STRUCTURAL PITCH FOR A PITCH-TO-VANE CONTROLLED WIND TURBINE ROTOR

Transcription

1 ECN-C STRUCTURAL PITCH FOR A PITCH-TO-VANE CONTROLLED WIND TURBINE ROTOR DAMPBLADE project, task 3.4: Design application, sensitivity analysis and aeroelastic tailoring C. Lindenburg M.H. Hansen (Risø) E.S. Politis (CRES) OCTOBER 2004

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3 PREFACE Within the European research project DAMPBLADE investigations were performed into materials for wind turbine rotor blades with enhanced damping properties. The investigations in task 3.4 of this project were addressed to the potential increase in damping of blade vibrations by changing the layup of the blade material, also called Aeroelastic Tailoring. The DAMPBLADE project was supported by the European Commission: Project No. NNE , Contract number ENK6-CT The contribution of ECN in the DAMPBLADE project was partially funded by SenterNovem, order No: ACKNOWLEDGEMENT The author wants to thank Ir B. Roorda of Polymarin B.V. for his permission to use the sectional properties of the RB70 blade, and Dr Ir G.D. de Winkel of the Knowledge Center Wind turbine Materials and Constructions WMC for his permission to use the FAROB output files. Also the author wants to thank his colleagues Ir B.H. Bulder, Ir H.J.T. Kooijman, and Ir D. Winkelaar for their support on the work reported here. ABSTRACT Within the European research project DAMPBLADE investigations were performed into wind turbine rotor blade structures with enhanced material- and aeroelastic damping properties. Within task 3.4 of this project Design application, sensitivity analysis and aeroelastic tailoring, investigations were performed into the influence of structural modifications of a rotor blade that improve the aeroelastic stability and fatigue loading. These investigations were performed by CRES, ECN, and by Risø and focussed on the influence of Structural Pitch on the aerodynamic damping. Basis for these investigations was the RB70 rotor blade of Polymarin B.V., that was designed for a variable-speed pitch-to-vane wind turbine. The RB70 blade was modelled on basis of descriptions of several blade cross sections that were provided by WMC. Because the aerodynamic damping for the flatwise blade vibrations of a pitch-to-vane controlled wind turbine is inherently positive, only the influence of Structural Pitch on the damping of the edgewise vibrations is reported. From the calculations with BLADMODE, HAWCBladeStab, PHATAS, and Stab-Blade it follows that Structural Pitch can be used effectively to improve the aeroelastic response of rotor blade vibrations. The results from the time-domain code PHATAS did not show such a strong influence, while the results from the other aeroelastic analysis tools show quite similar trends for Structural Pitch. It was also shown that modelling of the steady deformed state does have an effect on the aerodynamic damping of the edgewise vibrations. Keywords Aerodynamic damping, Aeroelastic tailoring, Edgewise blade vibrations, Rotor blade, Structural Pitch, Wind turbine. ECN-C iii

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5 CONTENTS LIST OF SYMBOLS TERMINOLOGY vii viii 1 INTRODUCTION General Structure of the Investigations Basis for Chosing Structural Pitch Investigations and Comparisons Reported Here COMPARISON OF STATIC PROPERTIES Overall Structural Blade Properties Static Aerodynamic Properties Deformed Equilibrium State COMPARISON OF DYNAMIC PROPERTIES Edgewise Bending Frequencies Damping of the Bending Modes AERODYNAMIC DAMPING WITH STRUCTURAL PITCH Modelling of Structural Pitch Aerodynamic Damping from BLADMODE Aerodynamic Damping from HAWCBladeStab Aerodynamic Damping from Stab-Blade Influence of Structural Pitch on Flatwise Damping Aeroelastic Response from PHATAS RELATION WITH THE DIRECTION OF MOTION 27 6 STRUCTURAL CONSEQUENCES 31 7 INFLUENCE OF ELEMENT DISCRETISATION WITH STAB-BLADE 33 8 EFFECT OF THE DEFORMED EQUILIBRIUM STATE 35 9 CONCLUSIONS General conclusions on this investigation Conclusions with regard to Structural Pitch References 39 A RB70 ROTOR BLADE DESCRIPTION 43 ECN-C v

6 A.1 Aerodynamic Modelling A.1.1 Chord distribution A.1.2 Twist distribution A.1.3 Airfoil distribution A.2 Structural Dynamic Modelling A.3 BLADMODE input file with RB70 Blade Properties B BENDING STIFFNESSES WITH STRUCTURAL PITCH 51 B.1 General B.2 Structural Pitch Modifications with CROSTAB C STATIC OPERATIONAL CONDITIONS 59 D RB70 MODELLING FOR BLADMODE 61 D.1 BLADMODE modelling aspects of the RB D.2 BLADMODE modelling aspects of Structural Pitch E RB70 MODELLING FOR Stab-Blade 63 F RB70 MODELLING FOR PHATAS 65 F.1 Introduction on PHATAS F.2 Modelling the RB70 blade in PHATAS F.3 Wind Conditions F.4 Processing of Results vi ECN-C

