamic thrust [100kN]Idem, from BLADMODE

Figure 4 Stationary operational conditions calculated for the 6MW turbine concept

ECN-C--03-020 13

Wind Tip- Rotor Cp aero C axial Generator Axial Pitchspeed speed speed power force angle�m/s � ratio

�rpm � �

- � �- � �

kW � �kN � �

deg �3.0 16.940 7.531 0.1428 0.7365 -3.23 52.96 1.5003.5 14.539 7.541 0.2922 0.7569 66.70 74.08 1.4994.0 12.744 7.554 0.3730 0.7654 157.5 97.85 1.4384.5 11.351 7.570 0.4139 0.7680 267.8 124.27 1.2485.0 10.243 7.589 0.4419 0.7714 406.5 154.09 0.9865.5 9.340 7.613 0.4593 0.7673 574.5 185.47 0.7326.0 8.592 7.639 0.4652 0.7571 765.6 217.77 0.4516.5 7.962 7.670 0.4674 0.7461 986.2 251.88 0.1376.75 7.772 7.774 0.4683 0.7444 1111.5 270.99 0.0007.0 7.760 8.050 0.4678 0.7438 1240.1 291.20 0.0007.5 7.733 8.595 0.4669 0.7427 1528.2 333.79 0.0008.0 7.731 9.165 0.4661 0.7430 1857.1 379.93 0.0008.5 7.706 9.707 0.4657 0.7425 2229.2 428.62 0.0009.0 7.698 10.267 0.4647 0.7425 2646.3 480.54 0.0009.5 7.681 10.813 0.4635 0.7419 3112.0 534.96 0.000

10.0 7.674 11.372 0.4624 0.7420 3627.9 592.84 0.00010.25 7.563 11.488 0.4609 0.7355 3901.4 617.41 0.00010.5 7.413 11.534 0.4572 0.7172 4161.5 631.77 0.16911.0 7.131 11.625 0.4478 0.6765 4688.2 654.08 0.64211.5 6.874 11.714 0.4360 0.6386 5220.4 674.77 1.11712.0 6.636 11.801 0.4221 0.5994 5740.6 689.67 1.68512.5 6.591 12.210 0.3948 0.5378 6040.1 671.42 2.93413.0 6.271 12.082 0.3439 0.4449 5949.6 600.71 4.67313.5 6.023 12.050 0.3097 0.3902 5974.8 568.24 5.80514.0 5.805 12.044 0.2798 0.3461 5995.1 542.05 6.80314.5 5.587 12.006 0.2505 0.3053 5977.7 512.93 7.82415.0 5.399 12.001 0.2276 0.2747 5983.3 493.88 8.68616.0 5.073 12.029 0.1886 0.2246 5991.6 459.42 10.29617.0 4.793 12.076 0.1576 0.1866 5981.4 430.81 11.75818.0 4.532 12.089 0.1333 0.1576 5970.6 408.08 13.11019.0 4.294 12.090 0.1140 0.1351 5977.0 389.55 14.38420.0 4.077 12.085 0.0980 0.1168 5977.9 373.20 15.61521.0 3.884 12.086 0.0851 0.1021 5978.5 359.72 16.785

The rotor speed, aerodynamic thrust, and pitch angle are plotted in figure 4 as function of windspeed. The thin dashed line in figure 4 (coincides nearly with the thicker dashed line) is theaerodynamic thrust calculated with BLADMODE, for the rotor speed and pitch angle as listedabove. The linear relation of the rotor speed for a wind speed between 7m/s and 10m/s shows theconstant (optimal) lambda strategy. Figure 4 also shows the pitch actions in partial load for a windspeed exceeding 10m/s. The positive pitch angles in this wind regime reduce the maximum axialloads on the rotor, called ’thrust clipping’. The irregular rotor speed near 13m/s is caused by thedestabilizing rotor-speed derivative of the aerodynamic- and the generator torque.

14 ECN-C--03-020

4.2 Campbell Diagram

With the program BLADMODE the frequencies of the LMH64-5 blade concept were calculatedfor various rotor speed values including the apparent mass but excluding the aerodynamic stiffness.Here the pre-bend is omitted and the deformed state is not taken into account. Except for thereaction-less edgewise mode all other frequencies are for the collective modes which means thatthe tower flexibility and drive train dynamics are included.

Rotor speed Tower fore-aft Symmetric flat Reaction-less edge Collective edge0.0rpm 0.2256Hz 0.6500Hz 1.0567Hz 1.2459Hz6.0rpm 0.2256Hz 0.6637Hz 1.0590Hz 1.2464Hz7.0rpm 0.2256Hz 0.6686Hz 1.0598Hz 1.2466Hz8.0rpm 0.2256Hz 0.6741Hz 1.0608Hz 1.2469Hz9.0rpm 0.2256Hz 0.6804Hz 1.0619Hz 1.2471Hz

10.0rpm 0.2256Hz 0.6872Hz 1.0631Hz 1.2474Hz11.0rpm 0.2257Hz 0.6947Hz 1.0644Hz 1.2477Hz12.0rpm 0.2257Hz 0.7028Hz 1.0659Hz 1.2481Hz13.0rpm 0.2257Hz 0.7115Hz 1.0675Hz 1.2484Hz14.0rpm 0.2257Hz 0.7207Hz 1.0692Hz 1.2488Hz15.0rpm 0.2257Hz 0.7305Hz 1.0710Hz 1.2493Hz

From this table the following resonance rotor speed values were found, see also figure 5.

Speed Resonance9.1rpm 7P Reaction-less edge

10.3rpm 4P Symmetric flat10.6rpm 6P Reaction-less edge10.7rpm 7P Collective edge12.5rpm 6P Collective edge May give strong vibrations!12.8rpm 5P Reaction-less edge13.5rpm 1P Side-ways tower May give strong vibrations!

7 8 9 10 11 12 13 14Rotational speed [rpm]

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Fre

quen

cy [H

z]

1P, 4P, 5P, 6P, 7PCollective edge 1React−less edge 1Symmetric flat 1Tower fore−aftRotor speed limits

Figure 5 Campbell diagram of the 6MW concept with LMH64-5 blade concept

To analyse the resonance conditions of the operational envelope of the 6MW concept, the frequen-

ECN-C--03-020 15

cies were calculated for the wind-speed, rotor-speed, and pitch-angle combinations reported insection 4.1. This gives a better approach of the resonance speed values, e.g. because the interactionwith the tower fore-aft motion depends strongly on the blade pitch angle. In figure 6 the resultingfrequencies are plotted versus the wind speed.

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Wind velocity [m/s]

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Fre

quen

cy [H

z]

1P, 4P, 5P, 6PCollective edge 1Reaction−less edge 1Symmetric flat 1Tower fore−aft

Figure 6 Frequencies of the 6MW concept as function of wind speed

Because the frequencies plotted in figure 6 are calculated including the aerodynamic stiffness,they are slightly higher than those in the Campbell diagram of figure 5, especially for the flatwisemode. This aerodynamic stiffening of the flatwise frequency is mainly caused by the resultingblade torsional deformations. Figure 6 also contains the (thin) lines for the 1P, 4P, 5P, and 6Presonance frequencies. Because of the variable-speed generator characteristics in full-load, therotor-speed range of 11.844rpm to 13.5rpm results in a wide band for the resonance frequencies.

For the PHATAS tower model (which is more detailed) the calculated side-ways bending frequencyequals 0.2274Hz which is in 1P resonance at 13.6rpm. The tower may have serious side-waysbending resonance problems because the aerodynamic damping in this direction is small. Theside-ways tower frequency would be safe if the rotor remains out of the 0.8P - 1.2P resonancespeed range, which is between 11.4rpm and 17.1rpm.

With the combination of shaft flexibility and the variable speed generator characteristics, thecollective edgewise mode appears to be not much higher than the reaction-less edgewise mode.Because collective edgewise modes have positive damping from the generator below nominalspeed, the 7P resonance at 10.8rpm is not alarming. Above nominal rotor speed the generator hasnegative damping which means that the 6P resonance speed of 12.5rpm for the collective edgewisemode requires attention.

For a pitch-to-vane controlled turbine the blade flapping motion has a large aerodynamic dampingso the 3P (and 4P) resonances will not give problems.

16 ECN-C--03-020

Conclusions on the eigenfrequencies

From the frequencies in the Campbell diagram, the following recommendations are drawn:Tower side bending frequency The tower bending frequency has to be increased with at least

10%. Because of the variable-speed rotor characteristics and the high aerodynamic thrust ona 6MW turbine, a reduction of the tower bending frequency below the smallest rotor speed isnot feasible. A 10% increase in frequency implies a 20% increase in stiffness. Anticipating ona small increase in turbine weight and on possible scour, one may have to increase the towerbending stiffness with 25%. In practise tower resonances may be damped by a vessel of waterin the tower top.

Collective edgewise frequency The collective edgewise frequency (now slightly above nominalspeed) should be away from the variable-speed range, because in this range the generator torque-characteristics have a negative contribution to the damping of (rotor-)blade vibrations. Shiftingthe collective edgewise frequency below the nominal speed range requires a large reduction ofthe edgewise bending stiffness, which is not realistic for large size rotor blades. Increasing theedgewise bending stiffness implies also an increase of the reaction-less edgewise frequency,which is not desirable either. On basis of a calculation with the program BLADMODE, itfollows that increasing the shaft torsional stiffness with a factor 1.7 increases the 6P resonancespeed for the collective edgewise mode to 15.2rpm, which is an effective modification. For thisshaft torsional stiffness, the collective edgewise frequency in full-load (12.1rpm) matches with7.5P. In section 5.5 it is shown that increasing the rotor shaft torsional stiffness also reduces thenegative contribution from the generator characteristics to the damping.

