Aeroelastic Modelling of the LMH64-5 Blade. C. Lindenburg

Transcription

1 December 2002 DOWEC-02-KL-083/0 Aeroelastic Modelling of the LMH64-5 Blade C. Lindenburg

2 PREFACE Within the DOWEC research and development project for large size off-shore wind turbines an investigation was done into the aeroelastic stability of the 6MW concept study. The modelling of the 6MW concept with LMH64-5 rotor blades was done earlier but contained only bending stiffnesses which was one of the reasons to re-define the blade properties on basis of information from the FAROB file. The DOWEC research project was supported by the EET programme of the Dutch Ministry of Economic Affairs. The author wants to thank Henk-Jan Kooijman for his comments on preliminary versions of this document. Abstract Within the DOWEC project investigations were performed into the development of large size wind turbines for off-shore applications. Many of the studies in this project were performed for a 6MW concept of which the turbine was designed by NEG-Micon Holland and the blade designed by LM Glasfiber Holland. One of the tasks within this project was to investigate the aeroelastic stability problems for typical large size wind turbines which was performed for this 6MW concept. This document contains a description of the sectional properties of the LMH64-5 rotor blade, that was subjected to stability analyses within the DOWEC research and development project. The basis of the blade properties was a set of 55 files with the cross sectional layout, which are confidential so not listed here. Also the total mass properties and the eigen frequencies of the blade were calculated with BLADMODE and with PHATAS. For the first bending modes the so-called "structural pitch" was calculated for the rotating and non-rotating state, which can be used as hinge-orientation for hinge-spring-damper analysis tools. For some of the modes the resonance rotor speed values are listed. From the power curve calculated with PHATAS the quasi-stationary operational conditions are presented in terms of rotor speed and pitch angle as function of wind speed. These conditions were used as basis of analyses with programs such as the dedicated model of the TU-Delft or BLADMODE. The linearised aeroelastic stability was calculated with the program BLADMODE. Several parameter variations were performed, among which was the influence of the aerodynamic pitch angle, and the structural pitch. Finally a comparison was made of the aeroelastic behaviour of the original LMH64-5 blade design and a variant with a tapered chord distribution. Keywords Aero-elastic stability analysis Blade vibrations Off-shore wind Rotor blades Structural pitch Wind turbine 2 DOWEC-02-KL-083/0

3 CONTENTS 1. INTRODUCTION 5 2. LMH64-5 BLADE PROPERTIES Files with Sectional Description Retrieving Sectional Properties Aerodynamic Modelling Modelling in PHATAS Specific Items for BLADMODE 8 3. OVERALL MODEL PROPERTIES Total Mass Properties Frequencies Blade-Effective Direction of Motion Equivalent Model for Collective Edgewise Modes Parametrisation of Blade Properties OPERATIONAL ANALYSES Quasi-Stationary Operational Conditions Campbell Diagram Stationary Flapping Moments Linearised Stability Envelope PARAMETER VARIATIONS Stationary Deformed State and Torsion Aerodynamic Pitch Angle Dynamic Stall Effects Structural Pitch Drive Train Interaction Tapered Variant CONCLUSIONS 31 REFERENCES 33 APPENDIX A. BLADMODE INPUT FILE 35 APPENDIX B. NACA AERO COEFFICIENTS 40 DOWEC-02-KL-083/0 3

4 Aeroelastic Modelling of the LMH64-5 Blade 4 DOWEC-02-KL-083/0

5 1. INTRODUCTION Within the Dutch research and development project DOWEC investigations were done into large size wind turbines for offshore applications. This project was addressed to the development of commercial type of wind turbines and to explore the technology for future large size wind turbines. For this last part of the DOWEC investigations, studies were performed on basis of a 3-bladed 6MW concept turbine of which the pre-design was defined by NEG-Micon Holland. The predesign of the rotor blades for the 6MW turbine was defined by LM-Glasfiber Holland. These 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 give a 128.8m rotor diameter. Under loading, this diameter may be larger! One of the tasks within the DOWEC project was to investigate the aero-elastic stability of the 6MW turbine. 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 the University of Delft. In chapter 2 of this document a description is given of the structural dynamic properties of the LMH64-5 rotor blades. To allow verification of the modelling of the LMH64-5 rotor blades in the programs BLADMODE and PHATAS, the overall blade properties are summarised and compared in chapter 3. The stability envelopes calculated with the different analysis tools for the normal operating states of the 6MW NEG-Micon turbine are reported in chapter 4. This chapter also includes some parameters 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 which include some aspects of the aeroelastic analysis, among which is the influence of structural pitch and a tapered variant of the LMH64-5 blade design. Finally some conclusions are written in chapter 6. A listing of the input file for the program BLADMODE is given in appendix A and the aerodynamic coefficients for the tip airfoil NACA are listed in appendix B. DOWEC-02-KL-083/0 5