7 LIST OF SYMBOLS b Dimensionless damping coefficient. c [m] Blade chord. c l, c d, c m Dimensionless coefficients for aerodynamic lift, drag, and pitching moment (nose-up) of the airfoils. L [m] Spanwise coordinate, measured from the hub-radius. R [m] Rotor radius, or radial co-ordinate of the tip. r [m] Radial co-ordinate in the rotor system, measured from rotor centre. U wind [m/s] Undisturbed wind velocity. u, v [m] Flapwise (downwind) and lagwise blade bending deformation. x, y, z [m] Flapwise (downwind), lagwise, and spanwise co-ordinates which corresponds to the Germanischer Lloyd conventions. φ inf [rad] Inflow angle of the airflow on the blade w.r.t. the rotor plane. π Trigonometric constant: π = ρ [kg/m 3 ] Air density. θ [rad] Blade-effective direction of motion. θ eff [rad] Sum of blade twist, pitch, and elastic torsion: θ eff = θ tw +θ p φ z. θ p [rad] Blade setting angle or pitch angle. θ tw [rad] Direction of the local blade chord for a zero blade setting angle. Ω [rad/s] Rotor speed, positive for clockwise rotation. ECN-C vii

8 TERMINOLOGY In the description of the blade properties (loads, deformations, velocities) the directions are described among others with the following terms. Expression BLADMODE HAWCBladeStab PHATAS Stab-Blade Description Program of ECN for the rotor blade eigenmode analysis. Program of Risø for the aeroelastic stability of blade vibrations. Time-domain program for wind turbine response, by ECN. Program of CRES for the aeroelastic stability of blade vibrations. *.buc file File format that contains the geometry of a cross section, material definition, and the layup. This was introduced for buckling analyses. UD laminate Pre-bend Collective mode Reaction-less mode Apparent mass Aerodynamic stiffness Aeroelastic tailoring Bending-Torsion coupling Structural Pitch edge-wise flap-wise flat-wise lead-wise Laminate with all fibres in the same direction, Uni Directional. Flapwise (for zero pitch) geometrical curvature of a blade without loading. Sometimes an up-wind pre-bend is used which partly eliminates the elastic deformation under normal operating loading. In the programs BLADMODE and PHATAS the pre-bend is defined as the down-wind displacement of the blade tip. Mode of edgewise rotor blade vibration, of which the reaction loads on the rotor shaft add-up to each other. For this modes the blade-tips vibrate simultaneously and in opposite direction to the associated drive-train vibration. Simultaneous mode of vibration of rotor blades that gives no torque reaction loads on the rotor shaft, used for edgewise modes. The reaction-less edge modes may cause a vibration with the tower side-bending mode, if this tower frequency is either 1P larger or 1P smaller than the reaction-less edge frequency. Mass that is added to the blade mass to account for the inertia loads of the air for blade vibration. For flatwise vibrations this mass is larger than for edgewise vibrations. Aerodynamic load variations on a rotating blade that are proportional with the amplitude of vibration; positive in restoring direction. The flapping motion of blades with bending-torsion coupling is a clear example of aerodynamic stiffness, since a downwind flapping amplitude goes together with a decreased angle-of-attack so a reduction in aerodynamic flapping forces. Tuning the response of slender composite structures under aerodynamic loading to obtain the desired behaviour. Modification of the blade structure such that a bending moment gives a torsional deformation. This can be realised e.g. with off-axis UD laminates (symmetric w.r.t. the blade axis) or with an aft-swept blade tip. Modification of the blade structure that changes ( pitches ) the principal stiffness direction and thus also the directions of blade vibration. Along the local chord. Perpendicular to the plane of rotation, positive downwind. Perpendicular to the local chord, positive downwind. In the plane of rotation, positive in rotational direction (opp. to lag-wise ). viii ECN-C

9 1 INTRODUCTION 1.1 General Within the European research project DAMPBLADE [4] investigations were performed into materials for wind turbine rotor blades with enhanced structural and aeroelastic damping properties. Part of these investigations deal with the development and/or application of computer programs for the prediction of the aerodynamic damping or aeroelastic stability of rotor blade vibrations. In a former task of the DAMPBLADE project, a comparison benchmark of these computer programs was carried out for a 21m diameter stall-regulated rotor, reported by Hansen et al. [10]. Within task 3.4 of the DAMPBLADE project, investigations were performed into the influence of structural blade modifications on the aeroelastic stability of blade vibrations. These investigations were done for the RB70 rotor blade built by Polymarin B.V. (see A. Rob, [32, 33, 34]). The RB70 blade has NACA63- series airfoils and was designed for operation on a 3-bladed variable-speed pitchto-vane controlled wind turbine, which gives a 35.62m rotor radius. The objectives of this report are to learn about the effectiveness of Structural Pitch as method to improve the aeroelastic response and on how these effects/trends can be analysed with each of the analysis tools involved. 1.2 Structure of the Investigations The RB70 rotor blade was modelled in the program FAROB by the Knowledge Centre Wind turbine Materials and Construction, WMC. Detailed descriptions of the blade cross sections were provided by WMC to ECN. ECN processed these files to tables with sectional properties that served as input for the eigenmode and stability analyses on the influence of Structural Pitch variations. The RB70 blade properties (in BLADMODE format) are listed in Appendix A. The following analysis tools were involved: BLADMODE by ECN. With BLADMODE [24] the eigenmodes of a rotating rotor blade can be solved as harmonic vibrations. For each of these modes the aerodynamic damping is calculated, either from the linearised aerodynamic loads or integrated for finite amplitude vibrations. Stab-Blade by CRES. A tool developed for the aeroelastic stability of a single rotating blade. Linearised stability analyses can be done either by eigenvalue approach or by time-domain integration. Non-linear analyses can only be done by time-domain integration. The method of Stab-Blade is documented by Chaviaropoulos [5]. A short description of the Stab-Blade program is also given in section 2.1 of the DAMPBLADE benchmark-report, [10]. HAWCBladeStab by Risø. The stability tool of Risø is in fact based on the HAWC code, and will be developed further for the aeroelastic stability analysis of an entire wind turbine. The model for structural dynamics of the blade is based on Timoshenko s beam theory, which includes e.g. transverse shear deformation of the cross-sections, see [9]. For the linear approach, the eigenmodes are analysed with the aerodynamic loads linearised for small amplitude vibrations. A short description of HAWCBladeStab is given in section 2.3 of the DAMPBLADE benchmark-report, [10]. PHATAS by ECN. Time-domain code with which the response for the integrated aerodynamics, structural dynamics, and controller can be solved. The governing release "NOV-2003" is described in [27]. ECN-C