Second tower bending wind reaction-less edge The name ’Reaction-less’ edge mode refers tothe fact that this mode has no direct interaction with the drive train dynamics. However, thereaction-less edgewise modes have a reaction-force on the rotor hub ’rotating’ with the edgewisefrequency. On the tower-top this reaction has a side-ways excitation with a frequency that is1P higher or 1P lower than the edgewise frequency. For the reaction-less edge frequencyranging from 1.06Hz to 1.07Hz an interaction may occur with the second sideways towerbending frequency, which is 1.3523 (for variable-speed). After subtracting the 1P differencefor 13.5rpm gives a frequency ratio of 1.127Hz/1.065Hz = 1.05. This means that at least forthe prototype the second tower bending frequency has to be measured. Here resonances maybe damped by a vessel of water in the tower top.

ECN-C--03-020 17

4.3 Stationary Flapping Moments

The model of the TU-Delft [4] calculates the dynamic response for a hinged rotor blade using thehinge stiffnesses and orientation of the hinge as input. For this orientation the angle ’theta’ is used.The stationary state for this model is described with a hinge flap-angle

��which follows from the

hinge stiffness and the blade root flap bending moment. For calculation/comparison of the angle� �the flapping moments were calculated with BLADMODE. This calculation was without the

stationary deformed state, without pre-bend, but with the -2.5deg cone angle.

Wind Rotor Blade Flap Directionspeed speed pitch moment ��m/s � �

rpm � �deg � �

kNm � �deg �

3.0 7.531 1.500 1556 11.773.5 7.541 1.499 1846 11.774.0 7.554 1.438 2168 11.714.5 7.570 1.248 2535 11.525.0 7.589 0.986 2937 11.255.5 7.613 0.732 3356 10.996.0 7.639 0.451 3796 10.716.5 7.670 0.137 4256 10.397.0 8.050 0.000 4837 10.287.5 8.595 0.000 5493 10.338.0 9.165 0.000 6206 10.388.5 9.707 0.000 6949 10.449.0 10.267 0.000 7748 10.509.5 10.813 0.000 8583 10.56

10.0 11.372 0.000 9471 10.6310.5 11.534 0.169 10010 10.8311.0 11.625 0.642 10280 11.3411.5 11.714 1.117 10520 11.8512.0 11.801 1.685 10670 12.4712.5 12.210 2.934 10450 13.8613.0 12.082 4.673 9381 15.6813.5 12.050 5.805 8867 16.8714.0 12.044 6.803 8461 17.9215.0 12.001 8.686 7705 19.8916.0 12.029 10.296 7160 21.5917.0 12.076 11.758 6708 23.1418.0 12.089 13.110 6339 24.5619.0 12.090 14.384 6027 25.8920.0 12.085 15.615 5742 27.1721.0 12.086 16.785 5494 28.38

The first three columns were input for the program BLADMODE. The fourth column contains thecalculated blade root flap bending moment.

For a flapping frequency of 0.6985Hz at 11.844rpm (without apparent mass and aerodynamicstiffness) and with a flapping inertia of 11.4938

� � � � kg*m�

w.r.t. the blade root (at � = 1.8m) thestiffness is 221.39MNm/rad. The blade inertia w.r.t. the rotor centre is 12.7

� � � � kg*m�

.For a rotor speed of 11.844rpm the centrifugal stiffness of a flapping motion w.r.t. the blade rootis 19MNm/rad, so that the elastic stiffness in the hinge is 202MNm/rad.

The rightmost column in this table contains the direction of motion � of the reaction-less edge-wise mode, calculated with BLADMODE for a straight rotor and without apparent mass noraerodynamic stiffness. This direction � includes the blade pitch setting angle.

18 ECN-C--03-020

4.4 Linearised Stability Envelope

With BLADMODE the eigenmodes and their linearised damping were calculated for the opera-tional conditions listed in section 4.1. In these calculations the pre-bend was modelled while thestationary deformed state was calculated (it was thought unrealistic to describe the pre-bend only,see section 5.1). The aerodynamic damping of these modes was calculated with the linearisedaerodynamic loads following the first-order part of the heuristic dynamic stall model of Snel,[13]. These calculations were done for the collective and for the reaction-less (symmetric) bladebending modes. The calculated aerodynamic damping of the flatwise and the edgewise modes areplotted as function of wind speed in figure 7 and 8 respectively.

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Wind speed [m/s]

0

10

20

30

40

50

60

70

dam

ping

[%]

Figure 7 Damping of the collective flatwise mode calculated with BLADMODE

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Wind speed [m/s]

−4

0

4

8

12

16

20

24

28

32

36

40

44

48

dam

ping

[%]

Response mode on 1P gravity loadingReaction−less edge modeCollective edge mode, without generator char.Collective edge mode 1Collective edge mode 2

Figure 8 Edgewise aerodynamic (and generator) damping calculated with BLADMODE

ECN-C--03-020 19

Discussion on the Stability Envelope

From figure 7 it follows that the symmetric flatwise mode has an inherent positive aerodynamicdamping which appears proportional to the rotational speed. For this reason no effort is spent onfurther analysis of the flatwise modes. The asymmetric flatwise modes interact with the towertorsional dynamics and the yaw mechanism. Since the program BLADMODE does not describe’non-collective’ interactions of the blade dynamics with those of the tower, the damping of theasymmetric modes are not investigated here.

For the collective edgewise modes, figure 8, this damping was calculated with and without theinfluence of the generator torque-speed derivatives. It follows that the generator has a largecontribution to the damping of the edgewise vibrations, which is negative in full load. This stronginfluence from the generator is partly caused by the relatively flexible rotor shaft, which givesstrong generator-speed variations for the collective edgewise modes.

Figure 8 also contains the aerodynamic damping of the response on the 1P gravity loading. Sincethe 1P frequency is not an eigenfrequency, a negative aerodynamic damping for the 1P gravityloading will result in an amplification of the 1P response although it does not always lead toinstability.

Figure 9 through 11 show the edgewise modes calculated for the operational conditions at 10m/s.Knowing that for these plots the wind comes from the left the graphs show that the blades have adownwind stationary deformation. The reaction-less and collective edgewise modes show a strongsimilarity, which was also expected from the fact that the frequencies are close together.

Figure 9 Reaction-less edgewise mode at 10m/s wind

20 ECN-C--03-020

Figure 10 Collective edgewise mode 1 at 10m/s wind

Figure 11 Collective edgewise mode 2 at 10m/s wind

ECN-C--03-020 21

22 ECN-C--03-020

5. PARAMETER VARIATIONS

In this chapter the results of some parameter variations are reported. For all these variationsthe reference is the damping for the conditions reported in section 4.4. This includes torsionaldeformation, the pre-bend shape, the stationary deformed state, the contribution of the aerody-namic stiffness, and the damping following the linearised dynamic stall model. This reference isrepresented in the figures by a solid line.

For the collective edgewise modes the damping includes the contribution from the generatorcharacteristics, which is negative above nominal speed.

5.1 Stationary Deformed State and Torsion

For a blade with a flatwise curvature the edgewise and torsional vibrations interact strongly.This means that using the deformed state without modelling blade torsion makes little sense.The negative (up-wind) pre-bend of the LMH64-5 blade concept is eliminated by the elasticdeformation due to the aerodynamic thrust. Therefore, modelling an up-wind pre-bend withoutmodelling the stationary flapwise deformation is also unreasonable. For quantification of theeffects of blade deformation the frequencies and damping were calculated for the conditions:1. Straight blades, no deformed state, no torsion;2. Pre bend, calculate deformed state, no torsion.3. Straight blades, no deformed state, with torsion;4. Pre-bend, no deformed state, with torsion (unreasonable conditions);5. Pre bend, calculate deformed state, with torsion (reference);

For the second condition it has been investigated (but not reported) that the BLADMODE resultswithout torsion are close to the results with a very high torsional stiffness.

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Wind velocity [m/s]

−0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Dam

ping

[%

]

Straight blades, no deformation, no torsionPre−bend blades, deformed state, no torsionStraight blades, no deformation, with torsionPre−bend blades, no deformation, with torsion (unreasonable)Pre−bend blades, deformed state, with torsion (reference)

Figure 12 Aero. damping of the reaction-less edge mode for different structural modelling

Figure 12 shows that without modelling of the torsional deformation, the description of the pre-bend and/or the stationary deformed state have little effect on the damping. Figure 12 also showsthat the calculated damping of the reaction-less edge modes is smaller if torsion is included andthe smallest if blade bending and the pre-bend are taken into account.

ECN-C--03-020 23

The damping calculated with torsional deformation, with the pre-bend shape and including thestationary deformed state shows a drop for a wind near 21m/s. The conditions for 21m/s windhave a large pitch angle, which gives a low rotor disk loading, see also figure 4. For the low rotordisk loading at 21m/s the elastic blade deformation eliminates the pre-bend geometry such thatblade torsion and edgewise bending are uncoupled. For higher wind loading, the sum of bladedeformation and pre-bend shape is up-wind because of the larger blade pitch angle. This againgives a positive damping of the edgewise vibrations.

Because the interaction between edgewise bending and blade torsion depends strongly on thestationary deformed state, it is thus recommended to include both blade torsion and the deformedstate in aeroelastic stability analyses.

5.2 Aerodynamic Pitch Angle

The aerodynamic damping of a vibrating rotor blade depends directly on the variation of thelift-coefficient and to a less extent on the variation of the drag coefficient with angle of attack.For stall-regulated wind turbines, a strong negative slope of the lift curve may lead to the classical"stall instability". Modern large size wind turbines (as the DOWEC 6MW concept) fortunatelyhave a pitch-to-vane control. Still, these turbine concepts can have some negative damping of theedgewise vibrations. This negative damping is partly driven by variations in dynamic pressure� � � ��

�� and an increase in the drag coefficient with angle-of-attack. Figure 13 shows that theincrease in drag coefficient, also called "drag-stall" may start at smaller angles of attack than thedecrease ("stall") of the lift coefficient.

stall

dragstall

angle of attack

lift

Figure 13 Lift- and drag- stall of a common airfoil

To show the influence of the angle-of-attack, the aerodynamic damping of the reaction-lessedgewise modes was calculated for the normal rotor-speed values of the 6MW concept with apitch angle that was increased/decreased by 1deg. The results of these calculations are shownin figure 14. Because a blade pitch angle changes both the angle-of-attack and the direction ofmotion of the edgewise mode, the aerodynamic damping is also calculated with a modified versionof BLADMODE in which only the aerodynamic pitch angle was increased by 1deg, see the thinline in figure 14. This was done by shifting the tables with aerodynamic coefficients.