6 Aeroelastic Modelling of the LMH64-5 Blade 6 DOWEC-02-KL-083/0

7 2. LMH64-5 BLADE PROPERTIES For load-set calculations of the 6MW DOWEC turbine a description of the LMH64-5 rotor blades was made earlier on basis of an EXCEL file received from LM-Glasfiber Holland in November This description did not include the blade torsional stiffness, the transverse shear flexibility, nor the radii of gyration. The chord distribution over the midspan of the blade (between =20m and =55m) nearly follows the linear relation:. Especially because the pre-bend of the LMH64-5 rotor blades gives interaction between edgewise bending and torsion a correct modelling is of importance. 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 for aero-elastic investigations. 2.1 Files with Sectional Description In June 2002 LM-Glasfiber Holland did send the so-called *.buc files to ECN for 51 spanwise locations. These files are confidential but the resulting sectional properties could be distributed among the participants. Some of these files were for the hub (a radius smaller than 1.8m) and did describe a very stiff steel part. This part was not modelled in PHATAS and BLADMODE which means that it is rigid. In the selection of the locations for which *.buc files were provided special attention was paid to a detailed description of the locations where shear webs or other structural 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 over the root and middle section of the blade, and 3mm to 2mm towards the tip. It appears that most shear webs were modelled as one web for each of the 2 facings. These sets of webs were again defined as single web, for which the material was symmetric with respect to the web centreline. 2.2 Retrieving Sectional Properties With the tool CROSTAB the sectional properties were calculated. Since the program CROSTAB does not solve the transverse shear deformation the transverse shear flexibilities and the locations of the shear centre were calculated with the program MATEC. The input files for MATEC were generated with the program CROSTAB. From the output files of CROSTAB and MATEC the cross sectional properties were selected and converted to [kg], [m], and [N]. Unfortunately the program MATEC did not run correctly for some of the cross sections, for which locations the properties of neighbouring cross-sections were used. 2.3 Aerodynamic Modelling The aerodynamic chord and twist of the LMH64-5 rotor blade were still in accordance with the contents of the spreadsheet of November Because of the relative large contribution of the tip airfoil to the aero-elastic stability a comparison was made with the NACA airfoil coefficients generated with ATG for a Reynolds number 9M. The differences appeared to be small. So finally the airfoils for the original design were used, which are for a Reynolds number of 6M. Here it was realised that for aeroelastic stability it is important to have a realistic aerodynamic coefficients, also for drag ( drag-stall ), see section 5.1 DOWEC-02-KL-083/0 7

8 Aeroelastic Modelling of the LMH64-5 Blade 2.4 Modelling in PHATAS The input file of PHATAS can have tables with a maximum length of 22 records so that selections were made of the mass distribution, the bending stiffnesses, and the torsional stiffnesses. These selections were made for a minimum discrepancy with the complete distributions. Special attention was paid to the distribution of the mass in the tip region and of the stiffness in the root region. The aerodynamic chord and twist were still from the EXCEL file of November For the former load set calculations of the 6MW turbine with PHATAS by STENTEC an input file has been made using 14 elements to describe each blade. In the STABTOOL-3 project [2] it was found that for aero-elastic stability research one would preferably use at least 15 elements. For model of the LMH64-5 blade with 17 blade elements the so-called "airfoil matching" was found 96%, while the frequencies (from the eigenvalue module) were close to those calculated for 21 blade elements. Finally 17 blade elements were used. The first 2 elements had a drag coefficient only, as for a cylinder. Other modifications with respect to the "load-set" input file are: Modelling blade torsional deformation (0.48% damping); Modelling rotor shaft torsion; Setting the pre-bend on -2.05m (which was m for other DOWEC work). It was also discovered that the former PHATAS input did have a 10 times too high value for the shaft torsional stiffness. In accordance with the NEG-Micon specifications this was corrected to 3.29E+8Nm/rad. 2.5 Specific Items for BLADMODE In BLADMODE the complete distributions of mass, bending stiffness, and torsional stiffness were used. The geometrical properties were still those from the EXCEL file of November In release "APR-2002" of BLADMODE the pre-bend of the LMH64-5 blade was modelled from =17.9m to =35.7m, while the pre-bend at the tip is -2.05m (negative is upwind). In BLADMODE the turbine properties were copied from the description by NEG-Micon Holland. The tower fore-aft bending was modelled with a fore-aft translation of the nacelle with stiffness kN/m and a lumped mass (at the top) for tower motion of kg. This latter value includes the nacelle mass but not the 30000kg hub mass. The modelled drive train inertia was kg*m expressed with respect to the slow speed shaft. At the rotor-side of the shaft a hub inertia of 50700kg*m was added. 8 DOWEC-02-KL-083/0