10 Limitation of the work Because the DAMPBLADE project was addressed to the (structural) properties of a rotor blade, the investigations reported here were limited to the blade vibrations as if the blade is clamped at its root (although still rotating). By this limitation, discrepancies arising from different modelling of the drivetrain and turbine dynamics are excluded. Another limitation is that most of the investigations reported here were focussed on the mechanism that leads to aerodynamic damping of the edgewise vibrations, although the aerodynamic damping of the flapwise vibrations was also reported. 1.3 Basis for Chosing Structural Pitch The description of task 3.4 of the DAMPBLADE project was formulated in terms of aeroelastic tailoring, which covers a wide range of structural modifications of the rotor blade. As basis for defining the research within task 3.4 ECN prepared a document [23] in which different options for aeroelastic tailoring were described. This document was based to a large extent on former work on aeroelastic tailoring at ECN and at other institutes. When omitting options such as initial in-plane or out-of-plane curvature of the blade axis (which require modifications of the blade moulds) the most pronounced methods for aeroelastic tailoring are: Structural Pitch Structural Pitch is a modification of the blade interior structure such that the direction of the principal stiffnesses is rotated. The influence of Structural Pitch on the aeroelastic behaviour was already investigated in the STALLVIB project, see Petersen et al. [30]. For blades of pitch-to-vane controlled wind turbines this rotation also gives another direction of the modes of vibration. For the edgewise modes, a change in direction of vibration implies different variations in angle-of-attack and inflow velocity. Because this angle-of-attack variation is proportional with the velocity of blade vibration and thus gives an aerodynamic load variation that is proportional to the velocity of motion, it implies a direct contribution to the aerodynamic damping. Earlier Bjørck, Dahlberg, & Ganander [3] reported on the difference of the calculated aerodynamic damping due to (not) accounting for this Structural Twist. In their investigations, the Structural Twist gave an up-wind component for the lead-wise stroke of edgewise blade vibrations, leading to a more positive aerodynamic damping. Björck et. al concluded that the other aspects of relevance for prediction of aerodynamic damping are proper aerodynamic coefficients and well-tuned dynamic stall models. Bending-Torsion coupling Bending-Torsion coupling of a rotor blade is a modification of the blade structure such that a bending moment gives some torsional deformation. Bending-Torsion coupling of a rotor blade gives an angle-of-attack variation of the blade tip region proportional to the bending deformation. This means that the corresponding quasi-steady aerodynamic angleof-attack variations gives an aerodynamic stiffness contribution. Although Bending-Torsion coupling does not give a direct contribution to the aerodynamic damping of blade vibrations, the aerodynamic stiffness will reduce the structural load variations from gust response. When the unsteady aerodynamic effects from vortex shedding of a vibrating blade are included (such as initially described by Theodorsen) a flapwise vibrating blade with B-T coupling will have unsteady aerodynamic load variations that are leading compared with the geometric angle-of-attack variations due to the torsional deformation. This implies that compared to conventional blades, blades with B-T coupling will have a small negative damping for the flatwise blade vibrations. If the effects resulting from geometric blade twist are excluded, Bending-Torsion coupling can be realised by off-axis laminates in the outer walls of a blade cross section. Investigations into this phenomena require tools that are capable of modelling anisotropic laminates within a thinwalled multi-cell beam structure. 2 ECN-C

11 At ECN Kooijman investigated the influence of Bending-Torsion coupling for a single-cell blade structure [16]. The description of the sectional properties was partly based on similar investigations by Karaolis [15]. Kooijman concluded that without reducing the blade slenderness, Bending-torsion coupling gives too little induced twist for controlling the turbine power in full load. In partial load however, Bending-Torsion coupling can be used to improve the energy capture with about 1%. The effect of Bending-Torsion coupling towards stall gives a stronger dynamic gust response, which Kooijman addressed to the negative aerodynamic damping from wash-in. In the same period Leconte & Széchényi [18] explored the possibilities of Bending-Torsion coupling to reduce the unsteady blade bending moments on basis of an existing 300kW wind turbine. This investigation focussed on the 1 per rev. load variations due to wind shear and yaw misalignment. In 1998 the work of Kooijman was extended by De Goeij [7, 8] for two-cell beam structures. The investigations of De Goeij included finite-element analyses and a laboratory test of a two-cell carbon-fibre box-beam with Bending-Torsion coupling. Lobitz and Veers [28] investigated the boundaries of instability for different amount of bendingtorsion coupling. For large Bending-Torsion coupling towards stall the instability is characterised by divergence, while for large Bending-Torsion coupling towards vane the instability is characterised by flutter. Their publication also showed that small amount of Bending-Torsion coupling already has an effect on the aeroelastic behaviour while the reduction in sectional stiffness is quadratic (thus small) with the amount of coupling. Investigations by Lee and Flay in 1999 [19] were also addressed to the possible use of bendingtorsion coupling for power control. One of their conclusions was that for conventional rotor blades the B-T coupling will not provide the large elastic twist angles required. This conclusion was similar to that by Kooijman [16]. Many investigations into Bending-Torsion coupling have shown that the largest torsional deformation is realised with an off-axis orientation of the UD layers of about 20 o. For several blade cross sections Lindenburg [21] has shown that for a 20 o UD-layer orientation, the von-mises equivalent stress variation in the resin (for a given bending moment variation) is about 1.5 to 2.0 times larger than for conventional blades. This increase in resin stress variation is far less for off-axis orientations up to 5 o. This means that a moderate amount of Bending-Torsion coupling may improve the aeroelastic behaviour without much structural implications. More recently the application of Bending-Torsion coupling to wind turbine rotor blades has been investigated by Ashwill et al. [2], who investigated several blade configurations. The conclusions were that the extreme and the fatigue loads can be reduced considerably while the cost estimates indicate an increase of 34% to 137%. It was also concluded that the off-axis layers ( biased laminates) have additional interlaminar shear loads in the free-ends or in the connections of the double-box configurations. Later three blade designs with Bending-Torsion coupling were analysed with the F.E.M. package ANSYS, see Locke et al. [29]. One of these 9.2m span NPS-100 blades was manufactured and tested. These investigations showed an increased buckling sensitivity. Aft-Swept Blades Recently Zuteck [39] presented a study of a blade-concept in which Bending- Torsion coupling was realised by a lag-wise curved blade-tip. This study aimed at improving the aeroelastic response without the increased interlaminar resin stresses that are introduced at the fibre-ends of the off-axis layers. To achieve a substantial interaction with tip-torsion variations the blade-thickness at the midspan locations was reduced. ECN-C