For the high wind speed values the damping drops to small values, which is again due to thefact that the stationary state is approximately straight. For a 1deg increased blade pitch angle theaerodynamic blade loading is smaller in a way such that the low damping (related with the straightshape) occurs at the smaller wind speed of 19m/s.

24 ECN-C--03-020

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Wind speed [m/s]

−0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

dam

ping

[%]

Pitch angle 1deg larger (smaller angle of attack)Only aerodynamic pitch 1deg largerNormal operational conditionsPitch angle 1deg smaller

Figure 14 Edgewise aerodynamic damping for different pitch angles

ECN-C--03-020 25

5.3 Non-linear and Instationary Aerodynamic Effects

The aeroelastic damping was calculated in the following ways:1 Linearised quasi stationary airfoil loads, without aerodynamic stiffness;2 Linearised quasi stationary airfoil loads;3 Linearised airfoil loads with the 1-st order dynamic stall model of Snel [13] (reference);4 Quasi stationary airfoil loads, using finite amplitude vibrations;5 Airfoil loads with dynamic stall model, using finite amplitude vibrations.For the analyses without aerodynamic stiffness, some source code terms were set to zero. For thecalculations with damping from finite amplitude vibrations, the mode shapes were scaled with afactor 180 such that the amplitude of the reaction-less edge mode was 5m at the blade tip.(The 1P varying gravity load gives a varying tip displacement with an amplitude of 0.47m.)

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Wind velocity [m/s]

−0.20.00.20.40.60.81.01.21.41.61.82.02.22.42.6

Dam

ping

[%

]

Lin. quasi stationary airfoil loads, no aerod. stiffnessLin. quasi stationary airfoil loadsLin. airfoil loads with dynamic stall model (reference)Quasi stationary airfoil loads, finite amplitude vibr.Airfoil loads with dynamic stall, finite amplitude

Figure 15 Edgewise aerodynamic damping for different instationary aerodynamics

It follows that the aerodynamic stiffness as modelled in BLADMODE has a strong influence onthe aerodynamic damping from which it follows that it affects the mode shape seriously.

The use of the linearised dynamic stall model instead of the linearised stationary aerodynamicsgives a small reduction of the aerodynamic damping. For finite-amplitude vibrations it is remark-able that the damping is slightly smaller than calculated with the linearised aerodynamic loadvariations.

The small sensitivity for the non-linear and instationary aerodynamic modelling is because thepitch-to-vane controlled 6MW DOWEC wind turbine operates most frequently at relative smallangles-of-attack. For stall-controlled wind turbines the aerodynamic damping has the tendency toincrease (become less negative) with growing amplitude which results in so-called ’limit cycle’vibrations.

26 ECN-C--03-020

5.4 Structural Pitch

The term ’Structural Pitch’ is used for structural modifications that give a different direction ofthe principal stiffness. In general the blade-effective direction of motion � is strongly (althoughnot linearly) related to the principal stiffness directions of the cross sections. The blade-effectivedirection of motion � is a dominant parameter for the aeroelastic stability of a vibrating blade.

To get an idea of the most critical values of this direction, some BLADMODE input files weremade in which the layers forming the ’girders’ of the blade structure were shifted in chordwisedirection. These are in most cases UD-layers. In order to have ’Structural Pitch’ blade variationswithout longitudinal variations in fibre orientation (’joggles’), the chordwise shift of the ’girder-layers’ is chosen as a linear function of the spanwise coordinate. This linear function is a fractionof the linearised chord distribution given earlier � ��

��

� � � .

For the analyses shown here the girder-layers were shifted +2%, +1%, -1%, and -2% of the bladechord compared to the original LMH64-5 blade concept. Here a ’positive’ Structural Pitch meansthat the layers on the aerodynamic suction side were shifted to the trailing edge and the layerson the aerodynamic pressure side were shifted to the leading edge. The fibre-directions werenot corrected for Structural Pitch. The cross-section for a Structural Pitch of +2% of the chordis plotted with the conventional cross-section in figure 16 showing also the principal stiffnessdirection.

Figure 16 Cross section without (left) and with +2% (right) Structural Pitch.

The calculated aerodynamic damping of the reaction-less edgewise modes is plotted in figure 17versus wind speed. For a wind speed of 10m/s the corresponding angles � are included in thelegend of figure 17. It follows that the blade-effective direction of motion � is not perfectly relatedto the change in principal stiffness direction which means that the aerodynamic stiffness has alsoinfluence on the direction of motion. As expected, the value of the Structural Pitch, or the directionof the edgewise motion, has a strong influence on the aerodynamic damping. A positive value ofthe Structural Pitch gives an increased aerodynamic damping, both for partial-load operation and

ECN-C--03-020 27

for full-load operation at 21m/s wind (for which the blade is approx. ’straight’.

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Wind speed [m/s]

−0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0D

ampi

ng [

%]

Structural pitch +2% chord (theta = 4.61)Structural pitch +1% chord (theta = 2.69)No structural pitch (theta = 0.80)Structural pitch −1% chord (theta = −1.07)Structural pitch −2% chord (theta = −2.84)

Figure 17 Aerodynamic damping of the reaction-less edge mode for different Structural Pitch

The influence of the Structural Pitch on the aerodynamic damping of the collective edgewisemode is shown in figure 18, including also the blade-effective direction of motion � for 10m/s.Figure 18 shows the damping for a wind speed up to 18m/s because the damping of the collectiveedge mode does not show a local small value for the ’straight’ blade geometry at 21m/s. Fromfigure 18 it follows that the negative aerodynamic damping of 4% in full-load operation can notbe compensated by ’Structural Pitch’. This means that it is a property of the drive-train and thegenerator and that the dynamic behaviour can only be improved by generator torque control.

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Wind speed [m/s]

−5

−4

−3

−2

−1

0

1

2

3

4

5

6

Dam

ping

[%

]

Structural pitch +2% chord (theta = 4.20)Structural pitch +1% chord (theta = 2.60)No structural pitch (theta = 1.01)Structural pitch −1% chord (theta = −0.52)Structural pitch −2% chord (theta = −2.03)

Figure 18 Aerodynamic damping of the collective edge mode for different Structural Pitch

28 ECN-C--03-020

The influence of the Structural Pitch on the aerodynamic damping of the 1P gravity-response modeis shown in figure 19, including also the blade-effective direction of motion � in the legend.

3 4 5 6 7 8 9 10 11 12 13 14 15 16Wind speed [m/s]

−1

0

1

2

3

4

5

6

7

8

9

10

11

12

Dam

ping

[%

]Structural pitch +2% chord (theta = −9.36)Structural pitch +1% chord (theta = −7.13)No structural pitch (theta = −4.77)Structural pitch −1% chord (theta = −2.50)Structural pitch −2% chord (theta = −0.05)

Figure 19 Aerodynamic damping of the 1P gravity-response for different Structural Pitch

Although for the 1P response mode the Structural Pitch has an effect on the direction of motion �

that is opposite to the reaction-less modes, a positive Structural Pitch also appears to increase theaerodynamic damping. An explanation is that the direction of motion of these modes moves awayfrom the direction with the smallest aerodynamic damping, which may be near � = 0.0deg to � =-1.0deg.

Concluding remarks

The structural modifications of the rotor blade that dictate the principal stiffness directions, directlyinfluence the blade-effective direction of edgewise vibration called � . It follows that for somerange of � values, the aerodynamic damping of the edgewise modes have their smallest value. Awell-designed blade must thus have a value of � that differs from the value for ’smallest damping’.It may still depend on several aspects of the blade design what � values/range should be avoided.

ECN-C--03-020 29

5.5 Drive Train Interaction

As mentioned earlier, the negative slope of the generator torque-speed relation in full-load addsnegative damping to the collective edge modes. For the collective edgewise modes the bladesvibrate in a direction opposite to the generator speed variations. Because of the rotor shaftflexibility of the 6MW concept the generator speed variations of the collective edge modes aresomewhat large for which reason the influence of the generator torque-speed relation on thedamping of these modes is strong.

The damping of the collective edgewise modes was calculated with BLADMODE for the con-ventional rotor shaft torsional stiffness, for 1.7 times this stiffness, and without shaft torsionalflexibility. The resulting damping properties are shown in figure 20, which also includes thedamping calculated without the contribution from the generator.

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Wind speed [m/s]

−4

0

4

8

12

16

20

24

28

32

36

40

44

48

dam

ping

[%]

Collective edge mode with original drive trainCollective edge mode, 1.7 times stiffer shaftCollective edge mode, rigid shaftCollective edge mode, without generator char.

Figure 20 Edgewise aerodynamic damping for different drive train properties

The frequencies for the different shaft stiffnesses for a wind speed of 13m/s, a rotor speed of12.1rpm and a pitch angle of 3.0deg are:

Rotor shaft Collective edgeOriginal design 1.2443Hz = 6.17P1.7 times stiffer 1.5026Hz = 7.45PRigid 2.0425Hz = 10.13P

Results

The large additional contributions from the generator characteristics reflect directly the slope ofthe torque-speed relation shown in figure 3. Increasing the rotor shaft torsional stiffness appearsto reduce the aerodynamic damping of the collective edgewise modes, in the regions of bothpositive and negative damping. It thus follows that the negative damping from the generator canbe reduced by a stiff drive train, which reduces the generator speed variations associated withcollective edgewise vibrations.