9 3. OVERALL MODEL PROPERTIES This chapter reports on some overall blade properties while comparisons were made between the BLADMODE and PHATAS modelling. Also some parameter representations are added that can be used for specific applications such as controller design or the dedicated model of the TU-Delft. 3.1 Total Mass Properties BLADMODE PHATAS Rotor radius (excl. pre-bend) Aerodynamic area Aspect ratio Total mass Apparent mass Static moment X Static moment Y Static moment Idem w.r.t. centre Inertia E+07 (w.r.t. rotor centre) Rotor inertia E+07 Pitch inertia The total mass properties are close to each other, except for the smaller value of the pitch inertia in the PHATAS model. The smaller pitch inertia of the PHATAS model is because the out-of-chord locations of the mass distribution are not included. 3.2 Frequencies With BLADMODE and with PHATAS the eigen-frequencies were calculated for a rotational speed of rpm, without apparent mass, and without pre-bend or elastic deformation. The frequencies from PHATAS are the eigenvalue solutions and do not include the coupling between e.g. edgewise bending and torsion. Except for the tower bending frequency and the collective edgewise frequency the eigenmodes from BLADMODE listed below were calculated without interactions from the drive train or the tower, the so-called reaction-less modes. BLADMODE PHATAS Tower Flat Edge Flat Coll. edge Coll. edge Edge Torsion Most frequencies from PHATAS match well with those from BLADMODE except for the collective edgewise frequencies. This is caused by the fact that the PHATAS solution for the edgewise modes doesn t include the drive train in much detail. The blade torsional frequency shows a reasonable agreement. DOWEC-02-KL-083/0 9

10 Aeroelastic Modelling of the LMH64-5 Blade 3.3 Blade-Effective Direction of Motion For each of the eigenmodes the program BLADMODE calculates a mode-effective direction of motion for the aerodynamic loading. This is done by integration of the flapwise and the lagwise components of the eigenmodes multiplied by: the chord, the radius, and the amplitude of the eigenmode. The vectorial representation for the flatwise and edgewise components is expressed in the so-called angle, theta. This direction can be used in models with fixed directions of edgewise and flatwise motion, such as the dedicated model for "flap-lag-stall" instability [1] developed at the "Flight Mechanics and Propulsion" group of the faculty of Aerospace Engineering of the TU-Delft. The direction is measured similar as the geometric pitch and/or twist angle of the blade. With BLADMODE the angles of the LMH64-5 blade modes were calculated, without the apparent mass and without aerodynamic stiffness. The blades are also described without the pre-bend. For the collective edgewise modes the shaft torsional flexibility and the variable speed characteristics were included while the tower was assumed rigid. Frequency Hz Direction deg Mode Speed 0rpm rpm 0rpm rpm Reaction-less flat Collective flat Reaction-less edge Collective edge Collective edge Disregarding the 90deg difference between flap- and lead-lag direction the angles of these modes are similar. An exception is the direction of the collective-flat motion which is more in the downwind direction because of the interaction with tower bending. For a hinge-spring model in which terms for centrifugal loads are present, the reaction-less modes for the non-rotating state should be used giving a direction of 9deg to 9.5deg. This direction can be modified by shifting the UD layers within the cross section, of which an investigation is reported in section Equivalent Model for Collective Edgewise Modes For some applications, such as the design of controller algorithms, the collective edgewise modes have to be described with a 1-d.o.f. model of which the deformation is generalised as shaft torsion. This model has 3 parameters: Rotor inertia, Drive train inertia, and Torsional stiffness of the shaft that is in between. Using conservation of 1. total rotational inertia ( E+3kg*m ), 2. collective edgewise frequency (1.254Hz), 3. and ratio between kinetic energy and generator speed variations finally gives an effective drive inertia of kg*m, a E+3kg*m rotor inertia, and a 24141Nm/rad shaft torsional stiffness. It seems strange that the effective drive-train inertia is smaller than the generator inertia aft of the flexible shaft. 3.5 Parametrisation of Blade Properties Still for other applications, the blade mass and stiffness properties can be described with a few parameters. With conservation of the blade mass static moment w.r.t. the root, and of the rotor rotational inertia, a linearised mass distribution as function of the span is found with "! # 10 DOWEC-02-KL-083/0

11 4. OPERATIONAL ANALYSES 4.1 Quasi-Stationary Operational Conditions The DOWEC 6MW concept has a variable speed generator characteristics. These generator characteristics are realised by power electronics that give a constant generator power above the nominal speed of rpm. This means that the torque-speed relation has a negative slope above nominal speed, see figure 1. For variable speed wind turbines the rotor speed above nominal speed 6000 Shaft torque [knm] Rotor speed [rpm] Figure 1 Generator torque-speed relation is kept within its allowable range by a controller algorithm. Since not all stability analysis tools do have an option to model the controller algorithm, the envelope of the operational parameters was obtained from a power curve calculated with the program PHATAS. This power curve was calculated for the air density of 1.225kg/m, for a constant wind velocity, with a vertical shear exponent of 0.082, with a pitch error (related to blade 1) of +0.18deg and -0.18deg for blade 2 and 3 respectively, and with solving the blade bending and torsional deformation Rotor speed [rpm] Aerodynamic thrust [100kN] Pitch angle [deg] Wind speed [m/s] Figure 2 Stationary operational conditions for the 6MW concept study DOWEC-02-KL-083/0 11