12 In order to arrive at valuable results within the time available for task 3.4, the investigations were performed for one concept of aeroelastic tailoring. During the progress meeting in September 2002 it was decided to address the work for task 3.4 on Structural Pitch, because this has a direct and effective influence on the aeroelastic behaviour while it has little structural consequences (compared to the anisotropy of Bending-Torsion coupling). The fact that the aeroelastic analysis tools applied here do not describe the reduction in gust response of blades with B-T coupling was another reason for not investigating this concept of A-E tailoring. 1.4 Investigations and Comparisons Reported Here The investigations reported here were done by comparing calculated results from CRES, ECN, and Risø. To ensure that the conclusions on Structural Pitch and on the analysis tools involved are not disturbed by input errors, the overall (average) blade properties were compared first. These properties include the total mass, the eigenfrequencies, and the directions of blade motion, see chapter 2. Next the aerodynamic damping of the first flatwise and the first edgewise blade bending mode calculated with the different stability analysis tools are compared, see chapter 3. These aeroelastic stability analyses were done for the operational conditions (rotor speed and pitch angle as function of wind velocity) that were calculated earlier with PHATAS [27] for the RB70 blades mounted on a 1500kW wind turbine, see Appendix B. This comparison was given for quasi-steady and unsteady aerodynamic loads. The main part of this investigation deals with the influence of Structural Pitch, realised by shifting the UD layers in chordwise direction. This shift is opposite for the aerodynamic suction side and the pressure side. The most pronounced effect of this shift in girder laminates is a change in principal stiffness direction, which is represented in the input by the value of the stiffness term for coupling between flatwise and edgewise bending. The sectional properties with Structural Pitch modifications were generated with the program CROSTAB [20], see Appendix C. Because the aerodynamic stability analysis tools each have their characteristic modelling, the calculated aerodynamic damping will differ. Although the absolute values of the results may differ, it is generally accepted that the tools can be used for parameter studies, such as the influence of Structural Pitch investigated here. The investigations into the influence of Structural Pitch reported here were therefore not addressed to the absolute value of the aerodynamic damping, but to the trends for variations of Structural Pitch, see chapter 4. To obtain insight in the relation between Structural Pitch and aerodynamic damping, the latter is also compared on basis of the direction of blade vibration, see chapter 5. Chapter 6 reports on some consequences of Structural Pitch. The influence of the number of blade elements on the aerodynamic damping of the edgewise vibrations has been investigated by CRES with Stab-Blade and reported in chapter 7. The influence of modelling the curved blade axis of the equilibrium deformed state has been investigated by ECN with BLADMODE which is reported in chapter 8. Finally the conclusions are summarised in chapter 9. 4 ECN-C

13 2 COMPARISON OF STATIC PROPERTIES Prior to analysing and comparing the aerodynamic damping of the RB70 blade vibrations, it was tried to exclude or at least detect the differences between modelling in the aeroelastic stability analysis tools. 2.1 Overall Structural Blade Properties Using the description of the RB70 rotor blade in Appendix A the overall blade properties were calculated with the different tools. These calculations were performed for the blade mounted on a 1500kW wind turbine with a hub-radius of 1.32m and a zero cone angle. This gave an overall rotor radius of 35.62m. In the BLADMODE model the Aerodynamic area and the Aspect ratio are defined from the location at which the first airfoil starts: L = 4.573m or R = 5.893m. The properties in the following table are calculated without the geometric pre-bend, so as if the blade is straight, and for a zero blade pitch angle. For the blade eigenfrequencies the influence of the aerodynamics ( apparent mass and aerodynamic stiffness ) was excluded, while the tower and the drive train were modelled rigid. The rotating blade frequencies were calculated for a fixed speed of 19.0rpm, which is slightly above the nominal speed of 18.5rpm. Property BLADMODE HAWCBladeStab PHATAS Stab-Blade Root vortex radius [m] n.a n.a. Aspect ratio n.a n.a. Total blade mass [kg] Static moment [kgm] n.a. Inertia w.r.t. root [kgm 2 ] n.a. Pitch inertia [kgm 2 ] n.a n.a. Flat frequency (0rpm) [Hz] Direction of motion Θ [ o ] n.a Flat frequency (19rpm) [Hz] Direction of motion Θ [ o ] n.a Edge frequency (0rpm) [Hz] Direction of motion Θ [ o ] n.a Edge frequency (19rpm) [Hz] Direction of motion Θ [ o ] n.a Torsion (0rpm) [Hz] n.a. Torsion (19rpm) [Hz] n.a. In this table n.a. stands for not available or not applicable. The direction of motion Θ is defined in the same direction as the blade pitch angle, see Figure 1. This means that the lagwise direction is 0 o, the downwind flapwise direction 90 o, the leadwise direction 180 o etc. In the table given here, the direction of motion from BLADMODE is at 80.6% radius. The direction Θ from the HAWCBladeStab model is for r = 28.83m, or at 80.9% radius. The directions of motion from Stab-Blade are blade-effective values. ECN-C