30 ECN-C--03-020

6. INVESTIGATIONS FOR THE THE TAPERED VARIANT

The investigations reported in the previous chapter were for the original LMH64-5 blade concept.During the investigations within the DOWEC project, it was found that a more tapered modificationof the LMH64-5 blade concept may give some alleviation of the blade root bending moments bya reduction of the loads on the blade tip, in particular from gusts.

In this chapter a comparison is given between the original LMH64-5 blade concept and the taperedvariant described in [8]. The aim of this comparison was to describe the aeroelastic properties ofa representative large size wind turbine.

6.1 Increased Shaft Torsional Stiffness

For this purpose the torsional stiffness of the rotor shaft was increased with a factor 1.7 whichgives less negative damping from the generator and which avoids resonance for the collectiveedgewise mode, see also section 5.5. For a tubular (hollow) shaft, a 1.7 times increase in shafttorsional stiffness is realised by a 19% increase of the shaft diameter. For the comparison ofthe aerodynamic damping of the original blade geometry with the tapered variant, the stationaryconditions were also calculated with PHATAS for this tapered variant.

Most of the former investigations (e.g. load-set calculations) on the 6MW turbine concept withthe LMH64-5 blades were performed without modelling the torsional flexibility of the rotor shaftand the blades.

6.2 Description of the Tapered Variant

The original LMH64-5 blade concept has a chord distribution with a relatively small taper andwith its maximum chord at a relatively small radial position. A comparison of the blade chord ofthe original LMH64-5 blade concept with the tapered variant is shown in figure 21.


0

1

2

3

4

5

Cho

rd [m

]

Original LMH64−5 conceptTapered variant

Figure 21 Chord distribution of the tapered variant versus original design

To investigate the influence of this somewhat wide chord on the dynamic loads, a variation onthis blade was defined that had an increased taper. In this variation, the same airfoils were usedand the blade was given a similar characteristic shape. The mass and stiffness distribution wereunchanged. It appeared that for the tapered blade geometry the pre-cone angle could be 0.1degless negative without reducing the blade-tower clearance, which was thus set at -2.4deg. Thedesign of this tapered variant is described in a DOWEC note [8].

ECN-C--03-020 31

Similar as for the original LMH64-5 blade concept the quasi-stationary conditions were calculatedwith PHATAS for the tapered variant. From these stationary conditions, the annual energy capturewas integrated for a Weibull wind distribution with an average wind of 9m/s and a shape factor

= 2.08. For the original LMH64-5 blade concept this energy capture is 24.5934GWh/y and forthe tapered variant this is 24.4981GWh/y. Here it should be noted that this depends strongly onthe radius from which the root airfoils are modelled.

The stationary operational conditions for the tapered variant are presented in the following table

Wind Tip- Rotor Cp aero C axial Generator Axial Pitchspeed speed speed power force angle�m/s � ratio

�rpm � �

- � �- � �

kW � �kN � �

deg �3.0 16.945 7.533 0.2076 0.8814 8.54 63.39 1.5003.5 14.543 7.542 0.3390 0.8660 77.24 84.77 1.5004.0 12.746 7.555 0.4074 0.8509 165.4 108.80 1.4264.5 11.354 7.571 0.4441 0.8392 275.9 135.80 1.2345.0 10.245 7.590 0.4675 0.8301 413.2 165.84 0.9765.5 9.342 7.614 0.4819 0.8170 579.6 197.50 0.7246.0 8.593 7.640 0.4853 0.7991 768.7 229.88 0.4476.5 7.962 7.669 0.4831 0.7805 982.1 263.51 0.1276.75 7.754 7.756 0.4822 0.7740 1103.1 281.83 0.0007.0 7.743 8.032 0.4817 0.7733 1230.9 302.82 0.0007.5 7.714 8.573 0.4804 0.7716 1516.1 346.85 0.0008.0 7.711 9.141 0.4794 0.7718 1842.7 394.70 0.0008.5 7.686 9.681 0.4780 0.7702 2210.7 444.70 0.0009.0 7.678 10.239 0.4768 0.7700 2624.9 498.41 0.0009.5 7.661 10.784 0.4762 0.7697 3086.4 555.10 0.000

10.0 7.653 11.341 0.4749 0.7695 3597.5 614.92 0.00010.25 7.559 11.481 0.4725 0.7625 3863.8 640.17 0.00010.5 7.408 11.526 0.4679 0.7444 4113.4 655.82 0.13111.0 7.128 11.618 0.4593 0.7042 4650.4 680.94 0.56811.5 6.869 11.706 0.4464 0.6634 5170.7 701.09 1.05412.0 6.631 11.792 0.4320 0.6222 5683.9 715.97 1.63112.25 6.519 11.833 0.4240 0.6024 5936.8 722.40 1.92312.5 6.594 12.214 0.4090 0.5651 6048.7 705.60 2.85213.0 6.265 12.069 0.3545 0.4608 5949.2 622.32 4.88713.5 6.021 12.045 0.3184 0.4029 5971.9 586.85 6.08414.0 5.799 12.030 0.2889 0.3591 6012.7 562.45 7.08614.5 5.596 12.023 0.2576 0.3153 5979.1 529.68 8.17915.0 5.402 12.006 0.2335 0.2827 5987.6 508.23 9.10516.0 5.081 12.046 0.1925 0.2300 5988.7 470.57 10.79017.0 4.790 12.065 0.1606 0.1908 5990.0 440.52 12.31018.0 4.535 12.096 0.1347 0.1599 5970.6 413.89 13.72719.0 4.290 12.079 0.1148 0.1366 5977.0 393.95 15.05720.0 4.080 12.090 0.0985 0.1178 5977.5 376.49 16.30721.0 3.886 12.092 0.0851 0.1025 5978.4 361.31 17.515

For each combination of wind speed, rotor speed, and pitch angle the aerodynamic damping ofthis tapered variant was calculated with BLADMODE. The results for the edgewise modes arecompared in figures 22 through 24. For the collective edgewise mode, the shaft torsional stiffnesswas increased 1.7 times. From these figures it follows that the tapered variant has a somewhatsmaller aerodynamic damping. This may be due to the fact that for the smaller tip-chord of thetapered variant the angle-of-attack is generally higher.

32 ECN-C--03-020

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Wind speed [m/s]

−0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6D

ampi

ng [

%]


Figure 22 Comparison of the aerodynamic damping of the reaction-less edge mode

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Wind speed [m/s]

−4

−3

−2

−1

0

1

2

3

4

5

6

Dam

ping

[%

]


Figure 23 Comparison of the aerodynamic damping of the collective edge mode

ECN-C--03-020 33

3 4 5 6 7 8 9 10 11 12 13 14 15 16Wind speed [m/s]

0

1

2

3

4

5

6

7

8

9

10

11

Dam

ping

[%

]


Figure 24 Comparison of the aerodynamic damping of the 1P gravity response

34 ECN-C--03-020

Because of the smaller tip chord of the tapered variant, the tip loads are smaller which results insmaller deformations. With BLADMODE the deformations for the stationary state were calculatedfor the original design and for the tapered variant. The results are plotted in figures 25 and 26.

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Wind speed [m/s]

−1

0

1

2

3

4

5

Fla

pwis

e tip

dis

plac

emen

t [m

]


Figure 25 Stationary flatwise tip deformation

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Wind speed [m/s]

−1.4

−1.2

−1.0

−0.8

−0.6

−0.4

−0.2

0.0

Tip

tors

ion

[deg

]

Tapered variantOriginal LMH64−5 concept

Figure 26 Stationary tip torsional deformation

The blade torsional deformation is smaller for the tapered variant. Also the flat bending deforma-tion of the tapered variant is slightly smaller, except for the full-load operational state.

ECN-C--03-020 35

36 ECN-C--03-020

7. CONCLUSIONS

This report is related to aeroelastic analyses of the LMH64-5 blade concept, which was performedwith BLADMODE release "APR-2002". The validation of BLADMODE was completed recentlyand will be reported in [9].

Because the program BLADMODE does not include the Coriolis-effects and it does not describethe multi-mode interactions for flapping and lead-lag bending, the quantitative value of the stabilityanalyses reported here is limited. However, the trends following from the parameter studies inchapter 5 are considered as valuable.

From the results presented in this report the following conclusions are drawn.Aeroelastic Stability of the LMH64-5 blade concept

For pitch-to-vane controlled wind turbines the aerodynamic damping of the blade flappingmotion is always high. Edgewise blade vibrations however can have a small aerodynamicdamping. From the calculations reported here the aerodynamic damping of the reaction-lessedgewise bending modes of the LMH64-5 blade concept is mostly positive. It may be expectedthat due to multi-mode interactions the aerodynamic damping can be slightly negative. However,given the fact that a rotor blade always has some structural damping, unstable blade vibrationsare not expected.The collective edgewise modes have a very small aerodynamic damping while the negative slopeof the generator torque characteristics gives an additional negative damping. The aeroelasticstability of the collective edgewise vibrations can be improved with an advanced generatortorque control.

Value of Stability AnalysisFrom the investigations reported here it follows that stability analyses for parameter variationsprovide a means to improve the aerodynamic damping (see conclusions on Structural Pitch) orto reduce the interaction with the drive train dynamics (which adds negative damping abovenominal speed).Thus a proper blade stability analyses should be performed both on the final design, and in thepre-design phase.

Tower Resonance FrequencyAlthough not a subject of the investigation reported here, it was found that in full-load operationthe tower bending frequency lies in the variable-speed range. This may result in sideways towerbending vibrations.If tower bending vibrations appear on the prototype, a practical solution for the damping maybe to install a drum half filled with damping fluid in the tower top.