12 Aeroelastic Modelling of the LMH64-5 Blade Wind Tip- Rotor Cp aero C axial Generator Axial Pitch Torque/ speed speed speed power force angle m/s ratio rpm - - kw kn deg knm/(rad/s) The last column in this table contains the rotor-speed derivative of the (quasi stationary) generator torque for the governing rotor speed. This derivative adds some damping to the collective in-plane vibrations, which is used in the program BLADMODE. Above nominal speed the values in this last column are simply the derivative of the torque-speed relation at 12rpm, which is rather negative and therefore conservative. The variable speed generator has its most negative slope just above nominal speed which is -3900kNm/(rad/s). The rotor speed, aerodynamic thrust, and pitch angle are plotted in figure 2 as function of wind speed. Figure 2 clearly shows the action of the pitch controller in partial load. The aerodynamic thrust on the rotor shows that the positive pitch angles just around nominal speed directly reduce the maximum axial loads on the rotor, called thrust clipping. 12 DOWEC-02-KL-083/0

13 OPERATIONAL ANALYSES 4.2 Campbell Diagram With the program BLADMODE the frequencies of the LMH64-5 blade were calculated for 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 the symmetrical (reaction-less) edgewise mode all other frequencies are for the collective modes which means that the tower flexibility and drive train dynamics are included. Rotor speed Tower Flat-1 Symm. edge Collective edge 0.0rpm Hz Hz Hz Hz 5.0rpm Hz Hz Hz Hz 6.0rpm Hz Hz Hz Hz 7.0rpm Hz Hz Hz Hz 8.0rpm Hz Hz Hz Hz 9.0rpm Hz Hz Hz Hz 10.0rpm Hz Hz Hz Hz 11.0rpm Hz Hz Hz Hz 12.0rpm Hz Hz Hz Hz 13.0rpm Hz Hz Hz Hz 14.0rpm Hz Hz Hz Hz 15.0rpm Hz Hz Hz Hz 16.0rpm Hz Hz Hz Hz From this table the following resonance rotor speed values were found, see also figure 3. Speed Resonance 9.4rpm 7P Reaction-less edge 10.4rpm 4P Collective flat 10.8rpm 7P Collective edge 11.0rpm 6P Reaction-less edge! 12.6rpm 6P Collective edge! 13.2rpm 5P Reaction-less edge 13.7rpm 1P Side-ways tower! 14.6rpm 3P Collective flat For the PHATAS tower model (which is more detailed) the side-ways bending frequency is Hz which is in 1P resonance at 13.7rpm. The tower frequency may have serious sideways bending resonance problems since the aerodynamic damping in this direction is small. The side-ways tower frequency would be safe if it remains out of the 0.8P - 1.2P resonance speed range, which is from 11.4rpm to 17.1rpm. Of all edgewise blade resonance frequencies the 6P reaction-less edge is the most alarming because this is in the rotor speed range where the generator torque has a steep slope and therefore gives small speed variations. This means that at certain wind conditions the rotor speed may stay for some period near the 6P edge-resonance speed. The 6P resonance speed is also unfavourable because it coincides with 2 times the blade passing frequency. With the combination of shaft flexibility and the variable speed generator characteristics the collective edgewise mode appears to be not much higher than the reaction-less edgewise mode. Because the collective edgewise modes have positive damping from the generator below nominal speed, the 7P resonance at 10.8rpm is not alarming. Above nominal rotor speed the generator has negative damping which means that the 6P resonance speed of 12.6rpm for the collective edgewise mode requires attention. For a pitch-to-vane controlled turbine the blade flapping motion has a large aerodynamic damping so the 3P (and 4P) resonances will not give problems. DOWEC-02-KL-083/0 13

14 Aeroelastic Modelling of the LMH64-5 Blade Frequency [Hz] P, 3P, 4P,... 7P Coll. edge 1 Edge mode 1 Flat mode 1 Tower fore aft Rotational speed [rpm] Figure 3 Campbell diagram of the 6MW turbine with LMH64-5 rotor blades 14 DOWEC-02-KL-083/0