14 Theta Direction of vibration Wind Rotational direction Figure 1: Direction of motion theta Although special effort was made by ECN to use the same mass distribution in BLADMODE and in PHATAS, the total blade mass of the PHATAS model is missing 6.4kg, or 0.11%. A probable reason is that only a selection of the sectional data is used. The static moment and the rotational inertia of the PHATAS model are 0.1% larger than those of the BLADMODE model. The small value of the pitch inertia calculated with PHATAS is because the blade mass is assumed on the chord-line. This has its largest contribution at the blade root area, which has little effect on the blade torsional frequency. The collective edgewise frequency calculated with PHATAS is over-estimated because in the routine for the blade eigenvalues the radius of the hub, or blade-root is not included. This omission is only in the routine for the eigen frequencies and does not have any effect on the calculated aeroelastic response in time-domain. The blade bending frequencies calculated with PHATAS are a little smaller than those calculated with BLADMODE, while one would expect them to be larger because PHATAS does not account for the out-of-plane shear deformation. The calculations with Stab-Blade were performed without blade torsion, see also Appendix E. The torsional frequency calculated with PHATAS is clearly smaller. One may conclude that this is caused by the smaller pitch inertia, but Figure 12 also shows a smaller equilibrium torsional deformation. The (reaction-less) edge bending mode has a frequency close to 6P. For a rotor speed of 17.6rpm the reaction-less edge mode is in 6P resonance. At 17.6rpm the generator torque-speed relation is rather steep, which means that for the corresponding wind velocity (10.5m/s, see Appendix C) the rotor speed variations are small so that the resonance state may occur for several vibration periods, and finally lead to large response amplitudes. Fortunately for a rotor speed above 17.5rpm (= Ω rated -1rpm) the partial-load pitch strategy has a target pitch setting angle of +2 o which corresponds to moderate angles-of-attack and thus gives aerodynamic damping. 6 ECN-C

15 2.2 Static Aerodynamic Properties In some of the tools the aerodynamic damping is calculated for vibrations around a static equilibrium state. For the analyses with BLADMODE it was chosen to calculate the aerodynamic loading for this equilibrium state with the vortex-wake model. For the wind velocity of 11m/s (and the corresponding 2.0 o pitch angle and 17.91rpm rotor speed) the vortex wake structure from the BLADMODE solution is shown in Figure 2. As can be seen in Figure 2 the deformed blade geometry is included in the vortex-wake solution. Figure 2: Vortex-wake structure calculated with BLADMODE for 11m/s The steady aerodynamic power and rotor thrust, in Figure 3 and 4 respectively, show that the overall aerodynamic modelling in BLADMODE, HAWCBladeStab, Stab-Blade, and PHATAS are nearly the same. This indicates that no serious errors have to be expected from differences of modelling in the different tools. The local differences near 8m/s to 10m/s wind from Stab-Blade are caused by the larger wind-speed intervals used in the analyses, viz 1.0m/s. For the calculation of the aerodynamic damping, the slope of the lift and drag curves have a strong influence. This means that the angles-of-attack and likewise the induced velocity distribution is an indicative parameter for a fair comparison. Comparisons of the spanwise distribution of the axial and angular induced velocity factors and of the angles-of-attack are given in Figure 5 through 10. These distributions were calculated for a wind velocity of 7m/s and 11m/s, using pitch angles of -2.0 o and 2.0 o and using rotor speed values of rpm and 17.91rpm respectively, see Appendix C. Figure 5 and 8 show the local induced velocity factors at the blade, and not the annulus-averages after multiplication with the tip-loss factor (so for PHATAS without the Prandtl-factor). The jogs in the distributions of the induction factors and angle-of-attack from BLADMODE (that uses a vortex-wake model with a large number 75 blade elements) reflect the transitions of the airfoil coefficients-files that were used, since each airfoil may have a different zero-lift angle-of-attack. ECN-C

16 Aerodynamic power [kw] BLADMODE (ECN), vortex wake HAWCBladeStab (Risoe) PHATAS (ECN), BEM Stab Blade (CRES) Wind speed [m/s] Figure 3: Comparison of aerodynamic power Axial force [kn] BLADMODE (ECN), vortex wake HAWCBladeStab (Risoe) PHATAS (ECN), BEM Stab Blade (CRES) Wind speed [m/s] Figure 4: Comparison of axial force on the rotor Disregarding local differences due to the blade-element discretisation, the spanwise distribution of the induced velocities from BLADMODE, HAWCBladeStab, PHATAS, and Stab-Blade compare very well. Near the root and also near the airfoil transitions the results from BLADMODE show pronounced steps which is caused by the fact that the vortex-wake model includes the influence of neighbouring elements. The good agreement for the power curve and the total rotor thrust shows that a different loading on the blade root has little effect on the overall rotor performance. The angle-of-attack calculated with PHATAS is about 0.5 o smaller than calculated with the other tools, which does have some influence for the aeroelastic stability analyses. This smaller angle-of-attack may be caused by the 5 o tilt angle in the PHATAS model, which BLADMODE represents as a rotor-average approximation. 8 ECN-C