Collective Edgewise VibrationsFor a rotor speed near 12.5rpm the rotor may be in 6P resonance for the collective edgewisemode, which has a negative damping due to the decreasing slope of the generator torque-speedrelation. The de-stabilising contribution from the generator is rather large because the relativelyflexible rotor shaft gives large generator speed variations. The interaction of the collectiveedgewise modes with drive train dynamics gives an opportunity to add damping by:� increasing the rotor shaft torsional stiffness.

An increase with a factor 1.7 brings the collective edge frequency on 7.5P;� an active control of the generator torque;� adding some time delay in the power electronics for the generator torque.

The effectiveness of this measure has not yet been investigated.

ECN-C--03-020 37

Drag StallFrom stall controlled wind turbines it was found that airfoils with strong discontinuous stallcharacteristics have negative aerodynamic damping of the flap bending mode. If stall occursover the entire span this may lead to large (limit-cycle) vibrations.Rotor blades of pitch-to-vane controlled wind turbines operate at smaller angles of attack so thatstall instability of the flap bending mode is unlikely to occur. For the in-plane blade vibrationsthe increase in drag coefficient with angle of attack may give load variations with negativeaerodynamic damping. Therefore, realistic aerodynamic drag coefficients must be available forthe aeroelastic analysis of rotor blades. If the edgewise vibrations of a rotor blade appear to beunstable in a part of the operational range, the pitch angle for those situations can be increasedslightly, giving a reduction of the angle-of-attack.

Aerodynamic StiffnessThe aerodynamic stiffness has a surprisingly large influence on the aerodynamic damping, soprobably also on the mode shapes.

Finite Amplitude VibrationsFor the pitch-to-vane controlled 6MW concept, the aerodynamic damping calculated for fi-nite amplitude vibrations appears to be slightly smaller than the damping from the linearisedaerodynamic loads.

Structural PitchAs it was expected, changing the principal stiffness directions is an effective method to changethe aerodynamic damping. If the structural properties are such that a leadwise motion has someup-wind flapwise motion the aerodynamic damping is mostly positive.Increasing the Structural Pitch of a rotor blade introduces some side-effects of which theconsequences are not fully known. One of these effects is that the lead-lag moment variationsfrom gravity loading give 1P varying flap motions.

Tapered VariantThe aerodynamic damping calculated for the tapered variant is slightly smaller than the dampingfor the original design, although still positive. This smaller damping is caused by the largerangle of attack that is associated with a blade-design with a smaller tip chord.The stationary blade torsional deformations are slightly smaller than those for the originaldesign.

38 ECN-C--03-020

REFERENCES

[1] Ammerlaan, Th.M.H. and Hendriks, H.B. ;‘MATEC-I PROGRAM VERIFICATION,Mechanical Analysis Tool for Elastic Cross-sections’.ECN-R--93-010, Petten, May 1995.

[2] Bot, E.T.G. ;‘Aerodynamische Tabel Generator, Handleiding’ (in Dutch).ECN-C--01-077, Petten, August, 2001.

[3] Holten, Th. van;‘Aeroelastic Tools to Assess the Stability of Large Wind Turbines,Final Report STABTOOL Phase III ’.FM&P-02-004, TU-Delft, June 2002.

[4] Holten, Th. van, and Mulder Th.J. ;‘Partially linearised model for flap-lag-stall instability’.FM&P-02-12, TU-Delft, 2002.

[5] Kooij, J. (LM Glasfiber Holland);EXCEL file: ‘LMH64-5 geometry’ .e-mail correspondence, November 12, 2001.

[6] Kooijman, H.J.T., Lindenburg, C., Winkelaar, D., and van der Hooft, E.L. ;‘DOWEC 6 MW PRE-DESIGN, Aeroelastic modelling of the DOWEC 6 MW pre-designin PHATAS’.DOWEC-F1 W2-HJK-01-046/2, ECN-CX--01-135, Petten, August 2002.

[7] Lindenburg, C. ;‘STABLAD, Stability analysis Tools for Anisotropic rotor BLADe panels’.ECN-CX--99-013, (confidential) Petten, June 1999.

[8] Lindenburg, C. ;‘TAPERED LMH64-5 BLADE, 6MW Blade Variant with Increased Taper’.DOWEC-02-KL-084, DOWEC Memo, Petten, September 2002.

[9] Lindenburg, C. ;‘BLADMODE, Program for Rotor Blade Mode Analysis’.ECN-C--02-050, Petten, July 2003.

[10] Lindenburg, C. ;‘INVESTIGATION INTO ROTOR BLADE AERODYNAMICS,Results from testing the UAE rotor in the NASA-Ames wind tunnel ’.ECN-C--03-025, Petten, June 2003.

[11] Lindenburg, C. ;‘STATUS OF PHATAS RELEASE "OCT-2002", Unix and Windows version’.ECN-I--03-001, Petten, June 2003.

ECN-C--03-020 39

[12] Lindenburg, C. ;‘PHATAS-IV Release "OCT-2002", User’s Manual ’.ECN-I--03-006, Petten, June 2003.

[13] Snel, H. (ECN);‘DYNAMIC STALL MODELLING: SOME RESULTS’.Contribution to the 11-th IEA Symposium on Aerodynamics of Wind Turbines,Held at ECN, Petten, December 1997.

40 ECN-C--03-020

APPENDIX A. DESCRIPTION OF THE PROGRAMBLADMODE

The program BLADMODE was developed at ECN Unit Wind Energy. This development originallystarted at the end of the Dutch STABTOOL-2 research project, for the evaluation of the eigenmodesand -frequencies of rotor blades on which laboratory tests have been performed.

The model of BLADMODE describes vibrations of a rotor blade. By assuming the edge constraintat the root ’clamped’ or with some elastic relation, the user can chose between the modes for anindividual blade (’Reaction-less’ modes) or simultaneous or ’Collective’ modes of vibration.For the latter modes, the flexibility of tower fore-aft motion and the drive train dynamics is appliedas edge constraint at the blade root after dividing the stiffnesses by the number of blades.

In the following STABTOOL-3 project BLADMODE was extended subsequently with:� Apparent mass for the flatwise motion of blade sections;� Aerodynamic stiffness;� A model for the pre-bend geometry;� A B.E.M. model with which the stationary induced velocity distribution is calculated;� The stationary deformed state, which is the combination of the elastic deformation

and the pre-bend shape;� The aerodynamic damping from the linearised aerodynamic loads;� Idem, including a first-order ’Heuristic’ Dynamic stall model;� The contribution of the generator torque-speed relation to the damping of

the ’collective’ edgewise blade vibrations;� An option to calculate the aerodynamic damping by integration of the blade loads

for finite amplitude vibrations.

The program BLADMODE was also used in the European research project DAMPBLADE, whichis addressed to structural modifications that enhance the aeroelastic behaviour. Within this lastproject the program BLADMODE has been documented [9].

Limitations

Because the program BLADMODE calculates the aerodynamic damping for each of the eigen-modes it does not describe multi-mode interactions, which means that e.g. ’Coriolis-effects’ arenot accounted for.

Advantages

The program BLADMODE has a very detailed description of the structural blade properties,including not only the mass centreline, but also the location of the aerodynamic centre and theshear centre. The latter was however not used in the analyses reported here. The blade model alsodeals with transverse shear flexibility. Blades with bending-torsion coupling can also be described.

The stationary state used for the vibrations accounts for the curved blade axis, which is the sumof the pre-bend shape and the elastic deformation.

Because of its speed, sensitivity analysis can be performed within a reasonable time.

ECN-C--03-020 41

APPENDIX B. DESCRIPTION OF THE PROGRAMPHATAS

The computer program PHATAS ’Program for Horizontal Axis wind Turbine Analysis andSimulation’ was developed at ECN unit Wind Energy, and can be used for the time-domaincalculation of the dynamic behaviour of a horizontal axis wind turbine. The results of PHATASinclude the load time series (sectional forces and moments) in the main components of the turbinesuch as the rotor blades, the rotor shaft and the tower.

The structural model of the wind turbine in PHATAS describes most of the bending and torsionflexibilities of the blades and the tower. The model of the drive train and rotor hub has (optional)variables for the generator torque-speed characteristics, for the torsional deformation of the rotorshaft and gearbox support, for a teeter hinge, and for passive blade pitch motion.

The aerodynamic model in PHATAS is based on Blade Element Momentum theory (BEM). Thismodel has terms for the instationary response of the rotor wake and a model to describe the wakeeffects for oblique inflow. The blade loads can be calculated from stationary airfoil coefficients orwith a first-order dynamic stall model.

The program PHATAS has a P-D algorithm for control of the generator power or of the rotor speedby means of pitch actions. In addition to this PHATAS has a user-reserved routine from whichdedicated control algorithms can be linked to the code.

Disadvantages for stability analyses

Because PHATAS is a time-domain code, it has some numerical damping that is related to thetime-increment of the solution procedure. This numerical damping can be reduced by using asmaller time-increment, which has the consequence of a larger analysis time.

The stability of a rotor has to be evaluated from the amplitude of vibration, while the PHATASoutput does not give direct insight into the mechanism if vibrations or instabilities. In this respecteach time-domain code is trial and error method.

Advantages

The advantages of PHATAS for aeroelastic stability analyses is that it describes many structuraldynamic degrees of freedom with all their mutual interactions.

Another advantage is that the interactions between rotor vibrations and the controller can beinvestigated.