15 OPERATIONAL ANALYSES 4.3 Stationary Flapping Moments The Dedicated Model of the TU-Delft calculates the dynamic response for a hinged rotor blade using the hinge stiffnesses and orientation of the hinge as input. For this orientation the so-called structural pitch is used. The stationary state for this model is described with a hinge-angle which is calculated with a blade element momentum model. For comparison of this hinge-angle the flap-bending moments were calculated with the program PHATAS. In this calculation the blades were rigid but still have the -2.05m pre-bend and the -2.5deg cone angle in the hub. For a flapping frequency at rpm of Hz and with a flapping inertia w.r.t. the rotor centre of 12.7E+6 kg*m the hinge stiffness is 226.7E+6 Nm/rad. With this hinge stiffness, with the flapping inertia, and with the root bending moments calculated for a rigid blade the following stationary hinge-flapping angles were calculated: Wind Rotor Flap Flap Blade Structural speed speed moment angle pitch pitch m/s rpm knm deg deg deg The rightmost column in this table contains the blade pitch angle used for the BLADMODE analyses and the resulting structural pitch. Here the structural pitch was calculated for a straight rotor blade without solving the stationary deformed state and without aerodynamic stiffness nor apparent mass. Here the structural pitch was taken from the BLADMODE output, using the rotor speed values as reported in section 4.1. These structural pitch values include the blade pitch angle. DOWEC-02-KL-083/0 15

16 Aeroelastic Modelling of the LMH64-5 Blade 4.4 Linearised Stability Envelope With BLADMODE the eigenmodes and their linearised damping were calculated for the operational conditions listed in section 4.1. In these calculations the pre-bend was modelled while the stationary deformed state was solved (it was thought unrealistic to describe the pre-bend only, see section 5.1). These calculations were done for the collective and for the reaction-less (symmetric) blade bending modes. The calculated aerodynamic damping of the first edgewise modes are plotted in figure 4 as function of wind speed. The aerodynamic damping of the edgewise modes was calculated with the linearised aerodynamic loads following the first-order part of the heuristic dynamic stall model of Snel, [8]. For the collective edgewise modes this damping was calculated with and without the contribution of generator torque-speed derivatives listed in section 4.1. The higher modes are assumed to have a relatively larger structural damping while the flatwise modes have sufficient aerodynamic damping. damping [%] Response mode on 1P gravity loading Reaction less edge mode Collective edge mode, without generator char. Collective edge mode Collective edge mode Wind speed [m/s] Figure 4 Edgewise aerodynamic (and generator) damping calculated with BLADMODE Figure 4 also contains the aerodynamic damping of the response on the 1P gravity loading. Since the 1P frequency is not an eigenfrequency, a negative aerodynamic damping for the 1P gravity loading will result in an amplification of the 1P response but not always lead to instability. In full load the collective edgewise mode has a relatively large negative damping from the generator characteristics. This strong influence from the generator is partly caused by the relatively flexible rotor shaft, which gives strong generator-speed variations for the collective edgewise modes. Figure 5 through 7 show the edgewise modes calculated for the operational conditions at 10m/s. Knowing that for these plots the wind comes from the left it follows that the blades have a downwind stationary deformation. The reaction-less and collective edgewise modes show a strong similarity, which also follows from the fact that the frequencies are close together. 16 DOWEC-02-KL-083/0

17 OPERATIONAL ANALYSES Figure 5 Reaction-less edgewise mode at 10m/s wind Figure 6 Collective edgewise mode 1 at 10m/s wind DOWEC-02-KL-083/0 17

18 Aeroelastic Modelling of the LMH64-5 Blade Figure 7 Collective edgewise mode 2 at 10m/s wind 18 DOWEC-02-KL-083/0

19 5. PARAMETER VARIATIONS In this chapter the results of some parameter variations are reported. For all these variations the reference is the analysis in the previous chapter, which includes torsional deformation, the pre-bend shape, the stationary deformed state, the contribution of the aerodynamic stiffness, and the damping following the linearised dynamic stall model. The reference has a solid line. For the collective edgewise modes the damping includes the contribution from the generator characteristics, which is negative above nominal speed. 5.1 Stationary Deformed State and Torsion For a blade that has a flatwise curvature the edgewise and torsional vibrations have a strong interaction. This means that using the deformed state without modelling blade torsion makes little sense. The negative (up-wind) pre-bend of the LMH64-5 rotor blades will be eliminated by the elastic deformation due to the aerodynamic thrust. This means that modelling an up-wind pre-bend without modelling the stationary flapwise deformation makes little sense. For quantification of the effects of blade deformation the frequencies, damping, and structural pitch were calculated for the conditions: 1. Straight blades, no deformed state, no torsion; 2. Straight blades, no deformed state, with torsion; 3. Pre-bend, no deformed state, with torsion (unreasonable conditions); 4. Pre bend, solve deformed state, with torsion (reference); 5. Pre bend, solve deformed state, no torsion. It has been shown that for the last condition the BLADMODE results without torsion are close to the results with a very high torsional stiffness. Damping [%] Straight blades, no deformation, no torsion Straight blades, no deformation, with torsion Pre bend blades, no deformation, with torsion (unreasonable) Pre bend blades, deformed state, with torsion (reference) Pre bend blades, deformed state, no torsion Wind velocity [m/s] Figure 8 Aerodynamic damping of the reaction-less edge mode for different structural modelling Figure 8 shows that without modelling the torsional deformation the description of the pre-bend and solution of the stationary deformed state have little effect on the damping. From the calculations with torsional deformation it follows that an upwind curvature increasesand a downwind curvature decreases the aerodynamic damping. Modelling an up-wind pre-bend DOWEC-02-KL-083/0 19