17 0.4 Axial induction factor BLADMODE (ECN), vortex wake HAWCBladeStab (Risoe) PHATAS (ECN), BEM Stab Blade (CRES) Radial location [m] Figure 5: Distribution of axial induction factors for 7m/s; rpm; -2 o pitch Tangential induction factor BLADMODE (ECN), vortex wake HAWCBladeStab (Risoe) PHATAS (ECN), BEM Stab Blade (CRES) Radial location [m] Figure 6: Distribution of tangential induced velocities for 7m/s; rpm; -2 o pitch Angle of attack [deg] BLADMODE (ECN), vortex wake HAWCBladeStab (Risoe) PHATAS (ECN), BEM Stab Blade (CRES) Radial location [m] Figure 7: Angle-of-attack distribution for 7m/s; -2 o pitch ECN-C

18 0.3 Axial induction factor BLADMODE (ECN), vortex wake HAWCBladeStab (Risoe) PHATAS (ECN), BEM Stab Blade (CRES) Radial location [m] 0.25 Figure 8: Distribution of axial induction factors for 11m/s; 17.91rpm; +2 o pitch Tangential induction factor BLADMODE (ECN), vortex wake HAWCBladeStab (Risoe) PHATAS (ECN), BEM Stab Blade (CRES) Radial location [m] Figure 9: Distribution of tangential induction factors for 11m/s; 17.91rpm; +2 o pitch Angle of attack [deg] BLADMODE (ECN), vortex wake HAWCBladeStab (Risoe) PHATAS (ECN), BEM Stab Blade (CRES) Radial location [m] Figure 10: Angle-of-attack distribution for 11m/s; +2 o pitch 10 ECN-C

19 2.3 Deformed Equilibrium State A pre-cone such as in the RB70 blade gives coupling between edgewise and torsional deformations. This coupling occurs even stronger for an equilibrium flapwise deformation of the rotor blades since this has a curvature in the outer part of the blade. The steady deformation calculated for the conditions given in Appendix C are compared in Figure 11 and 12. Flapwise tip displacement [m] BLADMODE, without pre bend HAWCBladeStab, without pre bend Stab Blade, without pre bend BLADMODE, with pre bend PHATAS, with pre bend Wind speed [m/s] Figure 11: Comparison of equilibrium flapwise blade tip deformation Tip torsional deformation [deg] BLADMODE (ECN) HAWCBladeStab (Risoe) PHATAS (ECN) Wind speed [m/s] Figure 12: Comparison of equilibrium blade tip torsional deformation Because Stab-Blade does not model the geometric pre-bend shape of the RB70 blade, the equilibrium flapwise deformation was also calculated for comparison with BLADMODE. Figure 11 shows that the deformation from BLADMODE and Stab-Blade (both without pre-bend) agree very well. Agreement is also found for the blade deformations from BLADMODE and PHATAS, both including pre-bend. Figure 12 shows a somewhat larger tip torsional deformation calculated with PHATAS. This may have the same cause as the under-estimation of the blade torsional frequency, which indicates some deviation of the PHATAS model for blade torsion, see also section 2.1. ECN-C

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21 3 COMPARISON OF DYNAMIC PROPERTIES 3.1 Edgewise Bending Frequencies In general the eigenfrequencies of a rotor blade are calculated for a zero pitch angle and for the undeformed state (see chapter 2). Whether a rotor has resonance problems or not depends on the eigenfrequencies over the entire operating range which includes the rotor speed, the pitch angle, and the deformed state for each wind velocity. For a pitch-to-vane controlled wind turbine the flatwise modes have a fairly positive aerodynamic damping as will be shown later. The investigations into Structural Pitch deal with the edgewise vibrations. Here the edgewise vibrations that do not interact with the torsional drive-train dynamics are called reaction-less modes, while the simultaneous edgewise vibrations are called collective edgewise modes, see Figure 13. Figure 13: Reaction-less (left) and collective (right) edgewise mode at 11m/s wind For the reaction-less edgewise modes, the frequencies are plotted in Figure 14 versus wind velocity. The difference with the frequencies in the previous chapter is that in Figure 14 the influence of the aerodynamics is included while the vibrations are calculated for a deformed equilibrium state. The rotor speed and pitch angle used in the calculation of the frequencies shown in Figure 14 are those listed in Appendix C. The PHATAS frequencies were obtained with a Fourier transformation of the the blade deformations at the 81.7% location (near the node of the second bending modes), calculated for turbulent wind, see Appendix F. The frequency spectrum of the blade deformations from PHATAS do not show a distinct peak, which is partly due to the rotor speed variations. As can be seen in Figure 14, the reaction-less edgewise frequencies show little variation with the operational conditions. For a wind speed in the range from 9m/s to 12m/s the reaction-less edgewise frequency is close to the 6P resonance frequency. The influence of this 6P resonance may be described with e.g. the time-domain calculations in which the effects of blade-tower interaction and of turbulence crossing are included. ECN-C