42 ECN-C--03-020

APPENDIX C. BLADMODE INPUT FILE< ’bladmode’ input file for the LMH64−5−X00 blade.<< Latest modification by C. Lindenburg; May 2, 2003.< Use blade properties on basis of orthotropic ROV806 material,< and set the location of the shear centre on zero.<nr_modes 5 < Number of modes that are required.torsion_modes ON < If ’ON’ include torsional deformation.deformed_state ON < Solve the stationary elastic deformation.aerodynamics ONair_density 1.225dynamic_stall 1 < Refers to the first−order dynamic stall model.amplitude 0.0 < Vibration amplitude factor used for damping.<length 62.7 < [m] Length of the blade.root_radius 1.80 < [m] Radius of hub.cone_angle −2.5 < [deg]tilt_angle 5.0 < [deg]pitch_angle 0.0 < [deg]<rotational_speed 11.844 < [rpm] The nominal speed.hinge_stiffness 2.E+30 < [Nm/rad] Large value indicates ’rigid’.pitch_stiffness 2.E+30 < [Nm/rad] Large value indicates ’rigid’.<tip_bending −2.05 < [m] Undeformed bending deformation at tip.pre_bend_begin 17.9 < [m] With conservation of the tip radius.pre_bend_end 53.7 < [m] With conservation of the tip radius.< < Following are properties of the turbine, which are only< relevant for rotor shaft torsion and fore−aft tower bending.nr_blades 3 < number of rotor blades.<< For drive−train dynamics.shaft_stiffness 3.29E+8 < [Nm/rad] Stiffness of main shaft.<<<shaft_stiffness 5.593E+8 < [Nm/rad] 1.7x Stiffness of main shaft.variable_speed ON < If ’ON’, then collective lead−lag modes.generator_curve 7.53148 0.0, 7.53705 49783.8, 7.55695 0.224706e+6, 7.59094 0.524160e+6, 7.68095 1.3296e+6, 8.03177 1.46345e+6, 9.1791 1.94073e+6, 10.3265 2.48965e+6, 11.3591 3.03882e+6, 11.4509 3.08987e+6, 11.5 3.2916e+6, 11.8 4.63942e+6, 11.844 4.8375e+6, 12.0 4.77465e+6, 12.3 4.65816e+6, 12.6 4.54729e+6, 13.0 4.40734e+6, 13.5 4.24413e+6, 13.9975 4.09327e+6, 14.1375 8.10548e+6<hub_inertia 50700.0 < [kg*m^2]drive_inertia 5025.5E+3 < [kg*m^2] All components behind the shaft.<< For fore−aft tower motion.hub_mass 30000.0 < [kg]tower_top_mass 79468.4 < [kg] Tower mass lumped at the top.tower_top_mass 267468.4 < [kg] Now with nacelle mass, without rotor.tower_top_mass 283000.0 < [kg] For matching with the fore−aft frequency.tower_stiffness 742.39E+3 < [N/m] Stiffness for the first fore−aft mode.<

Input file for BLADMODE, page 1 of 5

ECN-C--03-020 43

<wind_velocity 10.0airfoil_table TABEL < Spanwise distribution of the airfoils. 8.35 DU40_A17, < 40.50%, positioned from (largest chord pos) − 3.6 m. 13.20 DU35_A17, < 35.09%, starts at 37.795% relative thickness 18.69 DU30_A17, < 30.00%, starts at 32.55% ’’ 24.99 DU25_A17, < 25.00%, starts at 27.50% ’’ 32.42 DU21_A17, < 21.00%, starts at 23.00% ’’ 40.67 NA64_A17 < 18.00%, starts at 19.50% ’’. 3D_correction ON<<twist_related OFF < If ON the blade properties are w.r.t. twist.<< Geometrical properties are from the EXCEL file of November 2001.< Span chord twist Xac Yac< [m] [m] [deg] [m] [m]geometrical_data 0.00 3.5 13.4 −0.203 −0.851, 1.002 3.5 13.4 −0.203 −0.851, 2.001 3.614 13.4 −0.196 −0.825, 10.501 4.586 13.4 −0.142 −0.598, 10.701 4.609 13.4 −0.141 −0.593, 12.001 4.692 13.07 −0.133 −0.571, 14.001 4.661 11.76 −0.119 −0.57, 15.001 4.635 11.22 −0.113 −0.568, 20.001 4.379 9.82 −0.093 −0.539, 23.201 4.216 8.92 −0.082 −0.521, 25.001 4.111 8.39 −0.075 −0.508, 30.701 3.751 6.65 −0.054 −0.466, 33.001 3.613 5.98 −0.047 −0.449, 35.001 3.493 5.41 −0.041 −0.435, 36.001 3.433 5.12 −0.038 −0.427, 40.001 3.193 3.98 −0.028 −0.398, 40.701 3.151 3.79 −0.026 −0.393, 43.201 3.001 3.18 −0.021 −0.375, 44.001 2.953 3.02 −0.019 −0.369, 50.001 2.593 1.86 −0.011 −0.324, 55.001 2.293 0.89 −0.004 −0.287, 56.001 2.232 0.7 −0.003 −0.279, 58.001 2.023 0.36 −0.002 −0.253, 59.6 1.617 0.24 −0.001 −0.202, 61.001 1.097 0.13 0.0 −0.137, 62.7 0.35 0.0 0.0 −0.044


44 ECN-C--03-020

<< In the following tables X is downwind and Y is to the trailing edge.< Span mass Xcg Ycg rdelXX rdelYY rdelXY< [m] [kg/m] [m] [m] [m^2] [m^2] [m^2]mass_data 0.000 697.970 0.00004 0.00017 1.43287 1.43316 0.00007, 0.200 697.970 0.00004 0.00017 1.43287 1.43316 0.00007, 1.200 797.760 −0.00536 −0.02394 1.40945 1.37510 −0.00793, 2.200 761.780 0.00266 0.00246 1.30255 1.40999 0.03172, 3.200 760.900 0.01383 0.04211 1.17967 1.48114 0.08452, 4.200 613.030 0.01892 0.05770 1.09316 1.46929 0.10676, 5.200 467.830 0.02128 0.06404 1.01193 1.42197 0.11790, 6.200 441.330 0.02506 0.07701 0.94127 1.40000 0.13318, 7.200 417.650 0.02760 0.08492 0.87355 1.36933 0.14445, 8.201 396.190 0.05098 0.10276 0.82236 1.29092 0.15999, 9.200 413.590 0.05053 0.10986 0.75464 1.26990 0.17113, 10.200 440.100 0.06271 0.16042 0.67426 1.28823 0.19622, 11.200 430.490 0.07265 0.22423 0.58807 1.37783 0.23571, 12.200 419.640 0.08378 0.30755 0.52850 1.48785 0.26699, 13.201 394.620 0.07604 0.30438 0.48733 1.44197 0.25554, 14.200 363.120 0.06075 0.26620 0.45294 1.33697 0.22971, 15.200 359.580 0.05510 0.26079 0.42233 1.30705 0.22262, 16.200 356.470 0.05014 0.25172 0.40222 1.26754 0.21489, 18.201 348.900 0.04001 0.23371 0.36475 1.18266 0.20083, 20.200 339.220 0.03115 0.20683 0.32923 1.10683 0.18761, 22.200 330.860 0.02282 0.20252 0.29099 1.04984 0.17579, 24.200 322.330 0.01695 0.19661 0.25393 0.99246 0.16316, 26.200 302.820 0.01944 0.15448 0.21118 0.90526 0.13306, 28.201 294.790 0.03612 0.15853 0.17100 0.83534 0.11327, 30.200 268.610 0.04803 0.13551 0.14101 0.75235 0.09200, 32.200 258.200 0.06209 0.13613 0.11447 0.71832 0.07885, 34.200 246.390 0.07693 0.14325 0.09121 0.67791 0.06499, 36.200 225.160 0.08083 0.14240 0.07810 0.61694 0.05421, 38.201 204.620 0.08296 0.15402 0.06602 0.58601 0.04502, 40.200 183.540 0.08592 0.17637 0.05518 0.55105 0.03535, 42.200 169.040 0.08716 0.24963 0.04398 0.60157 0.02716, 44.200 158.210 0.08347 0.26015 0.04004 0.55773 0.02088, 46.200 142.580 0.07486 0.22612 0.03708 0.50593 0.01459, 48.201 133.040 0.07073 0.22824 0.03346 0.47597 0.01082, 50.200 109.240 0.06456 0.20553 0.03119 0.42400 0.00502, 52.200 100.660 0.06006 0.21581 0.02769 0.40068 0.00205, 54.200 92.044 0.05538 0.22664 0.02439 0.37756 −0.00061, 55.200 84.755 0.05177 0.22983 0.02316 0.36256 −0.00306, 56.200 74.612 0.05375 0.14850 0.02308 0.27758 0.00060, 57.200 70.432 0.05176 0.15350 0.02151 0.27037 −0.00014, 57.700 67.877 0.05006 0.15378 0.02010 0.25903 −0.00037, 58.201 60.849 0.04780 0.09590 0.01841 0.19631 0.00063, 58.700 57.321 0.04456 0.09128 0.01586 0.17618 0.00068, 59.200 53.788 0.04135 0.08661 0.01349 0.15730 0.00073, 59.700 50.319 0.03794 0.08123 0.01130 0.13983 0.00085, 60.200 46.932 0.03408 0.07157 0.00905 0.12223 0.00101, 60.700 42.646 0.02802 0.05447 0.00603 0.09670 0.00123, 61.200 12.348 0.02156 0.05328 0.00307 0.08201 0.00121, 61.700 10.379 0.01629 0.04993 0.00180 0.05583 0.00093, 62.200 7.4324 0.01173 0.04798 0.00114 0.02944 0.00023, 62.600 6.4244 0.00862 0.02680 0.00058 0.01177 0.00008<