20 Aeroelastic Modelling of the LMH64-5 Blade geometry without solving the stationary deformed state will thus lead to an over-estimation of the stability and is therefore an unreasonable effort. 5.2 Aerodynamic Pitch Angle The aerodynamic damping of a vibrating rotor blade depends directly on the variation of the lift-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) however have a pitch-to-vane control. Still these turbine concepts can have some negative damping of the edgewise vibrations. This negative damping is partly driven by a change in dynamic pressure and an increase in the drag coefficient with angle-of-attack. Figure 9 showns that the increase in drag coefficient, also called "drag-stall" may start at smaller angles of attack than the decrease ("stall") of the lift coefficient. lift stall drag stall angle of attack Figure 9 Lift- and drag- stall of a general airfoil To show the influence of the angle-of-attack the aerodynamic damping of the reaction-less edgewise modes was calculated for the normal rotor-speed values of the 6MW concept but with a pitch angle that was increased/decreased 1deg. The results of these calculations are shown in figure 10. Because a pitch angle also changes the direction of motion of the edgewise mode, the aerodynamic damping is also calculated with a modified version of BLADMODE in which only the aerodynamic pitch angle was increased 1deg. From figure 10 it follows that increasing the pitch angle, so decreasing the angle-of-attack, improves the aerodynamic damping. Because a pitch angle also changes the direction of motion of the edgewise mode, the aerodynamic damping was also calculated with a modified version of BLADMODE in which only the aerodynamic pitch angle was increased with 1deg. 20 DOWEC-02-KL-083/0

21 PARAMETER VARIATIONS 5 damping [%] Pitch angle 1deg larger (smaller a.o.a.) Only aerodynamic pitch 1deg larger Normal operational conditions Pitch angle 1deg smaller Wind speed [m/s] Figure 10 Edgewise aerodynamic damping for different pitch angles DOWEC-02-KL-083/0 21

22 Aeroelastic Modelling of the LMH64-5 Blade 5.3 Dynamic Stall Effects The aeroelastic stability has to be calculated for the following conditions: 1 Quasi stationary airfoil loads, without aerodynamic stiffness; 2 Quasi stationary airfoil loads; 3 Linearised dynamic stall model of Snel [8] (reference); 4 As 3. but with the empirical relation for dynamic drag, following Montgomerie [5, 7]. For the analyses of the first condition, some source code terms were set on zero. Damping [%] Quasi stationary airfoil loads, no aerodynamic stiffness Quasi stationary airfoil loads Linearised dynamic stall model of Snel (reference) Idem, using the Prandtl factor for aero. damping Idem, with Montgomerie s drag correction Wind velocity [m/s] Figure 11 Edgewise aerodynamic damping for different instationary aerodynamics It follows that the aerodynamic stiffness as modelled in BLADMODE has a strong influence on the aerodynamic damping so that it must affect the mode shape seriously. Using the linearised dynamic stall model instead of the linearised stationary aerodynamics has a small influence on the aerodynamic damping, which can be expected for pitch-to-vane controlled wind turbines. 5.4 Structural Pitch The term structural pitch is used for structural modifications that give a different direction of the principal stiffness. In general the mode-effective direction of motion is strongly (although not linearly) related to the principal stiffness directions of the cross sections. The mode-effective direction 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 were made in which the layers forming the girders of the blade structure were shifted in chordwise direction. These are in most cases UD-layers. In order to have blade variations with structural pitch without longitudinal variations in fibre orientation, the chordwise shift of the girder-layers is a linear function of the spanwise coordinate. This linear function is a fraction of the linearised chord distribution given earlier. For the investigations shown here the girder-layers were shifted 2%, 1%, -1%, and -2% of the blade chord compared to the original LMH64-5 design. Here a positive structural pitch means that the layers on the aerodynamic suction side were shifted to the trailing edge and the layers on the aerodynamic pressure side were shifted to the leading edge. The fibre-directions were 22 DOWEC-02-KL-083/0

23 PARAMETER VARIATIONS not corrected for the structural pitch. The cross-section for a structural pitch of 2% of the chord is plotted with the conventional cross-section in figure 12 showing also the principal stiffness direction. Figure 12 Cross section without (left) and with 2% (right) structural pitch. The calculated aerodynamic damping of the reaction-less edgewise modes are plotted in figure 13 versus wind velocity. Damping [%] Structural pitch +2% chord (theta = 6.93) Structural pitch +1% chord (theta = 4.12) No structural pitch (theta = 1.78) Structural pitch 1% chord (theta = 1.07) Structural pitch 2% chord (theta = 3.40) Wind speed [m/s] Figure 13 Aerodynamic damping of the reaction-less edge mode for different structural pitch For a wind velocity of 10m/s the corresponding angles are included in the legend of figure 13. DOWEC-02-KL-083/0 23