22 Frequency [Hz] BLADMODE (ECN) HAWCBladeStab (Risoe) FFT of PHATAS response (ECN) Stab Blade (CRES) 6P (six times the rotor speed) Wind speed [m/s] Figure 14: Reaction-less edge frequencies 3.2 Damping of the Bending Modes For mutual comparison of the tools, the damping for the first flatwise and edgewise bending modes without Structural Pitch are compared in Figure 15 and 16 respectively. These figures contain the damping for the quasi-steady aerodynamics and with a model for the unsteady aerodynamics, except for the damping from BLADMODE. The program BLADMODE does have a (linearised) model for dynamic stall, but this does not describe the unsteady aerodynamics in attached flow. To still present an interesting difference the damping is calculated with BLADMODE with and without torsional flexibility. More detailed investigations into the modelling of the equilibrium deformed state are presented in chapter 8. These unsteady aerodynamics models for the different tools are: Tool: Unsteady aerodynamics model: BLADMODE First-order dynamic stall model of Snel [36] (steady in attached flow) HAWCBladeStab Beddoes-Leishman, see Hansen [11] Stab-Blade ONERA Lift (& Drag) model for unsteady aerodynamics, see Petot [31] In this comparison the aerodynamic damping from PHATAS was not included because it is hard to retrieve from the dynamic time response. The aerodynamic damping in the BLADMODE model is based on the assumption that the aerodynamic and structural damping are small and that the different damping properties (structural, aerodynamic, drive train) can simply be added to each other. For the flatwise bending mode the damping is large which means that flatwise vibrations are not an item of concern. The aerodynamic damping for the edgewise modes is small because the motion involves small angleof-attack variations while the variations in relative inflow velocity have a negative contribution to the damping of the motion. The trend in the edgewise damping calculated with HAWCBladeStab and with Stab-Blade are similar, both for the quasi-steady and for the unsteady aerodynamic load variations. This similarity is in agreement with the fact that these programs both have a model for unsteady aerodynamics even in attached flow. The edgewise damping from BLADMODE without torsional flexibility matches well with the edgewise bending from Stab-Blade using unsteady aerodynamics. This is in agreement with the fact that the Stab-Blade analyses were done without modelling blade torsion. This agreement is still surprising because in the BLADMODE analyses only the unsteady aerodynamics in stall were modelled. At 8.5m/s and at 10.0m/s the rotor has a stepwise 2 o increase in the blade pitch angle, see Appendix C. 14 ECN-C

23 Aerodynamic damping as log. decr [%] BLADMODE, no torsional flexibility BLADMODE, with torsional flexibility HAWCBladeStab, quasi steady HAWCBladeStab, unsteady Stab Blade, quasi steady Stab Blade, unsteady Wind speed [m/s] Figure 15: Aerodynamic damping of the flatwise mode Aerodynamic damping as log. decr [%] BLADMODE, no torsional flexibility BLADMODE, with torsional flexibility HAWCBladeStab, quasi steady HAWCBladeStab, unsteady Stab Blade, quasi steady Stab Blade, unsteady Wind speed [m/s] Figure 16: Aerodynamic damping of the reaction-less edge mode In the former STALLVIB research project [30] it was already concluded that for pitch-to-vane changes, the different direction of vibration gives an increase in edgewise damping, while following linearised aerodynamics the influence of the reduced angle of attack is of a smaller order. This agrees with the positive steps in the damping calculated with BLADMODE, while the quasi-steady predictions with HAWCBladeStab and with Stab-Blade show a decrease in damping for the pitch steps at 8.5m/s and 10.0m/s. Knowing that unsteady aerodynamic effects (the influence of vortex shedding) gives a negative contribution to the aerodynamic damping, it is not understood why the unsteady predictions with Stab-Blade gives an increase of the aerodynamic damping for positive pitch steps. ECN-C

24 16 ECN-C

25 4 AERODYNAMIC DAMPING WITH STRUCTURAL PITCH 4.1 Modelling of Structural Pitch The name Structural Pitch is used for modifications in the layup or the location of load-carrying laminates that lead to changes in the principal stiffness directions, and thus a different direction of the blade vibrations. In particular for the pre-dominant edgewise modes this change in motion directly increases or decreases the aerodynamic damping. Since the DAMPBLADE project deals with the aeroelastic behaviour of the blades, this study focuses on the reaction-less edgewise vibrations. For the variation in Structural Pitch the program CROSTAB has been modified (see Appendix B) such that the girder laminates on the suction side and on the pressure side of the blade contour are shifted, see Figure 17. In Figure 17 the wall thicknesses and the shear webs were modified for reasons of confidentiality of the RB70 blade construction. The dashed line in Figure 17 indicates the qualitative change in the principal stiffness direction. Figure 17: Cross section without (left) and with 2%c (right) Structural Pitch To maintain their structural efficiency and to avoid secondary disturbances within the cross-section, the UD laminates should run as straight as possible. This means that the UD layers should preferably be shifted with a linear function of the spanwise coordinate. In this study it was chosen to fit this linear function with the chord distribution (which is also given in Appendix A): chord (L) = 3.66m L. With the modified version of the program CROSTAB, the sectional properties were calculated for a Structural Pitch of -3%, -2%, -1%, +1%, +2%, and +3% of this linearised chord. If the UD layers are shifted more than 3%c, the girder laminates are not directly connected with the shear web anymore. The fibre direction appears to be o for a shift of 1% of the linearised chord. Although its effect is very small, this change in orientation was included in calculating the sectional properties with CROSTAB. The cross sections near R = 35.5m are very thin and have very thin UD layers for which reason the laminates were not shifted here. In the following, the amount of Structural Pitch is expressed ECN-C