ECN-C--03-020 45

<< Span EIflat EIedge EIcross Sh_XX Sh_YY Sh_XY Xea Yea< [m] [N*m^2] [N*m^2] [N*m^2] [1/N] [1/N] [1/N] [m] [m]bending_data 0.000 1.76183e+10 1.76210e+10 6.89553e+05 1.031e−09 9.080e−10 −3.129e−11 0.0000 0.0001, 0.200 1.76183e+10 1.76210e+10 6.89284e+05 1.031e−09 9.080e−10 −3.129e−11 0.0000 0.0001, 1.200 1.88016e+10 1.89993e+10 6.02935e+07 8.196e−10 8.711e−10 1.263e−11 0.0001 −0.0013, 2.200 1.69588e+10 1.90096e+10 5.79426e+08 9.127e−10 8.955e−10 −6.824e−12 0.0087 0.0267, 3.200 1.48403e+10 1.92976e+10 1.23210e+09 9.715e−10 8.896e−10 −2.554e−11 0.0209 0.0704, 4.200 1.03770e+10 1.43554e+10 1.11487e+09 1.183e−09 1.010e−09 −5.211e−11 0.0270 0.0899, 5.200 6.91510e+09 9.78592e+09 8.17735e+08 1.539e−09 1.275e−09 −8.354e−11 0.0297 0.0983, 6.200 6.02701e+09 8.70224e+09 7.74455e+08 1.741e−09 1.291e−09 −1.381e−10 0.0309 0.1016, 7.200 5.27559e+09 7.60648e+09 6.85667e+08 1.993e−09 1.329e−09 −1.947e−10 0.0290 0.0938, 8.201 4.79357e+09 6.50215e+09 5.25375e+08 2.473e−09 1.558e−09 −2.519e−10 0.0219 0.0652, 9.200 4.77121e+09 6.60984e+09 5.67669e+08 2.756e−09 1.523e−09 −3.511e−10 0.0177 0.0515, 10.200 4.54565e+09 6.74741e+09 6.60860e+08 3.079e−09 1.520e−09 −4.244e−10 0.0160 0.0472, 11.200 3.82054e+09 6.82803e+09 8.55909e+08 3.488e−09 1.590e−09 −5.170e−10 0.0237 0.0837, 12.200 3.26751e+09 6.58844e+09 8.95509e+08 3.850e−09 1.721e−09 −5.583e−10 0.0266 0.1178, 13.201 2.82514e+09 5.75263e+09 7.51862e+08 4.219e−09 1.821e−09 −5.925e−10 0.0100 0.0774, 14.200 2.49172e+09 4.67580e+09 5.44078e+08 4.936e−09 2.169e−09 −6.794e−10 −0.0102 0.0123, 15.200 2.31812e+09 4.58594e+09 5.41327e+08 5.156e−09 2.152e−09 −6.923e−10 −0.0135 0.0129, 16.200 2.20614e+09 4.45817e+09 5.30423e+08 5.321e−09 2.194e−09 −7.232e−10 −0.0164 0.0116, 18.201 1.99309e+09 4.17471e+09 5.21085e+08 5.701e−09 2.266e−09 −7.681e−10 −0.0214 0.0130, 20.200 1.77932e+09 3.93968e+09 4.98288e+08 6.112e−09 2.325e−09 −8.225e−10 −0.0267 0.0104, 22.200 1.54707e+09 3.71351e+09 4.79286e+08 6.566e−09 2.281e−09 −8.798e−10 −0.0312 0.0141, 24.200 1.32704e+09 3.49086e+09 4.55447e+08 7.131e−09 2.359e−09 −9.625e−10 −0.0329 0.0165, 26.200 1.07459e+09 3.21087e+09 3.97538e+08 8.021e−09 2.417e−09 −1.032e−09 −0.0125 0.0114, 28.201 8.54398e+08 2.92674e+09 3.42350e+08 9.197e−09 2.439e−09 −1.125e−09 0.0099 0.0199, 30.200 6.69245e+08 2.59677e+09 2.77325e+08 1.138e−08 3.268e−09 −1.239e−09 0.0273 0.0120, 32.200 5.25471e+08 2.43010e+09 2.36841e+08 1.277e−08 3.301e−09 −1.317e−09 0.0448 0.0177, 34.200 4.01975e+08 2.22164e+09 1.90588e+08 1.467e−08 3.402e−09 −1.387e−09 0.0631 0.0322, 36.200 3.08916e+08 1.73003e+09 1.32353e+08 1.467e−08 3.402e−09 −1.387e−09 0.0659 0.0179, 38.201 2.34054e+08 1.49804e+09 9.92023e+07 1.467e−08 3.402e−09 −1.387e−09 0.0699 0.0342, 40.200 1.72196e+08 1.25043e+09 6.67791e+07 1.467e−08 3.402e−09 −1.387e−09 0.0751 0.0634, 42.200 1.23070e+08 1.12288e+09 4.58375e+07 2.062e−08 4.972e−09 −1.366e−09 0.0778 0.0988, 44.200 1.04705e+08 9.66408e+08 3.14639e+07 2.174e−08 5.292e−09 −1.052e−09 0.0759 0.1201, 46.200 8.86365e+07 7.50278e+08 2.06502e+07 2.282e−08 5.252e−09 −9.965e−10 0.0717 0.0932, 48.201 7.43707e+07 6.67908e+08 1.45309e+07 2.390e−08 5.548e−09 −9.536e−10 0.0684 0.1055, 50.200 6.00038e+07 4.98265e+08 7.47386e+06 2.705e−08 9.782e−09 −1.150e−09 0.0647 0.0884, 52.200 4.85938e+07 4.37602e+08 3.98398e+06 2.848e−08 1.013e−08 −1.410e−09 0.0611 0.1041, 54.200 3.86084e+07 3.80245e+08 1.20838e+06 3.008e−08 1.071e−08 −1.158e−09 0.0574 0.1212, 55.200 3.39756e+07 3.39896e+08 −8.18904e+05 3.144e−08 1.177e−08 −8.039e−10 0.0559 0.1399, 56.200 2.97824e+07 2.93843e+08 −6.52835e+05 3.255e−08 1.229e−08 −1.205e−09 0.0547 0.1334, 57.200 2.59468e+07 2.71379e+08 −1.35964e+06 3.363e−08 1.224e−08 −9.044e−10 0.0525 0.1433, 57.700 2.33115e+07 2.52505e+08 −1.47048e+06 3.477e−08 1.266e−08 −8.253e−10 0.0507 0.1459, 58.201 1.92002e+07 1.51000e+08 1.21655e+05 3.797e−08 1.139e−08 −9.826e−10 0.0488 0.0661, 58.700 1.56522e+07 1.31440e+08 2.51001e+05 4.146e−08 1.166e−08 −1.435e−09 0.0453 0.0654, 59.200 1.25455e+07 1.13554e+08 3.63749e+05 4.550e−08 1.196e−08 −1.124e−09 0.0419 0.0645, 59.700 9.86318e+06 9.74054e+07 4.73730e+05 5.047e−08 1.210e−08 −1.463e−09 0.0384 0.0629, 60.200 7.38108e+06 8.17366e+07 6.00730e+05 5.775e−08 1.147e−08 −1.303e−09 0.0345 0.0593, 60.700 4.50531e+06 6.20362e+07 7.82166e+05 7.274e−08 1.083e−08 −1.197e−09 0.0284 0.0503, 61.200 1.87052e+05 5.05476e+06 7.49575e+04 1.330e−07 3.933e−08 4.155e−10 0.0212 0.0534, 61.700 9.65212e+04 2.97313e+06 4.92998e+04 1.869e−07 4.324e−08 −2.896e−11 0.0161 0.0490, 62.200 4.70413e+04 1.22438e+06 9.81098e+03 6.605e−07 3.821e−08 −2.337e−09 0.0117 0.0455, 62.600 2.14401e+04 4.25039e+05 2.91460e+03 9.290e−07 3.751e−08 −8.008e−09 0.0086 0.0248<


46 ECN-C--03-020

<< Following are the torsional stiffnesses.< Span GJt Xshc Yshc H42 H43< [m] [N*m^2] [m] [m] [rad/Nm] [rad/Nm]torsion_data 0.000 7.2112e+09 0.0 0.0 0.0 0.0, 0.200 7.2112e+09 0.0 0.0 0.0 0.0, 1.200 7.0585e+09 0.0 0.0 0.0 0.0, 2.200 6.3325e+09 0.0 0.0 0.0 0.0, 3.200 5.9386e+09 0.0 0.0 0.0 0.0, 4.200 4.6745e+09 0.0 0.0 0.0 0.0, 5.200 3.2708e+09 0.0 0.0 0.0 0.0, 6.200 2.7357e+09 0.0 0.0 0.0 0.0, 7.200 2.3439e+09 0.0 0.0 0.0 0.0, 8.201 1.7492e+09 0.0 0.0 0.0 0.0, 9.200 1.5383e+09 0.0 0.0 0.0 0.0, 10.200 1.3284e+09 0.0 0.0 0.0 0.0, 11.200 1.0787e+09 0.0 0.0 0.0 0.0, 12.200 9.2988e+08 0.0 0.0 0.0 0.0, 13.201 8.0467e+08 0.0 0.0 0.0 0.0, 14.200 5.9386e+08 0.0 0.0 0.0 0.0, 15.200 5.5019e+08 0.0 0.0 0.0 0.0, 16.200 5.1607e+08 0.0 0.0 0.0 0.0, 18.201 4.6059e+08 0.0 0.0 0.0 0.0, 20.200 4.0446e+08 0.0 0.0 0.0 0.0, 22.200 3.5323e+08 0.0 0.0 0.0 0.0, 24.200 3.0521e+08 0.0 0.0 0.0 0.0, 26.200 2.5327e+08 0.0 0.0 0.0 0.0, 28.201 2.0814e+08 0.0 0.0 0.0 0.0, 30.200 1.3740e+08 0.0 0.0 0.0 0.0, 32.200 1.1573e+08 0.0 0.0 0.0 0.0, 34.200 9.5146e+07 0.0 0.0 0.0 0.0, 36.200 7.6232e+07 0.0 0.0 0.0 0.0, 38.201 6.0190e+07 0.0 0.0 0.0 0.0, 40.200 4.6358e+07 0.0 0.0 0.0 0.0, 42.200 3.5493e+07 0.0 0.0 0.0 0.0, 44.200 3.1433e+07 0.0 0.0 0.0 0.0, 46.200 2.7627e+07 0.0 0.0 0.0 0.0, 48.201 2.4498e+07 0.0 0.0 0.0 0.0, 50.200 1.4572e+07 0.0 0.0 0.0 0.0, 52.200 1.2781e+07 0.0 0.0 0.0 0.0, 54.200 1.1072e+07 0.0 0.0 0.0 0.0, 55.200 9.7641e+06 0.0 0.0 0.0 0.0, 56.200 9.1055e+06 0.0 0.0 0.0 0.0, 57.200 8.3643e+06 0.0 0.0 0.0 0.0, 57.700 7.7017e+06 0.0 0.0 0.0 0.0, 58.201 6.5062e+06 0.0 0.0 0.0 0.0, 58.700 5.5262e+06 0.0 0.0 0.0 0.0, 59.200 4.6368e+06 0.0 0.0 0.0 0.0, 59.700 3.8391e+06 0.0 0.0 0.0 0.0, 60.200 3.0707e+06 0.0 0.0 0.0 0.0, 60.700 2.1164e+06 0.0 0.0 0.0 0.0, 61.200 4.8278e+05 0.0 0.0 0.0 0.0, 61.700 2.7149e+05 0.0 0.0 0.0 0.0, 62.200 1.3292e+05 0.0 0.0 0.0 0.0, 62.600 5.6959e+04 0.0 0.0 0.0 0.0<