24 Aeroelastic Modelling of the LMH64-5 Blade It follows that the blade-effective direction of motion is not perfectly related to the change in principal stiffness direction which means that the aerodynamic stiffness has a strong influence on the direction of motion. As expected the value of the structural pitch, or the direction of the edgewise motion, has a strong influence on the aerodynamic damping. The influence of the structural pitch on the aerodynamic damping of the 1P gravity-response mode is shown in figure 14, including also the blade-effective direction of motion in the legend. Although for the 1P response mode the structural pitch has an opposite effect on the direction of Damping [%] Structural pitch +2% chord (theta = 9.82) Structural pitch +1% chord (theta = 7.59) No structural pitch (theta = 5.66) Structural pitch 1% chord (theta = 3.23) Structural pitch 2% chord (theta = 1.21) Wind speed [m/s] Figure 14 Aerodynamic damping of the 1P gravity-response for different structural pitch motion than for the reaction-less modes, it appears that a positive structural pitch also increases the aerodynamic damping. An explanation for those trends may be that the direction of motion of both modes move away from the direction with the smallest aerodynamic damping, which may be near = -1.0deg. 24 DOWEC-02-KL-083/0

25 PARAMETER VARIATIONS 5.5 Drive Train Interaction As mentioned earlier the negative slope of the generator torque-speed relation in full-load adds negative damping to the collective edge modes. For the collective edgewise modes the blades vibrate in opposite direction as the generator. Because of the rotor shaft flexibility of the 6MW concept the generator speed variations of the collective edge modes are somewhat large for which reason the influence of the generator torque-speed relation on the damping of these modes is strong. With BLADMODE the damping of the collective edgewise modes was calculated for the conventional rotor shaft flexibility, for half of this flexibility, and without shaft torsional flexibility. The resulting damping properties are shown in figure 15, where also the damping is included without the contribution from the generator. damping [%] Collective edge mode with complete drive train Collective edge mode, 2 times stiffer shaft Collective edge mode, rigid shaft Collective edge mode, without generator char Wind speed [m/s] Figure 15 Edgewise aerodynamic damping for different principal stiffness directions The large additional contributions from the generator characteristics reflect directly the slope of the torque-speed relation shown in figure 1. Increasing the rotor shaft torsional stiffness shows to reduce the aerodynamic damping of the collective edgewise modes, in the regions of both positive and negative damping. DOWEC-02-KL-083/0 25

26 Aeroelastic Modelling of the LMH64-5 Blade 5.6 Tapered Variant The original LMH64-5 blade design has a chord distribution with a relatively small taper and with its maximum chord at a relatively small radial position. A comparison of the blade chord of the original LMH64-5 blade design and the tapered variant is shown in figure Chord [m] Original chord Tapered variant Location from blade root [m] Figure 16 Chord distribution of the tapered variant versus original design To investigate the influence of this too wide chord on the dynamic loads a variation on this blade was defined that had an increased taper. In this variation the same airfoils were used and the blade was given a similar characteristic shape. The mass and stiffness distribution were kept the same. It appeared that for the tapered blade geometry the pre-cone angle could be 0.1deg less negative, which was thus set on -2.4deg. The design of this tapered variant is described in a DOWEC note [6]. Similar as for the original LMH64-5 blade design the quasi-stationary conditions were calculated with PHATAS. 26 DOWEC-02-KL-083/0

27 PARAMETER VARIATIONS Wind Tip- Rotor Cp aero C axial Generator Axial Pitch Torque/ speed speed speed power force angle m/s ratio rpm - - kw kn deg knm/(rad/s) For each combination of wind speed, rotor speed, and pitch angle the damping of this tapered variant was calculated with BLADMODE. The results are compared in figure 17. It follows that the aerodynamic damping calculated for both blade designs is nearly identical. DOWEC-02-KL-083/0 27

28 Aeroelastic Modelling of the LMH64-5 Blade Damping [%] Reaction less edge mode, Original design Reaction less edge mode, Tapered variant Collective edge mode, Original design Collective edge mode, Tapered variant Wind speed [m/s] Figure 17 Edgewise aerodynamic damping for the original design and the tapered variant 28 DOWEC-02-KL-083/0