26 as the shift of the UD layers as fraction of the chord. Principal stiffness direction [deg] Structural pitch +3% chord Structural pitch +1% chord Original RB70 design Structural pitch 1% chord Structural pitch 3% chord Radial location [m] Figure 18: Principal stiffness direction for different Structural Pitch Figure 18 shows the influence of shifting the girder laminates on the principal stiffness direction. For radial locations near 5m to 7m the sensitivity of the principal stiffness direction for structural modifications shows be very strong because this area does not have pronounced principal stiffnesses. However shifting the girder-layers in this area is still effective because here it will result in a (larger) difference between the principal stiffnesses. In section 3.2 it was found that the aerodynamic damping of the flatwise bending mode for a pitch-tovane controlled wind turbine is fairly positive (a decrement of at least 150% per cycle). To be complete in the investigation, the influence of Structural Pitch on the damping of the flatwise modes is finally presented in section 4.5, especially because for these modes the trends are opposite. 18 ECN-C

27 4.2 Aerodynamic Damping from BLADMODE For some Structural Pitch variations, the aerodynamic damping of the reaction-less edgewise mode was calculated with BLADMODE, using the operational conditions presented in Appendix C. This calculation included the apparent mass, aerodynamic stiffness, blade torsional deformation, the equilibrium state with the vortex-wake model, and the aerodynamic damping linearised dynamic stall model of Snel [36]. The (edgewise) eigenmodes for which the damping was calculated describe vibrations about an equilibrium deformed state. The air density was 1.225kg/m 3 following the IEC recommendations. For some of these variations this damping is plotted as function of wind speed in Figure 19. The angles Aerodynamic damping in log decr [%] SP +3%c (theta = 11.63) SP +1%c (theta = 7.43) Original blade (theta = 5.36) SP 1%c (theta = 3.29) SP 3%c (theta = 0.12) Wind speed [m/s] Figure 19: Damping of the edge mode from BLADMODE for different Structural Pitch theta mentioned in the legend of Figure 19 are the blade-effective directions of motion, defined as (see also section 5.3 of [24]): r=r tan(theta) = ( sign(v) u c r r=r u 2 + v 2 dr )/( sign(v) v c r u 2 + v 2 dr ). r=root r=root Here r is the local radius, c is the chord, and u and v are the flapwise and lag-wise components of the mode shape. The angle theta is zero for an in-plane motion and is positive in the same sense as a positive blade pitch, see Figure 1 on page 12. The theta values listed in Figure 19 were calculated for 11m/s wind velocity and the corresponding blade pitch and rotor speed given in Appendix C. The peak-shaving pitch angle steps at 8.5m/s and 10.0m/s wind give an increase of the calculated aerodynamic damping, except for the negative Structural Pitch variations. This fits the expectations on basis of the mechanism of drag stall, see also Figure 1.3 of the Stabtool report [13]. Conclusions From the investigations with BLADMODE it follows that a Structural Pitch of +1% to +2% of the chord may be applied to avoid negative damping of the edgewise blade vibrations. Whether a larger Structural Pitch has to be applied depends on the other effects that are introduced, see also chapter 5 and 6. ECN-C

28 4.3 Aerodynamic Damping from HAWCBladeStab The following results were contributed by M.H. Hansen of Risø. Figure 20 and 21 show the aerodynamic damping of the edge motions calculated with HAWCBladeStab using quasi-steady and unsteady aerodynamics respectively. Aerodynamic damping in log decr [%] SP +3%c SP +1%c Original blade SP 1%c SP 3%c Wind speed [m/s] Figure 20: Influence of Structural Pitch on the edge damping; HAWCBladeStab, quasi-steady Aerodynamic damping in log decr [%] SP +3%c SP +1%c Original blade SP 1%c SP 3%c Wind speed [m/s] Figure 21: Influence of Structural Pitch on the edge damping; HAWCBladeStab, unsteady The calculations with HAWCBladeStab show a consequent increasing aerodynamic damping for increasing Structural Pitch. Figure 20 shows that the peak-shaving pitch actions to vane at 8.5m/s and at 10.0m/s wind give a reduction of the aerodynamic damping. This is in contrast to what is calculated with BLADMODE. The calculations with unsteady aerodynamics in Figure 21 show however that the increase in pitch angle at 10m/s wind gives an increase in aerodynamic damping. 20 ECN-C

29 4.4 Aerodynamic Damping from Stab-Blade The contents of this section were provided by E.S. Politis of CRES. The aerodynamic damping of the first edge-wise mode was calculated with Stab-Blade for six Structural Pitch configurations in the range -3%c, +3%c with a 1%c increment, along with the original blade design using models with 11 elements. These calculations were carried out using quasi-steady aerodynamics and unsteady aerodynamics, of which the results are presented in Figure 22 and 23 respectively. Similar as for the results from HAWCBladeStab, the damping for -2%c and +2%c Structural Pitch were not included for simplicity. Aerodynamic damping in log decr [%] SP +3%c SP +1%c Original blade SP 1%c SP 3%c Wind speed [m/s] Figure 22: Influence of Structural Pitch on the edge damping, from Stab-Blade; quasi-steady Aerodynamic damping in log decr [%] SP +3%c SP +1%c Original blade SP 1%c SP 3%c Wind speed [m/s] Figure 23: Influence of Structural Pitch on the edge damping, from Stab-Blade; unsteady Figures 22 and 23 show the same trends for Structural Pitch variations as calculated with BLAD- MODE and HAWCBladeStab. Any increase in the Structural Pitch results in an increase in damping of the edge-wise modes, while the damping of the flap-wise mode decreases slightly, see section 4.5. However, for low speeds the damping values obtained using unsteady aerodynamics are lower compared to the ones obtained by quasi-steady aerodynamics. The wind speed value for which unsteady aerodynamics result in more stable predictions than the quasi-steady aerodynamics, decreases as the ECN-C