Input file for BLADMODE, last page

ECN-C--03-020 47

48 ECN-C--03-020

APPENDIX D. NACA64-618 AERODYNAMICCOEFFICIENTS

## 2−D profiel coefficienten NACA 64−618# Henk−Jan Kooijman 8 dec. ’95## Gegevens uit document LD95TN2303 (Laurens Drost)# van 16 juni ’95 voor Cl van −12 tot +24 graden# en Cd tussen −12 en +8 graden invalshoek.# Aanvullingen coefficienten volgens ’NACA 64−618_2d’# uit geodat_2d file (ECN).## Momentcoefficienten: 11 January ’96 H−J K.# taken from: LD95TN2303. Version 2, 3 January ’96 p.A21## HJK, 14 Nov. ’01: files received from Koert today,# using stc with aspect ratio = 17 for DOWEC 6MW blade.# Reynolds number at 2/3 rotor span is 4.5E6 < Re < 8.5E6,# hence data below for 6E6 is ok.# Re = 6E6 is conclusive when comparing data with# those depicted on page 586 in A&D, appendix 4.## Aerodynamic airfoil coefficients in deep stall# from ’StC’, ’STall Coeff’, release ’MAR−2001’# calculated for geometry parameters:# nose_radius 0.02208# nose_camber 16.6992# low_tail_angle 0.00000# up_tail_angle 19.5562# aspect_ratio 17.000# alpha(Cl=0) [deg] 92.064# Cd_2D (alpha=90) 1.4565# X_cp (alpha=90) 0.2649# Cd_2D (alpha=−90) 1.3587# X_cp (alpha=−90) 0.2676# Cd (alpha=180) 0.0198## alpha C_lift C_drag C_momt−180.0 0.0000 0.0198 0.0000−175.0 0.3744 0.0341 0.1880−170.0 0.7488 0.0955 0.3770−160.0 0.6585 0.2807 0.2747−155.0 0.7358 0.3919 0.3130−150.0 0.7831 0.5086 0.3428−145.0 0.8028 0.6267 0.3654−140.0 0.7977 0.7427 0.3820−135.0 0.7705 0.8537 0.3935−130.0 0.7236 0.9574 0.4007−125.0 0.6598 1.0519 0.4042−120.0 0.5814 1.1355 0.4047−115.0 0.4908 1.2070 0.4025−110.0 0.3903 1.2656 0.3981−105.0 0.2822 1.3104 0.3918−100.0 0.1687 1.3410 0.3838 −95.0 0.0517 1.3572 0.3743 −90.0 −0.0665 1.3587 0.3636

Airfoils coefficients file NACA64-618, page 1 of 3

ECN-C--03-020 49

−85.0 −0.1841 1.3456 0.3517 −80.0 −0.2989 1.3181 0.3388 −75.0 −0.4089 1.2765 0.3248 −70.0 −0.5121 1.2212 0.3099 −65.0 −0.6063 1.1532 0.2940 −60.0 −0.6894 1.0731 0.2772 −55.0 −0.7593 0.9822 0.2595 −50.0 −0.8135 0.8820 0.2409 −45.0 −0.8500 0.7742 0.2212 −40.0 −0.8662 0.6610 0.2006 −35.0 −0.8599 0.5451 0.1789 −30.0 −0.8287 0.4295 0.1563 −25.0 −0.8525 0.3071 0.1156 −24.0 −0.8696 0.2814 0.1040 −23.0 −0.8895 0.2556 0.0916 −22.0 −0.9112 0.2297 0.0785 −21.0 −0.9343 0.2040 0.0649 −20.0 −0.9581 0.1785 0.0508 −19.0 −0.9819 0.1534 0.0364 −18.0 −1.00500 0.12876 0.02184 −17.0 −1.08200 0.10365 0.01290 −16.0 −1.11300 0.07855 −0.00279 −15.0 −1.10500 0.05345 −0.02513 −14.0 −1.07800 0.02834 −0.04190 −13.5 −1.053 0.01579 −0.05207 −13.0 −1.015 0.01511 −0.06100 −12.0 −0.904 0.01337 −0.07073 −11.0 −0.807 0.01212 −0.07218 −10.0 −0.711 0.01106 −0.07339 −9.0 −0.595 0.00992 −0.07723 −8.0 −0.478 0.00905 −0.08070 −7.0 −0.375 0.00857 −0.08250 −6.0 −0.264 0.00823 −0.08324 −5.0 −0.151 0.00788 −0.08413 −4.0 −0.017 0.00722 −0.08691 −3.0 0.088 0.00640 −0.09117 −2.0 0.213 0.00542 −0.09461 −1.0 0.328 0.00519 −0.09711 0.0 0.442 0.00524 −0.10140 1.0 0.556 0.00524 −0.10760 2.0 0.670 0.00526 −0.11260 3.0 0.784 0.00531 −0.11570 4.0 0.898 0.00535 −0.11990 5.0 1.011 0.00581 −0.12400 6.0 1.104 0.00905 −0.12340 7.0 1.185 0.01127 −0.11840 8.0 1.263 0.01255 −0.11630 8.5 1.300 0.01317 −0.11630 9.0 1.335 0.01389 −0.11600 9.5 1.366 0.01474 −0.11540 10.0 1.394 0.01568 −0.11490 10.5 1.41500 0.02760 −0.11450 11.0 1.43200 0.03953 −0.11430 11.5 1.44500 0.05145 −0.11470 12.0 1.45700 0.06337 −0.11580

Airfoils coefficients file NACA64-618, page 2 of 3

50 ECN-C--03-020

12.5 1.46900 0.07530 −0.11650 13.0 1.48000 0.08722 −0.11530 13.5 1.48500 0.09914 −0.11310 14.0 1.48400 0.11106 −0.11120 14.5 1.48400 0.12299 −0.11010 15.0 1.48800 0.13491 −0.11030 15.5 1.49300 0.14683 −0.11090 16.0 1.49700 0.15876 −0.11140 16.5 1.49600 0.17068 −0.11110 17.0 1.49300 0.18260 −0.10970 17.5 1.49600 0.19453 −0.10790 18.0 1.50700 0.20645 −0.10800 18.5 1.51400 0.21837 −0.10900 19.0 1.51200 0.23029 −0.10860 19.5 1.50500 0.24222 −0.10770 20.0 1.49800 0.25414 −0.10990 21.0 1.47600 0.27799 −0.11690 22.0 1.44000 0.30183 −0.11900 23.0 1.38700 0.32568 −0.12350 24.0 1.31400 0.34952 −0.13930 25.0 1.2670 0.3703 −0.1440 26.0 1.2196 0.3915 −0.1486 28.0 1.1272 0.4349 −0.1577 30.0 1.0439 0.4798 −0.1668 32.0 0.9769 0.5261 −0.1759 35.0 0.9227 0.5983 −0.1897 40.0 0.9222 0.7225 −0.2126 45.0 0.9026 0.8435 −0.2344 50.0 0.8615 0.9583 −0.2553 55.0 0.8014 1.0646 −0.2751 60.0 0.7248 1.1607 −0.2939 65.0 0.6343 1.2449 −0.3117 70.0 0.5321 1.3162 −0.3285 75.0 0.4206 1.3736 −0.3444 80.0 0.3020 1.4164 −0.3593 85.0 0.1786 1.4442 −0.3731 90.0 0.0525 1.4565 −0.3858 95.0 −0.0742 1.4533 −0.3973 100.0 −0.1994 1.4345 −0.4075 105.0 −0.3207 1.4004 −0.4162 110.0 −0.4360 1.3512 −0.4231 115.0 −0.5431 1.2874 −0.4280 120.0 −0.6395 1.2099 −0.4306 125.0 −0.7228 1.1196 −0.4304 130.0 −0.7904 1.0179 −0.4270 135.0 −0.8397 0.9064 −0.4196 140.0 −0.8680 0.7871 −0.4077 145.0 −0.8724 0.6627 −0.3903 150.0 −0.8500 0.5363 −0.3665 155.0 −0.7981 0.4116 −0.3349 160.0 −0.7138 0.2931 −0.2942 170.0 −0.7488 0.0971 −0.3771 175.0 −0.3744 0.0334 −0.1879 180.0 0.0000 0.0198 0.0000

Airfoils coefficients file NACA64-618, Last page

ECN-C--03-020 51

Documents

Aeroelastic Analysis of the LMH64-5 Blade Concept · PREFACE Within the DOWEC research and development project for large size offshore wind turbines, an investigation was done into