29 PARAMETER VARIATIONS Because of the smaller tip chord of the tapered variant, the tip loads will be smaller which will finally lead to smaller deformations. With BLADMODE the deformations for the stationary state are calculated for the original design and for the tapered variant. The results are plotted in figure 18 and Flapwise tip displacement [m] Tapered variant Original design Wind speed [m/s] Figure 18 Stationary flatwise tip deformation 0.0 Tip torsion [deg] Tapered variant Original design Wind speed [m/s] Figure 19 Stationary tip torsional deformation The blade torsional deformation is smaller for the tapered variant. Also the flat bending deformation of the tapered variant is slightly smaller, except for the full-load operational state. DOWEC-02-KL-083/0 29

30 Aeroelastic Modelling of the LMH64-5 Blade 30 DOWEC-02-KL-083/0

31 6. CONCLUSIONS This report is related to aeroelastic analyses of the LMH64-5 blade. This was done to a large extent with the program BLADMODE of which the validation was completed recently. This fact and the omission in BLADMODE of Coriolis-effects implies that the stability predictions have limited quantitative value. From the results presented in this report the following conclusions can be drawn. Tower resonance frequency Although not a subject of the investigation reported here it was found that the tower bending frequency is in the variable-speed range in full-load operation. This may give rise to sideways tower bending vibrations. Collective edgewise vibrations At a rotor-speed near 12.6rpm the rotor may be in a 6P resonance state for the collective edgewise mode, which has a negative damping from the decreasing slope of the generator torque-speed relation. The de-stabilising contribution from the generator is rather large because of the relatively flexible rotor shaft, which results in large generator speed variations. The interaction of the collective edgewise modes with the drive train dynamics gives an opportunity to add damping by either 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. Structural design From the comparison of the deformed state of the original LMH64-5 design and of the tapered variant, it followed that the stationary blade torsional deformation is relatively large. This is probably caused by the long spanwise area that has an 18% thickness. Response on gravity loading The gravity loading on the rotor blades causes 1P edgewise blade motions. For the LMH64-5 rotor blades these edgewise motions have a negative structural pitch which gives a small but negative aerodynamic damping from = 9.5m/s to = 12.5m/s. Although this negative damping wil amplify the 1P edgewise motions it will probably not lead to instability since the 1P motion is far away from the eigenfrequencies. Drag stall From stall controlled wind turbines it was investigated that airfoils with a strong discontinuous stall characteristics have negative aerodynamic damping of the flap bending mode. If stall for those blades takes place over 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 which means that stall instability of the flap bending mode is unlikely to occur. For the in-plane blade vibrations the increase in drag coefficient with angle of attack may give load variations that have negative aerodynamic damping. For the aeroelastic analysis of rotor blades this means that realistic aerodynamic drag coefficients must be available. If the edgewise vibrations of a rotor blade appear to be unstable in a part of the operational range, the pitch angle for those situations can be increased slightly, giving a reduction of the angle-of-attack. DOWEC-02-KL-083/0 31

32 Aeroelastic Modelling of the LMH64-5 Blade Structural pitch As was expected, changing the principal stiffness directions is an effective measure to change the aerodynamic damping. If the structural properties are such that a leadwise motion has some up-wind flapwise motion the aerodynamic damping is usually positive. Increasing the structural pitch of a rotor blade introduces some side-effects of which the consequences are not fully known. One of these effects is that the lead-lag moment variations from gravity loading give 1P varying flap motions. Aerodynamic Stiffness The aerodynamic stiffness has a surprisingly large influence on the aerodynamic damping, so probably on the mode shapes. Tapered variant The aerodynamic damping calculated for the tapered variant is nearly the same as the amping for the original design. The stationary blade torsional deformations are smaller than those for the original design. The stationary flapwise deformations are only marginally smaller. 32 DOWEC-02-KL-083/0

33 REFERENCES [1] Holten, Th. van, and Mulder Th.J.; Equations of motion for aeromodel IV. FM&P-02-??, TU-Delft, [2] Holten, Th. van; Aeroelastic Tools to Assess the Stability of Large Wind Turbines, Final Report STABTOOL Phase III. FM&P , TU-Delft, June [3] Kooijman, H.J.T., Lindenburg, C., Winkelaar, D., and van der Hooft, E.L.; DOWEC 6 MW PRE-DESIGN, Aero-elastic modelling of the DOWEC 6 MW pre-design in PHATAS. DOWEC-F1 W2-HJK /2, ECN-CX , Petten, August [4] Lindenburg, C. and Schepers J.G.; PHATAS-IV AEROELASTIC MODELLING, Release "DEC-1999" and "NOV-2000". ECN-CX , (Confidential) Petten, April [5] Lindenburg, C.; BLADMODE, Program for Rotor Blade Mode Analysis. ECN-C , Petten, December [6] Lindenburg, C.; TAPERED LMH64-5 BLADE, 6MW Blade Variant with Increased Taper. DOWEC-02-KL-084, DOWEC Memo, Petten, September [7] Montgomerie, B.; DYNAMIC STALL MODEL CALLED "SIMPLE". ECN-C , Petten, January [8] 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 DOWEC-02-KL-083/0 33